WEB STRESSES IN REINFORCED CONCRETE BEAMS BY SABRO UCHIMURA Ko-Gaku-Shi Imperial University, Japan, 1920 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN THEORETICAL AND APPLIED MECHANICS IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS, 1922 URBANA, ILLINOIS Digitized by the Internet Archive in 2015 https://archive.org/details/webstressesinreiOOuchi I > o this purpose. However, on the other side, if the„ cracks do not open, and there is no relieving action, many cracks may be observed. (2) To transfer the shearing stress across the crack from the middle portion of the beam to the end portion, the part of the shearing stresses transferred by the horizontal reinforce- ment is carried by the action of stirrups to the end portion beyond the crack. r - . ( ► ' . t . 9 For this purpose, strength of vertical steel or stirrups control the resisting strength of the beam. The shearing stress distribution in a beam with stirrups may be shown in Fig. 3. Fig. 3. C. Beams with bars bent up.- Generally speaking, the distribution of web stresses in beams with bars bent up is very complicated and indeterminate. Due to distortion which takes place in the concrete the assumption that a plane section remain a plane section after bending may not be exactly true, but it is used in the following* analysis. Fig. 4 * In Pig* 4 consider that part of the bars are hent up along CD and that the remainder run straight toward the end B* At A these bars have same amount of tensile stress* However, at the point E the bent up bar carries lower stress than the straight bar carries at P, and the tensile stress caused by bending moment is zero at the point G* The bent-up bar carries some amount of shearing stress, is especially after the crack^developed* However, the bond stress from C to G may be very large, and also the stretching action at C; the bond stresses in this part may be one of the weak points of the beam* In the straight bars at the bottom, the stress at P some times may not be much less than at C, since at B it is taking the larger part of the bending moment, and hence the bond stress developed in the portion CG will be less than that found in the case where all bars are straight, while beyond H and toward B the .decrease in stress will be rapid and the bond stress developed will be correspondingly greater. ' * . ] 1 Fig. 5 shows the stress diagram in the straight bars and bent up bars. It would seem, then, that the bending up of the bars tesults in greater vertical shearing stresses between C and G, and that a large part of the diagonal tension developed here will be caused by the bent reinforcement: and also that in the lower set there is less bond developed between C and H and hence the diagonal tension throughout this portion is less than might other- wise be expected. If, how, another bar be bent up, the stress diagram is shown in Pig. 6. Pig. 6. D. Action of Bent-up Bar.- The action of a bent-up bar may also be divided in two parts as that of the vertical stirrups. (1) To prevent crack openings which cross the bent-up bars. For this purpose, if the angle of bend is proper, the bent up bar may act better than the vertical stirrups. (2) However, for transferring the shearing stresses to the end portion from the other, stirrups have more advantages « f 13 As the shearing stress is very small in the flange shearing failure at the flange may he very rare, and in the deep beaip with short span, shearing resistance in concrete is very high. The T -shaped beam may oarry a very high load if the web reinforcement used is placed in the proper position. c r ' ;l ■ - II. MATERIALS, TEST PIECES, APPARATUS, AND METHODS OF TESTING. 15 LI. MATERIALS, TEST PIECES, APPARATUS , AND METHODS OP TESTI1TG 5. Materiel s . - The materials used in making the test beams were similar in character to those used for several years past at the Uniy ersity of Illinois in making reinforced concrete test specimens, and they may be considered to be represents ive of the best 1 a terials used for this class ofw«rk in this section of the country. The cement wa.s furnished by the Universal Portland Cement Company. The mild steel rods used for web reinforcement ?®re furnished by the Illinois Steel Company. The. corrugated bars used for longitudinal reinforcement were supplied by the Corru- » gated Bar Company. Steel. - Por horizontal reinforcement 1 l/4in.round high- carbon corrugated steel bans were used, and for vertical strings 3/8, 1/2, and 5/8 in. round mild steel bars were used. Coupons* for tension tests were cut from the ends of bans used in the beams. The results of the test were quite uniform. Ta/ble / shows the average data of the tests. < ; ; - . . . . TABLE 1 16 w \ TENSION TESTS OE STEEL No. Diameter Kind Unit stress Ultimate Percent Percent of Bar of steel at yield point lbs. per sq. m 1 3/8 Mild 42,380 2 1/2 40,120 3 5/8 » 39,610 4 i i/f High Car- bon Corr. 52,400 strength elongation reduction IBs. per sq. in. in 8 in. of ar 57,330 30.2 67.3 57,700 29.2 67.8 61,270 28.3 63.9 88,570 21.3 26.7 Cement . - Universal portland cement was used. This cement was new, having Been received from the factory in December ,1921. It passed satisfactorily the tests required By the standard specifications for cement of the American Society for Testing Materials. The water required for -plasticity By the Vicat test was found to Be 24.5 percent By weight. The specific gravity By the Le Chatelier flash test was 3.12. Tests of tensile and compressive strength are given in Table 3, wherein the values represent the average of tension tests on six Briquettes and compression tests on five 2 x 4 -in. cylinders. The mo r tan mix- tures are 123 By weight. Table 2 TESTS OE CEMENT AND MORTAR Material Tensile strength IB. Tier sq. in. Compressive strength IB. per sq. in. 7 days 28 days 28 days i Neat Cement — 697 8345 1:3 Ottawa, sand mortar 214 311 3320 — • 3 At tic a sand mortar 309 488 4220 n Fine aggregate . - The sand used was N good quality, clean, hard and well graded, obtained from near Attica, Indiana. It weighed 112 lbs. per cu. ft. compacted in the standard way, and its specific gravity was 2.67. The voids in the dry sand we re 33.2 percent. Table 3 gives the results of mechanical anaJLysis of this sand, from which the fineness modulus is found to be 3.35 and the surface modulus, 16.6. TABLE 3 MECHANICAL ANALYSIS OE SAND ( Tyler Standard Sieves) Sieve No. Percent passing 3/8 100 4 97 8 78 14 51 28 25 48 10 100 4 For use in designing the concrete mixture, mortar -voids tests were made using this sand. Curves showing the vaAue of the voids in the mortar, Vm, and the water content of the mor- tar, Wm, for different mixes and water contents are given on the following page. The volume of water per unit volume of mor- tar that produces the maximum density is used as a standard for reference and is termed the "Basic" water content. < « , • i i ' ; :> \la -b V* 5 * £ ( •5 & 5; •JQ s o.s o o.4c a 3o 0.2o Charactamsh'c McAor Voids Curve.* for rfttica Sand |. lr> GdSlc |,4- T3«s>'c 1.2- (basic ).0 (3asit < 5 ?/ _ Absalo4 iZ Wn/umr? — of SanJ T SC j4bz>° / utzvo I u m a erf Camanr C \ 3 s *2.0 10 20 OJO Vo wafer per 0.3 0 04-0 o.so pT -\«x ■« &;nuUV| SVj\ v>Ytarc\ \o Xo'-j -V\vv\i >&c\ -vvWj 'oV la Coarse Aggregat e. - The coarse aggregate used was a good quality of screened gravel from near Attica, Indiana, of sizes varying from 11/4 in. to 1/4 in., according to the sieve analy- sis of Table 4. The pebbles were rounded and somewhat irregu- lar and mainly of calcareous material. The specific gravity was 2.69 and the weight per cubic foot under standard methods of compacting was 101 pounds; the voids in the gravel are hence found to be 40.0 percent. TABLE 4 MECHANICAL ANALYSIS OF GRAVEL (Tyler Standard Sieves) Sieve Percent No. passing 1 1/2 in. 100 1 1/4 H 98 1 « 89 3/4 M 59 1/2 " 35 3/8 " 13 No . 4 3 Con crete . - The concrete was 1:2:4 mixture by loose vol- ume and the proportions by weight were also determined. V/ith these proportions the ratio of absolute volumes of send and ce- ment was 2,75. Basic water content was determined by means of themo.rtar-vo ids test on the sand and cement end 1.2 times basic water conoenc was used throughout all specimens. 19 In making the beams the workability of each batch of con- crete was measured, by means of the slump and flow table test. In the slump test the settlene nt or slump, of a truncated cone of fresh concrete was measured when the mold was removed. The cone was 12 in. high, and the bases were 4 and 8 in. 'in diam- eter. In the flow test a, truncated cone about 6 inches high and having bases 6 and 11 in. in diameter was placed on a table, the mold was removed, and the table was raised and dropped thru a distance of 1/2 inch fifteen times. The flow is measured as°^ the final diameter to the original diameter of the bottom of the cone. Care was taken in measuring, mixing and tamping to secure as uniform a concrete as possible. Men accustomed to nixing concrete and making test beams were employed in the work. The mixing was done with a Wonder batch mixer, of which the capacity is about 6 cu. ft. The rectangular beams required 4 batches and the £ -beams required 5 batches. For the first batch in each beam, gravel pe„ssing all/2 in. screen Y/as used in order to allow the concrete to flow easily around the reinforcing bars. In mixing the concrete, the mixer was first washed out, then sand, gravel and cement were introduced in order named, and the mixing water was added last. The batch was then mixed for four minutes, dumped into a tight metal pan, and shoveled into the form. Control cylinders were made with each batch; most of these were tested with the beams but a few were tested at 7 and 28 days. The average strength at 7 days was 1950 lb. per sc:, in.; at 28 days, 3230 lb. per sq. in. The average strength 20 of cylinders tested at the age of the "beams with which they were made is given in Table 5 together with the data on slump, flow, and density of the freshly mixed concrete. TABLE 5 PHYSICAL PROPERTIES OP CONCRETE (Each value represents ave. of 4 or 5 6 x 12 in. cylinders) Corres . Beam Ho. Age at Test Bays Compressive Mod. of Strength Elasti- Ib.per sq.in. city Slump in. Plow Density Percent of of Orig.Dian. Concrete 221-1 61 4076 4,165,000 0.4 149 s'. 221-2 61 3696 3,575,000 0.5 164 .882 222-1 60 4522 4,030,000 0.9 151 / .099 222-2 59 4337 5,360 ,000 0.4 155 .806 / .390 223-1 60 4124 4,355,000 0.7 156 223-2 61 3689 4,440,000 0.6 158 .806 ) .877 i 224-1 62 ■4106 4,131,000 0.8 149 224-2 61 3790 4,130,000 0.4 157 ,88p 225-1 62 3788 3,990,000 1.0 147 .8^2 225-2 61 4041 4,375,000 1.4 159 .882 1 226-1 62 4037 3,920,000 1.1 152 .809 { 226-2 60 4331 4,916,000 0.3 145 .8^ / .800 227-1 62 3799 3,894,000 1.4 158 227-2 60 4346 4,272,000 0.5 159 .802 f 228-1 62 4058 4,540,000 1.0 150 .887 228-2 60 4152 4,788,000 0.8 168 { .882 229-1 62 3931 4,315,000 1.9 163 .882 229-2 60 4203 4,675,000 0.4 153 i .882 Average 4057 4,326,000 0.85 155 - — — — — i — .883 , . >, .-'v’ , ; t c > < t • t ' 9 . t * c c 6. Test Beams . - Two beams of each of the nine types, a to- tal of eighteen, were made. Three types were j t -shaped, and the rest were rectangular beams. The latter have a cross sec- tion of 8 x 24 in. , and the former were of such a cross section that the flange width was 20 in. , flange depth, 6 in. , web width, 8 in. , and total depth, 24 in. The centroid of the lon- gitudinal reinforcement, which was placed in two layers, was 21 in. below the top surface, and extended the full length of all beams except in No. 229-1 and 2, which had two bent up bars in the outer third of the span length. The percentage of longitu- dinal. steel in all beams was 2.33 percent. All horizontal reinforcing ba.rs had hooks of 3 1/2 in. ra- dius at both ends except No. 221-1 and 2, which had straight horizontal bars without hooks. In beams No. 229-1 end 2, having bars bent up, the first bend began at a point 6 in. outside the load point and passed diagonally upward at about 45 degrees with the horizontal, axis. A second ba.r was bent up parallel to the first and so hooked that the highest part of the hook came about 2 inches below the top surfa.ce, and 2 ig. from the end of the beam. The general, arrangement of reinforcement and other details of these beams are shown in Figure 15 In the beams with stirrups, the latter passed under the longitudinal, bars and extended to within 1 in. of the top surface. Two u stirrups T;ere used to form the equiv- alent of a W- shaped stirrup in all cases. The upper ends of all stirrups had hooks of about 1 1/2 in. radius. Table 6 gives the details of the stirrups used. 22 TABLE 6 SPACING AND SIZE OE VERTICAL STIRRUPS Beam No Stirrups Type Spacing-in. Liameter-in 228-1 & 2 22 4-1 & 2 225-1 & 2 223-1 & 2 Rectangular 227-1 & 2 226-1 & 2 Tee-Section ii 11 11 4 4 7 7 3/8 1/2 5/8 3/8 1/2 5/8 7. Making of the Beams . - The beams were made in built-up wooden forms' on the floor of the Concrete Laboratory, being pre- vented from adhering to the floor by a strip of building paper. The forms are shown by the photographs on following pages. In placing the steel in the forms, care was taken to locate it as nearly as possible in the position shown on the details. The longitudinal steel was supported by 1/4 in. bars at the proper distance above the bottom of the beam, while the stirrups were wired at the bottom to the longitudinal reinforcement, and at the top to a 1/4 in. horizontal spacing bar. This wiring and bracing kept the stirrups in position during the pouring of the concrete. Corks about 11/4 in. in diameter and from 5/8- to 3/8 in. in height for the different diameters of stirrups were lacked to the form in all places where gage points were to be located and served not only to save much chipping in exposing the steel lines, out also helped to keep stirrups in their nrouer position during pourin.< . rectangular be ans 26 After the steel and corlcs had been placed, the concrete was poured. In depositing the concrete, care was taken to get it around all of the steel, and it wa s well puddled to prevent the formation of pockets of any kind. In addition to the tamping, the sides of the form were rapped with mallets to aid in compact- ing the material and to improve the appearance of the surface. 8. Storage of Specimens . - The forms were removed in five to seven days after the beams were made, and the beams were stored in the laboratory and covered with burlap which was made wet from time to time. The temperature of the room in which the beams were cast and stored ranged from 68 to 80 degrees Fahrenheit. The cylin- ders were stored in the damp a,ir of the moist room at a temper- ature of about 70 degrees F. , and were removed to the testing laboratory one day before testing. 9. Method of Testin g. - The tests were made in the 300,000 lbs. Olsen testing machine. The span length Y/as 9 ft. The beam was supported at the ends by rocker bearings which in turn rested on the table of the machine, as shoYrn by the photograph on the following page. The top of the rocker carried a cylindrical steel bearing of 3/4 in. radius, while the bases were slightly curved to allow a rocking action with changes in the length of the lov/er surface of the beam. The beam was loaded at the one-third points of the span, the load being transferred from the machine through a spherical hearing block, 24-in. I-beam, and two cylindrical rol- lers. Iron bearing plates 1 x 5 x 8.5 in. were placed between 27 the beam and the roclcer supports. A layer of plaster of paris v/ as placed between these bearing plates, and the beam to overcome uneveness of surface and was allowed to set under such load a,s came from the weight of the beam and the apparatus used in load- ing. A load of 5000 lbs. was used as an initial load in order to tighten up all the loading apparatus before starting the test. Deflection was observed at the middle of the span by means of a fine copper wire suspended at constant tension between points over the supports and at the middle of the depth of the beam. The wire passed in front of a paper scale attached to the side of the beam at midspan. The scale was pasted on the face of a minor and readings were obtained by lining up the thread and its reflection. These readings were accurate to 0.01 in. To obtain the longitudinal elongation and shortening at the top and bottom of the beam, the strain gage v/a,s used. Dour strain gages were used for this test; namely, No. 1, No. 2040, No. 1603, and No. 1604. These are all of the Derry type of strain gage, concerning which informalion is given in Table 7. TABLE 7 STPAIN GAGE CONSTANTS Gage i No. Gage Length Hul tiplication Satio From Used for Calibration Calculation Material of Instrument No. 1 8” 7.587 7.5 Steel No. 2040 8" and 4” 5.089 5.0 "Invar” steel No. 1603 4« 7.473 7.5 Aluminum No. 1604 4» 75.36 7.5 n lhe photograph on a following page shows the strain gages and their applicalion. 30 For a more general description of this type of extensometer and its use, reference is made to a paper by Willis A Skater end Herbert F. Moon, in the "American Society for Testing Materials" 1913, on "The Use of the Strain Gage in the Testing of Materials"* and to Bulletin Ho. 64, University of Illinois. The method out- lined in these papers was followed in these tests. Crack openings we re measured with a fair degree of accuracy by comparison with the opening of a screw micrometer. In the test of the first beam, it was found that the ribst important feature of preparing a beam for strain gage tests lies in the preparation of gage holes. If the holes we re good, the readings could be taken quickly and accurately. However it was impossible to obtain reliable readings from shallow or irregular holes. The gage line is a gaged length between a pair of gage holes and is the length over which the deformation is measured. The gage holes were small holes about 0.05 inch in diameter, drilled in the steel reinforce- ment and in steel plugs which were imbedded in the concrete at the top surface of the beam. In order to expose the steel so that ga,ge holes might be drilled, corks were attached to the forms in the proper places before pouring the concrete. After the drilling of the gage holes, the specimens were white-washed before being placed in the testing machine in order that the cracks might be easier to find and mark. Loe,ds were applied at a slow speed of the machine the rate of speed being .05 in. per min. with the machine mnning idl e . g Str -in gages Application of strain g~ge in testing oo Cracks were noted and marked at loads of 15,000, 25,000, 35.000, 50,000, 60,000, 70,000, 80,000, 90,000, 105,000 and 120,000 11). and at additional increments of 10,000 lb. Strain measurements were taken at loads of 35,000, 70,000, 105,000, 150.000, and 200,000 lbs. and in the case of higher loads, fur- ther readings were taken at the maximum load. At the initial loading two sets of zero readings were taken for all gage lines and the average of these was used as the zero readings. In the numbering of gage lines, a. uniform system v/as udgd. Beginning at the south end on the west side an the beam was set in the machine, gage lines on the first stirrup were numbered from 1 to 5, on the second from 11 to 15, etc., starting from the top. Similarly, slanting on the ea.st side at the south end, the gage lines on the first sturrup were numbered from 6 to 10, on the second, from 16 to 20, etc. On the longitudinal bars all gage lines v/ere numbered from 101 on the west side and from 201 on the east side, numbering from the south end northward; on the compression fa.ce the gage lines were numbered beginning with 300 at the south end. In a few of the tee -beams, additional gage lines on the com- pression face were numbered beginning with wi on the west side of -me center line, and El on the ea,st side; also a. few lines set on the sides of the tie-flange were numbered A1 on the west side, and B1 on the east side. 34 III. EXPERIMENTAL DATA ALTD DISCUSSION 1 0 . De scrmti o n of Figure s t Ph otographs raid Table s Eor use in the explanation of analysis or stress distribution figures have been made and inserted in a convenient place to use. Typical figures showing all detalLs required for the construc- tion of the beams are inserted on page s > 7 to 231 . Seven photographs were taken to show clearly about the equip- ment used and are inserted in suitable planes. The five photographs shown on pages __ 71 tO 63 were taken to show the typical failures. Thirty- six photographs on pages 84 fto 101 were taken on each side of each beam to show the location of creeks and also the loads as the creeks progressed. The figure on the cracks de- note the load in units of 1000 lbs. Dia.gram No. 1 shows the characteristic mortar void curves for the seed used in the beams. Diagram No. 2 shows the observed relation between distance from load point and angle of inclination of cracks. Diagrams on pages to t22 show the relation between the unit stress in the stirrups and the applied load for each gage line. Diagrams on pages n_8 to 226. show the relation between crack opening and stress carried by web reinforcement and hori- zontal bars. Beam deflection diagrams are shown on pages to no - ■ ■ ■ ■ ■ ■ ■ L - ■ " - 1 *"" — . < • - X •. :■ r ~ •* * .. ... : . * *■ i n , Tables were ms.de and inserted in suitable places when it was thought that they would add to the clearness of the work. 11. D eflections of Berms . - The lpad- deflection diagrams show the deflection of the beams at loads at which the stress measurements were made. It appears that while diagonal tension cracks were developing the rigidity of the outer thirds of the beams decreased somewhat making the deflection of the outer thirds comparatively large a,s compared to the deflection at mid- span. However, at loads near tensile failure at midspan, the shape of the deflection curve changed again and the deflection at the center increased more rapidly. The difference in the rate of deflection is apparent in the load-deflection diagrams. The usual calculation of deflection in reinforced concrete beams are based upon the following assumptions: 1. The representative or mean section ha,s a depth equal to the distance from the top of the beam to the center of the steel. 3. Tlie material sustains tension as well as compression) both following the linear law. 3. The proper mean modulus of elasticity of concrete equals the average or secant modulus computed at the working compressive stress. 4. The allowance for steel in computing the moment of inertia, of the mean section should be based on the amount of steel in the mid-section. The effect of cracks is partly covered by neglecting the concrete belo w the horizontal reinforcement. However, in deep beams with small spans, the effect of diagonal shearing cracks . r , 36 and deflection due to direct shearing stress may need to he taken into consideration in computing the total deflection. In this thesis, the limited time does not allow further stu- dy of the relations between the deflections and the other elastic properties of the beams. A. Beams Without Web Reinforcement 12. Motes of Test . - The location of cracks are all referred to the load points and supports. The abbreviation for north-west load point is M.W.L. , and of south-east support is S.E.S., etc. Most of the cracks apparently extended through the thickness of the bean, but in these notes the cracks on each side were treated as if they were separate ones. a. Beams without Hooks . Beam Mo. 221-1: Two cracks appeared at the load of 25,000 lbs. 10 in. from S.W.L. and in mid-span in W. side. At the load of 50,000 lbs, several cracks appeared in both West and East sides, some of them reading about 11 in. from the bottom. The first diagonal crank appeared at Morth side 10” Morth from M.W.L. at the load of 55,000 lbs., stenting from near the horizontal bar and making an angle of nearly 45 degrees with the horizontal, until the middle depth of web was reached; with increasing loads this cra,ck developed both upward and downward. At the load of 75,000 lbs. diagonal tension crack appeared a.t both sides at both ends and the diagonal tension crack in 1: * '■ * side °P ened so tila t if the horizontal bars had no cor- rugations the beam might have failed at a lower load. At the lrjr of 90 » 000 lbs * c racks reached about 4” below the load point 37 and shear failure approached. At the load 12,000 lbs. diagonal tension crack opening observed as follows: IT. 7/. .05"; 17. E. .04"; S, T .Y. .02"; S.E. .02". The failure came suddenly at the load 154,100 lbs. by slipping of bare ombined with shearing failure atthe top of the beam near the load point. Beam l!o. 221-2: Cracks did not appear until at the load 50.000 lbs. where a crack under the S .71. L. went up about 12 in. A diagonal tension crack was found at the load 60,000 lbs, v/ent up about 14" high starting from 14 in. South from the S.E.S. to- ward the S.E.L. At the load 70,000 lbs. a diagonal tension crack appealed in S. W. side and developed quickly. At the load. 13.000 lbs. and 14,000 lbs. horizontal cracks eh the ends of the beam from 10 "to 8" high from the bottom appealed, showing some tensile stress in this part. At 150,000 lbs. when the testing machine was stopped to start measuring strains at this load, the beam failed suddenly by the vertical tension failure at the ITorth end together with shear failure at the top. The vertical tension failure followed very suddenly from this point to the other end of the beam. b. Beams with Hooks . Beam Bo. 222-1: On each side of the beam two large holes under the reinforcement v/ere visible. The first crack appeared ah 25,000 lbs. at 6" from S.E.L. under the horizontal reinforce- ment, and at 30,000 lbs. two cracks were found; at 6" and 14" north from the S.E.L. and 6" south from S.W.L.At the load 45,000 l^.j. many small cracks appeared all over the middle third adid some of them were found a few inches outside of it. At the load 38 65.000 lbs. first diagonal tension crack was observed at 14” north from S.V/.L. and at the load 70,000 lbs. this crack lengthened about 24” to a point about 8” under the top surface. At the load 80,000 lbs. a big diagonal tension crack was observed at the northeast side and developed rapidly. The diagonal tension crank in the south side reached a point 5” under the S.E.L. Crack openings were almost same width on both sides; at the load • * 105.000 lbs. they were about .025” and at the load 135, ;00 lbs. .05”, and at the load 151,000 lbs., .07”. Shearing stress in the concrete at the top of the beam near the IT. L. caused the failure. It should be noticed that horizontal cracks appeared on the N.E. side at the loa,d of 110,000 lbs. and also alter failure tension crack appeared in the top of the beam 9” north from the N.W.L. at the top of the beam. Ultimate load was 167,500 lbs. Beam Ho. 222-2: N o cracks appeared at the load 25,000, 35,000, 40,000 lbs. First cracks appeared at the load 50,000 lbs. 6” north from S.W.L. , 6” high; 14” north from S.W.L. , 10.5” high; 14” south from N.W.L. , 1” high; 10” north from H.W.L. , 1” high; 2” south from S.E.L. ,10” high; 1” south from center in E. side, 10” high; 2” south from 1T.E.L. , 10” high; 6” south from U.E.L. , 6” high. At the load 70,000 lbs. first diagonal cracks were observed at both ends except N.W. side. At the load 76,000 lbs. big diagonal tension cracks suddenly appeared at the sixth end and beam of the testing machine dropped for a while. At the load 120,000 lbs. this crack opened 0.675" on the S.E. side. Failure oceured at the load 128,000 lbs., caused by vertical shear at the south side load point, load dropped off to 125,000 lbs. I' ", < 1 * 39 13. Be iams Without Y/eb Reinf orcement The dangerous diagonal tension cracks usually appeared about at the middle point of the outer third of the span start- ing from the reinforcement at the load from 55,000 to 70,000 lbs. It should be borne in mind that the horizontal reinforcement was not plain rods but high carbon corrugated steel bans. On the appearance of these cracks, their direction curved bending toward the load point. As the load on the machine was increased, the cracks lengthened and extended upward to within a few inches un- der the load point, and the upward extension of this crank almost stopped, while new, large diagonal tension cracks appeared neaner the support, suddenly connecting these former cracks in nearly a straight line, and in some cases the load dropped for a while. After these cracks were connected, the diagonal tension cranks opened widely, causing the bond resistance between con- crete and steel reinforcement to fail suddenly. If the plain rods had been used instead of corrugatedbar as in the longitudinal reinforcemen t failure might have come at low- er loads. Maximum crack opening for these final diagonal tension cracks were observed to be about 0.1 in. wide. Shearing stress carried by the horizontal bars near the cranks, acted as a tearing stress or a vertical tensile stress of which the intensity is a. maximum at the crack and decreased toward the end, between concrete and reinforcement, end whenever tensile strength in the concrete between horizontal reinforcing oa.rs and also oe u, r een horizontal reinforcing bans and outer sur- face oi the web of the beam, reaches the ultimate strength, the beam may fail by slipping of the horizontal reinforcement. } . >■ < ' I i . ■ 40 On the other hand concrete at the top of the beam carrying shearing stress, lost much area as the diagonal tension crack extended toward the load point. If the shearing resistance in concrete reached the ultimate, failure of the "beam may he caused hy this shear failure. Failure of the beans with straight bars cane suddenly with shear failure at the top and the failure caused by slipping of bars at the bottom at the sane time in both causes; it is inpos- sible to find which failure occurred first, and thus to distin- guishthe critical source of the failure. In the beans vhich lave hooks on the horizontal bars, slip- ping of the bars may be prevented by the hooks to some extent, and failure of this kind of beans are caused by shearing stress in the concrete at the top followed by large cracks appearing at the ends around the hooks. The beans without web reinforcement carried an average load of 157,000. The average unit shear was 525 lbs. per sq. in. This means 0.121 of the average ultimate compressive strength of the concrete. 1 4 . Effect of Hooks at the Ends of Beans . Effect of hooks on the horizontal bars prevent slipping of reinforcement in the concrete, consequently crack opening may be prevented to some extent. It may be the reason that the final large cracks started from the points nearer the support in the beans with hooked bars than the one in the beans with straight bars. However, they did not show any effect shearing resistance in the concrete at the materially on the o0 P of the beans . 41 Beams with hooks at the ends of the reinforcement all failed hy shearing failures at the top of the beam, and did not fail by vertical tensile failure at the bottom of the beam. Therefore in the deep beams for a short span with web reinforcement, it may also be necessary to have hoolcs at the ends of the reinforcement even when corrugated bars are used. 1 5 . Positio n of the Feutral Axis In the beam under flexure, the location of the neutral axis depends upon the s tx eng^h of concrete and reinforcing steel, or at*- in other words, the ratio of modulus of elasticities between con- A crete and steel, and also on the an ount of steel reinforcemeat used. Table 8 shows the values of k and also j. In this table, the tensile resistance of the concrete is neglected. However, in the sedtion where the concrete has some tensile resistance the value of k becomes somewhat larger. The formation of tension cracks may change the position and the curvature of the neutral axi s . After a large diagonal tension ha„s developed and arch actionhas developed to some extentinthe web of the beam between the load point and the support, the location of the neutral axis may change greatly. Sometimes it may be possible that the neutral axis will cut the top surface in the outer third of the length of the beam though of course this is not the neutral axis of beam action, but it may be called the axis of zero stress. TABLE 8 Value of k sjid j when / Zpri t p z h z n a 7 and p = i 1 i ~n « J )k & k 3 0.1 .437 .853 0.2 .442 .850 0.3 .447 .847 0.4 .453 .843 0.5 .460 .839 0.6 .467 .835 0.7 .473 .830 0.8 .480 .825 0.9 .488 .820 1.0 .495 .815 .0233 43 16* Value of Vertical Shearing; Stress *- In a beam under flexure, the total tension in the reinforcing bars varies along the length of the beam, as does also the total compressive stress. The horizontal shearing stress is seen to be neces- sary in order that the increments or increase of the total tensile stress in the reinforcing bars may be transmitted to the corresponding increments of compression In the compression area of the concrete, the concrete thus acting as the stiffening web of the beam. The vertical shearing stress is also seen to be necessary in order that the increment of the totsl moment in any vertical sections between load point and support may be trans- mitted to the corresponding increments of the horizontal stresses to keep equilibrium condition. I’or this reason, at any point in a beam, the vertical shearing unit stress is equal to the shearing horizontal unit stress there developed. If V^ denotes the part of the total vertical shear which is proportional to the resisting moment attributed to the tensile stresses in the concrete, then 88 \ bdi where v^ * vertical or horizontal shearing stress per unit of area in the concrete due to V^ d^ = distance from the center of gravity of compressive stresses to the center of gravity of tensile stresses in concrete. And also V 2 denotes the rest of the total shear, the amount 44 being proportional to the part of the resisting moment that is due to the tensile stress in the reinforcing bars* v 2 = V 2 'BcT' where v 2 = vertical or horizontal shearing stress per unit of area in the concrete due to Vg d* = distance from the center of the reinforcement to center of gravity of compressive stresses* If the tensile stress in the concrete is neglected, then and v 2 = V v = Y TTd 1 The distribution of these shearing stresses is shown in Pig* 8 The calcu- lated shearing stresses for these two cases are shown in Table 9 • (a) (b) Pig. 8 45 The follov.'ing calcui&ions wewre used prewiring Table 9. The bending moment, i 2 > w 1 3p==f s pjbJ : 0T T = fsi-Fj-- In the beams tested, p=.0233 b=8in. d=21in. l=108in. so that “P = (c» 0233 yg Jo bf 5 . Rectangular beams with 7 in. spacing of the stirrups. Beam 224-1. This beam had not a good surface on the web and it was very hard to distinguish the cracks. A very small crack appeared 2 in. north from S.E.L. about 1 in. high at 35 000 lb. At the load of 45 000 lb. two cracks appeared 6 in. from S.E.L. and S.W.l. about 2 in. high. At the load of 55 000 lb. these cracks lengthened and a new crack appeared in the middle third. The first diagonal cracks appeared at the south side at the load of 80 000 lb. After this load, the vertical cracks did not lengthen so much and diagonal cracks appeared rapidly. At the load of 200 000 lb. the maximum width of the diagonal tension cracks became .005 in. However, after this load the diagonal tension cracks rather closed to some extent and tension cracks in the middle third developed rapidly again, and the yield point of the horizontal reinforcement was soon passed. The failure caused crushing of concrete at the top of the beam above the crack. The ultimate load was 220 500 lb. Beam 224-2. The first crack appeared at 35 000 lb. at center about 2 in. high. At the load of 50 000 lb. seven cracks were observed in which the first diagonal cracks appeared 14 in. south from the S.E.l. was included. At the load of 80 000 lb. this diagonal crack extended about the middle height of the web of the beam. i 1 - t • . * r ► 51 After the applied load reached 90 000 lb* the development of tension cracks seemed to stop and at the load of 105 000 lb. many diagonal cracks were observed at both ends of the beam* The beam failed by tension at the load of 218 000 lb. followed immediately by the crushing of the concrete at the top of the beam. The load dropped ■ ^ 0 '1 151 400 lb* 0* Kectangular beams with 11 in* spacing of the stirrups* Beam 225-1* Jj'or this beam the whitewash made of neat cement and lime was so thick that it was very hard to find the cracks* Five small cracks, most of them about 1 in. high, appeared bet ween or a few inches outside the load point at the load of 35 000 lb* Until the load of 50 000 lb* was reached these cracks lengthened and became about 10 in* high and four new cracks also appeared. A diagonal tension crack was observed at the load of 80 000 lb. in the S.E. side. At the load of 200 000 lb. the maximum opening of the diagonal tension crack in the U*W* side was about 0*01 in* At the load of 229 300 lb* tensile stress in the horizon- tal steel passed the yield point and the crack opening became 0*09 in. Crushing of concrete at the top of the beam soon followed* Beam 225-2. Four very small tension cracks were observed at the load of 35 000 lb* at the center of the span in east side and also under the load points. Up to the load of 50 000 lb. ten new tension cracks distributed over the total length of the beam were observed. 52 The first diagonal cracks appeared at the load of 70 000 lb* on S*i^* side; at the load of 80 000 lb* many compara- tively large diagonal tension cracks appeared near the both ends* At the load of 200 000 lb* the maximum opening of the diagonal tension cracks at both ends was 0*02 in. The tensile stress in the horizontal steel passed the yield point at the load of 214 250 lb* followed by compression failure in the concrete at the top of the beam and the load dropped to 184 000 lb* 19* Rectangular Beams with Vertical Stirrups *- The first diagonal tension crack usually was observed at a load from 50 000 to 80 000 lb* and in most cases these cracks are short, starting from one stirrup and ending at the next stirrup* As the vertical stirrups and horizontal bars kept the crack from widening, there were no crack openings larger than 0*02 inches*. However, there were many diagonal cracks developed as the load increased, and some of them started from near the support of the beam toward the load point. The phenomena of the action of the beams may be consid- ered in three stages* (1) Tension crack stage* Small tension cracks appeared in the midspan or near the load point at loads between 25 000 and 50 000 lb* These tension cracks developed until the diagonal tension cracks were observed on both sides at the loads between 80 000 and 120 000 lb* After this load was reached the development of the tension cracks became very slow, and diagonal tension cracks appeared quickly and lengthened as the load inc reased* 53 (2) Diagonal tension cracks stage. The first diagonal tension cracks usually appeared at a load from 60 000 lb. to 80 000 lb* At the load of 80 000 to 120 000 lb. diagonal tension cracks were observed on each side of the beam. Prom the first appearance at this load the cracks were very long and the length of many of them were more than 20 in. and developed rapidly. Except under the load point, cracks however did not go up beyond the two-third? of the total beam height. The angles between cracks and horizontal reinforcement are almost equal and about 50 degrees. Such a large angle compared with the angles of the diagonal cracks in the beam without web reinforcement may be due to the fact that vertical shearing stress is transferred by the web reinforcement. Some of these cracks first were observed above the middle height of the web inclining upward; the lower part of the cracks were not observed until a few thousand pounds additional load was applied. The first cracks appearing were usually those nearest the load point, and the later cracks at increased load appeared near the support. Dew cracks sometimes, however, were seen between these previous cracks as the load increased. After the diagonal tension cracks prevailed, the way of distribution of load may change, resembling that of a load at many points, and the deflection at the center may be relieved to some extent. These phenomena continued until the failure stage was reached. . . . - . . , •: . ' * , r : - < > (3) The failure stage* The failure of the beam will come in the weakest point in the beam, either tensile stress in the horizontal bar; compressive stress or vertical shearing stress on the concrete at the top or vertical tensile stress and bond stress in the concrete at the bottom* Most of the beam&tested, failed by tension at first* Afte • a load from 210 000 lb* to 220 000 lb* tension cracks in the mid- span became suddenly wide, and went up very high to the upper part of the web and crack opening became about 0*1 in* to 0*08 in* showing the yield point had passed* At the same time, diagonal tension cracks seemed to be suddenly stopping increasing in width* Pinal failure came by compression in the concrete, the resisting area becoming very small and carrying load decreased suddenly. 20* Stress in Stirrups . Diagram p.l 7 shows the unit stress in each stirrup. The amount of stress transferred by the stirrups largely depends upon the cracks opened across them, therefore the stress distribution in every stirrup is not uniform* As usual cracks are wide near the horizontal reinforce- ment, stresses developed near the bottom are the highest, and their intensity is decreased toward the top of the beam. The stirrups nearest the support carry a very small amount of stress, and even compressive stress, caused by concen- trated reaction and the stiffness of the beam was observed* The amount of compressive stress in the stirrup varied as the distance from the support. The stirrups nearest the load points also show compre- ssion at the lower load. However, after the cracks crossed over the stirrup they carried large tensile stresses* 55 The maximum stress in the stirrups was usually observed at the middle position after the load of 150 000 lb. of the outer third of the beam as the cracls develop most there. Table II shows the maximum unit stress in each side of the beams at the load of 200 000 lb. It should be noted that the beamS did not fail by the diagonal tension* TABLE 11. Maximum Unit Stress anxL? Stress in the Stirrups at the load of 200 000 lb. Beam Bo* W - c ^ J ~ l E Gage 'I/o'. Un'i'i Stress in Gage No * Unit Stress in Stress Stirrups Stress Stirrups nr ’54 & 74 ’ W SI s 34 34 000 3750 39 32 000 3530 223-2 E 75 35 500 3920 79 30 000 3310 s 32 25 500 2820 29 32 000 3530 224-1 E 75 30 000 5900 79 26 000 5110 S 14 & 24 32 000 6280 29 28 000 5500 224-2 E 75 30 000 5900 88 27 000 5300 S 24 34 000 6680 29 29 000 5700 j 220-1 E 74 30 000 9200 68 27 000 8280 S 14 23 000 7060 28 24 000 7360 228-2 E 74 31 000 9510 79 28 000 8590 S 14 28 000 8590 19 27 000 8280 21. Effect of Spacing of the Stirrups . The first diagonal cracks usually appeared at the load of 80 000 lb. In one beam the first diagonal eraclss were noted at 50 000 lb. and 70 00C lb* 56 There was no difference in load at which the first diagonal crack was noticed in the hearns with different spacings of the stirrups. The beams with larger spacings of stirrups have wide crack openings at the middle of the spacings. The maximum crack opening in the beams with 4 in. spacing of stirrups was .01 in. and in the beams with 11 in. spacing of stirrups was .02 in. However, the widths of cracks on the stirrups were almost the same with all these beams. The beams with closer spacings of stirrups have a larger number of small cracks than the beams with larger spacings of stirrups. Perhaps they come from wider cracks giving some relief in the internal stresses. If the spacing is wide, the amount of shearing stresses transferred by stirrups becomes small. The ratio between the observed maximum stresses S and total calculated stresses S c are shown in the table 12. The ^ tensile in the stirrups stresses we re ^ calculated by the following formula, ^ -_Z- .jl. where P = applied load in lb. s = spacing or 4 in., 7 in., and 11 in. A = number of bars used as the stirrups = S = 5740® for 4 in. spacing = 10 075s for 7 in. " * 1578* for 11 in. " 5 = .85 TABLE IS. Ratio between Observed and Calculated stirrups Stress. Beam Ho. s Load m S/S c 209000 lb. S s/s 0 225-1 . it 5510 .577 "' -z> - ■ A 101 47 and 48 Beam Ho. 22,9-E. Load m pouna/ 3 140 000 ids 120000 100 000 80000 60.000 40.0 00 20,000 0 ,05 Jo .IS .20 .0 OS JO ,/s T)0 J V_-i. i\- 30. 0 :r-'‘ f.\ c\£ \ \ SS .o'A £-\.S£ ;o\\ y 0\ U’ 0 »: 0 r J <5 £ ooCOb OOO'^’- oa-aos \, \: ov. ■ ?.c r4j\\OC*\ S.A C'-O'-V: .>\\30. OiA \ s. s. o V‘n load m pounds. 104 ZOO 000 /$0ooo / 60 000 / 4 cooo J. 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A V- - *' A \ '■--5 Or" V A A rx ” £a» JL„ 04 * aE ,0c CJi 01 01 e o W-. dS", £ _ ,^ 5 -xyT. **’} -—A'-.,, . vv ' - AAA g rKxW, 0.y( c-.A '' ~'t{ ' r •••i ; " • «; a v-a, o"< •>* :A A ; ' : ■ i ^ c- ■■■ o 6 & - a ■- jlsh .v- -• — - - v i- *1^ __>i — , — >: 0 < .• :• ' ■ , ' V V 'A, A Oo A ' ;VV>: 2 ;•>. AN A 'A> AVA, \> v - • v C/n/f £>fr /. .y •■v ^ rtiOOo,-r ' V - .✓ A. -’9 ■ 1 • \ cs: 01 o T~ > yj -yoi'- . V ip. v • y^Kvyov: Unit Jfrosj in Thousands of Pounds x; x V\ i " i JetiM: V iisO, ■ , ■ -• . ct r.K 'it 0< . *\ c „ \>~ : "-. ooo cc \ * \ —X'. O Jo •oiit ' *V CA ‘ ^ *s£/ ■ • . -••w . o>:, >5" 7 ' .;>•• '#' / * aS K\ ■ .-«$»•* '** ' •<< ■ j \ .oei <>* < 0~. .:. ... i v&r 01 fj 2 o o o r>- cs ■;A 01 O 5 A CJti/f dtrass in Thousands of Pounds. 45 r r 7 I ■ 1 \\'.Vv^-^' CUl ■ ... ;■ ’ * ; a 1. ■ / i Jv / a ) \ } 0 r, » -a ■ \\A ;v •" V; -'A ’ ' Un/T JTnzss in Thousands of dounds . I . ■ ■■ ' ■ r : .c Unit Stress in Thousands of Founds r :1 : 3 -'K Ql- A / . c c < | Ci O 0 i Q i \ . 0 — c-" — Cf' H -c- - -O - ' Cv - 'v - ■<< ., 4 -,; ,o t'' \> o-"-- O' d! QOO 01 A . o p d ' ■> "°* O'' - *■ • „ > • .. •'.•••J ! O .. ■ •>• 1 z. c T i Or \l \ \ - 3 . V ’^v Ns,\- 3 k * ' o or 03 , zi 0 ; £ $r. A O- C .-*■> O' 21 o o' A. c< u j f, / i \ , i JL... ,# v ' oe\ 4 #'^ - . /at o>> • . ie - x Oc \ /*> \ - ;. o x - / t'* «j«, s ) 00 r - •cdlOOOCCi JU S'lOC w "■V, w Uniffytress in Thousands of 'Pounds. Unit Stress in Thousands of Poun c/s. \ Vy'KVk a <->v_y.p Cv\ •: :\o: Unit Jfnzsz /n Thonsann/j ofPounn/n. c\\>\\ '->\N \\\ ' * 0 - ' -v \ > J y ~ /'n joounds- Unit- Caress m CH'irrupj l in = 20000 i&per ^. in. 2 2,3-1 W 8 .. Sr'Xl . ■ w • * > ! c, >!i ! P <5 9 9 / i \ 9 a f t- / : t!i c ioo Sit 6 ic e- X o P i X \ 0 V-C 9 \ . c / / 4 \ f) 1VOC0U. \ r* <-‘.-OOCiO\ w V V Si '> V ^ X.QD1L. <7 o 9 9 \ \ tv a. V X 'X \ J \ \ o o % X H ■-9 66 \ . ' o 9. K ’ \ 0 \ <9 a \ \ '9 9 6 \ \ j eOOO?\ 9 O-J 5VU' V C< . \ o:. '■• OOt. >2. / / ( o ■> i< ,r - voor> x -• <»’■ ! wsimrVC m .'’•■-/vi 1 !- '!*aU- H . S' C> J C . > £punoqg/ in pounds 132 Unrh 5-J-r Oi Q - V ■J O 0 0 cl CjQGODI iitfOU?. * V J a r ,- \ i \ 9 \ 9 < K . V \ ob Qtican. A i •■. o I c o i /i^ooO! ■; A r fi. : A. - ,A / 5 i/ '•» r. \ X o. X s Os. X \ f T \ \ \ \ \ k X a •> \ • \\ O' .> X- •:> O *• V ■- ■’ 0 p ft ft O £3 A o .'.ft. ».>, P\ ' va\ <:• c *A* C X -X Un'/fdfrossin Thousands of -pounds. /' \ a 0,00 0,0's oe w . f .XT or sc; c.oooci v. --ti.* 04 , > r?c Ot / r ,.-o .o; oooeoi oS , 0.1 / o"" - v' O' — c- •'O'O: ooo^f: \ _ ■ \ \ o a. •? y s — :f — i i - -■ o *- ■-' s , s>St 3 'Vj.f.C '«:■ -i ot O O 0 >V/ ' r ■ a 0* X *A ’ V 7> 0 \ -o v .ot. 1? o r t x| o v i i ? a EA -feJi * tql 0C\>8f;S . J'J ‘v'SJS r i W JS ■ UnifPfross in Thousands of Pounds. ^ r r '.s - r ° ° ^ /'•-,% ' > ' w ' • c C*, O •<-£*»• ..-.*?• ’".-7 ° ' c ■- - ' 'r ,.' " ? ,. ^ 7 : *■< '.^' •• ° ■ i . '-- 'V ■ * ' ' *•■ 7 '/%/ H.J :sr'1 ?”O k \ '74)7 c. is O .. 85 200 0 O 0 200000 1 l50 000f iooooo' 0 1 22 I23 , Unrf~ /n Sf/rf^up^ / *n, = 20000 /&. p i c o 0 GOCtf'O^ I X wooe 1 ooo'-> Oi j 4 \ oof.os v Y j • \ . \ ■ ■ 6 - ■ {.« ! i • \ \ v. \ V \ -o oooow-: c> 0O< .-rV / qoooo; '• A 4-M X 0 Si.'; i'W y \ C \ \ V \ ■v. \ \ X V. \\ \ \ \ \ \ \ b u V \ \ X \ \ \ 6 ' 1 6 £' • ' 6 ' S& X ry 00 f - l I CrtOCiS: y W30O0I 7 . f I oocufc. X i ' I - » i o • *••• • •- - \ • -XW'y'x :C u\ . par$^. m. Z 2,3-2 W. t o- _,tv. r-~v 'a. d\ •oo.o'.'J.S: •• .cV \V*. Unit Jfrejj in lhousanc/5 of Pounds. ;X "O'— Q. .fccs; OOOOOS, V "c / / 1 ,o — ■ “• -a, WIOOO0S! ' <: \ \ Ok > i i * j / oi — ... / o o.:.oi f -O-- o-- - . o. _ \ \ / / * ' ,W! O-OOOT V \ / O' dS OS "dl cr'' ~~0 o— — G Q — .sal ooo dc c> X- - Vi ' V - j^V-a^V^Yl X UpCV. Unit Stress in Thousands of Pounds. • ■% 30 ZO to 2000 OO lbs. 20 10 15000 o tbs. 105000 It73. 10 70 000 lb y. 5 0 35 000 Ifrx E. 223-2 U.L. ZI3000 L&s. 911 / \ / A 05 ", ; V / // 1 / T3 , / / 7 A / ■' 7 / 7 // ,y CCJ! OG 0 GOS .•Cdi COOQcl ,-v- ' -X-- / A? ' & ijr / \ s / \ -' . o:- „.. Ql. o% oi ’■- ** v. >» S^G;-;..,' ?.«; oo-o ■" d - '-, ? :■-•■•-_:• >^ 5 ^=:;" _ _ i -luSiG.,. - j-=h _■ d! C OO if. .:':-- v s a fo -0L o n o o Oo«up;3 A , v* > - ' • . .\ • \v •• y* °A\ • CJi< /• ‘ / . t 7 r A c > , 3 ~' / / j-rtr-: )<%rf J a ~ r or. ,. c~u - - ’ - o -.., o vC e -a . , O y. x ,! . •• - ;> o A\c ' . c -• ,.c< . - c / s/{ fh** •\ -j i v z/^ # 77 A ■ V Nr-t 51 »..«»i> j i in in.* «■— .-w ~ . ■■ '»» w • s ?.cn oOva>;:: .j .u m-sss T ,27 C /23 C Unit- Stress in 5hrruc 13 . /// 1 1 , — 20000 lb. par /n. 22,3-2 E. \ c-C'k esj> if Uh I \ 4 t- i ■e. V 4 O! 6 e 4 t si 1 A OUti 00?, s -> OGGQS! " > 00601 4 \ ODt'02 ■0 do 0 \ V N \> '■•», \ X V C <<• A ; . \ , • '•'> o .9 \ \ 9 \ Y f VT^ dT 0 «. x \ V •Y A \ \ os 5> f'-’i sib ; '6 ^? ■ j’ooOCio; go; . c.i. ! r. % h X \ Si \ Q 'V \ > 4 4 O .0 o i \\ 6 o So J ?oi tYo f Y> \X. i) >> \ ■ • ODU 00- \ 6 ! o \ \V. •no, ..v, - ijtf X-vv T'vfr'., > 'V.c.Vi : .i $;• > SS b . y QOO'OG. ,-\ £>.'• o. V- 5^^ VO ' >C' 0 1 O 6 36 1 37 i3S <£39 c (40 1 i) 56 < ,57 £ 58 5 59 < 1 6o Uoth&ress m c 'S-f'/rruD ■V. / /n. = 20000 /h 5(7. /2 ■ l / 22 , 3-2 E Itt /'; *: 0 U \ *\ O o r’ ■r;> .: / of' I /fl w >< O. £ 2 2 - a ov- er' £ OtO Co,;., .., iU .{• VO Unifytnzss in Thousands of Pounds. 30 20 10 200 0 00 lbs. 20 10 |50 0 O O lbs. to 105000 ib^. 10 TO OOP Ib5. 35000 lbs W. 224-i U.L 22 0 500 lbs. p * X / * M \ ! 4 - / \ ' / / \ . \ w • y / " ' . v. \ ' / v ; '-5 v./ wa A •*J! OOO 0.0$, i ■■'■/' \ \ ■ K / A \ \\ •\ • /. * \ V V'*" v \ \\ ^x \ 0 £ OS 0; ■ v .K OS ! »' \ _* \ .'/■ \ ' O a . ■< /v \\ Of ■■ . - .At xv: ■ - 4 ■«RJ! 1)00.0?! f s / ^ V, X \\ ^ \/ \ N 0 4 ^ ' ~ t •: ^4 0 0 QgO! •=. 01 0 o; ‘“W CV* ' — i.. .^1 •:-V— ■ • •• ‘ • C O’ . L .. - '■j/ldJL • • - . - — -,\- & 0 0 o c *'j <>*•■’ V- f. ■: , -J "- ' ' ' X «/ ■ / ?• *2 ' '■'*'/ - 4 , ; yO ' C •' -a £•- S/c v o 0 ' 0$ ' i £di 00 e 0 C ‘S •i-4' ao 'A' 0 <} O 0 C 5 r, ■o-O- \c \ 0 0 0 O •. 45 'P , - \ 0 O X. i, ’\ \ V c 0 0 *• ■ ,4 CH*,) "S.JJ t* ■ "X" X>5*Q.Z V V^^V353kV\^>. Load /n pounds 144 22,4-1 W A A 0 / j ! : , : t \ e«;i xi, ip l. c •%& 9 v' ••: \J \ f u / V •> 6 ; y* .C4C jL •> Of<(W3i ? 1 6 ° \ V \ \ - \ I a c. i \ j f r f / a*; c-: s*i I ' \ \ ; \ ■ . -.\ V X !,ao! c £ • it ?s • *£ j m i ss J ii i .o- ••••*>»• -a '> vtin dS, - e»v\ '(j "X; ■■ \ \ V \ ? i t 5o (< - : -r- c , C.o $ Sd o > n 1 *» \ v' O \ \ I \ s a 0 M M M < 5 ^/ <• V :al \ \ 'M : ^ y ail > Si / % 7 ! q r / C • ;J iu NJ O \ 2*4 ; 'i t t V •• i ' Q o .»*- '■o.i • t : 1 *V.< > •'.' ; > I { 3 u 9 ■ A r\ S+‘- '~ ‘ ✓ rT S: orOOO'i,., ’• -movQ \ . v !. ... 6 ' ,>0«! f • .oS • •• 7.ryyvv.Vc ' . G7^v:U AV. I " r- "-U Unit direjs in Tfnouzando of Voundo 3 £ Un/f~J7re3s in Thousands of Founds Load tn Thou jo no of fLu/ido . 148 22,4-1 E*. 1 ' U/iif /h ^yfr'rrupz /,*.= 20000 /&?. 22 .. 4 --\ E, (Snif'Cflresz in Uiousannin of Fbunc/n j Qpuncy_ jo QpuoQnoqi u/ zzvjjp pup Ldac/ m "Thousands' of Pounds- 15 Unit 5 fr A c8 i -kg* c? o SS oos "<> <5 Ocl ■ 1 y'JOt ■ P f u? '/ V \ S:j \> v. \ X \ f ! t ? •a vr > ct i t ‘ - 5 M 0 \ » • i OOS r K x \ V ? >v] es.; R>.i Ptvo ss { > j s 61 k62. J , 63 1 Zoo 51 6 52 i 53 TS U/iif Jfnzos in dtirru/ 03 . /in . = 20 ooo/fe. 22 , 4 - 2 , w. Un if Sires ^ in Thousands oT Pounds. \v.V: v r Vy\J^ ^ \vv y3f^ : Unit Stress in Thousands of Sounds tr i )y 1 A, ■■ A •x - '7 -4 //.*. » ' - V . . K W -- •> A '"\ idi ofjooos VO! u o O Odi * / \ M /' \ "V V »\\ -A f \ A - A : a 3 £ 00 •">1 • 4 > f -- 3 - Oi '.‘ A - lid! c '.; CAe 01 - vis - i ' Ql ■ail O C O OT -•of ,0 A o \\ r - L_ ... o • 1 c ; 0 G rj<-; o*s „ o r < "c* * Cl ‘ * <>«' (j> ; %-> V ' •• •| 5 ‘\ 4 . V! - v 7 i *5 > 4 CQ* . a '• *' • " 4 .■ • -a ' . . ri ■LiiMlAjjJijM, ;>^\\- ^% q . o . \\s acy-vx C A A - ' V,;o Load in Idousands of Pounds. 200 1 50 (OO 9 SO J 6 It i 200 l 9 7 ^ 98 i |O0 » < ,20 28 ^29 Z//7/7 4 in Liirupj //n = 2 o ooo /I5 22 - 4 - 2 . E . 0 \ X o k f OC \ p 6 c ee 89 * Ye i A \ V. OP. h | 0 '•• 1 I H X \ ! b > 6 'V? r 0 J U-. c.0.3 X' X c * * 2 ts> X. ' 2 ? > -O ? 00 lC O O, & 4 di o !.. £_ \ o. \ - \ \ \ 0 . ! \ X \ \ \ X \ 'V ’ V \ f f \ 9 ; 9 as J ., \ P •; P.'Vo . 8*.' • 'T.| d : r i ooo os v. \ -■ S\\ o' XX %0\ as \ 002 oei o 00 | as.* o Load in Jhousanc/s of Tbunds. 2oo 150 A i oo<» 5o 36 1 37 1 33 Zoo ISO 100 j 39 < / 40 / 157 66 ,46 i49 \50 i>56 A57 Unit Trass in dh'rrups. /;» = 20 000 /^. 22 ,4-2 E. V pr \ l 0<-» y \ OOi \ i oe . i ,c;- - •-. ,o'; ‘ ' " ''.V -3 -*vSS. ro^;\ '.‘ A yy . Unit dfrcss in Wousonds of Pounds Unit' Stress in IPousands oi Pounc/s. Y\\ V r /'V,N. l_o&c/ /n TfiouSjprtdj of f&vnc/o. ZZ£ -i w. t '■iti * -vxa 4 63 / i o $8 f t A I I ! r / 3 ^ --•• <£ / I \ t t Oi\ : i o^\ 0? . o o u \. 1 ^ V \ ( \ \ \ : V v \ \ V * . \ ;\ \ \ \ \ 1 V X \ \ \ \ \ V, I \ i \ i i--To *o\ > \ \ \ c - \ , \ n H \ \ \ \ v 3 \ ■x \ \ \ mm ! ; 1 - P -Nsi ssi \ r, 0C0. r 06 , | C0\ 02. I : o . Unit iJfrooo in Ifouoandy of Vo undo Unit' Pfross in Thousands oi Pounds. f .. V. /r ' .'<• V'! A ■ // / • // cuf o q > oos , 4 x A . ■ •••••? r Cy! o O O O / ! ooo?.c ..•-(ji OO O O's z%\ 0002 , V, > ! J I 4 o c> «/£ ■< ! ’/ / £ o o 0-^ . o '^W O ,.v, / 053 *”7 • : ,«:r„ / O ,x*' ’} ■ r . » ' 08/ *• ’ ** j- •/ • J ;• ... c.OS...' : 5 • -5: 3 ..-c a V V \C •Xi I *1 Ot- 10 . i » ( "Y* ■: « , f V.- , >• I t Load in TFTouoands of Pounds. Load in Pousands of Pounds. — i— ! < » / a ^ \\\c* - -x\\? • v ! - Unit Jtross in Thousands ot "Pounds. 33 . /■ <-/ :;4\ 0 0 0 0 0'S: Y / id.i O C 0 C ! T* .a •" I / / / -cv ' tdf o qo a. o i --Oi. V o- ... — o- f. i'jl.tJPQOT V, .-a p~. .irtiQOOc' rH -r* -- -P . I v 4 V i r o »•* J ! \ [.Laj.Li-.l~i ii .. Unit fnJfiodsooc/o of 7^0 u no fa 1$7 30 2o 10 A, 'Zooooo its ^ 20 /Jjy' 10 0 10 150000 lbs. 05 0 00 lt?J. 10 0 5 o 70 o OO lbs. 35000 lbs 22,5-2 UL.ZI4950 lbs. ft! : V\\ s,\>, // / if r Ilf ■' * \ v ' 3 / / if A / ’y P#"“ • f / • .X- - . CCj! O C. A •ad i O O O O Z ! JET 4 K Ia // \ / X*' V A s?!, k \ \ o S c .1 / /*v 00 // ' •> s 01 £/.■ ■. .'-v ■ ' / \ 0 ! .A •/-' X X r*y r ^ . . X ■ ZxJ- .OO IcOi X . V"'' \ ] 0 A . . f ‘ ' ' * -•'H ^ v . 01 .she- - -iv i^pSS£i- «: «ji >o o ov sen oo a 5. o • - - ■. - - - - ~ Jp - - ■ -** t & * 1 V' > A' ✓ ' • 0 \s o> o' s\ / c 8 - gj z- % % o Jr, Cs J - JL o o o o c&$? , om,, 'y Cxi ■ s' *->"h I „ O'A 0 ‘ ' OK\. o \ o*. •....«, ".O ’.- 7 /' 0/ N i \ ,. .9 \ X « '> ° ' £ . • ' *> - ; x p / ! ). , f c,: ; • No-op. . . 'x °V ,... c ‘ . ■ ' ■ J ' M | V A Load /h 7doUJando of bounds. Load in Thousands oT fdurtdj. Un/'f J fre^o //? Thousands of T^ound^ ov Unit Stress in Thousands of Founds. 171 30 20 10 A / / \ \v \ / \ 'X 200 00 0 lb-5- 20 r/' 10 o 150000 lb-3. 10 105000 lt?3. 10 70 0 00 Ib3 5 o 35000 lbs. ==te= r- +* i A /95 / OT 150 ^ Jf§ 3 . 714° \]B° 2.(0 |4?L(20 Yso ° X y-2K) ' dv*(AO 50 T60 I 50 V70 /6^, V ^60 h$° 3<2«>V5o ipsj4o F\i to L_ J \35 dp~^o- o o o o o o & s o 40 o 1 w E. 225- 2 U,L 214950153 T I? I Of / / ■' ’W~ ' V V v \ \ \ A* \v ‘ /* y y' iX \ A. \ i "X.. ~ - — -.r " Xs £. v > c i .ssjl 0002.01 .: .- CO O OV cm oooes \ » \ . / v OV / \ ' ' /■■ ■ N -A \ \ \ V ' V’, V ■ -;f .'A C' 01 .0. v s •— - — i , OS 01 // , \ -V-jy ^ .c;c\\ O! C Oi . JSA -4-^0. .C ^ r, c A On y o % y r) s', I A O* V. Ar. 'i- o , ' / «.<» . • P OtC - < nr * r? -Cb O;-- 'j'S ; / - :• <■ . * - ; \ 1 + d?.] ; ,S A\ : ° . c !. ' ’ -X o r *> '•» — \ 04 ’'‘Vi ^vX ." 0 •A. -i'cc oao Ox N v. \ 0 'A.' cjp\ c xe ® ' X/-K, , ° j Vi 7 l ; . v\ ^ l \ 7 7 X- * 1 <’■ r. l>;- !.b )lk» A). \ v® v£» . ; iX.1 j£c \v;0 j ’ '■ -C; oc; c . i i Load in ITFot/sanc/j of Pour? cty. £2,5-2 E. Loads /n TJwc/jtfnd^ of fdundj. 17 22,5-2. E f Unit J Tress in Thousands of Vo undo Unit 'Stress in TFiousa ndo of T^ounds 1 Vi 30 20 10 200000 \Y>5- 20 10 15 0 0 0 0 1175. 10 o to 105000 lb3. 70 0 0 0 lt?5. 5 0 35 0 00 lbs W. 22.6-1 U.L. 262340 Ita. Lonni /n Thousands of TUnnUs 176 200 ISO too 5 0 0 1*23 \24- i 1 25 0 63 1 64 i ft S ,7 y V V ^ V-/ | Q v> <_/ Unit Cttr 0\-_ \S A - ''XXX . load fn Thousands of Tfonda 2 °o a- _ 7 /so <* / l / ■ J / , , 1 1 /oo T i f / I I / 5 0 / <■ / \ \ ) 0 / 33 1 34 V 35 1 i 53 4 i , 55 Unit d/reoo in df/'rru oo /l. -Zoooo /£>5. 22 , 6-1 W. UftifSiress in Pounds of Pounds . / / / d / o' ,a r / d 7 cr .cdS OOOOV Unif JVresj in Thousands of do undo. 17 ‘- 30 20 ZOO OOO lbs. 20 50 00 0 \b 5. io 1050 OO lbs. 10 0 70 O OO lb?. 35 0 0 0 lb?. C 160 E. 22,6-1, U.L.262 34-0 lb? •:v e , v\ ' ">4 '•A - //■ - / : .'OOOO V , / A ! / \ ; x 4 Av . ■ ' V -V " cii o o 6 : c : ■ 1 / >4 i’i i C 0 G v. C *T ■/ v'.. m • \ / \\ a"' - / s : t — V r! — r " I -v > Cl g (Ud 0 . .. OA d . 4 , r Y ....... ^,... o tffv « r -*x : .. y :i i , 7 v ; i . **}:) \ ' I 'v;N- O :'•■ 0 ‘ jYY’ 7/JyY. ■ ' ; : . •' - ' r.dt <>• r-c '£ dS • J }J .!- - ' * id C\. -j V \ 1 «\ w ■r >- ^ ; ; } :>ci e.s/ „U , os * a\ im r \C OO^. Oi\ 0 0 \ 1 1 ? r; Q 2-v O'-A 0 f. o ooo ^\\8 l vVo8\-> cy v Load in Jfiousando of TbundJ 181 22,6-1 E. 181 * \ C - . . f y^s±.K\\ Z'V-yr'SvC, vS\ \\) \WS\ >\ \sV v^vy,^. o\ \ly •-••.' \: cpUnOcl fO ZpUOQDOLlL UJ 4! up Un if' Stress in Thousands of Tbunds. Load in TiTounandn of Tdunds 2o o 15 0 loo 50 200 150 100 50 00 r i 18 < C.O u f 15 0 / j / 0 0 . / i"0 23 124 63 64 }> 65 Unit J/rkjj in df irrupt. /in. = 20 000 /bs. 22,6-2 w. Load in Thousands offbunds £00 p D / / /5 0 1/1 100 9 9 9 50 / / \ 0 1 3 3 i 34 \> 35 ,53 ,54 55 A V Unit Stress in Stirrups. / in ,—2oooo /bo. 2 . 2 , 6 -2 W. Unit Jtreos in Thousands oT Founds. Un/'fyfrz55 in Thousands of Pounds zoo 15 0 /O 0 so 0 20 0 15 0 /OO SO o 200 /SO / 0 0 50 0 188 8 \ 3 V, 10 Unit stress in Stirrups ! m.- fujtffljMjt ! i 1 1 22,6-2 E. Load in Thousands of Fdunds. 189 20 o / C f) to 0 5 o 38 39 \ 40 58 J59 dO Unit Stress in Of/rrupo / in = 2o ooo it&. 22 , 6-2 Un/f ddreoo'jn TFiou sands of Toon c/o. Un/f dines j in Thousands of founds 191 30 20 10 200 0 00 lbs. 2o 10 50 OOO lbs 10 O 10 05 0 00 lbs. o 5 O TOO on ibs. 550 00 lbs W 22.7-1 UL, 261300 |bs. 20 0 /5 0 10 0 SO o 2oo 150 / 0 0 50 0 20 0 /5 0 10 0 SO 0 19 22-7- 1 W 20 0 15 0 10 0 5 O o 20 0 150 /OO 50 0 22,7-1 VV Un/T Sfrass in Thousands oT Pounds. Unit Ptress in thousands of Pounds 30 20 IO 20 0 0 00 Jfc>. 20 10 o I50O00 Ibi IO o 0 50 QO\bs 10 o TO OOP lbs 5. o 35QOO lbs T T 22,7-1. U.L 26 1 300 ibj. '■V. \ ; / \ / / : ' \ \ \\ ,-l ! X - ■ ' aU \ / A \ V/ - A ' // 4 / \ A * s' , ' -V y a~£3Btg A ( t !/ A A .yv \ v t k . 01 t 1 / / / ■ \W / d'- \ »: ' ao ; / / \ \ • : ff \\ \\ N ji . v’ • • K \\ y, AC ; ~ 0 O 01 ! / A : A \ ■ ■ -• ■ ■ i . A A - - A - 0 - ££& SL r» rs a: -T ■ &L1LQ l£jSL5.. s-.. •v. v .y' -- : ^ o' y A y o A s Qj fj. A '1 .0 , t o OS. A >< p 0; pi § ,0, 'C c< 01' £r 2.0 o 15 0 io o 5 0 0 Zoo 15 0 IQ O 50 o ZOO 150 100 So 0 22.7-1 E. O ?X \ , \ [ ' -t c 6 >V \ t \ Ofci (:'<> 88 o V \ T\ a . V i OS c 6 ! A Oii\ 0 C" 0 c. \ °\ \ \ \ V \ X t, o 'a "9 t\ o "k ■ kx -X x cos OSA GG\ 0 Q l \ \ 0<4 vTi o Si! a u OZ A 1> s i i 3 Si Oc ■a\ ocxooS” \ cjd^yvv^G c\\ z'c-rv-C r\ .S.SL xVAy Vo ^iyv:^vv:\ • C\ Vpr\VKyV 2.0 o IS 0 10 0 50 0 200 150 10 o 50 0 197 Unit Jfmsj in Stirrups. /m =20000 227-1 E. UnifJfrz ^ j m TF)oU,jando of Pounds. , ,J r .y <»1 GOO GO' --o ■ " ... .dCSiOC'C ./PJ GE / id* COO BO! ■ Oil 0 C : _> OT P. CK aHOOOBF. G. ay . A j Jtx. Wi... iv k " 1 S " ■ ; i ■ yf: y kf ■ * ' £ : 2 Z , ' / ••*. O O o H '>» ■ ( \ cc\ " ' V— c,X ooooos \: -r / p u. / cd! OOOO?! \ \ \\ 'x \ \ \ r V- \ : / A / M! COOcOI , \ N o X. / / -« • . /X., >o». \J \ r i-1i 0 0 o c f y '0 ...-.; ; l : \ \ -O'-" ■ --o <‘~d QZ Zb Ob tl as Qi n if C n,. }/ ■*** O tf ■ n b C‘ s \y G ">■ •y\ a c ^ n % O h X (y Unit J?r3 . 10 TO OOO |bJ. 3 5000 tbs. E. 22.7-2 U.L. 26 8 ' ; • > " / ■ \ V V fit - *< - . •*. •CCJ! 00 00 i- '. /V ./ ooi. ,, :oi / ' 1 iff! OT'O ■ x ' ! 0 > / oo 4 ..... ■ . Q t V. % o, 0 . & 5 a. C'i p c O' • C- 6 ' JM)Oa Oj: si O r.JSS. . .3 Load in Thousands of bounds Unit stress in J tirrupz. On. =2oooo tbs 22,7-2- E. 00 1 * i ee 1 be ! * i ;•> » o\\ 00 ^ po\ Cc 0 Oi\ 00 \ Oil 0 \ < V \ ' V s’ * \ } f> \ 0'.:\ :yi\ gs\ V. ” . '0 c- ZQ\\ r Wt C vVv -07/^7, '^v> '^ c -v\ v,\ o\„ vpm^o; Load in Thousands of Pounds. 22 . 7-2 ? E. 0 0's r C •- ; a \v, Vw'V.v v r •- f. v ;o : ■ v\ -X' Un/fCyfress in Thousands of Poundo fn Jdou-oando of 7-b undo . Load in Thousands of Pounds. .■cJ i / f 3 • / / \ -N i o \ I . ' \ . \ \ \ ' \ ciri \ 'f*0 « oc ■i ; / \ \ c. ( vi X>\\ -• , Oc'i oos 01 \ oov \'-y \\yo«ro^viv-;, 7. o\ ' c pr\\^ Load /n IPousanduoL Pounds. 22.8-1 w. OZ'i A3 n l \ \ i ?.:• ; COS 02.: OOi 02 OOOOS = cvi\ .-i^rr^C cm zzsrtTj %\V2 \g)W^ ^\\^vi^o Un/f JTress in Thousands oT Po unds. Unit JYrczs in Thousands of doundo " ■ O) 000 cOi r.d! OO OOT Of ' i 1 \ v '-s ’ v'V N.. '■ N N.V o’ M r ..s K ' A i rril 000 z.& ? J'Sm at 1 ■ si, — ■ p sab*. ‘ c .L ‘ “T" 7 o vT 07 ,7"' '’~‘v \ o — V / •.:/ 70 , .: r / f ) c ~"> e ■ p V n : •- : ? 1 , 1 *V T P\.^. «. ’ // oi [ "*h > V. ' ■ %/^yf ^ ? O'. L\ '\ i f ; i T . . ■■ 1 | V: ‘ O 0 _£> . 3 S . j .u ’ '“o.S ;l . 3 ! j J. 250 2.0 o 15 O 10 0 50 0 250 200 150 100 50 0 250 200 150 100 50 0 V \v, ; vf.-> Load in Thousands of Pounds 13 Unit S tress' in Stirrups. / m - 20 000 It & 3 . 22.6-1 E. Un/t-Jfr' j|: : . jrfe - * — Q\ i'i i , n 'V 01 / y •kv I 20 10 o 240000 lbs. 200 000 lbs. 20 10 150 OOO lbs- 10 0 5 OOO lbs 10 TO OOO lbs. 5 o 35000 lbs. E. 22.3-2 U.L. 260.000 lbs f! Q O “'A X \ fj \ w X Sv a v j ! >\\ V\ ! W V ■ \ V -V-i V-\ T 7 ?' ■ ■ / » f | y\ -A vN / ~>a- > .X-C-X — ■T.a / C C CiOdS aooo^s : •:. OC 0 3 i / X vr; /' ,- r . n ‘ --jJ£rrs»*"« ; Z J ,' r _! j Q O ' ' ! /// !/; X r/ ,o //f-" ' ' X \ \\ Oc os . Ay \\\ V\ ■ _4 Uv~~£- ' \\ iQli v\. v A //. \ \* ft i ^ > \ v\ w I // Or \ -Vv- / *^ V * /Xv> / \ X. // \'X // " ' \ X- /> /X-' ‘ •'/ •:••/ Xv- V 0$. o< u 01 cw'i oooe z 0! x e ; .. Load in ITTou-jando oL Pounds. i ! 221 r< \ ■\ j / : i ! j i \ ! i / 1 i i i i I oe / 1 \ \ \ \ / \ ; U evi i X \ \ \ \ \\ \ / \ \ \ - \ \ \ \ *» # Y O'U > • A oor. • { I } 1 / J Oi i C i V \ \ \ \ % \ \ \ \ N \ % < ' £ 0 S: o i\ c.o\ 01 . W.X V^VOKWiO.'AO: Q\ Load in Thousands of Fbundo 2 2,8-2 E. Unit' Jiress in Thousands of 'Pounds. ■ V V, v ^ ,.A\ ft \ A ft A :dl 0.0Q O OS \ \ A , \ / \ ' •f-J ? I i A i X ; i \ / • V / V-'- V—*"' \ ;OCQOcij v a K / ' v J V \ I I ! x 1 ' r / ; A/' A .A* > 00 ?. O! \ V"' \ I I t i / ■ / / A / ' / \ / \ A A I III / / / V..,/ VW \ / " / ■' / / ' • p / i / // « / / C 2L / A / A rrv '/ A.\ / /s ^ / wv ‘V J -' • \ ' ^--O. v ••:di OO O OT i - i . I V . A 'i i \ I i \ \ , ■ie ce zt Mi u 0 £ ,«•' \ ■ i \ 2 S /' A\ / ^ \ V A / \, \ U 0! a . Cdl O O o V V \ v \ ' •A o V AAA '' ■> .V^OC%Q.^'AOa 'A zpUHOp JO OpUDQDOLJJ U/ ££2>JJQJ/Up) OY I ! ( A ■ \ i \ I h \-j ? ? iv / ■ \ i \ k" \ / \ / v / \, "'V -«j| O O D O 0 S A , / \ /N- t / k a \ s \ ! 0 \zfi>O 0 . 00 ?J < !\ \ X I \ t ■ \ I i i r v i i \ n V : 00 c! >1 A I i \ I \ t \ I ' / i i • : I i , I A * /\ : GO COY \ I \ I \ I i AA « A f A --A,'- . s /, 9 — A ■ / •’.cv />O0?t 1 cd ! 0 3 1 1 i 1 \ \ i ; : \ Od \ 1 . • ! 1 , 3> i 1 i 1 OA U 1 '' V-?i 1 1 k it \ 1' | Oc K v i 1 i iSi \ ■ i • j OS. \ \ \ \ \ ' I ?.i >- -o \ 1 • \ \ \i . \ 01 v “A \ \ \ Ht* \ \ \ Cr yl ' *> \ ‘ _*■ I i-' M t r ■ 0 ■o c*N L-- ,ry 'DA O cs V. 1 £ JL •f • ■*' Aivon . ?'*// ao/ "XL e fir cr* „ \ / V ; i \ / \ U V \ \ \ i \ zdlOO 0 CY \ / V v.\ / 1 A \ M A v% ' .> 0 O 0 d c X. V I \\ V— V- V V 3 ' OH e-t- 04 dF ■0£ dS. oa 01 o r >-■ »f *r a , OT \* X / \ 7 4 \ y v \;V ! A ' “1 u 1H 1 X o '"•D .1 y_. o! 5 y A '•V “T ' \\i v4C)^\0.4\v^ i A?. '4\; \-.pX\4 Unit Stress in Pou sands of Pounds i r k r < i ' ' ! ‘ V I i !/ \ f I 1 ' A . I 'i \ /V i / ! \ / "-A ; I ! ,'OOOCS 7 ( w I ' • A ! f ; i. A /' ■ V 3 — & N/ x-- " i V j: 1 1 i i i 4 ''a j V A /..V jcdi o o o ov: . X ..A v \ N •' 1 \ / i ^ f ' t , ,, I ’ r" \ i / I ' ! J / \ 7^JA \ / * i i 11 ; ~ ■ \ ?-;i COOZOi ,1 Y < '' V J. cdl 00,0 0V '5 A 1 / / / j// ; ?/.A' / o — 7 \ v ■ \ A > ' V V V ■ j>V V \ I \ ' \ : /■■ w' /•’• . A '--r-'TA —•--■/ v \ i, .«# 0007 . z * <0, V ov Oc Fd Ct 04 s - d£ Ofc cx os. 01 V\ ■:c\ 5 . •'*1 AST ’’ JL_. a^i ;<> 301 r Cji 0 ?!‘( ■ - *■ ' . \ * ■ • J |‘7 Q e/'o t/'-o l) O. 6 . .’rA.-OV^’ ^ ' •:. - O ' o . •;. . :■: .. .T- 7 - I CYi'W '.v;-^0 a vV ; . Ov_ \,4V' . A'-a 227 L *- j ,t • 00 • • 1 • % . s —>• 04 N 04 £ <3 & CD v6 04 * ~rr vO :<> o *>o n T S .11 «0 O o 04 vO t 00 <0 ro 04 T" ? i i $ ■3" 1 'lL j/[b S':, s 2 - 2 ^ ;/\0 3 &eQrr\ tV o. 22 , (o Z30 0 cam hfo 22 9 F'3 15 O' c? Qisssui wo ssa 2S 2 . Summary Beam No. Section V 6 rie-ly Age Maximum Load pounds 6 X/2 /n. Culindcr Tesfj Un if load pounds 3+irrup5. At +he Load of 200 ooo lbs Maximum grosses in 5 +irrups. 3hear- ingjtifcss tfie^Ul-H. Load Ib/in z Manner o-f Failure vSpdt mg in 5 T Section- al m* Jurfa ce /wa m 2 Calculat- ed Un .507 (,23 .546 790 •/ -2 61 218000 3790 1# •1 St 30 ooo 27 nan 34000 29 000 S3 6 .526 603 .566 7SI *t 2 25-1 ft v5firrup5 1 I'Spacinq 62 229 300 3788 II Vs 3067 1.963 5l4oo 30 ooo 27 000 23 ooo 24000 .532 .524 447 466 $22 */ -2 // r 3 ft 61 f j 214 500 4041 it 31 Ooo 2 8 ooo 2 &ooo 2700 c .603 54-4 .544 .524 769 •/ 22 . 6-1 T-shaped Ofirrups 4",5pacinq 62 262340 4 037 4 Vs .1 104 M78 4s Soo 32 Soo 3o duo 27 OOO 30 ooo .671 .619 557 >19 940 -2 n f J 6 o 245300 4331 n U 31 Ooo 26 ooo 28000 3f ooo 439 .5 3 6 .578 .641 390 fearing Fa.'lur 94$ r t '2 h // 60 26o ooo 4152 0 n 23 ooo 2 3 ooo 29 5oo 33 ooo ,£p 0 (? .416 481 (o30 932 '» 22 . 9-1 ’J&dranqulor j3en+up .Bars 62 225400 3931 'j -2 // n 60 213 700 4203 766 'r o>oa SZ/A % 4:< 7 / #9