Franklin Institute Librart FHILllDELFHM Class 691.1 Book Accession.!! tained the sanction of the Committee. The second class shall Include those books intended for circulation. Artic le VI. — The Secretary shall have authority to loan to members and to holders of second class stock, any work belonging to the second ( I- ASS, subject to the following regulations. Section 1. — No individual shall be permitted to have more than two boohs out at one time, without a written permission, signed by at least two members of the Library Committee, nor shall a book be kept out more than two weeks; but if no one has applied for it, the former bor- rower may renew the loan. Should any person have applied for it the latter shall have the preference. Section 2. — A fine often cents per week shall be exacted for the detention of a book beyond the limited time; and if a book be not re- turned within three months it shall be deemed lost, and the borrower shall, in addition to his fines, forfeit its value. Section 3. — Should any book be returned injured, the borrower shall pay for the injury, or replace the book, as the Library Committee may direct ; and if one or more books, belonging to a set or sets, be lost, the borrower shall replace them or make full restitution. Artici.e VII. — Any person removing from the hall, without permis- sion from the proper authorities, any book, newspaper or other property in charge of the Library Committee, shall be reported to the Committee, who may inflict any line not exceeding twenty-five dollars. Article VIII. — No member or holder of second class stock, whose annual contribution for the current year shall be unpaid or who is in arrears for fines, shall be entitled to the privileges of the liibrary or Reading Koom. Article IX. — If any member or holder of second class stock, shall refuse or neglect to comply with the foregoing rules, it shall be the duty of the Secretary to report him to the Committee on the Library. Article X.— Any member or holder of second class stock, detected in mutilating the newspapers, pamphlets or books belonging to the Insti- tute shall be deprived of his right of membership, and the name of the offender shall be made public. TABLES STRENGTH AND DEFLECTION TIMBER. By WILLIAM LEA, SURVEYOR. LONDON : SIMPKIN, MARSHALL & CO., STATIONERS' HALL COURT. E. C. OSBOENE, BIRMINGHAM. 1850. CO/\/S SD 4-34- L43 I8S0 lB,\\Xtxzis at Stationers' fl|an. bieminoham: PRINTED BY E. C. OSBORNE, BENNETT's HILL. THE GETTY CE;C£rt PREFACE. The following tables are construcffed for the purpose of determining by inspection, or by simple multiplication and division, the dimensions of any description of timber requisite to carry a given weight, or to have, when loaded, a given deflection. They are designed for the use of Architects, Builders and Carpenters; Engineers, Ship Builders, Surveyors ; and others, who may be in any way interested in converting timber into scantlings for building purposes generally, or for otherwise sustaining transversely any given pressures. The outline of the work may be stated as follows : — The timber selected as the unit or standard of comparison, is Red Pine of a given strength and elasticity ; and the constants for various species of timber are derived from the mean results of an extensive series of Experiments made principally by Professor Barlow, upon " woods not of the best but more common quality, in order to furnish " data for practical cases," the specimens for that purpose having been selected from all the timber in store in Woolwich Dock Yard. For the convenience of reference, and in order to keep the subjects distinct, the work is arranged in four divisions ; namely. Three Series of Tables and several Miscellaneous Tables. By the First Series of Tables may be found the Scantlings of Red Pine, and thence by a Table of Constants those of any other descrip- tion of timber, sufficient to carry given heavy weights, and to have when loaded given deflections. The Second Series or Tables of Weights shew one-eighth of the breaking weight in cwts. uniformly loaded, or one-fourth of the same when suspended from the middle, of Red Pine of any usual scantling iv PREFACE. not exceeding 32 feet long. At the foot of each table the deflections corresponding to the weights in the tables are given; and by this Series and the Table of Constants to the same, the scantlings of other kinds of timber may be found sufficient to carry, when loaded, any given por- tion of the breaking weight. By the Third Series may be found the scantlings of Red Pine and of other species of timber, when pressed by two forces acting respec- tively in the directions of the depth and the breadth, so as to have given equal deflections. By this Series, the scantlings for purlins, brest- summers, &c., are found, when pi^ssed by the weight of a roof, or by loaded beams inclined at given angles to the horizontal plane. Miscellaneous Tables, &c. The greatest weight in cwts. upon each foot in length of a joist, beam, lintel, &c., being ascertained or given, then by the first of these tables may be found the breadth of the same, for any usual depth or length sufficient to carry, when loaded, any given portion of the breaking weight. The Second Table shews the deflection of Red Pine scantlings, of any breadth and of any usual depth and length, when loaded with one- fourth of the breaking weight. By the seven following tables may be determined the depths of Ceiling Joists, Rafters, Floor Joists, Bridging Joists, Binding Joists, &c., from U inches to 3 inches in breadth, the deflection being of an inch to the foot when uniformly loaded with the weights given in the tables. At the foot of each of these tables there is a multiplier to each column, by which may be found the breaking weight of every scantling therein. Similar multiphers are given in the First and Third Series ; and it may here be remarked, as one of the leading features in the con- struction of this work, that the breaking weight and the deflection when loaded with the tabular weight, are given for every scantling throughout the whole of the tables. The tenth and eleventh of the Miscellaneous Tables shew the data upon which the Tables of Constants are founded; and at the end of the work there are several equations with examples, which may be use- ful in computing the true content of earthwork, to any given slope, in railway cuttings and embankments. PREFACE. V At the foot of each page of the tables there is an explanatory exam- ple. The use of the work is further and fully shewn in the various diagrams and practical Examples which precede the tables. If a joist, beam, lintel, brest-summer, or purlin, uniformly loaded with a given weight, be assumed as a Standard by which to determine the scantlings of other joists, beams, lintels, brest-summers, or purlins, to carry a similar weight; the dimension, or one near to it, of the for- mer will be found in some one of the tables in the First or Third Series; by which table the scantlings for that and other lengths are given, to carry the same weight, and to have the same deflection for each foot in length, as the standard bearing timber so assumed. As'accuracy is of the utmost importance in a work of this description, the Author has spared no pains in carefully revising, correcting, and checking, in several ways, every calculation in the original manuscripts, and from those, the proof sheets ; both of which have been again minutely revised. BiKMINOHAM ; May, 185(>. TABLE OF CONTENTS. PAGE Construction of the Tables xiii Description and Use of the Tables xvii Examples to the First Series of Tables, viz. — To find the Scantlings of Red Pine sufficient to carry a given weight uniformly loaded, and to have with that weight a given deflection xviii To find the Scantlings of Red Pine sufficient to carry a given weight suspended from the middle, and to have with that weight a given deflection xxi To find the Scantlings of any Species of Timber to have the same strength or deflection as those of Red Pine of a given length; being Examples to the Table of Constants, No 1 ... xxii Examples to the Second Series of Tables, viz. — To find the breaking weight of any Species of Timber of any dimension in the Second Series of Tables xxiv To find by the Table of Constants, No. 2, and the Second Series of Tables, the Scantlings of any Species of Timber sufficient to carry a weight, which shall be any given portion of the breaking weight xxv i TABLE OF CONTENTS. Vll o find the Scantlings of any Species of Timber sufficient to carry a weight, which shall be any given portion of the breaking weight, when the timber projects with one END HORIZONTALLY FROM A WALL XXviii ?o find the Scantlings of Red Pine sufficient to carry a weight, PLACED IN ANY POSITION UPON THE SCANTLING, which Weight shall be any given portion of the breaking weight xxix )iAGRAMS, shewing the Pressures upon Brest-summers, Plates and Purlins plate, page xxxiii Jf the Pressures upon Brest-summers, Plates and Purlins, sus- taining loaded beams and rafters, inclined at given angles to the horizontal plane xxxiii Examples to the Third Series of Tables xxxvi A. Table, by which may be found the Scantlings of Red Pine Brest-summers and Purlins sufficient to carry, in the di- rection of the depth or greatest side, any given portion of the breaking weight xxxviii Examples to the same xxxix Note, on the Table No. 3 in Tredgold's Elementary Principles of Carpentry xl TABLES. Table of Constants, No. 1,— By which may be found the Scantlings of various Species of Timber, to have the same strength or deflection as those of Red Pine 2 VIU TABLE OF CONTENTS. FIRST SERIES OF TABLES, By which may be found the Scantlings of any species of Timber sufficient to carry a given weight, and to have with that weight a given deflection. — Deflection in the Weight upon each foot in length = W middle for each foot in length ~ " X) Page. In tba. In cwts. In parts of an inch Table I 1 -000 -nnSQ uuoy 4V 5 Table II 8-000 -0714 U / 1 ^ ■4' 0 0 Table TIT 1 V/CO I0i)0 4^ 7 Table IV 97-nnn •OA 1 n ■fcT 8 Table V 42-875 4V 9 Table VI yJrt UUV/ "^7 1 A ••• 4% ... 10 Table VII 91-125 •81 "^fi Clou I 40 1 1 1 1 Table VIII 1 2.'5-oon l/^iJ \J\J\J 1-11 fin 111 DU To 12 Table IX . 1 •Afi'\A 1 4tC3t)'t ••■ ••• 13 Table X. ^ L\J \J\J\J 1 -Qosi'^; 1 y-cOtj To 14 Table XI 274-625 2-4520 I ... 4-5- ... Id Table XII 343-000 I 40 1 Q 10 Table XIII 421-875 •7fifi7 I 4 -Q oci Table XIV /jl 2-000 4-.'=;7 14 ^ t> / 14 ... ... ■dz Table XV 648-000 O / 3-- E = —— = 230000. If the weight W be uniformly loaded, and L be the length in feet, we V 1 184000 bS ) ^ ' and if W = weight in lbs. upon each foot in length, and S = ^ of an inch to the foot, fc3/(_!L. X W (2): V 1 4600 b j by which equation Tables I. to XXVI. in the First Series are cal- culated. In equation (2), W is assumed successively as follows, viz. : Tables I. to XIV 2^; 2-53; 33; 3-53; 7-53; 83; and in Tables XV. to XXVI., 93; 103; IP; 123; 133; 193; 203; the depths throughout the tables for the same values of b and L are therefore in arithmetical progression. In the Tables, the weight in lbs. upon each foot in length is, in Tables I. to XIV., as above, viz F; 23; 2-53; 33; 7-53; 83; and in Tables XV. to XXVI., 93X40X8'; 103 X 40XS'; 203X40XS'; in which 8' = 3% ; T^^, respectively. Since the breaking weight in lbs., uniformly loaded, of a scantling of the standard strength 1344, is -y—= (suppose) MXWXL, we have M = ^ (3) Substituting in (3), the value of in (2), we have M=c' X^ -i^; there- fore the multipliers M are independent of d and L. In Tables I. to XIV., M for the same value of b is in arithmetical progression, and in Tables XIV. to XXVI. constant throughout. xiv CONSTRUCTION OF THE TABLES. THIRD SERIES OF TABLES. Let P = pressure, 8 = deflection in the direction of the depth ; Let Q = pressure, 8' = deflection in the direction of the breadth ; then from ( 1 ) from which we have X L^ X L^ (4), (5) which are general equations for determining the scanthngs to have any given deflections. If 8 = S' ; and Q — ?^.P ; ^=(^)*x(l)* b = ^/^\d (7) ; by which equations the 6 Tables in the Third Series are calculated ; c being = ; P = pressure in lbs. upon each foot in length ; and 8 = ^ of an inch to the foot, as before. P in (6), is assumed as are the terms of the progression, 14; 24; 2-54; 34; 3-54; 44; 4-54; 54; 9-54; 104. In the Tables, in Cols. L to VL, P = H; 24; 2-54; 34; 3-54; 44; and in Cols. VII. to XVIII., P = 4-54 X 40 X 8'; 64 X 40 X 8' ; 104 X 40 X 8' ; in which 8' = -f^; -rs^ as before. Substituting the values of d and bin (6) and (7), in the equation ]Vi = the multipliers M are evidently independent of b and d ; and in Cols. VI. to XVIII. constant for the same length. CONSTRUCTION OF THE TABLES. XV The Second Series of Tables is calculated by the equation W= -——,= one-fourth of the breaking weight in cwts., suspended from Ij the middle (8). In the Miscellaneous Tables, I? Table I. is calculated by the equation b — (9). Table II. „ by „ S = '03287 X—.,. (10). d Tables III. to IX. inclusive, are formed from and by inter- polating the First Series of Tables. THEOREM. ( Corollaiy from Equations, page xiii.) Let W = one-fourth of the breaking weight, uniformly loaded, of a scant- ling of the strength 1344, of which the length in feet is L, and depth in inches d. L5 = deflection of the same, when uniformly loaded with the weight c= deflection of a scantling 1 inch square and 1 foot long of the same strength, when uniformly loaded with one-fourth of the breaking weight : which for Red Pine is c=^-^. We have then the following relation, viz. : WhenW'=W, L = — (a). For Red Pine L = 30-423 X d8. If d = 14" and B = then L = 10-648. Therefore, if a Red Pine beam be 14 inches deep, and less than 10 feet 7-77 inches long, the weight which produces a deflection of ^ of an inch to the foot, exceeds one-fourth of the breaking weight. DESCRIPTION AND USE OF THE TABLES. The outline of this work is described in the Preface, and the further description and use of the tables are shewn by the following Examples. THE FIRST SERIES OF TABLES, By which and the Table of Constants No. 1, may be found the Scant- lings of any description of Timber sufficient to carry a given weight, and to have with that weight a given deflection. The greatest weight upon a joist beam or lintel being ascertained or given, and the deflection when loaded with that weight assumed, the scantlings are found by the First Series of Tables. The weight being ascertained, if the tabular deflection be that as- sumed, the scantlings are given by inspection of the tables. If the assumed deflection be greater or less than the tabular deflec- w tion, the scantlings are found by means of the expression — , at the head of each table. In Ihis case it will be requisite to fix upon the least breaking weight of the required scantling, and then by the multi- pliers and weights in the table find the breaking weights of the scant- lings, as in Examples 4 and 6. w When the weight or the value of — falls between two of the tables, the depth may be found as in Example 1 . In the following Examples, W=weight in lbs., cwts., or tons ; either upon each foot in length, uniformly loaded, or suspended from the middle, as the case may be ; and D = deflection in inches or parts of an inch. If W= weight upon each foot in length, then D = deflection for each foot in length. If W= weight either uniformly loaded or suspended from the middle, then D = deflection in the middle of the scantling. c = constant in any column in the Tables of Constants, No. 1, 2 and 3. d xviii EXAMPLES TO THE FIRST SERIES. To find the Scantlings of Red Pine sufficient to carry a given weight UNIFORMLY LOADED, and to have with that weight a given deflection. Example 1.— Required the Scantlings of Red Pine 14 feet long suffi- cient to carry a weight of 800 lbs. to the foot, or 100 cwts. uniformly loaded upon the beam, the deflection to be as given by the tables. The scantlings are given by Table XVI. If the breadth be 8 inches, the depth is 12-63 inches, and the deflec- tion is 1^ of an inch. If the weight be 968 lbs. to the foot, or 121 cwts. uniformly loaded upon the beam, the scantlings are given by Table XVII. If the breadth be 8 inches, the depth is 13-89 inches, and the deflec- tion is If of an inch. Therefore, For 100 cwts. uniformly loaded, the Scantling is 12-63 X8; say 13 X8. For 121 cwts. uniformly loaded, the Scantling is 13-89 X8 ; say 14 X8. And for those and intermediate weights the Scantlings are, 13 X 8; 13i X 8; or 14 X 8. The same also are the scantlings for weights varying from 62-50 cwts. to 75-62 cwts. suspended from the middle. Example 2.— The greatest weight, uniformly loaded upon a Red Pine joist of any length, is 144 lbs. to the foot. Required the Scant- lings which with that weight deflect ^ of an inch to the foot. W = 144 lbs. D = w 144 — = — =: 144 X 60 = 8640 lbs. uniformly loaded. The Scantlings are given by Table X., and every scantling therein with 144 fbs. weight to the foot uniformly loaded, deflects in the middle ^ of an inch to the foot. Example 3. — Required the size of the Joists and Beams for a Ware- house Floor upon the following data : — Data for the Joists. Joists distant apart from middle to middle, 14^ inches; Greatest load upon the floor, 3 cwt. per superficial foot; Deflection when loaded, -^V of an inch to the foot. EXAMPLES TO THE FIRST SERIES. xix 3 X 14'5 The weight upon each foot in length of a joist is = 3*625 cwts. 12 W = 3-625 cwts. D = 3IJ. W 3-625 77 = — T- = 3'625 X 50 = 181-25 cwts. uniformly loaded. The scantlings are given by Table XIV. If the length of the joists be 7 feet, the scantlings are, — ..8-02X2; 7-71 X2J; 7-44 X2i; 7X3; 6-65X3^; &c. Deflection ^ of an inch. If the length of the joists be 8 feet, the scantlings are, — .. 9-16X2; 8-81X2i; 8-5lX2i; 8X3; 7-60X3i; &c. Deflection 3^ of an inch. And so on for other lengths. Data for the Beams. Beams distant apart from middle to middle, 8 feet ; Weight upon each foot in length, 8 X 3 = 24 cwts. ; Deflection, of an inch to the foot. W = 24 cwts. D = ^. W 24 — ^ = — = 24 X 40 = 960 cwts. uniformly loaded. W By Table XX., — = 980 cwts. uniformly loaded : the scantlings are given by that table. If the length of the beams clear of the supports be 12 feet, the scant- lings are, — .. 15-15X8; 14-57X9; 14-07X10; 13-63X11; 13-24X12; &c. The weight upon each of the beams is 12 X 24 = 288 cwts. And if 14-07 X 10 be the size of the beams, the breaking weight of each beam by Table XX. is 7-85 X 168= 1318-8 cwts. And HE! = 4-57. 288 That is, about 4^ times the weight upon the floor is the breaking weight of the beams ; the deflection of each beam with 288 cwts. uniformly loaded is i§ or XX EXAMPLES TO THE FIRST SERIES. Example 4 —Required the Scantlings of Red Pine sufficient to carry 71 tons, or 150 cwts., uniformly loaded ; and deflect with that weight ^*of an inch. The breaking weight to be not less than 4 X 160 = 600 cwts. W = 7-5 tons. D = i. W 7" 5 — = — = 7-5 X 8 = 60 tons, uniformly loaded. D 8 The scantlings are given by Table XXI. Tf the length clear of the supports be 6 feet, the Scantlings are, — 9-49X5; 8-93X6; 8-49X7; 6-58X15. Here the first six scantlings in the table are rejected, because the breaking weight of each is less than 600 cwts. The breaking weight of 9-49 X5, is 6-231 X 96-42 = 600-79 cwts. A joist 9i X5, contains the least quantity of timber, and is the weakest of the 1 1 scantlings in the table to be selected from, to fulfil the above conditions. Example 5.— Required the depth of a lintel to carry a 14-inch brick wall 20 feet high over an 8-feet opening ; the lintel to deflect in the middle ^ of an inch. Suppose the weight of 1 cubic foot of brickwork to be 125 lbs. or 1-115 cwts., then the weight upon the lintel is, — 8 X 20 X -if X 1-115 = 208-13 cwts. W = 208-13 cwts. D = A. — = z= 208-13 X 8 = 1665-04 cwts. uniformly loaded. The breadth being 14 inches, the depth by Table XXIII. is 10-18 inches. If the Imtel carry the ends of a floor of joists 16 feet in length, and if the greatest weight upon the floor be 1-5 cwts. per superficial foot, the additional weight upon the lintel is 8 X 1-5 X8=96 cwts. W = 208-13 + 96 = 304-13 cwts. D = as before. — _ ^^11^ _ 304-13 X 8 = 2433-04 cwts. uniformly loaded. The breadth being 14 inches, the depth by Table XXV. lis 1 1-38 inches. EXAMPLES TO THE FIRST SERIES. xxi To find the Scantlings of Red Pine sufficient to carry a given weight SUSPENDED FROM THE MIDDLE, and to have with that weight a given deflection. Example 6. — Required the Scantlings of Red Pine sufficient to carry 7i tons or 150 cwts. suspended from the middle, and deflect with that weight ^ of an inch. The breaking weight to be not less than 4X150=600 cwts. W = 7-5 tons. D = ^L. W 7-5 -p7 = — = 75 tons suspended from the middle. The scantlings are given by Table XXV. If the length clear of the supports be 7 feet, the Scantlings are, 12-54X7; 1200X8; 11-53X9; 11-14X10; &c. The first five scantlings in the table are rejected, because the breaking weight of each is less than 600 cwts. The breaking weight suspended from the middle of Red Pine 7 feet long 12-54 X7, is 5-576 X 112-81=629 cwts ; the scantlings are 12| X7 12X8, 1UX9, &c. Example 7.— Required the Scantlings of Red Pine 14 feet lono- suf- ficient to carry 1260 lbs. or 11-25 cwts. or -5625 tons suspended" from the middle, and deflect of an inch. W = 1260 lbs. ; or 1 1-25 cwts. ; or -5625 tons ; as the case may be. — To- = 5400 lbs. \ = 48-21 cwts. I suspended from the middle. = 2-41 tons , The ScantHngs are given by Table X. viz. : — . . 12-03X2; ll-57X2i; 11-16X2^; 10-51X3; 9-98X3^; 9-54X4; !)18X4i; 8-86X5; 8-34X6; 7-92X7; 7-58X8; 7-28X9; 7-03X10; (i-SlXll; 6-62X12. Deflection of each of the scantlings with the above weights, of an inch. w 1260 1260 X 30 d" 7 IS ~ 7 w 11-25 11-25 X 30 1) ~ is ~ 7 w -5625 ■5625 X 30 d" 7 7 xxii EXAMPLES TO THE FIRST SERIES. To find the Scantlings of any Species of Timber to have the same strength or deflection as those of Red Pine of a given length. The dimensions of Red Pine being given, the depth or breadth of other species of timber to have the same strength as Red Pine are found by Columns 2 and 3, and to have the same deflections by Col. 5 and 6, in the Table of Constants No. 1, page 2. Examples to the Table of Constants, No. 1. Let it be required to find, by way of Example, the depth or breadth of Riga Fir 10 feet long, to have the same strength and elasticity as Red Pine 10 feet long 10 in. by 3 in. Weight, Depth, and Breadth, to have the same strength. By the Second Series of Tables, p. 70, the breaking weight of Red Pine 10 feet long 10 in. by 3 in., is 4 X30= 120 cwts. suspended from the middle. Example to Column I. p 2. Relative strength : Red Pine 1-0000; Riga Fir -8029. 120 X -8029 = 96-348 cwts. The breaking weight of Riga Fir 10 feet long 10 X3, is 96-348 cwts. suspended from the middle. Example to Col. II. Depth to have the same strength : Red Pine 1-000; Riga Fir 1-116. 10 X 1-116 = 11-16 inches. The breaking weight of Riga Fir 10 feet long 11-16X3, is 120 cwts. suspended from the middle. Example to Col. III. Breadth to have the same strength: Red Pine 1-000; Riga Fir 1-245. 3 X 1-245 = 3-735 inches. The breaking weight of Riga Fir 10 feet long 10X3-74, is 120 cwts. suspended from the middle. EXAMPLES TO THE FIRST SEEIES. xxiii Minimum, Mean, and Maximum Strength. By Table X. p. 146, the mean results of 71 Experiments upon various species of timber are, — Minimum strength, '897. Mean strength, 1-000. Maximum strength, 1-077. If the greatest variation in the strength of sound timber of the same species be 10 per cent, below, and 8 per cent, above, the mean strength, the depth and breadth for those strengths are given by Cols. II. and III. p. 2. Thus, if 10X3 be the scantling for the mean strength, then 10-54X3 or 10X3-33 are the scantlings for the minimum strength ; and 9-62X3 or 10X2-78 are the scantlings for the maximum strength. Breadth, Depth, and Weight, to have the same deflection. By the Second Series of Tables, p. 70, Red Pine 10 feet long 10 in. by 3 in., with 30 cwts. uniformly loaded, deflects -164 of an inch. Example to Col. IV. Relative elasticity: Red Pine 1-000; Riga Fir 1-6033. •164 X 1-6033 = -263 of an inch. Riga Fir 10 feet long 10 X3, with 30 cwts. uniformly loaded, deflects •263 of an inch. The weight and depth being the same, the breadth varies as the elasticity. 3 X 1-6033 = 4-8099 inches. Riga Fir 10 feet long 10 X4-81, with 30 cwts. uniformly loaded, deflects -164 of an inch. Example to Col. V. Depth to have the same deflection: Red Pine 1-000; Riga Fir 1-170. 10 X 1-170 =11-70 inches. Riga Fir 10 feet long 1 1-70 X3, with 30 cwts. uniformly loaded, deflects • 1 64 of an inch. Example to Col. VI. Weight to have the same deflection; Red Pine 1-000; Riga Fir -623. 30 X -623 = 18-69 cwts. Riga Fir 10 feet long 10 X3, with 18-69 cwts. uniformly loaded, deflects •164 of an iuch. Xxiv EXAMPLES TO THE SECOND SERIES. EXAMPLES TO THE SECOND SERIES OF TABLES. Table of Constants No. 2, p. 50. By this and the Second Series of Tables may be found the Scantlings of various Species of Timber, sufficient to carry when loaded, any given portion of the breaking weight. By the same tables also may be found the Deflection and Breaking Weight of any scantling of timber of the several species therein specified. To find the breaking weight of any Species of Timber of any dimension in the Second Series of Tables. When the weight is uniformly loaded. The value of c in Col. I. p. 50, multiplied by the tabular weight for the scantling in the Second Series of Tables gives the breaking weight. Example 8.— Required the breaking weight, uniformly loaded, of Riga Fir 16 feet long 12 in. by 8 in. By Col. I. p. 50, for Riga Fir ; c = 6-423. By Table XIII. p. 76, the tabular weight for 16 feet long 12 X 8, is 72 cwts. 6-423 X 72 = 462-45 cwts. ; the breaking weight required. When the weight is suspended from the middle. The value of c in Col. III. p. 50, multiplied by the tabular weight for the scantling in the Second Series, gives the breaking weight. Example 9. — Required the breaking weight, suspended from the middle, of Riga Fir 12 feet long 10 X 6. By Col. IIL p. 50, for Riga Fir ; c = 3-211. By Table X. p. 70, the tabular weight for 12 feet long 10 X6 is 50 cwts. 3-211 X 50 = 160-55 cwts.j the breaking weight required. EXAMPLES TO THE SECOND SERIES. XXV To find by the Table of Constants, J^o. 2, and the Second Series of Tables, the Scantlings of any Species of Timber sufficient to carry a weight, which shall be any given -portion of the breaking weight. Weight uniformly loaded. The breaking weight in cwts, multiplied by the value of c in Col. II. p. 50, gives the tabular weight in the Second Series of Tables ; and the scantling opposite thereto, or to the next greater weight, is one of the scantlings required. Example 10.— Required the Scantlings of English Oak 12 feet long, sufficient to carry 80 cwts. uniformly loaded ; the breaking weight to be 10 times that weight, or 10 X 80 = 800 cwts. uniformly loaded. By Col. II. p. 50, for English Oak; c = -1176. 800 X -1176 = 94-08 cwts. ; the tabular weight. By the Second Series of Tables, the following are the scantlings and weights for 12 feet long : — Oak Scantlings. Tabular Weights. Notes. Table IX, ... 9 X 14 94-50 cwts. // X. ... 10 X lU 95-83 « 91'66 ..100"00 : g^.g"3 2 " " ... mx \0i 96-46 " 87-50 X 1-1025 = 96-46 " XI. ... 11 X 9i 95-79 » 90-75 . 100-83 " XII.... 12 X 8 96-00 " " " ... 12^ X 7i 97-65 » 90 X 1-085 = 97-65 To find the deflection of English Oak 12 feet long 12X8, uniformly loaded with -j?^th of the breaking weight. By Table II. p. 129, the deflection of Red Pine 12 inches deep and 12 feet long, uniformly loaded with ^th of the breaking weight, is By Col. VI. p. 50, for English Oak ; c = 1-684. 1-684 X -1576 = -265 of an inch; the deflection required. Example 1 1.— Required the Joists and Beams for a Warehouse Floor, upon the following data : — Data for the Joists. Joists 8 feet long clear bearing, and 15 inches apart from middle to middle. XXvi EXAMPLES TO THE SECOND SERIES. Greatest weight upon the floor, 3 cwts. per superficial foot. Breaking weight of the joists, 6 times the weight upon the floor. 3 X 15 X 8 The weight upon each joist is — = 30 cwts. The breaking weight of each joist is 6 X 30 = 180 cwts. If the joists be Red Pine, then Col. II. p. 50 ; c = -125 = J ; 180 And — -— = 22-50 cwts.; the tabular weight. By the Second Series of Tables, the following are the scantlings and weights for 8 feet long : — Scantlings of the Joists. Tabular Weights. Notes. Table VIII.... 8X3 24-00 cwts. 8i X 2i 25-78 " 30 X 1-289 = 25-78 " IX. ... 9 X 2i 22-78 ,/ 9i X 2 22-56 « 20-25 X 1-114 = 22-56 Data for the Beams. Beams 15 feet long and 9 feet apart from middle to middle. Greatest weight upon each beam, 9 X 3 X 15 = 405 cwts. Breaking weight of the beams, 4 times the weight upon the floor. The breaking weight of each beam is 4 X 405 = 1620 cwts. If the timber be sound Memel, then Col. II. p. 50; c = -097 ; and 1620 X -097 = 157-14 cwts. ; the tabular weight. By the Second Series of Tables, the following are the Scantlings and Weights for 15 feet long: — Scantlings of the Beams. Tabular Weights. Notes. Table XIII. . 13 X 14* 157-73 cwts. // II m X 164-02 " 152-10 X 1-0784 = 16402 « XIV. . 14 X 12 156-80 " // // 14i X Ui 161-18 " 150-26 X 1-7027 = 161-18 XV. . 15 X m 157-50 " 150 + 2 165 157-50 EXAMPLES TO THE SECOND SERIES. xxvii If the beams are mortised for the joists, add from ^ an inch to an inch to the depth or breadth of the beams. *** In determining the Scantlings for Raking Beams to carry a Gallery Floor, the horizontal distance between the brest-summer and the wall should be taken for the length of the beam, and the scantlings calculated as though the floor were level. The greatest weight upon a gallery floor, includmg the weight of the floor, ceiling, and framing, may be estimated at about 1-5 cwts. per superficial foot; and the breaking weight should be not less than 4 times the greatest weight. Weight suspended from the middle. The breaking weight in cwts, multiplied by the value of c in Col. IV. p. 50, gives the tabular weight. Example 12. — Required the scantlings of English Oak 12 feet long, sufficient to carry 80 cwts. suspended from the middle ; the breaking weight to be 5 times that weight. By Col. IV. p. 50, for EngUsh Oak ; e = -2353. 5 X 80 X -2353 = 94-12 cwts. ; the tabular weight. The scantlings are the same as in Example 1 0. Example 13. — What should be the size of a beam 16 feet long clear bearing, to support a pair of scales suspended from the middle, for the purpose of weighing 2 tons of metal ?* Suppose the scales, weights, metal, and one-half the beam to weigh 86 cwts. If the timber be Red Pine, and the deflection as in the First Series of Tables, then by Table XVII. p. 28, the Scantlings are,— 15-87X8; 15-26X9; 14-74X10; 14-28X11; 13-87X12; 13-50X13; &c. Deflection of each scantling of an inch. If the beam be 13i X 13, then nearly 7 times the weight of the metal, &c., is the breaking weight of the beam. * The consitleration of the above question, put to the Author May 24, 1847, led to the construction and eventually to the publication of these tables. XXVIU EXAMPLES TO THE SECOND SERIES. If the Scantlings be required which break with 4 times the suspended weight, the same are found by the Second Series of Tables. For Red Pine, 86 cwts. is the tabular weight ; and the following are the scantlings for 16 feet long; viz. : — 10X14; llXlli; 12X10; 12^X9; 13X8i; 13iX8; 14X7i; 14JX6J; 15X6i; 151 X5|; 16X5*. The deflections are given by the same tables. To find the Scantlings of any Species of Timber sufficient to carry a weight vjhich shall be any given portion of the breaking tveight, WHEN THE TIMBER PEOJECTS WITH ONE END HORIZONTALLY FROM A WALL. Weight uniformly loaded. The deflection of a joist or beam projecting with one end horizon- tally from a wall, with a given weight uniformly loaded, is 19-2 times the deflection of the same joist or beam supported at each end and uni- formly loaded with the same weight ; and the strength in the former position is to that in the latter as 1 is to 4. For Red Pine, one-half of the breaking weight uniformly loaded, is the tabular weight in the Second Series of Tables. Example 14. — Required the Scantlings of Red Pine, of any projec- tion, sufficient to support 8 cwts. uniformly loaded ; the scantlmgs to break with 10 times that weight. 10 X 8 — - — = 40 cwts. is the tabular weight ; in the Second Series of Tables, the Scantlings for 2 feet, 3 feet, and 4 feet projections, are as foUow, viz. : — Length or Projection, in feet. Scantlings by the Second Series of Tables. 2 3X9; 4X5; 5X3^; 6 X 2^. 3 4X8; 5X5; 6X3*; 7X2*; 8X2, 4 4X10; 5X6*; 5iX5*; 6X4*; 7X3*; 8X2*; 9X2 EXAMPLES TO THE SECOND SERIES. Xxix By Table IV. p. 54, Red Pine 4X5 and 2 feet long with 8 cwts. uni- formly loaded, deflects X -016 = -0032 of an inch ; therefore. Red Pine 4X5 and 2 feet projection with 8 cwts. uniformly loaded, deflects 19-2 X -0032 = -061 of an inch. Weight suspended from the extremity. The deflection of a joist or beam, projecting with one end horizon- tally from a wall, with a given weight suspended from the extremity, is 32 times the deflection of the same joist or beam supported at each end, with the same weight suspended from the middle; and the strength in the former position is to that in the latter as 1 is to 4. For Red Pine, the breaking weight suspended from the extremity, is the tabular weight in the Second Series of Tables. Example 15. — Required the Scantlings of Red Pine, of any projection, sufficient to support 4 cwts. suspended from the extremity ; the scant- lings to break with 10 times that weight, 10 X 4 = 40 cwts. is the tabular weight in the Second Series. The scantlings for 2 feet, 3 feet and 4 feet projection are the same as in the last Example. By Table IV. p. 54, Red Pine 4X5 and 2 feet long with 4 cwts. suspended from the middle, deflects X -026 = -0026 of an inch ; there- fore. Red Pine 4X5 and 2 feet projection with 4 cwts. suspended from the extremity, deflects 32 X -0026 = -0832 of an inch. Tojind the Scantlings of Red Pine sufficient to carry a weight, placed IN ANY POSITION UPON THE SCANTLING, which Weight shall be any gii>en 'portion of the breaking iveight. Weight uniformly loaded upon a portion of the Beam. When the weight is uniformly loaded upon a portion of a beam, find the weight uniformly loaded upon the whole of the beam which shall XXX EXAMPLES TO THE SECOND SEKIES. have the same stress upon the middle of the beam as the given weight: the scantlings for the uniform load so found are those required. Example 16.* — In Fig 1, let AB represent a beam 16 feet long; let C be the middle of the beam, and let 32 cwts. and 64 cwts. be placed upon AB, in the several positions shewn in the figure. Required the Scant- lings which just break with 8 times those weights in the seve- ral given positions. The uniform loads in Fig. 2, are found as below ; and the scantlings to break with 8 times those or the given weights, are found by the Second Series of Tables. Fig. 1. H ir m: I ! ?> ! 2 5tr Fig. 2. m Weight ( = W), upon the seve- ral parts of the beam AB in Fig. 1. Weight iu Fig. 2, uniformly loaded upon the beam AB, to have the same stress in the middle as the weight W iu Fig. 1. Scantling 16 inches deep. Upon AD .. 32 cwts. = f X 32 = 8 cwts. 16 X i Upon DE .. 64 II AC = 1 X 64 = 64 " 16 X 4 Upon EC ... 32 II AE.AC^^ AC = y X 32 = 56 „ 16 X3i Upon LC ... 64 II BL + BC „^ BC = If X 64 = 96 " 16 X 6 Upon BL ... 64 II — XW BC = 1 X 64 = 32 « 16 X 2 Upon AB ..256 cwts. 256 cwts. 16 X 16 Examples 16 and 17 shew the method of fiuding the scantlings in other cases. EXAMPLES TO THE SECOND SERIES. xxxi Scantlings of nearly equal strength, sufficient to carry the weights in Figs. 2 or 1, the breaking weight being 8 times the respective weights. Weight uniformly loaded in Fig. 2. Scantlings by the Second Series of Tables. Length 1 6 feet clear bearing. AG = 8 cwts. 4X8; 5X5i; 6X3i; 7X2f; 8X2. DH = 64 II (9X13; lOXlOi; 11X8^; 12X7^; 13X6^; 14X5J; 1 15X41; 16X4. EI = 56 II (8X14; 9X111; 10X9; 11X7J; 12X6^; 13X5^; 1 14X4f ; 15X4; 16X3^. LI = 96 II 11X13^ 12X101; 13X9i; 14X7|; 15X7; 16X6. BM = 32 II (6X14i; 7X11; 8X8; 9X6i; 10X5^; 11X4J; 1 12X3i; 13X3i; 14X2f; 15X2i; 16X2. JVotes to the preceding Example, JVb. 16. 1. If the weight DH be placed in the middle between A and C, then AD + AE = AC; and the stress at C from the weight DH in Fiff. 1, = stress at C from the weight DH uni- formly loaded ; as in the Example. 2. If the middle of the beam or the point C be between E and L, the weight uniformly loaded to have tlie same stress at C as the weight EM may be found thus : — Let the weight EM = W' = 96 cwts., then the weight uniformly loaded to have the same stress at C as the weight EM, is . AE X EC + BL X LC 12 + 16 W + — X W = 96 + — X 96 = 152 cwts. ; AC X EL 48 and the Scantling for that weight by Table XVI., is 16 x 9i : or 15x11; 14| x llj ; 14xl2i; 13^x131; &c. 3. If CE = CL or AE = BL, then the required weight uniformly loaded is , AE W + — X W = 96 + f X 96 = 156 cwts. 4. In Fiff. 1, join LK; let the weight of the triangular prism of which the section is LBK = W'=32 cwts.; then the weight uniformly loaded to have the same stress at C as LBK is, BL f X — X TV' = f X I X 32 = lOf = 10-66 cwts. ; and the length being 16 feet, the scantlings for 10'66 cwts. or the next greater weight are, 4xlOh 5x7; 6x4i; 6ix4i; lx3k; lixH; 8x2f; 8^x2^; 9x2i; 9ix 2. 5. The stress at C from the weight LBK, is i of the stress at C from the weight BM. xxxii EXAMPLES TO THE SECOND SERIES. Weight suspended from a given point. and the scantlings are very readily found by the Second Series of Tables. Example 17. — Required the Scantlings of Red Pine 16 feet long to support 128 cwts. suspended 4 feet from the wall; the breaking weight of the scantlings to be 4 times that weight. AB=16; AC = 8; AD = 4; DB=12; W' = 128 cwts.; From (a) we have W = ^^^^ X W'= X 128 = 96 cwts. suspended from the middle, which being one-fourth of the breaking weight, by the Second Series of Tables, the Scantlings for 16 feet long are, — 11X12J; 12X10f; 12^X10; 13X9i; 13^X8^; 14X8; 14iX7i; 15X7; 15JX6i; 16X6. Multiplying the breadths by ; ^; -i^L; |; &c, ; the scantlings are found which break with 4i times, 5 times, 5 J times, 6 times, See- the tabular or given weight. Note. — The breadth of Trimmer Joists, to have the same strength as the joists in the same iloor, may be found as follows : — Let W= the weight at D, from one end of a trimmer fixed to AB at D ; W = stress at C, found as above, from the weight W'; W" = one half of the weight uniformly loaded upon a floor joist ; b = breadth of a joist ; then, the length and depth being the same, for a trimmer joist AB to have the same Strength as the joists in the same floor, the breadth of AB should be, — W + W" — w'r- ^ ^ • (»)• EXAMPLES TO THE THIRD SERIES. XXXlll OF THE PRESSURE UPON BREST - SUMMERS, PLATES, AND PURLINS, SUSTAINING LOADED BEAMS AND RAFTERS, INCLINED AT GIVEN ANGLES TO THE HORIZONTAL PLANE. In Fig. 4, in the annexed plate, let the beam AC, fixed in position, be inclined to the horizontal and vertical planes, AB, BC at the angles CAB, ACB ; through G the centre of gravity of AC draw the vertical line FGH; through C draw any line ICE cutting FH in E; join EA and produce EA to K; then AC will be retained in its position by the ropes EC, EA ; or by the props CI, AK ; or by the rope EC and prop AK ; or by the rope EA and prop CT ; or by the brest-summers, plates or purhns P and Q ; the plane surfaces of which, viz. Qe, Ad, are at right angles to EC, EA respectively. Let the weight of the beam AC and the load thereon = W. Let Ec = 1-00 represent W ; draw ca, cb, parallel to EI, EK, cutting EK, EI in a and b ; then Pressure upon P in the direction EC = E6 XW (1); Pressure upon Q in the direction EA = EaXW (2). The beam AC, the centre of gravity G, and the vertical line FH through G, being fixed in position, let ICE, cutting FH in E, and the plate or purlin P, revolve round C as a centre, then E'AK' being drawn, the relative positions of P and Q are given which retain AC in equili- brium ; E'c'= 1-00 represents, as before, the weight AC, and E'6', E'a', the relative pressures upon P and Q respectively. When ICE coincides with BC, then KE is parallel to IE, and the surfaces Ce, Ad, perpendicular thereto, are horizontal, as in Figs. 7 and 8 ; in which case there is evidently no horizontal thrust. In Fig. 7, let W = weight of AC ; then AD Vertical pressure p' upon P = ^^'^^^ DB Vertical pressure p upon Q = ;^ (4). If AD = DB, or the centre of gravity G be in the middle of AC, the vertical pressures upon P and Q — i weight of AC ; and In Fig. 8, the vertical pressure upon Q = weight of GG. Fig. 10.— When ICE, Fig. 4, is at right angles to AC, the relative positions of P and Q are as in Fig. 10. / xxxiv EXAMPLES TO THE THIRD SERIES. If the centre of gravity G be in the middle between P and Q, and if W = weight of the rafter between P and Q; then if Ec = 1-00, we have Pressure upon P in the direction E6 = X W (5) ; Pressure upon Q in the direction Ea = Ea X W (6) ; or twice those pressures, if the rafters are continued to the purlin P', and to a purlin Q', at the same distance apart, from P towards C. In Figs. 8 and 10, the pressures upon P and Q, arising from the WEIGHT OF THE ROOF ALONE, are in the direction of the depth only; therefore the scantlings may be found by the First or Second Series of Tables. Scantlings fixed by the rule derived from Fig. 4, so as to have one pressure only, and that in the direction of the depth, should be firmly secured at each end in the required position, with only the one bearing surface in contact with AC as shewn in the figures; other- wise, the pressures being changed, the equilibrium of the whole will be thereby destroyed. When ICE is parallel to BA, the position of P is the same as in Fig 5 ; but the position of Q not being at right angles to EA, Q in Fig. 5 is subjected to two pressures p and q, as shewn in the figure; and the scantlings for Q to sustain such pressures, may be found by the Table page xxxviii., or by the Third Series of Tables. To measure the relative pressures, it will be convenient to set off Ec = 1 inch, the inch being divided into tenths, or set offEc = 10 feet from any scale ; then the various lines in any of the parallelograms Fiacb, measured by the same scale, give the relative pressures upon P and Q; which relative pressures being multiplied by the weight of AC, the actual pressures upon P and Q are given in the several direc- tions. In Fig. 5, Ec = I'OO, represents the vertical pressure p upon Q; and ca = Fib, the pressures q and q'. In Fig. 6, Ec being I'OO, Ec? is the measure of the vertical pressure p ; Ee is the measure of the vertical pressure p' : and da = eb is the measure of the pressures q and q' . Since p + j^' = Erf + Ee = Ec ; the sum of the vertical pressures upon P and Q, is always equal to the weight of AC. In Fig. 9, the purlins P and Q are fixed at right angles to the back of the rafter, and are supposed to sustain the whole pressure of the roof, in the directions E6 and CA. If Ec represent the weight of the rafter between P and Q, then EXAMPLES TO THE THIRD SERIES. XXXV E6, and bd = da are the pressures to be sustained by each of the purlins P and Q ; the pressures being twice those, if the rafters are continued as in the description to Fig. 10. When BC = AB, as in the figure, then = E6; the purlins are square, and the scantlings are found by Table VI. in the Third Series ; or by Col. X. page xxxviii. When BC = \ AB, then 6c? = J E6 ; the sides of the purlins are to one another as 1 to or as 10 to 7'07, and the scantlings are found by Table IV. Third Series, or by Col. VII., page xxxviii. In Fig. 11, the purlin P is at right angles to the back of the rafter, as in Fig. 9. cb represents the weight of the roof acting vertically, and ac the force of the wind acting at right angles to AC ; completing the parallelogram Eac6, Ec is the position of a purlin to resist the two pressures be, ac, acting together, so as to have only one thrust, and that to be in the direction of the depth of the purlin ; P being the position to resist with greatest effect the pressure from the wind alone, and Q the position to resist the weight of the roof alone. When the two forces act together, Ec? is the pressure upon P in the direction ac, and dc is the pressure upon P in the direction dc. In like manner Fc' = a'd' -\-b'c' is the pressure upon Q in the direction Fc' ; d'c' the pressure upon Q in the direction d'c' ; and by dividing the least pressure by the greatest, the scantlings may be found by the Third Series of Tables, or by the Table before referred to at page xxxviii. THE THIRD SERIES OF TABLES; By which maybe found the Scantlings of any description of Timber, to have given equal deflections when acted upon by two forces ; viz., one in the direction of the depth, the other in the direction of the breadth. The pressures upon a brest-summer or purlin being ascertained or given, and the deflection with those pressures assumed, the scantlings are found by the Third Series of Tables. If the assumed deflection be the tabular deflection, the scantlings are given by inspection of the tables. If the assumed deflection be less than the tabular deflection, the scantlings are found by means of the expression — at the foot of each table. xxxvi EXAMPLES TO THE THIRD SERIES. In other cases it will be more convenient to find the scantlings by the table page xxxviii. The DEPTH is the greatest side ; the breadth, the least side of the scantling. P is the pressure in lbs. or cwts. in the direction of the depth. D, the deflection in inches or parts of an inch. p and denote the relative pressures as described in the Explana- tion to the diagrams. The least divided by the greatest pressure determines the table by which the scantUngs are found, thus : — If -y or = -le, the Scantlings are found by Table I. ; If or — -25, the Scantlings are found by Table II. ; and so on. In the following Examples, the scantlings are those of Red Pine. The scanthngs of other kinds of timber are found by the Table of Con- stants, No. 3, p. 96. EXAMPLES TO THE THIRD SERIES OF TABLES. Example 18. — Required the Scantling for any given length of the Brest-summer Q, Fig. 5, upon the following data, viz. : Centre of gravity G in the middle of AC ; BC = i AB ; Weight of AC for one foot in length of Q=1225 cwts.; Pressure uniform ; the deflection to be as given by the table. The diagonal Ec, and the sides ca, Eb, of the parallelogram Each, axe equ> 1. Ec = ca = p = q. The scant ings are gWer. by Table VI. The pressure upon each foot in length being 12-25 cwts. ; the scant- lings are given by Col. XII. p. 120. If the length be 9 feet, the scantling is 10-07 X 10-07. If the length be 10 feet, the scantling is 10-89 X 10-89. Deflections each way, -7?^ of an inch to the foot. Breaking weight, upwards of 8 times the pressure upon the brest- summer. EXAMPLES TO THE THIRD SERIES. XXXvii Example 19. — The data in other respects being the same as in the last Example, — Required the ScantUng of the Brest-summer Q, 12 feet long, to support the same pressures, and deflect each way of an inch. P= 12 X 12-25= 147 cwts.; 0=^%. P 147 = -7" = 147 X 10 = 1470 cwts. uniform pressure. To" By Col. XIV. p. 120, — = 1462-85 cwts. Scantling, 14-28 X 14-28. If the same pressure be in the middle of Q, — By Col. XVI. ~ = 1464-50 cwts. Scantling, 16-06 X 16-06. Example 20. — Required the Scantlings, for any given length, of the Brest-summer Q, Fig. 6. Having drawn the figure, let the relative pressures measure as fol- low, viz. : — Ec = 1-00 ; Ed = -60 ; dc = -40 ; da = eb = -22. Pressure p = F,d = -60; pressure q = da = -22, Least pressure g "22 G7^i^;S^s-^=7 = -60 = *^^' scanthngs are given by Table III. If the pressure upon Q be uniform, and the weight of AC be 9-9 cwts. to the foot, the greatest pressure {p) upon Q =z -60 X 9-9 = 5-94 cwts. to the foot. The scantlings are given by Col. IX. p, 107. If the length be 1 0 feet, the scantling is 9-73 X 5-84. If the length be 11 feet, the scantling is 10-45 X 6-27. Deflection each way, -/y of an inch to the foot. Breaking weight, upwards of 7 times the pressures upon Q. X Example 21. Fiff. 6.— Let the weight of AC, resting upon the middle of Q, be 80 cwts. Length of Q, 12 feet ; Deflection of Q each way, ' of an inch. Pressures as in the last Example. The greatest pressure {p) upon Q, is Ed X80=-60 X80 = 48 cwts. P = 48 cwts. D = i . P 48 '^ — 'Y~ '^^^ pressure in the middle. By Col. XL p. 108, ~ = 398-45 cwts. Scantling, 13-18 X 7-91. xxxviii EXAMPLES TO THE THIRD SERIES. A TABLE By which may be found the Scantlings of Red Pine Brest-summers and Purlins sufficient to carry, in the direction of the depth or greatest side, any given portion of the breaking weight. Pressure Pressure PRESSURE IN THE DIRECTION OF THE BREADTH. in the Greatest uniform. middle. side, or Depth •04 •09 •16 •25 •36 •49 -64 •81 1-00 Product of the Length in Feet; by the incheSf oreaKing we LEAST SIDE, OR BREADTH IN INCHES. by the Factor for the pressure. 4 •80 1^20 1-60 2-00 2-40 2^80 3-20 3-60 4-OU 512 256 4i •90 1-35 1-80 2-25 2^70 3^15 3-60 4^05 4-50 729 364 5 1-00 l^oO 2-00 2^50 3-00 3^50 4-00 4-50 5-00 1000 500 tj 2 MO 1-66 2-20 2-76 3-30 3-85 4-40 4-95 5-50 1331 665 6 1-20 1^80 2-40 3^00 3^60 4^20 4-80 5-40 6-00 1728 864 6i 1-30 1-95 2^60 3^25 3-90 4^55 5-20 5-85 6-50 2197 1098 7 1-40 2-10 2-80 3-50 4-20 4-90 5-60 6-30 7-00 2744 1372 1-50 2-25 3^00 3^75 4^50 5^25 6-00 6-75 7-50 3375 1687 g 1-60 2^40 3^20 4-00 4^80 5^60 6-40 7-20 8-00 4096 2048 8^ 2 1-70 2-55 3^40 4^25 5^10 5^95 6-80 7-65 8-50 4913 2456 9 1-80 2-70 3^60 4-50 5-40 6^30 7-20 8-10 900 5832 2916 9i 1-90 2^85 3-80 4-75 5^70 6^65 7-60 8-55 9-50 6859 3429 10 2-00 300 4^00 5^00 6^00 7^00 8-00 9^00 10-00 8000 4000 2^10 3-16 4^20 5-25 6^30 7-35 8-40 9-45 10-50 9261 4630 11 2-20 3-30 4-40 5^50 6-60 7^70 8-80 9^90 11-00 10648 5324 Hi 2-30 3^46 4-60 5-75 6^90 8-06 9-20 10^35 11-50 12167 6083 12 2^40 3^60 4^80 6-00 7-20 8^40 9-60 lO^SO 12-00 13824 6912 m 2^50 3^75 5 '00 6^26 7^50 8-75 lO'OO 11-26 12-50 15625 7812 13 2^60 3^90 5-20 6^50 7-80 9-10 10-40 11-70 1300 17576 8788 13i 2-70 4^05 5-40 6-75 8-10 9^45 10-80 12-15 13-50 19683 9841 14 2^80 4-20 5^60 7^00 8-40 9-80 11-20 12-60 14-00 21952 10976 14* 2-90 4^35 5-80 7^25 8-70 10-15 11-60 13-05 14-50 24389 12194 15 3^00 4-50 6^00 7^50 9^00 10-50 12-00 13-50 15-00 27000 13500 151 3^10 4-66 6-20 7^75 9^30 10-85 12-40 13-95 1550 29791 14895 16 3-20 4-80 6-40 8^00 9-60 11-20 12-80 14-40 16-00 32768 16384 Factors for the Pressure in the direction of the Breadth. Note. — The pressure in the direction of 5. 10 5 2. 5 10 5 10 1. the Depth is 1. y y 1"' y T' T' I. 1 II. III. IV. V. VI. VII. VIII. IX. X. 1 XL 1 XII. EXAMPLES TO THE THIRD SERIES. xxxix EXAMPLES TO THE ANNEXED TABLE. The Depth, is the greatest side ; the Breadth, the least side ; with- out reference to the position of the scantling. In the direction of the depth, the least pressure divided by the greatest, gives the pressure in the direction of the breadth. Multiply together The length in feet ; The breaking weight in cwts. ; and The factor for the pressure. If the pressure be uniform, the Scantling is found by Column XI. If the pressure be in the middle, the Scantling is found by Col. XII. Example 22. — Required the Scanthng of a Brest-summer to support a Shed Roof, fixed as in Fig. 5, {plate, p. xxxiii) upon the following Data. Length of the Brest-summer Q, clear of the supports, 20 feet. Weight of the Roof AC, 20 X 2-5 = 50 cwts. Pressure upon Q, uniform. Breaking weight of Q, 8 times the pressure upon Q. Centre of gravity G, in the middle of AC ; BC = i AB. Since BC = J AB ; Ec (= 1"00), = ca,= pressure p, = pressure q ; therefore The pressures p and q are each equal to the weight of the roof; P — - z= 1-00; = pressure for the breadth (Col. X.) Length 20 feet; Breaking weight 50 X 8 = 400 cwts.; Factor L 20 X 400 X 1 = 8000, the tabular number. Pressure unifoim. Scantling, Cols. X. and I., 10 X 10. (See also page 71.) By Table IT. (p. 130), a Red Pine brest-summer 10 inches deep and 20 feet long, uniformly loaded with one-eighth of the breaking weight, deflects each way ^ ^' ^ = -657 of an inch. 8 If the deflections be too great, the scantling for any other deflection may be found by Table VI. in the Third Series of Tables, thus :— Let the deflection each way of the brest-summer be I of an inch ; P = 20 X 2-5 = 50 cwts. ; D = i. P 50 ^ = — = 50 X4i=: 200 cwts. Pressure uniform. By Col. VIIL (p. 119), -^ = 223'21 cwts. Scantling 13-09 X 13-09. xl EXAMPLES TO THE THIRD SERIES. Example 23. — Fig. 5. — Required the Scantling of the Brest-summer Q, 20 feet long, upon the following Data. Weight of the raking beam AC, resting upon the middle of Q, 50 cwts.; Breaking weight of Q, 10 times the pressure upon Q. Let EC = i AB, then {Ex. 22) pressure p = q = weight of AC. Length 20 feet ; Breaking weight of Q, 10 X 50 = 500 cwts.; Factor for the pressure, TOO. 20 X 500 X 1-00 = 10000, pressure in the middle. Col. XII. p. xxxviii., opposite 10976, the Scantling is 14 X 14. Deflection each way (p. 130), t^L^l x -8 = -j^ of an inch. Example 2L—Fig. 5.— Let BC = AB. Data in other respects as in Example 22. Required the Scantling of Q. Since BC = AB, we have ca = i Ec; or p = 1-00, q = -50. Least pressure ^ J_ ^ ^= -50 ; the breadth is found by Col. VII. Greatest pressure p I'OO Length 20 feet ; Breaking weight 50 X8=400 cwts. ; Factor V°- 20 X 400 X y = 1 1428, the tabular number. Pressure uniform. Opposite 12167, Col. XI., the scantling is lU X 8-05. Deflection each way, (p. 130), i^lii^ = -571 of an inch. If the pressure 50 cwts. be in the middle of Q, — Opposite 12194, Col. XII., the scantling is 14i X 10-15. 4 X "907 Deflection each way (p. 130), — — X -8 = -362 of an inch. By the Table p. xxxviii., may be found the scantlings of beams, &c., pressed by one force only, such as beams for warehouse floors, &c., the sides of which shall be in any usual proportion, and sufficient to carry any given portion of the breaking weight. If the beams be square, the scantlings are found by Col. X. If in the proportion of 10 to 8,. by Col. VIII. ; and so on. Joists continued over beams, beams and brest-summers over columns, rafters oyer purlins, purlins over principals, &c., in all such cases where the ends are continued and fixed, the strength of the intermediate lengths is increased one half. In reducing the scantlings accordingly, it will be requisite to bear in mind the maxim, that. The strength of a floor OR ANY SYSTEM OF FRAMING, DOES NOT EXCEED THAT OF THE WEAKEST PART. Note, on the Table No. 3 in Tredgold's Elementary Principles of Carpentry. Let the Scantlings for Single Joisting, &c., in the Table No. 3 in Tredgold's Carpentry be those of Red Pine, of the standard strength and elasticity assumed throughout these tables, then every scantling therein, uniformly loaded with a weight of 1814 ibs. = 16-197 cwts., deflects in the middle -J- of an inch to the foot. If, therefore, 1814 be divided by the length in feet, the scantlings there given, within the limits of 20 feet long and 3 inches in breadth, may be found, nearly, by the Miscellaneous Tables, Nos. 3 to 9, in this work. 2 FIRST SERIES OF TABLES. TABLE OF CONSTANTS. No. 1. By which may be found the Scantlings of the following species of Timber, to have the same strength or deflection as those of Red Pine.* Name of the Wood. Standard, I Strength ,..1344) Red Pine J Elasticity 230000 j Acacia Ash Beech Birch, American black ... „ Common Bullet tree Cabacally Deal, Christiana „ Memel Elm Fir, Mar Forest „ New England Riga Green-heart Larch Locust tree Norway spars Oak, Adriatic „ African, superior quality „ Canadian „ Dantzic „ English Pine, Pitch „ Red, mean strength 1 341 -3 Poon Teak Tonquin bean STRENGTH. ELASTICITY. Relative Strength. Depth to have the same strength. Breailth to have the strength. Relative Elasticity. Depth to have the same deflection. Weight to have the (amc deflection. C = S. 1 1 s * c=E. 1 1-0000 1*000 1*000 1*0000 1*000 POOO I '3891 •848 •720 1*5972 1*169 •626 1*5084 •814 •663 1*1185 1-038 894 1*1588 •929 •863 1*3594 1-108 •735 1*3526 •860 •739 1*2459 1-076 •802 1*4345 •835 •697 1*1 186 1-038 *894 1*9717 1^404 •507 *6999 -888 1-428 1*8735 •731 •534 *9961 •999 1*004 1*1577 •929 •864 1*1575 \-060 -864 1*2879 •881 •776 1*1197 1*038 *893 *7552 1-151 1^324 2*6781 1-389 •373 •9044 •1051 1-106 2*1865 1*298 *457 *8203 M04 1-219 1*2327 1*072 *8U *8029 1-116 1-245 1*6033 1*170 *623 2*0364 •701 -491 *6928 *885 1-443 *7444 1-159 1-343 2*0096 1*262 *497 2*5572 Oo L 1 yjo 1 1*0959 -955 -912 1*2620 1*081 *792 1*0286 '986 -972 1-8940 1*237 *528 1*8571 -734 •538 •7983 *928 1*252 1*3144 •872 •761 •9507 *983 1*051 1*0937 -956 •914 1-5778 1*164 •633 1*0621 •970 •942 1*5857 1*166 •630 1*2141 •908 *824 1*5024 1*145 •665 *9980 1*001 1*002 1-0000 1*000 1^000 1*6523 •778 *605 1-0892 1-029 •918 1-8326 •739 *546 •7623 •913 1-311 2*6979 •609 *371 *6928 •885 1-443 *9000 1^054 1*111 1*0000 1*000 1-000 1*0800 *962 *926 Col. I. IL III. IV. V. VI. Minimum Strength. Mean Strength .... Maximum Strength * See Examples, page xxii. The values of S and E are founded upon the mean values of S and p. 146—148. Tables X. and XI. FIRST SERIES OF TABLES : BY WHICH AND THE TABLE OF CONSTANTS MAY BE FOUND THE SCANTLINGS OF ANY SPECIES OF TIMBER SUFFICIENT TO CARRY A GIVEN WEIGHT, AND TO HAVE WITH THAT WEIGHT A GIVEN DEFLECTION. FIRST SERIES TABLES OF SCANTLINGS. 5 TABLE I.— Red Pine. Weight upon each foot in length, 1 lb. Deflection in the middle for each foot in length, ^ of an inch. Weight uniformly loaded. W lbs, P = 40 w Weight suspended from the middle, ~ = 25 Length BREADTH IN INCHES. Weight in feet, H 2 2i 2i 3 3^ uniformly lo&ded, bearing. DEPTH IN INCHES. in lbs. 1 •16 •15 •14 •14 •13 •13 •12 "Too 2 •32 •30 •29 •28 •27 •25 •24 200 *3 •47 •45 •43 •41 •40 •38 •36 3-00 4 •63 •60 •57 •55 •53 •50 •48 4-00 5 •79 •75 •72 •69 •66 •63 •59 5^00 ~T •90 •86 •83 •80 •75 •71 6-00 7 110 \-05 1-00 •96 •93 •88 •83 7-00 8 1^26 1-20 115 MO 1-06 l-OO •95 800 9 1-42 1^35 1-29 1^24 1^20 M3 1-07 900 10 1-58 1-50 143 1-38 1-33 1-25 119 10-00 TT 1-73 1-65 1-57 1^51 1-46 1-38 1^ Th)0 12 1-89 1-80 1-72 1-65 1-59 1-50 1-43 1200 13 2-05 \-9o 1-86 1-79 1-73 \-63 154 13^00 14 2^21 2-10 200 1-93 1-86 1-75 1-66 14^00 15 2-36 2^25 215 2^07 1-99 1-88 1-78 15 00 Weight suspended from the middle, in lbs. •62 1-25 1- 87 2- 50 312 3^75 4- 37 5- 00 5^62 6^25 ~6W 7- 50 8- 12 8- 75 9- 37 Deflectioa ill the middle, in parts of an inch. 4^ 3 4^ 4. 5 6 7 4 o 8 9 I o 40 4^ I 2 I 3 40 1 4 4S 1 5 4^ Multipliers to give the breaking weight of every Scantling in each column respectively. I33^37j35^ i2i36^73;3»^2 1 |39^56l42^04 |-26^69'28^10 29^38 30^57 31-65I33-63 44-25 35-40 Uniformly loaded. Suspended frotn the middle. * Example. — Red Pine 3 feet long, -4? in. hy 1^ in , or -45 by If, or -43 by 2, or •41 by 2i, or -40 by 2|, or -38 by 3, or -36 by 3^, with 3 lbs. uniformly loaded, or r87 lbs. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 3 ft. long, "47 in. by 1| in , is 33.37 x 3 =100 lbs. uniformly loaded, or 26-69 x 1-87 = 50 lbs. suspended from the middle. The breaking weight of Red Pine 4 ft. long, -63 in. by 1| in., is 33-37 x 4=133 lbs. uniformly loaded, or 26-69 x 2 50 = 66 lbs. suspended from the middle ; and so on throughout the table ; the breaking weight suspended from the middle being, in all cases, one half of the weight uniformly loaded. *^* To find the depths of other kinds of timber to have the same deflection or strength as Red Pine, also for the use of the expression see the Table of Constants and Examples. 6 FIRST SERIES TABLES OF SCANTLINGS. TABLE II.— Red Pine. Weight upon each foot in length, 8 lbs. Deflection m the middle for each foot in length, of an inch. W Weight uniformly loaded D ~ W Weight suspended from the middle, = 200 Length in feet, clear bearing. BREADTH IN INCHES. li 2i 3* DEPTH IN INCHES. 1 •32 •3U •29 •28 •27 •25 •24 2 •63 •60 •57 •55 •53 •50 •48 3 •95 •90 •86 •83 •80 •75 •71 *4 1-26 1-20 115 MO bOO •95 5 1-58 1-50 1^43 1-38 \-23 1-25 M9 6 r89 1^80 r72 1-65 ~f69 T50 T43" 7 2-21 2^10 2-00 ]-93 1-86 1-75 1-66 8 252 239 229 2-20 2-13 2-00 1-90 9 2'84 2^69 2-58 2^48 2-39 225 2^14 10 315 2-99 2^86 2^75 2-66 2-50 2^38 Tr ¥47 3-29 345^ ¥03 2^92 ¥75 2-61 12 3-78 3-59 3^44 3^30 3-19 3-00 2-85 13 410 3-89 3^72 3-58 3^46 3-25 3^09 14 441 4^19 4-01 3^86 372 3^50 3^33 15 473 4^49 4^30 4-13 3^99 3-75 3^56 5-04 4^79 4-58 441 4^ 4^00 's-W 17 5^36 5-09 4^87 4^68 4-52 4^25 4-04 18 5-67 5-39 5^15 4^96 4-78 4-50 4-28 19 5^99 5^69 5^44 523 5^05 4^75 4-51 20 6^30 5-99 5^73 5^51 5-32 5-00 4^75 Weight uniformly loaded, iu lbs. 8^00 16^00 24^00 32-00 4000 48^ 56-00 64^00 72^00 80-00 88-00 96-00 104-00 112-00 120-00 128^00 136-00 144-00 152-00 160-00 Weight suspended from the middle, in lbs. 5-00 10-00 15-00 20-00 25-00 30^00 35-00 40-00 45-00 50^00 55^00 60^00 65-00 70-00 75-00 "80^ 85-00 90-00 95^00 100^00 Deflectiou in the middle, in parts of an inch. 40 2 4"S- 40 5 4 O 6 40 7 "4^ 8 TS- _9_ 40 I o 40 I* 40 15. 40 I 6 4^ I 7 I 8 4^ I 9 40 a o Multipliers to give the breaking weight of every Scantling in each column respectively. 16^68| 17-56 13-34114-05 18-36 14-69 19-10 15^28 19^78 15^82 21^02 16^81 22^12 17^70 Uniformly loaded. Suspended from the middle. * Example.— Bei Pine 4 feet long, 1'26 in. by 1^ in., or I'SO by If, or I'lS by 2, or 1-10 by 2i, or 1-06 by 2i or 1-00 by 3, or "95 by 3|, with 32 lbs. uniformly loaded, or 20 lbs. suspended from the middle, deflects ^ of an inch. The breaking weight of Red Pine 4ft. long, 1-20 in. by 1| in., is 17-56 x 32 = 562 lbs. uniformly loaded, or 14-05 x 20 = 281 lbs. suspended from the middle. The breaking weight of Red Pine 5 feet long, 1-50 in. by If in., is 17"56 x 40 = 702 lbs. uniformly loaded, or 14-05 x 25 = 351 lbs. suspended from the middle: and so on, throughout tiie table. FIRST SERIES TABLES OF SCANTLINGS. 7 TABLE III.— Red Pine. Weight upon each foot in length, 15*625 lbs. or '1395 of a cwt. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded vy lbs. cwts. ton. —=625 =5-58 =-279 W Weight suspended from the middle, ^ =390=3'48=:-174 Length in feet, BREADTH IN INCHES. Weight Weight suspended from the middle, in cwts. U If 2 2i 1 2i 1 3 1 3i unifoitoly loaded, bearing. DEPTH IN INCHES. ill cwts. 1 •39 •37 •36 •34 •33 •31 •30 •13 •08 2 •79 •75 •72 •69 •66 •63 •59 •27 •17 3 M8 M2 1^07 1-03 100 •94 •89 •41 •26 4 1^58 1-50 [•43 |-3« 1-33 {•25 M9 •55 •34 *5 1^97 \-87 1^79 1-72 1-66 1-49 •69 •43 6 2^36 2-15 2-07 T99 •52 7 2-76 2-62 2^51 241 2-33 '2-\9 2-08 •97 •61 8 315 2^99 2-86 2-75 2-66 2-50 2^38 Ml •69 • 9- 3-55 3-37 3-22 3^10 2^99 2^81 2-67 •78 10 3^94 3-74 3^58 344 3-32 3^13 2^97 1^39 •87 11 4-33 4^12 3-94 3-79 3^ 3-44 3^ 1^ ^5" 12 4-73 4-49 4-30 4-13 3-99 3-75 3^56 1-67 1^04 13 5^12 4^86 4-65 447 4-32 4^06 3^86 1^81 M3 14 5-52 5-24 5^01 4^82 4-65 4^38 4^16 1^22 15 5-91 5-61 5^37 5-16 4^98 4^69 4-46 2^09 1-30 16 "6^0 5^99 5^73 532 5^00 4^75 ^2^3" 17 6-70 6-36 6-08 5-85 5^65 5-32 5^05 2^37 ]^48 18 709 6-74 6^44 6-20 5^98 5-63 5-35 2^51 l^56 19 7-49 712 6-80 6-64 6^31 5^94 5^64 2^65 20 7-88 7-48 7-16 6-88 6^65 6^25 5^94 2^79 174 Deflection in the middle, in parts oi an iucii. 3 4 O 4 TS' 5 Tg 40 7 To 8_ 40 To 1 3 4 O I 4 40 I 5 _4^ I 6 I 7 1 8 1 9 40. 2 O T^ Mtiltipliers to give the breaking weight of every Scautling in each column respectively. 13^34| 14^05 10-67 11-24 14-69il5-28|15^82 11-75| 12-221 12-66 16-81 13^45 17^70 14^16 Uniformly loaded. Suspended from the middle. * Example. — Red Pine 5 feet long, 1-97 in. by H in., or 1-87 by If, or 1^79 by 2, or 1-72 by 2^ or 1-66 by 2^ or 1-56 by 3, or 1-49 by 3^, with -69 cwts. uniformly loaded, or '43 cwts. suspended from the middle, deflects J-^ of an inch. The breaMng weight of Red Pine 5 ft. long, 1-79 in. by 2 in., is 14-69 x '69 = lO'l cwts. uniformly loaded, or 11-75 x -43 = 5'0 cwts. suspended from the middle. The breaking weight of Red Pine 6 feet long, 2'15 in, by 2 in., is 14"69 x -83 = 12-2 cwts, uniformly loaded, or 11-75 x -53 = 6-1 cwts. suspended from the middle, and so on, throughout the table. 8 FIRST SERIES TABLES OF SCANTLINGS. TABLE IV.— Red Pine. Weight upon each foot in length 27 lbs, or '241 of a cwt. Deflection in the middle for each foot in length, of inch. Weight uniformly loaded Wr llJS' cwts. ton. — =:1080=9-64=-482 * W Weight suspended from the middle, — = 675=6-02=-301 BREADTH IN INCHES. li I li 2i DEPTH IN INCHES. 1 "47 4:0 •A 1 •40 oo ou 2 •95 ou OO •SO 1 o •71 3 1-42 1-35 1-29 1-24 1-20 M3 1-07 4 1-89 1-80 1-72 1-65 1-59 1-50 1-43 5 2-36 2-25 2-15 2-07 1-99 1-88 1-78 *6 9'fiQ 9'^Q /C oy 9-1/1 7 O O I •^•14 O 1 'I O W 1 ^ DO 9-dQ 8 3-78 3-59 3-44 3-30 3-19 3-00 2-85 9 4-25 4-04 3-87 3-72 3-59 3-38 3-21 10 4-73 4-49 4-30 4-13 3-99 3-75 356 11 5-20 T94 4-72 4-54 4-39 4-13 T92" 12 5-67 539 515 4-96 4-78 4 -.50 4-28 13 6-15 5-84 5-58 5-37 5-18 4-88 4-63 14 6-62 6-29 6-01 5-78 5-58 5-25 4-99 15 7-09 6-74 6-44 6-20 5-98 5-63 5-35 J6 ~T66 7-18 6-87 ~6^6T 6-38 ~6<)0 ~5^0 17 8-04 7-63 7-30 7-02 6-78 6-38 6-06 18 8'0l 8-08 7-73 7-43 7-18 6-75 6-42 19 8-98 8-53 8-16 7-85 7-58 7-13 6-77 20 9-45 8-98 8-59 8-26 7-97 7-50 7-13 21 9-93 902 8-67 ~8^37 7-88 7-48 22 10-40 9-88 9-45 9-09 8-77 8-2-0 7-84 23 10-87 1033 9-88 9-50 9-17 8-63 8-20 24 11-35 10-78 10-31 9-91 9-57 9-01 8--55 25 11-82 11-23 10-74 10-33 9-97 9-38 8-91 Weight uniformly loaded, in cwts. -24 •48 -72 •96 1-20 Til 1-68 1- 92 2- 16 2-41 2^ 2- 89 3- 13 337 3-61 3- 85 4- 09 4-33 4-58 4-82 5-06 5-30 5-54 5- 78 6- 02 Deflection in the middle, in parts of an inch. T3^ 2 3 5 6 4^ 7 4^ 43- 1 o AS 40 I z T5- I 3 40 JL4 40 I 5 I 6 4^ 1 7 4^ I 8 4^ 1 9 2 O 40 2 I 4-5- 2 2. 40 2^3. 40 2 4 4 O 2^1. 4 o Multipliers to give the hreaking weight of every Scantling in each column respectively. 11-12 11-70 12 24 12-73 13-18 14-01 8^89 9-36 9-79 10-19 10-55 11-21 14-75 1 1-80 Uniformly loaded. Suspended from the middle. * Example.— Pine 6 feet long. 2-84 in. by U in., or 2-69 by If, or 2-58 by 2, or 2-48 by 2i, or 2-39 by 2|, or 2-25 by 3, or 2-14 by Z\, -with 1-44 cwts. uniformly loaded, or '90 cwts. suspended fi'om tie middle, deflects.^ of an inch. The breaking weight of Red Pine 6 ft. long 2-48in. by 2iin., is 12-73 x 1-44 = 18-3 cwts. uiiiformly loaded, or 10-19 x •90 = 9'1 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 9 TABLE v.— Red Pine. Weight upon each foot in length, 42"875 lbs. or '3828 of a cwt. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded. ■l\7' lbs. cwts. ton. — = 1715=15-31 = -765 W Weight suspended from the middle, ^ = 1071= 9-57= -478 Length BREADTH IN INCHES. Weight Weight from the middle, in cwts. in feet, clear H U 2 1 21 1 91- 3 Si uriit'ormly loaded, bearing. DEPTH IN INCHES. in cwts. 1 •55 •52 -50 •48 -47 •44 •42 -38 •23 2 rio 1-05 1 -00 •96 •93 -88 •83 -76 •47 3 1-65 1-57 1-50 1-45 1-40 1-31 1-25 1-14 •71 4 2-21 2-10 2-00 1^93 1^86 1-75 1-66 1-53 •95 5 2-76 2-62 2-51 2-41 2-33 2-19 2-08 1-91 M9 6 3-3 1 3-14 ~3-0l ~2^ 2-79 2-63 2-49 2-29 ~1^ *7 3'86 3*67 3-51 3-37 3-26 3-06 2-91 2-67 1-67 8 4-4 1 4-19 4-01 3-86 3-72 3-50 3-33 3-06 1-91 9 4-96 4-71 4-51 4-34 4-19 3-94 3-74 3-44 2- 15 10 5-52 5-24 5-01 4-82 4-65 4-38 4-16 3-82 2-39 11 6-07 6-76 5-51 5-30 5-12 T82 "4^7" 4-2 1 12 6-62 6-29 6-01 5-78 5^58 5-25 4-99 4-59 2-87 13 7-17 6-81 6-51 6-26 6-0o 5-69 5-41 4-97 3-11 14 7-72 7-33 7-01 6-75 6-51 6-13 5-82 5-35 3-34 15 8-27 7-86 7-52 7-23 6-98 6^57 6-24 5-74 3-58 "¥82 8-38 "8'-02 7^71 7-44 6-65 ~6'-12" ~¥82~ 17 9-38 8-91 8-52 8-19 7^91 7-44 7-07 6-50 4-06 18 9-93 9-43 9-02 8-67 8^37 7-88 7-48 6-89 4^30 19 10-48 9-95 9-52 9-16 8-84 8-32 7-90 7-27 4^54 20 11-03 10-48 10-02 9-64 9-30 8^7o 8-32 7^65 4^78 21 11 -58 11 -uu 10-52 10-12 9-77 "^49 8^73 8-03 ~5^ 22 12-13 U-53 11-02 10-60 10-23 9-63 9^1 5 8-42 5^26 23 12-69 12-06 11-52 11-08 10-70 10-07 9-56 8-80 5-50 24 13-24 12-57 12-02 11-57 1 1-16 10-51 9-98 9-18 5-74 2-5 13-79 13-10 12-53 12-05 11^63 10-94 10-40 9^57 5^98 Deflection in the middle, in parts of an inch. 2 3 40 T5- 6 4^ 7 4^ 9 I o 4^ t I 4Tr I z 4^ 1 3 4^ I 4 T3- I 5 Tg I 6 TET ■ii 4^ I 8 4^ 1 9 TS- 2 o Tg 2 I T5- 2 2 ^ 4g 2 4 Tg 2 5 Miiltipliers to give the breaking tvclght of every Scautliiig in each column respectively. 9-53 10-03 10-49 10-91 11-30 1201 12-64 Uniformly loaded. 7-62 8-02 8^39 8-73 9-04 9-61 10^11 Suspended from the middle. * Example.— ReA Pine 7 feet long, 3-86 in. by 1^ in., or 3-67 by If, or 3-51 by 2, or 3-37 by 2i, or 3-26 by 2^ or 3 06 by 3, or 2'91 by 3^ with 2-67 c\vts. uniformly loaded, or 1'67 cwts. suspended from tlie middle, deflects -1^ of an inch. Thebrealdiig weight of Red Pine 7 feet long 3-26 in. by 2i in. is 11-30 x 2'67 = 30-l cwts. uniformly loaded, or 9"04 x 1"67 = 15"0 cwts. suspended from the middle. 10 FIRST SERIES TABLES OF SCANTLINGS. TABLE VL— Red Pine. Weight upon each foot in length, 64lbs. or '5714 of a cwt. Deflection in the middle for each foot in length, ^ of an incli. W Weight uniformly loaded = 2560= 22-85 =1-142 W Weight suspended from the middle, — = 1600=14-28= '714 Length BREADTH IN INCHES. Weight uniiorinly loaded. clear U If 2 2i 2^ 3 H bearing. DEPTH IN INCHES. in cwts. 1 -63 -60 •57 -55 -53 •50 •48 •57 O 1-26 1 -20 1-15 1- 10 rOo 1 UU yo 1-14 3 1-89 1-80 1-72 1-65 1-69 1-50 1-43 1-71 4 2-52 2-39 2-29 2-20 2-13 2-00 1-90 2-28 5 3-15 2-99 2-86 2-75 2-66 2-50 2-38 2-85 6 3-78 3-59 3-44 3-30 3-19 o UU o.o ^ 2 oo 3-42 7 4-41 4-19 4-01 3-86 3-72 3-60 3-33 4-00 *8 6-04 4-79 4-58 4-41 4-25 4-00 3-80 4-57 9 5-67 5-39 5-15 4-96 4-78 4-50 4-28 5-14 10 6-30 5-99 5-73 5-51 5-32 5-00 4-75 5-71 11 6-93 6-59 6-30 6-06 5-85 5-50 T2ar "~6^8" 12 7-56 7-18 6-87 6-61 6-38 6-00 5-70 6-85 13 8-19 7-78 7-44 7-16 6-91 6-60 6-18 7-42 14 8-82 8-38 8-02 7-71 7-44 7-00 6-65 8-00 15 9-45 8-98 8-59 8-26 7-97 7-50 7-13 8-57 16 10-09 9-58 9-16 8-81 8-51 ~8-00 7-60 9-14 17 10-72 10-18 9-74 9-36 9-04 8^50 8-08 9-71 18 11-35 10-78 10-31 9-91 9-57 9-01 8-55 10-28 19 11-98 11-38 10-88 10-46 10-10 9-51 9^03 10-85 20 12-61 11-97 11-45 11-01 10-63 10-01 9-50 11-42 21 13-24 12.57 12^ 11-57 11-16 10-51 9-98 12-00 22 13-87 13-17 12-60 12-12 11-70 11-01 10 45 12-57 23 14-50 13-77 13-17 12-67 12-23 11-51 10-93 13-14 24 1513 14-37 13-74 13-22 12-76 12-01 11-40 13-71 25 15-76 14-97 14-32 13-77 13-29 12-51 11-88 14-28 Weight jsiispended from the middle, in cwts. -35 -71 1-07 1-42 1- 78 2ir 2- 50 2- 85 3- 21 3;57 ¥92" 4- 28 4- 64 5- 00 5- 35 "5^ 6- 07 6-42 6- 78 7- 14 "7^ 7- 85 8- 21 8-57 8-92 Deflection ill ihe middle, in parts of an inch. 40 2_ 40 3 ■4^ 4 6 8 Q Tcy I o 4-5- 1 I 1 2 4-b I 3 T63 10-01 9-60 17-85 Trie 13-39 12-72 12-17 11-70 11-30 10-63 10-10 18-97 1 1-85 14-18 13-47 12-89 12-39 1 1-96 11-26 10-69 20-08 12-55 14-97 14-22 13-60 13-08 12-63 11-88 11-29 21-20 13-25 14-97 14-32 13-77 13-29 12-51 11-88 22-32 13-95 16-03 14-46 13^ 13-13 12-47 '23-43" 15-14 14-62 13-76 13-07 24-55 15-34 15-28 14-38 13-66 25-66 16-04 15-01 14-26 26-78 16-74 15-63 14-85 27-90 1 7-43 Deflection in the middle, in parts of an inch. 40 3 4 5 4T5- 8 40 9 I o 40 Xi. 40 I 2 40 I 3 I 4 To I 5 40 I 6 Xl. 40 1 8 T5" 1 9 4 o t o _ZE- 2 I 4-5 2 T. 40 2l3 40 24 -A^ 2 5 Multipliers to give the breaking weight of every Scantling in each column respectively. 6-674 7-025 7-346 7-642 7-912 8-409 8-851 Uniformly loaded. 5-339 5-620 5-877 6-114 6-330 6-727 7-081 Suspended from the middle * Example— Rei Pine 10 feet long, 7-88 in. by 1| in., or 7-48 by If, or 7-16 by 2, or 6-88 by 2i, or 6-65 by 2^, or 6-25 by 3, or 5-94 by Bi, with 11-16 cwts. unifonnly loaded, or 6'97 cwts. suspended from the middle, deflects ^° of an inch. The breaking weight of Red Pine 10 feet long, (VSS in. by 3 in., is 8-409 x 11-16 = 93-8 cwts. uniformly loaded, or 6-727 x 0-97 = 46-9 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 13 TABLE IX.— Red Pine. Weight upon each foot in length, 166-375 lbs., or 1-4854 cwts. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded XV" lbs. cwts. tons. —=6655=59-4] =2-970 Weight suspended from the middle, — = 4159=37-13= 1-856 D Length BREADTH IN INCHES. Weight in feet, clear U 1 n 1 2 1 2i 1 2i 1 ^ 1 3i- loaded, bearing. DEPTH IN INCHES. in cwts. 1 •87 /o • '7Q lO oy DO 1-48 o 1-73 1-65 1-57 1-51 1-46 1-38 1-31 2-97 Q O 2-60 2-47 2-36 2-27 2-19 2-06 1-96 4-45 A 3-47 3-29 3-16 3-03 2-92 2-75 2-61 5-94 o 4-33 4-12 3-94 3-79 3-65 3-44 3-27 7-42 D 5-20 4-94 4-7-2 4-54 4-39 4-13 3-92 8-91 4 6-07 5-76 5-51 5-30 5-12 4-82 4-57 10-39 Q O 6-93 6-59 6-30 6-06 5-85 5-50 5-23 1 1-88 9 7-80 7-41 7-09 6-82 6-58 6-19 5-88 13-36 10 8-67 8-23 7^87 7-57 7-31 6-88 6-53 14-85 *11 9-53 9-06 8-66 8-33 8'04 7-57 7-19 16-34 12 10-40 9-88 9-45 9-09 8-77 8-25 7-84 17-82 13 11-27 10-70 10-24 9-84 9-50 8-94 8-49 19-31 14 1-2-13 11-53 11-02 10-60 10-23 9-63 9-15 20-79 15 13-00 12-35 11-81 11-36 10-96 10-32 9-80 22-28 16 13-87 13-17 12-60 12-12 11-70 11-01 10-45 23-76 17 14-73 14-00 13-39 12-87 12-43 11-69 11-11 25-25 18 14-82 14-17 13-63 13-16 12-38 11-76 26-73 19 14-96 14-39 13-89 13-07 12-41 28-22 20 15-14 14-62 13-76 ,13-07 29-70 21 15-36 14-45 13-72 31-19 22 15-13 14-37 32-68 23 15-03 34-16 Weight suspended from the middle, in cwts. -92 1- 85 2- 78 3- 71 4- 64 5- 57 6- 49 7- 42 8- 35 9- 28 10- 21 11- 14 12- 06 1300 13- 92 14- 85 15- 78 16- 71 17- 64 18- 56 middle, in parts of an inch. 2_ 3 _4 5 T5- 6 4^ 7 Ti3- 8 9 1 o 4^ I 2 I 3 I 4 4^ I 5 40 19- 49 20- 42 21- 35 I 6 T5- I 7 4-S- I 8 4T3- 1 9 2 O 40 2 I 2.2. 40 A3. 4 O Maltipliers to give the breaking weight of every Scantling in each column respectively. 6-067 6-387 6-678 6-948 7-193 7-644 8-047 4-854 5-109 5-342 5-558 5-754 6-115 6-437 Uniformly loaded. Suspended from the middle * Example.-— KgA Pine 11 feet long, 9-53 in. by 1^ in., or 9-06 by If, or 8-66 by 2 or 8-33 by 2i, or 8 04 by 2^, or 7-57 by 3, or 7-19 by 3^ with 16-34. cwts. uniformly loaded, or 10'21 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 11 feet long, 8-04 in. by 2^ in., is 7193 x 16 34 = 117-5 cwts. uniformly loa'led, or 5-754 x 10-2 1 = 58-7 cwts. suspended from the middle. c 14 FIRST SERIES — TABLES OF SCANTLINGS. TABLE X.— Red Pine. Weight upon each foot in length, 216 lbs. or 1'9285 cwts. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded TV" lbs. cwts. tons. — =8640=77-14=3-857 D W Weight suspended from the middle, — =5400=48-21 = 2-410 Xjengih in feet, clear bearing. 6 7 8 9 10 Tf *12 13 14 J 5 "16 17 18 19 20 BREADTH IN INCHES. 21 22 23 24 25 1 1 1 li i 2 1 2i 1 2i 1 3 1 3i 1 A 1 * 1 4A 1 42 1 5 DEPTH IN INCHES. -95 •90 -8d -83 •80 -75 -71 DO DO 1-89 1-80 1-72 1-65 1-59 1-50 1-43 1 ■'id 101 2*84 2-69 2-58 2-48 2-39 2-25 214 z uo 1 -07 1 y / 3-78 3-59 3-44 3-30 3-19 3-00 2 85 4/0 ^ 04 473 4-49 4-30 4-13 3-99 3-75 3-56 3-41 3-28 3-16 5-67 5-39 5-15 4-96 4-78 4-50 1^ 4 uy 0 9o •J -si A 6-62 6-29 6-01 5-78 5-58 5-25 4-99 4-77 4-oy 4 4o 7-56 7-18 6-87 6-61 6-38 6-00 5-70 5-45 5-24 0 Uo 8-51 8-08 7-73 7-43 7-18 6-75 6-42 6-14 5 90 0 TO O i/O o ov 8-26 7-97 7-50 7-13 6-82 6-55 6-33 To^ 9-88 9-45 9-09 "¥77 ~a25 7-84 7-50 7-21 6-96 11-35 10-78 10-31 9-91 9-57 901 8-55 8-18 7-87 7-60 12-29 11-68 11-17 10-74 1037 9-76 9-27 8-86 8-52 8-23 13-24 12-57 1203 11-57 11-16 10-51 9-98 9-54 9-18 8-86 14-18 13-47 12-89 12-39 11-96 11-26 10-69 10-23 9-83 9-49 15-13 14-37 13-74 13^ 12-76 12-01 11-40 10-91 10-49 10-13 15-27 14-60 14-04 13-56 12-76 12-12 11-59 11-14 10-76 15-46 14-87 14-35 13-51 12-83 12-27 11-80 11-39 15-70 1515 14-26 13-54 12-95 12-45 12-03 15-01 14-26 13-63 13-11 12-66 14-97 14-32 13-77 13-29 15-00 14-42 13-92 15-08 14-56 15-73 15-19 ... ... 15-82 Multipliers to give the breaUmi weight of every Scantline; in each column respectively. 5-562 5-854 6-121 6-369 6-593 7-0U7 7-376 7-712 8-021 8-308 4-449 4-683 4-897 5-095 5-276 5-606 5-901 6-170 6-417 6-647 XliJ^U/lf^JJVC* J.VCU. i liiC XA> ICCb XUllgjj AJ. J,iJ, VJJ J-a J-v I ^ --J -^4J ^* -J 2, . . or 9-01 by 3, . . or 7-87 by 4^ or 7-60 by 5, with 23a4 cwts. uniformly loaded, or 14-46 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 12 ft. long, 9-01 in. by 3 in., is 7-007 x 23-14= 162 1 ewts. uniformly loaded, or 5-606 x 14-46 = 81-0 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 15 TABLE X. Continued.— Red Pine. Weight upon each foot in length, 216 lbs. or 1*9285 cwts. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded \\r lbs. cwts. tons. — = 8640 =77- 14 =3-857 D W Weight suspended from the middle, — =5400=48-21=2-410 Length BREADTH IN INCHES. Weight Weight suspended from the middle, in feet, clear 7 8 1 9 1 10 1 11 1 12 uniformly loaded, Ijearing, DEPTH IN INCHES. in cwts. 1 '60 -57 -54 -62 -50 •49 4 / 1 a 4, 1 -90 1 . 1 o 1 ly 1-13 1-08 1-04 1-00 -97 0 *oO 2-41 Q o 1 .TO 1 /y 1-70 1-62 1-56 1*51 1-4d 1 -49 5-78 3-61 A 2-26 2-16 208 Z V 1 I yo 1 -RQ 1 Ot7 7-71 4-82 O 2 yo 2-83 2-71 2-60 2 4o ^ ou 6-02 6 3*57 3-39 325 3-12 3-01 2-92 I 1 •■^7 I I 0 / / zo "7 / 4 1/ 3-96 3-79 3-64 3-52 3-41 001 1 0 O^J g.43 Q O 4 /o 4-53 4-33 4-16 4-02 3-89 0/0 o y 0 cSo 5-09 4-87 4-68 4-52 4-38 1 / 00 1 U o yb 5-66 5-41 6-20 5-02 4-87 4/0 11 6-55 6-22 5-95 5-72 T53 5-36 5-20 2F2T 13-25 *12 7-15 6-79 6-49 6-24 6-03 5-84 5-67 23-14 14-46 13 7-74 7-35 7-03 6-76 6-53 6-33 6-16 26-07 15-66 14 8-34 7-92 7-58 7-28 7-03 6-81 6-62 27-00 16-87 15 8-93 8-49 8-12 7-80 7-53 7-30 7-09 28-92 18-08 16 9-53 9-05 8-32 8-04 7-79 7-66 3(^85 T9^ 17 10-13 9-62 9-20 8-84 8-54 8-27 8-04 32-78 20-49 18 10-72 10-18 9-74 9-36 9-04 8-76 8-51 34-71 21-69 19 11-32 10-75 10-28 9-88 9.64 9-25 8-98 36-64 22-90 20 11-91 11-31 10-82 10-40 10-05 9-73 9-45 38-57 24.10 21 12-51 11-88 11-36 10-92 10-55 10-22 9-93 40-50 25^ 22 1310 12-45 11-90 11-44 11-05 10-71 10-40 42-42 26-51 23 13-70 13-01 12-45 11-96 11-66 11-19 10-87 44 35 27-72 24 14-29 13-58 12-99 12-48 12-06 11-68 11-35 46-28 28-92 25 14-89 14-14 13-53 13-01 12-56 12-17 11-82 48-21 30-13 Deflection in the middle, ia parts ot au iuch. 5 6 7 8 9 4^ I o I I •4^ I z 4T5- I 3 44 1 5 1 6 I 7 I 8 I 9 4^ a o 4TT T3- a 3 24 2 5 Multipliers to give the breaking weight of every Scantling in each column respectively. 8-829 9-293 9-717 10 10 10-461 10-80 11-12 Uniformly loaded- 7-063 7-434 7-774 8-08 8-37i 8-64 8-89 Suspended from the middle. * Example.— 'Rei Pine 12 feet long, 7-15 in. hy 6 in., or 6-79 by 7, or 6-49 by 8, or 6-24 by 9, or 6-03 by 10, or 5-84 by 11, or 5-67 by 12, with 2314 cwts. uniformly loaded, or 14-46 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 1 2 ft. long, 7-15 in. by 6 in., is 8-829 x 23-14 = 204-3 cwts. uniformly loaded, or 7'063 x 14-46 = 102-1 cwts. suspended from the middle. 16 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XL— Red Pine. Weight upon each foot in length, 274'625 lbs., or 2*452 cwts. Deflection in the middle for each foot in length, ^ of an inch. Weight uniformly loaded —=10985=98.08=4.904 D Weight suspended from the middle, — = 6865=61.30=3.065 Length BREADTH IN INCHES. in feet, clear H li 2 1 2i 1 2i 1 3 3i 4 1 4* 1 5 bearing. DEPTH IN INCHES. "T" 2 3 • 4 5 1- 02 2- 05 4- 10 5- 12 •97 1-95 3- 89 4- 86 •93 1-86 3^72 4-65 •89 1-79 Z bo 3- 58 4- 47 •86 1- 73 2- 59 3- 46 4- 32 •81 1-63 244 3- 25 4- 06 •77 1- 54 2- 32 3- 09 3-86 •74 1^48 2-22 2- 95 3- 69 71 1- 42 2- 13 2- 84 3- 55 -69 1- 37 2- 06 2- 74 3- 43 6 7 8 9 10 6- 15 7- 17 8*19 9-22 10-24 5- 84 6- 81 7*78 8- 76 9- 73 5- 68 6- 51 7- 44 8'38 9-31 5- 37 6- 26 7- 16 8- 05 8-95 518 605 6- 91 7- 77 8- 64 4- 88 5- 69 6- 50 7- 32 8- 13 4- 63 5- 41 6- 18 6- 95 7- 72 4- 43 5- 17 5- 91 6- 65 7- 39 4-26 4- 97 5- 68 6- 39 710 4-11 4- 80 5- 49 6- 17 6-86 11 12 *13 14 15 11- 27 12- 29 13- 32 14- 34 10- 70 11- 68 12- 65 13- 62 14- 59 10- 24 11- 17 12- 10 13- 03 13-96 9-84 1074 11- 63 12- 53 13- 42 9-50 10- 37 11- 23 12- 09 12-96 8- 94 9- 76 10- 57 11- 38 1219 8- 49 9- 27 10-04 10- 81 11- 58 8-12 8- 86 9- 60 10- 34 11- 08 7- 81 8- 52 9- 23 9-94 10-65 7- 54 8- 23 8- 91 9- 60 10-29 16 17 18 19 20 14-89 14- 32 15- 21 13- 82 14- 69 15- 55 13-01 13- 82 14- 63 15- 45 12- 36 13- 13 1390 14- 67 15- 44 11- 82 12- 56 13- 29 14- 03 14-77 11- 36 12- 07 12- 78 13- 49 14- 20 10- 97 11- 66 12.34 13-03 13-71 21 22 23 24 25 15-51 14- 91 15- 62 14- 40 15- 08 15-77 Multipliers to give the breaking iveight of every Scantling in each column respectively. 5-134 4-107 5-404 4-323 5-651 4-520 5-879 4-703 6-086 4-869 6-468 5 174 6-809 5-447 7-119 5-695 7-404 5-923 7-669 6-135 * Example.— Ktd, Piue 13 feet long, 13-32 in. by li iu., or 12-65 by If, or 12-10 by 2, . . or 10-57 by 3, . . or 9-23 by 4|, or 8-91 by 5, with 31-87 cwts. uniformly loaded, or 19-92 cwts. suspended from the middle, deflects JL3 of an inch. The breaking weight of Red Pine 13 feet long, 10-04 in. by 3i in., is 6-809 x 31-87 = 217-0 cwts. uniformly loaded, or 5-447 x 19-92 = 108-5 cwts, suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 17 TABLE XI. Continued. — Red Pine. Weight upon each foot in length, 214:'Q2b lbs., or 2*452 cwts. Deflection in the middle for each foot in length, ^ of an inch. XTTT . 1 . ./. , , W" cw'*- tons. Weight uniformly loaded — = 10985=98-08=4-904 Weight suspended from the middle, ^= 6865 =61-30= 3-065 Length BREADTH IN INCHES. Weight uniformly loaded, Weight suspended from the middle, in cwts. Deflection in feet, clear bearing. 6 7 1 8 9 1 10 ! 11 12 iu the middle, in DEPTH IN INCHES. in cwts. parts of an inch. 1 2 3 4 5 -65 1-29 1- 94 2- 58 3- 23 -61 1-23 1- 84 2- 45 3- 06 •59 1-17 1- 76 2- 34 2-93 -56 1-13 1- 69 2- 25 2-82 •54 1-09 2^18 2^72 -53 1-05 1- 58 2- 11 2-64 •51 1-02 1^54 2^05 2^56 2-45 4-90 7-35 9-80 1226 1-53 3^06 4^59 6- 13 7- 66 I 2 5 4^ 6 7 8 9 10 3- 87 4- 52 5- 16 5- 81 6- 45 3- 68 4- 29 4- 90 5- 52 6- 13 3- 52 4- 10 4- 69 5- 28 5-86 "3^ 3- 95 4- 51 5- 07 5-64 3-27 3- 81 4- 35 4- 90 5- 44 ~3^ 3-69 422 4^75 5^27 3^07 3^58 4^10 4^61 5^12 14-71 17-16 19-61 22-06 24-52 ~9-19 10-72 12- 26 13- 79 15-32 '6 7 4^ 3 Ti3- 9 4^ I o 40 11 12 *13 14 15 7-10 7- 74 8- 39 9- 03 9-68 6- 74 7- 35 7- 97 8- 58 9- 19 6- 45 7- 03 7- 62 8- 21 8-79 6-20 6- 76 7- 33 7- 89 8- 45 5- 99 6- 53 7- 07 7-62 8^16 5^80 6^33 6- 86 7- 38 7-91 5^63 6- 15 6^66 7- 17 7^68 29-42 31-87 34-32 36-78 1 fi'S"; 1 o oo 18- 39 19- 92 21- 45 22- 98 I I 4^ 1 2 I 5 16 17 18 19 20 10^2 10- 97 11- 61 12- 26 12-90 9-81 10- 42 11- 03 11- 64 12- 26 9-38 9-97 10- 55 11- 14 11-72 '9-02 9-58 10-14 10- 71 11- 27 8- 71 9- 25 9-80 10-34 10-88 8-44 8- 96 9- 49 10-02 10-55 8^19 8- 71 9^22 9- 73 10-24 39-23 41-68 44-13 46-58 49-04 26- 05 27- 58 29- 11 30- 65 I 6 Ts- I 7 T5 I 8 4^ 1 9 srs 2 0 Tg 21 22 23 24 25 13^55 14-20 14- 84 15- 49 16- 13 12- 87 13- 48 14- 10 14- 71 15- 32 12-31 12- 90 13- 48 14- 07 14-66 11- 84 12- 40 12- 96 13- 53 14- 09 11-43 11- 97 12- 52 13- 06 13-60 11-07 11- 60 12- 13 12- 65 13- 18 10- 75 11- 27 11- 78 12- 29 12-80 51-49 53^94 56^39 58-84 61^30 3248 33-71 35^24 36^78 38^31 2 I To 2 2 4^ 2 3 4^ 2 4 2 5 Multipliers to give the breaking weight of every Scantliug in each column respectively. 8-150 6-520 8-578 6-862 8-970 7-176 9-328 7-462 9-662 7-729 9-975 7-980 10-26 8-31 Uniformly loaded. Suspended from the middle * Example.— nei Pine 13 feet long, 8-39 in. by 6 in., or 7-97 by 7, or 7-62 by 8, or 7-33 by 9, or 7-07 by 10, or 6-85 by 11, or 6-66 by 13, with 31-87 cwts. uniformly loaded, or 19-92 cwts. suspended from the middle, deflects ±^ of an inch. The breaking weight of Red Pine 13 feet long, 7-97 in. by 7 in., is 8-578 x 31-87 = 273-3 cwts. uniformly loaded, or 6-862 x 19 93 = 136 6 cwts. suspended from the middle. 18 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XII.— Red Pine. Weight upon each foot in length, 343 lbs. or 3*0625 cwts. Deflection in the middle for each foot in length, ^ of an inch. V\r lbs. cwts. tons. Weight uniformly loaded, —= 13720= 122-50=:6-l25 Weight suspended from the middle, — = 8575= 76-56=3-828 in feet, clear BREADTH IN INCHES. H 1 t H 1 2i 1 3 1 3i 1 A A 1 1 42 1 5 bearing. DEPTH IN INCHES. r 2 3 MO 2- 21 3- 31 1- 05 2- 10 3- 14 1- 00 2- 00 3- 01 -96 1- 93 2- 89 •93 1- 86 2- 79 •88 1- 75 2- 63 -83 1- 66 2- 49 "oO 1- 59 2- 39 /D 1 • AO 2 2y .74 1- 48 2- 22 4 4-41 4-19 4-01 3-86 0 72 0 OK) 0 go 3-I8 3-O6 2-95 5 0 yj I 4-82 4-d5 4 00 4 ID 3-98 3-82 3-69 6 7 8 6*62 7'72 8*82 6- 29 7- 33 o.oo o-oo 6- 01 7- 02 8- 02 5- 78 6- 75 7- 71 "5-58 6-51 7.44 5- 25 6- 13 7- 00 4- 99 5- 82 6- 65 111 001 0 OD 4 Oa tJ 00 fi 19 T43 517 5-91 9 10 9*93 1 1 .HQ 9-43 lU 4(3 9-02 1 A.no lU U,6 8- 67 9- 64 8- 37 9- 30 7- 88 8- 75 7- 48 8- 32 / ID 7-95 u 00 7-65 6- 65 7- 38 I \ 12 13 11-53 rH)2 10-60 10-23 9-63 ^5 "¥75 ~8^ 12 13-24 12-57 12-03 11-57 11-16 10-51 9-98 9-54 9-18 8-86 13 14-34 13-62 13-03 12-53 12-09 11-38 10-81 10-34 9-94 9-60 *14 14-67 14-03 13-49 13-02 12-26 11-64 11-13 10-71 10-34 15 15-03 14-46 13-95 13-13 12-47 11-93 11-47 11-08 16 14-88 14-01 13-31 12^73 "12^ 11-81 17 14-88 14-14 13-52 13-00 12-55 18 14-97 14-32 13-77 13-29 19 15-11 14-53 14-03 20 15-30 14-77 21 15^1 22 23 24 25 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-767 5-018 5-247 6-459 5-651 6-006 6-322 6-610 6-875 7-121 3-814 4-014 4-197 4-367 4-521 4-804 5-058 5-288 5-500 5-697 * Example.— Uti Pine 14 feet long, . 14-67 in. by If in., or 14-03 by 2, . . or 1 2-26 by 3, . . or 10-71 by 4^, or 10-34 by 5, with 42-87 cwts. uniformly loaded, or 26-79 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 14 feet long, 11-13 in. by 4 in. is 6-61 x 42-87 = 283-3 cwts. uniformly loaded, or 5-288 x 36-79 = 141.6 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 19 TABLE XII. Co7itinued.— Red Pine. Weight upon each foot iu length, 343 lbs. or 3*0626 cwts. Deflection in the middle for each foot in length, of iiich. AI/" lbs. cwts. tons. Weight uniformly loaded = 13720= 122-50=6-125 W Weight suspended from the middle, —= 8575= 76-56=3-828 Length iu feet, clear BREADTH IN INCHES. Weight Weight suspended from the middle, 6 7 8 10 11 12 uniformly loaded, bearing. DEPTH IN INCHES. in cwts. 1 1 •69 •66 -63 -61 •59 -67 •55 0 \J\J 1 'Ql 1 y 1 2 1-39 1-32 1-26 1-21 M7 1-14 1-10 6-12 3-82 3 li yjo 1 -QS 1 yo 1 oy 1 -89 1 o.^ 1 •7fi 1 1 V 9-18 5.74 4 9-78 4> oo 2-34 2-27 2-21 12-25 7^65 5 O i u 2*93 2*84 2-76 15.31 9-57 « u 4-17 3-96 3-79 3-64 3-52 3-41 3-31 18-37 1 1 .AQ. 1 1 TbO 7 4-86 4-62 4-42 4-25 4-10 3-97 3-86 21*43 13.39 fi o 5-56 5-28 5-05 4-86 4^69 4-54 4-41 24-60 15-31 9 6-25 5-94 5-68 5-46 5-27 5-11 4-96 27-56 17-22 10 6-95 6-60 6-31 6-07 5-86 5-68 5-52 30'62 19-14 1 1 "7^4 T-26 6-94 6-68 6-45 6-25 6-07 33^68 2 1-05 12 8-34 7-92 7-58 7-28 7-03 6-81 6-62 36^75 22-96 13 9-03 8-58 8-21 7-89 7-62 7-38 7-17 39-81 24-88 *14 9-73 9-24 8-84 8-50 8-20 7-95 7-72 42-87 26-79 15 10-42 9-90 9-47 9-10 8-79 8-52 8-27 46^93 28-71 16 1112 10-56 10-10 9-71 9-38 9-08 8-82 49^00 30^ 17 11-81 1 1-22 10-73 10-32 9-96 9-65 9^38 52-06 32-53 18 12-51 11-88 11-36 10-92 10-55 10-22 9^93 55-12 34^45 19 13-20 12-54 12-00 11-53 11-13 10-79 10^48 58-18 36-36 20 13-90 13-20 12-63 12-14 11-72 11-36 11^03 61-25 38-28 21 14-69 13^ 12^26 12-75 12-31 11-92 11^58 64-31 To'49" 22 15-29 14-52 13-89 13-35 12-89 12-49 12-13 67-37 42-10 23 15-98 15- is 14-52 13-96 13-48 13-06 12-68 70-43 44-02 24 15-84 15-15 14-57 14-07 13-63 13-24 73-50 45-93 25 15-78 15-17 14-65 14-20 13-79 76-56 47-85 Deflection in the middle, in parts of an inch. T5- 4 5 6 7 8 Tsr 9 T3- I o 4^ I I I 2 4^ I 3 I 4 1 5 _±?_ I 6 4^ I 7 4^ I 8 TS- 1 9 z o •4^ 4 4T 11 12 13 14 *15 8- 93 9- 74 10- 55 11- 36 12- 18 8- 58 9- 36 10-15 10- 93 11- 71 8- 29 9- 04 9-80 10- 55 11- 30 8-03 8- 76 9- 49 10-22 10-95 7- 80 8- 51 9- 22 9-93 10-64 7- 59 8- 28 8- 98 9- 67 10-36 ~7^l 8-08 8- 76 9- 43 10-10 "63^64 69-42 75-21 81-00 86-78 39^77 43-39 47-00 50-62 54-24 I I TT I 2 4T I 3 4T I 4 4T I 5 4 5 16 17 18 19 20 12- 99 13- 80 14- 61 15- 42 16- 23 12- 49 13- 27 14- 05 14- 83 15- 61 12-06 12- 81 13- 56 14- 32 15- 07 TF68 12- 41 13- 14 13- 87 14- 60 rr35 12 05 12- 76 13- 47 14- 18 11-05 11- 74 12- 43 13- 12 13-81 10- 78 11- 45 12- 12 12- 80 13- 47 92-57 98-35 104-14 109-92 115-71 57-85 61-47 65-08 68-70 72-32 I 6 TT I 7 TT 1 8 TT I 9 TT 20 TT 21 22 23 16-39 15- 82 16- 58 15- 33 16- 06 16-79 T?89 15- 60 16- 31 14- 50 15- 19 15-88 14-15 14- 82 15- 49 121-50 127-28 133-07 75 93 79-55 83-16 2 I TT 2 2 TT 23 TT Multipliers to give the breaking weight of every Scantling in each column respectively. 7-288 7-579 7-850 8-105 8-343 8-568 8-783 5-830 6-063 6-280 6-484 6-674 6-854 7-026 Uniformly loaded. Suspended from the middle. * Example.— Uei Pine 15 feet long, 12-18 in. by 8 in., or 11-71 by 9, or ll'SO by 10, or 10-95 by 11, or 10-64 by 12, or 10-36 by 13, or lO'lO by 14, with 86-78 cwts. uniformly loaded, or 54' 24 cwts. suspended from the middle, deflects ±^ of an inch. The breaking weight of Red Pine 15 ft. long, 10-95 in. by 11 in., is 8-105 x 86-78 = 703 3 cwts. uniformly loaded, or 6"484 x 54-24 = 351-6 cwts. suspended from the middle. 26 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XVI.— Red Pine. Weight upon each foot in length, 800 lbs. or 7'1428 cwts. Deflection in the middle for each foot in length, 3^ of an inch. ly lbs. cwts. tons Weight uniformly loaded — = 40000 = 357-14 = 17-857 Weight suspended from the middle, ^ = 25000 = 223-21 = 11-160 Length in feet, clear bearing. BREADTH IN INCHES. 2i 3i I 4 I U DEPTH IN INCHES. 1 1-43 1-33 1-25 M9 1-14 1-09 1-05 •99 -94 .90 2 2-86 2-66 2-50 2-38 2-27 2-19 2-11 1-99 1-89 1-80 3 4-30 3-99 3-75 3-56 3-41 3-28 3-16 2-98 2-83 2-71 4 5-73 5-32 5-00 4-75 4-55 4-37 4-22 3-97 3-77 3-61 5 7-16 6-65 6-25 5-94 5-68 5-46 5-27 4-96 4-71 4-51 6 8-59 7-97 ~~Td6 ~7T3 '6^6 6 33 5-96 5-66 "5^1 7 10-02 9-30 8-75 8-32 795 7-65 7-38 6-95 6-60 6-31 8 11-45 10-63 10-01 9-50 9-09 8-74 8-44 7-94 7-54 7-22 9 12-89 11-96 11-26 10-69 10-23 9-83 9-49 8-93 8-49 8-12 10 14-32 13-29 12-51 11-88 11-36 10-93 10-55 9-93 9-43 9-02 11 14-62 13-76 1307 12^0 1202 iTeo 10-92 10^7 ~9^2 12 15-01 14-26 13-64 1311 12-66 11-91 11-31 10-82 13 15-45 14-77 14-20 13-71 12-90 12-26 11-72 *14 15-91 15-30 14-77 13-90 13-20 12-63 15 15-82 14-89 14-14 13-53 16 15^8 15^9 14-43 17 16-03 15-33 18 16-23 19 20 21 22 Multipliers to give the breaking weight of every ScautKng in each column respectively. 4-591 4-945 5-255 5532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— KtSi Pine 14 feet long, 15-91 in. by 4 in., or 15-30 by 4i or 14-77 by 5, or 13-90 by 6, or 13-20 by 7, or 12-63 by 8, with 100 cwts. uniformly loaded, or 62*50 cwts. suspended from the middle, deflects ^ of an inch. The breaking weight of Red Pine 14 feet long, 13-20 in. by 7 in., is 6-97 x 100 = 697 cwts. uniformly loaded, or 5-576 x 62-5 = 348'5 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 27 TABLE XVI. Continued.— Red Pine. Weight upon each foot in length, 800 lbs. or 7' 1428 cwts. Deflection in the middle for each foot in length, of an inch. ■ry lbs. cwts. tons. Weight uniformly loaded = 40000 = 367-14 = 17-857 w Weight suspended from the middle, ^ = 25000 = 223-21 = 11-160 JLength in feet, clear beariDg. 1 2 3 4 5 "T 7 8 9 10 11 12 13 *14 15 16 17 18 19 20 IT 22 BREADTH IN INCHES. 9 I 10 I 11 i 12 I 13 I 14 I 15 DEPTH IN INCHES. •87 1- 73 2- 60 3- 47 4- 34 5- 20 6- 07 6- 94 7- 80 8- 67 9-54 10- 41 11- 27 12- 14 13- 01 13- 87 14- 74 15- 61 16- 48 •84 1- 67 2- 51 3- 35 4- 19 5-02 5- 86 6- 70 7- 54 8- 37 9-21 10-05 10-88 ir72 12-56 13- 40 14- 23 15- 07 15- 91 16- 74 •81 1- 62 2- 43 3- 24 4- 06 4- 87 5- 68 6- 49 7- 30 8- 11 8- 92 9- 73 10- 54 11- 36 12- 17 12- 98 13- 79 14- 60 15- 41 16- 22 •79 1- 58 2- 36 316 3- 94 4- 73 5- 52 6- 30 7- 09 7-88 8- 67 9- 45 10- 24 11- 03 11-82 12- 61 13- 39 14- 18 14- 97 15- 76 16-56 •77 1- 53 2- 30 3- 07 3-84 4-60 5^37 6-14 6- 90 7- 67 8- 44 9- 21 9-97 10- 74 11- 51 12^ 13-04 13- 81 14- 68 15- 34 leTi 16- 88 •75 1- 50 2- 25 2- 99 3- 74 4- 49 5- 24 5- 99 6- 74 7- 48 'F23 8- 98 9- 73 10- 48 11- 23 11^98 12- 72 13- 47 14- 22 14-97 15- 72 16- 47 ■73 1- 46 2- 19 2- 93 3- 66 4- 39 5- 12 5- 85 6- 58 7- 31 8-05 8-78 951 10-24 10-97 11- 70 12- 43 13- 17 13- 90 14- 63 15- 36 16- 09 Weight uniformly loaded, III cwts. 7-14 14-28 21-42 28-67 35-71 Weight suspended from the middle, in cwts. 42-85 50-00 67-14 64-28 71-42 78-67 85-71 92-85 100-00 107-14 114-28 121-42 128-57 135-71 142-85 16000 157-14 4-46 8-92 13-39 17-85 22-32 26-78 31-25 35-71 40-17 44-64 49-10 63-57 68-03 62-60 66-96 Deflection iu the middle, ia parts of an inch. 2 4 5 T5 71-42 75-89 80-35 84-82 89-28 93-75 98-21 8 I o I I I z I 5 I 6 1 8 19 2 o 2 I 2 2 7ty Multipliers to give the breaking weight of every Scantliug in each column respectively. 7-579 7^850 8-105 8-343 8-568 8-783 8-988 Unifonnly loaded. 6-063 6^280 6-484 6-674 6-854 7-026 7-190 Suspended from the middle. * Example.— Hei Pine 14 feet long, 12-14 in. by 9 in., or 11-72 by 10, or 11-36 by 11, or 11-03 by 12, or 10-74 by 13, or 10-48 by 14, or 10-24 by 15, with 100 cwts. uniformly loaded, or 62-50 cwts. suspended from the middle, deflects ^ of an inch. The breaking weight of Red Pine 17 ft. long, 13-04 in. by 13 in., is 8-568 x 121-42 = 1040 3 cwts. uniformly loaded, or 6-854 x 75-89 = 520-1 cwts. suspended from the middle. 28 FIRST SERIES — TABLES OF SCANTLINGS, TABLE XVII.— Red Pine. Weight upon each foot in length, 968 lbs. or 8*6428 cwts. Deflection m the middle for each foot in length, of an inch. Weight uniformly loaded — =53240=475'35=23-767 Weight suspended from the middle,— =33275=297-09= 14*854 Length BREADTH IN INCHES. in feet, clear bearing. 2 2 1 3 1 3^ 1 4 i 4* 5 6 1 7 1 8 DEPTH IN INCHES. 1 1-57 1-46 1-38 1-31 i-25 1-20 1-16 1-09 1-04 -99 2 3-15 2-92 2-75 2-61 2-50 2-40 2-32 2-18 2-07 1-98 3 4-72 4-39 4-13 3-92 3-75 3-61 3-48 3-28 311 2-98 4 6-30 5-85 5-50 5-23 5-00 4-81 4-64 4-37 415 3-97 5 7-87 7-31 6-88 6-53 6-25 6-01 5-80 5-46 5-19 4-96 6 "9^45 8-77 8-25 7-84 7-50 7-21 6-96 6-55 ~6^22 5-95 7 11-02 10-23 9-63 9-15 8-75 8-41 8-12 7-64 7-26 6-94 8 12-60 11-70 11-01 10-46 10-00 9-61 9-28 8-74 8-30 7-94 9 1417 13-16 12-38 11-76 11-25 10-82 10-44 9-83 9-33 8-93 10 14-62 13-76 13-07 12-50 12-02 11-60 10-92 10-37 9-92 11 1513 T?38 13^75 12-76 12-01 11-41 10-91 12 15-68 15-00 14-42 13-92 13-10 12-45 11-90 *13 15-62 15-08 14-20 13-48 12-90 14 15-29 14-52 13-89 15 15-56 14-88 16 17 18 19 20 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— K^d. Pine 13 feet long, 15-62 in. by 4^ in., or 15-08 by 5, or 14-20 by 6, or 13-48 by 7, or 12-90 by 8, with 112-35 cwts. uniformly loaded, or 70-22 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 13 feet long, 12-90 in. by 8 in., is 7-288 x 112-35 = 818-8 cwts. uniformly loaded, or 5-83 x 70-22 = 409-4 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 29 TABLE XVII. Continued.— Red Pine. Weight upon each foot in length, 968 lbs. or 8*6428 cwts. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded VJ' lbs. cwts. tons. —=53240 = 475-35 = 23767 D w Weight suspended from the middle,^ =33275 = 297-09= 14-854 Length BREADTH IN INCHES. Weight uniformly loaded, Weight suspended from the middle^ Deflection in the middle, iu parts of an inch. in feet, clear 9 10 11 12 13 14 15 beariug- DEPTH IN INCHES. in cwts. in cwts. 1 2 3 4 5 •95 1- 91 2- 86 3- 82 4- 77 -92 1- 84 2- 76 3- 68 4- 60 •89 1- 78 2- 68 3- 57 4- 46 •87 1- 73 2- 60 3- 47 4- 33 •84 1- 69 2- 53 3- 38 4- 22 -82 1- 65 2- 47 3- 29 4- 12 -80 1- 61 2- 41 3- 22 4- 02 8-64 17-28 25-92 34-57 43-21 5-40 10-80 16-20 21-60 27-00 I 7T % TT 3 TT 4 TT 5 TT 6 7 8 9 10 5- 72 6- 68 7- 63 8- 58 9- 54 5- 53 6- 45 7- 37 8- 29 9- 21 5- 35 6- 25 7- 14 8- 03 8-92 5- 20 6- 07 6- 93 7- 80 8- 67 T06 5- 91 6- 75 7- 59 8- 44 4- 94 5- 76 6- 59 7- 41 8- 23 4^83 5- 63 6- 44 7- 24 8- 05 51-85 60-50 69-14 77-78 86-42 ~32^4T 37-81 43-21 48-61 54-01 6 TT 7 TT 8 TT 9 TT I o TT 11 12 *13 14 15 10- 49 11- 45 12- 40 13- 35 14- 31 10- 13 11- 05 11- 97 12- 89 13- 81 9-81 10- 71 11- 60 12- 49 13- 38 9-53 10- 40 11- 27 12- 13 13- 00 '¥28 10-13 10- 97 11- 81 12- 66 9-06 9-88 10- 70 11- 53 12- 35 ~8^ 9-65 10- 46 11- 26 12- 07 95-07 103-71 112-35 121-00 129-64 59-41 64-82 70-22 75-62 81-02 1 r 5 S I 2 TT I 3 TT I 4 TT I 5 TT 16 17 18 19 20 15- 26 16- 22 14- 74 15- 66 16- 58 1^28 15- 17 16- 06 13- 87 14- 73 15- 60 16- 47 13- 50 14- 35 15^19 16-03 16-88 13- 17 14- 00 14- 82 15- 64 16- 47 12^ 13- 68 14- 48 15- 29 16- 09 138^28 146-92 155-57 164-21 172-85 "86^42 91-83 97-23 102-63 108-03 I 6 TT I 7 TT I 8 TT I 9 TT 20 TT Multipliers to give the breaking weight of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 Uniformly loaded. 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Suspended from the middle. * Example— Pine 13 feet long, 13-40 in. by 9 in., or 11.97 by 10, or 11-60 by 11, or 11-27 by 12, or 10 97 by 13, or 10-70 by 14, or 10 46 by 15, with 112 35 cwts. uniformly loaded, or 70'22 cwts. suspended from the middle, deflects -L^ of an inch. The breaking weight of Red Pine 17 feet long, 14 in. by 14 in., is 8-783 x 146-92 = 1290-4 cwts, uniformly loaded, or 7'026 x 91-83 = 645-2 cwts. suspended from the middle. E 30 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XVIII.— Red Pine. Weight upon each foot in length, 1152 lbs. or 10*2857 cwts. Deflection in the middle for each foot in length, ^ of an inch. 'VU' lbs. cwts. tons. Weight uniformly loaded, — =69120=617-14=30-857 Weight suspended from the middle, —=43200=:385-71 = 19-285 Length BREADTH IN INCHES. in feet, clear 2* 3 3i 4 4i 6 7 bearing. DEPTH IN INCHES. 1 1 2 3 4 5 1-72 3-44 5- 15 6- 87 8-59 1-59 3- 19 4- 78 6- 38 7- 97 1-50 3- 00 4- 50 6- 00 7- 50 1- 43 2- 85 4- 28 5- 70 7-13 1- 36 2- 73 4- 09 5- 45 6- 82 1- 31 2- 62 3- 93 5- 24 6- 56 1- 27 2- 53 3- 80 5- 06 6- 33 1- 19 2- 38 3- 57 4- 76 5- 96 113 2- 26 3- 39 4- 53 5- 66 1- 08 2- 16 3- 25 4- 33 5- 41 6 7 8 9 10 10-31 12- 03 13- 74 15-46 9-57 11- 16 12- 76 14-35 9-00 10-51 12- 01 13- 51 15-01 8- 55 9- 98 11- 41 12- 83 14-26 8- 18 9- 55 10-91 12- 27 13- 64 7-87 9-18 10- 49 11- 80 1311 7- 60 8- 86 10- 13 11- 39 12- 66 7- 15 8- 34 9- 53 10- 72 11- 91 "6^79 7-92 9-05 10- 18 11- 32 ~¥49 7- 58 8- 66 9- 74 10-82 11 *12 13 14 15 15-68 15-00 14- 42 15- 73 13-92 15-19 1310 14- 29 15- 49 12^ 13- 58 14- 71 15- 84 1^90 12-99 14- 07 15- 15 16- 23 Te" 17 18 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— -Rei Pine 12 ft. long, 1573 in. by 4^ in., or 1519 by 5, or 14-29 by 6, or 13-58 by 7, or 12-99 by 8, with 123-42 cwts. uniformly loaded, or 77'14 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 12 ft. long, 13-58 in. by 7 in. is 6-97 x 123-42 = 860-2 cwts. uniformly loaded, or 5-576 x 77'14 = 430.1 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 31 TABLE XVIII. Cotitinued.—RED Pine. Weight upon each foot in length, 1152 lbs. or 10*2857 cwts. Deflection in the middle for each foot in length, -g?^ of an inch. ■\X^ Ibj. cwts. tons. Weight uniformly loaded ^=69120=617-14=30-857 w Weight suspended from the middle, ^=43200=385-71 = 19-285 Length in feet, clear BREADTH IN INCHES. Weight uniformly loaded, Weight suspended from the middle, in cwts. 10 11 12 13 14 15 bearing. DEPTH IN INCHES. in cwts. I 1-04 1-00 •97 -95 -92 •90 •88 10-28 6-42 2 2-08 2-01 1-95 1-89 1-84 1-80 1-76 20-57 12-85 3 3-12 3-01 2-92 2-84 2-76 2-69 2-63 30-85 19-28 4 4-16 4-02 3-89 3-78 3-68 3-59 3-51 41-14 25-71 5 5-20 5-02 4-87 4-73 4-60 4-49 4-39 51-42 32-14 6 6-24 6-03 5-84 5-67 5-52 "d^ 5-27 61-71 "38^ 7 7-28 7-03 6-81 6-62 6-44 6-29 6-14 72-00 45-00 8 8-32 8-04 7-79 7-56 7-36 7-18 7-02 82-28 51-42 9 9-37 9-04 8-76 8-51 8-28 8-08 7-90 92-57 57-85 10 10-41 10-05 9-73 9-45 9-21 8-98 8-78 102-85 64-28 11 11-45 11-05 FoTT 10-40 10-13 9-88 9-65 113-14 70-71 *12 12-49 12-06 11-68 11-35 11-05 10-78 10-53 123-42 77-14 13 13-53 13-06 12-65 12-29 11-97 11-68 11-41 133-71 83-57 14 14-57 14-07 13-63 13-24 12-89 12-57 12-29 144-00 90-00 15 15-61 15-07 14-60 14-18 13-81 13-47 13-17 154-28 96-42 16 16-65 16-08 15-57 15-13 14-73 14-37 14-04 164-57 102^ 17 16-55 16-07 15-65 15-27 14-92 174-85 109-28 18 16-57 16-17 15-80 185-14 115-71 Deflection in the middle, in parts of an inch. 3 5 6 7^ 7 8 9 I o I I I a 1 3 "5T3- I 4 1 5 •5~g I 6 "5T3- I 7 s^y I 8 Multipliers to give the hreaUng weight of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 Uniformly loaded. 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Suspended from the middle. * Example.— Kti Pine 12 feet long, 12-49 in. by 9 in., or 12-06 by 10, or 11-68 by 11, or 11-35 by 12, or 11-05 by 13, or 10 78 by 14, or 10-53 by 15, wth 123;42 cwts. uniformly loaded, or 77-14 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 12 feet long, 12-06 in. by 10 in., is 7-85 x 123-42 = 968-8 cwts. uniformly loaded, or 6-38 x 77-14=484-4 cwts. suspended from the middle. 32 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XIX.— Red Pine. Weight upon each foot in length, 1362 lbs. or 12*0714 cwts. Deflection in the middle for each foot in length, of an inch. YY IDS. cwis. tons. Weight uniformly loaded — = 87880 = 784-64 = 39-232 Weight suspended from the middle, — = 54925 = 490-40 = 24-520 length BREADTH IN INCHES. in feet, clear 2 1 2i 3 3i 1 4 1 4i 1 5 6 7 8 beariug. DEPTH IN INCHES. 1" 1-86 1-73 1-63 1-54 1-48 1-42 1-37 1-29 1-23 1 17 2 3-72 3-46 3-25 3-09 2-95 2-84 2-74 2-58 2-45 2-34 3 5-58 5-18 4-88 4-63 4-43 4-26 411 387 3-68 3-52 4 7-44 6-91 6-50 6-18 5-91 5-68 5-49 5-16 4-90 4-69 5 9-31 8-64 8-13 7-72 7-39 7-10 6-86 6-45 6-13 5-86 6 11-17 10-37 9-76 9-27 8-86 8-52 8-23 T74 7-35 "7^ 7 1303 12-09 11-38 10-81 10-34 9-94 9-60 9-03 8-58 8-21 8 14-89 13-82 13-01 12-36 11-82 11-36 10-97 10-32 9-81 9-38 9 14-63 13-90 13-29 12-78 12-34 11-61 1 1-03 10-55 10 15-45 14-77 14-20 13-71 12-90 12-26 11-72 *Tr 16-25 15-62 15^ 14-20 3-48 l¥90 12 16-46 15-49 14-71 14-07 13 15-94 15-24 14 16-41 15 16 17 Multipliers to give the breaking weight of every Scantling in each column respectively. 4'591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example. — Red Pine 11 feet long, .... 16-25 in. by 4 in., or 15-63 by 4^, or 15-08 by 5, or 14-20 by 6, or 13-48 by 7, or 12 90 by 8, wth 13278 cwts. uniformly loaded, or 82-99 cwts. suspended from the middle, deflects i-i of an inch. The breaking weight of Eed Pine 11 ft. long, 14-20 in. by 6 in., is 6-621 x 132-78 = 879'1 cwts. uniformly loaded, or 5'297 x 82-99=439-5 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 33 TABLE XIX. Continued.— Red Pine. Weight upon each foot in length, 1352 lbs. or ]2"0714 cwts. Deflection in the middle for each foot in length, ^ of an inch. cwts. tons. Weight uniformly loaded — = 87880 = 784-64 = 39-232 Weight suspended from the middle, ^ = 54925 = 490-40 = 24-520 Length BREADTH IN INCHES, Weight Weight in feet, clear 9 1 10 1 11 1 12 i 13 1 14 15 uniformly loaded, suspended from the bearing. DEPTH IN INCHES. in cwts. middle, in cwts. 1 M3 1-09 1-05 1-02 1-00 •97 •95 1207 7-54 2 2-25 2-18 2-11 2-05 1-99 1-95 1-90 24-14 15-08 3 3-38 3-27 3-16 3-07 2-99 2-92 2-85 36-21 22-63 4 4-51 4-35 4-22 4-10 3-99 3-89 3-80 48-28 30-17 5 5-64 5-44 5-27 5-12 4-99 4-86 4-75 60-35 37-72 6 "¥76 6-53 6-33 ^8 5-84 5-71 ~72^42 7 7-89 7-62 7-38 7-17 6-98 6-81 6-66 84-50 52-81 8 9-02 8-71 8-44 8-19 7-98 7-78 7-61 96-57 60-35 9 10-15 9-80 9-49 9-22 8-98 8-76 8-56 108-64 67-90 10 11-27 10-88 10-54 10-24 9-97 9-73 9-51 120-71 75-44 *11 12-40 11-97 11-60 11-27 10-97 10-70 HMe" l32^ "82^99 12 13-53 13-06 12-65 12-29 11-97 11-68 11-41 144-85 90-53 13 14-66 14-15 13-71 13-32 12-96 12-65 12-36 156-92 98-08 14 15-78 15-24 14-76 14-34 13-96 13-62 13-31 169-00 105-62 15 16-91 16-33 15-82 15-36 14-96 14-59 14-26 181-07 113-16 16 16-87 16-39 15-96 15^7 15-21 193^14 120^ 17 16-95 16-54 16-16 205-21 12825 Deflection in the middle, in parts of an inch. "5T 2 ■5T 3 "TT 4 Ts 5 •gT 6 TT 7 sr 8 sr 9 "6T I o ■5T I I 1 z -sr I 3 "5T I 4 "5T I 5 "5T I 6 I 7 Multipliers t 3 give t le break ing wei ght of e eery Sea ntliii gin ■ ~" -5T each eolumn respectively. 7-579 6-063 7-850 6-280 8-105 6-484 8-343 6-674 8-568 6-854 8-783 7-026 8-988 7-190 Uniformly loaded. Suspended from the middle. * Example.— R^di Pine 11 feet long, 12-40 in. by 9 in., or 11-97 by 10, orir60 by 11, or 11-27 by 13, or 10-97 by 13, or 10-70 by 14, or 10-46 by 15, with 132-78 cwts. uniformly loaded, or 82-99 cwts. suspended from the middle, deflects ^ of an inch. The breaking weight of Red Pine 12 feet long, 13-06 in. by 10 in., is 7-85 x 144-85 = 1137 cwts. uniformly loaded, or 6-28 x 90-53 = 568-5 cwts. suspended from the middle. 34 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XX.— Red Pine. Weight upon each foot in length, 1568 lbs. or 14 cwts. Deflection in the middle for each foot in length, of an inch. Ay lbs. cwts. tons. Weight uniformly loaded, — = 109760 =980-00 =49-000 Weight suspended from the middle, — = 68600=612-50=30-625 in feet, clear BREADTH IN INCHES. 2i 3 3^ 4 4i 6 7 8 bearing. DEPTH IN INCHES. 1 2-00 1-86 1-75 1-66 1-59 1-53 1-48 1-39 1-32 1-26 2 4-01 3-72 3-50 3-33 3-18 3-06 2-95 2-78 2-64 2-53 3 6-01 5-58 5-25 4-99 4-77 4-59 4-43 4-17 3-96 3-79 4 8-02 7-44 7-00 6-65 6-36 6-12 5-91 5-56 5-28 5-05 5 10-02 9-30 8-75 8-32 7-95 7-65 7-38 6-95 6-60 6-31 6 12-03 11-16 10-51 9-98 9-55 9-18 8-86 8-34 7-92 7-58 7 14-03 13-02 12-26 11-64 11-14 10-71 10-34 9-73 9-24 8-84 8 14-89 14-01 13-31 1-2-73 12-24 11-81 11-12 10-56 10-10 9 15-76 14-97 14-32 13-77 1.3-29 12-51 11-88 11-36 *10 15-91 15-30 14-77 13-90 13-20 12-63 11 16-25 15-29 14-52 13-89 12 16-68 15-84 1515 13 16-41 14 15 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— Pine 10 feet long, 15-91 in. by 4 in., or 15-30 by 4 J, or 14-77 by 5, or 13-90 by 6, or 13-20 by 7, or 12-63 by 8, with 140 cwts. uni- formly loaded, or 87-50 cwts. suspended from the middle, deflects ^ of an inch. The brealdng weight of Red Pine 10 feet long 14-77 in. by 5 in. is 6 231 x 140 = 872-3 cwts. uniformly loaded, or 4-985 x 87'5 = 436-1 cwts. suspended from the middle. ■i FIRST SERIES — TABLES OF SCANTLINGS. 35 TABLE XX. Continued.— Red Pine. Weight upon each foot in length, 1568 lbs. or 14 cwts. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded \y lbs. cwts. tons. — = 109760 =980-00 =49-000 D W Weight suspended from the middle, — = 68600 =612-50 =30-625 Length BREADTH IN INCHES. Weight Weight iu feet, clear 10 11 12 13 14 15 uniformly loaded. suspended from the middle, bearing. in cwts. DEPTH IN INCHES. in cwts. '~T 1-21 1-17 1-14 1-10 1-07 1-05 1-02 14-00 8-75 2 2-43 2-34 2-27 2-21 2-15 2-10 2-05 28-00 17-50 3 3-64 3-52 3-41 3-31 3-22 3-14 3-07 42-00 26-25 4 4-86 4-69 4-54 4-41 4-30 4-19 4-10 56-00 35-00 5 6-07 5-86 5-68 5-52 5-37 5-24 5-12 70-00 43-75 ~~6~ 7-28 7-03 6-81 6-62 6-44 6-29 6-14 84-00 52-50 7 8-50 8-21 7-95 7-72 7-52 7-33 717 98-00 61-25 8 9-71 9-38 9-08 8-82 8-59 8-38 8-19 112-00 70-00 9 10-93 10-55 10-22 9-93 9-67 9-43 9-22 126-00 78-75 *10 12-14 11-72 11-36 11-03 10-74 10-48 10-24 140-00 87-50 11 13-36 12-89 12-49 12-13 11-81 11-53 11-26 154-00 96-25 12 14-57 14-07 13-63 13-24 12-89 12-57 12-29 168-00 105-00 13 15-78 15-24 14-76 14-34 13-96 13-62 13-31 182-00 113-75 14 16-41 15-90 15-44 15-04 14-67 14-34 196-00 122-50 15 16-55 16-11 15-72 15-36 210-00 131-25 Deflection in the middle, in parts of au inch. 2 4 5 7T5- 8 9 I o I I TS I 2 7-5- I 3 I 4- I 5 7-g Multipliers to give the breaking weight of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 Uniformly loaded. 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Suspended from the middle * Example.— Rei Pine 10 feet long, 12-14 in. by 9 in., or 11-73 by 10, or 11-36 by 11, or 11-03 by 12, or 10-74 by 13, or 10-48 by 14, or 10-24 by 15, with 140 cwts. nniformly loaded, or 87' 50 cwts. suspended from the middle, deflects ^° of an inch. The breaking weight of Red Pine 14 feet long, 15-04 in. by 13 in., is 8-568 x 196 = 1679-3 cwts. uniformly loaded, or 6-854 x 122-5 = 839-6 cwts. suspended from the middle. 36 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XXL— Red Pine. Weight upon each foot in length, 1800 lbs. or 16*0714 cwts. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded TY" lbs. cwts. tons. —=135000= 1205-35 =60-267 D W Weight suspended from the middle, ^ = 84375= 753-34=37-667 Length in feet, clear BREADTH IN INCHES. 2 2i 3i 4 1 4* 1 5 1 6 1 7 1 8 bearing. DEPTH IN INCHES. 1 2-15 1-99 1-88 1-78 1-70 1-64 1-58 1-49 1-41 1-35 2 4-30 3-99 3-75 3-56 3-41 3-28 3-16 2-98 2-83 2-71 3 6-44 5-98 5-63 5-35 5-11 4-92 4-75 4-47 4-24 4-06 4 8-59 7-98 7-50 7-13 6-82 6-56 6-33 5-96 5-66 5-41 5 10-74 9-97 938 8-91 8-52 8-19 7-91 7-45 7-07 6-76 6 12-89 11-96 11-26 10-69 1023 9-83 9-49 8-93 8-49 8-12 7 15-03 13-96 13-13 12-47 11-93 11-47 11-08 10-42 9-90 9-47 8 15-01 14'26 13-64 13-11 12-66 11-91 11-32 10-82 *9 15-34 14-75 14-24 13-40 12 73 1218 10 15-82 14-89 1414 13-53 11 15-56 14-88 12 16-23 13 14 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5;297 5-676 5-830 * Example. — Red Fine 9 feet long, .... 15-34 in. by 4 iu., or 14-75 by 4^ or 14-24 by 5, or 13-40 by 6, or 12-73 by 7, or 12-18 by 8, with 144-64 cwts. uniformly loaded, or 90-40 cwts. suspended from the middle, deflects of an inch. The breaMng weight of Red Pine 9 feet long, 14-75 in. by 4^ in., is 6-016 x 144-64 = 870-1 cwts. uniformly loaded, or 4-813x90-4 = 435-0 cwts. suspended from the middle. ■i FIRST SERIES — TABLES OF SCANTLINGS. 37 TABLE XXI. Continued. — Red Pine. Weight upon each foot in length, 1800 lbs., or 16*0714 cwts. Deflection in the middle for each foot in length, of an inch. ■m" lbs. cwts. tons. Weight uniformly loaded — = 135000= 1205-35 =60-2&7 w Weight suspended from the middle, ^= 84375= 753-34=37-667 Length BEEADTH IN INCHES. Weight Weight suspended from the middle, in cwts. Deflection in the middle, in parts of an inch. in feet, clear 9 10 1 12 1 13 1 14 15 uniformly loaded, bearing. DEPTH IN INCHES. in cwts. 1 2 3 4 5 1- 30 2- 60 3- 90 5- 20 6- 50 1- 26 2- 51 3- 77 5- 02 6- 28 1- 22 2- 43 3- 65 4- 87 6-08 1- 18 2- 36 3- 55 4- 73 5- 91 1- 15 2- 30 3- 45 4- 60 5- 75 1- 12 2- 25 3- 37 4- 49 5- 61 1- 10 2- 19 3- 29 4- 39 5- 49 16-07 32-14 48-21 64-28 80-35 10-04 20-08 30-13 40-17 50-22 I TT z 7T tV 5 TT 6 7 8 10 7-80 9-11 10- 41 11- 71 13-01 7- 54 8- 79 10- 05 11- 30 12- 56 7- 3U 8- 52 9- 73 10-95 12-17 7- 09 8- 27 9- 45 10- 64 11- 82 6-90 8- 06 9- 21 10- 36 11- 51 6- 74 7- 86 8- 98 10- 10 11- 23 6- 58 7- 68 8- 78 9- 87 10-97 96-42 112-50 128-57 144-64 160-71 60-26 70-31 80-35 90-40 100-44 6 TT 8 TT 9 TT I o TT 11 12 13 14 14- 31 15- 61 13-81 15- 07 16- 33 13- 38 14- 60 15- 82 13- 00 14- 18 15- 36 16- 55 12- 66 13- 81 14- 96 16-11 12- 36 13- 47 14- 59 15- 72 12- 07 13- 17 14- 26 15- 36 176-78 192-85 208-92 225-00 1 10-49 120-53 130-57 140-62 I I TT I 2 TT H Multipliers to give the breaking weight of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Uniformly loaded. Suspended from the middle. * Example.— Red Pine 9 feet long, ll ^l in. by 9 in., or 11-30 by 10, or 10 95 by 11, or 10-64 by 12, or 10-36 by 13, or 1010 by 14, or 9-87 by 15, with 144 64 cwts. uniformly loaded, or 90-40 cwts. suspended from the middle, deflects of an inch. The breaking weight of Red Pine 11 ft. long, 13-00 in. by 12 in., is 8-343 x 176-78 = 1474-8 cwts. uniformly loaded, or 6-674 x 110-49 = 737-4 cwts. suspended from the middle. F 38 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XXII.— Red Pine. Weight upon each foot in length, 2048 lbs., or 18*2857 cwts. Deflection in the middle for each foot in length, of an inch. W lbs. cwts. tons. Weight uniformly loaded — = 163840= 1462-85=73-142 w Weight suspended from the middle, —= 102400= 914-28=45-714 l«ngth BREADTH IN INCHES. in feet, clear 2 1 2i 1 3 1 3* 1 4 1 4i 6 7 8 bearing. DEPTH IN INCHES. 1 2-29 2-13 2-00 1-90 1-82 1-75 1-69 1-59 1-51 1-44 2 4-58 4-25 4-00 3-80 3-64 3-50 3-38 3-18 3-02 2-89 3 6-87 6-38 6-00 5-70 5-45 5-24 5-06 4-76 4-53 4-33 4 9-16 8-51 8-00 7-60 7-27 6-99 6-75 6-35 6-03 5-77 5 11-45 10-63 10-01 9-50 9-09 8-74 8-44 7-94 7-54 7-22 6 13-74 12-76 12-01 11-41 10-91 10-49 10-13 9-53 9-05 8-66 7 14-89 14-01 13-31 12-73 12-24 11-81 11-12 10-56 10-10 *8 16-01 15-21 14-54 13-99 13-50 12-71 12-07 11-54 9 16-36 15-73 15-19 14-29 13-58 12-99 10 16-88 15-88 15-09 14-43 11 16-60 15-87 12 13 14 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— Pine 8 feet long, . . 16-01 in. by 3 in., or 15-21 by 3^ or 14-54 by 4, or 13-99 by 4^ or 13-50 by 5, or 1271 by 6, or 12-07 by 7, or 11-54 by 8, with 146'28 cwts. uniformly loaded, or 91'42 cwts. suspended from the middle, deflects ^ of an inch. The breaking weight of Red Pine 8 ft. long, 14-54 in. by 4 in., is 5-784 x 146-28 = 846 cwts. uniformly loaded, or 4'627 x 91-42=423 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 39 TABLE XXII. Continued.— Red Pine. Weight upon each foot in length, 2048 lbs. or 18*2857 cwts. Deflection in the middle for each foot in length, -g^ of an inch. Tjy lbs. cwts. tons. Weight uniformly loaded = 163840 = 1462-85 = 73-142 W Weight suspended from the middle,— = 102400 = 914-28 = 45-714 Length in feet, clear BREADTH IN INCHES. Weight Weight suspended from the middle, in cwts. Deflection in the middle, in parts of an inch. 10 11 12 13 14 15 uniformly loaded. bearing. DEPTH IN INCHES. iu cwts. 1 2 3 4 5 1- 39 2- 78 4- 16 5- 55 6- 94 1- 34 2- 68 4- 02 5- 36 6- 70 1- 30 2- 60 3- 89 5- 19 6- 49 1- 26 2- 52 3- 78 5- 04 6- 30 1- 23 2- 45 3- 68 4- 91 6-14 1- 20 2- 39 3- 59 4- 79 5- 99 1- 17 2- 34 3- 51 4- 68 5- 85 18-28 36-67 54-85 73-14 91-42 11-42 22-85 34-28 45-71 57-14 I TS 2 5 "S^ 6 7 *8 9 10 8- 33 9- 71 11- 10 12- 49 13- 88 8- 04 9- 38 10-72 12- 06 13- 40 7-79 9-08 10- 38 11- 68 12- 98 7- 56 8- 82 10- 09 11- 35 12- 61 7- 36 8- 59 9- 82 11- 05 12- 27 7- 18 8- 38 9- 68 10- 78 11- 97 7- 02 8- 19 9- 36 10- 53 11- 70 109-71 128-00 146-28 164-57 182-85 68-57 80-00 91-42 102-85 114-28 6 TS 7 8 T3- 9 T5- I o "S^ 11 12 13 14 15- 26 16- 65 14-74 16-08 14- 27 15- 57 16- 87 13-87 15- 13 16- 39 13- 50 14- 73 15- 96 13- 17 14- 37 15- 57 16- 76 12-87 14- 04 15- 21 16- 38 201-14 219-42 237-71 256-00 125-71 137-14 148-57 160-00 I I I z -^s I 3 1 4 To Multipliers to give the breaking weight of every Scantliug in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Suspended from the middle. * Example.— Red. Pine 8 feet long, 11-10 in. by 9 in., or lO'TS by 10, or 10-38 by 11, or 10-09 by 12, or 9-82 by 13, or 9-58 by 14, or 9-36 by 15, with 146-28 cwts. uniformly loaded, or 91-42 cwts. suspended from the middle, deflects of au inch. The breaking weight of Red Pine 10 ft. long, 12-98 in. by 11 in., is 8-105 x 182-85 = 1483 cwts. uniformly loaded, or 6-484 x 114-28 = 741 cwts. suspended from the mid^e. 40 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XXIII.— Red Pine. Weight upon each foot in length, 2312 lbs. or 20*6428 cwts. Deflection in the middle for each foot in length, of an inch. Weight uniformly loaded — = 196520 = 1754*64 = 87-732 Weight suspended from the middle,— = 122825 = 1096-65 = 54-832 Length BREADTH IN INCHES. in feet, clear 2 3 4 H 6 7 8 bearing. DEPTH IN INCHES. 1 2-43 2-26 213 2-02 1-93 1-86 1-79 1-69 1-60 1-53 2 4-87 4-52 4-25 4-04 3-86 3-71 3-59 3-38 3-21 3-07 3 7-30 6-78 6-38 6-06 5-80 5-57 5-38 5-06 4-81 4-60 4 9-74 9-04 8-50 8-08 7-73 7-43 7-17 6-75 6-41 6-13 5 12-17 11-30 10-63 10-10 9-66 9-29 8-97 8-44 8-02 7-67 ~~6~ 14-60 13-56 12-76 12-12 11-59 11-14 10-76 0-13 ~9^ 9-20 *7 15-82 14-88 14-14 13-52 13-00 12-55 ] 1-81 11-22 10-73 8 15-45 14-86 14-35 ] 3-50 12-82 12-27 9 16-14 ] 15-19 14-43 13-80 10 16-03 15-33 11 12 13 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Emmple.—-Rei Pine 7 feet long, . 15-82 in. by 2h in., or 14-88 by 3, or 14-14 by 3i or 13-52 by 4. or 13-00 by 4i, or 12-55 by 5, or 11-81 by 6, or 11-22 by 7, or 10-73 by 8, with 144-50 cwts. uniformly loaded, or 90-31 cwts. suspended from the middle, deflects 7 of an inch. The breaking weight of Red Pine 7 feet long, 14-14 in. by 3i in., is 5-532 x 144-5 = 799-3 cwts. uniformly loaded, or 4-425 x 90-31 = 399-6 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 41 TABLE XXIII. Continued.— Red Pine. Weight upon each foot in length, 2312 lbs. or 20*6428 cwts. Deflection in the middle for each foot in length, of an inch. TV" lbs. cwb. tons. Weight uniformly loaded, ^ = 196520 = 1754-64 = 87-732 Weight suspended from the middle,^= 122825 = 1096-65 = 54-832 6 *7 8 9 10 11 12 13 BREADTH IN INCHES. 9 I 10 I 11 I 12 I 13 I 14 I 15 DEPTH IN INCHES. 1- 47 2- 95 4- 42 5- 90 7-37 8-85 10- 32 11- 79 13- 27 14- 74 16-23 1- 42 2- 85 4- 27 5- 69 712 8- 54 9- 96 11- 39 12- 81 14-23 15-66 1- 38 2- 76 4- 14 5- 52 6- 89 8- 27 9- 65 11- 03 12- 41 13- 79 1517 16-55 1- 30 2- 61 3- 91 5- 22 6- 52 7-82 9-13 10- 43 11- 74 13-04 rf35 15- 65 16- 95 1- 27 2- 54 3- 82 5- 09 6- 36 7- 63 8- 91 1018 11- 45 12- 72 iToo 15- 27 16- 54 1- 24 2- 49 3- 73 4- 97 6-22 7- 46 8- 70 9- 95 11- 19 12- 43 13- 68 14- 92 16-16 Weight aniformly loaded, in cwts. 20-64 41-28 61-92 82-57 103-21 123^ 144-50 16514 185-78 206-42 227-07 247-71 268-35 Weight suspended from the middle, in cwts. 12-90 25-80 38-70 51-60 64-50 "77^ 90-31 103-21 116-11 129-01 I4r92 154-82 167-72 Deflection in the middle, iu parts of an inch. rr TT 3 TT 6 TT tV 8 TT 9 TT I o TT I I TT I 2 TT I 3 TT Multipliers to give the breaking weight of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Uniformly loaded. Suspended from the middle. * Example.— Rei Pine 7 feet long, 10-32 in. by 9 in., or 9-96 by 10, or 9-65 by 11, or 9-38 by 12, or 9-13 by 13, or 8 91 by 14, or 8-70 by 15, with 144-50 cwts. uniformly loaded, or 90-31 cwts. suspended from the middle, deflects ^ of an inch. The breaking weight of Red Pine 9 feet long, 12-05 in. by 12 in., is 8-843 x 185-78 = 1549-9 cwts. uniformly loaded, or 6-674 x 116-11 = 774-9 cwts. suspended from the middle. 42 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XXIV.— Red Pine. Weight upon each foot in length, 2592 lbs. or 23*1428 cwts. Deflection in the middle for each foot in length, -5% of an inch. w lbs. cwts. tons. Weight uniformly loaded ^ = 233280 =2082-85= 104-142 Weight suspended from the middle,— = 145800 = 1301-78= 65-089 Length BREADTH IN INCHES. iu feet, clear 3 H 4 4i 1 6 7 8 bearing. DEPTH IN INCHES. 1 2 3 4 5 2-58 5-15 7-73 10-31 12-89 2-39 4-78 7-18 9-57 11-96 2-25 4-50 6-75 9-00 11-26 2-14 4-28 6-42 8-55 10-69 2-05 4-09 6-14 8-18 10-23 1-97 3-93 5-90 7-87 9-83 1-90 3-80 5-70 7-60 9-49 1-79 3-57 5-36 7- 15 8- 93 1-70 3-39 5- 09 6- 79 8-49 1-62 3- 25 4- 87 6-49 8-12 7 8 9 10 15-46 13^1 15-76 12-83 14-97 12-27 14-32 11-80 13-77 15-73 11-39 13-29 15-19 10-72 12-51 14-29 16-08 10- 18 11- 88 13-58 15-28 9-74 11- 36 12- 99 14-61 16-23 11 12 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— Rei Pine 6 feet long, 15-46 in. by 2 in., or 14-35 by 3^, or 13-51 by 3, or 12-83 by 3^ or 12-27 by 4, or 11-80 by 41, or 11-39 by 5, or 10-72 by 6, or 10-18 by 7, or 9-74 by 8, with 188-85 cwts. uniformly loaded, or 86'78 cwts. suspended from the middle, deflects ^ of an inch. The breaMng weight of Red Pine 6 feet long, 13-51 in. by 3 in., is 5-255 x 138-85 = 729-6 cwts. uniformly loaded, or 4-204x 86-78 = 364-8 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 43 TABLE XXIV. Continued.— Red Pine. Weight upon each foot in length, 2592 lbs. or 23*1428 cwts. Deflection in the middle for each foot in length, of an inch. lbs. cwts. tons. Weight uniformly loaded — = 233280 =2082-85= 104-142 Weight suspended from the middle,^= 145800 = 1301-78= 65-089 Length BREADTH IN INCHES. Weight uniformly loaded, Weight suspended from the middle, in cwts. iu feet, clear bearing. 9 JO 11 12 13 14 15 DEPTH IN INCHES. in cwts. 1 2 3 4 5 1-56 3- 12 4- 68 6- 24 7- 80 1-51 3- 01 4- 52 6- 03 7- 54 1- 46 2- 92 4-38 6- 84 7- 30 1- 42 2- 84 4- 25 5- 67 7-09 1- 38 2- 76 4- 14 5- 52 6- 90 1- 35 2- 69 4- 04 5- 39 6- 74 1- 32 2- 63 3- 95 5- 27 6- 58 23-14 46-28 69-42 92-57 115-71 14-46 28-92 43-39 57-85 72-32 *6 7 8 9 10 9-37 10-93 12-49 14- 05 15- 61 9^ 10-55 12- 06 13- 56 15-07 8-76 10- 22 11- 68 13- 14 14- 60 8- 51 9- 93 11- 35 12- 76 14-18 ~8^9 9-67 11- 05 12- 43 13- 81 8- 08 9- 43 10-78 12- 12 13- 47 "7^0 9-22 10- 53 11- 85 13-17 138^ 162-00 185-14 208-28 231-42 ~86^8 101-25 115-71 130-17 144-64 11 12 16-06 15-60 15- 19 16- 57 14-82 16-17 15-80 25?57 277-71 13940 173-57 Deflection in the middle, in parts of an inch. 2 3 4 __5 9 O' 6 7 8 9 90 I o I I 9^ I 2 9^ Multipliers to give the breaking weight of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Suspended from the middle. * Example.— R^di Pine 6 feet long. 9'37 in. by 9 in., or 9-04 by 10, or 8 76 by 11, or 8-51 by 12, or 8-29 by 13, or 8-08 by 14, or 7-90 by 15, with 138-85 cwts. uniformly loaded, or 86-78 cwts. suspended from the middle, deflects of an inch. The breaking weight of Ked Pine 6 feet long, 8-08 in. by 14 in., is 8-783 x 138-85 = 1219-5 cwts. uniformly loaded, or 7"026 x 86-78 = 609-7 cwts. suspended from the middle. 44 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XXV.— Red Pine. Weight upon each foot in length, 2888 lbs. or 25'7857 cwts. Deflection in the middle for each foot in length, of an inch. ly lbs. cwts. tons. Weight uniformly loaded —=274360=2449'64= 122-482 w Weight suspended from the middle, — = 171475= 153 1-02= 76-551 BREADTH IN INCHES. Length in feet, clear 2 2^ 3 1 3k 1 4 1 4i 1 5 1 6 1 7 1 8 bearing. DEPTH IN INCHES. 1 2-72 2-53 2-38 2-26 2-16 2-08 2-00 1-89 1-79 1-71 2 5-44 5-05 4-75 4-51 4-32 4-15 4-01 3-77 3-58 3-43 3 8-16 7-58 7-13 6-77 6-48 6-23 6-01 5-66 5-37 5-14 4 10-88 10-10 9-51 9-03 8-64 8-30 8-02 7-54 7-17 6-85 *5 13-60 12-63 11-88 11-29 10-80 10-38 10-02 9-43 8-96 8-57 6 14-26 13-54 12-95 12-46 12-03 11-32 10-75 10-28 7 15-80 1511 14-53 14-03 13-20 12-54 12-00 8 16-03 15-09 14-33 13-71 9 16-12 15-42 10 11 Multipliers to give the breaking weight of every ScantlLiig in each column respectively. 4-591 4-945 5-255 5-532 5-784 6-016 6-231 6-621 6-970 7-288 3-673 3-956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— R^i Pine, 5 feet long, 13-60 in. by 2 in., or 12-63 by 2h, or 11-88 by 3, or 11-29 by 3i, or 10-80 by 4, or 10-38 by 4i, or 10-02 by 5, or 9-43 by 6, or 8-96 by 7, or 8-57 by 8, with 128 92 cwts. uniformly loaded, or 80-58 cwts. suspended from the middle, deflects -Jj of an inch. The breaking weight of Red Pine 5 feet long, 12-63 in. by 2i in., is 4-945 x 128-92 = 637-5 cwts. uniformly loaded, or 3-956 x 80 58 = 3187 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 45 TABLE XXV. Continued.^RED Pine. Weight upon each foot in length, 2888 lbs. or 25-7857 cwts. Deflection in the middle for each foot in length, ^ of an inch. XXT lbs. cwts. tons. Weight uniformly loaded —=274360 =2449-64 = 122-482 Weight suspended from the middle.— = 171475 = 1531-02 = 76-551 Length iu ItBt, clear BREADTH IN INCHES. Weight Weight suspended irom the middle, in cwts. Deflection in the middle, in parts of an inch. 9 1 10 1 11 1 12 1 13 1 14 1 15 uniformly loaded, bearing. DEPTH IN INCHES. in cwts. 1 2 3 4 *5 1-65 3- 30 4- 94 6-59 8-24 1-59 318 4-77 6- 36 7- 95 1-54 3- 08 4- 62 6- 16 7- 71 1- 50 2- 98 4- 48 5- 98 7-48 1- 46 2- 92 4- 37 5- 83 7-29 1- 42 2- 84 4- 27 5- 69 7-11 1- 39 2- 78 4- 17 5- 56 6- 95 25-78 51-57 77-35 103-14 128-92 16-11 32-23 48-34 64-46 80-58 I 2 9T 3 5 ~ 7 8 9 10 9-89 11-53 13- 18 14- 83 16-48 9-54 11- 14 12- 73 14- 32 15- 91 9-25 10-79 12- 33 13- 87 15-41 8-97 10- 47 11- 97 13- 46 14- 96 8-75 10- 20 11- 66 13- 12 14- 58 8- 53 9- 95 11- 38 12- 80 14-22 8- 34 9- 73 1112 12- 51 13- 90 l5f7T 180-50 206-28 232-07 257-85 ~96^ 112-81 128-92 145-04 161-16 6 9 9 S I o 9 5 11 16-46 16-03 15-64 15-29 283-64 177-27 I I Multipliers to give the breaking weight of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 Uniformly loaded. 6-063 6-280 6-484 6-674 6-854 7-026 7-190 Suspended from the middle. * Example. — Red Pine 5 feet long, 8-24 in. by 9 in., or 7-95 by 10, or Y'Tl by 11, or 7-48 by 12, or 7-29 by 13, or 7-11 by 14, or 6-95 by 15, with 128-92 cwts. uniformly loaded, or 80'58 cwts. suspended from the middle, deflects .Jj of an inch. The breaking weight of Red Pine 5 feet long, 7-95 in. by 10 in., is 7-85 x 128-92 = 1012 cwts. uniformly loaded, or 6'23 x 80-58 = 506 cwts. suspended from the middle. 46 FIRST SERIES — TABLES OF SCANTLINGS. TABLE XXVI.— Red Pine. Weight upon each foot in length, 3200 lbs. or 28*5714 cwts. FLECTION ill the middle for oach foot in length, of an inch. Weight uniformly loaded ..c —=320000= 2857-14= 142-857 Weight suspended from the middle,— = 200000= 1785-71 = 89-285 Length BREADTH IN INCHES. in teet, clear 2 1 2i 1 3 1 3^ 4 4* 1 5 1 6 1 7 1 8 bearing. DEPTH IN INCHES. 1 2-86 2-66 2-50 2-38 2-27 2-19 2-11 1-99 1-89 1-80 2 5-73 5-32 5-00 4-75 4-55 4-37 4-22 3-97 3-77 3-61 3 8-59 7-97 7-50 7-13 6-82 6-56 6-33 5-96 5-66 5-41 *4 11 45 10-63 10-01 9-50 9-09 8-74 8-44 7-94 7-54 7-22 5 14-32 13-29 12-51 11-88 11-36 10-93 10-55 9-93 9-43 9-02 ~6~ 15-95 15-01 14-26 13-64 13-11 12-66 11-91 11-32 10-82 7 15-91 15-30 14-77 13-90 13-20 12-63 8 9 15-88 15-09 14-43 16-23 10 11 Multipliers to give the breaking weight of every Scantling in each column respectively. 4-591 4-945 5-255 5-532 5-784 6016 6-231 6-621 6-970 7-288 3-673 3956 4-204 4-425 4-627 4-813 4-985 5-297 5-576 5-830 * Example.— nei Pine 4 feet long, 11-45 in. by 2 in., or 10 63 by 2i, or 10-01 by 3, or 9-50 by 3i or 9-09 by 4, or 8-74 by 4^ or 8-44 ..y 5, or 7 94 by 6, or 7-54 by 7, or 7-22 by 8, with 114-28 cwts. uniformly loaded, or 71-42 cwts. sus- pended from the middle, deflects of an inch. The brealdng weight of Red Pine 4 feet long, 11-45 in. by 2 in., is 4-591 x 114-28 = 524-6 cwts. uniformly loaded, or 3-673 x 71-42 = 262-3 cwts. suspended from the middle. FIRST SERIES — TABLES OF SCANTLINGS. 47 TABLE XXVI. Continued.— Red Pine. Weight upon each foot in length, 3200 lbs. or 28*5714 cwts. Deflection in the middle for each foot in length, -j-J^ of an inch. TXr cwts. tODS. Weight uniformly loaded — = 320000= 2857-14= 142-857 w Weight suspended from the middle,— = 200000= 1785-71 = 89-285 Length in feet, clear BREADTH IN INCHES. 9 10 11 12 13 • 14 15 bearing. DEPTH IN INCHES. 1 1-73 1-67 1-62 1-58 1-53 {-50 1-46 2 3-47 3-35 3-24 3-16 3-07 2-99 2-93 3 5-20 5-02 4-87 4-73 4-60 4-49 4-39 *4 6-94 6-70 6-49 6-30 6-14 5-99 5-85 5 8-67 8-37 8-11 7-88 7-67 7-48 7-31 ~~6~ ioTi 10-05 y-73 9-45 9-21 8-98 "¥78 7 12-14 11-72 11-36 11-03 10-74 10-48 10-24 8 13-88 13-40 12-98 12-61 12-27 il-97 il-70 9 15-61 15-07 14-60 14-18 13-81 13-47 13-17 10 16-75 16-22 15-76 15-34 14-97 14-63 11 16-88 16-47 16-09 Weight uiiilormly loadrd, in cwts. Weight Deflection suspeiiiied | in the iVoin the middle, middle, in parts of in cwts. an inch. 28-57 17-85 57-14 35-71 H5-71 53-57 114-2e 7142 142-85 89-28 17W2;107M4 200-001 125-00 228-57i 142-83 257- 14! 160-71 285-7 1 1 178-57 314-281 196-421 -^'^ I oT? 2 1 o5 _3. 1 o o ± loo S I ca" S roo 1 o o I o Multipliers to give the breaking weicjfit of every Scantling in each column respectively. 7-579 7-850 8-105 8-343 8-568 8-783 8-988 6-063 6-280 6-484 6-674 6-854 7-026 7 190 Uniformly loaded. Suspended from the middle. * Example. — Red Pine 4 feet long, 6-94 in. by 9 in., or 0-70 by 10, or 6-49 by 11, or 6-30 by 12, or 6-14 by 13, or 5-99 by 14, or 5-85 by 15, with 114-23 cwts. uniformly loaded, or 71'42 cwts. suspended from the middle, deflects of an inch. The breaking we'2;lit of Red Pine 4 feet long, 6-'.)4 in. by 9 in.^ is 7-579 x 114-28 = 866 cwts. uniformly loaded, or G'OGo x 7r4i = 433 cwts. suspended from the middle. 50 SECOND SERIES OF TABLES. TABLE OF CONSTANTS. No. 2. By which, and the Second Series of Tables, may be found the Scantling of the following species of Timber sufficient to carry, when loade( any given portion of the breaking weight.* Name of the Wood. Factors 1 to give the breaking 1 weight of ! Reciprocal every'Scant- of the same ling in the I Second I Series, Whight uniformly loaded. Weight suspended from the middle. Factors to give the breaking weight of every Scant- ling in the Second Series, c=8S. 8S Reciprocal of the same. c = 4S. 1 Deplkction. Relative deflection when loaded with the same weight. c = E. Standard, I Strength, ...1344| Red Pine j Elasticity, 230000 J Acacia Ash Beech Birch, American black ... „ Common Bullet tree C abac ally Deal, Christiana „ Memel Elm Fir, Mar Forest „ New England » Riga Green-heart Larch Locust tree Norway spars Oak, Adriatic „ African (superior quality) „ Canadian „ Dantzic „ English ... Pine, Pitch „ Red, mean strength, 1341'3 Poon Teak Tonquin bean 8- 000 11- 113 12- 067 9- 270 10- 821 11- 476 15- 773 14-988 9-261 10-303 6- 041 7- 235 6-562 6- 423 16- 291 5-955 20- 458 8- 767 8-229 14-857 10-515 8-750 8- 497 9- 713 7- 983 13- 218 14- 661 21- 583 Col. I. 1250 0899 0828 1078 0924 0871 0633 0667 1079 0970 1655 1382 1523 1556 0613 1678 0488 1140 1215 0673 0951 1142 1176 1029 1252 0756 0682 0463 II. 4- 000 5- 556 6- 033 4- 635 5- 410 5-738 7- 886 7- 494 4- 630 5- 151 3-020 3-617 3-281 3- 211 8- 145 2- 977 10-229 4- 383 4- 114 7-428 5- 257 4-375 4-248 4-856 3- 991 6- 609 7- 330 10-791 III. 2500 1799 1657 2157 1848 1742 1267 1334 2159 1941 3310 2764 3047 3113 1227 3357 0977 2281 2430 1346 1902 2285 2353 2059 2505 1513 1364 0926 IV. 1-000 1-597 1-118 1-359 1-245 1-118 -700 -996 M57 1- 119 2- 678 2-186 1-232 1- 603 •692 2- 009 -945 1-262 1-894 •798 -950 1.577 1-585 1-502 1-000 1-089 -762 •692 V. * See Examples, page xxiv. SECOND SERIES — TABLES OF WEIGHTS. 51 TABLE I. SCANTLINGS, U in. and If inches Deep. The Weights in this table are — NE-EiGHTH of the breaking weight of Red Pine, uniformly loaded; or NE-FOURTH of the Same, when suspended from the middle. Size of cantmngs, in inches. LENGTH IN FEET , CLEAR BEARING. 1 1 2 3 1 4 1 5 6 7 8 9 1 10 epih. Breadth. WEIGHT IN CWTS. 1 i V 1 HX 11 HX H ^HX i| HX 2 it i O 2- 81 3- 37 3- 93 4- 50 1.10 1-40 1-68 1- 96 2- 25 •75 •93 M2 1^31 1-50 •56 •70 •84 •98 1-12 •45 •56 •67 •78 •90 •37 •46 -56 •65 •75 •32 •40 •48 •56 -64 -28 •35 -42 •49 -56 •31 -37 •43 •50 •99 •28 •33 •39 •45 HX 3 HX 4 HX 5 HX 6 HX 7 ~6^ 9-00 11-25 13..50 15-75 3- 37 4- 50 5- 62 675 7-87 2- 2o 3- 00 3- 75 4- 50 5- 25 1^6» 2-25 2- 81 3- 37 3-93 I -30 1- 80 2- 25 2-70 315 1-12 1-50 1- 87 2- 25 2-62 -90 1-28 J -60 1- 92 2- 25 •»4 112 1-40 1-68 1-96 •75 1-00 1^25 1-50 1-75 -67 •90 M2 1-35 1-57 HX 8 HX 9 HXIO Hxil HX12 Ts-oo 20-25 22-50 24-75 27-00 9-00 10- 12 11- 25 12- 37 13- 50 6-Ou 6- 75 7- 50 8- 25 9- 00 4- 50 5- 06 5- 62 6- 18 6-75 3- dU 4- 05 4-50 4- 95 5- 40 3-OU 337 3- 75 4- 12 4-50 2-57 2-89 3^21 3^53 3^85 2-25 2-53 2- 81 3- 09 3-37 2-25 2-50 2- 75 3- 00 1- 80 2- 02 2-25 2-47 2^70 Deflection ia inches of Red Pine 1^ inches deep, loaded with the weights in tliis table. 'eight uniform- \ ly loaded | •on 1 -044 -099 -175 -274 •394 537 •701 -887 1 1-096 Pt. suspended ) Dm the middle f -0171 -070 •158 •280 •438 •631 ! ^859 M22 1-420| 1-753 4e.* For Scantlings If inches deep, multiply the weights in this table by 11= 1-3611, and the deflections by |.= -857.1 * Example 1. — Red Pine \ \ in. by 1| in., 7 feet long, with "56 cwts. uniformly loaded, )Tie-eighlh the breaking weight) deflects -537 of an inch ; and with -56 cwts. suspended from le middle, (one-fourth the breaking weight) the deflection is '859 of an inch. [ f* Example 2 — Red Pine If in. by If in., 7 feet long, with -56 x 1-36 = 76 cwts. uni- armly loaded, (one-eiglith the breaking weight) deflects "537 y- ^='460 of an inch ; and with i?6 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 859 X 6 = 736 of an inch. *^* To find the Scantlings of Red Pine and other kinds of timber, sufficient to carry, when loaded, one-re"" part, or any givon portion of the breaking weight, see the Table and i Examples referred to in the preceding page. 52 SECOND SERIES — TABLES OF WEIGHTS. TABLE II. SCANTLINGS, 2 in. and 2h inches Deep. The Weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; o] One-fourth of the same when suspended from the middle. Scantlings, ir. inches. 1 2 3 4 5 6 7 8 1 9 1 10 Depth, nreadth. WEIGHT IN CWTS. 2 X U 2 X If *2 X 2 2 X 21 2 X 2i 6- 00 7- 00 8- 00 9- 00 10-00 3-00 3- 50 4^00 4- 50 6-00 2-00 2-33 2- 66 3- 00 3-33 1-50 1- 75 2^00 2- 25 2-50 1-20 1-40 1- 60 \-80 2- 00 1-00 1-16 1-33 1-50 J-66 •85 1-00 M4 1^28 1-42 -75 •87 1^00 112 1-25 •66 •77 •88 1-00 1-11 -6( •7( •8( -9i l-0( 2X3 2X4 2X5 2X6 2X7 12-00 16-00 20-00 24-00 28-00 6-00 8-00 10-00 12-00 14-00 4- UO 5- 33 6- 66 8- 00 9- 33 3- 00 4- 00 6-00 6- 00 7- 00 2- 40 3- 20 4- 00 4- 80 5- 60 2^00 2- 66 3- 33 4- 00 4-66 1- 71 2- 28 2- 85 3- 42 4- 00 1- 50 2- 00 2- 50 3- 00 350 1-33 1- 77 2- 22 2- 66 3- 11 1- 6( 2- 0( 2-4( 2-8( 2X8 2X9 2 XIO 2 Xll 2 X12 32-00 36-00 40-00 44-00 48-00 16-00 18-00 20-00 22-00 24-00 10-66 12- 00 13- 33 14- 66 16-00 8- 00 9- 00 10- 00 11- 00 12- 00 6- 40 7- 20 8- 00 8- 80 9- 60 5- 33 6- 00 6- 66 7- 33 8- 00 4^57 5-14 5- 71 6^28 6- 85 Too 4- 50 5- 00 550 6- 00 ~3^5 4-00 4-44 4- 88 5- 33 "3^1 3- 6( 4- 01 4-4( 4-8( Deflectiou in inches of Red Pine 2 inches deep, loaded with the weights in this table. Weight uiiiiorm- ) ly loaded J Wt. suspended ) from the middle j •008 •013 •033 -053 -074 •118 •131 •210 -205 •329 •296 •473 1 403 -644 -526 -841 •666 1-065 •82i 1-31^ For Scantlings 2i inches deep, multiply the weights in this tabh by 1-5625, and the deflections by -S.f * Example 1.— Red Pine 2 in. by 2in., 8 feet long, with 1 cwt. uniformly loaded (one eighth the breaking weight) deflects -526 of an inch; and with 1 cwt. suspended from thi middle (one-fourth the breaking weight) the deflection is -841 of an inch. f* Example 2.— Red Pine 2i in. by 2 in., 8 leet long, with 1 x 1-5625 = 1-5625 cwts uniformly loaded (one-eighth the brealdng weight) deflects -526 x -8 = '4208 oi an inch ; aa( with 1-5625 cvds. suspended trom the middle (oae-tourth the breaking weight) the deflectioi is -841 X -8 = -6728 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 53 TABLE III. SCANTLINGS, 3 m. and 3^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SiZB OF Scantlings, in inches. Depth. Breadth 3 *3 3 3 3 X 2 X 2i X 2h X 2f X 3 X 3i X 4 X 8 X 9 XIO XII X12 LENGTH IN FEET, CLKAR BEARING. I 1 2 1 3 1 4 1 6 1 6 1 7 1 8 1 9 10 WEIGHT IN CWTS. 18-00 20-25 22-50 24-75 27-00 YfEb 36-00 45-00 54-00 63-00 "72^ 81-00 90-00 99-00 108-00 9-00 10- 12 11- 25 12- 37 13- 50 15-75 18-00 -22-50 27-00 31-50 36-00 40-50 45-00 49-50 54-00 6-00 6- 75 7- 50 8- 25 9- 00 10-50 12-00 15-00 18-00 21-00 24-00 27-00 30-00 33-00 36-00 4- 50 5- 06 5- 62 6- 18 6-75 7-87 9-00 11-25 13-50 15-75 18-00 20-25 22-50 24-75 27-00 3- 60 4- 05 4-50 4- 95 5- 40 6- 30 7- 20 9-00 10-80 12-60 14-40 16-20 18- 00 19- 80 21-60 3-00 3-37 3- 75 4- 12 4-50 5- 25 6- 00 7- 50 9-00 10-50 12- 00 13- 50 15- 00 16- 50 18-00 2-57 2- 89 3- 21 3-53 3-85 4- 50 5- 14 6- 42 7- 71 9-00 10- 28 11- 57 12- 85 14- 14 15- 42 2-25 2-53 2- 81 3- 09 3-37 3- 93 4- 50 5- 62 6- 75 7- 87 ^^0 10- 12 11- 25 12- 37 13- 50 2-00 2-25 2-50 2- 75 3- 00 3- 50 4- 00 500 6- 00 7- 00 8- 00 9- 00 10- 00 11- 00 12- 00 1- 80 2- 02 2-25 2-47 2-70 3-15 3- 60 4- 50 5- 40 6- 30 T-20 8- 10 9- 00 9-90 10-80 Deflection in inches of Red Pine 3 inches deep, loaded with the weights in this table. Weight uniform- ] ly loaded J -005 -022 -049 •088 -137 •197 •268 -351 -444 -548 Wt. suspended ] -009 •035 -079 •140 •219 •316 •430 -561 •710 •877 from the middle J For Scantlings 3^^ inches deep, multiply the weights in this table by -ff = 1^3611, and the deflections by ^=-857.f * Example 1.— Red Pine 3 in. by 2k in., 3 feet long, with 6-75 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "049 of an inch ; and with 6-75 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is "079 of an inch. f* Example 2.— Red Pine 3^ in. by 2^ in., 3 feet long, with 675 x 1-36 = 918 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "049 x |. = -042 of an inch ; and with 9-18 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -079 X 6 =-068 of an inch. H 54 SECOND SERIES — TABLES OF WEIGHTS. TABLE IV. SCANTLINGS, 4 in. and 4i inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 Depth Breadth. WEIGHT IN CWTS, 4 X 2 32-00 16-00 10-66 8-00 6-40 5-33 4-57 4-00 3-55 3-20 4 X 2i 36-00 18-00 12-00 9-00 7-20 6-00 5-14 4-50 4-00 3-60 *4 X 2i 40-00 20-00 13-33 10-00 8-00 6-66 5-71 5-00 4-44 4-00 4 X 3 48-00 24-00 16-00 12-00 9-60 8-00 6-85 6-00 5-33 4-80 4 X 3i 56-00 28-00 18-66 14-00 11-20 9-33 8-00 7-00 6-22 5-60 ~4 "xT 4 64-00 32-00 21-33 16-00 12-80 10-66 9-14 8-00 7-11 6-40 4 X 4i 72-00 36-00 24-00 18-00 14-40 12-00 10-28 9-00 8-00 7-20 4 X 5 80-00 40-00 26-66 20-00 16-00 13-33 11-42 10-00 8-88 8-00 4 X 6 96-00 48-00 32-00 24-00 19-20 16-00 13-71 12-00 10-66 9-60 4 X 7 112-00 56-00 37-33 28-00 22-40 18-66 16-00 14-00 12-44 11-20 4 X 8 128-00 64-00 42-66 32-00 25-60 21-33 18-28 16-00 14-22 12-80 4 X 9 144-00 72-00 48-00 36-00 28-80 24-00 20-57 18-00 16-00 14-40 4 XIO 160-00 80-00 53-33 40-00 32-00 26-66 22-85 20-00 17-77 16-00 4 Xll 176-00 88-00 58-66 44-00 35-20 29-33 25-14 22-00 19-55 17-60 4 X12 192-00 96-00 64-00 48-00 38-40 32-00 27-42 24-00 21-33 19-20 Deflection in inches of Red Pine 4 inches deep, loaded with the weights in this table. Weight uDiform- ly loaded Wt. suspended from the middle -004 -016 -037 -066 .103 -148 •201 •263 -333 •007 •026 -059 •105 •164 -237 -322 •421 •532 -411 •657 * :* For Scantlings 4i inches deep, multiply the weights in this table by 1-2656, and the deflections by |-=-888,f * Example 1.— Red Pine 4 in. by 2^ in., 4 feet long, with 10 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -066 of an inch ; and with 10 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is '105 of an inch. f * Example 2.— Red Pine 4^ in. by 2h in., 4 feet long, with 10 x 1-2656 = 12-656 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -066 x 8.= -059 of an inch ; and with 12-656 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is-105x|. = -093 ofaninch. SECOND SERIES — TABLES OF WEIGHTS. 65 TABLE IV. Continued. SCANTLINGS, 4 in. and 4i inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SiZK OK Scantlings, in inches. Deplh. Breadth LENGTH IN FEET, CLEAR BEARING. 11 I 12 I 13 I 14 I 15 I 16 I 17 I 18 I 19 | 20 WEIGHT IN CWTS. 4 X 2 2-90 2-66 2-46 2-28 2-13 2-00 1-88 4 X 2i 3-27 3-00 2-76 2-57 2-40 2-25 2-11 *4 X 2i 3-63 3-33 3-07 2-85 2-66 2-50 2-35 4 X 3 4-36 4-00 3-69 3-42 3-20 3-00 2-82 4 X 3^ 5-09 4-66 4-30 4-00 3-73 3-50 3-29 4 X 4 5-33 4-92 4-.57 4-26 4-00 3-76 4 X a 6-54 6-00 5-53 5-14 4-80 4-50 4-23 4 X 5 7-27 6-66 6-15 5-71 5-33 5-00 4-70 4 X 6 8-72 8-00 7-38 6-85 6-40 6-00 5-64 4 X 7 10-18 9-33 8-61 8-00 7-46 7-00 6-58 4 X ¥~ 11-63 10-66 9-84 9-14 8-53 8-00 7-52 4 X 9 13-09 12-00 11-07 10-28 9-60 9-00 8-47 4 XIO 14-54 13-33 12-30 11-42 10-66 10-00 9-41 4 Xll 16-00 14-66 13-53 12-57 11-73 11-00 10-35 4 X 12 17-45 16-00 14-76 13-71 12-80 12-00 11-29 1- 77 2- 00 2-22 2- 66 3- 11 3- 55 4- 00 4- 44 5- 33 6- 22 7- 11 8- 00 8- 88 9- 77 10-66 1-68 1- 89 2- 10 2-52 2-94 3-36 3- 78 4- 21 505 5- 89 6- 73 7- 57 8- 42 9- 26 10-10 1-60 1- 80 2- 00 2-40 2- 80 "3^ 3- 60 4- 00 4- 80 5- 60 7- 20 8- 00 8- 80 9- 60 Deflection in inches of Red Pine 4 inches deep, loaded with the weights in this table. Weight uniform- 1 ly loaded. J -497 -592 -694 •805 -924 1-052 1-187 1-331 1-483 1*644 Wt. suspended ) from the middle ) •795 •947 1-111 1-288 1-479 1-683 1-900 2-130 2-373 2-630 For Scantlings 4i inches deep, multiply the weights in this table by 1-2656, and the deflections by|-=-888.t * Example 1.— Red Pine 4 in. by 2h in., 11 feet long, with 3-63 cwts uniformly loaded, (one-eighth the breaking weight) deflects -497 of an inch; and with 3-63 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -795 of au inch. f * Example 3.— Red Pine 4>h in. by 2^ in., 11 feet long, with 3-63 x 1-2656 = 4*59 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -497 x |-= '442 of an inch ; and with 4-59 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -795 X 8 =-707 of an inch. 56 SECOND SERIES TABLES OF WEIGHTS. TABLE V. SCANTLINGS, 5 in. and 5i inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. LENGTH in FEET, CLEAR BEARING. in inches. t • 2 3 1 4 1 5 6 7 8 1 9 Depth. Breadth. WEIGHT IN CWTS. 5 X 2 .50-00 25-00 16-66 12-50 10-00 8-33 7-14 6-25 5-55 5 X 2i 56-25 28-12 18-75 14-06 11-25 9-37 8-03 7-03 6-25 5 X 2^ 62-50 31-25 20-83 15-62 12-50 10-41 8-92 7-81 6-94 *5 X 3 75-00 37-50 25-00 18-75 15-00 12-50 10-71 9-37 8-33 5 X 3^ 87-50 43-75 29-16 21-87 17-50 14-58 12-50 10-93 9-72 6 X 4 100-00 ~50^ 33-33 25-00 20-00 16-66 14-28 12-50 11-11 5 X 4i 112-50 56-25 37-50 28-12 22-50 18-75 16-07 14-06 12-50 5 X 5 125-00 62-50 41-66 31-25 25-00 20-83 17-85 15-62 13-88 5 X 5i 137-50 68-75 45-83 34-37 27-50 22-91 19-64 17-18 15-27 5 X 6 150-00 75-00 50-00 37-50 30-00 25-00 21-42 18-75 16-66 5 X 7 175-00 87-50 5«-33 43-75 35-00 29-16 25-00 21-87 19-44 5 X 8 200-00 100-00 66-66 50-00 40-00 33-33 28-57 25-00 22-22 5 X 9 225-00 112-50 75-00 56-25 45-00 37-50 32-14 28-12 25-00 5 X 0 250-00 125-00 83-33 62-50 50-00 41-66 35-71 31-25 27-77 5 Xll 275-00 137-50 91-66 68-75 55-00 45-83 39-28 34-37 30-55 5 X12 300-00 150-00 100-00 75-00 60-00 50-00 42-85 37-60 33-33 5 X13 325-00 162-50 108-33 81-25 65-00 54-16 46-42 40-62 36-11 5 X14 350-00 175-00 116-66 87-50 70-00 58-33 50-00 43-75 38-88 5 X15 375-00 187-50 125-00 93-75 75-00 62-50 53-57 46-87 41-66 Deflection in inches of Red Pine 5 inches deep, loaded with the weights in this table. Weight uniform. \ ly loaded J •003 -013 -030 •053 •082 •118 -161 •210 •266 Wt. suspended 1 from the middle J -005 •021 •047 •084 •131 -189 -258 •337 •426 *** For Scantlings 5^ inches deep, multiply the weights in this table by 1-21, and the deflections by -f5.=-909.f . * Example 1. — lied Pine 5 in. by 3 in., 5 feet long, with 15 cwts. uniformly loaded, (one- eighth the breaking weight) deflects -082 of an inch; and with 15 cwts. suspended from the middle, (one fourth the breaking weight) the deflection is -131 of an inch. f* Example 2.— Red Pine 5i in. by 3 in., 5 feet long, with 15 x 1-21 = 18-15 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '082 x ^ = -075 of an inch; and with 1815 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -131 X |o = .ii9 of ail SECOND SERIES — TABLES OF WEIGHTS. 57 TABLE V. Continued, SCANTLINGS, 5 in. and bk inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SlZK OF Scantlings, in inches. Depth. Breadth 5 5 5 *5 5 X 2 X 2i X 2i X 3 X 3i X 4 X 4i 5 6 X 7 X 8 X 9 XIO Xll 5 XI2 5 X13 5 X14 5 X15 length in feet, clear bearing. 10 I 11 I 12 13 14 I 15 I 16 17 18 I 20 WEIGHT IN CWTS. 5-00 5- 62 6- 25 7- 50 8- 75 To^ 11- 25 12- 50 13- 75 15-00 17-50 20-00 22-50 25-00 27-50 30-00 32-50 35-00 37-50 4- 64 5- 11 5- 68 6- 81 7- 95 9-09 10- 23 11- 36 12- 50 13- 63 15-90 18-18 20-45 22-72 25-00 27-27 29-54 31-81 34-09 4-16 4- 68 5- 20 6- 25 7- 29 8- 33 9- 37 10- 41 11- 45 12- 50 1^58 16-66 18-75 20-83 22-91 25-00 27-08 •29-16 31-25 3- 84 4- 32 4- 80 5- 76 6- 73 7- 69 8- 65 9- 61 10- 57 11- 53 l3^ 15-38 17-30 19-23 21-14 23^07 25- 00 26- 92 28-84 3-57 3-33 4-01 3-75 4-46 4-16 5-35 5-00 6-25 5-83 7-14 6-66 8-03 7-50 8-92 8-33 9-82 9-16 10-71 10-00 12-50 11-66 14-28 13-33 16-07 15-00 17-85 16-66 19-64 18-33 21-42 2000 23-21 21-66 25-00 23-33 26-78 25-00 3-12 3-51 3- 90 4- 68 5- 46 6- 25 7- 03 7- 81 8- 59 9- 37 10^ 12-50 14- 06 15- 62 17-18 18-75 20- 31 21- 87 23-43 2- 94 3- 30 3- 67 4- 41 5- 14 5- 88 6- 61 7- 35 8- 08 8-82 10- 29 11- 76 13- 23 14- 70 16-17 Tt^ 19- 11 20- 58 22-05 2- 77 3- 12 3- 47 4- 16 4-86 5- 55 6- 25 6- 94 7- 63 8- 32 9-72 11- 11 12- 50 13- 88 15-27 fe-ee 18- 05 19- 44 20- 83 2-50 2- 81 3- 12 3- 75 4- 37 '5'^60 5- 62 6- 25 6- 87 7- 50 8-75 10- 00 11- 25 12- 50 13- 75 16^6 16- 25 17- 50 18- 75 Deflection in inches of Red Pine 5 inches deep, loaded with the weights in this table. Weight \iniform- ly loaded Wt. suspended from the middle •329 •398 •473 •555 ■644 -739 •841 •950 1-065 •526 •636 •757 •889 1-031 1-183 1-346 1-520 1-704 1- 315 2- 104 * . For Scantlings 5i inches deep, multiply the weights in this table by 1-21, and the deflections by 44=-909.f * Example 1.— Red Pine 5 in. by 3 in., 10 feet long, with 7"50 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -329 of an inch; and with 7'50 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -526 of an inch. f » Example 2.— Red Pine 5i in. by 3 in., 10 feet long, with 7-5 x 1-21 = 9-075 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -329 x ^ = -299 of an inch ; and with 9-075 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -526 X .i_o = -478 of an inch. 58 SECOND SEEIES — TABLES OF WEIGHTS. TABLE VI. SCANTLINGS, 6 in. and 62^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Scantlings, in inches. Depth. Breadth LENGTH IN FEET, CLE AR BEARING. I 3 I 4 I 5 I 6 I 7— WEIGHT IN CWTS, 6X2 6 X 2k 6 X 2k 6X3 *6 X 3i 72-00 81-00 90-00 108-00 126-00 36-00 40-50 45-00 54-00 63-00 24-00 27-00 30-00 36-00 42-00 18-00 20-25 22-50 27-00 31-50 14-40 16-20 18-00 21-60 25-20 12- 00 13- 50 15-00 18-00 21-00 10- 28 11- 57 12- 85 15-42 18-00 6X4 6 X 4| 6X5 6 X 5i 6X6 144-00 162-00 180-00 198-00 216-00 72-00 81-00 90-00 99 00 108-00 48-00 64-00 60-00 66-00 72-00 36-00 40-50 45-00 49-50 54-00 28-80 32-40 36-00 39-60 43-20 24-00 27-00 30-00 33-00 36-00 20-57 2314 25-71 28-28 30-85 6 X 61- 6X7 6X8 6X9 6 XIO 234-00 252-00 288-00 324-00 360-00 117-00 126-00 144-00 16200 180-00 78-00 84-00 96-00 108-00 120-00 58-50 63-00 72-00 81-00 90-00 46-80 50-40 57-60 64-80 72-00 39-00 42-00 48-00 54-00 60-00 33-42 36-00 41-14 46-28 51-42 6 Xll 6 X12 6 X13 6 X14 6 X15 396-00 432-00 468-00 504-00 540-00 198-00 216-00 234-00 252-00 270-00 132-00 144-00 156-00 168-00 180-00 99-00 108-00 117-00 126-00 135-00 79-20 86-40 93-60 100-80 108-00 66-00 72-00 78-00 84-00 90-00 56-57 61-71 66-85 72-00 77-14 9-00 10-12 11 25 13-50 15-75 1800 20-25 22-50 24-75 27-00 29-25 31-50 36-00 40-50 45-00 49-50 54-00 58-50 63-00 67-60 8- 00 9- 00 10-00 1200 1400 Woo 18-00 20-00 22-00 24-00 2&00 2800 32-00 36-00 4000 4f00 48-00 52-00 56-00 60-00 Deflection in inches of Ked Pine 6 inches deep, loaded with the weights in this table Weightuniform- ) ly loaded J •003 •Oil -025 •044 •068 -099 -134 •175 -222 Wt. suspended 1 from the middle | •004 •018 •039 •070 •110 -158 -215 -280 -355 *** For Scantlings 6^ inches deep, multiply the weights in this table hy 1-1736. and the defl ections by i|=-923.f * Example 1.— Red Pine 6 in. by 3| in., 6 feet long, with 21 cwts. uniformly loaded, (one-eighth Ihe breaking weight) deflects -099 of an inch; and with 21 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -158 of an inch. f* Example 2.— Red Pine G^in. by 3| in., 6 feet long, with 21 x 1-1736 = 24-64 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "099 x ^ = -091 of an inch; and with 24-64 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -158x||. = -146 of an inch. & fa / SECOND SERIES — TABLES OF WEIGHTS. 59 TABLE VI. Continued. SCANTLINGS, 6 in. and 6i inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size op Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 10 11 12 I 1.3 I 14 I 15 I 16 I 17 I 18 | 20 Depth. Breadth WEIGHT IN CWTS. 6 6 6 6 *6 2 2i 2i 3 X 3i 7- 20 8- 10 9- 00 10-80 12-60 14-40 16-20 18- 00 19- 80 21-60 6 \ 61 6X7 6X8 6X9 6 XIO 23-40 25-20 28-80 32-40 36-00 6 Xll 6 X12 6 X13 6 X14 6 X15 39-60 43-20 46-80 50-40 54-00 6- 64 7- 36 8- 18 9- 81 11-45 13- 09 14- 72 16-36 18- 00 19- 63 21- 27 22- 90 26-18 29-45 32-72 36-00 39-27 42-54 45-81 49-09 6-00 6- 75 7- 50 9-00 10-50 12- 00 13- 50 15- 00 16- 50 18-00 19-50 21-00 24-00 27-00 30-00 33^ 3600 39-00 42-00 45-00 18- 00 19- 38 2216 24-92 27-69 30-46 33-23 36-00 38-76 41-53 5-14 5- 78 6- 42 7- 71 9 00 10- 28 11- 57 12- 85 14- 14 15- 42 16-71 1800 20-57 23-14 25-71 28^ 30-85 33-42 36-00 38-57 4- 80 5- 40 6- 00 7- 20 8- 40 9-60 10-80 1200 13- 20 14- 40 15- 60 16- 80 19-20 21-60 24-00 26-40 28-80 31-20 33-60 36-00 14- 62 15- 76 18-00 20-25 22-50 24-75 27-00 29-25 31-50 33-75 4-23 4- 76 5- 29 6- 35 7- 41 ~8^ 9-53 10- 58 11- 64 12- 70 13- 76 14- 82 16-94 19-06 21-17 23-29 25-41 27-52 29-64 31-76 4-00 4- 50 5- 00 6- 00 7- 00 8- 00 9- 00 10- 00 11- 00 12- 00 Tsm 14-00 16-00 1800 20-00 22-00 24-00 26-00 28-00 30-00 3- 60 4- 05 4- 50 5- 40 6- 30 T20 8- 10 900 9- 90 10-80 11- 70 12- 60 14-40 16-20 18-00 19^0 21-60 23-40 25-20 27-00 Deflection in inches of Red Pine 6 inches deep, loaded with the weights in this table. Weight utiiform ) ly loaded J •274 •331 •394 •463 •637 •616 -701 •792 -887 l'Q96 Wt. suspended 1 from the middle J -438 -630 •631 •741 •859 •986 1-122 1-267 1-420 1-753 *.){.* For Scantlings 6^ inches deep, multiply the weights in this table by -fff =M736, and the deflections by 4.f = -923.f * Example 1. — Red Pine 6 in. by 3t in., 12 feet long, with lO'SO cwts. uniformly loaded, (one-eighth the breaking weight) deflects -394 of an inch ; and with 10-50 cwts. suspended from the middle, (one-fuurth the breaking weight) the deflection is -631 of an inch. f * Example 2.— Red Pine 6Uu. by 3^ in., 12 feet long, with 10 b x 1-1736 = 12-32 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '394 x _i 2. = .363 of an inch; and with 12-32 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -631 X ^.| = -582 of an inch. 60 SECOND SERIES — TABLES OF WEIGHTS. TABLE VII. SCANTLINGS, 7 in. and Ik inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SizK OK length in feet, clear bearing. Scantlings, in inches. 1 1 2 1 3 1 4 1 5 1 6 7 8 Depth. Breadth. WEIGHT IN CWTS. 7X2 7 X 2i 7 X 2 k 7X3 7 X 3i 98-00 110-25 122-50 147-00 1 7 1 -50 49-00 55-12 61-25 73-50 85-75 32-66 36-75 40-83 49-00 57* 16 24-50 27-56 30-62 36-75 42-87 19-60 22-05 24-50 29-40 34-30 16-33 18-37 20-41 24-50 28-58 14^00 15^75 17-50 21-00 24-50 12- 25 13- 78 15-31 18-37 21-43 *7 X 4 7 X 4i 7X5 7 X 5J 7X6 196-00 220-50 245-00 269-50 294-00 98-00 110-25 122-50 134-75 147-00 65-33 73-50 81-66 89-83 98-00 49-00 55-12 61-25 67-37 73-50 39-20 44-10 49-00 53-90 58-80 32-66 36-75 40-83 44-91 49-00 28-00 31-50 35-00 38-50 42-00 27-56 30-62 33-68 36-75 7X7 7 X 7i 7X8 7X9 7 XIO 343-00 367-50 392-00 441-00 490-00 171-50 183-75 196-00 220-50 245-00 114-33 122-50 130-66 147-00 163-33 85-75 91-87 98-00 110-25 122-50 68-60 73-50 78-40 88-20 98-00 57-16 61-25 65-33 73-50 81-66 49-00 52-50 56-00 63-00 70-00 "42^ 45-93 49-00 55-12 6V25 7 Xll 7 X12 7 X13 7 X14 7 X15 539-00 588-00 637-00 686-00 735-00 269-50 294-00 318-50 343-00 367-50 179-66 196-00 212-33 228-66 245-00 134-75 147-00 159-25 171-50 183-75 107-80 117-60 127^40 137-20 147-00 89-83 98-00 106-16 114-33 122-50 77-00 84-00 91-00 98-00 105-00 "67"^ 73^50 79-62 85-75 91-87 Deflection in inches of Red Pine 7 inches deep, loaded with the weights in this table. Weight uniform- ) ly loaded J -002 -009 -021 •038 -059 •085 •115 •150 Wt. suspended ] from the middle j -004 •015 -034 -060 -094 •135 •184 •240 *** For Scantlings 7h inches deep, multiply the weights in this table by 4-f4-= 1-148, and the deflections by ^=-93'd.j- * Example 1. — Red Pine 7 in. by 4 in., 7 feet long, with 28 cwts. uniformly loaded, (one- eighth the breaking weight) deflects -115 of an inch ; and with 28 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 'ISi of an inch. f * Example 2.— Red Pine 7^ in. by 4 in., 7 feet long, with 28 x 1-148 = 32-14 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -115 x -933 = -107 of an inch; and with 32-14 cwts. suspenlbd from the middle, (one-fourth the breaking weight) the deflection is -184 X -933 = -172 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 61 TABLE VII. Continued. SCANTLINGS, 7 in. and inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of length in I'RET, CLEAR BEARING. 0CANT1.IN08, in inches. 9 i 10 11 12 13 14 15 16 WEIGHT IN CWTS. 7 X ^ lU OO if OU 8*90 o lo 7 Do 7.AA 7 UU 6'12 7 X 2i 12-26 11-02 10*02 A. 1 O 9-18 o 48 7.Q7 / o7 7-36 6-89 7 X 21- 13-61 12-25 1 1*13 10-20 Q.7^ o 70 8-16 7-65 7X3 16-33 14-70 13^36 12 25 I 1 .O A I I oO lU 01) 9-80 9-18 7 X 3i 19-06 17-15 XrJ ijij 14-29 13-19 12-25 11-43 10-71 J y ou 17-81 16-33 15-07 14-00 xO \jyJ 12-25 7 X 4i 24-60 22-05 20-04 18-37 16-96 16-75 14-70 13-78 7X5 27-22 24-50 22-27 20-41 18-84 17-60 16-33 15-31 7X5^ 29-94 26-95 24-50 22-45 20-73 19-26 17-96 16-84 7X6 32-66 29-40 36-72 24-50 22-61 21-00 19-60 18-37 7X7 38-11 34-30 31-18 28-68 26-38 24-50 22-86 21-43 7 X 7i 40-83 36-75 33-40 30-62 28-26 26-25 24-50 22-96 7X8 43-55 39-20 36-63 32-66 30- 15 28-00 26-13 24-50 7X9 49-00 44-10 40-09 26-75 33-92 31-60 29-40 27-56 7 XIO 54-44 49-00 44-54 40-83 37-69 35-00 32-66 30-62 7 Xll 59-88 63-90 49-00 44-91 41-46 38-50 35-93 33 68 7 X12 65-33 58-80 53-45 49-00 45-23 42-00 39-20 36-75 7 X13 70-77 63-70 57-90 53-08 49-00 45-50 42-46 39-81 7 X14 76-22 68-60 62-36 67-16 52-76 49-00 45-73 42-87 7 X15 81-66 73-50 66-81 61-25 66-63 52-60 49-00 46-93 Deflection in inches of Red Pine 7 inches deep, loaded with the weigh ;s in this table. Weight uniform. ) ly loaded J -190 -235 284 -338 -397 -460 -528 -601 Wt. suspended ) •304 •376 •465 -641 •635 -736 •845 -962 from the middle J For Scantlings 7^ inches deep, multiply the weights in this table by 4f^= 1-148, and the deflections by i-f=-933.t * Example 1.— Eed Pine in- by 4 in., 14 feet long, with 14 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -460 of an inch; and with 14 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -736 of an inch. f* Example 2.— Red Pine, in. by 4 in., 14 feet long, with 14 x 1-148 = 16-07 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "46 x -933 = 429 of an inch ; and with 16-07 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -736 X -933 = -687 of an inch. 02 SECOND SERIES — TABLES OF WEIGHTS. TABLE VII. Continued. SCANTLINGS, 7 in. and Ik inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of Scantlings, LENGTH IN FEET, CLEAR BEARING. in inches. 17 18 19 20 21 22 23 24 Depth Breadth. WEIGHT IN CWTS. 7 X 2 5*76 5-44 5-15 zl-QO A-fifi 4 /cO 7 X 2i 6-48 6-12 OV/ O O I O V I A •'7Q 4 oy 7 X 2i 7'20 6*80 U 1 ,^ o Oo O OV O O l\' 7 X 3 8-64 8-16 1 oo D DO D oy 7 X 3^ 10-08 9-52 9-02 8-57 8-16 7-7Q 7-1 d. *7 X 4 11-52 10-88 10-31 9-80 9-33 8-90 8-52 8-16 7 X 4i 12-97 12-25 11-60 11-02 10-50 1002 9-58 9-18 7 X 5 14-41 13-61 12-89 12-25 11-66 1113 10-65 10-20 7 X 5i 15-85 14-97 14-18 13-47 12-83 12-25 11-71 11-22 7 X 6 17-29 16-33 15-47 14-70 14-00 13-36 12-78 12-25 7 X 7 20-17 1905 18-05 17-15 16-33 15-59 14-91 14-29 7 X 7i 21-61 20-41 19-34 18-37 17 50 16-70 15-97 15-31 7 X 8 23-05 21-77 20-63 19-60 18-66 17-81 17-04 16-33 7 X 9 25-94 24-50 23-21 22-05 21-00 20-04 19-17 18-37 7 XIO 28-82 27-22 25-78 24-50 23-33 22-27 21-30 20-41 7 Xll 31-70 29-94 28-36 26-95 25-66 24-50 23-43 '22^ 7 X12 34-58 32-66 30-94 29-40 28-00 26-72 25-56 24-50 7 X13 37-47 35-38 33-52 31-85 30-33 28-95 27-69 26-54 7 X14 40-35 38-11 36-10 34-30 32-66 31-18 29-82 28-58 7 X15 43-23 40-83 38-68 36-75 3500 33-40 31-95 30-62 Deflection in inches of Red Pine 7 inches deep, loaded with the weights in this table. Weightunifonn- 1 ly loaded J -678 •761 -848 •939 1-035 1-136 1-242 1-352 Wt. suspended ) from the middle j 1-086 1-217 1-356 1-503 1-657 1-818 1-987 2-164 For Scantlings 7i inches deep, multiply the weights in this table by 1-148, and the deflections by 44=-933.f * Example 1.— Red Pine 7 in. by 4 in., 21 feet long, with 9-33 cwts. uniformly loaded, (one-eighth the breaking weight) deflects 1-085 inciies; and with 9-33 cwts. suspended from the middle, (one-fom-th the breaking weight) the deflection is 1-657 inches. t* Example 2.— Red Pine 7k in. by 4 in., 21 feet long, with 9-33 x 1-148 = 10-71 cwts. uuifoi-mly loaded, (one-eighth the breaking weight) deflects 1-035 x -933 = -966 of an inch ; and with 10-71 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 1-657 X -933 = 1-546 inches. SECOND SERIES— TABLES OF WEIGHTS. 63 TABLE VIII. SCANTLINGS, 8 in. and 8i inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-1'ourth of the same, when suspended from the middle. Size ov Scantlings, in inches. Depth. Breadth length in feet, clear bearing. 6 weight in cwts. 8 X 2 128-00 64-00 42-66 32-00 25-60 21-33 18-28 8 X 2i 144-00 72-00 48-00 36-00 28-80 24-00 20-57 8 X 2i 160-00 80-00 53-33 40-00 32-00 26-66 22-85 8 X 3 192-00 96-00 64-00 48-00 38-40 32-00 27-42 8 X 31 224-00 112-00 74-66 56-00 44-80 37-33 32-00 8 X 4 256-00 12tt-00 85-33 64-00 51-20 42-66 36-57 *8 X 4i 288-00 144-00 96-00 72-00 57-60 48-00 41-14 8 X 5 320-00 160-00 106-66 80-00 6400 53-33 45-71 8 X 5h 352-00 176-00 117-33 88-00 70-40 58-66 50-28 8 X 6 384-00 192-00 128-00 96-00 76-80 64-00 54-85 8 X 7 448-00 224-00 149-33 112-00 89-60 74-66 64-00 8 X 8 512-00 256-00 170-66 128-00 102-40 85-33 73-14 8 X 8i 544-00 272-00 181-33 136-00 108-80 90-66 77-71 8 X 9 576-00 288-00 192-00 144-00 115-20 96-00 82-28 8 XIO 640-00 320-00 213-33 160-00 128-00 106-66 91-42 8 XII 704-00 352-00 234-66 176-00 140-80 117-33 100-57 8 X12 768-00 384-00 256-00 192-00 153-60 128-00 109-71 8 X13 832-00 416-00 277-33 208-00 166-40 138-66 118-85 8 X14 896*00 448-00 298-66 224-00 179-20 149-33 128-00 8 X15 960-00 480-00 320-00 240-00 192-00 160-00 137-14 16-00 18-00 20-00 24-00 28-00 ~32-00 36-00 40-00 44-00 48-00 56-00 64-00 68-00 72-00 80-00 88-00 96-00 104-00 112-00 120-00 Deflectiou in inches of Red Pine 8 inches deep, loaded with the weights iu this tahle. Weight uniform- ly loaded Wt. suspended from (he middle -002 •008 -018 -033 -051 -074 -101 -003 -013 -030 -053 -082 -118 -161 -131 •210 *** For Scantlings 81 inches deep, multiply the weights in this table by M289, and the deflections by 4-f =-941.t * Example 1. — Red Pine 8 in. hy 4^ in., 8 feet long, with 36 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '131 of an inch ; and with 86 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is "210 of an inch. t* Example 2.— Red Pine 8h in. by 4^ in., 8 feet long, with 36 x 1-1289 = 40-64 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '131 x '941 = 123 of an inch; and with 40-64 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -21 x -941 = -198 of au inch. 64 SECOND SERIES — TABLES OF WEIGHTS. TABLE VIII. Continued. SCANTLINGS, 8 in. and 8^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same when suspended from the middle. SiZB OF Scantlings, in inches. LENGTH IN FEET CLEAR BEARING. 9 10 12 13 14 15 16 Depth. Breadth WEIGHT IN CWTS. 8X2 8 X 2i 8 X 24 8X3 8 X 34 14-22 16- 00 17- 77 21-33 24-88 12-80 14-40 16-00 19-20 22-40 11-63 1309 14-54 17-45 20-36 10-66 12- 00 13- 33 16-00 18-66 9-84 11- 07 12- 30 14-76 17-23 9^14 10- 28 11- 42 13-71 16-00 8^53 9-60 10-66 12-80 14-93 8- 00 9- 00 10-00 12-00 14-00 8X4 *8 X 44 8X5 8 X 54 8X6 28-44 32-00 35-55 39-11 42-66 25-60 28-80 32-00 35-20 38-40 23-27 26-18 29-09 32-00 34-90 21-33 2400 26-66 29-33 32-00 19-69 22-15 24-61 27-07 29-53 18-28 20-57 22-85 25-14 27-42 17-06 19-20 21-33 23-46 25-60 16^00 18-00 20-00 22-00 24-00 8X7 8X8 8 X 84 8X9 8 XIO 49-77 56-88 60-44 64-00 71-11 44-80 51-20 54-40 57-60 64-00 40-72 46-54 49-45 52-36 58-18 37^33 42^66 45-33 48-00 53-33 34-46 39-38 41-84 44-30 49-23 32-00 36-57 38-85 41-14 45^71 29-86 34- 13 36 26 38-40 42^66 28^ 32-00 34-00 36-00 40-00 8 Xll 8 X12 8 X13 8 X14 8 X15 78-22 85-33 92-44 99-55 106-66 70-40 76-80 83-20 89-60 96-00 64-00 69-81 75-63 81-45 87-27 58-66 64^00 69-33 74-66 80-00 54-15 59-07 64-00 68-92 73-84 50^28 54^85 59^42 64-00 68-57 46-93 51-20 55-46 59-73 64-00 'Woo 48-00 52-00 56-00 60-00 Deflection in inches of Red Pine 8 inches deep, loaded with the weights in this table. Weight aniform- ) ly loaded. ) •166 •205 •249 -296 •347 •403 •462 •526 Wt. suspended ) from the middle ) •266 •329 -398 -473 •556 •644 •740 •841 For Scantlings 84 inches deep, multiply the weights in this table by f||= 1-1289, and the deflections by 4f =-941.t * Example 1. — Red Pine Sin. by 4i in., 16 feet long, with 18 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '526 of an inch ; and with 18 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -841 of an inch. f * Example 2.— Red Pine 8i in. by 4§ in., 16 feet long, with 18 x 1-1289= 20-32 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -526 x -941 = '495 of an inch; and with 20-32 cwts. suspended from the middle, (one-fourth the breaking weight) the deflec- tion is -841 X -941 = -791 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 65 TABLE VIII. Continued. SCANTLINGS, 8 in. and 8^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN TEET, CLEAR BEARING. 17 18 19 20 21 22 23 24 Depth Breadth. WEIGHT IN CWTS. 8 X 2 7-52 7-11 6-73 6-40 6-09 5-81 5-56 5-33 8 X 2i 8-47 8-00 7-57 7-20 6-85 6-54 6-26 6-00 8 X 2i 9-41 8-88 8-42 8-00 7-61 7-27 6-95 6-66 8 X 3 11-29 10-66 1010 9-60 9-14 8-72 8-34 8-00 8 X Si 1317 12-44 11-78 11-20 10-66 10-18 9-73 9-33 8 X 4 15-05 14-22 13-47 12-80 12-19 11-63 1113 10-66 *8 X 4i 16-94 16-00 15-15 14-40 13-71 13-09 12-52 1200 8 X 6 18-82 17-77 16-84 16-00 15-23 14-54 13-91 13-33 8 X 5i 20-70 19-55 18-52 17-60 16-76 16-00 15-30 14-66 8 X 6 22-58 21-33 20-21 19-20 18-28 17-45 16-69 16-00 8 X 7 26-35 24-88 23-57 22-40 21-33 20-36 1947 18^6 8 X 8 30-11 28-44 26-94 25-60 24-38 23-27 22-26 21-33 8 X 8i 32-00 30-22 28-63 27-20 25-90 24-72 23-65 22-66 8 X 9 33-88 32-00 30-31 28-80 27-42 26-18 25-04 24-00 8 X 10 37-64 35-55 33-68 32-00 30-47 29-09 27-82 26-66 8 Xll 41-41 39-11 37-05 35-20 3352 32-00 30-60 29-33 8 X12 45- 17 42-66 40-42 38-40 36-57 34-90 33-39 32-00 8 X13 48-94 46-22 43-78 41-60 39-61 37-81 36-17 34-66 8 XI4 52-70 49-77 47-15 44-80 42-66 40-72 38-95 37-33 8 X15 56-47 53-33 50-52 48-00 45-71 43-63 41-73 40-00 Deflection in inches of Red Pine 8 inches deep, loaded with the weights in this table. Weightuuiform. ] ly loaded, J -594 -666 -742 -822 -906 -994 1-087 1-183 Wt. suspended ] from the middle J -950 1-065 1-187 1-315 1-450 1-591 1-739 1-893 *#* For Scantlings 8 J inches deep, multiply the weights in this table by 1-1289, and the deflections by ^=-Ml.f * Example 1. — Bed Pine 8 in. by 4i iu., 24 feet lon^, with 12 cwts. uniformly loaded, (oue-eiorhth the breaking weight) deflects 1-183 inches; and with 12 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 1-893 inches. f * Example 2.— Red Pine 8^ in. by 4^ jii., 24 feet long, with 12 x 1-1289 = 13-54 cwts. uniformly loaded, (one-eighth the breaking weight) deflects 1-183 x -941 = 1-113 inches; and with 13-54 cwts. suspended from the middle, (oue-fourth the breaking weight) the deflectioa is 1-893 X -941 = 1-781 inches. 66 SECOND SEKIES — TABLES OF WEIGHTS. TABLE IX. SCANTLINGS, 9 in. and H inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. LENGTH in FEET, CLEAR BEARING. iSCANTLINGS, in inches. 1 2 3 4 5 6 7 8 Depth. Breadth. WEIGHT IN CWTS. 9X2 9 X 2i 9 X 2i 9X3 9 \ 3k 162-00 182-25 202-50 243-00 283-50 81-00 9112 101-25 121-50 141-75 54-00 60-75 67-50 81-00 94-50 40^50 45-56 50-62 60-75 70-87 32-40 36-45 40-60 48-60 56-70 27^00 30-37 33-75 40-50 47-25 23-14 26-03 28-92 34-71 40-50 20^25 22^78 25-31 30-37 35-43 9X4 9 X 4i *9 X 5 9 X 5i 9X6 324-00 364-50 405-00 445-50 486-00 162-00 182-25 202-50 222-75 243-00 108-00 121-50 135-00 148-50 162-00 81-00 91-12 101-25 111-37 121-50 64-80 72-90 81-00 89-10 97-20 54-00 60-75 67-50 74-25 81-00 46-28 52-07 57-85 63-64 69-42 40-50 45-56 50-62 55-68 60-75 9X7 9X8 9X9 9 X 9i 9 XIO 567-00 648-00 729-00 769-50 810-00 283-50 324-00 364-50 384-75 405-00 189-00 216-00 243-00 256-50 270-00 141-75 162-00 182-25 192-37 202-50 113-40 129-60 145-80 153-90 162-00 94-50 108-00 121-50 128-25 135-00 81-00 92-57 104-14 109-92 115-71 70-87 81-00 91-12 96-18 101-25 9 Xll 9 X12 9 X13 9 X14 9 X15 891-00 972-00 1053-00 1134-00 1215-00 445-50 486-00 526-50 567-00 607-50 297-00 324-00 351-00 378-00 405-00 222-75 •243-00 263-25 283-50 303-75 178-20 194-40 210-60 226-80 243-00 148-50 162^00 175-50 189-00 202-50 127-28 138-85 150-42 162-00 173-57 111-37 121-50 131-62 141-75 151^87 Deflection in inches of Red Pine 9 inches deep, loaded with the weights in this tahle. Weightuniform- 1 ly loaded j •002 -007 •016 •029 •046 -066 •089 •117 Wt suspended 1 from the middle J -003 •012 •026 -047 •073 -105 •143 •187 For Scantlings 9^ inches deep, multiply the weights in this table by f|i=M142, and the deflections by 4|z=-947.t * Example 1. — Red Pine 9 in. by 5 in., 5 feet long, with 81 cvrts. uniformly loaded, (one-eighth the breaking weight) deflects -046 of an inch ; and with 81 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -073 of an inch. t* Example 2.— Red Pine 9^ in. by 5 in., 5 feet long, with 81 x 1-1142 = 90-25 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -046 x -94? = -044 of an inch ; and with 90-25 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -073 x -947 = '069 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 67 TABLE IX. Continued. SCANTLINGS, 9 in. and 9h inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 10 11 1 12 13 14 15 16 Depth Breadth. WEIGHT IN CWTS. Q X 2 18-00 16-20 14-72 13-50 12-46 11-57 10-80 10-12 9 X 2i 20"25 18-22 16-56 15-18 14-01 13-01 12-15 11-38 9 X 2i 22 '50 20-25 18-40 16-87 15-57 14-46 13-50 12-65 9 X 3 27-00 24-30 22-09 20-25 18-69 17-35 16-20 15-18 9 X 3i O 1 00 28-35 25*77 23-62 21-80 20-25 18-90 17-71 9 X 4 36-00 32-40 29-45 27-00 24-92 23-14 21-60 20-25 9 X 4i 40-50 36-45 33-13 30-37 28-03 26-03 24-30 22-78 X 5 45-00 40-50 36-81 33-75 31-15 28-92 27-00 25-31 9 X 5i 49-50 44-55 40-50 37-12 34-26 31-82 29-70 27-84 9 X 6 54-00 48-60 44-18 40-50 37-38 34-71 32-40 30-37 9 X 7 63-00 56-70 51-54 47-25 43-61 40-50 37-80 35-43 9 X 8 72-00 64-80 58-90 54-00 49-84 46-28 43-20 40-50 9 X 9 81-00 72-90 66-27 60-75 56-07 52-07 48-60 45-56 9 X 9h 85-50 76-95 69-95 64-12 59-19 54-96 51-30 48-09 9 XIO 90-00 81-00 73-63 67-50 62-30 57-85 54-00 50-62 9 Xll 99-00 89-10 81-00 74-25 68-53 63-64 59-40 55-68 9 X12 108-00 97-20 88-36 81-00 74-76 69-42 64-80 60-75 9 X13 117-00 105-30 95-72 87-75 81-00 7.5-21 70-20 65-81 9 X14 126-00 113-40 103-09 94-50 87-23 81-00 75-60 70-87 9 X15 135-00 121-50 110-45 101-25 93-46 86-78 81-00 75-93 Deflection in inches of Red Pine 9 inches deep, loaded with the weights in this table. Weight uniform. ) ly loaded ) •148 -183 •221 •263 •309 -358 -411 -467 Wt suspended ) from the middle / -237 -292 -354 •421 -494 -573 -657 -748 *»* For Scantlings 9^ inches deep, multiply the weights in this table by |4^= 1-1142, and the deflections by f|=-947.t * Example 1. — Red Pine 9 in. by 5 in., 9 feet long, with 45 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -148 of an inch ; and with 45 cwts. suspended from the middle, (one-fourth the breaJdng weight) the deflection is -237 of an inch. f* Example 2.— Red Pine 9i in. by 5 in., 9 feet long, with 45 x 1-1142 = 50-13 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -148 x -947 = "140 of an inch ; and with 5013 cwts. suspended from the middle, (one-fourth the breaking weiglit) the deflection is -237 x "947 = -224 of an inch. 68 SECOND SERIES — TABLES OF WEIGHTS. TABLE IX. Continued. SCANTLINGS, 9 in. and 9^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 17 1 18 19 20 21 22 23 24 Depth. Breadth WEIGHT IN CWTS. y X 2 9-62 9-00 8-52 8-10 7-71 7-36 704 O'tO Q y X 2i 10-72 10-12 9-59 9-11 8-67 8-28 7-92 7 oy Q y X 2i 11-91 1 1-25 10-65 10-12 9-64 9-20 8 •80 o 4o y X 3 14-29 13-50 12-78 1215 11-57 11 04 10-56 10-12 o y X 3^ 15-75 14-92 14-17 13-50 12-88 12-32 11-81 9 X 4 19-05 1800 17-05 16-20 15-42 14-72 14-08 13-50 9 X 4i 21-44 20-25 19-18 18-22 17-35 16-56 15-84 15-18 9 X 5 23-82 22-50 21-31 20-25 19-28 18-40 17-60 16-87 9 X 5^ 26-20 24-75 23-44 22-27 21-21 20-25 19-36 18-56 9 X 6 28-58 27-00 25-57 24-30 23-14 22-09 21-13 20-25 9 X 7 33-35 31-50 29-84 28-35 2700 25-77 24-65 23-62 9 X 8 38-11 36-00 34-10 32-40 30-85 29-45 28-17 27-00 9 X 9 42-88 40-50 38-36 36-45 34-71 33-13 31-69 30-37 *9 X 9* 45-26 42-75 40-50 38-47 36-64 34-97 33-45 32-06 9 XIO 47-64 4500 42-63 40-50 38-57 36-81 35-21 33-75 9 Xll 52-41 49-50 46-89 44-55 42-42 40-50 38-73 37-12 9 X12 57-17 54-00 51-15 48-60 46-28 44-18 42-26 40-50 9 X13 61-94 58-50 55-42 52-65 50-14 47-86 45-78 43-87 9 X14 66-70 63 00 59-68 56-70 54-00 51-54 49-30 47-25 9 X15 71-47 67-50 63-94 6075 57-85 55-22 52-82 50-62 Deflection, in inches of Red Pine 9 inches deep, loaded with the weights in this tahle. Weight uniform. ) ly loaded ) -528 •592 •659 -730 -805 -884 -966 1-052 Wt. suspended ) from the middle | -844 •947 1-055 1-169 1-289 1-414 1-546 1-683 *** For Scantlings 9 J inches deep, multiply the weights in this table by |4^= 1-1142, and the deflections by 4|=-947.t * Example 1. — Red Pine 9 in. by 9^ in., 17 feet long, with 45-26 cwts. uniformly- loaded, (one-eighth the breaking weight) deflects -528 of an inch ; and with 45-26 cwts. sus- pended from the middle, (one-fourth the breaking weight) the deflection is -844 of an inch. f* Example 2.— Red Pine 9i in. by 9^ in., 1? feet long, with 45-26 x 1-1142 = 50-43 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -528 x -947 = '500 of an inch ; and with 50-42 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -844 x -947 = "799 of an inch. SECOND SERIES — TABLES OF WEIGHTS, 69 TABLE X. SCANTLINGS, 10 in. and lOh inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SlZB OF Scantlings, LENGTH IN I'EET, CLEAR bearing. in inches. 1 2 1 3 1 4 1 5 1 6 1 7 1 8 Depth. Breadth. weight in cwts. lOX 2 200'00 100-00 66-66 50*00 40-00 33-33 28-57 2500 10 X 2i 225*00 112-50 75-00 56*25 45-00 37-50 32- 14 28-12 10 X 2h 250*00 1 25-00 83-33 62*50 50-00 41-66 35-71 31*25 10 X 3 oOO'OO 150-00 100-00 75-00 60-00 50-00 42-85 37-50 10 X 3i 350*00 tJz^xJ \J\J 175*00 1 1 V o # o\j 70-00 oo oo TtO to 10 X 4 400-00 200-00 133*33 loFoo 80-00 66-66 57-14 5000 10 X 4i 450-00 225-00 150*00 112-50 90*00 75-00 64*28 56-25 10 X 5 500-00 250-00 \66-66 125-00 100*00 83-33 71-42 62-50 10 X 5i 550-00 275*00 183*33 137-50 110*00 91*66 78-57 68*75 *10X 6 600^00 30000 200 00 150-00 120*00 100-00 8571 75*00 lOX 7 700-00 350-00 233-33 175-00 140*00 116-66 100-00 87-50 lOX 8 800-00 400*00 266-66 200*00 160-00 133*33 114-28 100-00 10 X 9 900-00 450-00 300 00 225*00 180-00 150-00 128-57 112 50 10X10 1000-00 500-00 333-33 250*00 200-00 166-66 142-85 12500 lOXlOi 1050-00 525*00 350*00 262-50 210-00 175-00 150-00 131-25 10X11 1100-00 550*00 366*66 275*00 220-00 183-33 157-14 137-50 10X12 1200-00 600*00 400*00 300*00 240-00 200*00 171-42 150-00 10X13 1300-00 650*00 433*33 325*00 260-00 216-66 185-71 162-50 10X14 1400-00 700*00 466-66 350-00 28000 233*33 200-00 175-00 10X15 1500-00 750*00 500*00 37500 300-00 250*00 214-28 187-60 Deflection in inches of Red Pine 10 inches deep, loaded with the weights in this table. Weight unirorm- ly loaded Wt, suspended from the middle -002 -007 ■015 -026 •041 *059 -081 -003 •Oil -024 •042 -066 •095 •129 •105 •168 For Scantlings 10^ inches deep, multiply the weights in this table by m= 1-1025, and the deflections by f?^=-952.f * Example 1. — Red Pine 10 in. by 6 in., 6 feet long, with 100 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '059 of an inch ; and with 100 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is '095 of an inch. f* Example 2.— Red Pine \0k in. by 6 iu., 6 feet long, with 100 x 1-1025 = 110-25 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '059 x '952 = '056 of an inch ; and with 110-25 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 095 X -952 = -090 of an inch. K ■ 70 SECOND SERIES — TABLES OF WEIGHTS. TABLE X. Continued. SCANTLINGS, 10 in. and 10^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of in inches. LENGTH IN FEET, CLEAR BEARING. 9 10 1 12 1 13 1 14 1 15 16 Depth. Breadth. WEIGHT IN CWTS. lOX 2 10 X 2i 10 X 2i 10 X 3 10 X 3i 22-22 25-00 27-77 33-33 oo oo 20-00 22-50 25-00 30-00 oo uu 18-18 20-45 22-72 27-27 1 -SI o 1. ol 16^66 18-75 20-83 25-00 4\) 10 15-38 17-30 19-23 23-07 14-28 16- 07 17- 85 21-42 <;0 UU 13-33 15- 00 16- 66 20-00 12-50 14- 06 15- 62 18-75 07 lOX 4 10 X 4i 10 X 5 10 X 6\ *10X 6 44-44 50-00 55-55 61-11 66-66 40-00 45-00 50-00 55-00 60-00 36-36 40-90 45-45 50-00 54-54 33-33 37-50 41-66 45-83 50-00 30-76 34-61 38-46 42-30 46-15 28-57 32-14 35-71 39-28 42-85 26-66 30-00 33-33 36-66 40-00 "25^ 28-12 31-25 34-37 37-50 lOX 7 10 X 8 10 X 9 10X10 lOXlOi 77-77 88-88 100-00 111-11 116-66 70-00 80-00 90-00 100-00 105-00 63-63 72-72 81-81 90-90 95-45 58-33 66-66 75-00 83-33 87-50 53-84 61-63 69-23 76-92 80-76 50-00 57-14 64-28 71-42 75-00 46-66 53-33 60-00 66-66 70-00 43-75 50-00 56-25 62-50 6562 10X11 10X12 10X13 10X14 10X15 122-22 133-33 144-44 155-55 110-00 120-00 130-00 140-00 150-00 100-00 109-09 118-18 127-27 136-36 91-66 100-00 108-33 116-66 125-00 84-61 92-30 100-00 107-69 115-38 78-57 85-71 92-85 100-00 107-14 73-33 80-00 86-66 93-33 100-00 68-75 75-00 81-25 87-60 93-75 Deflection in inches of Ked Pine 1 0 inches deep, loaded with the weights in this table. Weightuniform- ) ly loaded j 133 -164 •199 -237 •278 -322 -370 •421 Wt. suspended I from the middle f 213 •263 •318 -379 -444 -515 -592 -673 For Scantlings lOi inches deep, multiply the weights in this table by ^4^= 1-1025, and the deflections by f ° — -952.t * Example 1.— lied Pine 10 in. by 6 in., 10 feet long, with 60 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "164 of an inch ; and with 60 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is '263 of an inch. f* Example 2.— Red Pine 10.i in. by 6 in., 10 feet long, with -60 x 1-1025 = 66-15 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -164 x •952 = -156 of an inch; and with 66-15 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -263 X -952 = -250 of an inch. SECOND SERIES TABLES OF WEIGHTS. 7 1 TABLE X. Continued. SCANTLINGS, 10 in. and 10^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. length in feet. CLEAR BEARING. 17 18 19 20 21 22 23 24 Depth. Breadth. weight in cwts. lOX 2 10 X 21 10 X 2k 10 X 3 lOX 3i 11-76 13- 23 14- 70 17-64 11- 11 12- 50 13- 88 16-66 10- 52 11- 84 13-15 15-78 lo 42 10- 00 11- 25 12- 50 15-00 9-52 10- 71 11- 90 14-28 1 D DO 9-09 10- 22 11- 36 13-63 1 A, OA 8- 69 9- 78 10-86 13-04 8- 33 9- 37 10-41 12-50 1 A-KQ. 14 Oo lOX 4 10 X 4i 10 X 5 10 X 5* *10X 6 23-52 26-47 29-41 32-35 35-29 22-22 25-00 27-77 30-55 33-33 21-05 23-68 26-31 28-94 31-57 20-00 22-50 25-00 27-50 30-00 19-04 21-42 23-80 26-19 28-57 18-18 20-45 22-72 25-00 27-27 17-39 19-66 21-73 23-91 26-08 16-66 18-75 20-83 22-91 25 00 10 X 7 lOX 8 10 X 9 10X10 lOXlOi 41-17 47-05 52-94 58-82 61-76 38-88 44-44 50-00 55-55 58-33 36-84 42-10 47-36 52-63 55-26 35-00 40-00 45-00 50-00 52-50 33-33 38-09 42-85 47-61 50-00 31-81 36-36 40-90 45-45 47-72 30-43 34-78 39-13 43-47 45-65 29-16 33-33 37-50 41-66 43-75 10X11 10X12 10X13 10X14 10X15 64-70 70-58 76-47 82-35 88-23 61-11 72-22 11-11 83-33 67- 89 63-15 68- 42 73-68 78-94 55-00 60-00 65-00 70-00 75-00 52-38 57-14 61-90 66-66 71-42 50-00 54-54 59-09 63-63 68-18 47-82 52-17 56-52 60-86 65-21 45-83 50-00 54-16 58-33 62-50 Deflection in inches of Red Pine 10 inches deep, loaded with the weights in this table. Weightauiform. ) ly loaded J •475 532 •593 -657 •725 -795 -869 -947 Wt. suspended \ from the middle j -760 852 •949 1-052 1-160 1-273 1-391 1-515 For Scantlings 10| inches deep, multiply the weights in this table by ^=1-1025, and the deflections by |4=-952.f . * Example 1. — Red Pine 10 in. by 6 in., 18 feet long, with 33-33 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "532 of an inch; and with 33-33 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -852 of an inch. f* Example 2.— Red Pine lOi in. by 6 in., 18 feet long, with 33'83 x 1-1025 = 36-75 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '532 x -952 = '506 of an inch; and with 36"75 cwts. suspended from the middle, (one-fourth the breaking weight) the deflec- < ion is -852 X -952 = -811 of an inch. 72 SECOND SERIES — TABLES OF WEIGHTS. TABLE XI. SCANTLINGS, 11 in. and lU inches Deep. The weights in this table are — On E-EiGHTH of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, LENGTH IN FEET, CLEAR BEARING. in inches. 1 3 4 6 7 8 WEIGHT IN CWTS. 1 1 V o 242-00 121-00 80-66 60-50 48-40 40-33 34-57 30-25 11V 0 1 272-25 136-12 90-75 68-06 54-45 45-37 38-89 34-03 11 X 2I 302-50 151-25 100-83 75-62 60-50 50-41 43-21 37-81 11X3 363-00 181-50 121-00 90-75 72-60 60-50 51-85 45-37 11 X 3i 423-50 211-75 141-16 105-87 84-70 70-58 60-50 52-93 11V A 484-00 242-00 161-33 121-00 96-80 80 66 69-14 60-50 11V AX. 544-50 27225 181-50 136-12 108-90 90-75 77-78 68-06 605-00 302-50 201-66 151-25 12100 100-83 86-42 75-62 IIX 6\ 665-50 332-75 221-83 166-37 133-10 11091 95-07 83-18 IIX 6 726-00 363-00 24200 181-50 145-20 121-00 103-71 90-75 *11X 7 847-00 423-50 282-33 211-75 169^40 141-16 121-00 105-87 IIX 8 968-00 48400 322-66 242-00 193-60 161-33 138-28 121-00 IIX 9 1089-00 544-50 363-00 272-25 217-80 181-50 155-57 136-12 11 XIO 121000 605 00 403-33 302-50 24200 201-66 172-85 151-25 11X11 1331-00 665-50 443-66 332-75 266-20 221-83 19014 166-37 11 XUi 1391-50 695-75 463-83 347-87 278-30 231-91 198-78 173-93 11X12 1452-00 72600 484-00 363-00 290-40 242-00 207-42 181-50 11 X13 1573-00 786-50 524-33 ;J93-25 314-60 262 16 224-71 196-62 11 X14 1694-00 847-00 564-66 423-50 338-80 282-33 242-00 211-75 11 X15 1815-00 907-50 605-00 453-75 36300 302-50 259-28 226-87 Deflection in inches of Red Pine 11 inches deep, loaded with the weights in this tahle. Weight uniform. ] ly loaded. / Wt. suspended | from the middle ) -001 -006 •013 •024 •037 •054 •073 -002 •010 -022 •038 •060 •086 •117 •096 •153 *** For Scantlings Hi inches deep, multiply the weights in this table by if|= 1-093, and the de flections by -|f =-956.-|- * Example 1.— Red Pine 11 in. by 7 in., 7 feet long, with 121 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -073 of a inch; and with 121 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -117 of an inch. f * Example 2.— Red Pine llj in. by 7 in., 7 feet long, with 121 x r093 = 132-25 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -073 x -956 = "070 of an inch; and with 132-25 cwts. suspended from the middle, (one-fourth the breakiuc weight) the deflection is -117 x ■y56 = -112 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 73 TABLE XI. Co7itinued. SCANTLINGS, 11 in. and Hi inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SiZB OP SCANTMNGS, in inches. Depth. Breadth. II X 11 X IIX 11 X 11 X 11 X 11 X IIX 11 X 11 X *11 X 7 IIX 8 IIX 9 11 XIO 11X11 11 XIU 11 X12 11 X13 11 X14 11 X15 LENGTH IN FEET, CLEAR BEARING. 10 11 12 13 14 15 16 WEIGHT IN CWTS. 26-88 30-25 33-61 40-33 47-05 53-77 60-50 67-22 73-94 80-66 94-11 107-55 121-00 134-44 147-88 154-61 161-33 174-77 188-22 1201-66 24-20 27-22 30-25 36-30 42-35 48-40 54-45 60-50 66-55 72-60 84-70 96-80 108-90 121-00 133-10 139-15 145-20 157-30 169-40 181-50 22-00 24-75 27-50 33-00 38-50 44-00 49-50 55-00 60-50 66-00 77-00 88-00 99-00 110-00 121-00 126-50 132-00 143 00 154-00 165-00 20-16 22-68 25-20 30-25 35-29 40-33 45-37 50-41 55-45 60-50 70-58 80-66 90-75 100-83 110-91 115-95 121-00 131-08 141-16 151-25 18-61 17-28 20-94 19-44 23-26 21-60 27-92 25-92 oz 0/ 37-23 34-57 41-88 38-89 46-53 43-21 51-19 47-63 55-84 51-85 65-15 60-50 74-46 69-14 83-76 77-78 93-07 86-42 102-38 95-07 107-03 99-39 111-69 103-71 121-00 112-35 130-30 121-00 139-61 129-64 16-13 18-15 20-16 24-20 28-23 32-26 36-30 40-33 44-36 48-40 56-46 64-53 72-60 80-66 88-73 15-12 17- 01 18- 90 22-68 26-46 30-25 34-03 37-81 41-59 45-37 92-76 96-80 104-86 112-93 121-00 52-93 60-50 68-06 75-62 83-18 86-96 90-75 98-31 105-87 11343 Deflection in inches of Red Pine 11 inches deep, loaded with the weights in this tahle. Weight uniform- ) ly loaded j •121 •149 -181 -215 -253 •293 •336 •382 Wt. suspended ) from the middle J •194 -239 -289 •344 •404 •468 •538 •612 *** For Scantlings lU inches deep, multiply the weights in this table by 4:11= 1-093, and the deflections by ^=^966.f * Example 1. — Red Pine 11 in. by 7 in., 11 feet long, with 77 cwts, uniformly loaded, ;(one-eigh(h the breaking weight) deflects "181 of an inch ; and with 77 cwts. suspended from tlie middle, (one-fourth the brenking weight) the deflection is '289 of an inch. f* Example 2.— Red Pine 11^ in. by 7 in., 11 feet long, with 77 x 1 093 = 84-16 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -181 x -956 = -173 of an inch; and with 84-16 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -289 x 956 = 276 of an inch. ' 74 SECOND SERIES — TABLES OF WEIGHTS. TABLE XI. Continued. SCANTLINGS, 11 in. and lU inches Deep. The Weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of LENGTH IN FEET, CLEAR BEARING. SCANTLINOS, in iiicli6s< 17 18 19 20 21 22 23 1 24 Depth. Breadth. WEIGHT IN CWTS, 11 X 2 14-23 13-44 12-73 12-10 11-52 11-00 10-52 10-08 11 X 2J 16-01 1512 14-32 13-61 12-96 12-37 11-83 11-34 1 1 X 2^ 17-79 16-81 15-92 15-12 14-40 13-75 13-15 12-60 11X3 21-35 20-16 19-10 18-15 17-28 16-50 15-78 15-12 11 X 3i 24-91 23-52 22-28 21-17 20-16 19-25 18-41 17-64 11X4 28-47 26-88 25-47 24-20 23-04 22-00 21-04 20-16 11X4? 32-02 30-25 28-65 27-22 25-92 24-75 23-67 22-68 11X5 35-58 33-61 31-84 30-25 28-80 27-50 26-30 25-20 IIX 5i 39-14 36-97 35-02 33-27 31-69 30-25 28-93 27-72 IIX 6 42-70 40-33 38-21 36-30 34-57 33-00 31-56 30-25 *11X 7 49-82 47-05 44-57 42-35 40-33 38-50 36-82 35^ 11 X 8 56-94 53-77 50-94 48-40 46-09 44-00 42-08 40-33 IIX 9 64-05 60-50 57-31 54-45 51-85 49-50 47-34 45-37 11X10 71-17 67-22 63-68 60-50 57-61 55-00 52-60 50-41 11X11 78-29 73-94 70-05 66-55 63-38 60-50 57-86 55-45 11 xiu 81-85 77-30 73-23 69-57 66-26 63-25 60-50 57-97 11 X12 85-4 i 80-66 76-42 72-60 69-14 66-00 63-13 60-50 11 X13 92-52 87-38 82-78 78-65 74-90 71-50 68-39 65-54 11 X14 99-64 94-11 89-15 84-70 80-66 77-00 73-65 70-58 11 X15 106-76 100-83 95-52 90-75 86-42 82-50 78-91 75-62 Deflectiou in inches of Red Pine 11 inches deep, loaded with the weights in this table. Weight uniform- ) ly loaded J -432 -484 •539 •598 •659 •723 •790 •861 Wt. suspended ) from the middle j •691 •774 •863 •956 1-054 M57 1-265 1-377 *** For Scantlings 1 U inches deep, multiply the weights in this table by |-|f= 1-093, and the deflections by ff=-956.f * Example 1.— Red Pine 11 in. by 7 in., 19 feet long, with 44-57 cwts. uniformly loaded,, (one-eighth the breaking weight) deflects -539 of an inch; and with 44 57 cwts. suspended from the middle (one-fourth the breaking weight) the deflection is -863 of an inch. | f * Example 2.— Red Pine 11| in. by 7 in., 19 feet long, with 44-57 x l-093 = 48-7l|j cwts. uniformly loaded (one-eighth the breaking weight) deflects -539 x -956 = '515 of an inch; and with 48-71 cwts. suspended from the middle (one-fourth the breaking weight): the deflectiou is "863 x -956 = '835 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 75 TABLE XII. SCANTLINGS, 12 in. and 12^ inches Deep. The weights iii this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 1 3 4 1 5 1 6 1 7 8 Depth. Breadth. WEIGHT IN CWTS. 12X 2 12 X 2i 12 X 2J 12X 3 i 12 X 3i 288-00 324-00 360-00 432-00 144-00 162-00 180-00 216-00 96-00 108-00 120-00 144-00 iocs UU 72-00 81-00 90-00 108-00 1 Ofl.AA 1.^0 UU 57-60 64-80 72-00 86-40 lUU oU 48-00 54-00 60-00 72-00 o4 UU 4M4 46^28 51^42 61-71 170. AA 36-00 40-50 45-00 54-00 Do UU ;"l2X 4 12 X 4i 12X 5 12 X 5k 576-00 648-00 720-00 792-00 864-00 288-00 324-00 360-00 396-00 432-00 192-00 216-00 240-00 264-00 288-00 144-00 162-00 180-00 198-00 216-00 115-20 129-60 144-00 158-40 172-80 96-00 108-00 120-00 132-00 144-00 82^28 92^57 102^86 113-14 123-42 "72^ 81-00 90-00 99-00 108-00 12 X 7 *12X 8 12 X 9 12X10 12X11 1008-00 1152-00 1296-00 1440-00 1584-00 504-00 576-00 648-00 720-00 792-00 336-00 384-00 432-00 480-00 528-00 252-00 288-00 324-00 360-00 396-00 •201-60 230-40 259-20 288-00 316-80 168^00 192^00 216-00 240-00 264-00 164-57 185-14 205-71 226-28 126-00 144-00 162-00 180-00 198-00 12X12 12X12i 12X13 12X14 12X15 1728-00 180000 1872-00 2016-00 2160-00 864-00 900-00 936-00 1008-00 1080-00 576-00 600-00 624-00 672-00 720-00 432-00 450-00 468-00 504-00 540-00 345-60 360-00 374-40 403-20 432-00 288^ 300-00 312-00 336-00 360-00 246^ 257-14 267-42 288-00 308-57 216-00 225-00 234-00 252-00 270-00 Deflectioa in inches of Red Pine 12 inches deep, loaded with the weights in this table. Weightuniform- ) ly loaded j -001 -005 •012 -022 -034 •049 -067 •088 Wt. suspended ] from the middle J -002 -009 •020 -035 -055 •079 -107 •140 *** For Scantlings 12i inches deep, multiply the weights in this table by 4fi= 1'08507, and the deflections by f|=-96.f * Example 1. — Red Pine 12 in. by 8 in., 8 feet long, with 144 cwts. uniformly loaded, [one-eighth the breaking weight) deflects "088 of an inch; and with 144 cwts. suspended ;rom the middle, (one-fourth the breaking weight) the deflection is '140 of an inch. [ f* Example 2.— Red Pine 12| in. by 8 in., 8 feet long, with 144 x 1-085 = 156-25 cwts. aniformly loaded, (one-eighth the breaking weight) deflects '088 x '96 = -084 of an inch; and vith 156-25 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection s -14 X -96 = -134 of an inch. 76 SECOND SERIES — TABLES OF WEIGHT*. TABLE XII. Continued. SCANTLINGS, 12 in. and I2h inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SlZi£ OF ScANTHNGS, in inches. length IN FEET, CLEAR BEARING. 10 11 12 13 14 15 16 Depth. Breadth. WEIGHT IN CWTS. 12X 2 32-00 28-80 26-18 24-00 22-15 20-57 19-20 18-00 12 X 2i 12X 2^ 36-00 32-40 29-45 27-00 24-92 23-14 21-60 20-25 40-00 36-00 32^72 30-00 27-69 25-71 24-00 22-50 12X 3 48-00 43-20 39-27 36-00 33-23 30-85 28-80 27-00 12 X 3i 00 uu "in. /in 40 ol OO /O ob UU OO oU o 1 OU 12 X 4 64-00 57-60 52-36 48-00 44-30 4M4 38-40 36-00 12 X 4^ 72-00 64-80 58-90 54-00 49-84 46-28 43-20 40-50 12 X 5 80-00 72-00 65-45 60-00 55-38 51-42 48-00 45-00 12X 61 88-00 79-20 72-00 66-00 60-92 56-57 52-80 49-50 12 X 6 96-00 86-40 78-54 72-00 66-46 61-71 57-60 54-00 12 X 7 112-00 100-80 91-63 84-00 77-53 72-00 67-20 63-00 *12X 8 128-00 115-20 104-72 9600 88-61 82-28 76-80 72-00 12 X 9 144-00 129-60 117-81 108-00 99-69 92-57 86-40 81^00 12X10 160-00 14400 130-90 120-00 110-76 102-85 96-00 90-00 12X11 176-00 158-40 144-00 132-00 121-84 113-14 105-60 99-00 12X12 192-00 172-80 157-09 144-00 132-92 123-42 115 20 ro¥oo 12X12i 200-00 180-00 163-63 15000 138-46 128-57 120-00 112-50 12X13 208-00 187-20 170-18 156-00 144-00 133-71 124-80 117-00 12X14 224-00 201-60 183-27 168-00 155-07 144-00 134-40 12600 12X15 240-00 216-00 196-36 180-00 166-15 154-28 144^00 135-00 Deflection in inches of Red Pine 12 inches deep, loaded with the weights in this table. Weight uniform- ) ly loaded / •111 •137 ■166 •197 -231 •268 •308 -351 Wt. suspended | from the middle ) •178 •219 •265 -316 -370 -430 -493 •561 *#* For Scantlings 12^ inches deep, multiply the weights in this table by ff^= 1-08507, and the deflections by |4=-96.t • Example 1. — Red Pine 12 in. by 8 in., 12 feet long, with 96 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "197 of an inch ; and with 96 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is '316 of an inch. f* Example 2.— Red Pine 12^ in. by 8 in., 12 feet long, with 96 x 1-085 = 104-16 cwts. uuifortnly loaded, (one-eighth the breaking weight) deflects -197 x -96 = '189 of auiuch; and with 104-16 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -316 X -96 = -303 of an inch. SECOND SERIES TABLES OF WEIGHTS. 77 TABLE XII. Continued. SCANTLINGS, 12 in. and 12^ inches Deep. The Weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size op Scantlings, in inches. length in feet. CLEAR BEARING. 17 18 19 20 21 22 23 24 Depth. Breadth. weight in CWTS. 12 X 2 io UO 14 40 lo / i 1 o.An 13-09 12 62 1 O.A/ 1 12 00 12 X 21 1 Q.n'^ ly uo 1 o 00 17 00 Id 20 ID 42 14 /2 1 A .AO 14 Oo 1 O. AA lo 00 12 X 2| O 1 • 1 "7 a£0 00 lo 94 lo 00 17 14 10 ,30 10 DO 1 A.AA 10 00 12 X 3 ^4 00 zZ to 21 bO 20 57 19-03 lo /O 1 O.AA lo 00 12 X 3i 29-64 28-00 26-52 25-20 24-00 22-90 21-91 21-00 12 X 4 33-88 32-00 30-31 28-80 27-42 26^18 25-04 24-00 12 X 4i 38-11 36-00 34-10 32-40 30^85 29-45 28-17 27-00 12 X 5 42-35 40-00 37-89 36-00 34^28 32-72 31-30 30-00 12 X 6i 46-58 44-00 41-68 39-60 37^71 36-00 34-43 33-00 12 X 6 50-82 48-00 45-47 43-20 4M4 39-27 37-56 36-00 12 X 7 69-29 56-00 53-05 50-40 48-00 45-81 43-82 42-00 *12X 8 67-76 64-00 60-63 57-60 54-85 52-36 60-08 48-00 12 X 9 76-23 72-00 68-21 64-80 61-71 58-90 66-34 54-00 12X10 84-70 80-00 75-78 72-00 68-57 65-45 62-60 60-00 12X11 93-17 88-00 83-36 79-20 75-42 72-00 68-86 66-00 12X12 101-64 96-00 90-94 86-40 82-28 78-54 75-13 72^0 12X12* 105-88 100-00 94-73 90-00 85-71 81-81 78-26 75-00 12X13 110-11 104-00 98-52 93-60 89-14 86-09 81-39 78-00 12X14 118-58 112-00 106-10 100-80 96-00 91-63 87-65 84-00 12X15 127-05 120-00 113-68 108-00 102-85 98-18 93-91 90-00 Deflection in inches of Red Pine 12 inches deep, loaded with the weights in this table. Weight uijiform- 1 ly loaded. f -396 •444 •494 -548 -604 •663 -725 -789 \Vt. suspended ) from the middle. J" -633 -710 -791 •877 -966 1-061 1-159 1-262 For Scantlings 12* inches deep, multiply the weights in this table by |-f^|= 1-08507, and the deflections by f f-=-96.f * Example 1. — Red Pine 12 in. by 8 in., 20 feet long, vrith 57"60 cwts. uniformly loaded, {one-eighth the breaking weight) deflecis "548 of an inch ; and with 57'CO cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 'S?? of an inch. f* Example 2.— Red Piue 12| in. by 8 in., 20 feet long, with 57-6 x 1-085 = 62-50 cwts. uniformly loaded, (oue-eighth the breaking weight) deflects '548 x -96 = -526 of an inch; and with 62-50 cwts. suspended from the middle, (oue-fourth the breaking weight) the deflection is -877 X -96 = -842 of an inch. L 78 SECOND SERIES TABLES OF WEIGHTS. TABLE XIII. SCANTLINGS, 13 in. and I3i inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Scantlings, in inches. 1| 2|3|4|5|6|7|8 Depth. Breadth. WEIGHT IN CWTS. 13 X 2 13 X 21 13 X 3 13 X Si 13 X 4 338-00 422-50 507-00 591-50 O/D w 169-00 211-25 253-50 295-75 ooo uu 112^66 140-83 169-00 197-16 84-60 105-62 126-75 147-87 169-00 67^60 84-50 101-40 118-30 135-20 56-33 70-41 84-50 98-5S 1 12-66 48-28 60-35 72-42 84-50 96-57 42-25 52-81 63^37 73^93 84-50 ~i3">r4i 13X 5 13 X 5i 13 X 6 13 X 6i 760-50 845-00 929-50 1014-00 1098-50 380-25 422-50 464-75 507-00 549-25 253-50 281-66 309-83 338-00 366-16 190-12 211-25 232-37 253-50 274-62 T52'-T0 169-00 185-90 202-80 219-70 126-75 140-83 154-91 169-00 183-08 108-64 120-71 132-78 144-85 156-92 95-06 105^62 116^18 126-75 137^31 13 X 7 13 X 8 *13X 9 13X10 13X11 1183-00 1352-00 1521-00 1690-00 1859-00 591-50 676-00 760-50 845-00 929-50 394-33 450-66 507-00 563-33 619-66 295-75 338-00 380-25 422-50 464-75 236-60 270-40 304-20 338-00 371-80 197-16 225-33 253-50 281-66 309-83 169-00 193-14 217-28 241-42 265-57 147-87 169-00 190-12 211-25 232-37 13X12 13X13 13X13i 13X14 13X15 2028-00 2197-00 2281-50 2366-00 2535-00 1014-00 1098-50 1140-75 1183-00 1267-50 676-00 732-33 760-50 788-66 845-00 507-00 549-25 570-37 591-50 633-75 405^ 439-40 456-30 473-20 507-00 338-00 366-16 380-25 394^33 422^50 289-71 313-85 325-92 338-00 362-14 253-50 274-62 285-18 295-75 316-87 Deflection in inches of Red Pine 13 inches deep, loaded with the weights in this table. Weight uniform. ) ly loaded. J Wt. suspended ) from the middle. J -001 -002 •005 •008 -Oil -018 •020 •032 •032 -051 •046 •073 •062 •099 -081 -129 For Scantlings 13| inches deep, multiply the weights in this table by ^= 1-0784, and the deflections by ^^=-963. f * Example 1. — Red Pine 13 in. by 9 in., 5 feet long, with 304-20 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -032 of an inch; and with 304'20 cw^s. suspended from the middle, (one-fourth the breaking weight) the deflection is -051 of an inch. f * Example 2.— Red Pine 13^ in. by 9 in., 5 feet long, with 304-2 x 1-0784 = 328 05 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -032 x '963 = -031 ofau inch; and with 328-05 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -051 x -963 = -049 of an inch. SECOND SERIES TABLES OF WEIGHTS. 79 TABLE XIII. Continued. SCANTLINGS, 13 in. and 13i inches Deep. The weights in this table are — One-icighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 10 1 11 1 12 1 13 1 14 1 15 16 Depth. Breadth. WEIGHT IN CWTS. 13 X 2 017. AC 2o Id Ofl.AA OA•^ A 22 0<5 2112 13 X 2i A f!.Q/l QQ./f A 00 4(J Q A. OA Q A. 1 T OQ. 1 ft 2o Id Oft. /(A 20 4U 13 X 3 OD'Od OU 7U 4o uy 4.tf 20 QO.AA oy uu 00-21 00. QA 00 oU 0 1 00 13 X 3i 00 4 A oy 10 00 77 A 0.00 4y^<^y A ^A 40 OU 42 20 oy-4o 00 yo 13 X 4 75- 11 67-60 61-45 56-33 52-00 48-28 45-06 42-25 13 X 4i 84-50 76-05 69-13 63-37 68-50 54-32 50-70 47-53 13 X 5 93-88 84-50 76-81 70-41 65-00 60-35 56-33 52-81 13 X 6i 103-27 92-95 84-50 77-45 71-50 66-39 61-96 68-09 13 X 6 112-66 101-40 92-18 84-50 78-00 72-42 67-60 63-37 13 X 6J 122-05 109-85 99-86 91-54 84-50 78-46 73-23 68-65 13 X 7 131-44 118-30 107-54 98^58 91-00 84-50 78-86 73-93 13 X 8 150-22 135-20 122-90 112^66 104-00 96-57 90-13 84-50 *13X 9 169-00 152-10 138^27 126-75 117-00 108-64 101-40 95-06 13X10 187-77 169-00 153-63 140-83 130-00 120-71 112-66 105-62 13X11 206-55 185-90 169^00 154-91 14300 132-78 123-93 116-18 13X12 225-33 202-80 184-36 169-00 156-00 144-85 135-20 126-75 13X13 244-11 219-70 199^72 183-08 169-00 166-92 146-46 137-31 13X13i 253-50 228-15 207^40 190-12 175-50 162-96 152-10 142-59 13X14 262-88 236-60 215-09 197-16 182-00 169-00 157-73 147-87 13X15 281-66 253-50 230-45 211-25 196-00 181-07 169-00 158-43 Deflection in inches of Red Pine 13 inches deep, loaded with the weights in this table. Weightuniform. ) ly loaded. J -102 •126 •153 -182 -214 -248 -284 -324 Wtsnspended 1 from the middle. J -164 •202 •245 -291 -342 -396 -455 •518 For Scantlings 13^ inches deep, multiply the weights in this table by -^1=1-0784, and the deflections by |^=^963.-f- * Example 1. — Red Pine 13 in. by 9 in., 13 feet long, with 117 cwts. uniformly loaded, (one-eighth the breaking weight) deflects 2]4i of an inch ; and with 117 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is '342 of an inch. t* Example 2.— Red Pine 13i in. by 9 in., 13 feet long, with 117 ^ 1 0784 = 126 17 cwts. uniformly loaded, (one-eighth the breaking weight) deflects '214 x '963 = '206 of an inch ; and with 126'17 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -342 x -963 = -329 of an inch. 80 SECOND SriRIES — TABLES OF WEIGHTS. TABLE XIII. Continued. SCANTLINGS, 13 in. and 13^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SiZB OP Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 Depth. Breadth. WEIGHT IN CWTS. 13 X 2 19"88 18*77 17"78 16^90 16*09 15*36 14'69 14^08 13X 2h 24*85 23*47 22^23 21*12 20*1 1 19*20 18*36 17'60 13X 3 29*82 28*16 26*68 25*35 24*14 23*04 22*04 2P12 13 X 3i 34*79 32*86 31*13 29*57 28*16 26*88 25*7 1 24"64 13 X 4 39*76 37*55 35*57 33*80 32*19 30-72 29-39 28-16 13 X 4i 44*73 42-25 40*02 38*02 36*21 34-56 33*06 31*68 13 X 5 49*70 46*94 44-47 42*25 40*23 38-40 36*73 35*20 13 X 6h 54*67 51*63 48*92 46*47 44*26 42*25 40*41 38-72 13 X 6 59*64 56*33 53*36 50*70 48*28 46*09 44-08 42*25 13 X 6i 64*61 61*02 57*81 54*92 52*30 49^93 47*76 45*77 13 X 7 69*58 65*72 62*26 59*15 56*33 53^77 51-43 49*29 13 X 8 79*52 75*11 71*15 67*60 64*38 6r45 58*78 56*33 *13X 9 89*47 84*50 80*05 76*05 72*42 69*13 66*13 63*37 13X10 99*41 93*88 88*94 84*50 80-47 76-81 73*47 70^41 13X11 109*35 103*27 97*84 92-95 88*52 84*50 80*82 77^45 13X12 119*29 112*66 106*73 101*40 96*57 92-18 88-17 84*50 13X13 129*23 122*05 1 15*63 109*85 104*61 99*86 95-52 91*54 13X131 134*20 126*75 120*07 114*07 108*64 103*70 99*19 95*06 13X14 139*17 131*44 124*52 118*30 112*66 107*54 102*86 98*58 13X15 149*11 140*83 133*42 126*75 120*71 115-22 110*21 105*62 Deflection in inches of Red Pine 13 inches deep, loaded with the weights in this table. Weight miifuim- ) ly loaded. J •365 *410 •456 •506 •558 -612 •669 •728 Wt. suspended ) from the middle, f *585 •655 •730 *809 *892 •979 1*070 1*165 For Scantlings 13|^ inches deep, multiply the weights in this table by ^=1*0784, and the deflections by =-963.t * Example 1. — Red Pine 13 in. by 9 in., 21 feet long, with 72-42 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -558 of an inch; and with 72*42 cwts. suspended from the middle, (one-foui-th the breaking weight) the deflection is -892 of an inch. f* Example 2.— Red Pine, 13| in. by 9 in., 21 feet long, with 72-42 x 1-0784 = 78-10 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -558 x -963 = -537 of an iuch ; and with 78^10 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -892 x •963 = *859 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 81 TABLE XIII. Continued. SCANTLINGS, 13 in. and 13^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. length in eeet. CLEAR BEARING. 25 26 1 27 1 28 1 29 1 30 1 31 1 32 Depth. Breadth. WEIGHT IN CWTS. 13 X 2 13 X 2i 13 X 3 13 X 3i 13 X 4 13-52 16-90 20-28 23-66 27-04 13-00 16-25 19-50 22-75 26-00 12-51 15-64 18-77 21-90 4,0 \jO 12-07 15-08 18-10 21-12 11-65 14-56 17-48 20-39 OQ.Q 1 40 O I 11-26 14-08 16-90 19-71 10-90 13-62 16-35 19-08 21-80 10-56 13-20 15-84 18-48 21-12 13 X 4i 13 X 5 13 X 61 13 X 6 13 X 6i 30-42 33-80 37-18 40-56 43-94 29-25 32-50 35-75 3900 42-25 28-16 31-29 34-42 37-55 40-68 27-16 30-17 33-19 36-21 39-23 26-22 29-13 32-05 34-96 37-87 25-35 28-16 30-98 33-80 36-61 24-53 29-98 32-70 35-43 23-76 26-40 29-04 31-68 13 X 7 13 X 8 *13X 9 13X10 13X11 47-32 54-08 60-84 67-60 74-36 45-50 52-00 58-50 65-00 71-50 43-81 50-07 56-33 62-59 68-85 42-25 48-28 54-32 60-35 66-39 40-79 46-62 52-44 58-27 64-10 39-43 45-06 50-70 56-33 61-96 38-16 43-61 49-06 54-51 59-96 36-96 42-25 47*53 52-81 58-09 13X12 13X13 13X13i 13X14 13X15 81-12 87-88 91-26 94-64 101-40 78-00 84-50 87-75 9100 97-50 75-11 81-37 84-50 87-62 93-88 72-42 78-46 81-48 84-50 90-53 69-93 75-75 78-67 81-58 87-41 67-60 73-23 76-05 78-86 84-50 65-41 70-87 73-59 76-32 81-77 63-37 68-65 71-29 73-93 79-21 Deflection in inches of Red Pine 13 inches deep, loaded with the weights in this tahle. W eightuniform. ) ly loaded. J -790 -855 •922 -991 1-063 1-138 1-215 1-295 VVt. suspended I rrom the middle. J 1-264 1-367 1-475 1-586 1-701 1-820 1-944 2-071 *** For Scantlings 13^ inches deep, multiply the weights in th] by 7-1^1= 1-0784, and the deflections by f f—.ggs s table * Example 1. — Red Pine 13 in. by 9 in., 25 feet long, with 60-84 cwts. uniformly loaded, (oBe-eighth the hreaMng weight) deflects -790 of an inch ; and with 60"84 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 1-264 inches. f * Example 2.— Red Pine 13^ in. by 9 in., 25 feet long, with 60-84 x 1-0784 = 65-61 cwts. uniformly loaded, (otie-eighth the breaking weight) deflects -79 x -963 = -761 of au nch ; and with 65-61 cwts. suspended from the middle, (one-fourth the breaking weight) the- deflection is 1-264 x -963 = 1-217 inches. 8-2 SECOND SERIES — TABLES OF WEIGHTS. TABLE XIV. SCANTLINGS, 14 in. and 14^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN feet, CLEAR BEARING. 1 2 1 3 1 4 1 5 1 6 1 7 1 8 Depth. Breadth WEIGHT IN CWTS. 14 X 14X 14 X 14 X 14 X 392-00 490-00 588-00 686-00 784-00 14 X 14 X 14 X 14 X 14X 4i 5 5i 6 6k 882-00 980-00 1078-00 1176-00 1274-00 14 X 7 14 X 8 14 X 9 *14X10 14X11 1372-00 1568-00 1764-00 1960-00 2156-00 14X12 14X13 14X14 14X14i 14X15 2352-00 2548-00 2744-00 2842-00 2940-00 196-00 245-00 294-00 343-00 392-00 441-00 490-00 539-00 588-00 637-00 686-00 784-00 882-00 980-00 1078-00 1176-00 1274-00 1372-00 1421-00 147000 130-66 163-33 196-00 228-66 261-33 294-00 326-66 359-33 392-00 424-66 457-33 522-66 588-00 653-33 718-66 784-00 849-33 914-66 947-33 980-00 98-00 122-50 147-00 171-50 196-00 220-50 245-00 269-50 294-00 318-50 343-00 392-00 441-00 490-00 539-00 588-00 637-00 686-00 710-50 735-00 78-40 98-00 117-60 137-20 156-80 176-40 196-00 215-60 235-20 254-80 274-40 313-60 352-80 392-00 431-20 470-40 509-60 548-80 568-40 588-00 65-33 81-66 98-00 114-33 130-66 147-00 163-33 179-66 196-00 212-33 228-66 261-33 294-00 326-66 359-33 392-00 424-66 457-33 473-66 490-00 56-00 70-00 84-00 98-00 112-00 126-00 140-00 154-00 168-00 182-00 196-00 224-00 252-00 280-00 308-00 ,336-00 364-00 392.00 406-00 420-00 49-00 61-25 73-5( 85-7^ 98-0( 110-2^ 122-5(| 134-75 147-OQ 159-25 171-5C 196-00 220-5C 245-OC 269-5C 294-OC 31850 343-0( 355-2£ 367-5C Deflection in inches of Red Pine 14 inches deep, loaded with the weights in this table. Weightuniform- ly loaded, Wtsuspeuded fromthemiddle; -001 -005 -Oil -019 -029 -042 -058 -002 -008 ■017 -030 •047 -068 -092 •071 •12C For Scantlings 14^ inches deep, multiply the weights in this table by -ffi= 1-0727, and the deflections by || = -965.t * Example 1. — Red Pine 14 in. by 10 in., 6 feet long, with 326-66 cwts. uniformly loaded (one-eighth the breaking weight) deflects -043 of an inch ; and with 326-66 cwts. 8uspeude( from the middle, (one-fom-th the breaking weight) the deflection is -068 of an inch. f* Example 2.— Red Pine Ui in. by 10 in., 6 feet long, with 336-66 x 1-0727 = 350-4; cwts. uniformly loaded, (one-eighth the breaking weight) deflects -042 x -965 ='041 of a] inch ; and with 350-41 cwts. suspended from the middle, (one-fourth the breaking weight) th deflection is -068 x -965 = -066 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 83 TABLE XIV. Continued. SCANTLINGS, 14 in. and 14^ inches Deep. The weights in this table are — Dne-eighth of the breaking weight of Red Pine, uniformly loaded; or Dne-fourth of the same when suspended from the middle. Size of LENGTH IN FEET CLEAR BEARING. Scantlings, in inches. 10 12 13 14 15 Depth- Breadth WEIGHT I 1^ CWTS. 14 X 2 43-55 OA. /JO «50 Do DO AKJ \J\J 26^13 24-50 14 X 2i 54-44 49-00 44 04 4U OO O / Ut7 32^66 30-62 14 X 3 65-33 58-80 Oo 40 4y uu 49 no 39-20 36-75 14 X 3i 76-22 68-60 0^ OO O 1 ID 49-00 45-73 42 o7 14 X 4 87-11 78-40 7r27 65-33 60-30 56-00 52-26 4y uu 14 X 4i 98-00 80^18 73-50 67-84 63-00 58-80 55-12 14 X 5 108-88 98-00 89-09 81-66 75-38 70-00 65^33 61-25 14 X 5^ 119-77 107-80 98-00 89-83 82-92 77-00 71-86 67-37 14 X 6 130-66 117-60 106-90 98^00 90-46 84-00 78-40 73-50 14 X 6i 141-55 127-40 115-81 106^16 98-00 91-00 84^93 79-62 14 X 7 152-44 137-20 124-72 114-33 105-53 98-00 91-46 85^75 14X 8 174-22 156-80 142-54 130-66 120-61 112-00 104-53 98^00 14 X 9 196-00 176-40 160-36 147-00 135-69 126-00 117-60 110^25 *14X10 217-77 196-00 178-18 163-33 150-76 140-00 130-66 122-50 14X11 239-55 215-60 196-00 179-66 165-84 15400 143-73 134-75 14X12 261-33 235-20 213-81 196-00 180-92 168-00 156-80 147-00 14X13 283-11 254-80 231-63 212-33 196-00 182-00 169-86 159-25 14X14 304-88 274-40 249-45 228-66 21107 196-00 182-93 171-50 14X14i 315-77 284-20 258-36 236-83 218-61 203-00 189-46 177-62 14X15 326-66 294-00 267-27 245-00 226-15 21000 196-00 183-75 Deflection in inches of Red Pine 14 inches deep, loaded with the weights in this tahle. Weight uniform- ) ly loaded. ) -095 -117 •142 •169 •198 •230 -264 -301 Wt. suspended 1 •152 •188 -227 •270 -317 •368 •423 -481 from the middle. J * For Scantlings 14i inches deep, multiply the weights in this table by 84:1.= 1-0727, and the deflections by -965.1 * Example L— Red Pine 14 in. by 10 in., 14 feet long, with 140 cwts. uniformly loaded, (oue-eighth the breaking weight) deflects -230 of an inch; and with 140 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -368 of an inch. f * Example 2.— Red Pine 14J in. by 10 in., 14 feet long, with 140 x 1'0727 = 150-17 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -23 x -965 = -223 of an inch; and with 150-17 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is '368 x -965 = '355 of an inch. 84 SECOND SERIES TABLES OF WEIGHTS. TABLE XIV. Continued. SCANTLINGS, 14 in. and 14i inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 17 18 19 20 21 22 1 23 24 Depth. Breadth. ^ WEIGHT IN CWTS. 14 X 2 ly loaded. ) •001 •004 •010 -018 -027 -039 -054 •070 Wt. suspended 1 from the middle. J •002 -007 -016 -028 -044 -063 -086 •112 For Scantlings 15J inches deep, multiply the weights in this table by 1-0677, and the deflections by |° = -968.t * Example 1. — Red Pine 15 iu. by 11 in., 7 feet long, with 353-57 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -054 of an inch ; and with 353-43 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -086 of an inch. f* Example 2.— Red Pine 15Hn. by 11 in., 7 feet long, with 353-57 x l-0677 = 377-53 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -054 x -968 = -052 of an inch ; and with 377'53 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -086 x -968 = -083 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 87 TABLE XV. Continued. SCANTLINGS, 15 in. and 15^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SiZB OF SCANTLINGSj in inches. LENGTH IN FEET, CLEAR BEARING. 9 10 11 12 13 14 15 16 Depth. Breadth. WEIGHT IN CWTS. 15 X 2 50-00 4500 40^90 37-50 34-61 32-14 30-00 28-12 15 X 2i 62-50 56-25 51-13 46-87 43-26 40-17 37-50 35-15 15X 3 7500 67-50 61-36 56-25 51-92 48-21 4500 42-18 15 X 3i 87-50 78-75 71-59 65-62 60-57 56-25 52-50 49-21 15 X 4 100-00 90-00 8181 75-00 6923 64-28 60-00 56-25 15 X 4i 112-50 101-25 92-04 84-37 77-88 72-32 67-50 63-28 15 X 5 125-00 112-50 102-27 93-75 86-53 80-35 75-00 70-31 15 X 5} 137-50 123-75 112-50 103- 12 95-19 88-39 82-50 77-34 15 X 6 150-00 13500 122-72 112-50 103-84 96-42 90-00 84-37 15 X 6i 162-50 146-25 132-95 121-87 112-50 104-46 97-50 91-40 15 X 7 175-00 157-50 143-18 131-25 121-15 112-50 105-00 98-43 15 X 8 200-00 180-00 163-63 150-00 138-46 128-57 12000 112 50 15 X 9 225-00 202-50 184-09 168-75 155-76 144-64 135-00 126-56 15X10 250-00 225-00 204-54 187-50 173-07 160-71 150-00 140-62 *15X11 275-00 247-50 225-00 206-25 190-38 176-78 165-00 154-68 15 X 12 300-00 27000 245-45 225-00 207-69 192-85 180^00 168-75 15X13 325-00 292-50 265-90 243-75 225-00 208-92 195-00 182-81 15X14 350-00 315-00 286-36 262-50 242-30 225-00 210-00 196-87 15X 15 375-00 337-50 306-81 281-25 259-61 241-07 225-00 210-93 15X15i 387-50 348^75 31704 290-62 268-26 249-10 232-50 217-96 Deflectiou in inches of Red Pine 15 inches deep, loaded with the weights in this table. Weight uniJorin- ) ly loaded. J •089 •110 -133 -158 -185 -215 -247 -280 Wt. suspended ) from the mi ddle. ) •142 •175 -212 •252 -296 -344 -394 -449 For Scantlings 15^ inches deep, multiply the weights in this table by |4s= 1"0677, and the deflections by |°=:-968.f * ETample 1. — Red Pine 15 in. by 11 in., 15 feet long, with 165 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -247 of an inch; and with 165 cwts. suspended from the middle, (one-fourth the brealdug weight) the deflection is -394 of an inch. f* Example 2. — Red Pine 15 J in. by 11 in., 15 feet long, with 165 x 1-0677 = 176-18 cwts. uniiformly loaded, (one-eighth the breaking weight) deflects -247 x -968 = -239 of an inch; amd with 176-18 cwts. suspended from the middle, (one-fourth the breaking weight) the defleiction is -394 x 968 = -381 of an inch. 88 SECOND SERIES — TABLES OF WEIGHTS. TABLE XV. Continued. SCANTLINGS, 15 in. and 15^ inches Deep. The Weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size op Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 17 18 19 20 21 22 23 24 Depth. Breadth. WEIGHT IN CWTS. 15 X 2 15 X 2k 15 X 3 15 X 3 J 15 X 4 26-47 33-08 39-70 46-32 52-94 25-00 31-25 37-50 43-75 50-00 23-68 29-60 35-52 41-44 47-36 22-50 28-12 33-75 39-37 45-00 21^42 26-78 32-14 37-50 20-45 25-56 30-68 35-79 19-56 24-46 29-34 34-23 Oo 1 O 18-75 23-43 28-12 32-81 O 4 0\J 15X Ah 15 X 5 15 X 5i 15 X 6 15X 61 59-55 66-17 72-79 79-41 86-02 56-25 62-50 68-75 75-00 81-25 53-28 59-21 65-13 71-05 76-97 50-62 56-25 61-87 67-50 73-12 48-21 53-57 58-92 64-28 69-64 46-02 51-13 56-25 61-36 66-47 44-02 48-91 53-80 58-69 63-58 "42-18 46-87 51-56 56-25 60-93 J5X 7 15 X 8 15 X 9 15X10 *15X11 92-64 105-88 119-11 132-35 145-58 87-50 100-00 112-50 125-00 137-50 82-89 94-73 106-57 1 18-42 130-26 78-75 90-00 101-25 112-50 123-75 75-00 85-71 96-42 107-14 117-85 71-59 81-81 92-04 102-27 112-50 68-47 78-26 88-04 97-82 107^60 65-62 75-00 84-37 93-75 10312 15X12 15X13 15X14 15X15 15X15^ 158-82 172-05 185-29 198-52 •205-14 150-00 162-50 175-00 187-50 193-75 142-10 153-94 165-78 177-63 183-55 135-00 146-25 157-50 168-75 174-37 128-57 139-28 150-00 160-71 166-07 122-72 132-95 143-18 153-40 158-52 117^39 127-17 136-95 146-73 151-63 112-50 121-87 131-25 140-62 145-31 Deflection in inches of Red Pine 15 inches deep, loaded with the weights in this tahle. Weight uniform- ) ly loaded. | -317 -355 -396 •438 -483 -530 -580 •631 Wt. suspended ) fromlhemiddle. ) -507 -568 •633 •701 -773 -848 -927 rolo *#* For Scantlings 15^^ inches deep, multiply the weights in this table by 96^=1-0677, and the deflections by |f^=-968.-t- * Example 1. — Red Pine 15 in. by 11 in., 23 feet long, -with 107'60 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "580 of an inch ; and with 107-60 cwts. suspended from the middle (one-fourth the breaking weight) the deflection is -927 of an inch. f* Example 2.— Red Pine 15^ in. by 11 in., 23 feet long, with 107-6 x 1-0677 = 114-89 cwts. uniformly loaded (one-eighth the breaking weight) deflects -58 x -968 = -561 of an inch; and with 114-89 cwts. suspended from the middle (one-fourth the breaking weight) the deflection is '927 x -968 = -897 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 89 TABLE XV. Continued. SCANTLINGS, 15 in. and 15^ inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. SiZU OK LENGTH IN FEET, CLEAR BEARING. Scantlings, in inches. 25 26 27 28 29 30 31 1 32 Depth. Breadth. WEIGHT IN CWTS. 18*00 17*30 16*66 16*07 15*51 15*00 14*61 14*06 15 X 2i 22'50 21*63 20*83 20*08 19*39 18*75 18*14 17*57 15 X 3 27*00 25*96 25*00 24*10 23*27 22*50 21*77 21*09 15 X 3i 31*50 30*28 29* 16 28*12 27*15 26*25 25*40 24*60 15 X 4 OO UU o4 Ol QQ.OQ OO'OO oo.no 28*12 15 X 4:^ 40*50 38*94 37*50 36*16 34*91 33*75 32*6^ 31 '64 15 X 5 45*00 43*26 41*66 40*17 38*79 37*50 36*29 35*15 15 X 5i 49*50 47*59 45*83 44*19 42*67 41*25 39*91 38*67 15X 6 54*00 51*92 50*00 48*21 46*55 45*00 43*54 42*18 15 X 6i 58*50 56*25 54*16 52*23 50*43 48*75 47*17 45*70 15 X 7 63*00 60*57 58*33 56*25 64*31 52*60 50*80 49-21 15 X 8 72*00 69-23 66*66 64*28 62*06 6000 58*06 56*25 15X 9 81*00 77*88 75*00 72*32 69*82 67*50 65*32 63*28 15X10 90*00 86*53 83*33 80*35 77*58 75*00 72-58 70*31 *15X11 99*00 95*19 91*66 88*39 85*34 82*50 79*83 77*34 15X12 108*00 103*84 100*00 96*42 93*10 90*00 84*37 15X13 117*00 112*50 108*33 104*46 100*86 97*50 94*35 91-40 15X14 126*00 121*15 116*66 112*50 108*62 105*00 101*61 98*43 15X15 135*00 129*80 125*00 120*53 116*37 112-50 108*87 105*46 15X15i 139-50 134*13 129*16 124*55 120*25 116*25 112*50 108*98 Deflection in inches of Red Pine 15 inches deep, loaded with the weights in this table. Weight uniform- ) ly loaded. J *685 *741 •799 •859 •921 •986 1^053 1*122 Wt. suspended ) fromthe middle. J 1*096 1-185 1*278 1*374 1-474 1^578 1*685 1*795 *** For Scantlings 15^ inches deep, multiply the weights in this table by 11^=1*0677, and the deflections by |5^=*968.t • Example 1. — Red Pine 15 in. by 11 in., 27 feet long, with 91-66 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -799 of an inch ; and with 91-66 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 1-278 inches. f * Example 2.— Red Pine 15i in. by 11 in., 27 feet long, with 91-66 x 1-0677 = 97-87 cwts. miiformly loaded, (one-eighth the breaking weight) deflects '799 x '968 = -773 of an inch ; and with 97-87 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 1278 x -968 = 1-237 inches. 90 SECOND SERIES — TABLES OF WEIGHTS. TABLE XVI. SCANTLINGS, 16 in., 17 in. and 18 inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 1 2 1 3 1 4 1 5 1 6 7 8 Depth. Breadth WEIGHT IN CWTS. 16X 2 512-00 256^00 170-66 128-00 102-40 85-33 73*14 6400 16 X 2i 640-00 320-00 213-33 160-00 128-00 106-66 91-42 80-00 16 X 3 768-00 384-00 256-00 192-00 153-60 128-00 109-71 9600 16 X 3i oyo uu 448-00 298-66 iCiC^ \J\J 1 7Q'9n 1 1 9-nrt I LA yjyj 16X 4 1024-00 512-00 341-33 256-00 204-80 170-66 146-28 128-00 16 X 4i 1152-00 576-00 384-00 288-00 230-40 192-00 164-57 144-00 16X 5 1280-00 640-00 426-66 320-00 256-00 213-33 182-85 160-00 16 X 5i 1408-00 704-00 469-33 352-00 281-60 234-66 201-14 176-00 16X6 1536-00 768-00 512-00 384^00 307-20 256-00 219-42 192-00 16 X 6i 1664-00 832-00 554-66 416-00 332-80 277-33 237-71 208-00 16 X 7 1792-00 896-00 597-33 448-00 358-40 298-66 256-00 224-00 1 fi V A lO /N O 204800 1024-00 682-66 512-00 409-60 341-33 292-57 25600 16 X 9 2304-00 1152-00 768-00 576-00 460-80 384-00 329-14 288-00 16X10 256000 1280-00 853-33 640^00 512-00 426-66 365-71 320-00 16X11 2816-00 1408-00 938-66 704-00 563-20 469-33 402-28 352-00 *16X12 3072-00 1536-00 1024-00 768-00 614-40 512-00 438-85 384^ 16X13 3328-00 1664-00 1109-33 832-00 665-60 554-66 475-42 416-00 16X14 3584-00 1792-00 1194-66 896-00 716-80 597-33 512-00 448-00 16X15 3840-00 1920-001280-00 960-00 768-00 640-00 548-57 480-00 16X16 4096-00 2048-001365-33 1024-00 819-20 682-66 585-14 512-00 Deflection m inches of Ked Pine 16 inches deep, loaded with the weights in this table. Weight uniform- ] ly loaded. J •001 -004 •009 •016 •026 -037 •050 •066 Wt. suspended \ from themiddle. | •002 •007 •015 •026 •041 •059 •081 -105 For Scantlings 17 inches deep, multiply the weights in this table by 141=1-1289, and the deflections by ^■=-M\. For Scantlings 18 inches deep, multiply the weights in this table by 1-2656, and the deflections by |=-888. * Example. — Eed Pine 16 in. by 12 in., 8 feet long, with 384 cwts. uniformly loaded, (one-eighth the breaking weight) deflects "066 of an inch; and with 384 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -105 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 91 TABLE XVI. Continued. SCANTLINGS, 16 in., 17 in. and 18 inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. length in feet, CLEAR bearing. 9 10 11 12 13 14 15 16 Depth. Breadth. weight in CWTS. 16X 2 56-88 51-20 46-54 42-66 39^38 36^57 34^1 3 32-00 16 X 2i 7111 64-00 58-18 53-33 49-23 45*71 42-66 40-00 16X 3 85-33 76-80 69-81 64-00 59-07 54-85 51-20 48^00 16 X 3i 99-55 89-60 81-45 74-66 68-92 64-00 59-73 56-00 16 X 4 113-77 102-40 93-09 85-33 78-76 73-14 68-26 64-00 16 X 4i 128-00 115-20 104-72 96-00 88-61 82-28 ~76^ 72-00 16 X 5 142-22 128-00 116-36 106-66 98-46 91-42 85-33 80-00 16 X 5^ 156-44 140-80 128-00 117-33 108-30 100-57 93-86 88-00 16 X 6 170-66 153-60 139-63 128-00 118-15 109-71 102-40 96-00 16 X 6i 184-88 166-40 151-27 138-66 128-00 118-85 110-93 104-00 16X 7 199-11 179-20 162-90 149-33 137-84 128-00 119-46 11200 16 X 8 227-55 204-80 186-18 170-66 157-53 146-28 136-53 128-00 16X 9 256-00 230-40 209-45 192-00 177-23 164-57 153-60 144-00 16X10 284-44 256-00 232-72 213-33 196-92 182-85 170-66 160-00 16X11 312-88 281-60 256-00 234-66 216-61 201-14 187-73 176-00 *16X12 341-33 307-20 279-27 256-00 236-30 219^42 20^80 192^0 16X13 369-77 332-80 302-54 277-33 256-00 237-71 221-86 208-00 16X14 398-22 358-40 325-81 298-66 275-69 256-00 238-93 224-00 16X15 426-66 384-00 349-09 320-00 295-38 274-28 256-00 240-00 16X16 455-11 409-60 372-36 341-33 315-07 292-57 273-06 256-00 Deflection in inches of Red Pine 1 6 inches deep, loaded with the weigh ;s in this table. Weight uniform- ) ly loaded. J •083 •103 -124 •148 •174 -201 -231 -263 Wt. suspended ) from the middle, j -133 •164 •199 -237 •278 •322 -370 •421 *#* For Scantlings 17 inches deep, multiply the weights in this table by f||=M289, and the deflections by ^^=-941. For Scantlings 18 inches deep, multiply the weights in this table by |i= 1-2656, and the deflections by |-=.888. * Example. — Red Pine 16 in. by 12 in., 16 feet long, with 192 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -263 of an inch ; and with 192 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -421 of an inch. 92 SECOND SERIES TABLES OF WEIGHTS. TABLE XVI. Continued. SCANTLINGS, 16 in., 17 in. and 18 inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded ; or One-fourth of the same, when suspended from the middle. SlZB OF Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 17 18 19 20 21 22 23 24 Depth. Breadth. WEIGHT IN CWTS. 16 X 2 16 X 2i 16 X 3 16 X 3i 16X 4 30- 11 37-64 45-17 52-70 60-23 28-44 35-55 42-66 49-77 56-88 26-94 33-68 40-42 47-15 53-89 25-60 32-00 38-40 44-80 51-20 24-38 30-47 36-57 42-66 48-76 23-27 29-09 34-90 40-72 46-54 22-26 27-82 33-39 38-95 44-52 21-33 26-66 32-00 37-33 42-66 16 X 4^ 16X 5 16 X 5i 16 X 6 16 X 6i 67-76 75-29 82-82 90-35 97-88 64-00 71-11 78-22 85-33 92-44 60-63 67-36 74-10 80-84 87-57 57-60 64-00 70-40 76-80 83-20 54-85 60-95 67-04 73-14 79-23 62-36 58-18 64-00 69-81 75-63 50-08 55-65 61-21 66-78 72-34 48-00 53-33 58-66 64-00 69-33 16 X 7 16 X 8 16 X 9 16X10 16X11 105-41 120-47 135-52 150-58 165-64 99-55 113-77 128-00 142-22 156-44 94-31 107-78 121-26 134-73 148-21 89-60 102-40 115-20 128-00 140-80 85-33 97-52 109-71 121-90 134-09 81-45 93-09 104-72 116-36 128-00 77-91 89-04 100-17 111-30 122-43 ~7l'^ 85-33 96-00 106-66 117-33 *16 X12 16X13 16X14 16X15 16X16 180-70 195-76 210-82 225-88 240-94 170-66 184-88 199-11 213-33 227-55 161-68 175-15 188-63 202-10 215-57 153-60 166-40 179-20 192-00 204-80 146-28 158-47 170-66 182-85 195-04 139-63 151-27 162-90 174-54 186-18 133-56 144-69 155-82 166-95 178-08 12800 138-66 149-33 160-00 170-66 Deflection in inches of Red Pine 16 inches deep, loaded with the weights in this table. Weightaiiiform. ) ly loaded. J -297 -333 -371 •411 •453 •497 •543 •592 Wt. suspended ) -475 -532 •593 •657 -725 •795 •869 •947 from the middle. ) For Scantlings 17 inches deep, multiply the weights in this table by f||= M289, and the deflections by if =-941. For Scantlings 18 inches deep, multiply the weights in this table by 1^= 1-2656, and the deflections by l=-888. * Example.— Rei Pine 16 in. by 12 in., 24 feet long, with 128 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -592 of an inch; and with 128 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is -947 of an inch. SECOND SERIES — TABLES OF WEIGHTS. 93 TABLE XVI. Continued. ' SCANTLINGS, 16 in., 17 in. and 18 inches Deep. The weights in this table are — One-eighth of the breaking weight of Red Pine, uniformly loaded; or One-fourth of the same, when suspended from the middle. Size of Scantlings, in inches. LENGTH IN FEET, CLEAR BEARING. 2-5 26 27 28 29 30 31 1 32 Depth. Breadth. WEIGHT IN CWTS. Ifi V 9 20*48 19-69 18-96 18-28 17-65 17-06 16-51 16^00 16 X 2i 25-60 24-61 23-70 22-85 22-06 21-33 20-64 20^00 16 X 3 30-72 29-53 28-44 27-42 26-48 25-60 24-77 24^00 16 X 3i 35-84 34-46 6Z\}\) 6\} oy 28-90 28-00 16 X 4 40-96 39-38 37-92 36-57 35-31 34-13 33-03 32-00 16 X Al\ 46-08 '±'± ou 42-66 41-14 39-72 38-40 Of 1 \J 36-00 16 X 5 51-20 49-23 47-40 45-71 44-13 42-66 41-29 40-00 16 X 5i 56-32 54-15 52-14 50-28 48-55 46-93 45-41 44-00 16 X 6 < 61-44 59-07 56-88 64-85 52-96 51-20 49-54 48-00 16 X 6i 64-00 61-62 59-42 57-37 55-46 53-67 52-00 16 X 7 71-68 68-92 66-37 64-00 61-79 69-73 57-80 56-00 16X 8 81-92 78-76 75-85 73-14 70-62 68-26 66-06 64-00 16X 9 92-16 88-61 85-33 82-28 79-44 76-80 74-32 72-00 16X10 102-40 98-46 94-81 91-42 88-27 85'33 82-58 80-00 16X11 112-64 108-30 104-29 100-57 97-10 93-86 90-83 88-00 *16X12 122-88 118-15 113-77 109-71 105-93 102-40 99-09 96-00 16X13 133-12 128-00 123-25 118-85 114-75 110-93 107-36 104-00 16X14 143-36 137-84 132-74 128-00 123-58 119-46 115 61 112-00 16X15 153-60 147-69 142-22 137-14 132-41 128-00 123-87 120-00 16X16 163-84 157-53 151-70 146-28 141-24 136-53 132-12 128-00 Deflection in inches of Red Pine 16 inches deep, loaded with the weights in this table. VVeightuniform. » ly loaded. ) -642 •694 -749 -805 •864 -924 •987 1052 Wt. suspended > from the middle. J 1-027 1-111 1-198 1-289 1-382 1-479 1-579 1-683 For Scantlings 17 inches deep, multiply the weights in this table by f|-|= 1-1289, and the deflections by 4-f=-941. For Scantlings 18 inches deep, multiply the weights in this table by 11= 1-2656, and the deflections by 1= -888. * Example.— '^^i. Pine 16 in. by 12 in., 28 feet long, with 109-71 cwts. uniformly loaded, (one-eighth the breaking weight) deflects -805 of an inch ; and with 109 71 cwts. suspended from the middle, (one-fourth the breaking weight) the deflection is 1-389 inches. N THIRD SERIES: BY WHICH MAY BE FOUND THE SCANTLINGS OF ANY DESCRIPTION OF TIMBER TO HAVE GIVEN EQUAL DEFLECTIONS, WHEN PRESSED BY TWO FORCES; VIZ. ONE IN THE DIRECTION OF THE DEPTH; THE OTHER IN THE DIRECTION OF THE BREADTH. 96 THIKD SERIES OF TABLES. TABLE OF CONSTANTS. No. 3. By which, and the Thh-d Series of Tables, may be found the Scantlings of the following species of Timber to have the same strength or DEFLECTION as Red Pine, when acted upon by two forces, viz., one in the direction of the depth, the other in the direction of the breadth. Name of the Wood. Standard-Red Pine { ^^^^Jj;^ 230000 Acacia Ash Beech Birch, American black „ Common Bullet tree C abac ally Deal, Christiana „ Memel Elm Fir, Mar Forest „ New England „ Riga Green-heart Larch Locust tree Norway spars Oak, Adriatic • „ African (superior quality) „ Canadian „ Dantzic „ English Pine, Pitch „ Red, mean strength, 1341-3 Poon Teak Tonquin bean Factors to give the Factors to give the depth and breadth, depth and breadth, to have the same to have the same Strensjih. Deflection. 1 c=4/E 1 \J\J\J 1-000 •896 1124 •872 1^028 •952 l^OSO •904 1^057 •887 1-028 •797 •915 •811 •999 -952 1-037 .919 1-029 1-098 1-279 1-034 1-216 1-068 1-054 • 1-076 1-125 -789 •912 1-103 M91 -731 •986 -970 1-060 •991 M73 •814 •945 -913 •987 •971 M21 •980 1-122 •937 1-107 rool 1-000 -846 1-022 •817 •934 •718 •912 Col. T. [T. THIRD SERIES OF TABLES. 97 Note. — To find the Scantlings of Red Pine Brest-summers and Purlins, — see the Diagrams and Examples p. xxiA\ — xli. *** The Scantlings of other kinds of timber to have the same Strength or Deflection as Red Pine, are found by the Table of Constants, No. 3 ; as in the following Example. ' Example to the Table of Constants. No. 3. By Table IV. page 111, Red Pine 8 feet long 7-18 in.X5-08 in., with 8X500=4000 lbs. pressure in the direction of the depth, and with •50X4000=2000 lbs. pressure in the direction of the breadth, deflects each way of an inch. Required the Scantlings of Riga Fir to have the same strength, and also the same deflection as Red Pine. 1. To find the Scantling of Riga Fir to have the same Strength as Red Pine. By Col. I. (p. 96,) for Riga Fir, c= 1-076; 7-18Xl-076 = 7-725; 5-08Xl-076=5-466. Scantling, 7-73 X5-47. The breaking weight of Riga Fir 8 feet long, 7-73 in. X5-47 in., is the same as that of Red Pine 8 feet long, 7-18 in. X5-08 in.; viz., 8 X 500 X 7-325 = 29300 lbs., in the direction of the depth ; or 8 X -5 X 500 X 10-36 = 20720 tbs., in the direction of the breadth; the pressure being uniform in both cases ; or one half of those weights if the pressures act in the middle. 2. To find the Scantling of Riga Fir to have the same Deflection as Red Pine. By Col II. for Riga Fir, c= 1-125; 7-18X1-125 = 8-077; 5-08 X 1-125=5-715. Scantling 8-08 X 5-72. Riga Fir 8 feet long, 8-08 in. X 5-72 in., with a pressure of 4000 lbs, in the direction of the depth, and 2000 fbs. in the direction of the breadth, deflects each way of an inch ; the pressures being uniform. 98 THIRD SERIES ; — TABLES OF SCANTLINGS TABLE I. Scantlings of Red Pine when acted upon by two forces P and Q, viz. P in the direction of the depth, Q in the direction of the breadth. lu this table, Q,="16 P; P = pressure upon each foot in length;) B READ TH The deflections each way of the timber are equal ) DepTH Length in feet, clear bearing. Value of P. 1-0000 lbs. •0089 cwts. Value of P. 16-0000 lbs. •1428 cwts. Value of P. 39-0625 lbs. •3487 cwts. Value of P. 81-0000 lbs. •7232 cwts. Value of P. 150 0625 lbs. 1-3398 cwts. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth 1 2 3 4 *5 •35 X -14 •59 X -23 •79 X ^32 •98 X -39 M6X ^47 •70 X -28 M7X -47 1-59 X -63 1- 97 X -79 2- 33 X -93 •87 X -35 r46X ^59 1^98 X -79 2-46 X -98 2-91 XM6 1^04 X -42 1- 76 X -70 2- 38 X -95 2- 95X1-18 3- 49 X 1-40 1- 22 X -49 2^05 X -82 2- 78X1-11 3- 45 X 1-38 4- 07 X 1-63 6 7 8 9 10 1-33 X ^53 1-60 X -60 1^66X -66 1-81 X ^72 1-96 X -78 2^67 X 1-07 3-00X1-20 3-31 X 1-32 3-62X1-45 3-91 X 1-57 3-34X1-33 3- 74X1-50 4- 14X1-66 4-52X1-81 4-89 X 1-96 4-00 X 1-60 4-49X1-80 4- 97X1-99 5- 43X2-17 5-87 X2-35 4- 67X1-87 5- 24X2-10 5- 79X2-32 6- 33X2 53 6-85 X 2-74 11 12 13 14 15 2-lOX -84 2-24 X -90 2^38 X ^95 2-52 X 1^01 2-65 XI •oe 4-20X1^68 4-49X1-80 4- 77X1-91 5- 04X2-02 5-31X2-12 5-26X2-10 5-61 X2-24 5- 96X2-38 6- 30X2-52 6-63X2-65 6-31 X2-62 6- 73X2-69 7- 15X2-86 7-56X302 7^96X3-18 7-36X2-94 7- 85X3-14 8- 34X3-34 8- 82 X3-53 9- 28X3-71 16 17 18 19 20 2- 78 X Ml 291 XM7 3- 04 XI ^22 3^17Xl-27 3^29 XI -32 5-57 X2-23 5- 83X2-33 6- 08X2-43 6-33X2-53 6-58X2-63 6- 96X2-78 7- 28X2-91 7-60X3-04 7- 92X3-17 8- 23X3-29 8^35 X3-34 8- 74 X3-50 9- 12X3-65 9-50X3-80 9-87X3-95 9-75X3-90 10-20X4-08 10- 65X4-26 11- 09X4-43 11-52X4-61 Deflections in the middle for each foot in length. Value of D of an inch. of an inch. of aninch. of an inch. ^of an inch. Value of P ~D 40-00 lbs. •35 cwts. 640-00 lbs. 5-71 cwts. 1562-50 lbs. 13-94 cwts. 3240-00 lbs. 28-92 cwts. 6002-50 lbs. 53-59 cwts. Value ol P IT 25-00 lbs. •22 cvvts. 400-00 lbs. 3-57 cwts. 976-56 lbs. 8-71 cwts. 2025 00 lbs. 18-08 cwts. 3751-56 lbs. 33-49 cwts. Factors to^ive breaking weight. Column I. Factor 4, II. 1 Factor 2. III. Factor IS. IV. Factor |. V. Factor f.f * Example. — Red Pine 5 feet long, 1-16 in. by -47 in., with 5x1 = 5 lbs. pressure in tlie direction of the depth, and with -16 x 5 = -8 lbs. pressure in the direction of the breadth, de- flects each way -J^ of an inch. The breaking weight, in the direction of the depth, of Red Pine 5 feet long, 1-16 in. by -47 ill., is 5 X 1 X 5-648 x 4 = 112-96 lbs. ; and in the direction of the breadth, the breaking weight is 5 X 1 X -16 X 14-123 x 4 = 45-19 lbs. ; the pressure being uniform in both cases. + Throughout these tables, in each of the columns VI. to XVIII, (both inclusive) the Factor to give, the breaking weight is ] . PRESSED BY TWO FORCI<:s P AND Q. 89 TABLE I. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, G = -16 P; P = pressm-e upon each foot in length; |Breadth The deflections each way of the timber are equal | Depth = •40. Length in feet, clear bearing. Value of P. 256-0000 lbs. 2-2857cwts. 1 2 3 4 *5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Depth. Breadth, 1- 39 X -56 2- 34 X -94 3- 17X1-27 3- 94X1-58 4- 66X1-86 6-34X2-13 5- 99 X2-40 6- 62X2-65 7- 23X2-89 7-83X3-13 8-41 8- 98 9- 53 10-08 10-61 X3-36 X3-59 X3-81 X4-03 X4-24 11-14 11- 66 12- 17 12-67 1317 X4-45 X4-66 X4-87 X5-07 X5-27 Value of P. 364-5000 lbs. 3'2544cwts. Depth. BreaJth. 1- 57 X -63 2- 63 XI -05 3- 57X1-43 4- 43 X 1-77 5- 24X2-09 6-00X2-40 6- 74X2-70 7- 45X2-98 8- 14X3-26 8-81 X3-52 9-46 X3-78 10-10X4-04 10- 72X4-29 11- 34X4-53 11-94X4-78 12- 53 X5-01 13- 11X5-25 13- 69X5-47 14- 25X5-70 14-81 X5-92 Value of P. 500-0O0O lbs. 4-4642cwts. Depth. Breadth. 1- 74 X -70 2- 93 XM7 3- 97 X 1-59 4- 92X1-97 5- 82 X2-33 6- 67 X2-67 7- 49 X3-00 8- 28X3-31 9- 04 X3-62 9-79X3-91 10- 51 X4-20 11- 22 X4-49 11- 91 X4-77 12- 60X5-04 13- 26 X5-31 13- 92X5-57 14- 57X5-83 15- 21 X6-08 15- 84X6-33 16- 46X6-58 Value of P. 665-5000 lbs. 5 9419cwts. Depth. Breadth. 1-91 X -77 3- 22X1-29 4- 36 X 1-75 5- 41 X2-17 6- 40X2-56 7- 34X2-94 8- 24 X3-30 9- 11 X3-64 9-95X3-98 10-76X4-31 11- 56X4-62 12- 34 X4-94 13- 11X5-24 13- 85X5-54 14- 59 X5-84 15- 31 X6-13 16- 03X6-41 16-73X6-69 Multipliers to give the breaking weight of every Scautling in the table. In the direc. lion of the depth. 3- 777 4- 492 4- 971 5- 342 5-648 5- 912 6- 144 6-353 6-543 6-717 6- 879 7- 030 7-173 7-307 7-434 7-555 7-670 7-780 7-886 7-988 lu the direc- tion of the breadth. 9-444 11- 230 12- 429 13- 355 14- 122 14- 780 15- 361 15- 882 16- 357 16-794 17-199 17-577 17- 932 18- 267 18-585 18- 888 19- 176 19-452 19-717 19-971 Value of I D I Deflections in the middle for each foot in length. of an inch. Value of P 10240-00 lbs. 91-42cwts. of an inch.l^ of an inch. j^VofanindTl Examples. 16402-50 lbs. 146-45cwts. 25000-00 lbs. 223-21 cwts. 36602-50 lbs. 326-80cwts. \ Pressure uniform. Wueof p 6400-00 lbs. 57-I4cwts. 10251-56 lbs. 91-53ewts. 15625-00 lbs. 139-50cwts. 22876 56 lbs. 204-25cwts. Pressure in the middle. VI. VII. VIII. IX. '■ Example.— Ilei Pine 5 feet long, 4-66 in. by 1-86 in., with 5 x 256 = 1280 lbs. pres- sure in the direction of the depth, and with '16 x 1280 = 204-8 lbs. pressure in the direction )f the breadth, deflects each way -J^ of an inch. The breaking weight, in the direction of the depth, of Red Pine 5 feet long, 4-66 in. by 36 in., is 5 x 256 x 5-648 = 7229-44 lbs.; and in the direction of the breadth, the breaking veight is 5 X 256 x -16 x 14-122 = 2892-18 lbs.; the pressure being uniform in both cases. To find the Scantlings of other kinds of timber to have the same deflection or strength as Red Pine, also for the use of the expression -L, see Note, page 97. 100 THIRD SERIES — TABLES OF SCANTLINGS TABLE I. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this tahle, Q=-16 P; P = pressure upou each foot in length ; | Breadth __ .^q The deflections each way of the timber are equal J DePTH Ijength in feet, clear bearing. Value of P. 864-0000 lbs. 7-7142 cwts. Value of P. 1098-5000 lbs. 9-8080cwts. Value of p. 1372-0000 lbs. 12-2500cwts. Value of P. 1687 5000 IDs 15-0669cwts. Value of P. ■iWxO UUOU IDS. 18-2857cwts. Depth. Breadth. Depth. Breadth Depth. Breadth.' Depth. Breadth. Depth. Breadth. 1 2 3 4 *5 2- 09 X -84 3- 51 XI -40 4- 76X1-90 5- 91 X2-36 6- 98X2-79 2- 26 X -90 3- 80X1-52 5- 16 X2-06 6- 40X2-56 7- 56X3-03 2-44 X -97 4- 10X1-64 5- 55 X2-22 6- 89X2-76 8-15X3-26 2-61 X 1-04 4-39X1-76 0 yo X2 00 7- 38X2-95 8- 73X3-49 2-78X1-11 4-68X1-87 7-88X3-15 9-31 X3-72 6 7 8 9 10 11 12 13 14 15 8-01 X3-20 8- 99 X3-59 9- 93X3-97 10- 85X4-34 11- 74X4-70 12- 61 X5-05 13 46X5-39 14- 30X5-72 15- 11 X6-05 15-92X6-37 8- 67X3-47 9- 74X3-89 10- 76X4-30 11- 76X4-70 12- 72X5-09 9-34X3-74 10- 48X4-19 11- 59X4-64 12- 66X5-06 13- 70X5-48 10- 01 X4-00 11- 23X4-49 12- 42X4-97 13- 56X5-43 14- 68X5-87 10- 67X4-27 11- 98X4-79 13- 24X5-30 14- 47X5-79 15- 66X6-26 13- 66X5-47 14- 59X5 83 15- 49 X6-20 16- 37X6-55 14- 72X5-89 15- 71 X6-28 16- 68X6-67 15- 77X6-31 16- 83X6-73 16-82X6-73 Deflections in the middle for each foot in length. Valneof D .5% of an inch. -g-^of aninch. y^of an inch. ^'^ of an inch. -j^igofaninch. Valueof P "d" 51840-00 lbs. 462-85 cwts. 71402-50 lbs. 637-52 cwts. 96040 00 lbs. 857-50 cwts. 126562 50 lbs. 11 3002 cwts. 163840 00 lbs. 1462-85 owts. Value „r P °' ~d" 32400 00 lbs. 289-28 cwts. 44626-56 lbs. 398-45 cwts. 60025-00 lbs. 535-93 cwts. 79101-56 lbs. 706-26 cwts. 102400 00 lbs. 914-28 cwts. X. XI. XII. XIII. XIV. * Example l.-Red Piue 5 feet long, 6-98 in. by 2-79 in., with 5 x 864 = 4320 lbs. pressure in the direction of the depth, and with -16 x4320 = 691-2 lbs. pressure m the direction of the breadth, deflects each way ^ of an inch ; the pressures being uniforai throughout the length. Example 2.-Red Pine 5 feet long, 6-98 iu. by 2-79 in., with | x 4320 = 2700 lbs. pressure in the direction of the depth, and with | x 691-2 = 432 lbs. pressure in the direction of the breadth, deflects each way of au inch ; the pressures in each case being in the middle. iVoie.— Uniform pressures, or fths of the same acting in the middle, the deflections are- the same in both cases ; as in the above examples. PRESSED BY TWO FORCES P AND Q. 101 TABLE I. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q,="16 P; P = pressure upon each foot in length;] Breadth The deflections each way of the timber are equal j DepTH Leingtb in leet, bearing. Value of P. 2456-5000 lbs 21-9330cwts. Value of P. 29 160000 lbs. 26-0357cwts. Value of P. 3429-5000 lbs. 30-6205c«'t3. Valu 4000-( 35-'" e of P. )000 lbs. ri42cwts. Multipliers breakin of every Sc Ub In the direc- tioD of the depth. to give tlie g weight mtling in the le. In the direc- tion of the breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 *5 2-96 XM8 4-98X1-99 6-74 X 2-70 8 37 X3-35 9-89 X3-96 3-13X1-25 5-27X2-11 7- 14X2-86 8- 86 X3-54 10-47X4-19 3-31 Xl-32 5-56 X2-22 7-54X3-01 9-35 X3-74 11-06X4-42 3-48 5-85 7-93 9-84 11-64 Xl-39 X2-34 X3-17 X3-94 /N 4 OU 3- 777 4- 492 4- 971 6-342 5- 648 9-444 11- 230 12- 429 13- 355 14- 122 6 7 8 9 10 11- 34X4-54 12- 73 X5-09 14- 07X5-63 15- 37X6-15 16- 64X6-65 12- 01 X4-80 13- 48X5-39 14- 90X5-96 16-28X6-51 12-68X5-07 14- 23 X5-69 15- 73 X6-29 13- 34 14- 98 16-56 X5-34 X5-99 5- 912 6- 144 6-353 6-543 6-717 14- 780 15- 361 15- 882 16- 357 16-794 11 12 13 14 15 ... 6- 879 7- 030 7-173 7-307 7-434 17-199 17-577 17- 932 18- 267 18-585 Deflections in the middle for each foot in length. See Examples. Value of D. ■g-y of an inch. of an inch. -gi^ of an inch. an inch. Value of P IT 208802-50 lbs. 1864-30cwts. 262440-OOlbs. 2343-21 ewts. 325802 50 lbs. 2908-95cwts. 40000 357 D-OOlbs. [-42owts. 1 Pressure uniform. Value of P 13050 1-56 lbs. 1165-19cwu. 164025-00 lbs. 1464-50cwts. 203626-56 lbs. 1818-09cwts. 25000 223 0-00 lbs. 2-14cwts. ) Pressure in the j middle. XV. XVI. XVII. X) ^III. * Example..— Red. Pine 5 feet long, 9-89 in. by 3-96 in., with 5 x 21-933 = 109-665 cwts. pressure in the direction of the depth, and with "16 x 109-665 = 17'5464 cwts. pressure iu the direction of the breadth, deflects each way ^ of an inch. The breaking weight, iu the direction of the depth, of Red Pine 5 feet long, 9'89 in. by 3-96 in., is 5 X 21-933 x 5-648 = 619-38 cwts.; and in the direction of the breadth, the breaking weight is 5 x 21933 x -16 x 14'122 = 247-79 cwts.; the pressure being uniform in both cases ; or one half of those weights, viz., 309-69 cwts. and 123-89 cwts. respectively, the pressures being in the middle. o 102 THIRD SERIES — TABLES OF SCANTLINGS TABLE II. Scantlings of Red Pine, when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. Ill this fable, Q,= -25 P; P = pressure upon each foot in length;] Bread TH The deflections each way of the timber are equal IDkpTH Length ill feet, clear beariog. Value of P. 1-0000 lbs. •0089 cwts. Value of P. 16-0000 lbs. ■1428 cwts. Value of P. 39 0625 lbs. •3487 cwts. Value of P. 81-0000 lbs. •7232 cwts. Value of p. 150 0625 lbs. 1-3398 cwts. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 •33 X •le •55 X -28 •75 X ^38 •93 X ^47 1 lU X 00 •66 X ^33 MIX ^55 r50X ^75 1-86 X ^93 •82 X -41 r38X -69 1- 88X -94 2- 33 XM6 O-T^ V 1 •'i>i i£ i O I oO •99 X -49 1- 66 X ^83 2- 25XM3 2-79X1-40 o OU 1 DO 1-15 X -58 1- 94 X -97 2- 63 X 1-31 3- 26 X 1-63 o OO A I yo *6 7 8 9 10 1-26 X -63 1-42 X -71 1-57 X -78 1-71 X -86 1 80 X •yo 2-52 Xr26 2- 83X1-42 3- 13X1-57 3-42X1-71 o /U X 1 00 3-15Xr58 3-54 Xr77 3- 91 X 1-96 4- 28X2-14 4. (to V O-'i 1 4 DO /. 2 / o 4- 42 X 2^21 4^96 X 2^48 5^48 X 2^74 5- 99 X 2-99 D hO /n O /i'iL 11 12 13 14 15 1- 99X ^99 2- 12 X roe 2-25 X113 2-38 XM9 2-51 X125 3- 98X1-99 4- 24X212 4-51X2-25 4- 76X2-38 5- 02X2-51 4-97X2-49 5^31 X 2-65 5^63X2-82 5^96X2-98 6-27X3-14 5- 96X2-98 6- 37X3-18 6-76X3^38 7^15X3-57 7^53X3-76 6- 96 X 3-48 7- 43 X 3-71 7- 89 X 3-94 8- 34 X 4-17 8-78 X 4-39 16 17 18 19 20 2-63 X 1-32 2^76 Xr38 2- 88 X 1-44 3- 00 X 1-50 311 X156 5-27X2-63 5-51X2-76 5-75X2-88 5- 99X3-00 6- 23 X3^ 11 6-58X3-29 6- 89X3-44 7- 20X3-60 7-49X3-74 7-78X3-89 7^90X3-95 8-27X4-13 8-63X4-31 8- 99X4-49 9- 34X4-67 9-22 X 4-61 9-65 X 4-82 10-07 X 5-03 10-48 X 5-24 10-90 X 5-45 Deflections in the middle for each foot in length. vai^eofj_i^ofan inch. ^^^of an inch. ^of an inch. ^of an inch. ^ of an inch. Value ol P 'd' 40 00 lbs. •35 cwts. 64000 lbs. 5-71 cwts. 1562-50 lbs. 13-94 cwts. 3240 00 lbs. 28-92 cwts. 6002 50 lbs. 53-59 cwts. Value of P Id" 25 00 lbs. •22 cwts. 400-00 lbs. 3"57 cwts. 976-56 lbs. 8-71 cwts. 2025-00 lbs. 18-08 cwts. 3751-56 lbs. 33-49 cwts. Factors to give the breaking weight. Column I. Factor 4, II. Factor 2. III. Factor 1-6. IV. Factor ^. V. Factor ^. ♦ Example. — Red Pine 6 feet long, 2^52 in. by 1-26 in., with 6 x 16 = 96 lbs. pressure in the direction of the depth, and with -25 x 96 = 24 lbs. pressure in the direction of the breadth, deflects each way of an inch. The breaking weight, in the direction of the depth, of Red Pine 6 feet long, 2-52 in. by 1-26 in., is 6 X 16 X 6-251 x 2 = 1200 lbs. ; and in the direction of the breadth, the breaking weight is 6 x 16 X -25 x 12-503 x 2 = 600 lbs. ; the pressure being uniform iu both cases ; or one half of those weights, if the pressures act in the middle. PRESSED BY TWO FOUCKS P AND Q. 103 TABLE II. Continued. ScANTMNGS of Red Pine when acted upon by two forces P and Q, viz., P in the dii'ection of the depth, Q in the direction of the breadth. In this table, Q, = "25 P; P = pressure upon each foot in length ;^ BreaDTH The deflections each way of the timber are equal Depth = •50. length in feet, clear bearing. *6 7 8 9 10 11 12 13 14 15 Value of P. 256 0000 lbs 2-2857cwts. Depth. Breadth 1-32 X -66 2'21XM1 3-00 XI -50 3- 72 X 1-86 4- 40X2-20 5-05 X 2-52 5- 67X2-83 6- 26X3-13 6- 84X3-42 7- 40X3-70 7- 95X3-98 8- 49X4-24 9- 01X4-51 9-53X4-76 10-04 X 5-02 16 17 18 19 20 10- 53 X5-27 11- 02X5-51 11-51 X5-75 11- 98X5-99 12- 45X6-23 Value of P. 364-5000 lbs. 3-2544cwts, Depth. Breadth. 1- 48 X -74 2- 49X1-25 3- 38X1-69 4- 19X2-09 4-95X2-48 5- 68X2-84 6- 37X3-19 7- 05X3-52 7- 70X3-85 8- 33X4-16 8- 95X4-47 9- 55X4-77 10-14X5-07 10- 72X5-36 11- 29X5-64 11- 85X5-92 12- 40X6-20 12- 94X6-47 13- 48X6-74 14- 01X7-00 Value of P. 500-OOOOlbs. 4-4642cwts. Depth. Breadth Value of P. 665-5000 lbs. 5-941 9cwts 1- 65 X -82 2- 77X1-38 3- 75X1-88 4- 66X2-33 5- 50X2-75 6- 31X3-15 7- 08X3-54 7- 83X3-91 8- 55X4-28 9- 26X4-63 9-94X4-97 10- 61 X5-31 11- 27X5-63 11- 91X5-96 12- 54X6-27 13-17X6-58 13- 78X6-89 14- 38X7-19 14- 98X7-49 15- 57X7-78 Depth. Breadth 1-81 X -91 3- 04X1-52 4- 13X2-06 5- 12X2-56 6- 05X3-03 6- 94X3-47 7- 79X3-90 8- 61X4-31 9- 41X4-70 10-18X5-09 10- 93X5-47 11- 67X5-84 12- 39X6-20 13- 10X6-55 13-80X6-90 14- 48X7-24 15- 16X7-58 15-82X7-91 Multipliers to give the breaking weight of every Scantling in the table. Inthedirec tion of the depth. 3- 994 4- 750 5- 256 5-648 5-972 6-251 6-497 6-717 6- 918 7- 103 7-274 7-434 7-584 7-726 7-860 7- 988 8- 110 8-227 8-339 8-447 In the direc- tion of the breadth. 7-988 9-500 10- 513 11- 297 11-945 12-503 12- 994 13- 435 13- 836 14- 206 14-548 14- 868 15- 169 15-452 15-721 15- 977 16- 221 16-454 16-678 16-894 Deflections in the middle for each foot in length. Value of D. of an inch. -^j- of an inch. -^Vof an inch. XT of an inch. See Examples. Value of P D 10240-00 lbs. 91-42cwts. 16402-50 lbs. I46-45cwts. 25000-00 lbs. 223-2 Icwts. 36602-50 lbs. 326-80cwts. 'ressure uniform. Value of P "d" 6400-00 lbs. 57-14cwts. 10251-56 lbs. 91-53cwts. 15625-00 lbs. 139-50cwts. 22876-56 lbs. 204-25cwts. Pressure iu the middle. VI. VII. VIII. IX. * Example.— Rei Pine 6 feet long, 5-68 in. hy 2-84 in., with 6 x 364-5 = 2187 lbs. pressure in the direction of the depth, and with '25 x 2187 = 546-75 lbs. pressure in the direction of the breadth, deflects each way of an inch. The bireaking weight, in the direction of the depth, of Red Pine 6 feet long, 5-68 in. by 2-84 in.,, is 6 X 364-5 x 6-251 = 13670 lbs. ; and in the direction of the breadth, the breaking weight is 6 x 364-5 x "25 x 12-503 = 7305 lbs. ; the pressure being uniform in both cases ; or oue half of those weights, if the pressures act iu the middle. 104 THIRD SERIES — TABLES OF SCANTLINGS TABLE II. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q,= *25 P; P = pressure upon each foot in length ; IBreaDTH The deflections each way of the timber are equal ] Depth 1 Length ill feet, clear bearing. Value of P. 864'0000 lbs. 7-7142 cwts. Value of P. 1098"5000lbs. 9-8080cwts. Value of P. 1372-OOOOlbs. 12-2500cwts. Value of P. l687-50001bs. 15-0669cwts. Value of P. 2048-OOOOlbs. 18-2857cwts. Depth. JJreadth. Depth. Breadth Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 1-97 X -99 3- 32X1-66 4- 50 XQ-25 5- 59X2-79 6- 60X3-30 2- 14X1-07 3- 60X1-80 4- 88 X2-44 6- 05 X3-03 7- 15X3-58 2- 30X1-15 3- 87X1-94 5- 25 X2-63 6- 52X3-26 7- 70X3-85 2-47X1-23 4- 15X2-08 5- 63 X2-81 6- 98X3-49 8-25X4-13 2-63 X 1-32 4-43 X 2-21 6- 00 X 3-00 7- 45 X 3-72 8- 80 X 4-40 *6 7 8 9 10 7- 57 X3-79 8- 50X4-25 9- 39X4-70 10- 26X5-13 11- 11 X5-55 8- 20X4-10 9- 21 X4-60 10- 18X5-09 11- 12X5-56 12- 03X6-02 8- 83X4-42 9- 92X4-96 10- 96X5-48 11- 97X5-99 12- 96X6-48 9-46X4-73 10- 62X5-31 11- 74X5-87 12- 83X6-41 13- 88X6-94 10- 10 X 5-05 11- 33 X 5-67 12- 53 X 6-26 13- 68 X 6-84 14- 81 X 7-40 11 12 13 14 15 11- 93X5-96 12- 73 X6-37 13- 52X6-76 14- 29X7-15 15- 05X7-53 12- 92X6-46 13- 79X6-90 14- 65X7-32 15- 49X7-74 16- 31 X8-15 13- 92X6-96 14- 86X7-43 15- 78X7-89 14- 91 X7-46 15- 92X7-96 15-91 X 7-95 16 15-80X7-90 Deflections in the middle for each foot in length. Value ol D -gVofaninch.l^'-^of an inch. -^■^ of an inch. | y\- of an inch. -g% of an inch. Valueof P "d" 51840 00 lbs. 462-85 cwts 71402-50 lbs. 637-52 cwts. 96040-00 lbs. 857-50 cwts 126562-50 lbs 1130-02cwts 163840-00 lbs. 1462-85cwts. Value of P 32400-00 lbs. 289-28 cwts. 44626-56 lbs. 398-45 cwts. 60025-00 lbs. 535-93 cwts 79101-56 lbs 706-26cwts 102400-00 lbs. 9]4-28cwts. X. XI. xir. XIII. XIV. * Example.— nei Pine 6 feet long, 8-20 in. by 4-10 in., with 6 x 9-808 = 58-848 cwts. pressure in the direction of the depth, and with -25 x 58-848 = 14-712 cwts. pressure in the direction of the breadth, deflects each way of an inch. The breaking -weight, in the direction of the depth, of Red Pine 6 feet long, 8-20 in. by 4-10 in., is 6 x 9-808 x 6-251 = 367-85 cwts.; and in the direction of the breadth, the breaking weight is 6 x 9-808 x -25 x 12-503 = 122-62 cwts. ; the pressui-e being uniform in both cases ; or one half of those weights, if the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. 105 TABLE II. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q, = '25 P; P = pressure upon each foot in length ;|BreaDTH The deflections each way of the timber are equal j Depth in feet, clear bearing. Value of P. 2456-5000 lbs 21-9330cwts. Value of P. 2916-0000 lbs. 26-0357cwts. Value of P. 3429-5000 lbs. 30-6205cwts. Val 4000- 35- [le of P. 0000 lbs 7I42cwts. Multipliers to give the breaking weight of every Scantling iu the table. In the direc- tion of the depth. In the direc- tion of the breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 2-80X1-40 4-71 X2-35 6- 38X3-19 7- 91X3-96 9-35X4-68 2-96X1-48 4-98X2-49 6-75X3-38 8- 38X4-19 9- 91 X4-95 3-13X1-56 5-26X2-63 7- 13X3-56 8- 84X4-42 10-46X5-23 3-2i: 5-54 7-5C 9-31 11-01 >Xl-65 1X2-77 )X3-75 X4-66 X5-50 3-994 4 / OU 5-256 5-648 5-972 7-988 y ouu 10- 513 11- 297 11-945 *6 7 8 9 10 10-73X5-36 12- 04X6-02 13- 31X6-65 14- 54X7-27 15- 73X7-87 11- 36X6-68 12- 75X6-37 14- 09X7-05 15- 39X7-70 11-99X5-99 13- 46X6-73 14- 88 X 7-44 16-25X8-12 12-6S 14- 17 15- 6e ,X6-31 'X7-08 .X7-83 6-251 6-497 6-717 6- 918 7- 103 12-503 12- 994 13- 435 13- 836 14- 206 11 12 13 14 15 7-274 7-434 7-584 7-726 7-860 14-548 14- 868 15- 169 15-452 15-721 16 7-988 15-977 Deflections in the middle for each foot in length. See Examples. Value of D of an inch. 0% of an inch. -^x of an inch. Fan inch. Value of P 208802-50 lbs. 1864-30cwts. 262440-00 lbs. 2343-21 cwts. 325802-50 lbs. 2908-95cwts. 4000C 357 )0-00lbs. l-42cwts. 1 Pressure uniform. Value of P ~D 130501-56 lbs. 1165-19cwts. 164025-00 lbs 1464-50cwts. 203626 '56 lbs. 1818-09cwts. 2500C 223 0-00 lbs. 214cwts. 1 Pressure in the j middle. XV. XVI. XVII. X^ ^III. * Example.— RtSi Pine 6 feet long, 11-36 in. by 5-68 in., with 6 x 26-0357 = 156-214cwt8. pressure in the direction of the depth, and with '25 x 156'214 = 39-053 cwts. pressure in the direction of the breadth, deflects each way _^ of an inch. The breaking weight, in the direction of the depth, of Red Pine 6 feet long, 11-36 in. by 5-68 in., is 6 X 26-0357 x 6-251 = 976-49 cwts. ; and in the direction of the breadth, the breaking weight is 6 x 26-0357 x -25 x 12-503 = 488-25 cwts. ; the pressure being uniform in both cases ; or one half of those weights, if the pressures act in the middle. 106 THIRD SERIES — TABLES OF SCANTLINGS TABLE III. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q = *36P; P = pressure upon each foot in length;"! Breadth The deflections each way of the timber are equal JDepth Length in feet, clear bearing. Value of P. 1-0000 lbs. •0089 cwts. Value of P. 1 6-0000 lbs. -1428 cwts. Value of P. 39-0625 lbs. •3487 cwts. Value of P. 81-0000 lbs. •7232 cwts. Value of P. 150-0625 lbs. 1-3398 cwts. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 ] -31 X -19 •53 X -32 -72 X -43 •89 X -53 •05 X '63 -63 X -38 1-06X -63 1-43 X -86 1- 78 X] -07 2- 10X1-26 -79 X -47 1-32 X -79 1- 79X1-08 2- 22X1-33 2-63X1-58 •94 X ^57 1- 59 X -95 2- 15X1-29 2- 67X1-60 3- 15X1-89 1-10 X -66 1- 85 X M 1 2- 51 X 1-51 3- 11 X 1-87 3-68 X 2-21 6 *7 8 9 10 1-21 X -72 1-35X -81 1-50X -90 1-63 X -98 1-77 X 1-06 2-41X1-45 2-71 X 1-62 2- 99X1-80 3- 27 X 1-96 3-54X2-12 3-01X1-81 3-38X2-03 3- 74X2-24 4- 09X2-45 4-42X2-65 3- 62X2-17 4- 06X2-44 4- 49 X 2^69 4^90X2^94 5- 31X3-18 4-22 X 2-53 4- 74 X 2-84 5- 24 X 3-14 5- 72 X 3-43 6- 19 X 3-71 7- 10 X 4-26 7-54 X 4-52 7- 97 X 4-78 8- 39 X 5 03 11 12 13 14 15 1- 90XM4 203X1-22 2- 15X1-29 2-28X1-37 2-40X1-44 3- 80X2-80 4- 06X2-43 4-31X2-58 4-55X2-73 4-79X2-88 4- 75X2-85 5- 07X3-04 5-38X3-23 5-69X3-41 5-99X3-60 5- 70X3^42 6- 08X3-65 6-46X3-88 6-83X4^10 7^19X4-31 16 17 18 19 20 2-52X1-51 2-63X1-58 2-75X1-65 2-86X1-72 2-97X1-78 5-03X3-02 5^27 X3- 16 5-50X3-30 5-72X3-43 5-95X3-57 6-29X3-77 6-58X3^95 6-87X4-12 7^16X4^29 7.44X4^46 7-55X4-53 7- 90X4-74 8- 24X4-95 8-59X5-15 8-92X5-35 8- 81 X 5-28 9- 22 X 5^53 9^62 X 5-77 10-02 X 6 01 10-41 X 6-25 Deflections in the middle for each foot in length. Value of D. ^of an inch. ^of an inch. -Jjj^of an inch. .^'^of an inch. 4^ of an inch. Value of P ~D 40-00 lbs. •35 cwts. 640 00 lbs. 5-71 cwts. 1562-50 lbs. 13-94 cwts. 3240 00 lbs. 28 92 cwts. 6002-50 lbs. 53 59 cwts. Value of P "dT 25-00 lbs. •22 cwts. 400-00 lbs. 3-57 cwts. 976^56 lbs. 8-71 cwts. 202500 lbs. 18-08 cwts. 375 1-56 lbs. 33-49 cwts. Factors to give the breaking weight. Column I. Factor 4. II. Factor 2. III. Factor 1-6. IV. Factor ^. V. Factor * Example.— Red Pine 7 feet long, 3-38 in. by 2-03 in., with 7 x 39-0625 = 273^4 lbs. pressure in the direction of the depth, and with '36 x 273"4 = 98'4 lbs. pressure in the direc- tion of the breadth, deflects each way -T^. of an inch. The breaking weight, in the direction of the depth, of Red Pine 7 feet long, 3-38 in. by 2-03 in., is 7 >< 39-0625 x 6-8 x 1-6 = 2975 lbs. ; and in the direction of the breadth, the breaking weight is 7 x 39-0625 x -36 x 11-333 x 1-6 = 1785 lbs.; the pressure being uniform in both cases ; or one half of those weights, if the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. 107 TABLE III. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q=-36P; P = pressure upon each foot in length;) B READ T The deflections each way of the timber ai-e equal j Depth « -fiO Length ill feet, clear beariug. Value of P. 256 0000 lbs. 2-2857cwt8. Value of P. 364-5000lbs. 3-2544cwts. Value of P. 500-0000 lbs. 4-4642cwts. Value of P. 665-5000 lbs. 5-9419 cwts. Multiplier breakin of every Sca la Inthedirei- tion of the depth. s to give the g weight ntliog in the 3le. Ill the direc- tion of the breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 1- 26X -75 2- 12X1-27 2- 87 XI -72 3- 56X2-13 4*21 X2 52 1- 42 X -85 2- 38X1-43 3- 23X1-94 4- 00X2-40 4-/3 X2-b4 1- 57X -94 2- 64X1-59 3- 58X2- 15 4- 45X2-67 5- 26 X3-15 1- 73X1-04 2- 91X1-75 3- 94X2-37 4- 89X2-94 5- 78X3-47 4-180 4- 971 5- 502 5- 912 6- 251 6967 8- 286 9- 170 9-853 10-419 6 *7 8 9 10 4- 82 X 2-89 5- 41X3-25 5- 98X3-59 6- 54X3-92 7- 07 X4-24 5- 43X3-26 6- 09X3-65 6- 73X4-04 7- 35X4-41 7-96X4-78 6-03X3-62 6- 77X4-06 7- 48X4-49 8- 17X4-90 8-84X5-31 6- 63X3-98 7- 44X4-47 8- 23X4-94 8- 99X5-39 9- 73X5-84 6-543 6- 800 7- 030 7-241 7-434 10- 905 1 1- 333 11- 718 12- 068 12-390 11 12 13 14 15 7- 60X4-56 8- 1 1X4-87 8- 61X5-17 9- 10X5-46 9-59 X 5-76 8- 55X513 9- 12X5-47 9-69X5-81 10-24X6-15 10-79X6-47 9-50X5-70 10-14X6-08 10- 77X6-46 11- 38X6-83 11-99X7-19 10- 45X6-27 11- 15X6-69 11- 84X7-11 12- 52X7-51 13- 18X7-91 7-613 7-781 7- 938 8- 086 8-227 12-689 12- 968 13- 230 1 '^•477 1 0 / / 13-712 16 17 18 19 20 10-06X6-04 10-53X6-32 10- 99X6-60 11- 45X6-87 11-90X7-14 11-32X6-79 11- 85X7-11 12- 37X7-42 12- 88X7-73 13- 38X8-03 12- 58X7-55 13- 16X7-90 13- 74X8-24 14- 31 X8-59 14-87X8-92 13- 84X8-30 14- 48 X8-69 15- 12X9-07 15- 74X9-44 16- 36X9-82 8-361 8-488 8-728 8-840 1 0 no 13- 935 14- 148 1 ^ 00 1 14-547 14-734 Deflections in the middle for each foot in length. See Ex amples. Value of D. ^ of an inch. 4:3- of an inch. •^■V of an inch. -jy of an inch. Value of P "d" 10240 00 lbs. 91 42cwts. 16402-50 lbs. 1 46-45 cwts. 25000-OOlbs. 22321cwts. 36602-50 lbs. 3-26-80 cwts. 1 Pressur e uniform. Value of P 640000 lbs. 57-14cwts. 10251-561bs. 91-53cwts. 15625-OOlbs. 139-50cwts. 22876-56 lbs. 204-25 cwts. ) Pressu J mi re iu the ddle. VI. VII. VIII. IX. * Example.— Rtdi Rine 7 feet long, 6-77 in. by 4-06 in., with 7 x 500 = 3500 lbs. pres- sure in the direction of the depth, and with -36 x 3500 = 1260 lbs. pressure in the direction of the breadth, deflects each way -3^ of an inch. The breaking weight, in the direction of the depth, of Eed Pine 7 feet long, 6-77 iu. by 4i 06 in., is 7 X 500 x 6-8 = 23800 lbs. ; and iu tiie direction of the breadth, the breaking weight is 7 X 500 x -36 x 11-333 = 14280 lbs.; the pressure being uniform iu both cases; or one half of those weights, if the pressures act in the middle. 108 THIRD SERIES — TABLES OF SCANTLINGS TABLE III. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q, = -36P; P = pressure upon each foot in length ;jBRE A DTK The deflections each way of the timber are equal 1 Depth Length in feet, clear bearing. Value of P. 864-0000 lbs. 7-7142 cwts. Value of p. 1098-5000 lbs. 9-8080cwts Value of p. 1372- 0000 lbs. 12-2500 cwts. Value of P. 1687-5000 lbs. 15-0669cwts Value of P. 2048-0000 lbs. 18-2857cwts. Depth. Breadth. Depth. Breadth. Depth. Breadih. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 1-89X1-13 3- 17X1-90 4- 30X2-58 5- 34X3-20 6- 31X3-79 204X1-23 3- 44X206 4- 66X2-80 5- 78X3-47 6- 84X4-10 2- 20 X 1-32 3- 70 X 2-22 5- 02 X 3 01 6- 23 X 3-74 7- 36 X 4-42 2- 36X1-42 3- 97X2-38 5- 38X3-23 6- 67X4-00 7- 89X4-73 2-52X1-51 4- 23X2-54 5- 74X3-44 7- 12X4-27 8- 41 X5-05 6 *7 8 9 10 7- 23X4-34 812X4-87 8- 98X5-39 9- 80X5-88 10-61X6-37 7- 84X4-70 8- 80X5-28 9- 72X5-83 10- 62X6-37 11- 50X6-90 8- 44 X 5-06 9- 47 X 5-68 10-47 X 6-28 11'44X 6-86 12-38X 7-43 9-04X5-43 10- 15X6-09 11- 22X6-73 12- 26X7-35 13- 26X7-96 9-65X6-79 10- 83X6-50 11- 97X7-18 13- 07X7-84 14- 15X8-49 11 12 13 14 15 11- 40X6-84 12- 17X7-30 12- 92X7-75 13- 66X8-19 14- 38X8-63 12- 35X7-41 13- 18X7-91 14- 00X8-40 14- 80X8-88 15- 58X9-35 13- 30 X 7-98 14- 19 X 8-52 15- 07 X 9-04 15- 93 X 9-56 16- 78X10-07 14- 25X8-55 15- 21X9-12 16- 15X9-69 15- 20X9-12 16- 22X9-73 16 17 18 15-10X9-06 15- 80X9-48 16- 49X9-89 16-35X9-81 Deflections in the middle for each foot in length. Value of D. .^of an inch . 1 -^of an inch. of an inch. y\of an inch. T5%of aninch. Value of P ~d" 51840-00 lbs. 462-85 cwts. 7 1402-50 lbs. 637-52 cwts. 96040-00 lbs. 857-50cwts. 126562-50 lbs. 1130-02cwts. 163840-00 lbs. 1462-85cwts. Value of P 32400-00 lbs. 289-28 cwts. 44626-56 lbs. 398-45 cwts. 60025-00 lbs. 535-93 cwts. 79101-56 lbs. 706-26cwts 102400-00 lbs. 914-28 cwts. X. XI. XII. XIII. XIV. * Example.— ReA Pine 7 feet long, 9-47 in. by 5-68 in., with 7 x 12-25 = 85-75 cwts. pressure in the direction of the depth, and with -36 x 85-75 = 30-87 cwts. pressure in the direction of the breadth, deflects each way or of an inch. The breaking weight, in the direction of the depth, of Red Pine, 7 feet long, 9-47 in. by 5-68 in. is 7 X 12-25 x 6-8 = 583-1 cwts. ; an'd in the direction of the breadth, the breaking weight is 7 x 12-25 x -36 x 11-333 = 349-8 cwts. ; the pressure being uniform in both cases; or one half of those weights, if the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. 109 TABLE III. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. lu this table, Q = -36 P; P = pressure upon each foot in length;] BreaDTH The deflections each way of the timber are equal j Depth •60. Length in feet, clear bearing. 6 *7 8 9 10 11 12 13 14 15 le 17 18 Value of P. 2456-50001bs. Value of P. 2916-OOOOlbs. Value of P. 3429-5000 lbs. 21-9330cwt3. 26-0357cwts. 30-6205 cwts. Depth. Breadth. Depth. Breadth. Depth. Breadth. 2-67 X 1-60 4-50X2-70 6- 09X3-66 7- 56 X4-54 2-83X1-70 4-76X2-86 6-45X3-87 8-01 X4-80 2-99 X 1-79 5- 02 X 3-01 6- 81 X 4-09 8-45 X 5-07 8-94X5-36 9-46X5-68 9^99 X 5-99 10-25 X6-15 ll'50X6-90 12- 72X7-63 13- 89X8-33 15-03X9-02 10-85 X6-51 12- 18X7-31 13- 46X8-08 14- 71 X8-82 15- 92X9-55 11- 45X 6-87 12- 86 X 7-71 14- 21 X 8-53 15- 52 X 9-31 16- 80X10-08 16-15X9-69 Value of P 4000-OOOOlbs, 35-7142cwts Depth. Breadth. 3-14X1-89 5-29X3-17 7- 17X4-30 8- 90X5-34 10-52X6-31 12- 06X7-23 13- 53X8-12 14- 96X8-98 16-34X9-80 Multipliers to give the breaking weight of every Scantling in the table. In the direc- tion of the depth. 4-180 4- 971 5- 502 5- 912 6- 251 In the direc- tion of the breadth. 6-967 8- 286 9- 170 9-853 10-419 6-543 6- 800 7- 030 7-241 7-434 7-613 7-781 7- 938 8- 086 8-227 8-361 8-488 8-611 Value of D Deflections in the middle for each foot in length. 10- 905 11- 333 11- 718 12- 068 12-390 12-689 12- 968 13- 230 13-477 13-712 13- 935 14- 148 14-351 Value of P •gVof an inch. 208802'50lbs, 1864-30cwts. 130501-56 lbs. 1165-19cwts. XV. 5^ of an inch. 26244000 lbs. 2343-2 lewis 16402500 lbs. 1464-50c«'ts. XVI, Jj- of an inch. 325802-50 lbs. 2908-95 cwts 203626-56 lbs. 1818-09cwts. XVII. ,-i^ofaninch 400000-00 lbs 3571-42cwt, 250000-00 lbs 2232-14cwts See Examples. I Pressure uniform. Pressure in the middle. XVIII. * Example— B.e(\ Pine, 7 feet long, 12-86 in. by 771 in,, with 7 x 30-6205 = 214-34 cwts. pressure in the direction of the depth, and with -36 x 214-84 = 77-16 cwts. pressure in the direction of the breadth, deflects each way Jy of an inch. The breaking weight, in the direction of the depth, of Red Pine 7 feet long, 12-86 in. by 7-71 in., is 7 x 30-6205 x 6-8 = 1457-5 cwts.; and in the directiou of the breadth, the breakmg weight is 7 x 30-6205 x -36 x 11-333 = 874-52 cwts. ; the pressure being uniform in both cases ; or one half of those weights, if the pressures act in the middle. P 110 THIRD SERIES — TABLES OF SCANTLINGS TABLE IV. Scantlings of Red Pine when acted upon by two forces P and Q, viz,, P in the direction of the depth, Q in the direction of the breadth. la this table, Q="50 P; P = pressure upon each foot in length ; IBreadTH The deflections each way of the timber are equal ] DepTH Length in feet, clear beariug. Value of P. 1-0000 lbs. -0089 cwts. Value of P. 16-0000 lbs. •1428 cwts. Value of P. 390625 lbs. •3487cwts. Value of P. 81-0000 lbs. -7232 cwts. Value of P. 150-0625 lbs. 1-3398 cwts. Depth. Jlreadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 O •30 X -21 •51 X -36 •69 X -49 •85 X -60 •60 X -43 1-02 X ^72 1-38X -97 1-71X1-21 -75 X -53 1-27 X -90 1- 72X1-22 2- 13X1^51 <£ OZ ?>> I to •91 X -64 1^52 X 1^08 2-06 X 1-46 2-56 Xr81 1-06 X -75 1- 78 X 1-26 2- 41 X 1-70 2-99 X 2^11 '^•^'^ X 2-50 6 7 *8 9 10 M6X -82 1-30X ^92 1^44 XI 02 1-57X1-11 i /UX 1-20 2-31X1-64 2-60X1-84 2- 87X2-03 3- 14X2-22 2^89X2-05 3-25X2-30 3-59X2-54 3-92X2-77 A ,Ci A W O.AA 4 24 Xo OU 3-47X2-45 3- 90X2-76 4- 31 X3-05 4-71 X3-33 0 09 Xo DU 4-05 X 2-86 4- 55 X 3-21 5- 03 X 3-55 5-49 X 3-88 11 12 13 14 15 1-82X1-29 1- 95X1-38 2- 07X1-46 2-18X1-54 2-30 X 1-63 3-65X2-58 3- 89X2-75 4- 13X2-92 4-37X3-09 4-60X3-25 4- 56X3^22 4^87X3^44 5- 17X3-65 5-46X3-86 5-75X4-07 5-47X3-87 5- 84X4-13 6- 20X4-38 6-55X4-63 6-90X4-88 6- 38 X 4-51 6^81 X 4-82 7^23 X 5-11 7- 65 X 5-41 8^05 X 5-69 16 17 18 19 20 2-41X1-71 2-53X1-79 2-64 X 1^87 2^75X1-94 2-85X2-02 4- 83X3^41 5^05 X 3^57 5- 28X3-73 5-49X3-88 5-71X4-04 6-04X4-27 6-32X4-47 6-59X4-66 6- 87X4-86 7- 14X5-05 7-24X5-12 7-58X5-36 7- 91 X5-60 8- 24 X5-83 8-56X6-06 8^45 X 5-98 8- 84 X 6-25 9- 23 X 6-53 9-61 X 6^80 9^99 X 7^06 Deflections in the middle for each foot in length. Value of D. ^of an inch. 4^of an inch. 4?oOf an inch. of an inch. ^of an inch. Value ol P "d" 40-00 lbs. •35 cwts. 640-00 lbs. 5-71 cwts. 1562-50 lbs. 13-94 cwts 3240-00 lbs. 28-92 cwts. 6002-50 lbs. 53-59 cwts. Value of P "d" 25-00 lbs. •22 cwts. 400-00 lbs. 3 57 cwts. 976-56 lbs. 8-71 cwts 202500 lbs. 18-08 cwts. 3751-56 lbs. 33-49 cwts. Factors to give the breakiii weight Column I, ; Factor 4. II. Factor 2. III. Factor 1-6. IV. Factor -f . V. Factor |-. * Example. — Red Pine 8 feet long, 4-31 in. by 3-05 in., with 8 x 81 = 648 lbs. pressure in the direction of the depth, and with -5 x 648 = 324 lbs. pressure in the direction of the breadth, deflects each way -^^ or ^ of an inch. The breaking weight, in the direction of the depth, of Red Pine 8 feet long, 4'31 in. by 3-05 in., is 8 X 81 X 7-325 = 4746 lbs. ; and in the direction of the breadth, the breaking weight is8x-5x81x 10-36 = 3356 lbs. ; the pressure being uniform in both cases ; or one half of those weights, if the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. Ill TABLE IV. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q = -50 P; P = pressure upon each foot in length;) BreadtH The deflections each way of the timber are equal j Depth = •707. Length in feet, clea bearing. 6 7 *8 9 10 11 12 13 14 15 16 17 18 19 20 Value of P. 256-0000 lbs. 2'2857cwts Depth. Breadth. 21 X -85 03 X 1-44 75X1-95 41 X2'41 04X2-85 63 X3-27 20X3-67 74X4-06 27X4-44 79 X4-80 29X5-16 78 X5-50 27X5-84 74X6-18 Value of P. 364-5000 lbs. 3-2544cwts Depth. Breadth 1- 36 X -96 2- 28X1-62 3- 10X2-19 3- 84X2-72 4- 54X3-21 5-21 X3-68 5- 85X4-13 6- 46X4-57 7- 06 X4-99 7-64X5-40 8-20X5-80 8- 76X6-19 9- 30X6-58 9-83 X6-95 9-20X6-51 10-35X7-32 9-66X6-83 10-87X7-68 10-11 X7-15 11-37X8-04 10-55X7-46 11-87X8-39 10- 99X7-77 12-36X8-74 11- 42X8-07 12-85X9-08 Value of P. 500-0000 lbs. 4-4642 cwts. Depth. Breadth 1- 51 2- 54 3- 44 4- 27 5- 05 X 1-07 X 1-79 X 2-43 X 3-02 X 3-57 579 6- 49 7- 18 7- 84 8- 49 4-09 4- 59 5- 08 5- 55 6- 00 9-12 9-73 10-33 10- 92 11- 50 X 6-45 X 6-88 X 7-31 X 7-72 X 8-13 12-07 12- 64 13- 19 13- 73 14- 27 X 8-54 X 8-93 X 9-33 X 9-71 X 10-09 Value of P. 665-5000 lbs. . 5-9419 cwts. Depth. Breadth. 1- 66 X 2- 79 X 3- 78 X 4- 70 X 5- 55 X 1-17 1- 97 2- 68 3- 32 3-93 6- 36 X 7- 14 X 7- 90 X 8- 63 X 9- 34 X 4- 50 5- 05 5- 58 6- 10 6-60 10-03 X 10- 70 X 11- 37 X 12- 02 X 12-65 X 7-09 7- 57 8- 04 8-50 8-95 13-28 X 9-39 13- 90 X 9-83 14- 51 X 10-26 15- 11 X 10-68 15-70X11-10 Multipliers to give the breaking weight of every Scautliug in the table. In thedirec. tion of the depth. 4- 355 5- 180 5- 732 6- 160 6-513 6- 817 7- 085 7-325 '4-544 7-746 7- 932 8- 107 8-271 8-425 8-572 8-711 8-844 8- 972 9- 094 9-211 lu the direc- tion of the breadth. 6- 160 7- 325 8- 107 8- 711 9- 211 9-641 10-019 10-360 10-669 10-954 11-218 11-465 11-697 11-915 12123 12-320 12-508 12-688 12- 861 13- 027 Deflections in the middle for each foot in length. Value of D :^of an inch. :^of aninch. "5% of an inch. j -5^5- of an inch.- See Examples. Value of P "d" 10240-00 lbs. 9l-42cwts. 16402-50 lbs. 146-45cwts. 25000-00 lbs. 223-21 cwts. 36602-50 lbs. 326-80cwts. Pressure uniform. Value of P "d" 6400-00 lbs. 57-14cwts. 10251-56 lbs. 9r53cwts. 15625-00 lbs. 139-50cwts. 22876-56 lbs. 204-25cwts. 1 , Pressure in the middle. VI. VII. VIII. IX. * Example.— R&i Pine 8 feet long, 7-90 iu. by 5-.58 in., with 8 x 665-5 = 5324 lbs. pressure in the direction of the depth, and with '5 x 5324 = 2662 lbs. pressure in the direction of the breadth, deflects each way -^-^ of an inch. The breaking weight, in the direction of the depth, of Red Pine 8 feet long, 7-90 in. by 5-58in., is 8 X 5-9419 x 7-325 = 348-16 cwts.; and in the direction of the breadth, the breaking weight is 8 X -5 X 5-9419 x 10-36 = 246-23 cwts.; the pressure being uniform in both cases ; or one half of those weights, if the pressures act in the middle. 112 THIRD SERIES — TABLES OF SCANTLINGS TABLE IV. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q,='50 P; P= pressure upou each, foot in length;) Breadth The deflections each way of the timber are equal J Depth Length in feet^ clear bearing. Value of p. 864-0000 lbs. / I ViZ CWIS. Value of P. 1098-5000 lbs. y ououcwis. Value of P. 1372-0000 lbs. Value of P. 1687-5000 lbs. Value of P. 2048-0000 lbs. 1 8-2857 cwts. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 1-81 X 1-28 3- 05 X 2-15 4- 13 X 2-92 5- 12 X 3-62 6- 06 X 4-28 1-96 X 1-39 3- 30 X 2-33 4- 47 X 3-16 5- 55 X 3-92 6- 56 X 4-64 2- 11 X 1-49 3- 55 X 2-51 4- 82 X 3-41 5- 98 X 4-23 7-06 X 5-00 2- 26 X 1-60 3- 81 X 2-69 5- 16 X 3-65 6- 40 X 4-53 7- 57 X 5-35 2-41 X 1-71 4- 06 X 2-87 5- 50 X 3-89 6- 83 X 4-83 8-07 X 5-71 6 7 9 10 6- 94 X 4-91 7- 79 X 5-51 0 Dl D Uf 9-41)i 6-65 10-18 X 7-20 7- 52 X 5-32 8- 44 X 5-97 ij OO /\ U \j\J 10- 19 X 7-21 11- 03 X 7-80 8- 10 X 5-73 9- 09 X 6-43 lO-O.'iX 7-11 10- 98 X 7-76 11- 88X 8-40 8- 68 X 6-14 9- 74 X 6-89 10- 77 X 7-61 11- 76 X 8 .32 12- 73 X 9 00 9-26 X 6-55 10- 39 X 7-35 11- 49X 8-12 12- 55 X 8-87 13- 58 X 9-60 11 12 13 14 15 10- 94 X 7-73 11- 68X 8-26 12- 40 X 8-77 13- 11 X 9 27 13-80 X 9-76 11- 85X 8-38 12- 65 X 8-94 13- 43 X 9-50 14- 20 X 1004 14-95X10-57 12- 76 X 9-02 13- 62 X 9-63 14- 47X10-23 15- 29X10-81 16- 10X11-39 13- 67 X 9-67 14- 60X10-32 15- 50X10-96 16- 38X11-59 14- 59X10-31 15- 57X11-01 16- 53X11-69 16 17 18 19 14- 49 X 10-24 15- 16X10-72 15- 83X11-19 16- 48 XI l-6£ 15- 70X11-1C 16- 43X11-61 ... 16-90X11-95 ... ... i)eilections in the midtUe for each foot in length. Value of D ^ of an inch. ^ofan inch. y^^of an inch. ^of an inch. ^ of an inch. Value of 51840-00 lbs. 71402-50 lbs. 96040-00 lbs. 126562-50 lbs. 163840-00 lbs. P "d" 46285 cwts. 637-52 cwts. 857-50 cwts. 11 3002 cwts. 1462-85 cwts. Valueof P "d" 32400-00 lbs. 289-28 cwts. 44626-56 lbs. 398-45 cwts. 60025-00 lbs. 535-93 cwts. 79101-56 lbs. 706-26 cwts. 102400-00 lbs. 91 4-28 cwts X. XI. XII. XIII. XIV. * Example.— Ktdi Pine 8 feet long, 10-77 in. by 7-61 in., with 8 x 15-0669 = 120-53 cwts. pressure in the direction of the depth, and with -5 x 120-53 = 60-26 cwts. pressure ia the direction of the breadth, deflects each way of an inch. The breaking weight, in the direction of the depth, of Red Pine 8 feet long, 10-77 in. by '^l in., is 8 X 15-0669 x 7-325 = 882-92 cwts. ; and in the direction of the breadth, the weight is 8 x -5 x 15-0669 x 10-36 = 624-37 cwts. ; the pressures being uniform -=8 ; or one half of those weights, if the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. 113 TABLE IV. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q=-50 The deflections each wa P; P = pressure upon each foot in length;] Breadth y of the timber are equal J Depth •707. Length in feet, clear bearing. 6 7 *8 9 10 11 12 13 14 15 16 17 18 19 Value of P. 2456-5000 lbs. 21-9330cwts. Value of P. 29160000 lbs. 26-0357cwts. Depth. Breadth, 2-57 X 4- 31 X 5- 85 X 7- 26 X 8- 58 X 1-81 3-05 414 513 6-07 9-84 X 6-96 11-04X 7-81 12'20X 8-63 13 33 X 9-43 14-43 X 10-20 15- 50 X 10-96 16- 54X11-70 Value of p. 3429-5000 lbs. 30-6-205cwts. Depth. Breadth 2 72X 4-57 X 6- 19 X 7- 68 X 9-08 X 1-92 3- 23 4- 38 6-43 6-42 10- 41 X 7-36 11- 69 X 8-27 12- 92 X 9-14 14- 12 X 9-98 15- 28X10-80 16-41 XI 1-60 Value of P. 40000000 lbs. 35-7142cwts. Depth. Breadth. 2-87 X 4-82 X 6-54 X 8- 11 X 9- 59 X 2- 03 3- 41 4- 62 5- 73 6- 78 10-99 X 7-77 12- 34 X 8-73 13- 64 X 9-65 14- 90X10-54 16-13X11-40 Depth. Breadth. In the direc- tioD of the depth. 3-02 X 5- 08 X 6- 88 X 8-54 X 10-09 X 2- 13 3- 59 4- 87 6- 04 7- 14 11- 57 X 8-18 12- 99 X 9-19 14- 36X10-15 15- 68X11-09 16- 97X12-00 Multipliers to give the breaking iveight of every Scantling in the table. 4- 355 5- 180 5- 732 6- 160 6-513 6- 817 7- 085 7-325 7-544 7-746 7- 932 8- 107 8-271 8-425 8-572 8-711 8-844 8- 972 9- 094 In the direc- tion of the breadth. 6160 7- 325 8- 107 8- 711 9- 211 9-641 10-019 10-360 10-669 10-954 11-218 11-465 11-697 11- 915 12- 123 12-320 12-508 12-688 12-861 Deflections in the middle for each foot in length. ^"d!"'^! "S"V '^^ an inch. | of an inch. ( -g^j- of an inch. Ixstt of an inch See Examples. Value of P 208802-50 lbs. 1864-30cwt3. 262440-OOlbs. 2343-21 cwts. 325802-50 lbs. 2908-95cwts. 400000-00 lbs. 3571-42cwts. - Pressure uniform. 13050 1-56 lbs. 1165-19cwts. 164025-OOlbs. 1464-50cwts. 203626-56 lbs. 1818-09cwts. 250000-00 lbs. 2232-14cwts. Pressure in the middle. XV. XVI. XVII. XVIII. * Example.— Red Pine 8 feet long, 14-36 in. by 10-15 in., with 8x 35-7142=286-71 cwts. pressure in the direction of the depth, and with '5 x 285-71 = 142-85 cwts. pressure in the direction of the breadth, deflects each way —1^ of an inch. The breaking weight, in the direction of the depth, of Red Pine 8 feet long, 14-36 in. by 10-15 in., is 8 X 35-7142 x 7-325 = 2092-85 cwts.; and in the direction of the breadth, the breaking weight is 8 x -5 x 35-7142 x 10-36 = 1480 cwts. ; the pressure being uniform in both cases ; or one half of those weights, if the pressures act in the middle. 114 THIRD SERIES — TABLES OF SCANTLINGS TABLE V. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q, = "75 P; *P = pressure upon each foot in length; IB REACT H The deflections each way of the timber are equal j Depth Length in feet, clear bearing. Value of P. 1-0000 lbs. •0089 cwts. Value of p. 16-0000 lbs. •1428 cwts. Value of P. 39-0625 lbs. •3487 cwts. Value of P. 81-0000 lbs. •7232 cwts. Value of P. 150-0625 lbs. 1-3398 cwts. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 •29 X -25 •48 X ^42 •65 X ^57 •81 X ^70 •96 X ^83 •57 X -50 •97 X -84 1-31X113 1-62 X 1-41 1-92 X 1-66 -72 X -62 1-21X1-04 1- 64X1-42 2- 03X1-76 2-40X2-08 •86 X -75 145X1-25 1- 96X1-70 2- 43 X2^ 11 2^88X2-49 1-00 X -87 1- 69 X 1-46 2- 29 X 1-98 2- 84 X 2-46 3- 36 X 2-91 6 7 8 *9 10 MOX ^95 1^23 X 1^07 1-36XM8 1^49 XI ^29 rei Xl-40 2^20 X 1^91 2-47X2-14 2^73 X 2^36 2^98X2^58 3^23X2-79 2- 75X2-38 3- 09 X 2^67 3-41X2-96 3- 73 X323 4- 03 X 3-49 3-30X2^86 3- 70 X321 4^09X3^55 4- 47X3-87 4-84X4-19 3- 85 X 3-33 4- 32 X 3-74 4- 78 X 4-14 5- 22 X 4-52 5-65 X 4-89 11 12 13 14 15 1^73 Xr50 1- 85 Xr60 r96xr70 2- 08 X 1-80 2^19 Xr89 3-47 X3 00 3-70X3-20 3- 93X3-40 4^15X3-60 4- 37X3-79 4-33 X3-75 4^63X4^01 4- 91X4-25 5- 19X4-50 5-47X4-74 5-20X4-50 5- 55 X 4-81 5^89X5^10 6- 23 X5-40 6^56X5-68 6-07 X 5-25 6-48 X 5-61 6- 88 X 5-95 7- 27 X 6-29 7-65 X 6^63 j6 17 18 19 20 2-30 Xr99 2^40 X 2-08 2^51X2^17 2^61 X2-26 2-71 X2-35 4-59X3-98 4- 80X4-16 5- 01X4-34 5-22X4^52 5-43X4-70 5- 74X4-97 6- 01X5-20 6-27X5-43 6-53 X5-65 6-78X5-88 6^89X5-96 7-21X6-24 7-52 X 6^51 7^83 X 6^78 8^14 X 7-05 8-03 X 6-96 8^4 1 X 7-28 8- 78 X 7-60 9- 14 X 7-91 9-50 X 8-23 Deflections in the middle for each foot in length. Value of D. 4^of an inch. ^Vof an inch. ^of an inch. ^of an inch. 4^ of an inch. Value of P 40 00 lbs. •35 cwts. 64000 lbs. 571 cwts. 1562-60 lbs. 13-94 cwts. 3240-00 lbs. 28-92 cwts. 6002^50 lbs. 53-59 cwts. Value of P "d" 25-00 lbs. •22 cwts. 400-00 lbs. 3-57 cwts. 976-56 lbs. 8-71 cwts. 2025-00 lbs. 18-08 cwts. 3751-56 lbs. 33-49 cwts. Factors to give the breaking weight. Column I. Factor 4. II. Factor 2. III. Factor 1-6. IV. Factor f. V. Factor -f . ♦ Example.— B,ei Pine 9 feet long, 5-22 in. by 4-52 in., with 9 x 150-0625 = 1350-56 lbs. pressure in the direction of the depth, and with -75 x 1350-56 = 1012-92 lbs. pressure in the direction of the breadth, deflects each way ^ of an inch. The breaking weight, in the direction of the depth, of Ked Pine 9 feet long, 5-22 in. by 4-52 in., is 9x 150 0625 x 7-936 = 10718 lbs.; and in the direction of the breadth, the breaking weight is 9 x '75 x 150 0625 x 9-164 = 9282 lbs. ; the pressure being uniform i« both cases ; or one half of those weights, jf the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. 115 TABLE V. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. 'n this table, Q, = '75 P; P = pressure upon each foot in length; ] BreadTH The deflections each way of the timber are equal JDepth ■ = •866. Length 'ii feet, clear ) earing. 6 7 8 *9 10 11 12 13 14 15 Tq 17 18 19 20 Value of P. •256 0000 lbs. 2-2857cwts. Depth. Breadth. M5X -99 1- 93 X 1-67 2- 62X2-27 3- 25X2-81 3-84X3-32 4- 40X3-8I .4-94X4-28 5- 46X4-73 5- 96X5-16 6- 45X5-59 6- 93X6-00 7- 40X6-41 7- 86 X 6-80 8- 31X7-19 8-75 X 7-58 9-18X7-95 9-61X8-32 10-03 X8-69 10-44 X9-04 10-85 X9-40 Value of P. 364-50001bs. 3-2544 cwts. Depth. Breadth 1- 29 X 2- 17X 2- 94 X 3- 65 X 4- 32 X 1-12 1- 88 2- 55 3- 16 3-74 4- 95 X 5- 56 X 6- 14 X 6- 71 X 7- 26 X 4-29 4- 81 5- 32 5- 81 6- 29 7- 80 X 8- 33 X 8- 84 X 9- 34 X 9-84 X 6- 75 7- 21 7- 66 8- 09 8-52 10-33 X 8-95 10- 81 X 9-36 11- 28X 9-77 11- 75X10-18 12- 21 X 10-58 Value of P. 500-OOOOlbs. 4-4642cwts. Depth. Breadth. 1- 43 X 2- 41 X 3- 27 X 4- 06 X 4-80 X 1- 24 2- 09 2- 83 3- 51 4- 15 5- 50 X 6- 17X 6- 82 X 7- 46 X 8- 07 X 4- 76 5- 35 5- 91 6- 46 6-99 8- 67 X 9- 25 X 9-82 X 10-38 X 10-94 X 7- 50 8- 01 8-51 8- 99 9- 47 11- 48X 9-94 12- 01X10-40 12- 54X10-86 13- 06X11-31 13-57X11-75 665-5000 lbs. 5-941 9cwts. Depth. Breadth 1- 58X 2- 65 X 3- 60 X 4- 46 X 5- 28 X 1- 37 2- 30 3- 12 3- 87 4- 57 6-05 X 6- 79 X 7- 51 X 8- 20 X 8-87 X 5-24 5- 88 6- 50 7- 10 7-69 9-53 X 8-25 10- 18X 8-81 11- 80X 9-36 11- 42X 9-89 12- 03X10-42 12- 62X10-93 13- 21X11-44 13- 79X11-94 14- 36X12-44 14-92X12-93 'alue of Deflections in the middle for each foot in length. 'alue of 4%- of an inch. 1024000 lbs. 91-42cwt3. 640000 lbs. 57-14cwts, VI. -V of an inch. 4 5 16402-50 lbs. 146-45cwts. 10251-56 lbs. 91-53cwts. VII. of an inch. 25000-00 lbs. 223-21 cwts. 15625-00 lbs. 139-50cwts. VIII. of an inch. 36602-50 lbs. 326-80cwts. 22876-56 lbs. 204-25cwts. IX. Multipliers to give the breaking weight of every Scantling in the table. In the direc tion of the depth. 4- 582 5- 449 6- 030 6-480 6-852 7-171 7-453 7-706 7- 936 8- 148 8-345 8-528 8-701 8- 863 9- 018 9-164 9-304 9-438 9-567 9-690 In the direc- tion of the breadth. 5- 291 6- 292 6- 963 7- 482 7-912 8-281 8-606 8- 898 9- 164 9-409 9-636 9-848 10-047 10-234 10-413 10-582 10-744 10- 898 11- 046 11-189 See Examples. I Pressure uniform. Pressure in the middle. Example. —RtA Pine 9 feet long, 5-96 in. by 516 in., with 9 x 256 = 2304 lbs. pressure the direction of the depth, and with -75 x 2304 = 1728 lbs. pressure in the direction of the ireadth, deflects each way ^ of an inch. The breaking weight, in the direction of the depth, of Red Pine 9 feet long, 5*96 in. by -16 in., IS 9 X 256 x 7-936 = 18284 lbs.; and in the direction of the breadth, the breaking weight is 9 X -75 x 256 x 9-164 = 15835 lbs.; the pressure being uniform in both cases; or ne half of those weights, if the pressures act in the middle. 116 THIRD SERIES — TABLES OF SCANTLINGS TABLE V. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q = -75 P; P = pressiire upon each foot in length;") Breadth •=•000. The deflections each way of the timber are equal j Depth Length in feet, clear bearing. 6 7 8 *9 10 11 12 13 14 15 16 17 18 19 20 Value of p. 864-0000 lbs. 7-7142cwts. Depth. Jireadth, 1- 72 X 2- 90 X 3- 92 X 4- 87 X 5- 76 X 1- 49 2- 51 3- 40 4- 22 4-99 6- 60 X 7- 41 X 8- 19 X 8- 95 X 9- 68 X 5- 72 6- 42 7- 09 7- 75 8- 38 40 X 10 X 79 X 46 X 12X 9-01 961 10-21 10- 79 11- 36 77 X 41 X 04 X 67 X 28 X 11- 93 12- 48 13- 03 13- 57 14- 10 Value of p. 1098-5000lbs. 9-8080cwts. Depth. 1-87 X 3- 14X 4- 25 X 5- 27 X 6- 24 X Breadth T-62 2- 72 3- 68 4- 57 5- 40 7- 15 X 8- 03 X 8- 87 X 9- 69 X 10-49 X 6-19 6- 95 7- 68 8- 39 9- 08 Value of P. 1372-OOOOlbs. 12-2500cwts. Depth. Breadth. 2- 01 X 3- 38 X 4- 58 X 5- 68 X 6- 72 X 1- 74 2- 93 3- 96 4- 92 5- 82 7- 70 X 8- 64 X 9- 55 X 10- 44 X 11- 29 X 6- 67 7- 48 8- 27 9- 04 9-78 11- 26X 9-76 12- 02X10-41 12- 77X11-06 13- 50X11-69 14- 22 X 12-31 14- 92 X 12-92 15- 61 X13-52 16- 30X14-11 16-97X14-70 12-13X10-51 12- 94X11-21 13- 75X11-91 14- 54X12-69 15- 31 X 13-26 16-07 X 13-91 16-82X14-56 Value of P. 1687-50001bs. 15-0669cwts. Depth. Breadth. 215X 3- 62 X 4- 91 X 6- 09 X 7- 20 X 1-86 3- 13 4- 25 5- 27 6- 23 8- 25 X 7-14 9- 26 X 8-02 10- 24 X 8-87 11- 18 X 9-68 12- 10 X 10-48 13-00 X 13- 87 X 14- 73 X 15- 57 X 16- 40 X 11- 26 12- 02 12- 76 13- 49 14- 20 Value of P. 2048-OOOOlbs. 18-2857cwts. Depth. Breadth. 2- 30 X 3- 86 X 5- 23 X 6- 49 X 7- 68 X 1-99 3- 34 4- 53 5- 62 6- 65 8- 80 X 7-62 9- 88 X 8-55 10- 92 X 9-46 11- 93X10-33 12- 91 Xll-18 13- 86 14- 79 15- 72 16- 61 X 12-01 X 12-82 X 13-61 X 14-39 Deflections in the middle for each foot in length. Value of j^Qf an inch, l-g^of aninch. of an inch. of an inch. of aninch. Valueof P ~d" 51840-00 lbs. 462-85 cwts. 71402-50 lbs. 637-52 cwts. 96040 00 lbs. 857-50 cwts. 126562-50 lbs. 1130-02cwts. 163840-00 lbs. 1462-85cwts. Value of P '0' 32400-00 lbs. 289-28 cwts. 44626-56 lbs. 398-45 cwts. 60025-00 lbs. 535-93 cwts. 79101-56 lbs. 706-26cwts. 102400-00 lbs. 914-28cwts. X. XI. XII. XIII. XIV. * Example.— B,ed. Pine 9 feet long, 11-93 in. by 10-33 in., with 9 x 18-2857 = 164-57 cwts. pressure in the direction of the depth, and with '75 x 164-57 = 123-42 cwts. pressure, in the direction of the breadth, deflects each way of an inch. The breaking weight, in the direction of the depth, of Red Pine 9 feet long, 11-93 in. by 10-33 in., is 9 x 18-2857 x 7-936 = 1306-05 cwts.; and in the direction of the breadth, the breaking weight is 9 x -75 x 18-2857 x 9-164 = 1131-09 cwts. ; the pressure being uni- form in both cases ; or one half of those weights, if the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. 117 TABLE V. Continued. JcANTLiNGs of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. Q this table, Q,=-75 P; P=pressure upon each foot in length ;")B 'he deflections each way of the timber are equal j D EPTH -=•866. Length D feet, clear earing. 6 7 8 *9 10 11 12 13 14 15 16 17 18 19 20 Value of P. 2456-5000 lbs. 21-9330cwts. Depth. Breadth 2-44 X 4- lOX 5- 56 X 6- 90 X 8-15 X 2- 11 3- 55 4- 81 5- 97 7-06 9-35 X 8-10 10- 50 X 9-09 1 1- 60 X 10-05 12- 67X10-97 13- 71X11-; 14- 73X12-76 15- 72X13-62 16- 70X14-46 Value of P. 2916-0000 lbs. 26-0357 cwts. Value of P. 3429-5000 lbs. 30-6205 cwts. Depth. Breadth. 2-58 X 4- 34 X 5- 89 X 7- 30 X 8- 63 X 2- 24 3- 76 5- 10 6- 33 7- 48 9-90 X 8-57 11- 11 X 9-62 12- 28X10-64 13- 42X11-62 14- 52X12-58 15- 60X13-51 16- 64X14-42 Depth. Breadth. 2-73 X 4-58 X 6- 21 X 7- 71 X 9-llX 2- 36 3- 97 5- 38 6- 68 7- 89 10- 45 X 9-05 11- 73X10-16 12- 97X11-23 14- 16X12-27 15- 33X13-27 16-46X14-26 Value of P. 4000-0000 lbs. 35-7142cwts. Depth. Breadth. 2-87 X 4-83 X 6-54 X 8- 12X 9- 59 X 2-48 4- 18 5- 66 7- 03 8- 31 ll'OOX 9-53 12- 35X10-69 13- 65X11-82 14- 91 X12-91 16-13X13-97 Multipliers to give the breaking weight of every Scantling iu the table. In the direc. tion of the depth. 4- 582 5- 449 6- 030 6-480 6-852 7-171 7-453 7-706 7- 936 8- 148 8-345 8-528 8-701 8- 863 9- 018 9-164 9-304 9-438 9-567 9-690 In the direc tion of the breadth. 5- 291 6- 292 6- 963 7- 482 7-912 8-281 8-606 8- 898 9- 164 9-409 9-636 9-848 10-047 10-234 10-413 10-582 10-744 10- 898 11- 046 11-189 •'ni-sVofaninch. Deflections in the middle for each foot in length. frW of an inch. of an inch. -^TT of an inch See Examples. alueof 208802-50 lbs. 1864-30cwu. 262440-00 lbs. 2343-21 cwts. 325802-50 lbs. 2908-95cwt3. 400000-00 lbs. 3571-42™t3. Pressure uniform. alueof p 130501-56 lbs. Il65-19cwts. 164025-00 lbs 1464-50ewts. 2036-26-56 lbs. 1818-09cwts. 250000-00 lbs. 2232-14cwts. Pressure in the middle. XV. XVI. XVII. XVIII. F.xample.—Rei Pine 9 feet long, 13-42 in. by 11-62 in., with 9 x 26-0357 = 234-32 cwts. ressure in the direction of the depth, and with -75 x 284-32 = 175-74 cwts. pressure in be direction of the breadth, deflects each way -^^ or of an inch. The breaking weight, in the direction of the depth, of Red Pine 9 feet long, 13-42 in. by 1-62 in., is 9 x 26-0857 x 7-936 = 1859-57 cwts.; and in the direction of the breadth, the reaking weight is 9 x -75 x 26-0857 x 9-164 = 1610-49 cwts.; the pressure being uniform in oth cases ; or one half of those weights, if the pressures act in the middle. Q 118 THIRD SERIES — TABLES OF SCANTLINGS TABLE VI. Scantlings of Red Pine when acted upon by two forces P and Q, viz. P in the direction of the depth, Q in the direction of the breadth. lu this table, Q = P; P = pressure upon each foot in length; The deflections each way of the timber are equal Breadth Depth 1-00. Length in feet, clear bearing. 6 7 8 9 *10 11 12 13 14 15 "Te" 17 18 19 20 Value of P. 1-0000 lbs. •0089 cwts. Depth. Breadth. •28 X -28 •47 X -47 •63 X ^63 •78 X -78 •93 X -93 1-06 xro6 1-19 X 1-19 r32X1^32 1-44 X 1-44 1-56 X 1^56 1-67 Xr67 1- 78 XI -78 r90Xl-90 2- 00 X 2-00 2^11 X211 Value of P. 16-0000 lbs. •1428 cwls, Depth. Breadth. •55 X -55 •93 X ^93 r26Xl-26 1-57 XP57 1- 85 X 1-85 2- 12X~2'a2' 2^38X2-38 2^63X2^63 2^88 X 2-88 3^11X3^11 2'21X2^21 2-32 X 2-32 2-42 X 2-42 2-52X2-52 2'62X2^62 3^34X3-34 3-57X3-57 3^79 X3^79 4^01 X4^01 4^22 X 4-22 4-43 X 4-43 4- 63 X4^63 4^84 X 4-84 5^04X5^04 5- 24 X 5^24 Value of P. 39-0625 lbs. •3487 cwts. Depth. Breadth. •69 X -69 M6XM6 1^58 XI -58 r96Xl-96 2-31 X2-31 Value of P. 81 0000 lbs. •7232 cwts. Depth. Breadth. 2^65 X 2-65 2^98X2-98 3-29X3-29 3-60X3^60 3-89X3^89 4-18X4^18 4-46X4^46 4- 74X4^74 5- 01X5^01 5^27X5-27 5- 54 X 5^54 5^79X5-79 6^05 X 6^05 6- 30X6-30 6-54X6-54 •83 X -83 1- 40 X 1-40 r89Xl-89 2- 35 X 2-35 2-78X2-78 3-18X3-18 3-57X3-57 3- 95X3^95 4^31 X 4-31 4- 67X4^67 5-02X5-02 5-35X5-35 5- 68X5-68 6- 01X6-01 6-33X6-33 Value of P. 150-0625 lbs. 1-3398 cwts. Depth. Breadth. -97 X -97 1- 63X1-63 2- 21X2-21 2- 74X2-74 3- 24 X3-24 3- 71X3-71 4- 17X4-17 4- 61X4-61 5- 03X5-03 5-45X5-451 6-64X6-64 6- 95X6-95 7- 26X7-26 7-56X7-56 7-85X7-85 5- 85X5-85 6- 25X6-25 6- 63X6-63 7- 01 X7-01 7-38X7-3 7- 75X7-7 8- 11 X8-11 8-47X8-47 8- 82X8-82 9- 16X9-16 i Deflections in the middle for each foot in length. v»i^^°f|^i^of aninch.|^of aninch.[^of aninch.j^of aninch.[^of aninch. 40-00 lbs. -35 cwts. 640-00 lbs. 5-71 cwts. 1562-50 lbs. 13-94 cwts. 3240-00 lbs. 28-92 cwts. 6002-50 lbs. 53-59 cwts. Value of P 25-00 lbs. -22 cwts. 400-00 lbs. 3-57 cwts. 976-56 lbs. 8-71 cwts. 2025-00 lbs. 18-08 cwts. •3751-66 lbs. 33-49 cwts. III. Factor 1-6. IV. Factor V. Factor ^ . Hi'F Column I. II. breaking Factor 4, I Factor 2. weight. * Example.— B,ei Pine 10 feet long, 4-6? in. by 4-67 in., with 10x81 = 810 lbs, pressure in the direction of the depth, and with 810 lbs. pressure in the direction of the breadth, deflects each way -i§ or i of an inch. The breaking weight, in the direction of the depth, and also of the breadth, of Red Pine 10 feet long, 4-67 in. by 4-67 in., is 10 x 81 x 8-447 x * = 9122 lbs., the pressure bein( uniform in both cases ; or cue half of that weight, viz., 4561 lbs., if the pressures act ii the middle. PRESSED BY TWO FORCES P AND Q. TABLE VI. Continued. Scantlings of Red Pine when acted upon by two forces P anc P in the direction of the depth, Q in the direction of the bre In this table, Gl = P; P = pressure upon each foot in length; IBreadT The deflections each way of the timber are equal j Dfpth 119 Q, viz., adth. - = 1-00. Length in feet, clear )earing. Value of P. 256 0000 lbs. 2-2857cwt8. Value of P. 364-5000 lbs. 3-2544cwts. Value of P. 500-0000 lbs. 4-4642cwts. Value of P. 665-5000 lbs. 5-941 9cwts. Multipli break of every S era to give the ng wciffht tcantling in the able. in the dire tion of th depth. c- e In the direc- tion of the breadth. Depth. Breadth. Depth. fireadth Depth. Breadth Depth. Breadth. 1 2 3 4 5 MIX Ml 1- 86 X 1-86 2- 52 X 2-52 3- 13X 3-13 0*70 X 3'70 1- 25 X 1-25 2- 09 X 2-09 2- 84 X 2-84 3- 52 X 3-52 4- 16X 4-16 1- 38 X 1-38 2- 33 X 2-33 3- 15X 3-15 3- 91 X 3-91 4- 63 X 4-63 1- 52X 1-52 2- 56 X 2-56 3- 47 X 3-47 4- 31 X 4-31 5- 09 X 5-09 4- 75( 5- 646 6- 251 6- 7n 7- 102 ) ] 1 \ 4-750 6-251 6- 717 7- 103 6 7 8 9 4-24 X 4-24 4- 76 X 4-76 5- 27 X 5-27 5- 75 X 5-75 6- 23 X 6-23 4- 78 X 4-78 5- 36 X 5-36 5- 92 X 5-92 6- 47 X 6-47 7- 00 X 7-00 5-31 X 5-31 5- 96 X 5-96 6- 58 X 6-58 7- 19 X 7-19 7-78 X 7-78 5- 84 X 5-84 6- 55 X 6-55 7- 24 X 7-24 7- 91 X 7-91 8- 56 X 8-56 7-434 7-72€ 7- 98S 8- 227 8-447 \ ! 7-434 4 1 ZK) 7- 988 8- 227 8-447 11 12 13 14 15 6- 69 X 6-69 7- 14 X 7-14 7- 58 X 7-58 8- 01 X 8-01 8-44 X 8-44 7- 52 X 7-52 8- 03 X 8-03 8- 53 X 8-53 9- 01 X 9-01 9-49 X 9-49 8-36 X 8-36 8- 92 X 8-92 9- 47 X 9-47 10-02X10-02 10-55X10-55 9-20 X 9-20 9-82 X 9-82 10- 42X10-42 11- 02X11-02 11-60X11-60 8-65C 8- 84C 9- 019 9-188 9-348 ! ! 8-650 8- 840 9019 9- 188 9-348 16 17 18 19 20 8- 86 X 8-86 9- 27 X 9-27 9-68 X 9-68 10 08X10-08 10-47 X 10-47 9-96 X 9-96 10-43X10-43 10- 88X10-88 11- 34X11-34 11-78X11-78 11-07X11-07 11- 59X11-59 12- 09X12-09 12- 60X12-60 13- 09X13-09 12-18X12-18 12- 75X12-75 13- 30X13-30 13- 86X13-86 14- 40X14-40 9-50C 9-645 9-784 9-917 10045 9-500 9-645 9-784 9-917 10-045 Deflections in the middle for each foot in length. SeeE xamples. 'alueofl IP • 1 D. 1 T5- 01 an men. -^j of an inch. of an inch. of an inch. 'alue of P D 10240-00 lbs. 9r42cwts. 16402-50 lbs. 146-45cwts. 25000-00 lbs. 223-21 cwts. 36602-50 lbs. 326-80cwts. 1 Pressu ire uniform. aluc of P ~d" 6400-00 lbs. 57-14cwts. 10251-56 lbs. 91-53cwts. 15626-00 lbs. 139-50cwts. 22876-56 lbs. 204-25cwts. 1 Press i " ure iu the oiddle. VI. VII. VIII. IX. * Example.— Rei Vme 10 feet long, 7-78 in. by 778 in., with 10x 500 = = 5000 lbs. iressure in the direction of the depth, and with 5000 lbs. pressure in the direction of the ireadth, deflects each way -i °. or ^ of an inch. The breaking weight, in the direction of the depth, and also of the breadth, of Red Pine ,0 feet long, 7-78 in. by 7-78 in., is 10x 500x 8-447=42235 lbs., the pressure being miform in both cases; or one half of that weight, viz., 21117 lbs., if the pressures act in the liddle. 120 THIRD SERIES — TABLES OF SCANTLINGS TABLE VI. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P in the direction of the depth, Q in the direction of the breadth. In this table, Q,=P; P = pressure upon each foot in length; IBreaDTH The deflections each way of the timber are equal j Depth Length in feet, clear Value of P. 864-0000 lbs. 7-7142 cwts. Value of P. 1098-5000 lbs. 9-8080cwts. Value of P. 1372-0000 lbs. 12-2500cwts. Value of P. 1687-5000 lbs 15-0669cwts. Value of P. 2048-0000 lbs. 18-2857 cwts. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 5 1*66 X 1-66 2- 79 X 2-79 3- 79 X 3-79 4- 70 X 4-70 5- 55 X 5-55 1-80 X 1-80 3- 03 X 3-03 4- 10 X 4-10 5- 09 X 5-09 6- 02 X 6-02 1-94 X 1-94 3- 26 X 3-26 4- 42 X 4-42 5- 48 X 5-48 6- 48 X 6-48 2- 08 X 3- 49 X 4- 73 X 5- 87 X 6- 94 X 2- 08 3- 49 4- 73 5- 87 6- 94 2- 21 X 2-21 3- 72 X 3-72 5- 05 X 5-05 6- 26 X 6-26 7*40 X 7-40 6 7 8 9 *10 6- 37 X 6-37 7- 15 X 7-15 7- 90 X 7-90 8- 63 X 8-63 9- 34 X 9-34 6- 90 X 6-90 7- 74 X 7-74 8- 56 X 8-56 9- 35 X 9-35 10-12 XlO-12 7- 43 X 7-43 8- 34 X 8-34 9- 22 X 9-22 1007X10-07 10-89 X 10-89 7- 96 X 7-96 8- 93 X 8-93 9- 87 X 9-87 10- 79 X 10-79 11- 67X11-67 8- 49 X 8-49 9- 53 X 9-53 10- 53X10-53 11- 51 Xll-51 12- 45 X 12-45 11 12 13 14 15 16 17 18 19 20 ] ] 1 ] ] ] ] ] 1 ] 0-03X10-03 0- 71 X 10-71 1- 37X11-37 2- 02 X 12-02 2-66X12-66 10- 87X10-87 11- 60X11-60 12- 32X12-32 13- 02X13-02 13-71X13-71 11- 70X11-70 12- 49X12-49 13- 27X13-27 14- 02X14-02 14-77X14-77 12- 54X12-54 13- 38X13-38 14- 21 X 14-21 15- 02X1502 15-82X15-82 13- 37X13-37 14- 28X14-28 15- 16X15-16 16- 03X16-03 16-88X16-88 3-29X13-29 3- 90X13-90 4- 51 X 14-51 5- 12X15-12 5-71 X 15-71 14- 39X14-39 15- 06X15-06 15- 72X15-72 16- 38X16-38 17- 02X17-02 15- 50X15-50 16- 22X16-22 16-93X16-93 16-61 X 16-61 Deflections in the middle for each foot in length. Value ol D ^ of an inch. ^Vof an inch. yVof an inch. y^5-of aninch. ■5^ of an inch. Valued P "F 51840-00 lbs. 462-85 cwts. 71402-50 lbs. 637-52 cwts. 96040-00 lbs. 857-50 cwts. 126562-50 lbs. 11 30-02 cwts. 163840-00 lbs. 1462-85 cwts. Value of P 32400-00 lbs. 289-28 cwts. 44626-56 lbs. 398-45 cwts. 60025-00 lbs. 535-93 cwts. 79101-56 lbs. 706-26 cwts. 102400-00 lbs. 914-28 cwts. X. XL XII. XIIL XIV. * Example.— ^ei Pine 10 feet long, 10-89 in. by 10-89 in., with 10x 12-25 = 122-5 cwts. pressure in the direction of the depth, and with 122-5 cwts. pressure in the direction of the breadth, deflects each way .i-g. or ^ of an inch. The breaking weight, in the direction of the depth, and also of the breadth, of Ked Pine 10 feet long, 10-89 in. by 10-89 in., is 10 x 12-25 x 8-447 = 1034-75 cwts., the pressure being uniform in both cases ; or one lialf of that weight, viz. 517"37 cwts., if the pressures act in the middle. PRESSED BY TWO FORCES P AND Q. 121 TABLE VI. Continued. Scantlings of Red Pine when acted upon by two forces P and Q, viz., P ia-the direction of the depth, Q in the direction of the breadth. In ttu table, Q,=P; P= pressure upon each foot in length; ]BreadTH The deflections each way of the timher are equal J DeptH Length in feet, clear jearing. Value of P. 2456-5000 lbs. 21-9330cwts. Value of P. 2916-0000 lbs. 26-0357cwts. Value of p. 3429-5000 lbs. 30-6205 cwts. Value of P. 4000-0000 lbs. 35-7142cwts. IMultipliers to give the breaking weight of every Scantliog in tlie table. In the direc- tion of the depth. In the direo- tioD of the breadth. Dtplh. Breadih. Depth. Breadth. Depth. Breadth. Depth. Breadth. 1 2 3 4 0 2- 35 X 2-35 3- 96 X 3-96 5- 36 X 5-36 6- 65 X 6-65 17,017 V T.Q'y To/ A 7 o7 2-49 X 2-49 4- 19 X 4-19 5- 68 X 5-68 7-05 X 7-05 Q.OO V/ 0.00 2-63 X 2-63 4- 42 X 4-42 5- 99 X 5-99 7-44 X 7-44 8 79 X 8 79 2-77 X 2-77 4-66 X 4-66 6- 31 X 6-31 7- 83 X 7-83 9-26 X 9-26 4-750 6-251 6- 717 7- 103 4-750 0 OftO 6-251 6- 717 7- 103 6 7 8 9 * lU 9-02 X 9-02 10- 12 X 10-12 11- 19X11-19 12- 23 X 12-23 io'2o X 13-23 9-55 X 9-55 10- 72X10-72 11- 85X11-85 12- 94 X 12-94 14-01 X 14-01 10- 08X10-08 11- 32X11-32 12- 51 X 12-51 13- 66X13-66 14- 79 X 14-79 10- 61 X 10-61 11- 91 Xll-91 13- 17X13-17 14- 38X14-38 15- 56 X 15-56 7-434 '7.'70f? 1 1 4,0 7- 988 8- 227 8-447 7-434 7 720 7- 988 8- 227 8-447 11 12 13 14 15 14- 21 X 14-21 15- 17X15-17 16- 11 X16-11 17- 03X17-03 15- 05X15-05 16- 06X16-06 17- 06X17-06 15- 88X15-88 16- 95X16-95 16-72X16-72 8-660 8- 840 9- 019 9-188 9-348 8-650 8- 840 9- 019 9-188 9-348 16 17 18 19 20 9-500 9-645 9-784 9-917 10-045 9-500 9-645 9-784 9-917 10-045 Deflections in the middle for each foot in length. See Examples. Value of D. of an inch. of an inch. of an inch, l-ris of an inch. Valne of P 17 208802-50 lbs. 1864-30c«.ts. 262440-00 lbs. 2343-21 cwts. 325802-50 lbs. 2908-95c»'t3. 400000-00 lbs. 357r42cwts. 1 Pressure uniform. I'alue of P "F 130501-561bs. 1165-19cwts. 164025-OOlbs. 1464-50cwt,. 203626-56 lbs. 181809cwts. 250000-00 lbs. 2232 14cwts. \ Pressure in the j middle. XV. XVI. XVII. XVIII. * Example.— Rtdi Pine 10 feet long, 15-56 m. by 15-56 in., with 10 x 35-7142 = 357-14 jwts. pressure in the direction of the depth, and with 357'14 cwts. pressure in the direction )f the breadth, deflects each way or JLj. of an inch. The breaking weight, in the direction of the depth, and also of the breadth, of Red Pine 10 feet long, 15-56 in. by 15-56 in., is 10 x 35-7142 x 8-447 = 3016-77 cwts., the pressure jeing uniform in both cases; or one half of that weight, viz., 1508-38 cwts., if the pressures ict in the middle. MISCELLANEOUS TABLES, &c. 124 MISCELLANEOUS TABLES. TABLE I. By which may be found the Scantlings of Red Pine, sufficient to carry, when loaded, any given portion of the breaking weight. *^* The breaMng weight of every scantling in this table is one cwt. to the foot, uuiformly loaded. Depth in LENGTH IN FEET CLEAH BEARING. 1 2 3 4 6 7 8 .inches. BREADTH IN INCHES. ■0139 •0556 '9999 •5000 •6806 •8889 3^ •0102 •0408 •0918 •1633 •255 1 •3673 •5000 •6531 4 •0078 •0313 •0703 •1250 •1953 •2813 •3828 ■5000 4i •0062 •0247 •0556 •0988 •1543 •2222 •3025 ■3951 6 •0050 •0200 •0450 •0800 •1250 •1800 •2450 3200 H •0041 •0165 UUU 1 •1488 •20*25 •2645 6 •0035 •0139 •0313 •0556 ■0868 •1250 •1701 •2222 6i •0030 •0118 •0266 •0473 •0740 •1065 •1450 ■1894 7 •0026 •0102 •0230 •0408 •0638 •0918 •1250 •1633 7i •0022 •0089 •0200 •0356 •0556 •0800 •1089 •1422 *8 •0020 •0078 \jO 1 o V/rtOO •0957 •1250 Si •0017 •0069 •0156 •0277 •0433 •0623 •0848 •1107 9 •0015 •0062 •0139 •0247 •0386 •0556 •0756 •0988 ^2 •0014 •0055 •0125 •0222 •0346 •0499 •0679 •0886 10 •0013 •0050 •0113 •0200 •0313 •0450 •0613 •0800 lOi •0011 •0045 •0102 •0181 •0283 •0408 •0556 •0726 11 •0010 •0041 •0093 •0165 •0258 •0372 •0506 •0661 114 •0009 •0038 •0085 •0151 •0236 •0340 •0463 •0605 12 •0009 •0035 •0078 •0139 •0217 •0313 •0425 •0556 124 •0008 •0032 •0072 •0128 •0200 •0288 •0392 •0512 13 •0007 •0030 •0067 •0118 •0185 •0266 •0362 •0473 134 •0007 •0027 •0062 •0110 •0171 •0247 •0336 •0439 14 •0006 •0026 •0057 •0102 •0159 •0230 •0313 ■0408 144 •0006 •0024 •0054 •0095 •0149 •0214 •0291 •0381 15 •0006 •0022 •0050 •0089 •0139 •0200 •0272 •0356 16 •0005 •0020 •0044 •0078 •0122 •0176 •0239 •0313 17 •0004 •0017 •0039 •0069 •0108 •0156 •0212 •0277 18 •0004 •0015 •0035 •0062 •0096 •0139 •0189 •0247 19 •0003 •0014 •0031 •0055 •0087 •0125 •0170 •0222 20 •0003 •0013 •0028 •0050 •0078 •0113 •0153 •0200 * Example. — The greatest weight, uniformly loaded, upon a Red Pine joist 8 inches deep and 8 feet long, is 3 cwts. to the foot ; then if 6 times that weight be the breaking weight to the foot, the breadth of the joist should be 6 x 3 x •1250 = 2"25 inches. By Table II. page 128, the deflection of a joist 8 inches deep and 8 feet long, uniformly loaded with one-sixth of the breaking weight, is ^ x "263 = '21 of an inch. MISCELLANEOUS TABLES. 125 TABLE I. Continued. By which may be found the Scantlings of Red Pine, sufficient to carry, when loaded, any given portion of the breaking weight. *#* The breaking weight of every scantling in this table, is one cwt. to the foot, uniformly loaded. Depth in LENGTH IN FEET , CLEAR BEARIN( 9 1 1^ 1 H 1 12 1 13 1 14 15 1 16 inches. BREADTH IN INCHES. 3 1 OOUD ^ UUUU o47^ 4,1 44,4 Q. 1 9^n 0 000\) 31 •8265 1 -0904 1 •9*^47 1 -4^04 1 -794 1 / 4^:0 4, UUUU 9-9Q.'iQ 4 4oOO 2-6122 4 "6328 i o\o 1 • 1 9'=in 1 1 40\J 1 •'^OCt'i I o4\.iO 1 •'5'^ 1 1 •7.'=i7S X 4010 9-0000 ^ \)\J\J\J 4i •5000 U 1 / o oooy I V^04 1 -9000 1^5802 5 •4050 0\J\J\} \)\iO\} •79nn .Qonn youu 1 -1 9.'in 1*2800 6\ .Ann A oyou Dyo4 ouyy .Q9Q7 y,«y / 1 •O'^TS^ 6 •2813 0'± 1 4 •4901 ooOo oouo •7S1 9 •8889 6i 4jOi) OOOK) ■49fin ovw 0 1 yy •fifi.'^7 •7574 7 4,0'J 1 «jD / 0 40 1 1 OUUU 0 1 'tU •6531 71 1 OV/U .9099 44it4i .oonn 04,\J\J 4000 0\)\J\J •5689 8 J OC5 Sh • 1 7Qn • 94 0 1 ^ly 1 •9Q94 vy*4 Otjy 1 •4429 9 •1 ftfi7 •9999 4,4,4.4, 0\j40 ••^479 •3951 9^ •1 199 • 1 lOCDO 1 D / D • 1 QQ4 1 yy4 • 9Q4 1 ,co4 1 •97 1 '^ 4,1 \ o ••^1 Ifi 0 1 lU •3546 10 1 W i O 1 <5UU • 9 1 I • •04 ^[\ •9Sil'^ •3200 lOi •0918 •1134 •1372 •1633 •1916 ^^22^ •255 1 •2903 ]1 •0837 •1033 •1250 •1488 •1746 •2025 •2324 •2644 lU •0766 •0945 •1144 •1361 •1597 •18-53 •2127 •2420 12 •0703 •0868 •1050 •1250 •1467 •1701 •19-53 •2222 •0648 •0800 •0968 •1152 •1.352 •1568 •1800 •2048 13 •0599 •0740 •0895 •1065 ~r250 •1450 •1664 •1893 ]3i •0556 •0686 •0830 •0988 •1159 •1344 •1543 •1756 *14 •0517 •0638 •0772 •0918 •1078 •12-50 •1435 •1633 14i •0482 •0595 •0719 •0856 •1005 •1165 •1338 •1522 15 •0450 •0556 •0672 •0800 •0939 •1089 •1250 •1422 16 ~0'396 ~b488 •0591 •0703 •0825 •0957 •1099 •1250 17 •0350 •0433 •0523 •0623 •0731 •0848 •0973 •1107 18 •0313 •0386 •0467 •0556 •0652 •0756 •0868 •0988 19 •0280 •0346 •0419 •0499 •0585 •0679 •0779 •0886 20 •0253 •0313 •0378 •0450 •0528 •0613 •0703 •0800 * £.ran*j9/e.— The greatest weight, uniformly loaded, upon a Red Pine beam 14 inches deep and 15 feet long, is 20 cwts. to tlie foot; then if 4 times that weight be the breaking weight to the foot, the breadth of the beam should be 4 x 20 x ■1435 = 11'48 inches. By Table II. page 129, the deflection of a Red Pine beam 14 inches deep and 15 feet long, uniformly loaded with one-fourth of the breaking weight, is '528 of an inch. R 1-26 MISCELLANEOUS TABLES. TABLE I. Continued. By which may be found the Scantlings of Rkd Pine, sufficient to carry, when loaded, any given portion of the breaking weight. *;,,* The breaking weight of every scantling in this table, is one cwt. to the foot, uniformly loaded. LENGTH IN FEET, CLEAR BEARING. Depth in 17 1 18 1 19 1 20 1 21 1 22 1 23 i 24 inches. BREADTH IN INCHES. 3 4 OUUU 0 Uloy 0 oOO\> fi. 1 9*»0 fi'7999 7-'^479 3i 9-Q4Qn 0 ouo 1 «3 000 / A-nsi f5 yJO 1 u A'^IOOO 5-3QS0 5-8775 4 / 0 "X- 1 9.'5n 0 i^vU 0 ^^tjtj 3.78J3 4.1328 4*5000 4i 1 •7840 o.nnf'kn 9'99Sd 3.7222 2*9877 3 • 2654 3*5556 5 1 .^900 1 yjA\J\j 1 OKjOKj 9'90.'i0 2-4200 2*6450 2^8800 H 1 • 1 Q/10 1 oooO 1 ./I Q 1 T 1 •ft99'.< 9-onoo 9- 1 ftfiO A lOUU 6 1 \J\JOO 1 •9^'^'^ 1 A'JOO 1 iJO 1 -C 1-6306 1*8368 2*0000 6i 1 UDO 1 1 • 1 J. 1 ^OA\J 1*5651 1*7041 7 •7*^79 1 0 i ^ .Q9nQ 1.3495 1*4694 7i oooy •QSOO 1 -1756 1-2800 8 0D40 /UO 1 /olo .af! 1 00 10 1 yjooA l'19.'i0 1 yAK}\j .A Ann .MAP, 0it40 •fiQ90 «7 I t/A •9965 9 •JUuU ••^^7 1 00 1 1 u 1 / 0 •74fiQ •8164 •8889 9^ •'\C\r\f\ owuu •'i'^/lO OOtKJ u 1 wo •7978 10 00 10 4tJ ItJ •'^OOO 0010 •7200 IO5 •3277 •3673 •4093 •4535 •5000 •5488 •5998 OOo 1 *11 •2986 •3347 •3729 •4132 •4556 •5000 •5465 •5950 lU •2732 •3062 •3412 •3781 •4168 •4575 •5000 •5444 12 •2509 •2813 •3134 •3472 •3828 •4201 •4592 •5000 m •2312 •2592 •2888 •3200 •3528 •3872 •4232 •4608 13 •2138 •2396 •2670 •2959 •3262 •3580 •3913 •4260 m •1982 •2222 •2476 •2744 •3025 •3320 •3628 •3951 14 •1843 •2066 •2302 •2551 •2813 •3087 •3374 •3673 m •1718 •1926 •2146 •2378 •2622 •2878 •3145 •3425 15 •1606 •1800 •2006 •2222 •2450 •2689 •2939 •3200 16 •1411 •1582 "^763" •1953 •2153 •2363 •2583 •2813 17 •1250 •1401 •1561 •1730 •1907 •2093 •2288 •2491 18 •1115 •1250 •1393 •1543 •1701 •1867 •2041 •2222 19 •1001 •1122 •1250 •1385 •15-27 •1676 •1832 •1994 20 •0903 •1013 •1128 •1250 •1378 •1513 •1653 •1.^ * Example. — The greatest weight, uniformly loaded, upon a Red Pine joist 11 inchM deep and 18 feet long, is 1*75 cwts. to the foot; then if 5 times that weight be the breakiia weight to the foot, the breadth of the joist should be 5 x 1*75 x -3347 = 2*93 inches. 1 By Table II. page 130, the deflection of a Red Pine joist 11 inches deep and 18 feet long, uniformly loaded with one-Jiflh of the breaking weight, is 4. x- '968 = •774 of an inch. MISCELLANEOUS TABLES. 127 TABLE I. Continued. By which may be found the Scantlings of Red Pine, sufficient to carry, when loaded, any given portion of the breaking weight, * The breaking weight of every scautling in this table, is one cwt. to the foot, uniformly loaded. LENGTH IN FEET, CLEAR BEARING. 25 26 27 28 29 30 31 32 BREADTH IN INCHES. 3 3^ 4 4i 5 5i 6 Qi 7 _Zi 8 8^ 9 9i 10 10^ 11 lU 12 12* 13 14 14i n5 16 17 18 19 20 8-6806 6-3776 4-8828 3-8580 3-1250 2-5826 2-1701 1-8491 1-5944 1-3889 1-2207 1-0813 •9645 -8657 •7813 •7086 •6457 •5907 •5425 •5000 •4623 •4287 •3986 •3716 -3472 -3052 •2703 •2411 •2164 •1953 9-3889 6-8980 5-2812 4-1728 3-3800 2-7934 2-3472 2-0000 1-7245 1-5022 1-3203 1-1696 1-0432 -9363 •8450 •7664 •6984 -6389 •5868 •5408 -5000 •4637 •4311 •4019 -3756 •3301 •2924 •2608 •2341 •2113 10-1250 7-4387 5-6953 4-5000 3-6450 3-0124 2-5313 2-1568 1-8597 1-6200 1-4238 1-2612 M250 1-0097 -9113 -8265 -7531 -6890 •6328 -5832 •5392 -5000 -4649 -4334 -4050 -3560 -3153 •2813 •2524 -2278 10-8889 8-0000 6-1250 4-8395 3-9200 3-2397 2-7222 2-3195 2-0000 1-7422 1-5313 1-3564 1-2099 1-0859 -9800 •8099 •7410 •6806 •6272 -5799 -5377 -5000 •4661 -4356 •3828 •3391 -3025 •2715 -2450 11-6806 8-5816 6-5703 6-1914 4-2050 3-4752 2-9201 2-4882 2-1454 1-8689 r6426 ]^4550 1-2978 1-1648 1-0513 •9535 •7949 •7300 •6728 •6220 •5768 -5364 •5000 -4672 •4106 •3638 •3245 •2912 •2628 12-5000 9-1837 7-0312 5-5556 4-5000 3-7190 3-1250 2-6627 2-2959 2-0000 1-7578 1-5571 1-3889 1-2465 1-1250 1-0204 -9297 -8507 -7812 •7200 •6657 •6173 •5740 •5351 •5000 -4395 •3893 -3472 -3116 -2813 13-3472 9-8061 7-5078 5-9321 4-8050 3-9711 3-3368 2-8432 2-4515 2-1356 1-8770 1-6626 1-4830 1-3310 1-2013 1-0896 -9928 -9083 •8342 •7688 •7108 -6591 -6129 -5713 -5339 •4692 •4157 -3708 -3328 -3003 * Example. — The greatest weight, uniformly loaded, upon a Red Pine beam 15 inches deep and 25 feet long, is, including always the weight of the beam, 10 cwts. to the foot; then if 4 times that weight be the breaking weight to the foot, the breadth of the beam should be 4 X 10 X •3472 = 13-89 inches. By Table II. page 131, the deflection of a Red Pine beam 15 inches deep and 25 feet long, uniformly loaded with one-fourth of Ihe breaking weight, is 1-37 inches. 128 MISCELLANEOUS TABLES. TABLE 11. DEFLECTION of Red Pine Scantlings, of any breadth, when uni- formly loaded with one-fourth of the breaking weight. *^* When one-fourth of the breaking weight is suspended from the middle, multiply the deflections in this table by "8. Depth LENGTH IN FEET , CLEAR BEARING. 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 inches. DEFLECTION IN INCHES. 3 •on •044 •099 •175 •274 •394 •537 •701 3^ •009 •038 •085 •150 •235 •338 •460 •601 4 •008 •033 •074 •131 •205 •296 •403 •526 4i •007 •029 •066 •117 •183 •263 •358 •468 5 •007 •026 •059 •105 •164 •237 •322 •421 " 2 •006 •024 •054 •096 •149 •215 •293 •383 6 •005 •022 •049 •088 •137 •197 'ZOO •351 ^ 2 •005 •OQO •046 •081 •126 •182 •248 •324 7 •005 •019 •042 •075 •117 •169 •230 •301 7i •004 •018 •039 •070 •110 •158 •215 •281 *8 •004 •016 •037 •066 •103 •148 •201 •263 8^ •004 •015 •035 •062 •097 •139 •190 •248 9 •004 •033 •058 •091 •132 •179 •234 9* •003 •014 •031 •055 •087 '125 •170 •221 10 •003 •013 •030 •053 •082 •118 •161 •210 lOi 003 •013 uou . 1 1 Q 1 IC) •153 •200 11 •003 •012 •027 •048 •075 •108 •146 •191 lU •003 •Oil •026 •046 •071 •103 •140 •183 12 •003 •on •025 •044 •068 •099 •134 •175 12i •003 •Oil •024 •042 •066 •095 •129 •168 13 ~003~ •010 •023 •040 •063 •091 •124 •162 m •002 •010 •022 •039 •061 •088 •119 •156 14 •002 •009 •021 •038 •059 •085 •115 •150 141 •002 •009 •020 •036 •057 •082 •111 •145 16 •002 •009 •020 •035 •055 •079 •107 •140 16 •002 •008 •019 •033 •051 •074 •101 •132 17 •002 •008 •017 ■031 •048 •070 •095 •124 18 •002 •007 •016 •029 •046 •066 •090 •117 19 •002 •007 •016 •028 •043 •062 •085 •111 20 •002 •007 •015 •026 •041 •059 •081 •105 * Example. — A Red Pine joist 8 inches deep and 8 feet long, uniformly loaded with one- fourth of the breaking weight, deflects in the middle •263 of an inch ; the same joist uni- formly loaded with one-Jiflh of the breaking weight, deflects ^ x 263 = '210 of an inch ; with OM-sirth of the breaking weight, the deflection is 4 x "263 = '175 of an inch ; and so on. MISCELLANEOUS TABLES. 129 TABLE II. Continued. DEFLECTION of Red Pine Scantlings, of any breadth, when uni- formly loaded with one-fourth of the breaking weight. *»* When one-fourth of the breaking weight is suspended from the middle, multiply the deflections iu this table by 'S. LENGTH IN FEET, CLEAR BEAKING. 9 1 10 11 1 12 1 13 1 14 15 1 16 DEFLECTION IN INCHES. 254 242 232 222 213 205 197 190 184 1_78_ T66 157 148 140 133 096 939 822 730 657 598 548 506 470 438 411 387 365 346 329 313 299 286 274 263 253" 244 235 227 219 205" 193 183 173 164 1-326 1-136 •994 •884 •795 •723 •663 •612 -568 •530 •497 •468 •442 •419 •398 1-578 1-352 1-183 1-052 •947 •861 •789 •728 •676 •631 •592 •557 •526 •498 •473 ^sT •430 •412 •394 ^9 •351 •338 •326 •316 •296 •278 •263 •249 •237 1-852 1-587 1-389 1-234 1-111 l-0\0 •926 •855 •794 •741 "•694" •654 •617 •585 •556 •529 •505 •483 •463 •444 •427 •412 •397 •383 ^47" •327 •309 •292 •278 2^148 1-841 1-611 1-432 1-289 M71 1^074 •991 -920 -859 •805 •758 •716 •678 •644 "6l4" •586 •560 •537 •515 •496 •477 •460 •444 •430 ^03" •379 •358 •339 •322 465 113 849 644 479 345 233 138 057 986 924 870 822 779 740 ~70l 672 643 616 592 569 548 528 510 493 462 435 411 389 370 2-805 2-404 2-104 1-870 1-683 1-630 1-402 1-295 1-202 1-122 1-052 -990 •935 •886 •841 •801 •765 •732 •701 •673 •647 •623 •601 •580 •561 •526 -495 •468 •443 •421 * Example. — A Red Pine beam 14 inches deep and 15 feet long, uniformly loaded with one-fourth of the breaking weight, deflects in the middle '528 of an inch; the same beam uniformly loaded with out-fifth of the brealiiug weight, deflects ^ x -528 = '422 of an inch. If one-fourth of the breaking weight be suspended from the middle, the deflection is •8 X -528 = '422 of an inch ; if o\^t-fifth of the breaking weight be so suspended, the deflec- tion is * X •538 = '338 of an inch ; and so on. 130 MISCELLANEOUS TABLES. TABLE II. Continued. DEFLECTION of Red Pine Scantlings, of any breadth, when uni- formly loaded with one-fourth of the breaking weight. When one-fourth of the breaking weight is suspended from the middle, multiply the deflections in this table by '8. LENGTH IN FEET, CLEAR BEARING. Depth in 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 inches. DEFLECTION IN INCHES. Q O 'i- 1 fi7 O lO / o ooyj 3-955 ft ooo 5-303 5^796 6^3 1 1 3J 2-714 3-043 3-390 O 1 O I 4-545 4^968 5^409 4 2-375 2-663 2-967 3*977 4-347 4^733 4i 2-111 2-367 2-637 3.535 3-864 4^207 5 1-900 2-130 2-373 2-630 2^899 3^182 3-478 3^787 0^ 1 •70'7 1 / At 4 ov 1 ~9'fi'^fi 3-162 "3-442 6 1-583 1-775 1-978 9- 1 Q 1 A 1 y 1 9-41 fi /6 4 lO 2^898 3-156 6i 1-461 1-638 1-826 Z ZO\J 2-675 2-913 7 1-357 1-521 1-695 1 o / y 9-07 1 9-973 2-484 2-705 7i 1-267 1-420 1-582 1-753 1-933 2-121 2-318 2-524 c5 1 •! $37 1 lo/ 1 •'i'i 1 1 OO I 1-483 1 O X 1 £70i7 ~2-"l74 "2^7~ 8i 1-118 1-253 1-396 X / \JO 1 -879 2-046 2-227 9 1-056 1-183 1-318 1 40 1 X O X X X / 00 1-932 2-104 9J 1-000 1-121 1-249 1 1 004 X t)*0 1-830 1-993 10 •950 1-065 1 -187 1-315 1-450 1-591 P739 1-893 1 ni 1 Ull 1-130 1-252 1-381 1-515 1-656 ^•803 * 1 1 11 •968 1-079 1-195 1-318 1-446 1-581 1-721 IH •826 -926 1-032 1-143 1-260 1-383 1-512 1-646 12 •792 -888 -989 1-096 1-208 1-326 1-449 1-578 m •760 -852 •949 1-052 1-160 1-272 1-391 1-515 13 -819 •913 1-011 M15 T22r T338" T456^ m •704 •789 •879 -974 1-074 1-178 1-288 1-402 14 •679 •761 -848 -939 1-035 1-136 1-242 1-352 -655 •735 -818 -907 1-000 1-097 1-199 1-306 15 -633 -710 -791 -877 -966 1-061 1-159 1-262 -594 -666 -742 -822 "^06" """-99^ 1-087 TTsiT 17 -559 -626 -698 •773 -853 -936 1-023 1-114 18 -528 -592 -659 •730 -805 -884 •966 1052 19 •500 -561 -625 •692 -763 -837 •915 •997 20 -475 -533 •593 •657 •725 •795 •869 •947 * Example. — A Red Pine joist 11 inches deep and 18 feet long, uniformly loaded with one-fourth of the breaking weight, deflects in the middle •QSS of an inch ; the same joist, uniformly loaded with one-Jifth of the breaking weight, deflects ^ x -968 = •774 of an inch. MISCELLANEOUS TABLES. 131 TABLE II. Continued. DEFLECTION of Red Pine Scantlings, of any breadth, when uni- formly loaded with one-fourth of the breaking weight. *** When oue-fourtli of the breaking weight is suspended from the middle, multiply the deflections in this table by "S. LENGTH IN FEET, CLEAR BEARING. Depth in AO 27 28 29 30 OA inches. DEFLECTION IN INCHES. 3 6-848 7-407 7-987 8-590 9-215 9-861 10-529 11-220 3^ 5-870 6-349 6-846 7-363 7-898 8-452 9-025 9-617 4 0 loo 0 000 5-991 6-443 6-911 7-396 7 oy7 0 4 10 4 ODO 5-325 5-727 6-143 6-574 H'A sn 0 A-AA A 4-792 5-154 5-529 5-917 fi.Q 1 ft 0010 fi-7'^9 5i ~3^35~ 4-040 T357^ ^-685" T026" "5^79" 5-743 6-120 6 3-424 3-703 3-994 4-295 4-608 4-931 5-265 5-610 oi 0 loi 3-419 3-687 3-965 4-253 4-551 4-8d0 0 1 /o 7 Z tfoo 0 174 3-423 3-681 3-949 4-226 4010 4 oUO •7 1 ^ /oy .6 yoo 3-195 3-436 3-686 3-944 /< .o 1 0 4V* 1.6 4 4c5c5 8 2-568 "2^7"78~ ^95" "3^2r ~3T5"5' "F698~ 1^949" 8i 2-417 2-614 2-819 3-032 3-252 3-480 3-716 3-960 9 2 2oo 2-469 2-663 2-863 3-072 3-287 3-510 0-74U n 1 A loo .4 oo9 2-522 2-713 2-910 3-114 0 0.^0 0 04t5 1 A Z U04 0.000 2-396 2-577 2-764 2-958 0 loy 0 ODD 10* T957" 2-116 ~2^282~ 2-454 ~2^33~ 2-817 "¥008" 3-206 11 1-868 2-020 2-178 2-343 2-513 2-689 2-872 3-060 lli 1-786 1-932 2-084 2-241 2-404 2572 2-747 2-927 12 1-712 1-852 1-997 2-148 2-304 2-465 2-632 2-805 1-644 1-778 1-917 2-062 2-212 2-367 2-527 2-693 13 1-580 1-709 1-843 1-982 2126 2-276 2-430 2-589 13i 1-522 1-646 1-775 1-909 2-048 2-191 2-340 2-493 14 1-467 1-587 1-712 1-841 1-975 2-113 2-256 2-404 14i 1-417 1-532 1-653 1-777 1-906 2-040 2-179 2-321 *15 1-370 1-481 1-598 1-718 1-843 1-972 2-106 2-244 "Te" 1-284 T3^~ 1-498 1-611 1-728 T849" 2-104 17 1-208 1-307 1-410 1-516 1-626 1-740 1-858 1-980 18 1-141 1-234 1-331 1-432 1-536 1-644 1-755 1-870 19 1-081 1-170 1-261 1-356 1-455 1-557 1-663 1-772 20 1-027 1-111 1-198 1-289 1-382 1-479 1-579 1-683 * Example. — A Red Pine beam 15 inches deep and 25 feet long, uniformly loaded with one-fourth of the breaking weight, deflects in the middle 1-370 inches ; if one one-fourth of the breaking weight be suspended from the middle, the deflection is "8 x 1-370 = 1'096 inches. 132 MISCELLANEOUS TABLES. TABLE III. By which may be determined the depths of Ceiling Joists, Rafters, Floor Joists, &c. ; the breadth being li inches, and the deflec- tion 4% of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length in feet, clear bearing 15-62 20-79 27^00 34-32 42-87 52^73 64-00 76^76 91-12 107-17 DEPTH IN INCHES. 1 2 3 4 5 •39 •79 M8 1-58 1-97 •43 •87 1-30 1-73 2^17 •47 •95 1-42 1- 89 2- 36 •51 1-02 1- 54 2- 05 2-56 •55 MO P65 2-21 2-76 •59 M8 1- 77 2- 36 2-95 •63 1-26 1- 89 2- 52 315 •67 1- 34 2- 01 2^68 3- 35 •71 1- 42 2^13 2- 84 3- 55 •75 1- 50 2- 25 2- 99 3- 74 *6 7 8 9 10 2-36 2- 76 3- 15 3-55 3-94 2^60 3^03 3^47 3^90 4-33 2- 84 3- 31 3-78 4^25 4^73 3-07 3- 58 4- 10 4^61 5- 12 "3¥r 3- 86 4- 41 4- 96 5- 52 3- 55 4- 14 4^73 5- 32 5-91 4- 41 5- 04 5- 67 6- 30 4-02 4- 69 5- 36 6^03 6- 70 4-25 4^96 5^67 6-38 7^09 4^49 5-24 5- 99 6- 74 7- 49 11 12 13 14 15 4^33 4- 73 5^12 6^52 5- 91 4- 77 5- 20 5^63 6- 07 6^50 "sYo" 6-67 6-15 6- 62 7- 09 5^63 6^15 6^66 7-17 7-68 ~6-07 6- 62 7- 17 7-72 8^27 ~6-50" 7-09 7- 68 8- 27 8-86 6-93 7^56 8^19 8- 82 9- 45 T37" 8-04 8-71 9^38 10^05 7- 80 8- 51 9- 22 9-93 10-64 8-23 8- 98 9- 73 10-48 11^23 16 17 18 19 20 6-30 6-70 7^09 I 7-49 1 7-88 ~6¥3" 7^37 7- 80 8- 23 8-67 7- 56 8- 04 8-51 8- 98 9- 45 8-19 8- 71 9- 22 9-73 10^24 8- 82 9- 38 9-93 10-48 iro3 9-45 10-05 10- 64 11- 23 11-82 10-09 10- 72 11- 35 ir98 12^61 10^72 11^39 12^05 12^72 13^39 11- 35 1205 12- 76 13- 47 14- 18 11-98 12^72 13^47 14-22 14-97 Multipliers to give the breaking weight of every Scantliug in each column respectively. 13-34 12-13 11-12 10-26 9-53 8-90 8^34 7^85 7-41 7^02 * Example. — If the weight upon a ceiling joist 6 feet long, 3-07 in. by Ij in., be 34-32 lbs. to the foot, the deflection in the middle is of an inch ; with one-half of that weight, or I7-I6 lbs. to the foot, the deflection is -^-^ or of an inch; with one-third of the same weight, or 11-44 ffis. to the foot, the deflection is or of an inch ; and so on, the de- flection varying according as the weight. The breaking weight of a Red Pine ceiliug joist 6 feet long, 3-07 in. by li in., is 6 k 34-82 X 10-26 = 2112 lbs. uniformly loaded, or 1056 lbs. suspended from the middle. The weight of a superficial foot of laths and hair mortar, may be estimated at 8 or 10 tbs. MISCELLANEOUS TABLES. 133 TABLE III. Continued. By which may be determined the depths of Ceiling Joists, Rafters, Floor Joists, &c. ; the breadth being 1| inches, and the deflec- tion of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. 125-0 144-7 166-3 190-1 216-0 244-1 274-6 307-5 343-0 381-0 DEPTH IN INCHES. 1 •79 -83 •87 2 1-58 1-65 1-73 3 2-36 2-48 2-60 4 3-15 3-31 3-47 5 3-94 4-14 4-33 6 4-73 4-96 5-20 7 5-52 5-79 6-07 8 6-30 6-62 6-93 *9 7-09 7-45 7-80 10 7-88 8-27 8-67 11 8-67 9-10 9-53 12 9-45 9-93 10-40 13 10-24 10-75 11-27 14 11 03 11-58 12-13 15 11-82 12-41 13-00 16 12-61 13-24 13-87 17 13-39 14-06 14-73 18 14-18 14-89 15-60 19 14-97 15-72 20 15-76 9-97 10- 87 11- 78 12- 69 13- 59 14- 50 15- 40 -95 1- 89 2- 84 3- 78 4- 73 5- 67 6- 62 7- 56 8- 51 9- 45 10- 40 11- 35 12- 29 13- 24 14- 18 15-13 •98 1-97 2^95 394 4-92 ~bm 6- 89 7- 88 8- 86 9- 85 10^ 11^82 12- 80 13- 79 14- 77 1 02 2-05 3^07 4- 10 5- 12 6- 15 7- 17 8- 19 9- 22 10- 24 11- 27 12- 29 13- 32 14- 34 1- 06 2- 13 3- 19 4- 25 5- 32 6- 38 7- 45 851 9-57 10-64 11- 70 12- 76 13- 83 14- 89 1- 10 2- 21 3- 31 4- 41 5- 52 "6^2" 7- 72 8- 82 9- 93 11-03 12- 13 13- 24 14- 34 Multipliers to give the breaking weight of every Scantling in each c alumn respectively. 6-67 6-35 6-06 5-80 5-56 5-34 513 4 94 4-76 4-60 The depth and weight being the same, the deflection varies inversely as Ihe breadth ; as in the example to this, and the following tables. • Example. — A Red Pine joist 9 feet long 7-09 in. by in., with 125 lbs. weight to the foot, unifonnly loaded, deflects in the middle -S^ of an inch ; with the same weight, 7'09 in. by If in. deflects of an inch ; 7'09 in. by 2 in. deflects -^j of an inch ; 7'09 in. by 2i in. deflects of an inch ; 7^09 in. by 2^ in. deflects of an inch ; 7"09 in. by 2f in. deflects 9 of an inch; and 7'09 in. by 3 in. deflects of an inch. 134 MISCELLANEOUS TABLES. TABLE IV. By which may he determined the depths of Ceiling Joists, Rafters, Floor Joists, Bridging Joists, &c.; the breadth being If inches, and the deflection -^^^ of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length 'clear ' 15-62 20-79 27-00 34-32 42-87 52-73 64-00 76-76 91-12 107-17 bearing. DEPTH IN INCHES. 1 2 3 4 5 •37 •75 112 1^50 1-87 -41 •82 1-23 1-65 2^06 •45 •90 V35 1- 80 2- 25 -49 •97 1-46 1- 95 2- 43 -52 1-05 1- 57 2- 10 2-62 •56 M2 1- 68 2- 25 2-81 •60 1-20 1- 80 2- 39 2-99 •64 1-27 1- 91 2- 54 3- 18 •67 1- 35 202 2- 69 3- 37 •71 1^42 213 2^84 3-55 7 8 9 10 2-25 2-62 2- 99 3- 37 3-74 2-47 2- 88 3- 29 3- 70 4- 12 "¥69 3^14 3^59 4^04 4-49 2- 92 3- 41 3- 89 4- 38 4-86 3-14 3- 67 4- 19 4- 71 5- 24 3-37 3- 93 4- 49 5- 05 5-61 3- 59 4- 19 4- 79 5- 39 5-99 3- 82 4- 45 5- 10 5- 73 6- 36 4-04 4^71 5^39 6^06 6-74 ~4-27 4- 98 5- 69 6- 40 7- 11 11 12 13 14 15 4-12 4-49 4- 86 5- 24 5^61 4-53 4- 94 5- 35 5- 76 6- 17 4- 94 5- 39 5- 84 6- 29 6-74 5-35 5- 84 6- 32 6- 81 7- 30 '¥76 6-29 6- 81 7- 33 7-86 6- 17 6^74 7- 30 7- 86 8- 42 6- 69 7- 18 7- 78 8- 38 8-98 7-01 7- 63 8- 27 8- 91 9- 54 7^41 8^08 8- 76 9- 43 10-10 7- 82 8- 53 9- 24 9-95 10-66 16 17 18 19 20 5- 99 6- 36 6- 74 7- 12 7-48 6- 59 7- 00 7-41 7- 82 8- 23 7-18 7- 63 8- 08 8-53 8-98 7- 78 8- 27 8- 76 9- 24 9-73 8-38 8- 91 9- 43 9-95 10-48 8- 98 9- 54 10-10 10- 66 11- 23 9-58 10-18 10- 78 11- 38 11-97 10-18 10- 81 11- 45 12- 09 12-72 10- 78 11- 45 12- 12 12- 80 13- 47 11- 38 12- 09 12- 80 13- 51 14- 22 Multipliers to give the breaking weight of every Scautling in each column respectively. 14-05 12-77 11-70 10-80 10-03 9-36 8-78 8-26 7-80 7-39 *^* The weight of Slating, including the force of the wind, may be estimated at 56 lbs., and that of Tiling, at 62 ibs. per superficial foot. * Example. — If the Rafters for a slated roof be 15 inches apart from middle to middle, the pressure upon each foot in length is 56 x l'//3" = 70 fbs. A Rafter 6 feet long, 3-82 in. by 1| in., with 7676 lbs. weight to the foot, deflects in the middle -A. of an inch; and the breaking weight of the same is 6 x 76'76 x 8-26 = 3804 ibs., the pressm'e being uniform, and at right angles to the plane of the roof. MISCELLANEOUS TABLES. 135 TABLE IV. Continued. By which may be determined the depths of Ceiling Joists, Rafters, Floor Joists, Bridging Joists, &c.; the breadth being If inches, and the deflection -^^ of an inch to the foot, when uniformly loaded with the weights in this table. weight in pounds upon each foot in length. Length in feet, clear bearing. 125-0 144-7 166-3 190-1 216-0 244-1 274-6 307-5 343-0 381-0 DEPTH IN INCHES. 1 3 4 & •75 1- 50 2- 25 2- 99 3- 74 •79 1- 57 2- 36 3- 14 3-93 -82 1- 65 2- 47 3- 29 4- 12 •86 1- 72 2- 58 3- 44 4- 30 -90 1- 80 2- 69 3- 59 4- 49 -94 1- 87 2- 81 3- 74 4- 68 -97 1- 95 2- 92 3- 89 4- 86 1- 01 2- 02 3- 03 4- 04 5- 05 1- 05 2- 10 3- 14 4- 19 5- 24 1- 09 2- 17 3- 26 4- 34 5- 43 6 i 8 *9 10 4- 49 5- 24 5- 99 6- 74 7- 48 4- 71 5- 50 6- 29 7- 07 7-86 4- 94 5- 76 6- 59 7- 41 8- 23 5- 16 6- 02 6- 89 7- 75 8- 61 5- 39 6- 29 7- 18 8- 08 8-98 5- 61 6- 55 7- 48 8- 42 9- 36 5- 84 6- 81 7- 78 8- 76 9- 73 10^ 11- 68 12- 65 13- 62 14- 59 6- 06 7- 07 8- 08 9- 09 10-10 6- 29 7- 33 8- 38 9- 43 10-48 6- 51 7- 60 8- 68 9- 77 10-85 11 12 13 14 15 8-23 8- 98 9- 73 10- 48 11- 23 8- 64 9- 43 10- 22 11- 00 11-79 9-06 9-88 10- 70 11- 53 12- 35 9-47 10- 33 11- 19 12- 05 12-91 9-88 10- 78 11- 68 12- 57 13- 47 To^ 11- 23 12- 16 13- 10 14- 03 TFir 12- 12 13- 13 14- 14 15- 16 11- 53 12- 57 13- 62 14- 67 15- 72 11-94 13- 02 14- 11 15- 19 16 17 18 19 20 11- 97 12- 72 13- 47 14- 22 14-97 12- 57 13- 36 14- 14 14- 93 15- 72 13- 17 14- 00 14- 82 15- 64 13- 77 14- 63 15- 49 14- 37 15- 27 14- 97 15- 90 15-57 Multipliers to give the breaking weight of every Scantling in each column respectively. 7-02 6-69 6-38 6-10 5-85 1 5-62 1 5-40 5-20 5-01 4-84 * Example. — A Red Pine Scantling 9 feet long 7'07 in. by If in., with 144-7 fbs. weight to the foot, uniformly loaded, deflects in the middle of an inch ; with the same weight, 7-07 in. by 2 in. deflects -^^ of an inch ; T'O? in. by 2i in. deflects of an inch ; T'O? in. by 2§ in. deflects of an inch ; 7'07 in. by 2f in. deflects -^^ of an inch ; and 7'07 in. by 3 in. deflects ^ of an inch. The breaking weight of Red Pine 9 feet long T'O? in. by 1| in., is 9 x 1447 x 6-69 = 8712 lbs. uniformly loaded, or 4356 lbs. suspended from the middle. 136 MISCELLANEOUS TABLES. TABLE V. By which may be determined the depths of CeiHng Joists, Rafters, Floor Joists, Bridging Joists, Binding Joists, &c. ; the breadth being 2 inches, and the deflection of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length in I'eetf clear 15-62 20-79 27-00 34-32 42-87 52-73 64-00 76-76 91-12 107^ 17 be&ring. DEPTH IN INCHES. ■~T 2 3 4 5 •36 •72 1-07 1-79 •39 •79 M8 L O 1 1-97 •43 '86 1- 29 1 •70 2- 15 •47 •93 1- 40 1 OO 2- 33 •50 1-00 1- 50 A \J\) 2- 51 •54 P07 1^61 9- 1 2-68 •57 M5 1- 72 9-90 2- 86 •61 1-22 1-83 3-04 •64 1-29 1-93 3-22 •68 1- 36 2- 04 9-79 Z iZ 3- 40 6 7 8 9 10 2-51 2- 86 3- 22 3-58 ^6" 2- 76 3- 15 3-54 3-94 3-01 3-44 3- 87 4- 30 2- 79 3- 26 3- 72 4- 19 4-65 ~3~oT 3-51 401 4^51 5-01 T22 3- 76 4- 30 4- 83 5- 37 344 4-01 4- 58 5- 15 5-73 ~3"m65 4-26 4- 87 5- 48 6- 08 "3^7" 4- 51 5- 15 5- 80 6- 44 4-08 4- 76 5- 44 6- 12 6-80 11 12 13 14 15 3- 94 4- 30 4- 65 5- 01 5-37 ^3' 4- 72 5- 12 5-51 5-91 4- 72 5- 15 5- 58 6- 01 6-44 5- 58 6- 05 6^51 6-98 "5^7 6-01 6- 51 7- 01 7-52 5- 91 6- 44 6- 98 7- 52 8- 05 ~6¥o' 6- 87 7- 44 8^02 8^59 7-30 7- 91 8- 52 9- 13 7-09 7- 73 8- 38 9- 02 9-66 8-16 8-84 9^52 10-20 16 17 18 19 20 5- 73 6- 08 6-44 6- 80 7- 16 ~6¥o 6- 69 7- 09 7-48 7-87 "¥87 7-30 7- 73 8- 16 8-59 7-44 7- 91 8- 38 8- 84 9- 31 8-02 8- 52 9- 02 9-52 1002 8- 59 9- 13 9-67 10-20 10-74 9-16 9-74 10-31 10- 88 11- 45 9-74 10-34 10- 95 11- 56 12- 17 10-31 10-95 11 60 12-24 1289 1^8' 11- 56 1-2-24 12- 92 13- 60 Multipliers to give the breaking weiyht of every Scantling in each column respectively. 14-69 13-35 12-24 11-30 10-49 9-79 9-18 8-64 8-16 7-73 *i* The greatest weight upon the floor of a crowded room is 120 ibs. per superficial foot, to which, in determining the scantlings, is to he added the weight of the floor and ceiling. The greatest weight will generally vary from about 140 fts. to 160 fbs. per foot super- ficial, and the hrealdng weight of every floor liable to be so weighted, should be not less than 4 times that weight, viz. 5 cwts. to the foot, or upwards. Joists of smaU scantlings, in short lengths, should be increased in the depth or breadth, or in both, according to the liability to decay, from the situation in which they may be placed. MISCELLANEOUS TABLES. 137 TABLE V. Continued, By which may be determined the depths of Ceiling Joists, Rafters, Floor Joists, Bridging Joists, Binding Joists, &c. ; the breadth being 2 inches, and the deflection ^ of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length in fuel, clear bearing 125-0 144-7 166-3 190-1 216-0 244-1 274-6 307-5 343-0 mi-0 DEPTH IN INCHES. 1 2 3 4 5 -72 1- 43 2- 16 4'tio 3- 58 -75 1- 50 2- 25 O.A 1 O 01 3- 76 -79 1- 57 2- 36 3 15 3- 94 -82 1- 65 2- 47 4-12 •86 1- 72 2- 58 0 44 4-30 •89 1- 79 2- 68 3- 58 4- 47 -93 1- 86 2- 79 3- 72 4- 65 •97 1- 93 2- 90 3- 87 4- 83 1 00 2- 00 3- 01 4- 01 5- 01 1- 04 2- 08 3- 11 4- 15 5- 19 6 7 8 9 10 4- 30 5- 01 5- 73 6- 44 7- 16 4- 51 5- 26 6- 01 6- 76 7- 52 4- 72 5- 51 6- 30 7- 09 7-87 4- 94 5- 76 6- 59 7- 41 8- 23 5- 15 6- 01 6- 87 7- 73 8- 59 5^37 6- 26 7- 16 8- 05 8-95 5- 58 6- 51 7- 44 8- 38 9- 31 6-80 6- 76 7- 73 8- 70 9- 66 6- 01 7- 02 8- 02 9- 02 10-02 6- 23 7- 27 8- 30 9- 34 10-38 11 12 13 *14 15 7- 87 8- 59 9- 31 10-02 10-74 8- 27 9- 02 9-77 10- 52 11- 27 8- 66 9- 45 10- 24 11- 02 11-81 9-06 9-88 10- 70 11- 53 12- 35 9-45 10- 31 11- 17 12- 03 12-89 9-84 10- 74 11- 63 12- 53 13- 42 W24 11- 17 12- 10 13- 03 13-96 10- 63 11- 60 12- 56 13 53 14-50 11- 02 12- 03 1303 14- 03 15- 03 Tr42" 12- 46 13- 49 14- 53 15- 57 16 17 18 19 20 11- 45 12- 17 12- 89 13- 60 14- 32 12-03 12- 78 13- 53 14- 28 15- 03 12- 60 13- 39 14- 17 14- 96 15- 75 T347" 13- 99 14- 82 15- 64 13- 74 14- 60 15- 46 14- 32 15- 21 15-82 15-46 Multipliers to give the breaking weight of every Scantliug in each column respectively. 7-34 6-99 6-67 6-38 6-12 5-87 5-65 5-44 5-24 5-06 * Example. — The greatest weight upon a floor being 140 lbs. per superficial foot; if the joists be 14 inches apart, from middle to middle, the weight upon one foot in length of a joist is 140 X l'«2" = 163-3 fts. A joist 14 feet long 11-02 in. by 2 iu., with 166-3 Ibs^ weight to the foot, uniformly loaded, deflects in the middle ^ of an inch ; with the same weight, 11-02 in. by 2i in. deflects of an inch; 11*02 in. by 2^ in. deflects of an inch; 11-02 in. by 2| in. deflects |.4 of an inch; and 11-02 in. by 3 in. deflects |4 of an inch. The breaking weight of a Red Pine joist 14 feet long 11-02 in. by 2 in., is 6-67 times the weight upon the floor, and the depth being the same, the strength increases as the breadth. 138 MISCELLANEOUS TABLES. TABLE VI. By which may be determined the depths of Ceiling Joists, Rafters, Floor Joists, Bridging Joists, Binding Joists, &c.; the breadth being 2i inches, and the deflection ^ of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length ill feet, cleat 20-79 27-00 34-32 42-87 52-73 64-00 76-76 9M2 107^1 125-0 bearing. DEPTH IN INCHES. 1 2 3 4 5 -38 •76 1-14 1-51 1-89 •41 -83 P24 1-65 207 •45 -89 1-34 1- 79 2- 24 •48 •96 P45 1- 93 2- 41 -52 1-03 1- 55 2- 07 2-58 •55 MO 1- 65 2- 20 2-75 •59 117 r76 2-34 2 93 •62 1-24 1- 86 2- 48 3^10 •65 1-31 1- 96 2- 62 3- 27 -69 1- 38 2- 07 2- 75 3- 44 6 7 8 9 10 2-27 2- 65 3- 03 3-41 3-79 2-48 2- 89 3- 30 3- 72 4- 13 313 3- 58 4- 03 4-47 2- 89 3- 37 3- 86 4- 34 4-82 3-10 3- 61 4- 13 4- 65 5- 16 3-30 3- 86 4- 41 4- 96 5- 51 3- 51 4^10 4- 68 5- 27 5-85 3- 72 4- 34 4- 96 5- 58 6- 20 3- 92 4- 58 5- 23 5- 89 6- 54 413 4- 82 5- 51 6- 20 6-88 11 12 13 14 15 4-16 4-54 4- 92 5- 30 5-68 4-54 4- 96 5- 37 5- 78 6- 20 4- 92 5- 37 5- 82 6- 26 6-71 5-30 5- 78 6- 26 6- 75 7- 23 6-20 6- 71 7- 23 7-74 6-06 6- 61 7- 16 7- 71 8- 26 6- 44 7- 02 7- 61 8- 19 8-78 "6^ 7- 43 8- 05 8- 67 9- 29 7- 19 7^85 8- 50 9- 16 9-81 7- 57 8- 26 8- 95 9- 64 10-33 16 17 18 19 20 6-06 6-44 6- 82 7- 19 7-57 6- 61 7- 02 7-43 7- 85 8- 26 7-16 7- 61 8- 05 8-50 8-95 7- 71 8- 19 8- 67 9- 16 9-64 8-26 8- 78 9- 29 9-81 10-33 8- 81 9- 36 9-91 10- 46 11- 01 9-36 9-95 10- 53 11- 12 11-70 9-91 10- 53 11- 15 11- 77 12- 39 10- 46 11- 12 12- 43 13- 08 11-01 11- 70 12- 39 13- 08 13-77 Multipliers to give the breaking weight of every Scantling in each Column respectively. 13-89 12-73 11-75 10-91 10-19 9-55 8-99 8-49 8-04 7-64 The weight of one cubic foot of water being 62-5 flbs., the pressure upon a floor, from a cistern 4 feet deep, lined with lead, and filled with water, may be estimated, without the weight of a ceiling, at 260 lbs. per foot superficial. If the joists to carry the same be 14 inches apart from middle to middle, the weight upon one foot in length of each joist, is 260x 1'h2" = 303 fts.; and the scantlings for various deflections may be found by these tables, as in the next example. MISCELLANEOUS TABLES. 139 TABLE VI. Continued. By which may be determined the depths of Ceihng Joists, Rafters, Floor Joists, Bridging Joists, Binding Joists, &c. ; the breadth being 2i inches, and the deflection ^ of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length in feet, clear ; bearing. 144-7 166-3 190-1 216^0 244-1 274-6 307-5 3430 381-0 421-8 DEPTH IN INCHES. 1 2 3 4 5 •72 1- 45 2- 17 2- 89 3- 61 •76 1- 51 2- 27 3- 03 3-79 •79 1-58 2 37 3^17 3-96 •83 1- 65 2- 48 3- 30 4- 13 -86 1- 72 2- 58 3^44 4-30 •89 1-79 2^68 3^58 4-47 •93 1- 86 2- 79 3- 72 4- 65 •96 1- 93 2- 89 3- 86 4- 82 1-00 2^00 2^99 3- 99 4- 99 1-03 2^07 3- 10 4- 13 5- 1& *6 7 8 9 10 4- 34 5- 06 5- 78 6- 51 7- 23 4- 54 5- 30 6- 06 6- 82 7- 57 4- 75 5- 54 6- 33 7^13 7- 92 4-96 5^78 6- 61 7- 43 8- 26 5^16 6-02 6- 88 7- 74 8- 61 5^37 6^26 7^16 8^05 8^95 5- 58 6- 51 7- 43 8- 36 9- 29 5- 78 6- 75 7- 71 8- 67 9- 64 5- 99 6- 99 7- 99 8- 98 9- 98 6^20 723 8-26 9^29 10-33 11 12 13 14 15 7- 95 8- 67 9- 40 10-12 10-84 8- 33 9- 09 9-84 10- 60 11- 36 8- 71 9- 50 10- 29 11- 08 11-88 9-09 9-91 10- 74 11- 57 12- 39 9-47 10^33 1M9 12^05 12-91 9-84 10^74 lb63 1253 13^42 10- 22 11- 15 12- 08 13- 01 13-94 10- 60 11- 57 12- 53 13- 49 14- 46 10- 98 11- 98 12- 98 13- 97 14- 97 11- 36 12- 39 13- 42 14- 46 15- 49 16 17 18 19 20 11- 57 12- 29 1301 13- 73 14- 46 12-12 12- 87 13- 63 14- 39 15- 14 12- 67 13- 46 14- 25 15- 04 15-83 13- 22 14- 04 14- 87 15- 70 13- 77 14- 63 15- 49 14^32 15-21 14- 87 15- 80 15-42 15-97 Multipliers to give the breaking weight of every Scantling in each column respectively. 7-27 6-94 6^64 6^36 6-11 5-87 5-66 5-45 527 5-09 * Example. — A joist 6 feet long 5'58 in by 2i in., with 307'5 fbs. weight to the foot, uniformly loaded, deflects in the middle of an inch ; with the same weight, 5-58 in. by 2|. in., deflects _6_ of an inch; 5'58 in. by 2| in., deflects -^^ of an inch; and 5-58 in. by 3 in. deflects -^-^ of an inch. If the joists to carry the cistern (p. 138) be 16 inches apart from middle to middle, the weight upon one foot in length of each joist is 260 x l'/;4" = 346-6 lbs. The scantlings are found by the next column, viz. 5-78 in. by 2i in. ; 5-78 in. by 2i in. ; &c, &c. 140 MISCELLANEOUS TABLES. TABLE VII. By which may be determmed the depths of Rafters, Floor Joists, Bridging Joists, Binding Joists, &c. ; the breadth being 2^ inches, and the deflection ^ of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length in feet, clear 27-00 34-32 42-87 52-73 64-00 76-76 91-12 107-1 125-0 144^7 bearing. DEPTH IN INCHES. nr 2 3 4 5 •40 •80 1-20 \-59 1-99 •43 •86 1-30 1-73 2^16 •47 •93 1-40 1- 86 2- 33 •50 1-00 1-50 1- 99 2- 49 •53 1-06 1- 59 2- 13 2^66 •56 1-13 1- 69 2- 26 2-82 •60 1-20 1- 79 2- 39 2-99 •63 1-26 1- 89 2- 53 3^16 •66 1-33 1- 99 2- 66 3- 32 •70 1^40 2^09 2^79 3-49 6 7 8 9 10 2-39 2- 79 3- 19 3^59 3-99 2- 59 3- 02 3-46 3- 89 4- 32 2- 79 3- 26 3- 72 4- 19 4-65 2- 99 3- 49 3- 99 4- 49 4-98 ~3^ 3- 72 4^25 4- 78 5- 32 3^39 3-95 4^52 5-08 5-65 3- 59 4- 19 4- 78 5- 38 5-98 "3^9 4- 42 5- 05 5- 69 6- 32 3^99 4^65 5^32 5- 98 6- 65 4- 88 5- 58 6- 28 6-98 11 12 13 14 15 4- 39 4^78 6-18 5- 58 5-98 4- 75 5- 18 5- 62 6- 05 6-48 5-12 5- 58 6- 05 6-51 6-98 5-48 5- 98 6^48 6- 98 7- 48 5- 85 6- 38 6- 91 7- 44 7-97 6-21 6- 78 7- 34 7- 91 8- 47 6- 58 7- 18 7^77 8- 37 8-97 6-95 ,7-58 8-21 8- 84 9- 48 7-31 7- 97 8- 64 9- 30 9-97 TeT 8- 37 9- 07 9-77 10-47 16 17 18 19 20 6- 38 6^78 7- 18 7^58 7-97 6- 91 7- 34 7- 77 8- 21 8-64 7-44 7- 91 8- 37 8- 84 9- 30 7- 97 8- 47 8- 97 9- 47 9-97 8- 51 9- 04 9-57 10-10 10-63 9-04 9-60 10-17 10- 73 11- 30 9-57 10-17 10- 76 [1-S6 11- 96 10-11 10- 74 11- 37 12- 00 12-63 10- 63 11- 30 11- 96 12- 63 13- 29 TT-Te" 11 ^86 12^56 13-26 13-95 Multipliers to give the breaking weight of every Scantling in each column respectively. 13-18 12-17 11-30 10-55 9-89 9-30 8-79 8-32 7-91 7-53 *t* If an imperial bushel of grain weigh 60 ibs., then one cubic toot of the same grain weighs 46-74 ibs., or -4173 cwts. If the grain upon a warehouse floor be 5 feet in depth, the weight upon the floor, allowing 10 3 ibs. to the foot for the weight of the boards and joists, is 244 ibs., or 218 cwts. per superficial foot. If the joists be 13^ inches, and the beams 9 feet apart, from middle to mid- dle, the weight upon one foot in length of each joist is 244 x I'hI^" =274-5 ibs., and of each beam 9 x 2-18 = 19-62 cwts., or say, including the weight of the beam, 20 cwts. The scantlings to carry those weights may be found by the Miscellaneous Tables, as in the annexed Example. MISCELLANEOUS TABLES. 141 TABLE VII. Continued. By which may be determined the depths of Rafters, Floor Joists, Bridging Joists, Binding Joists, &c.; the breadth being 2i inches, and the deflection of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. Length clear bearing. 166-3 1901 216-0 244-1 274-6 307-5 343-0 381-0 421-8 465-4 DEPTH IN INCHES. 1 2 3 4 5 •73 1- 46 2- 19 2- 92 3- 65 •76 1- 53 2- 29 3- 06 3-82 -80 1- 59 2- 39 3- 19 3-99 -83 1- 66 2- 49 3- 32 4- 15 -86 1- 73 2- 59 3- 46 4- 32 •90 1^79 2- 69 3- 59 4- 49 -93 1- 86 2- 79 3- 72 4- 65 -96 1- 93 2- 89 3- 85 4- 82 1-00 1- 99 2- 99 3- 99 4- 98 1- 03 2- 06 3- 09 4- 12 5*15 6 7 *8 9 10 4- 39 5- 12 5- 85 6- 58 7- 31 4- 59 5- 35 6- 11 6- 88 7- 64 4- 78 5- 58 6- 38 7- 18 7-97 ~4^ 5- 81 6- 65 7- 48 8- 31 5- 18 6- 05 6- 91 7- 77 8- 64 5- 38 6- 28 7- 18 8- 07 8-97 5- 58 6- 51 7- 44 8- 37 9- 30 6-78 6- 74 7- 71 8- 67 9- 64 5- 98 6- 98 7- 97 8- 97 9- 97 6-18 721 8- 24 9- 27 10-30 11 12 13 14 15 8-04 8- 77 9- 50 10-23 10-96 "s-ir 9-17 9-93 10- 70 11- 46 8- 77 9- 57 10- 37 11- 16 11-96 9-14 9-97 10- 80 11- 63 12- 46 9-50 10- 37 11- 23 12- 09 12-96 9-87 10- 76 11- 66 12- 56 13- 46 10- 23 11- 16 12- 09 13- 02 13-95 10- 60 11- 56 12- 53 13- 49 14- 45 10- 96 11- 96 12- 96 13- 95 14- 95 11- 33 12- 36 13- 39 14- 42 15- 45 16 17 18 19 20 11- 70 12- 43 13- 16 13- 89 14- 62 12-23 12- 99 13- 76 14- 52 15- 28 12- 76 13- 56 14- 35 15- 15 15-95 13- 29 14- 12 14- 95 15- 78 13- 82 14- 69 15^55 14- 35 15- 25 14- 88 15- 82 15-95 Multipliers i 0 give the breaking weight of every Scautliug ia each column respectively. 7-19 6-88 6-59 6-33 6-08 5-86 5-65 5-45 5-27 5-10 * Example. — A joist 8 feet long, 6'91 in. by 2^ in., with 274'6 lbs. weight to the foot, uniformly loaded, deflects in the middle Jt^ of an inch ; with the same weight, 6'91 in. by 2| in. deflects -^^ of an inch; 6'91 in. by 3 in. deflects of an inch ; and the breaking weight of Red Pine 8 feet long, 6"91 in. by 2^ iu., is 6-08 times the tabular weight. By Table I., page 125, the breadth of a Red Pine beam, 14 inches deep and 16 feet long in the clear, which \r{[\just break with 20 cwts. to the foot, is 20 x -1633 = 3-266 inches ; and if one-fourth of the breaking weight be the greatest weight' with which a beam ought to be loaded, the breadth of the beam should be 4 x 3'266 = 13"064 inches. Therefore, upon the data in this and the preceding page, the scantlings are, — joists 7 x 2J; beams 14 x 13, or if mortised for the joisis, say 14 x 14. By Table II., page 129, the de- flection of each beam is -GOl, or 3. of an inch. T 142 MISCELLANEOUS TABLES. TABLE VIII. By which may be determined the depths of Rafters, Floor Joists, Bridging Joists, Binding Joists, &c.; the breadth being 21 inches, and the deflection of an inch to the foot, when uniformly loaded with the weights in this table. WEIGHT IN POUNDS UPON EACH FOOT IN LENGTH. LeDgth iu feet, clear 34-32 42-87 52-73 64-00 76-76 91-12 1071 1250 144-7 166-3 bearing. DEPTH IN INCHES. ~r 2 3 4 5 •42 •84 1-26 1- 67 2- 09 •45 •90 1-35 1-80 2^25 •48 ■97 1-45 1-93 2^41 •52 1-03 1- 55 2- 06 2-58 •55 1-09 1- 64: 2- \9 2-74 •58 M6 174 2^32 2^90 •61 r-22 1- 83 2- 45 3- 06 -64 1-29 1- 93 2- 58 3- 22 •68 1- 35 2- 03 2- 70 3- 38 •71 1-42 212 2^83 3-54 6 *7 8 9 10 2-51 2- 93 3- 35 3- 77 4- 18 2- 70 3- 15 3- 61 4- 06 4^51 2-90 3^38 3^86 4-35 4-83 '¥69 3- 61 4- 12 4^64 5- 15 3-28 3- 83 4- 38 4- 92 5- 47 3^48 4^06 4^64 5^21 5^79 3^67 4-28 4- 89 5- 50 6- 12 3- 86 4- 51 5- 15 5- 79 6- 44 4-06 4- 73 5- 41 6- 08 6^76 4-25 4-96 5^67 6^37 7^08 11 12 13 14 15 4^60 5-02 5-44 5- 86 6- 28 4^96 5-41 5- 86 6- 31 6-76 5- 31 5^79 6^28 6- 76 7- 24 5- 67 6- 18 6- 70 7- 21 7-73 6-02 6- 57 7- 11 7^66 8- 21 6^37 6-95 753 8^11 8^69 6- 73 7- 34 7^95 8^56 9^17 7-08 7- 73 8- 37 9- 01 9-66 7- 44 8- 11 8^79 9- 46 10-14 7- 79 8- 50 9- 21 9-91 10-62 16 17 18 19 20 6- 70 7- 11 7-53 7- 95 8- 37 ~T2\ 7- 66 8- U 8- 56 9- 01 7- 73 8- 21 8- 69 9- 17 9-66 8- 24 8^76 9- 27 9^79 10-30 8- 76 9- 30 9-85 10-40 10-94 9-27 9-85 10- 43 11- 01 11-59 9-79 10- 40 11- 01 11^62 12- 23 10-30 10- 94 11- 59 12- 23 12-88 10^2' 11-49 12^17 12^84 13-52 11- 33 1204 12- 75 13- 45 14- 16 Multipliers to give the breaking weight of every Scantling in each column respectively. 12-56 11-67 10-89 10-21 9-61 9-07 8-59 8-16 7-92 7-42 * Example. — If the weight upon each foot in length of a floor joist 7 feet long, 4-06 in by 2| in., be 91'12 ibs. to the foot, the deflection is of an inch, and the brealcin weight of the same is 9 07 times the tabular weight ; if the weight upon each foot in length b 91-12 X 2 = 182-24 lbs. to the foot, the deflection is £^ x 2 = ^^ of an inch, and the multi plier to give the breaking weight is =4-53. MISCELLANEOUS TABLES. 143 TABLE VIII. Continued. By which may be determined the depths of Rafters, Floor Joists, Bridging Joists, Binding Joists, &c.; the breadth being 2f inches, and the deflection of an inch to the foot, when uniformly loaded with the weights in this table. weight in pounds upon each foot in length. Length in feet, clear beariug 190-1 216-0 244-1 274-6 307-5 343-0 381-0 421-8 465-4 512-0 depth in inches. J 2 3 4 5 •74 1- 48 2- 22 2- 96 3- 70 •77 1- 55 2- 32 309 386 •80 1- 61 2- 41 3- 22 4- 02 •84 1- 67 2- 51 3- 35 4- 18 -87 1- 74 2- 61 3- 48 4- 35 -90 1- 80 2- 70 3- 61 4- 51 •93 1- 87 2- 80 3- 73 4- 67 •97 \'9Z 2- 90 3- 86 4- 83 1-00 9-00 3^99 4-99 1-03 3- 09 4- 12 5- 15 6 7 8 9 *10 4- 44 5- 18 5- 92 6- 66 7- 40 4- 64 5- 41 6- 18 6- 95 7- 73 5- 63 6- 44 7- 24 8- 05 8- 85 9- 66 10- 46 11- 27 12- 07 5^02 5- 86 6- 70 7- 53 8- 37 9- 21 10-04 10- 88 11- 72 12- 55 ~5^ 6-08 6- 95 7- 82 8- 69 9- 56 10- 43 11- 30 12- 17 13- 04 5- 41 6- 31 7- 21 8- 11 9- 01 5- 60 6- 53 7- 47 8- 40 9- 33 5- 79 6- 76 7- 73 8- 69 9- 66 5^99 6-98 7^98 8-98 9^98 6- 18 7- 21 8^24 9-27 10-30 11 12 13 14 15 8-14 8- 88 9- 62 10- 36 11- 11 8- 50 9- 27 10-04 10- 82 11- 59 9-91 10- 82 11- 72 12- 62 13- 52 10- 27 11- 20 12- 14 13- 07 14- 00 10- 62 11- 59 12- 55 13- 52 14- 48 10- 98 11- 97 12- 97 13- 97 14- 97 11- 33 12- 36 13- 39 14- 42 15- 45 16 17 18 19 20 11- 85 12- 59 13- 33 14- 07 14-81 12- 36 13- 13 13- 91 14- 68 15- 45 12- 88 13- 68 14- 48 15- 29 16- 09 13- 39 14- 23 15- 06 15- 90 16- 74 13-91 14.77 15- 64 16- 51 14- 42 15- 32 16- 22 14- 94 15- 87 16- 80 15- 45 16- 42 15- 97 16- 97 16-48 Multipliers to give the breaking weight of every Scantling in each column respectively. 7-10 6-80 6-53 6-28 6-05 5-83 5-63 5-44 5-27 5-10 * Example.— The greatest weight upon a joist for a warehouse floor being 465-4 lbs to .the foot, a Red Pine joist 10 feet long, 9-98 in. by 2| in., uniformly loaded with that weight deflects m the middle ^ or i of an inch; with the same weight, 9 98 in. by 3 in. deflects ^ of an inch. The breaking weight of a Red Pine joist 10 feet long 9-98 in. by 2f in., is 5-27 times the tabular w-eis;ht. 144 MISCKLLANEOUS TA1$LKS. TABLE IX. By wWch may be deteraiined the depths of Rafters, Floor Joists, Bridging Joists, Binding Joists, &c.; the breadth being 3 inches, and the deflection of an inch to the foot, when uniformly loaded with the weights in this table. weight in pounds upon each foot in length. Length in feet, cleai' 42-87 52-73 64-00 76-76 91-12 107-1 125-0 144-7 166-3 190-1 bearing. DEPTH IN INCHES. 1 •47 -53 •56 -59 •63 •66 •69 -72 2 -88 •94 1-00 1-06 1-13 1-19 1-25 1-31 1-38 1-44 3 1-31 1 -41 1-50 1-59 1^69 1-78 1-88 1-97 2-06 2-16 4 1-75 ] •88 2-00 2-13 2-25 2-38 2-50 2-63 2-75 2-88 6 2-19 >-35 2-50 2-66 2-81 2-97 313 3-28 3-44 3-60 6 2-63 2-81 3-00 3-19 3-38 3-56 3-75 3-94 4-13 4-31 7 3-06 3-28 3-50 3-72 394 4-16 4-38 4-60 4-82 5-03 8 3-50 3-75 4-00 4-25 4-50 4-75 5-00 5-25 5-50 5-75 9 3-94 4-22 4-50 4-78 5-07 5-35 5-63 5-91 6-19 6-47 10 4-38 4-69 5-00 5-32 5-63 5-94 6-25 6-57 6-88 7-19 11 4-82 5-16 5-50 5-85 6-19 6-53 6-88 7-22 7-57 7-91 12 5-25 5-63 6-00 6-38 6-75 7-13 7-50 7-88 8-25 8-63 13 5-69 6-10 6-50 6-91 7-32 7-72 813 8-54 8-94 9-35 14 6-13 6-57 7-00 7-44 7-88 8-32 8-75 9-19 9-63 10-07 15 6-57 7-04 7-50 7-97 8-44 8-91 9-38 9-85 10-32 10-79 *16 7-00 7-50 8-00 8-50 9-00 9-51 1001 10-51 11-01 11-51 17 7-44 7-97 8-50 9-04 9-57 10-10 10-63 11-16 11-69 12-23 18 7-88 8-44 9-01 9-57 10-13 10-69 11-26 11-82 12-38 12-94 19 8-32 8-91 9-51 10-10 10-69 11-29 11-88 12-48 13-07 13-66 20 8-75 9-38 10-01 10-63 11-26 11-88 12-51 13-13 13-76 14-38 Multipliers to give the breaking weight of every Scantling in each colnmn respectively. 12-01 11-21 1 10-51 9-89 9-34 8-85 8-40 8-00 7-64 .7-31 * Example.— A joist 16 feet long, ll'Ol in. by 3 in., with 166-3 ibs. weight to the foot, imiformly loaded, deflects in the middle ^ or |. of an inch. The breaking weight of a Red Pine joist 16 feet long, H'Ol in. by 3 in., is 16 x 166-3 x 7-01 = 20328 ibs. = 181-5 cwts. uniformly loaded, or SO'? cwts. suspended from the middle. MISCELLANEOUS TABLES. 145 TABLE IX. Continued. By which may be determined the depths of Rafters, Floor Joists, Bridging Joists, Binding Joists, &c.; the breadth being 3 inches, and the deflection of an inch to the foot, when uniformly loaded with the weights in this table. weight in pounds upon each eoot in length. Length in feet, clear bearing. 216-0 244-1 274-6 307-5 343-0 381-0 421-8 465-4 512-0 561-5 depth i> r INCHES. 1 2 3 4 5 -75 1- 50 2- 25 3- 00 3-75 •78 1- 56 2- 35 3- 13 3-91 •81 1- 63 2- 44 3- 25 4- 06 -84 1- 69 2- 53 3- 38 4- 22 •88 1- 75 2- 63 3- 50 4- 38 -91 1- 81 2- 72 3- 63 4- 53 •94 1- 88 2- 81 3- 75 4- 69 •97 1- 94 2- 91 3- 88 4^85 1- 00 2- 00 3^00 4- 00 5- 00 1- 03 2- 06 3- 10 4- 13 5- 16 6 7 8 9 10 4- 50 5- 25 6- 00 6- 75 7- 50 4- 69 5- 47 6- 25 7- 04 7-82 4- 88 5- 69 6- 50 7- 32 8- 13 5- 07 591 6- 75 7- 60 8- 44 5- 25 6- 13 7- 00 7- 88 8- 75 5- 44 6- 35 7- 25 8- 16 9- 07 5-63 6^57 7-50 8^44 9-38 6- 82 6^79 7- 75 8- 72 9- 69 7- 00 8- 00 9- 00 10-01 6- 19 7- 22 8- 25 9- 29 10-32 *11 12 13 14 15 8- 25 9- 01 9-76 10- 51 11- 26 8- 60 9- 38 10-16 10- 94 11- 73 8- 94' 9- 76* 10- 57 11- 38 12- 19 9-29 10-13 10- 97 11- 82 12- 66 9-63 10- 51 11- 38 12- 26 13- 13 9-97 10- 88 11- 79 12- 69 13- 60 10-32 11^26 12^19 13^13 14-07 10- 66 11- 63 12- 60 13- 57 14- 54 11- 01 12- 01 13- 01 14- 01 1501 11- 35 12- 38 13- 41 14- 45 15- 48 16 17 18 19 20 12-01 12- 76 13- 51 14- 26 15- 01 12- 51 13- 29 14- 07 14- 85 15- 63 13-01 13- 82 14- 63 15- 45 16- 26 13- 51 14- 35 15- 20 16- 04 16-88 1401 14- 88 15- 76 16- 63 14^51 15- 41 16- 32 15^01 15- 95 16- 88 15- 51 16- 48 16-01 16-51 Multipliers to give the breaking weight of every Scantling in each column respectively. 7-00 6-72 6-46 6-22 6-00 5-79 5-60 5-42 5-25 5-09 * Example. — A Red Pine joist 11 feet long, H'Ol in. by 3 in., with 512 lbs. weight to the foot, uniformly loaded, deflects in the middle of an inch ; and 5-25 times that weight is the breaking weight of the same. *** When the breadth exceeds 3 inches, or the weight exceeds 561-5 its. to the foot, the Scantlings may he found by the First Series op Tables, of which this and the six preceding tables form, by interpolation, a part. 146 MISCELLANEOUS TABLES. TABLE X. Shewing the Strength and Elasticity of various species of Timber, according to the Experiments made at Woolwich Dock Yard, by Peter Barlow, Esq., F.R.S., &c. Values of S from the formula Relative Values of S, the mean ° a / w S=— value of S for each species of No. peri JName or the Wood. timher being I'OOO. H Minimiini Mean Maximum Minimum Mean Maximum Value ofS. Value of S. Value ofS. Value of S. Value of S. Value of S. Q O Teak 2152-5 2463-1 2677-5 •873 1^000 1-087 o 2178-7 2220-7 2257-5 .no 1 yol bOOO 1-016 6 1105-1 1427-5 1703-6 •774 rooo 1-193 3 „ Canadian ... 1708-8 1766-6 1858-5 •967 bOOO 1-052 3 loOO V •928 rooo 1-035 3 1312-5 1382-5 1470-0 •949 POOO 1-063 3 Ash 1995-0 2027-3 2047-5 •984 1-000 1-010 3 1483-1 1557-5 1614-3 •952 1-000 1-036 3 Elm 966-0 1015-0 1044-7 •951 1-000 1-029 3 1561-8 1631-8 1706-2 •957 1-000 1-045 3 1241-6 1341-3 1391-2 •925 1-000 1.037 3 Fir, New England 1057-8 1102-5 1170-7 •959 1-000 1-061 6 825-7 1079-2 1275-7 •765 1-000 1-182 10 „ Mar Forest... 945-0 1215-6 1350-0 •777 1-000 MIO 13 675-0 1000-6 1242-0 •674 1-000 1-241 3 1388-2 1473-0 1530-0 •942 1-000 r038 71 Mean results ■897 1-000 r077 *** By this table may be compared the least, mean, and greatest strength of the several spe- cies of timber, thus : — weakest English Oak : strongest Elm : : 1105-1 : 1044-? The mean strength of Dantzic Oak is the same as the greatest strength of Adriatic Oak, s. that the scantlings of the former are those of the latter. By means of the relative values of S may be found, if requisite, the scantlings for the weakest or strongest of the various species of timber. MISCELLANEOUS TABLES. 147 TABLE X. Continued. shewing the Strength and Elasticity of various species of Timber, according to the Experiments made at Woolwich Dock Yard, by Peter Barlow, Esq., F.R.S., &c. .2 a Xl,, Name of the Wood. w 3 Teak ^ 3 \ ^ o „ Canadian ... 3 3 3 A ell 3 3 Elm 3 3 3 Fir, New England 6 „ Riga 10 „ Mar Forest ... 13 3 71 Value of E from the formula 301730 211160 145040 241920 145770 121430 205630 169190 85880 153080 230000 186580 143450 105190 114450 182250 Greatest weight while the Elasticity remains per- fect, the breaking weight being 1-0000* •3197 •1773 •3231 •3343 •3571 •2848 •2913 •2528 •3232 •2412 •2935 •3571 •3082 •2746 •3230 •3055 Reci- procal of the same. 3-127 5-640 3-094 2^991 2- 800 3- 511 3^432 3-955 3- 093 4- 144 3-406 2- 800 3^244 3- 640 3^095 3-273 Specific gravity. 745 579 952 872 756 993 760 676 553 660 657 553 745 697 544 593 Weight of one Cubic Foot. InKs. Incwts. 46^56 36- 18 59-50 54-50 47-25 62-06 47-50 42- 25 34-56 41-25 41-06 34-56 46-56 43- 56 34-00 37- 06 ■4157 3231 5312 •4866 4218 5541 ■4241 3772 ■3086 •3683 ■3666 ■3086 -4157 •3889 •3035 -3309 ' When the weight is uniformly loaded, multiply the greatest weights &c. in col. 4 by -8; and the reciprocals of the same in col. 5 by 1'25. * * 28 of the above experiments were made upon scantlings 2 inches square and 6 feet long, and 43 upon scantlings 2 inches square and 7 feet long, clear of the supports ; the weig;hts in each experiment being suspended from the middle. This Table is constructed from the Experiments, in the Table of Data, published in Bar- low's Treatise on the Strength of Materials, 1845 edition, page 148. 148 MISCELLANEOUS TABLES. TABLE XT. Shewing the mean Strength and Elasticity of various species of Timbe according to the additional Experiments made by P. W. Barlcv Esq., C.E. 4 2 2 2 2 2 35 Name of the Wood. Acacia Oak „ superior quality... Tonquin Bean Locust Bullet Tree Greenheart Cabacally African Oak, superior] quality | American Black Birch Common Birch Ash Elm Christiana Deal Memel Deal Value of S from the formula S = — • 1867 1413 2149 3626 3437 2650 2737 2518 2496 1818 1928 2037 1118 1556 1731 Value of E from the formula ^ m' E = 144000 125900 192300 332000 243200 328600 332000 230900 288100 184600 205600 161100 92750 198700 205400 Specific gravity. 710 891 752 1058 954 1029 1000 900 983 649 711 714 543 689 590 Weight of One Cubic Foot In lbs. 44-37 55- 68 47-00 66-12 59-62 64-31 62-50 56- 25 61-43 40-56 44-43 44-62 33-93 43-06 36-87 In cwti 3965 497!l 419( 5904 5323 5742 558G 5022 548-3 3621 3967 3984 3030 3844 3292 The ahove experiments were made upon scantlings 2 inches square and 50 inches length, clear of the supports. — For the original table and experiments, see Barlow Treatise on the Strength of Materials, page 153. The Tables of Constants, in the former part of this work, are founded upon the mi values of S and E, for the various woods specified in this and the preceding table ; the val of S and E, for Oak, Ash, and Elm, being those given in Table X. ON THE ADMEASUREMENT OF EARTHWORK IN RAILWAY CUTTINGS AND EMBANKMENTS. 150 MISCELLANEOUS TABLES, ETC. ON THE ADMEASUREMENT OF EARTHWORK IN RAILWAY CUTTINGS AND EMBANKMENTS. Let Fig. 1 represent the plan of a railroad and cuttings ; Fig. 2, the cross section through EH ; and Fig 3, the longitudinal section through the middle of the roadway, parallel to BK or CL. Fl C I •i— — — 1 e F E J FIG 3 In Fig. 1, let BK be parallel to CL and at right angles to AD and IM ; let AB = CD ; and IK = LM ; bisect CL in F, through F draw EFGH intersecting DM, BK, AT, m !>, ^, In Fig. 2, let cd be parallel to ab ; and ae, i/ perpendicular to ah, cd; ce=fd. In ^ig 6, let ST, NP, be vertical to SN ; from T draw TO parallel to SN ; bisect SN iu R; and trom K draw EZQ paraUel to ST, NP ; intersecting TO, TP in Z, Q. Let SN = L; n. RQ,= GH = FE ; then the true content of the whole solid ABCDMLKIA = V, may be found by any of the following equations,* viz. :— EH2 — FG2 EGxGH 3 w.ZQ,^ 3 n.za2 xL. } I xL... I xL... Example to the first equation. .(1) .(2) .(3) Let the vertical ordinates in feet, be as in Fig. 4 and 1 chain apart; jj = 1-5; width of Roadway FG = 40 feet, then the true content of the whole figure by equation (1), is as follows: — Middle ordinate. Ordinate Difference RG2 RG. ST or NP. ZQ. za2. 25-00 5-0 000 5-0 25-00 198-81 141 10-0 4-1 16-81 453-69 21-3 18-2 31 9-61 707-56 26-6 28-8 2-2 4-84 1385-06 67-0 1385-06 X 1-5 = 2077-59 = RG^ x n 67-00 x 40 0 = 2680-00 = RGxFG 56-26 x -5 = 28-13 = ZG^x^ 4785-72 X 66 = 315857-520 ubio feet the true content. In the same Example if n = 2, i 5487-62 x 66 = 362182 92 Cubic feet, tnen the true jcontent is ) * See Note, page 152. MISCELLANEOUS TABLES, ETC. 151 Fig. 5, let DABC reprc- From the values of the middle ordinate RQ, in col. 2, n = i-5, and rG=40; the middle widths EH in Fi^. 1 are, 55-0; 82-3; 103-9; 119-8 ; respectively ; vyhich being substituted in (2) and (3), the same result is obtained as by equation (1.) If the values of ZQ, be small or nearly equal, so that by a few trials a mean value of ZQ? may be found sufficiently near the true average value, then, the slope n to 1, the width of the road PG and the length L being measured off or given, the only dimension requi- site to be taken, in equation (1), is the middle ordinate RQ,, and in (2) and (3), the middle width EH ; the squares of which in (1) and (2), may be written down from a table of squares, as in the preceding example. If the railway pass through the side of a hill, then sent a vertical middle section through EH in Fig. 1. Let the angle DAB = angle CBA, and let DA and CB produced, meet in S ; draw DL parallel to AB, cutting BC in E ; also draw SH perpendicular to AB, DE, bisecting the same in Oand N; let ra.SN=ND=NE; demit CF per- pendicular to DL, intersecting DL in F ; upon DF as a diameter describe the semicircle DMF, cutting SH in M; make N6=NM; from G draw GI at right angles to DL, intersecting BC in I ; from I draw IK parallel to LD, intersecting SD produced in K, and cutting SH in P; then the area of the quadrilateral KDEIK = area of the triangle DEC. From C, draw CR parallel to LD, intersecting SH in R, then a/RCI^NB— OB NM— AO 0P= = n n and the true content = V', of the solid, of which the middle section is DABC and the length L, may be found by either of the following equations, viz. : — , f RCxNB— 0B2 n.ZQ? ) 1 — + — pi- W v = |«.0Nx0R + (0N + 0R) 0B + — xL .(5) in which ZQ,, as before, is one-half the difference of the two end ordinates NP, ST in Fig. 3 ; ON, OR, in (5) and Fig. 5, being perpendiculars let fall from the points D and C, upon AB produced both ways. Moreover, RQ in Fig. 3, = OP in Fig 5, is the common intersec- tion of the two planes SNPT, KABI, Figs. 3 and 5 : also the end sections of the solid are each parallel to the plane DABC ; and the length L is limited by the distauce between the points in which D coincides with the extreme width of the road as at A, near each end of the cutting. £xaOT;>/e.— Let RC = 74; NE = 56; OB = 20; ZQ (Fi^-. 3) =6 ; w = r5 : then ON = NE— OB 56—20 RC— OB 74—20 ■=24; 0R= =— TT— = 36; and we have 1-5 From (4) V 1-5 74 X 56— 20 X 20 1-5 x 36 1-5 From(5) V'= |l-5 x 24 x 36 + 60 x 20 + the true content of the whole solid in either case. 3 1-5 X 2514 X L. X L = 2514 X L. 152 MISCELLANEOUS TABLES, ETC. The true content of the frustrum of the pyramid, and that of the ungula, may be found otherwise, thus : — Let ABCD and ABHI represent tlie end cross sections through the cutting. Let the angle DAB = angle CBA. Demit DG, IK, per- pendiculars upon EC, EH, respectively ; produce CB, DA, to intersect in E ; and draw EF perpen- dicular to AB, bisecting AB in F. Let the per- pendicular distance between the parallel planes DABC, IABH=L; and V" = volume of the whole frustrum of the pyramid limited by the same planes, viz. DEC, lEH ; then DG 6 \ IK EHrT^^ (7) The angle DAB = angle CBA being the same, as also the width of the road AB, the area of the triangular prism ABE is the same throughout the whole length of the cutting, and may therefore be deducted at one dimension ; namely, for the distance between the points in which D and I coincide with the eitremity of the road, as at A : moreover BE is constant, therefore by setting oif BE from zero on the scale, or by adding the same, the dimensions may be taken without intersecting CB, DA, in E. W W I ' If AB=W; then FE = --; BE =— n^ + l 2n 2« ^^ Example. — Let the dimensions in feet be as follow, viz. : EH2 80x 80 'eC2 100x100 64; DG = 60; — = — = 125; IK = 48; / EH2 \ V" = (EC-fEH + — ) EC2 ^ X L. .(6) EC +EH + - EC = 100; EH = then we have EC From (6) 100 EH 80 60 V"=(100 + 80+ 64)x — xL=2440xL. 6 48 From (7) V" =(100 + 80 + 125) x — x L=2440 x L. the same in both cases, as it ought to be. If AB = 33 and n = l-5; then FE = = 11 ; and the area of the prism ABE 2x1-5 = 16-5 X 11 = 181-5. Therefore the true content of the solid, limited by the parallel planes DABC, lABH, is (2440 — 181-5) X L = 2258-5 x L. iVoie.— Equations 1, 2, 3, 4, 5 (p. 150 and 151) evideuily give the same result as tl> following more general equation : viz. — Let the middle area represented by cabd in Fig. 2 or DABC in Fig. 5=M; and Ir V = volume, as before described ; then n.zm ^ (8) V= M + - Printed by E. C. Osborne, 29, Bennett's Hill, Birmingham. 3 3 / SV^fe 90- S^070 i - irinnnrLil tteiiiattflaflfia^