FRANKLIN INSTITUTE LIBRARY PHILADELPHIA Class G 9...0^.2Book~P2 8 *^ Accession J. P.^.H ^ MATERIALS AND CONSTRUCTION PRATT MATERIALS AND CONSTRUCTION A TEXT-BOOK OF ELEMENTARY STRUCTURAL DESIGN BY JAMES A. PRATT, "Mech. E. director of the williamson free school of mechanical trades; member of the American society of mechanical engineers WITH 85 ILLUSTRATIONS PHILADELPHIA P. BLAKISTON'S SON & CO. 1012 WALNUT STREET 1912 Copyright, 1912, by P. Blakiston's Son & Co THE- MAPLE- PRESS. TORK- PA PREFACE. The purpose in compiling this text and set of prob- lems has been to present such studies in the elementary- laws of construction as will give the student an under- standing of the more simple formulas, and ability to apply such to every-day practice. The work is so arranged that it is available after the student period is past, as a hand-book of the necessary formulas, and principles of constructive details, which one must keep fresh in the mind when deciding on sizes and elements to be used in a certain kind of constt-uction. It will be noticed that no attempt has been made to cover any advanced engineering work, the aim being rather to offer such material as is essential to the proper training of the young mechanic, or to the person aiming to be- come an assistant to the superintendent; the work is thus seen to be available as very good preparatory material. The problems hold very closely to the practical; all those presented for design work are such as have come to the author's notice in one way or another, during an experience in engineering work covering fifteen years. The outcome of association and relations with young men just leaving school indicates that they have great difficulty in properly analyzing structures for the purpose of applying formulas taken in student work to actual construction. It is true no less in the vi PREFACE. study of materials than in other subjects, that if the student meets the complicated details of actual con- struction in his problems, and has the guidance of a capable and careful teacher, he will get a satisfactory understanding of the subject in hand, and one of value in all practical work. The formulas given for solution of problems coming under reinforced concrete are taken for the most part from "Concrete"^ by Edward Godfrey, M. Am. Soc. C. E. These formulas were first presented by Mr. Godfrey in Engineering News, being quite thoroughly discussed, both favorably and otherwise, all of which discussion appears in the book mentioned. The formulas are notable for their simplicity; at the same time they point one to a definite result to be obtained which is an important factor for the beginner. The author has compared the formulas presented, with others of much more complicated arrangement and the differ- ence in results is comparatively small. In dealing with this material we must keep in mind the fact that work is being done in an element which does not lend itself to refined calculations, and for which we have at best only very unsatisfactory formulas, if results obtained by their use are expected to checkup with experiment. Paper No. 1250^ by Gaetano Lanza, M. Am. Soc. M. E., is interesting and should be carefully read by teachers handling this subject with classes. Throughout the work the principles should be brought out by the teacher, in the solution of problems before the class. ' Published by Edward Godfrey, Monongahela Bank Bldg., Pittsburg, Pa. ^ Published by Am. Soc. M. E., 29 West 39th Street, New York. PREFACE. VII Attention is called to the figures, used as illustra- tions, which in many cases were made from free hand sketches. The purpose in such a plan was to put be- fore the student just the kind of a sketch which he will often receive, and from which his superior expects him to work without taking any time to make a fin- ished drawing, developing his analysis from the figures given rather than by means of the related parts of a plan as they appear on a working drawing. Such a method is quite common in some plants where at times very sizable pieces of work are constructed en- tirely from sketches. The illustrations used have pur- posely been made rather large, so that figured dimen- sions, and letters may be clear. If the book is used in a trade school, where the build- ing and manufacturing classes are in difiEerent sections, the text is so arranged that certain features may be omitted without breaking the continuity of the work; for example, the building classes would not take those features applying to fixture design, or gear teeth, in strictly trade work. Looking at the text it will be seen that this can be omitted, and no general feature of structural work must be sacrificed in so doing. Through- out the book credit is given to authors from whose works tables and notes are taken; much material is presented from the writer's notes gathered at various times, from many sources, and the many technical papers must receive a portion of credit. Special thanks are extended to Mr. George W. Bartlett, Ph. B., for notes given the author while under the direction of this gentleman as a cadet engineer. Attention of the teacher is directed to the resume of notation at the VUl PREFACE. close of the book, which saves the time of looking through the text, when a particular formula is taken up, for the purpose of determining the application of the letters introduced in the formula construction. Williamson School. J. A. P. TABLE OF CONTENTS. CHAPTER I. Elementary Principles. Page Stress, tension, compression, shear and deforma- tion discussed and definition developed — Stress and strain — Compound stress and stress units — • Sections of elements — Word formulas for unit stress — Elasticity, elastic limit, yield point, ulti- mate strength and resilience — Factor of safety; dead and live loads, loads producing shocks — Problems 1-18 CHAPTER II. Materials. Kinds used in construction — Names of the common classes of stone construction — Trade classifi- cations — Gravel — Bricks classified — Lime, sand and cement — Sieve classification — Concrete ; strength and proportion of ingredients — Timber and timber grading — Wrought iron, malleable iron, steel — Problems i9~33 CHAPTER III. Elementary Calculations and Properties. Moments — Positive and negative moments — Beams and methods of loading — Cantilevers — Pro- perties of sections — Stresses in a simple beam — ■ Rectangular and polar moment of inertia — Fiber stress — Consideration of moments in beam stress — Resisting moment — Determination of reactions — Problems 34~56 ix X TABLE OF CONTENTS. CHAPTER IV. Beam Design. Page Bending moments — Comparison of resisting and bending moment to determine beam safety — Shear in beams — Illustrative problem in beam design — Uniformly loaded beams — Design of cantilevers — Problems 57-70 CHAPTER V. Columns. Column formulas — Classification of formulas — Eccen- tric loading of columns — ^Application of column formulas — Problems . 71-85 CHAPTER VI. Torsion. Resisting moment of shaft — Horse-power related to shaft properties — Belting — Arc of contact discussed — Pulley crowning — Shaft couplings — Strength of gear teeth — .Stresses in small tool design — Problems 86-109 CHAPTER VII. Action of Elementary Forces and their Consideration in Design; Proportions of Knees and Counters. The triangle of forces — Counterbracing — Illustrative problem in beam design introducing knee bracing — Considering the weight of members in a structure — Distribution of load on a floor joist^ — Lag screws — Rope 110-122 TABLE OF CONTENTS. XI CHAPTER VIII. Riveted Joints. Page Study of method of failure — Joint classification — Arrangement of rivets — Joint efficiency — Design of joints — Problems 123-134 CHAPTER IX. Re-inforced Concrete. Steel in re-inforced concrete— Placing of re-inforce- ment — Materials for re-inforced concrete — Tieing of joints — Notes on setting forms — Design calcu- lations — Process of beam design in concrete — Design of re-inforced columns and footings — Illustrative problem in concrete column and footing design • • • • i3 5-i55 Tables and Data. Elastic limit of metals — Ultimate strength of metals — Fiber stress values for gearing • — Ultimate strength of woods — Factors of safety — Ultimate strength of brickwork, stonework, concrete and and terra-cotta — Standard sizes of timbers — Formulas for properties of sections — Properties of I-beams, channels, angles, T-bars, T-rails — Dimensions of bolts and nuts — Upset screw ends for round and square bars — Data bearing on rivets — Weight of materials — Column constants — Polar moment of inertia formulas — Strength of hemp rope — Resume of notation — Shafting speeds — Horse-power required to drive various kinds of machines — Holding power of lag screws — Relation of plate thickness, diameter of rivet, and size of hole — Weight of electrical machinery . 155-187 Index of Tables i8g Index of Subjects 19 1-196 MATERIALS AND CONSTRUCTION. CHAPTER I. ELEMENTARY PRINCIPLES. All structures which are met in practical work sus- tain a load of some sort, and if properly designed they are safe. Some structures are designed with care, that is, the load which will come on each part is calculated, and the part proportioned for this weight; in other cases the work is put up simply by judgment, the man who is putting it up has either built so much work of the kind, or made enough calculations so that design in detail is unnecessary. This latter is the method commonly used in putting up scaffold or small hoists used about a building or factory; when, however, a floor is tp be designed to carry a certain load, or a support for a tank is to be built, it is customary to make some calculations. If there are very large and heavy pieces of construction, the design is usually given to an engineer; when it is of the smaller order, and not complicated, some me- chanic or foreman about the plant or operation will do what designing is necessary. This latter is the class of work to which we will devote our attention, viz.: The design of smaller pieces of work about the plant or operation, which are not sufficiently complicated to make necessary the services of an engineer but which 2 MATERIALS AND CONSTRUCTION. do require a knowledge of elementary structural work. All structures sustain their load because of their power to resist breaking under it, and this resistance is offered in part by each piece which is used to build the construction. Again, each particle in each member must prove strong enough to sustain the load put upon it without being destroyed for further practical use. Stress Defined. — ^The load on the structure of course is from without, while the power to sustain the load is within the members of the structure, so we see that an external or outward load is being sustained by an internal or inner power of the material forming the parts of the structure; when the members of any build- ing are exerting such a power against an outward load they are said to be under a stress, from such a discussion we conclude that "Stress is an inner resistance to an outer force." Since all structures with which the me- chanic deals are under a stress, he should be familiar with its development in a practical way as outlined above. Any body which exerts a stress is changed in shape to a certain extent; this change may be so slight that we cannot detect it with the eye alone in many materials, but if a piece of soft steel or any other material which is capable of stretching considerably before it breaks is put in the testing machine and subjected to a heavy load, we can readily notice the difference in form. Deformation. — ^This changing of shape due to loading is technically known as deformation. In practical construction, of course, no appreciable deformation should be allowed. Deformation is a general term applied to any kind ELEMENTARY PRINCIPLES. 3 of change of shape; there are, however, different kinds of this change of shape, each having a particular technical name; e.g., we take a rubber band and pull on it with the hands, it is readily seen to become longer; in strength of materials this particular deformation is called elongation. Again, if we take a sponge rubber and press it between the hands, it can readily be seen to grow shorter; this deformation is known as "com- pression," and so on, each deformation being classified under the kind of stress producing it, as torsional deformation from a twisting force, shearing deformation from a shearing force. Stress and strain are two terms often used to mean the same thing in practice as indicated under the definition of stress as given above. By some writers, however, "strain" is used in the sense implied by the term "deformation," as already defined; this same meaning is also much used by practical designers, so the young man may hear the word strain used to indi- cate either an external load, an internal resistance to that load, or a deformation. As to the propriety of these uses we will not spend time in discussion; we simply have certain conditions of practice, and one should understand the possibility of varied meanings. In this book, however, they, as well as all other terms, will be used in the sense im- plied by the definitions. Kinds of Stress. — There are five different kinds of stress as commonly classified; three of these are known as simple or direct stresses, while the other two are compound stresses; from this statement we conclude that simple stress is the effect of a direct action in such 4 MATERIALS AND CONSTRUCTION. a manner that only one kind of stress is produced on the piece loaded; we will find that Tension : caused by a load which tends to pull apart. Compression : caused by a load which tends to push together,, and Shear: caused by a load which tends to cut off; all produce such a simple stress. Compound Stress. — ^When a load is placed in the center of a beam, which is supported at each end, we do not find the beam subject either to tension, com- pression or shear alone, but all three are present; the shear is considered as a direct stress, in practical prob- lems, but the bending effect is producing what is tech- nically known as a compound stress. This is made up of both a tensile and compressive stress as we shall see by analysis later, hence it cannot be classified as a simple stress, because more than one kind of effect is created by the action of the load. A torsional stress, that created by twisting, is another compound stress, composed of a combination of shear- ing and tensile stresses. Stress Units. — In practical work as well as in experi- ments, it is necessary to have some definite relation between the load applied and the area of the member sustaining it. The area of elements used in structures is usually taken on a surface perpendicular to a line running lengthwise through their center; thus in fig. I we have a view of a simple structural or building form known in the trade as an I-beam. The line A.B. is its center line, known technically as its longitudinal axis, and if we cut the beam off on a line such as CD. looking at the end pieces cut, they will appear as at ELEMENTARY PRINCIPLES. 5 la; and wherever we cut the beam, if we do so per- pendicular to the line A.B., we will get a figure looking like fig. 2 anywhere in the length of the beam; such a C Fig. I. figure is known as the transverse section, and the area of it is known as the transverse sectional area of the beam. If the area of a section at any one point in the length of the beam, or other element, is the same as that found when the section area is taken at all other 6 MATERIALS AND CONSTRUCTION. points in its length, the piece is said to be of uniform sectional area. In making calculations dealing with materials, a unit of area must be used for purposes of reference; this unit, under our system of measurement, is the square inch; suppose now that on the end of the upright I- beam, as shown in fig. i, there rests a beam which causes a load of 5000 lbs. to be thrown on it; if we are using an upright I-beam having a sectional area of 5 sq. ins. then for each sq. in. sectional area of I-beam there will be or 1000 lbs. of load, and each sq. inch of 5 beam is stressed to this amount, which is known as the stress per unit area. If then we divide the total load in lbs. on an element by the area of the element in sq. ins. we have the stress per unit area which is being exerted. It should be kept carefully in mind, from this point on, that the unit area is the square inch (commonly indicated thus: U") and the unit load is the pound (indicated thus, #). The same method holds for de- termining stress per unit area in all three of the classes of simple or direct stress. If put in the shape of a word formula we have for determining stress the fol- Total load in / lowing: . = Stress per unit Total area subject to load area, which formula may be applied in tension, com- pression or shear. We will find the above formula quite valuable in the study of practical problems since, if we look it over, we note the following: Total load in # = Total area subject to load X stress per unit area ELEMENTARY PRINCIPLES. 7 also Total load in # a. . i i, • ^ ^ i ^ — = Total area subject to load. Stress per unit area Elasticity. — ^The application of a load to an element deforms it to a certain extent as already mentioned ; if the load is not too great, when it is removed the piece will return to its original shape; this property of ma- terials — ^namely, returning to a first shape — after having been deformed is known as elasticity, and is possessed to a greater or less degree by all bodies. Assuming that we continue to increase the load, we will eventu- ally find a weight which will deform the piece so much that no return to original shape will take place. In this process of loading, if we had our material where we could accurately measure both loads and deforma- tions, we would find that as the loads were increased, the deformation would increase in the same ratio ; that is, suppose we apply a load of iooo# and we find that the piece of material has increased in length 1/16"; apply a load of 2000/, or 1000/ more than the previous load, and we find that the piece has increased in length 1/8", or for the additional 1000/ it has increased 1/16" again; that is, every 1000/ added causes an increase of 1/16" over previous total length; doubling the load here doubles the total amount of elongation; continu- ing to add loads of iooo# we will find that at some point instead of an increase of 1/16" for the added load the piece stretches more than 1/16", and another load of iooo# causes a still greater increase of length; if we had removed the load while an increase of 1/ 16" for every 1000/ load was in order, we would have 8 MATERIALS AND CONSTRUCTION. found the piece returning to its original shape ; if, how- ever, we had removed the load as soon as it was noticed that an added 1000/ caused an added lengthen- ing of more than 1/16" we should have found that the piece of material would not have returned to its original shape; these are facts brought out in testing various materials. We conclude, then, that there is a certain limit to the elasticity of materials, and our conclusion is correct. Elastic Limit.— The point at which the deformation of a material begins to increase more rapidly than the load is known as the elastic limit. In the discussion above, it was the point at which we first noticed that for an added load of 1000^^ the length increased more than 1/16". The elastic limits have been determined approximately for many materials and Table i will serve as a guide; it should be kept in mind that different authors give varied values for the elastic limit, those given being presented as a safe average. In the designing of structures, the allowable stress in material must always be a great deal less than the elastic limit, about 1/3 for tension and about 1/9 for shear, if the elastic limit is used as a basis for permis- sible load. Some designers are working on such a basis but the practice is not common, the reason, as one would infer, being that the elastic limit is not very closely determined. Yield Point. — ^When the elastic limit is reached, the material does not immediately lose all power of resist- ance and give way, but continues to sustain additional weight without a very marked increase in deformation, though there is a small increase; this condition will ELEMENTARY PRINCIPLES. 9 continue for a few additions of load, after which the material acts as though it had very little resistance, showing a very large deformation for each addition of load. At a point, usually not a great deal beyond the elastic limit, in steel, the specimen yields very readily to the load applied; the point where this yielding takes place is technically known as the yield point and in practice we often hear this term used. The Inter- national Association for Testing Materials specifies all structural steel as having a yield point of not less than 1/2 the strength of the steel, measured in Ultimate Strength. — ^After the loads stressing steel to its elastic limit, and further loading stresses to its yield point, it will still carry added weight though it may be stretching or crushing very rapidly; continually adding loads, however, will finally break the piece with which we are dealing; we have now placed such a load that the full strength of the material has been used; the load which causes breakage, or "failure" as it is more often termed, is known as the ultimate load, and the stress in exerted by the piece at the time of breaking is known as its ultimate strength per unit area. Table No. 2 gives the ultimate strength of the commonly used metals, and No. 3 that of the woods. Resilience. — If we deform a piece of material to a certain extent within the elastic limit, and suddenly remove the weight causing the deformation, the piece will spring back a certain amount, exerting some force as it does so. A very common device known to all is the spring railway switch, much used on trolley tracks; the car passing in one direction opens the switch, com- lO MATERIALS AND CONSTRUCTION. pressing the spring in so doing; as soon as the car passes, the spring closes the switch. The spring being compressed, a certain amount of work was done, which was given out again when the spring was allowed to act ; this work which is done when a body is free to act after being deformed is technically known as "resilience." Factor of Safety. — Our study of materials thus far should have brought to our attention the fact that a body may be variously loaded, but at a certain point it begins to change its shape to a dangerous degree ; in putting up any kind of structure we must keep well within the limit of safety of the material of which the structure is built. The ratio of the ultimate strength of a given material to the actual load in lbs. gives the num- ber of times which the load might be increased before the structure would be destroyed; for example, suppose we load a piece of yellow pine, one sq. in. sectional area, so that in tension it is exerting a stress of itoof. Look- ing at the table of timber strength, we note that this wood has sustained a load of 13,000/, at which load it broke; if we apply the rule just mentioned we have ^ =8 + 16 or the load could be increased more than eight times, before the piece would break. The number of times which the applied load might be increased gives an idea of just how safe the structure is, and is technically known as the factor of safety. The word formula for its value is: Ultimate Strength ^ .or = Factor of baiety. Actual load ELEMENTARY PRINCIPLES. II In using the Table No. 4 of factors of safety, it must be borne in mind that these are simply averages, differ- ent writers and designers not of necessity using them; each firm will usually advise one in this connection, but for general purposes those given will serve as a guide. Dead and Live Loads. — It is not customary to use the same factor of safety in all structures, as much depends on the kind of work which we require of it ; in designing tools about the machine shop, one would not use the same factor of safety as he would in designing a support for a large water tank ; two general divisions of loading are recognized, the dead load and the live load. If a load is applied gradually, and remains steady, it is known as a dead load; for example, a store room usually carries a dead load, so classified, because articles are commonly put there and remain for some time, the whole load not being thrown on all at once, but the room is gradually filled by placing a few articles at a time ; on the other hand, if a stand is designed on which a motor is supported, it will be subject to a live load, because of the comparatively sudden application and release of the same. Load-producing Shocks. — In Table No. 4 will be noticed entries for factors of safety to be used on struc- tures, subject to load-producing shocks; such a load is a variety of live load of a very severe nature, making necessary unusually large factors of safety. Drop hammers, heading machines, swedging machines, pile drivers, and certain types of conveying machinery come under this class, and their supports should be liberally proportioned. 12 MATERIALS AND CONSTRUCTION. NOTE. Most of the problems presented are questions of design which have been presented to the author from time to time. Answers are not given in all cases, but a sufficient number are given to serve as a guide to the student if the book is used for home study; it should be kept in mind that an exact numerical result is not the essential sought in the solution of a problem, but rather a familiarity with the methods of applying the information contained in the text to conditions of practice. In actual design two equally capable men may select slightly different sizes of stock to do the same work, hence the student should be certain that his laws have been properly applied, then select the nearest standard stock available, when he may rest assured that his design will successfully do its work. The teacher's attention is called to the fact that many of the problems may be used for other questions than those asked ; thus any problem which requires determination of re- actions, may later be used for beam design work, and any Such problems presented for steel and timber construction may also be used for practice in reinforced concrete. PROBLEMS. The ton is taken at 2 0oo#. 1. Describe the effect of tension, compression and shear when applied to a piece of material. 2. Explain your understanding of the terms: Unit stress, deformation, elongation. 3. Some pieces of wrought iron which were being tested in tension, sustained loads as given in the table below; the diameter at the smallest part of the piece is given in the column opposite the load applied as the test progressed; calculate the unit stress on the smallest part of the rod, for each load. ELEMENTARY PRINCIPLES. 1 3 Load. Diam. at smallest part. iooo# 1/2" i47o# 1/2" i96o# 7/16" 2940# 3/8" Ans. for entry No. 3. 13066 or 13000+ #U" 4. A second test similar in all features to that given in prob. 3 developed the following facts : Load. Diam. at smallest part. 656o# .425" 707°# -415" 75oo# .410" ySgo^ .400" 8i6o# .395" 86oo# .385" 8890# .378" What was unit stress in smallest part of rod under each loading? Ans. for entry No. y. Soogojfn" 5. The diameter of a screw used in a jack is 2"; when in use a section of this screw is subject to a direct compressive load of 3 T. What unit stress is exerted by the screw? Ans. igioiU" 6. A brick pier, laid up in lime mortar, dimensions of which are 8"X4", fails under a load of 32,ooo#. What is stress in pounds per sq. in. at time of failure? Ans. iooo#D" 7. A brick pier i6"X8", laid as mentioned in prob. 6, fails under a load of 25,6000^. What was unit stress in this case, at time of failure? Ans. 2ooo# □" 8. In testing some samples of brick in compression, it was found that they crushed under the loads mentioned 14 MATERIALS AND CONSTRUCTION. below; if a brick is 8 i /4" long and 4" wide, what was unit stress in each case at time of crushing? Whole brick crushed under load of 4ooo#. Half brick crushed under load of 367o#. Ans. 2 2 2.7# 9. Average practice permits a load of 6 tons per sq. ft. to be placed on common red brick laid in lime mortar; under such conditions what load should be placed on an 8" X 8" pier? Ans. 5052. 6# 10. In testing a piece of sand stone which was 4" square, it completely failed under a load of i3,6oo# per sq. in. What was total load on block at time of failure ? Ans. 2i76oo# 11. Two brick piers 12" X 8" of common red brick are laid up, the first in common lime mortar, the second in a mixture of lime mortar three parts, and Portland cement mortar one part. The first pier failed under a total load of i5o,ooo#, and the second under a total load of 290,ooo#. How much greater, in pounds per sq. in., was pressure on second pier than on first at time of failure ? Ans. 1458. 3# 12. A freight store house is supported on four piers of rubble masonry; the floor is to carry a total load of 75,ooo#. What should be the area of the piers? See Table No. 5 for allowable load on rubble. Ans. 6.2 Qft 13. 'In the tension test of a piece of timber, which was i" wide and 1/2" thick, loads of iooo#, 2ooo#, 3ooo#, 4000^ and 5ooo# were applied. What was unit stress on section under each loading? Ans. for 40oo# load. 8ooo# 14. What is the stress per unit area at time of failure, if a piece of 8"X4" timber shears off, across the grain, under a load of 96,ooo# ? Ans. 3ooo# ELEMENTARY PRINCIPLES. 15 15. A total load of 4o,ooo# was necessary to shear off a piece of timber 4" X 2", across the grain. What was unit stress at time of failure? Ans. 5ooo# □" 16. A piece of timber, 3"X2", placed in double shear, along the grain, failed under a load of 720o#. What was unit stress at time of failure? Ans. 6oo# □" 17. A piece of 4" square poplar loaded in single shear across the grain, failed under a total load of 7o,4oo#. What was unit stress at time of failure. Ans. 4400/ □" 18. A piece of spruce 6"X4" parted under a load of 7200/' acting with the grain; a piece of white pine 4" square" under the same conditions failed under a load of 40oo#, which wood sustained the greater load per sq. in. and how much ? Ans. Spruce; 50# □" 19. If the ultimate tensile strength of soft steel is 55,000^ □", what total load must be exerted when a threaded bolt the diameter of which at the bottom of the thread is .508" is pulled apart? Ans. iiiio# 20. An engine cyhnder weights three tons; it rests on four feet, each of which is 8" square. Determine the unit stress on the face of the feet. Ans. 23.4# 21. Upon investigation it is found that a section of a cast iron engine frame is subject to a tensile stress of 47o,ooo#. If the section mentioned has an area of 485 □", what is unit stress? Ans. 969 + 22. (a) A shear used in cutting off machine steel is working on stock 3" wide and 1/2" thick; determine the total load necessary to cut this stock. (b) Determine the same when the shear is running on 3 /4" round bars. Ans. to (a) 105000^ i6 MATERIALS AND CONSTRUCTION. 23. A punch is running on machine steel 1/2" thick, piercing holes 1" diam. What total load must be applied to perform this operation. Ans. logpoof 24. If a press is running on machine steel, 1/16" thick, and the perimeter of a piece being punched is 2", what total load must be exerted in forcing the punch through the steel? Ans. 875o# 25. A press is running on open hearth machine steel washers 1/16" thich, having a hole 1/4" diam. and an outside diameter of 1/2"; at each stroke of the machine four washers are pierced and blanked. What is necessary load to force the punches through the steel ? Ans. 4i2i2+# 26. What load will be necessary to stress a piece of cast iron 3"Xi" in section, to the elastic limit, the test being made in tension? Ans. i^^oo# 27. In testing a piece of cast iron one square inch section area, if we find the following relation existing between load and elongation : Load in pounds. Elongation in 1000 .010 2000 .020 3000 .030 4000 .040 5000 .050 6000 .060 7000 .078 8000 .105 9000 . 120 plot a curve, presenting these figures graphically, and on this curve locate the elastic limit of the material tested. 28. In testing a bar of wrought iron, i □" in area, if the relation between load and elongation is as given below, plot a curve showing this relation, and indicate the elastic limit of the material on the same: ELEMENTARY PRINCIPLES. 17 Load in pounds, Elongation in inches. S,ooo 10,000 15,000 20,000 25,000 30,000 35>ooo .025 .050 • 075 . 100 .125 .165 .210 29. A steel eye bolt i 1/4" diam. is to support a hoist; if we stress bolt to 1/5 of elastic limit, what load may be lifted? Ans. 95i6# 30. What load may be placed on a 3/4" steel eye bolt, if it is stressed to the elastic limit? Diam. at bottom of thread on such a bolt, may be taken as . 620". Ans. ii739# 31 A motor weighing i6oo# is being lifted by means of a steel eye bolt; the diameter at bottom of thread of this eye bolt is 3/4". To what portion of the elastic limit is the bolt being stressed? Ans. i/io (Approximately) 32. What load may be put on a brick pier laid in lime mortar, 8"X4", if we use a factor of safety of 5? On a i6"X8" pier? Ans. (on 2>''X^") 2.66 tons. 33. If a piece of round steel i" diam. is loaded in tension with i6oo#, what is the factor of safety against breaking? Ans. 24 + 34. If a brick pier i6"X8" is loaded with 2 5,6ooo#, what is factor of safety against crushing? Specify method of laying which you selected. Ans. Portland cement mortar 1.04 35. In the design of a piece of conveying apparatus a load of two tons must be supported by means of an eyebolt, what diameter must this bolt be at the bottom of the thread? Ans. .704 O. H. Steel 2 i8 MATERIALS AND CONSTRUCTION. 36. A motor weighing i2oo# is to be hung from the ceiling by means of four bolts; working with a factor of safety of 10, what should be the diameter of these bolts, assuming that a belt pull of 2oo# must be added to above, making total load coming on bolts 1400!? Ans. .^00 (at bottom of thread). For safety this will require a 1/2" standard bolt. 37. A tie rod on a crane supports in tension, a load of 5 T. If this rod is to be of soft steel, what must be its diameter? Ans. .892 {at bottom of thread). CHAPTER II. MATERIALS. Kinds of Materials Used. — ^The materials commonly used in constructive work are stone, gravel, brick, lime, cement, terra cotta, sand, concrete, timber, cast iron, malleable iron, wrought iron, steel and brass. Each of these is used in various styles; stone is used as rip rap, when it is taken without much attention to size or shape, and dumped as filling to form a base for a footing; it is also used in the form of broken stone, which is rock after it has been run through a stone crusher; stone dust, the material obtained by sifting the broken stone after it comes from the crusher; none of the stone mentioned thus far is "laid up," that is, placed by hand in any particular order. Rip rap is simply dumped and leveled off; broken stone is used in the same way, if used alone, and if in concrete, it is mixed by volume with cement and sand. Beside the above classes, stone is laid with varying degrees of nicety in about the following order: Grouted, which is stone piled up, and a thin mixture of cement and sand run over it (mixture of cement and sand is commonly one of cement to one of sand by volume, and enough water added so the whole will run very freely) ; this is often used in foundations and is satisfactory for com- mon work. Rubble is work built up of stones, somewhat irreg- 19 20 MATERIALS AND CONSTRUCTION. ularly and roughly placed; the joints are made up with either lime or cement mortar and the only dressing Fig. 3. — Coursed ashler with chamfered edges. Stones faced and laid to form joints or courses on the face, but backed up with common rubble; fig. shows face and section. Fig. 4. — Dimension stone work; all stone cut to a specified size. Fig. s. — Broken ashler; jointed Fig. 6. — Random rubble; no work edges; stones of various sizes, faced on stone other than breaking; it is the and laid up in joint; backed with roughest laid stone work; not built rubble; fig. shows face and section. in courses. As " coursed rubble " this same work is coursed on the face, but otherwise the same; fig. shows face and sectino. done on such work is breaking with a hammer. Ashler is stone work having a dressed face; these styles of stone work are shown in figs. 3 to 6. MATERIALS. 21 Trade Classifications. — ^In buying stone from the quarry it is designated as broken stone, rubble and dimension stone; broken stone, rip rap and rubble are usually sold by the ton, while dimension stone is pur- chased by the cubic foot. In ordering stone the size required relative to the purpose for which it is to be used must be kept in mind; this is particularly im- portant in reinforced concrete work, where the steel rods used as reinforcement are laid across each other, and if stone too large in size is used in the concrete, it will not pass between the openings left by the rein- forcing bars; this will be seen as a factor when the study of concrete footings is taken up. If an order is given for "run of crusher" broken stone, one may receive stone varying in size from i /8" to about 2 1/2"; this is satisfactory for the average small job, where no reinforcing is used; when a fairly uniform size of ma- terial is wanted it is customary to specify the size sieve through which it shall and shall not pass; a very satis- factory stone for general stock, and the average run of work, is specified as "passing through a i 1/2" sieve, but not through a i" sieve. Rubble may be ordered as "run of quarry" when one may expect to receive anything from the size of the fist, to fairly large, sized boulders. The specification of the Chicago, Milwaukee and St. Paul Ry, for common rubble requires stone not less than 6" thick, 16" long, and 10" wide, dimen- sions being approximate, and no dressing of the stone in any manner. Rip -rap calls for no stone less than 20# weight, and nothing larger than can be handled by one man. Dimension stone is ordered to the size required for any particular job. 22 MATERIALS AND CONSTRUCTION. Gravel is composed of small stones taken from sand banks, gravel pits, and earth; it may be ordered as run of bank, and will be assumed to include anything from a pebble i/8" to as large as the fist; if a uniform size is wanted, it, like broken stone, should specify sieve through which. gravel must and must not pass. There are a great many tests of stone work prescribed for the engineer; only in comparatively few cases are they used, however, and though a knowledge of them is im- portant to the engineer, it is not required of the me- chanic, or man in charge of the field work, as a general rule. Bricks. — There are many different kinds of brick, graded as to quality and shape; for the elementary study in materials we will deal only with those known as common bricks, which are divided into 3 classes, according to their position in the kiln; originally they were known only by their position in the kiln while they were being burned; as different kinds of kilns are used in modern practice, this term relative to kiln po- sition means less, and a classification as to hardness has become common; both methods of grading are given in the list following: Arch bricks | Are the bricks nearest the fire Hard bricks | burned very hard. ■n 1 1 . 1 \ Are the best general purpose Red bricks , . , „r 11 -1 11-1 bricks; usually of a bright red Well-burned bricks , I color. Are the bricks in the kiln far- Salmon bricks thest from the fire, and usually Soft bricks soft; used largely for filling in a wall. MATERIALS. 23 Bricks are purchased by the thousand, and classified as above relative to quality. Brickwork should not be fully loaded directly upon its completion, because the mortar will be crushed out of the joints; it should be allowed to stand at least three or four days, before any load is placed, and full load should not be put on in less than from one to three months; if large factors of safety are employed, from 15 to 20, the full load may be put on in a month, and greater time should elapse as factors are reduced. These features do not affect the accupancy of a building as a rule, however, as the interior finishing and fitting usually require much more time than is necessary for the brickwork to set. Lime, Sand, Cement. — Lime, sand and cement are used in mixing the mortars for constructive work; lime sells by the barrel or bushel; a barrel weighs 220/ (2 0o# of Ume and 2o# for weight of barrel), and if purchased by the bushel, two and one-half bushels weighing 8o# each are regarded as equal to one bbl. Lime mortar is mixed one part lime paste to two parts sand (though amount of sand is often increased to 21/2 or 3 parts, giving a weaker mortar, which is satisfactory for certain classes of work) ; lime paste is made by putting lime directly from the barrel or bag in a box which is fairly water tight and flood- ing with about two parts water, by weight, to one of lime. A barrel of lime should make about 8 cu. ft. of paste. Sand. — Sand sells by the ton, and is classified as "pit" or "bank" sand, when it is taken from a sand bank, and as "bar" or "river" sand when it is taken from the sea shore, river beds, or shallow places in 24 MATERIALS AND CONSTRUCTION. water; sea sand should be washed thoroughly, but as this adds to the cost, it is frequently neglected. Sieve Classification.— Sand should be screened before using; for common brickwork it may be run through a sieve having i6 meshes to the sq. in. (known as a No. 4 sieve, because it has 4 meshes per inch of length, and 4 per inch of width) ; for rubble work sand is not screened as a rule; if special requirements are made, a screen of 3/8" mesh is often used. Occasionally one finds a locality where sand is sold by the load; a one-horse load is equal to about 22 cu. ft. while a two- horse is about 50 cu. ft. Cement.— Cement is sold by the barrel or bag; four bags usually equal a barrel; there are a number of different grades, but the two general classes are Rosen- dale or natural cement, and Portland cement; these two terms refer to the method of manufacture, Port- land being produced by a process different than that followed for Rosendale; this latter is commonly satis- factory for foundation work, but is not to be recom- mended for reinforced concrete. Terra Cotta.— Terra cotta is a kind of brick, being much used in modem construction; it is very satis- factory as a fire proofing material, and is used a great deal for exterior finishing purposes in modern buildings ; usually sold according to specification, the various forms being catalogued, the process of manufacture is one of forcing a plastic mass of clay, through or into a mold, and then baking; it is put on the market in dense, semi-porous, and porous varieties; the dense variety should be used in places where the work is exposed to much moisture, while porous and semi- MATERIALS. 25 porous goods may be used in dry places. Nails may be driven in the porous varieties, which is an advantage when it is desired to set moldings, etc.; terra cotta should be loaded only in compression, and Table 5 gives values in this connection which may be used as a guide. Concrete. — Concrete is really an artificial stone, made by mixing cement, sand and broken stone, cinders or gravel in the proper proportions; the single term "aggregate" is used to indicate the stone, gravel or cinders used in the mixture, hence when we hear the expression 1-2-4 concrete, it means one part cement, two parts sand, and four parts aggregate have been used to make the concrete mentioned. If the aggregate used is broken stone we have "stone concrete;" if gravel, it is spoken of as "gravel concrete," and if cinder, we know it as cinder concrete. Mixing Concrete. — Concrete is mixed by hand on a board for small jobs, and by a mixer for large ones; most of that which is now being put up is known as "slushed" concrete ; in mixing this it is just wet enough when mixed so that it will not remain in a pile, but runs slowly; this concrete is dumped into the forms set as described below, rammed with a rammer, and if smooth-face work is wanted, a shovel is worked up and down, next to the form, thus bringing the finer particles to the surface, and producing a satisfactory appear- ance when the form is removed. Forms. — ^The forms used should be of heavy material, well braced; fig. 7 gives a general idea of a form set up for a wall and at A is shown the method of bracing; if the forms are made of i" stuff, such braces should 26 MATERIALS AND CONSTRUCTION. be about i8" or 2 ft. apart, of 2^X4" material; if the form is i 1/2" plank, distance between braces should be about 30" and 2^X4" stuff for braces; for rough work the forms need not be finished, but if a good appearance is desired, the boards should be planed on the side lying next to the concrete, and edges matched as shown in fig. 7 at M; spruce and hemlock are satis- FlG. 7. factory for such forms, though other lumber may be used; in setting, one face of form should be set plumb, true, and braced as shown in figure; distance pieces should be inserted as shown, so that the required thickness of wall is obtained, and the other form tied to the one set, by means of lag screws, passing through the form and into the distance pieces; such distance pieces should be placed about every 3 or 5 feet in height, between every pair of battens or braces. After the forms are filled, and concrete allowed to remain MATERIALS. 27 about one or two weeks, all timber may be removed, the distance pieces driven out, and the holes filled with concrete, leaving a smooth wall; distance pieces may be about 2" square. In mixing concrete on a board the aggregate should first be thoroughly wet off the board separately, from the sand and cement ; the sand and cement should then be thrown on the board in proper proportions, and thoroughly mixed in the dry state; the aggregate is then thrown in, and water added, the mass being con- stantly turned over and worked till the desired con- sistancy is obtained. If mixing is done with a machine, the materials are put into the mixer as measured, and about 6 gals, of water for each whole bag of cement is poured in; when mixing on a board the condition of the concrete can be observed, and water stopped when the required stiffness is obtained; in the mixer, however, all must be put in together; after a batch is run through, it should be looked over, and if too wet the water reduced, or increased if too dry; amount above men- tioned gives a fair average for general work; in order that the concrete may be thoroughly mixed, the machine must run a specified length of time and the requirement of the National Board of Fire Under- writers is to the effect that the mixer shall make 25 complete revolutions. Proportions of Ingredients in Concrete. — ^The amounts of materials used in concrete vary, but the following, taken from "Godfrey's Concrete, gives an idea of the proportions used in practice. 'Published by Edward Godfrey, Am. Soc. C. E., Monongahela Bank Build- ing, Pittsburg, Pa. 28 MATERIALS AND CONSTRUCTION. Purpose. Walls and heavy work, Reinforced concrete, Cement. Sand. Aggregate. The aggregate suggested is broken stone or gravel; cinders, if clean, are a satisfactory aggregate for founda- tions of light buildings where great loads are not carried. Reinforced concrete is of sufficient importance to deserve a section by itself, and will be taken up as a later study. Strength of Concrete. — In putting up concrete, it must be borne in mind that this material does not attain its full strength immediately, but should be allowed to stand from one to two months before it is loaded ; the ultimate strengths given in Table 5 are for a cinder concrete 3 months old, of a careful mixture; no higher values are given because of unreUable con- ditions of mixing in practice, and inability to control to a nicety the placing in forms. Timber. — ^Timber is used very extensively in all the trades; it is sold by the board foot; the patternmaker uses a great deal of white pine for pattern work, while in building construction hemlock, spruce, yellow pine, and oak are used. The strengths of the various woods are given in Table 3 and factors of safety in Table 4; lumber should be fairly free from knots and cracks for structural work, and is more satisfactory if well sea- soned, since it is only about half as strong when wet as when dry, a fact to be kept in mind when using timber in constructive work, as it is not always possible to purchase seasoned material at short notice. In selecting sizes to be used, one should choose a standard size of material, since such as do not come MATERIALS. 29 within this class are sold at an advanced cost ; fractional lengths should be avoided, and Table 6 is compiled to cover these requirements; if material 11 ft. long be ordered for a job, we will find it necessary to pay for that which is 12 ft. long, since this is the common practice on the market. Grading of Lumber. — Lumber is graded according to specific trade terms, each of which has a distinct meaning on the market. "The standard classification of Yellow Pine Lumber" may be obtained at small cost from the secretary of the Yellow Pine Manufacturers Association at St. Louis, Mo. and the "Rules for Meas- urement and Inspection of Hardwood Lumber" from the National Hardwood Lumber Association, 1012 Rector Building, Chicago, 111. A copy of each of these pamphlets, which are copyrighted, should be in the teacher's hand, who may give notes. Each student may obtain a copy at a cost of a few cents. Metals. — Cast iron, wrought iron and steel are made from iron ore; the methods of manufacture are a very interesting and profitable series of studies in connection with the subject of chemistry; in this work only their application to structural work, of one sort or another, is taken up. Cast Iron. — Cast iron is much used in the machine industry, the heavy beds and supporting parts of nearly all kinds of machines being made of this mate- rial; it is cast in the desired form by making a sand mold from a pattern, and pouring the iron which has has been melted into this mold; the work of the pattern- maker is the making of the structure which is placed in the sand to form the proper shape of mold, that of 30 MATERIALS AND CONSTRUCTION. the molder is to place and remove this pattern so that he has a hollow shape, properly vented, into which iron may be poured in order to get a casting; this work of pouring also falls to the lot of the molder; the ma- chinist does the necessary finishing of the casting, in order that it may serve its proper purpose in the design, cast iron is also used as beams, braces, etc., in building work. In the use of this material for shop purposes, as in jigs, fixtures, etc., it is common practice to make a few necessary calculations for the parts sustaining the greatest load, and design the remainder of the device from experience, and in relation to the requirements of each particular case; cast iron is not so convenient a material for design purposes as steel, because it is not put on the market in the same standard forms, with tables of properties published in hand books. Table No. 2 has entries giving ultimate strength of cast iron in tension, compression and shear. Wrought Iron. — ^Wrought iron is used a great deal in forgings, but is not very common in structural work, average strengths given in Table No. 2. Malleable Iron. — Malleable iron is a kind of cast iron; when first taken from the mold in the foundry it is very hard and brittle; it is treated by heating in an oven, this heat treatment being known as "anneal- ing." After being subject to this process, castings in this material are quite strong, and permit of some bending, so are available for use in places where they are apt to be subject to bending slightly, or to shocks and more satisfactory results will be obtained than may be expected from ordinary cast iron, or gray iron, as the material coming directly from the foundry MATERIALS. 31 is known. Malleable iron is produced from a pig iron of different variety than that used for gray iron, which is another reason beside that of foundry treat- ment, for its increased tensile strength. Table No. 2 gives values which will serve as a guide in using this material. Steel. — Steel is produced from pig iron, which in turn is made from iron ore, by a number of different processes; it comes to the user as bar steel, sheet, and structural steel; bar stock is to be had in rectan- gular, square, hexagon, octagon, and round forms; as to material classification there are offered open hearth, cold rolled, crucible, and tool steel. Open hearth steel is a soft steel, commonly used for screws, bolts and general run of shop work; cold rolled is much used for shafting; crucible machine steel is used in machine construction for spindles, and similar work where a rigid reliable material is wanted for accurate work. Tool steel is a different material and as its name indi- cates is used for making tools ; all cutting implements are made of some grade of this material, which can be hardened, and tempered; sheet steel, manufactured by the open hearth process, is used for tanks, drums, boilers, receivers, etc. Structural steel is rolled to a great variety of shapes; in designing, some one or more of these must be used, which are furnished as standards on the market; the tables of properties introduced in this work are largely from the Cambria Steel Co.'s hand-book^ compiled by George E. Thackray, C. E., and are sufficient for the purpose which this book is intended to serve. ' Published by Cambria Steel Co., Johnstown, Pa. 32 MATERIALS AND CONSTRUCTION. Meaning of Terms used in Steel Manufacture.— The terms "open hearth," crucible, and Bessemer refer to different processes for making steel; they determine the three fundamental classifications of steel as used at the present time. Tool steel is a refinement of crucible steel, of which there are a great many grades, adapted to particular trade needs. The ultimate tensile strength in fU" is given in Table No. 2 for several grades of steel; the ratio of compression and shear to the tensile strength may be taken the same as will be found by comparison of these stresses in Table No. 2; Bessemer, cold rolled, and open hearth are regarded as soft steels, while crucible and tool steels are regarded as hard steels. In the use of all tables of strength given, it must be remembered that values are approximate ; wide varia- tions are often obtained in testing different samples of same materials, hence different authorities give varied quotations; again, the same class of materials put out by different manufacturers will differ widely, so that for general use one can but take an average, and depend on the factor of safety for a margin. The values of ultimate strength given in all tables are conservative. QUESTIONS. 1. Describe rip-rap, rubble, and ashler. 2. What do you understand by the specification "run of crusher" stone? 3. Give your specification for gravel, assuming that you wanted stock the grains of which are between 1/4" and 1/2". 4. How are bricks classified? What is mortar and for what purpose is it used? MATERIALS. 33 5. Write a brief composition, giving some information on stone, bricks, sand and cement. 6. A concrete wall 2 ft. thick and 6 ft. high is to be built; it must be smooth on both faces; give your specification for the concrete mixture, design the form complete, present- ing sketches, and write out your directions for placing the concrete. 7. What is the general difference between malleable iron and cast or "gray" iron as you understand these materials? 8. Write a brief composition on the different kinds of steel. 3 CHAPTER III. ELEMENTARY CALCULATIONS AND PROPERTIES. If a wrench be placed on a nut and one pulls at the end of the wrench, the nut will be turned a certain amount; this effect of one's strength on the nut to turn it about a center, through the medium of a wrench, is known as the moment of that strength relative to the center of the piece on which the nut is placed; if we regard our strength exerted simply as a force, we have in the combination described a moment effect. In actual work we have many applications of this effect, which is carefully analyzed in both physics and mechanics; we will briefly study it for purposes of application in the use of materials. Value of a Moment. — ^Assume that the wrench used was 12"= I ft. long, and that a force of 15 lbs. was exerted on it; the moment of the force relative to the center is the load multiplied by the length of the lever; this result will not give a single value of lbs. or feet, but a combination of both pounds and feet, and the single unit for moment measure will obviously be the pound foot or the effect of one pound acting through a lever arm one foot long; following instructions given above to determine numerical value of the moment tending to turn the nut we have : Load X Length of lever = Moment. 15/ X I ft. -15 lb. ft. 34 ELEMENTARY CALCULATIONS AND PROPERTIES. 35 The word formula just given will enable us to deter- mine any element of a moment combination, that is, load, lever arm, or moment, providing we know the other two because by inspection we see that : Moment Load — Length of arm Moment Length of arm = — — Load If we apply these simple formulas to the problem we have just been studying it will be found that results balance ; these principles apply the same when several forces act on a lever arm, as when but one acts, the total effective moment being equal to the sum of all the individual moments ; to illustrate, suppose we have a windlass on which two men are pushing, one at the end of the bar, and the other 8 ft. from the center; the individual moments are (fig. 8) if a man can pro- duce an effect of 15^ : 15 X 12 = 180 lb. ft. 15 X 8 = 120 lb. ft. 300 lb. ft. total moment. Positive and Negative Moments. — ^Moments are classi- fied as positive or negative, relative to their produc- tion of rotation in the same or opposite direction from the hands of a clock. Moments are said to be positive when they produce rotation, relative to their center of reference, in the same direction that the hands of a clock move; commonly known as "clock- wise"; they are said to be negative when the rotation which may be produced is opposite to the above, 36 MATERIALS AND CONSTRUCTION. commonly known as "counter clockwise." A study of fig. 8 will make this clearer; suppose we have the same windlass mentioned above, with two men push- ing on it, a little study shows us that the men who are pushing are creating a positive moment, because arrow K which indicates their direction of movement shows it to be the same as the hands of a clock, relative to center A. The load, however, creates a moment Fig. 8. in a direction opposite the hands of a clock relative to center A, hence is negative. This principle, though simple, should be thoroughly mastered, as its analysis is sometimes confusing when applied to beam loading. Beams and Methods of Loading. — There are two general types of beams used in elementary construc- tion, the simple beam and the cantilever; if we put up a piece of construction as indicated in fig. 9, we have what is commonly known as a "bent"; the main members are two posts or columns, with a beam laid across them, the beam (known particularly ELEMENTARY CALCULATIONS AND PROPERTIES. 37 as a "header" in such a case) is fastened to the posts. Such a design is the simplest possible piece of building construction, and a beam supported in this manner is known as a simple beam ; we are lead to define a simple beam, then, as a beam supported at its ends only. If we place on such a beam a load as indi- cated by the arrow yl, it is spoken of as a single concen- trated load ; such a load would be imposed by a hoist at- tached to a beam; there may be several concentrated loads, but the general method of calculations for such loads does not differ, whether there be one or several, as f Fig. 9. Fig. 9A. Fig. 9B. will be seen later. If instead of loading with either single or several concentrated loads, a general load is applied evenly for the whole length of the beam, we have a uniformly distributed load; such a condition obtains when a joist supports a floor. The unit used in connection with the uniformly distributed load is the weight per foot of length; e.g., if a beam is 10 ft. long, and has a total uniform load of 2500^, then the load per ft. of length is ~ °°= 250^ The simple beam is of very common application in the trades, being subject to both uniform and concen- trated loads. 38 MATERIALS AND CONSTRUCTION. Cantilevers. — beam set as indicated in either gA or B is known as a cantilever; such a beam may be loaded in the same ways as a simple beam; small cranes are very often built as cantilevers, and gear teeth are always considered as cantilevers. Properties of Sections. — Before we can take up any actual calculations, dealing with the stresses in struc- tural elements, we must study certain properties, of which we should have a working knowledge. Fig. lo represents a beam sustaining a single concentrated load, and for clearness the load is represented as being E 3 Fig. io. applied by a sharp-edged member, while the beam is being supported by two such sharp-edged posts. In practice the center lines of the columns are treated in calculation as though they were such sharp-edged posts, and dimensions for moments, etc., are taken from these center lines. The load on the beam causes a certain stress in the posts which support the beam; this stress of course is in a direction opposite to or against the load, hence is technically known as a reaction. ELEMENTARY CALCULATIONS AND PROPERTIES. 39 Stresses in a Simple Beam. — ^When a beam is loaded as shown in fig. 10, the top face D. E. becomes shorter than it was originally, while the bottom face F. G. becomes longer; somewhere in the beam, however, is a line which neither becomes longer or shorter, but retains its original length, providing we do not exceed the elastic limit of the material used as a beam; such being the case the stress above this line, which does not change length, must be compression, since it tends Fig. II. to shorten; below this line it must be tension, since it tends to lengthen. In addition to the above stresses of tension and compression, the beam is subject to a shearing action, tending to cut it ofE; such action is greatest at the supports, and when actual design is taken up we will find it necessary to make due allow- ance for it. At the line which we are discussing as remaining of a fixed length, there must be neither tension nor com- pression, because if there were, the line must change, 40 MATERIALS AND CONSTRUCTION. SO because it is not affected by the stress on either side of it we know it as the neutral line simply because it is not affected by the actions in the beam. The beam we have been studying thus far is a very thin piece as is indicated by the figure; really it is not a beam but a thin section of material; if we put several such together, we will have a beam, rectangular in cross-section; each of these thin beams will have a neutral line, and several such neutral lines, of as many thin beams, form the neutral plane a-b-c-d, fig. ii, of the large beam; at efhg in fig. ii is represented a sec- tion cut through the rectangular beam we have been studying; this section intersects the neutral surface in a line /. K. which is an axis of the section ; and since it is an intersection with the beam neutral surface, it is known as the neutral axis of the section. If we study the figure, we will question the necessity of the beam resting on the face zyxw, and the reason why it may not rest on the supports by means of the face u, y. x. t. will be sought; it may rest on either face, in fact a beam may be placed in any position desired, if it rests as shown in fig. ii, then /. K. is regarded as the neutral axis of the beam section; if we decide to let it rest on face u. y. x. t., then the same process of reasoning, which we have applied, will indi- cate that m. n. will be the neutral axis of the section. The axis used in calculation is always that one which lays perpendicular to the line of load. Thus in fig. ii, if the load is in a line parallel to L. 0. we must deal with neutral axis /. K., while if it is parallel to M. N. we will deal with neutral axis m. n. The location of the neutral axis for those shapes ELEMENTARY CALCULATIONS AND PROPERTIES. 4 1 most used is given in hand-books, and such as are needed for the work covered by this book are given in the tables of properties; it is necessary however to become acquainted with the method of its determina- tion and so we will study briefly the process of neutral axis location for those common shapes which are most used; for practical purposes we may consider the neu- FlG. 12. tral axis the same as the gravity axis, and hence if we find the center of gravity and pass a line through it perpendicular to the load line and in the plane of the section we have the location of the neutral axis. We will assume the section cut from cardboard and strung by one of the edges, which is parallel to the gravity axis we wish to locate, to a wire, let this edge be 42 MATERIALS AND CONSTRUCTION. D. E. fig. 12. Now as long as we hold the cardboard up with the finger it will remain in place, but when the' finger is removed, the piece will swing down and simpy hang on the wire; if the wire were strung through the gravity axis, the cardboard section would just balance on the wire; to find out where the line is which allows the cardboard to balance, we will divide the section into a number of small parts ; we know by inspection that if we had a section D. E. F. G. its gravity axis would lay half way between the two edes, and if we have a card like H. I. J. K. the same holds true; looking over the various parts which make up the whole section we are studying, we see that the gravity axis of D. E. F. G. is i" from the wire, while that of H. I.J. K. is 4 1/2" (2" + 2 1/2") from the wire; now this cardboard has weight, proportional to its area, being the same thickness throughout, hence we may use the area as weight for the calculation of moments. From our previous study of moments we may deduce the fact that the moment of the combined area D. E. J . K. G. D. about the wire is the same as the sum of the moments of the elementary areas added together; the only thing we do not know is the lever arm of this combined area relative to the wire; since the sum of the elementary moments must equal the moment of the whole area, and as we have both weights and lever arms of elementary areas, we may easily solve for the distance from the wire at which the weight of the whole area acts as follows: ELEMENTARY CALCULATIONS AND PROPERTIES. 43 [ (~0 'T- C "F') Hi 1^) *T ™ ') ] = ^ ^ \ \ ■>! ^ [(6X2) X d")] + [(5X3) X (4-5")] = Total area, times, lever arm of total area 27 X unknown making these calculations we have [(i2Xi(]+[(isX4.s)]=27s: or jc= 2.96" The distance from the wire at which the whole weight of the area acts is 2.96"; we also have as a truth in mechanics the fact that the whole weight of any section will act thfough its center of gravity, hence the line 2.96" from the wire is the gravity axis relative to the edge of the section with which we are dealing, and corresponds to the distance from the neutral axis to the outer face of the beam, or distance from neutra axis to outer fiber as it is technically termed ; this distance will be represented in the formulas we will use by "c," and when the neutral axis is not equally distant from both faces of a section, the greater distance is used as the value of "c." The same method outlined above may be applied to the location of the gravity axis relative to any one of the section edges; if it be used relative to K. J., we will get the same result as already found {Q. E. D., using other edges, and various sections shown in fig. 13). The various forms shown in fig. 13 are classified as follows : A is a T section B is a channel section. C is a channel section with rib. The dotted lines indicate the manner in which the 44 MATERIALS AND CONSTRUCTION. designer enlarges the outer parts of the pieee, and reinforces the corners to prevent breakage, but he does not consider these additions when finding gravity axis, simply using the block form as indicated by the full lines. Moment of Inertia.— This is one of the properties of constructive elements which must enter into all calculations of strength when a beam or column is under consideration; the study of this property is taken up at length in mechanics, but our use of it in this work '/ ^ V//niy^ (least side) ^ 5 x (least side) ^ 5 will go into 276 about 55 times and will not seriously affect our results, as we will see later that we will have to use a "commercial size" varying somewhat from -the actually calculated size, so we will make the can- cellation for convenience, and we will have 8o MATERIALS AND CONSTRUCTION. Ax I200 lOOOO == 55 I + (least side) 2 In practical solution no effort is made to work this formula to determine unknown quantities, but different sizes are "tried out" the same as already mentioned in connection with beams; first let us try a 4" sq. post and see if the equation will balance; if it does, then the following must be true: 16 X 1200 10000 = , 55 ' + x6 but when we work out the right-hand member of this equation we find that it equals something over 4000, much less than 10,000 which it should be; we conclude then that 4X4 is too small so we will try the next larger "commercial size" in square, see Table 6, which is 6"X6", and the values then become 36 X 1200 10000 = (.Aj , + 55 36 and our right-hand member works out to about 17000, or more than 10,000, so 6X6 is satisfactory; a smaller post would serve, but if we purchase "out of standard" we must pay an extra price, which is usually more than the cost of a stick of standard size, which is somewhat larger than we really need. The solution for any type of column studied thus COLUMNS. 8l far is carried out in exactly the same manner as above, using the proper formula for end classification, provid- ing there is no eccentric load. The following problem will illustrate the method of solution for eccentric loading: A piece of yellow pine is to be "built in" as described in the preceding problem, carrying a load composed of lo.oooyf direct from a header, and a bracket is bolted on, as shown in fig. 23, which carries a countershaft bearing, throwing a load of 600^ on the bracket as shown; select the proper size timber. First design the column as though it were carrying the entire load both eccentric and direct as a direct load, using the result thus obtained as a basis for the design of columns with eccentric load, and in the problems used as illustrations, such a plan will be followed. The total load, direct plus eccentric, in the problem with which we are dealing is io,ooo# + 600/= 10,600/, hence if, when the sizes of a selected stick are intro- duced in the right -hand member for safe load in formula A this member works up to a value of more than io,6oo#, the piece is safe; we have already seen that a 6X6 works to more than this value in our illustration for a directly loaded column, so we may use a 6 X 6 as a basis for our work; since 6X6 is quite a little too large for the direct load, it is possible that it will be satis- factory for the case carrying the countershaft, so we will make calculations. First we must determine the value of Su by use of formula No. 6. We used a safe direct compressive stress of 1200/ in our first solution which is taken as the value Su in formula 6, then 6 82 MATERIALS AND CONSTRUCTION. 20 1 20" = length of column, and 6" is its breadth; working this value we have 5^ = 960/ as the safe figure to be used in formula 5. For numerical values in this formula we have: Su =96o# Pm = I0600# A =36" d = .4 c =3" half width of trial post bh' I = . See Table 8. 1 2 6X6X6X6 or / = ■ = 108. 1 2 Introducing these values in formula 5 we have: 10600 10600X.4X3 Su = — 7- ^ ^ = 420 36 108 as we see, we may have a value of 960 for Su, it is evident that the 6X6 is amply safe, and we have a wide margin; as an exercise the 4X4 might be tried, and we will find that it is too srnall for the load im- posed. PROBLEMS. I. A yellow pine post 10 ft. long is to carry a load of 5ooo#, determine its size; the post is solidly built in both at top and bottom. Ans. 4X6 COLUMNS. 83 2. What size steel I-beam would you use to carry the load mentioned in prob. i under the same conditions? Ans. 3" medium 3. If a beam rests on two columns, 12 feet apart, such a beam carrying a total uniform load of i5,ooo#, what size steel I-beams may be used as columns to support this beam, such columns to be 12 ft. long and simply set on the foot- ings, no fastenings being used at joints. Ans. f light Fig. 24. 4. A bent is to be constructed; the header is to be 4 ft. between supports, and posts are to be 12 ft. long. A load of one ton is to be supported at the center; design steel columns. " Ans. 3" light 5. A tank contains an amount of water which weighs 5ooo#; it is supported by means of brackets on four columns, which are 5 ft. in length. Select proper size timber for the column. Ans. 4X4 6. Fig. 24 presents the construction of a transformer stand. Design the headers B and columns C all to be built of timber. Unless otherwise stated all joints are assumed to be solidly fastened. COLUMNS. 85 7. Fig. 25 shows the main supporting system for a plate bender. Design the cross-beams A, header B and columns C, the whole construction to be of steel. 8. Fig. 26 shows the construction used at the top of a building to support a water tank, which is to hold 3000 gals. Select the proper size slings S, columns C, and headers B, the entire construction to be of steel. 9. Design a support for a tank to carry 5000 gals, of water, presenting sketches showing the construction. It should meet the following specifications : Bottom of tank must be clear of floor 12 ft., supported by means of four columns, and the entire structure to be of steel. 10. Fig. 24 presents the desired construction for a movable shop crane. Select the proper sizes of various parts using materials indicated in the figure. CHAPTER VI. TORSION. The greater portion of our work under this heading will have to do with shafting, and, as we shall see later, it is important in making calculations to know the number of revolutions per minute that a shaft makes ; in some cases we may have to select the speed; Table No. 2 1 may be looked over at the beginning of this subject, and serve as a general guide in the solution of problems as well as in design. When a shaft is subject to a twisting or torsional effect, there is created a shearing stress, within the element; a brief study of any body which is being twisted, as it is commonly expressed, will show that we have neither a case of tension nor compression as an elementary stress because in torsion the fiber is not pulled apart, nor pushed together, but, instead, the particles composing the piece slide by each other thus giving evidence of shear; hence the strength of the material under discussion, in shear, is the property on which formulas for torsional strength are based. Materials are subject to torsional stress in all kinds of shafting, and as such equipment is extensively used in manufacturing plants, the young mechanic should be familiar with calculations applied to its design. The load applied to shafting is not commonly given 86 TORSION. 87 in pounds as has been the case with all of our previous work, but in horse-power, because shafting is used to transmit power, and the practical English unit for such is the horse-power ; we must have in mind the fact, how- ever, that a horse-power is but a certain number of pounds moved a number of feet, and this being true we readily see how and why it is preferable to state the load on shafting in horse-power if we study the following : Fig. 28. Fig. 28 represents a drum and shaft, with a handle, which may be used when properly supported to raise a weight; now the shaft A must transmit the necessary power to do the raising of the weight; we have here, then, a simple case of moments, in which the lever arm of the lifting power P is equal to B, taken in inches, and lever arm of load W is equal to the radius of the drum, also taken in inches, or C as shown on the sketch; the diameter of this drum is twice the radius or 2C and 88 MATERIALS AND CONSTRUCTION. circumference is 2tiC\ if now we turn the drum once around we will move the weight upward a distance equal to its circumference, assuming the weight to be attached to the drum by means of a rope, or 2716" inches, and the work done will be equal to the weight, multiplied by the number of inches moved, or W times 27iC inch- pounds, that is, W27tC in.-lbs. If instead of making but one revolution we turn the crank a number of times the work will be equal to that found above multi- plied by N or 1S!W2tiC in.-lbs. We recall the statement that the shaft must transmit all power necessary for lifting the load, and also the moment created by the load is WC; now in order to be safe the shaft must be able to resist this moment WC without breaking, so we have a case similar to the beam, in which an internal resisting moment of the shaft must be equal to or greater than the external moment of the load; the resisting moment of any shaft is determined by the use of the following formula: 5 / Resisting moment = (g) in which the following notation is used : 5s = Safe shearing strength of material used as shaft /p = Polar moment of inertia. Ys = Radius of shaft in ins. Since we have seen above that NWC2tz equals the amount of power necessary to move the load a certain distance, and if a shaft must transmit the power to move this load, and we also know that the shaft- resisting moment must equal the load moment, then TORSION. 89 the introduction in the above formula of the value of the shaft-resisting moment for the load moment, will give us the amount of power in inch-pounds trans- mitted by the shaft in doing this work or 5 I ^-2 7r = inch -pounds of work. (9) ra The number of turns N of the shaft might be made in a minute or an hour, however, and yet the same number of inch-pounds of work would have been per- formed. To be definite, then, we must limit the number of turns to a certain period of time, and as we must measure in horse-power, this time unit will be the minute ; one horse-power is equal to the performance of 396,000 inch-pounds of work in one minute; the value N is, then, taken as a certain number of turns per minute, commonly indicated by the letters R. P. M. in practice, so we have for the horse-power necessary to lift the weight W, with the device shown in fig. 30, ^ 27tWCN , ^ H. P. = -— (10) 396000 in which C = Drum radius. n =3.1416. W = Load lifted. N =R. P. M. In practice the problem comes simply in the form of a certain number of H. P. to be transmitted, and a careful study of the above will make clear the manner in which the term horse-power involves all the elements of load, diameter of pulley or drum, and revolutions per minute ; now the work required as found in formula 90 MATERIALS AND CONSTRUCTION. lo in horse-power terms must be carried by the shaft' and if we replace the load moment Wc in lo with the Ssl resisting moment of a shaft - --^ we have the horse-power which a shaft of given size will transmit, or knowing the H. P. we may determine the necessary diameter of shaft to transmit it, since the resisting moment of the shaft must be equal to or greater than the moment due to load; so we notice that the simple term "horse- power" (H. P.) on one side of the equation will involve all the features of load, diameter of pulley, and number of revolutions, for a given case, while, on the other side we have the necessary properties of the shaft and number of revolutions per minute as follows: 27rN S I H. P. = ^^^^x^^ (II) 396000 Ts to transmit a given horse-power. The proper meaning of each letter used in the above formula is: H. P. = Horse-power to be transmitted or which a given size shaft will transmit. 7T =3.1416 =R. P. M. at which shaft is to run. 5s = Safe shearing strength of material in f I p = Polar moment of inertia. Ts = Radius of shaft in inches. As an illustration of the application of this formula, we will determine the number of H. P. which can be transmitted by a 2" shaft, running 100 R. P. M. Numerical values are: 71 =3.141 N =100 TORSION. 91 Sg -7000 (Using factor of safety 10 for soft steel taken from Table 2. I J, ={il2nr') (See Table 19.) i/2X3-i4iX(i)S or 1.57. Inserting numerical values we have 2XS.141X100 7000X1.57 H. P. = ^— , X = 17 390000 I or such a shaft under the conditions mentioned will transmit seventeen horse-power. The formula may be used with equal ease in answering the question if put in the following form : What size shaft, running 100 R. P. M., must be used to transmit 17 H. P. (Q. E. D.). This formula gives a size of shaft available for trans- mitting power only, such as a countershaft; if main- line shafts or jack shafts are being designed, reduce the H. P. 50%, for example, if the above question called for a jack shaft we would say that it was avail- able for a power transmission of 8.5 or 9 H. P. Belting. — Belting is used in practically all work where shafting is introduced, hence it may be logically taken up in a brief way at this time; the belts commonly found in practice are made either of leather or rubber, and in ordering the specification should include the length, width and ply; thus in the case of leather belt, we may say, 40 ft. of single ply leather belt 6" wide, if we wish what is known as a single belt, or we introduce the word double ply, other items the same as above, if we want the same amount of double belt ; in plac- ing leather belt on the pulley, the best results are ob- 92 MATERIALS AND CONSTRUCTION. tained if the smoother side is next the pulley surface; belting is a very broad subject, much discussion has been brought to bear on it, and many rules laid down; in practice many such rules cannot be applied, but at the same time certain limits must be observed^ if reasonable satisfaction is expected, and the following notes are serviceable as a general guide: For main driving belts distance between shaft centers should not be much less than 20 ft., and for countershaft work, keep the shaft centers at least seven times the width of the belt apart; double belts should not be run on a pulley less than 12 or 14" diameter, and triple is best limited to about 24" as the smallest pulley, while quadruple (or four ply belts) should run on nothing smaller than 3 ft. Average practice for the surface speed, by which is meant the speed in feet per minute at which a point on the circumference of one of the pulleys travels, may be taken as about 3500 ft., though many belts are running at a much slower speed than this, while the greatest efficiency calls for a much higher speed. (See Kent's "Mech. Engs. Pocket-book on Belt- ing.") For the calculation of amount of power which a belt may be expected to transmit, the following formulas are serviceable, taken from Kent's "M. E. Pocket-book" : For a single belt. Ac WV -^ X = H. P. (12) 180 733 ^^2; In which the letters have the following meanings: ^c = Arc of contact in degrees. W = Width of belt in inches. V = Surface velocity of belt in feet per minute. TORSION. 93 A double belt is usually assumed to transmit about I I /3 times as much power as a single belt, hence from this fact we may easily deduce a simple formula for such application by multiplying the above by i i /3 or 4/3, hence we may say, formula for horse-power of double belt is as follows : Ac WV A ^ X =H. P. 180 733 3 the letters having the same application as in the previous case. Arc of Contact. — As the power of a belt is effective due to the fact that a certain portion of it is in contact with the surface of a pulley, it is but reasonable to Fig. 29. suppose that the portion of the pulley surface that is in contact with the belt will affect in a measure the amount of power transmitted, and this is in fact a truth ; looking at fig. 29 we see two conditions represented, one in which the belt embraces about one-half the circum- ference of the pulley on both driver and driven, while in the other case more than half of circumference 94 MATERIALS AND CONSTRUCTION. covered on the driver, but less on the driven. In such a case the calculation of the belt power is always based on the smaller of the two pulleys with which the belt is in contact; the portion of the circumference on which the belt bears is known as the arc of contact, which is clearly indicated in the cases of fig. 29 by the arrow points; this value is commonly measured in degrees, and enters into our calculation of belt power as follows : If the arc of contact is 180° the H. P. transmitted will be the same as that evolved by the formulas given, if 180 the first term is omitted since Ac= iSo and = i 180 but suppose we have an arc of contact of 90° then we will 90 use the formulas as given above and take as the 180 first term; this formula may be improved upon for surface speeds of over 3000 ft. per minute, by using methods contained in papers presented before the American Society of Mechanical Engineers by Messrs. Taylor and Earth. To determine the arc of contact, the pulleys may be laid out to scale for diameter and center distance, and the arc of contact determined with a protractor if the shafting has not yet been installed; if the shafting is in place, a string may be stretched over the two pulleys, and the length in contact with the pulley cut out; measuring this section into the circumference will give us the portion of 180° which is embraced by the belt, or the arc of contact. A single belt is about 1/4" thick, double 5/16", and triple 3/8" thick when of leather, and most belts now TORSION. 95 in use are of this material, though rubber belts are much used in places where there is considerable damp- ness; waterproof leather belting is being put on the market by manufacturers at the present time, and gives very satisfactory service; such material is sold under a special trade name, as a general rule. Pulley Crowning. — If the face of a pulley, that is, the surface on which the belt runs, is perfectly flat, or the Fig. 30. pulley is truly cylindrical in form, the belt will not remain in place but will run off the pulley when operat- ing ; to this end it is necessary to make the pulley larger at the center than at the edges, and such increase in diameter is known as "crowning" a pulley; different parties suggest various amounts of crowning, but average practice calls for an increase of about 3/8" in diam. per foot of length each side of center, so that if we had a pulley of 6" face there would be 3" each side of center, and as this is 3 / 1 2 or i / 4 ft. the increase in diam. g6 MATERIALS AND CONSTRUCTION. from edge of rim A, fig. 30, to the center will be 1/4 X = in designing a drive this feature must not be overlooked if success is expected. Other features in connection with the belt drive are methods of lacing, splicing, calculation of speed ratios, all of which must be well understood by the man in charge of a plant; such subjects however belong to shop calcula- tions and methods rather than in the class of materials with which this work deals. It is necessary, however, to know how much pull a belt exerts on any elements which act as supports for driving or driven machines ; the weight of the machine itself must always be considered in designing such sup- ports, this weight being obtained from the builder supplying the equipment, or the designer must deter- mine it himself; to this must be added the pull of the driving belt; if a given horse-power is to be transmitted, and the belt speed is known, it is a simple matter to determine the number of pounds pull due to such work; this pull is exerted by the driving or tight side of the belt, and there is also a load on the slack strand; it is evident that the support must carry both these loads; for average practice in such work one may assume the stresses equal in both strands, hence the load due to the drive, coming on the support, will be equal to twice the load, due to the transmitted H. P. Below will be found a problem illustrating the appli- cation of this principle. The simple calculation of speed for pulleys and gears is based on the rules of proportion, such speed being inversely proportional to the diameters of pulleys or gears; to illustrate, suppose we have a pulley 36" diam. TORSION. 97 on a driving shaft, and it runs 200 R. P. M.; we wish to drive another shaft 500 R. P. M., what diameter pulley should be placed on the driven shaft? A direct pro- portion will be: 36 : X : : 200 : 500 and inverting one of the ratios we have: 36 : X : : 500 : 200 or X = 14.4" The method of using the formulas for horse-power of belting and determination of pull on a support is illustrated in the following: A vertical belt is to be used for driving a machine, which requires 7.5 H. P. and runs 1500 ft. per minute; the complete countershaft weighs soo'Jf. This is to be supported by four lag screws. Select proper size single belt for this work, and give specifications as to size and boring of holes for lag screws. The arc of contact is 120°. Formula 12, p. 92, should be used for belt, and introducing known numerical values from the problem we have: 120 WXi'ioo -f- = 7.S H. P. or W=3-5" + i»o 733 width of belt will be 3 1/2". Relative to the pull on the lag screws we have: One H. P. = 33,000 ft. -lbs. per minute and 7.5 H. P. = 7.5 X 33,000 or 247,500 ft.-lbs. As the belt speed is 1500 ft. per minute the pull in pounds necessary is: 247500 . „ = i6s# 1500 In considering the stress on the supporting lag screws, however, this pull will be doubled, or we have 330^ to 98 MATERIALS AND CONSTRUCTION. this we add 300/, weight of counter and we have as a total load 63 o#; using a factor of safety of 10 we will select screws to carry 6300/; since each screw will carry 1/4 the total load We must carry 1 5 7 5# with each screw. If the wood into which screws were set was well sea- soned, we might use a 3/8" screw, but the wiser course would be to use a 1/2" screw, bore with a 3/8" bit, and Fig. 31. Flange Coupling Proportions. S = Diam. of shaft. H. D. = (Hub diam.) = 1.75 S+i" C= (Diam. of bolt circle) = 2.5 S+ 2" L = (Length of half couphng =1.2 S + i ") Number of bolts used = .5 S + 3. (If fractional use nearest whole number.) S Number used O. D. = (Outside diam.) = 1.4 C. f = (Thickness of flanges) =.58 + -6" W = (Width of face) = 2f . R= (Thickness of rim) = .12 S. Key, make square and equal .25 diam. o* shaft across flats, length = 2L. Diameter of bolts = ; set screw into wood 3 1/2" as we see by looking at Table #21 B. If the surface speed of the belt had not have been given direct, it would have been necessary to find it from the diameters and number of revolutions per minute of the pulley. TORSION. 99 Shaft Couplings. — In dealing with shafting, belting, etc., one is often called upon to design a connection for long lengths of shafting at the end ; many patent coup- lings are available through mill supply houses, but the Fig. 32. one known as a flange coupling, shown in fig. 31, when properly designed, is safe, efficient, and a good design; in the solution of problems given in connection with this chapter, it may be satisfactorily applied; the loo MATERIALS AND CONSTRUCTION. proportions of various parts are given directly on the figure. Strength of Gear Teeth. — gear tooth is a cantilever and in calculating its strength it will be well to look over p. 66, that the steps may be properly covered. A few gearing terms must be understood, if we wish to make practical use of this study, though the shop technic will be left for the work devoted to that subject. Fig. 32 presents such terms as are essential to the application .of the process of design presented ; here we see that the thickness of the whole gear at the section where the teeth are cut is known as the face; that the diameter of a circle, the extremities of which lay at mid-points of tooth depth is known as the pitch diameter; the distance from the center of one tooth to / / Fig. 33. TORSION. lOI the center of the next is known as the circular pitch and the width of the tooth W at the pitch line equals one-half the circular pitch. This value W is the one which we desire to determine, and knowing this, we may apply the specific rules of gearing, to determine any necessary data for use when making the gear in the shop. The pitch diameter will be introduced when we make calculations of speed, for determining number of pounds load due to a given horse-power transmitted, the same as was done in determining the pull coming on one strand of a belt (see p. 97). The weight in pounds thus obtained is treated as a load Pc, fig. 33, coming on one corner of the tooth and the section abce is treated as that of a rectangular beam, the length of which is mn, and height of which is W. The distance ab of course is the breadth b of the beam. The relation of these values to W are as follows: & = breadth of beam =1.93 W I = length of beam = .96 W h = height of beam = W On p. 59 we have given the relation existing between resisting moment and maximum bending moment, and if we work through the formula we shall find that Mr Mb 1 1 (13) from which we may determine W or the width of tooth on the pitch line. If the problem comes in the form of moving a given weight at a certain speed, the work of determining the load coming on a tooth is simplified, as an application of the principle of moment will give the tooth load I02 MATERIALS AND CONSTRUCTION. directly. To illustrate the application of the formula we may solve the following problem : A gear transmits 5 H. P. The velocity in feet per minute at the pitch line is loo; what should be the width of the tooth at pitch line? 5 H. P. = 5 X 33,000 = 165,000 ft. -lbs. per minute; as the velocity in feet per minute is 100 the load in pounds must be 1650, which is thrown on the tooth; introducing numerical values in formula (13), using a factor of safety of 4, we have 5m= 7500 Pc=i65o (See Tables 2 and 4) hence 1. 93 ly^X 7500 = 5.76 X 1650 W^=.6s or W=.Si" which will have to be changed to some extent to meet shop requirements. The value of Su in this illustrative example was taken from a common table, as used for beams, but unless the speeds are low it is best to use the values of Su given especially for gearing in Table 2 A, which are adapted from Kent's "M. E. Pocket-book." As noted in fig. 34, the width of face of a gear is 5!^. Such a proportion is good practice though it may often be departed from to a greater or less degree. Stresses and Calculations of Same in Small Tool Design. — ^The application of strength of materials in the design of small tools, such as jigs and fixtures, in- volves calculations for columns and beams, in the same manner as already studied; in cases of de- termining loads thrown on such tools due to cutting, TORSION. one must often adopt a comparative method of deter- mining the stresses, as will be noticed in calculations following in this section; small tools as referred to means cranes, trucks, jigs, and similar equipment; while there is much to jig design beside the simple cal- culation of stresses, the stress feature is the only one coming within the scope of this work. Fig. 13 shows several sections much used in this class of design, but stress calculations are made on the base form, not including the fillet / or ribs r which are introduced by the designer to prevent cracks and the rapid wearing out of clamp faces; malleable iron is often used as clamps, and sometimes cast iron; steel is by far the more common though, and the section commonly used for clamps is rectangular. In applying sections similar to those in fig. 13, A is, treated as a T- form, B and C as simple channels, while D and E are of rectangular and square section; the formulas of Table 8 may be used in determining the numerical values of properties of these sections. As an illustration of the method available in determining stresses by compari- son of conditions in separate elements we may study the case of a jig which is in service on a multi-spindle driller, to be used in drilling four i" holes at one time; the jig is to set on four feet; what would you make the combined area of these feet, that they may be safe against crushing under the greatest load that might be applied. The assumption is first made that the down- ward pressure would be so great that the drills might be twisted off, and feet designed to sustain this load, drills being taken in section equal to that of a i" tool steel bar. I04 MATERIALS AND CONSTRUCTION. Referring to pages 87 and 88, etc., the formulas are given as: WC the load moment and lor resistmg moment in dealing with a round bar. Numerical values are W= The load that will twist the drill off. C= Rad. of drill 1/2" or .5". 5= 90000/. See Table 2. Ip = — . See Table 18. 2 The calculation then is 90000X3.1 X 1/32 .5VK = FF=93,ooo# 2 approximately, to twist off one drill or 372,000/ neces- sary to twist off four drills; this is the load at the cir- cumference which would twist off a solid i" bar, multi- pHed by four; assuming that it requires the same pressure in all directions to force a cutter into metal, we say that this tangential force which we have just calculated is equal to the force required to "feed" or constantly push these four drills through the stock, and we have a load of 370,000/ coming on the feet of the jig. Using this as a dead load, since the drill starts gradually and "feeds" steadily we must use a factor of safety of four, and a stress in the feet of 2 2,5oo/n''' hence total 372000 area must be or about 16 sq. ins., and with four 22500 feet, each foot should have an area of four sq. ins. The same process of reasoning may be applied to TORSION. stops, supports, etc. In the case of milling fixtures the stress is that necessary to twist off the arbor used to drive the cutter, or in a lathe driving fixture that load necessary to break the tool of largest size which may be used in the post; as will be seen from the above illustration, no variation of the methods for simple calculation in compression, shear, beam design, or column work, are introduced, the only feature requiring special consideration being the determination of the load coming on the fixture; in some of the larger plants where many jigs are made, the load as determined above is decided by test, and values tabulated, in which case the assumptions presented are unnecessary. PROBLEMS. 1. Fig. 34 is a diagrammatic sketch of a small power hoist. Select the proper size shaft for the main gear as indicated at B and the proper width at pitch line of a gray iron gear tooth to carry the load assuming that a 5 H.P. motor is exerting full H. P., what should be width of face of gear and pinion? Ans. i 1/2" shaft . . . .25" . . . i 1/4" See Table 2 A for values of Su- 2. A shop for experimental work is to be equipped with the following tools: One shaper, one 10" lathe, one universal milling machine, a band saw, and a surfacer. All these tools are to be driven from one line shaft, by means of a motor, bolted to the ceiling, how many H. P. must motor be, assuming that all machines will be running at the same time, what size belt for a main driving belt, what size shaft for a main shaft, and what size bolts to hold motor to ceiling, assuming belt pull horizontal, and four bolts to be used. (See Tables 21A and 22.) Motor is to run 900 io6 MATERIALS AND CONSTRUCTON. R. P. M. and line shaft to run 175 R. P. M. State proper diameters of pulley on motor and line shaft, center dis- tance of shafts to be 8 ft. 3. Suppose the above motor were suspended from the ceiling as mentioned, but due to placing the line shaft against the wall below the motor, the pull on belt became vertical, what size bolts should be used for suspending same? 4. A hand winch is to be designed for shop use, similar in arrangement to that in fig. 34, except that the main gear is to be 48" P. D. and the small gear, to which a handle is attached instead of a motor, is to be 6" diam. a load of half a ton is to be lifted by means of a rope run- ning from the drum; select shaft through main gear and drum, also state thickness at pitch line of gear tooth, and width of gear face. 5. A testing frame used in the laboratory of an engineering works is supported by means of four angle irons which are eight ft. long. This frame carries a 15 H. P. motor run- Fig. 34. TORSION. ning looo R. P. M. geared to two countershafts, one of which runs 200 R. P. M. and the other 75 R. P. M. Assum- ing that at different times, the whole power of the motor may be transmitted through either counter, what diameter gears must be used for desired speed, size of tooth (pitch Hne width, and face) and what size shafts on the counters? Fig. 35- 6. The main driving shaft for a shop runs 200 R. P. M. and transmits 100 H. P. What size belt would you select, assuming a belt speed is 2500 ft. permin.? What size shaft to transmit this H. P. ? 7. Give your specifications as to tooth width at pitch line and face for a steel pinion to transmit 25 H. P. if it is 8" P. D. and runs 7 50 R. P. M. 8. Fig. 35 shows a diagrammatic arrangement of a boring fixture; the pulley carries a 21/2" belt running at rate of 1500 ft. per minute, 180° arc of contact. The gear A is 4" P. D. and other two are each 8" P. D. Give the speci- io8 MATERIALS AND CONSTRUCTION. fications for thickness and face of tooth, assuming belt is exerting full power, according to formulas given in this book. 9. In designing the clamping system for a jig it is decided to use as clamps, stock of ribbed channel section as shown at C fig. 35, malleable iron, the clamps are set up by means I I , — Fig. 36. of 5/8" bolts, if we desire the clamp to be sufficiently strong to stress the bolt, which is of soft steel, to the elastic, limit what size should the clamp be of malleable iron; fig. 36 shows the arrangement of clamp in jig. Cuttsr J>aLr Fig. 37. 10. A driving shaft must transmit 75 H. P.; it is equipped with a pulley 20" diam. and runs 200 R. P. M., from this I wish to run another shaft at 135 R. P. M. Select size of shaft for driver, size of belt and diameter of pulley for operating driven shaft. 11. An engine running 225 R. P. M. develops 8 H. P. It has on the driving shaft a pulley 8" diameter, which connects to a shaft running 80 R. P. M. If the shaft must carry the TORSION. horse power mentioned above, and belt pull is vertical, determine following : Diam. of pulley on shaft ; Diam. of shaft ; Pull due to belt. 12. In the design of a broaching attachment, a load of -250^ is thrown on the cutter bar which is driven by means of a rack and pinion as shown in fig. 37. What must be 1 -< Fig. 38. pitch line thickness of tooth and face if pinion makes 20 R. P. M., the pinion and rack teeth being made of hard steel? 14. Fig. 38 shows the gearing arrangement for a special facing fixture; it is driven by a i 1 1 2" single belt, and the pulley shown runs 75 R. P. M. Give specifications for thickness of tooth and width of gear face if the gears shown must carry the load due to the H. P. which the belt mentioned will carry. CHAPTER VII. THE ACTION OF ELEMENTARY FORCES AND THEIR CONSIDERATION IN DESIGN; PROPOR- TIONS OF KNEES AND COUNTERS. When a piece of construction is so put up that all forces act in the line of the members, such forces are taken as producing a direct stress, that is, in the piece of construction, fig. i, the load from beam on the column is carried by the end of the column and the forces acting that sustain the beam (reactions) are in line with the center of column as indicated by the arrows e. If we determine the amount of load coming at the beam end, then in this case we have all that is necessary, so far as the load is concerned, to select the size of the column; we do not have so simple a problem in all cases, however, as is illustrated in the design, fig. 39, which shows a wall crane much used in factories; in making the calculations on such a job, we determine stresses in the tie, and I-beam, as well as considering the stress in the wall in order that the crane may be properly supported. B represents a load at the end of the arm ; if we wish to know the stresses created by the load it will be necessary to apply the triangle of forces ; this combina- tion is much used in determining stresses. Assume no THE ACTION OF ELEMENTARY FORCES. Ill that the load B is represented by a straight line; it makes no difference what its length is, as it is not measured, in the method to be used; this line ab fig. 40, indicates the direction of the load; the angle X fig. 39, is known from the requirements of the job; we will draw a line ac and be; the first of these is Fig. 39, assumed to make the same angle with the load line in fig. 40 as the tie does in fig. 39, while be is parallel to the line of the beam; applying trigonometry we have ab ab — = cos X or = ac ac cos X if now we make ab equal to the load in units, we can easily determine the stress in ac; also 112 MATERIALS AND CONSTRUCTION. he — = tan X or be = ah tan x ab so knowing the load, we have been able to determine the stresses in the two other elements of our piece of con- struction. We see then, that the fact of a supporting element being out of line with the load makes a marked difference in the stress. In determining the nature of the stresses in these elements, that is, whether they be tension or compres- sion, place an arrow indicating the direction of load ah which is downward in this case, and from this point the arrows must continue in order around the figure until Fig. 4o. we reach the starting point a again. If the arrow on the diagram, representing the stress in any member, points toward the joint with another member, as arrow /, representing stress in the I-beam, points to- ward C it indicates that the member (I-beam in this case) is in compression; if the arrow points away from the joint, as arrow g, representing stress in tie, points away from joint C, it indicates that the member (tie in this case) is in tension; the design we are studying must have an I-beam acting as a column, a tie rod, and THE ACTION OF ELEMENTARY FORCES. "3 the wall of sufficient strength to take the thrust of I-beam and pull of tie safely. The load B may not be located at the extreme end ssctioy Y_ Fig. 41. TfaAJ>W/ly. Jlllllllll \\ / /'■'7\j£m / / Fig. 42. of the beam, but is moved to a point anywhere along its length in the case of a crane; the I-beam not only acts as a column under such conditions, but as a beam 8 114 MATERIALS AND CONSTRUCTION. also. The tie then simply acts as a support at one end of beam, and after determining reactions it may be selected; the load is assumed to be at the ends in the case of a crane when designing the supports, because in this position it carries the greatest stress to sup- ports, while for bending moments it is taken in such a position that the greatest moment is produced. The course of reasoning outlined above holds in all applications of the triangle to constructive work, it makes no difference whether the beam be supported through the medium of a tie, or by means of a brace as indicated by the dotted lines in fig. 39. Counterbracing is used for the purpose of giving rigidity to structures; figs. 41 and 42 show two forms, that at 41 being known as knee bracing; the design represents the section of a type of shelter shed used in parks, playgrounds and at railway sidings; the other design is used in building elevated walks or driveways; the proportions of these members are usually related to other members of the construction for which calcu- lation has been made in the design, rather than by calculation of stress in the braces themselves. The sectional area at the smallest part being made from half to full size of sectional area of the post or column ; if the counters are long, about equal to length of posts as in fig 42 at A, the sectional area at any place L, would be made equal to the post, being "halved" at the mid length and bolted together; these members are usually spiked in place; the beam B in fig. 42 is designed on the basis of the load it must carry, while the header H is made the same size as beam B. If THE ACTION OF ELEMENTARY FORCES. such a design is put up in steel, the beams and columns would be I-beams, and the counters channel beams. The action of the weight of a machine, resting on several feet, or a flanged base must be considered in the design of a structure to support it, as either a series of concentrated loads, or a uniform load; if the feet on which the machine rests are not more than one foot apart, the weight is assumed to be a uniform load, the ■ , — CRADLE Fig. 43- same as though it rested on a rib; such a case is illus- trated in fig. 43, where a water tank is shown hanging from a beam by means of slings, and also setting in a cradle, on top of the beam; both methods of support would be considered as producing a uniform load, in making calculations to determine the proper size beam to be used. If the supporting elements (feet or slings) are more than a foot apart, they are taken as points of application of concentrated loads, and the amount of Il6 MATERIALS AND CONSTRUCTION. such load on each shng will be the total weight to be supported, divided by the number of feet or slings; thus if we have a tank which with its supply of water weighs 2ooo'# and we have four slings, then each sling carries 500/. In the case of a machine we must look care- fully into the distribution of the weight, that we may be sure it is evenly placed; usually this is the case, however, and even when such is not strictly true, the designer of a supporting structure does not attempt to find out the variation, but assumes even distribu- tion and proceeds with his design, depending on the F. S. to cover all necessary requirements. The beginner should be careful, when working out a design, that he does not entirely neglect the effect of feet, or pads on a machine, in concentrating the loads on a structure; one very common error being the as- sumption that the whole weight of the machine is carried on one or two feet, due to a neglect in studying the construction of that part of the machine which rests on the floor or platform. Illustrative Problem in Beam Design Using Steel Construction and Bracing with Knees. Problem. — small blowing unit is carried on canti- levers as shown in fig. 44. Select proper steel for both cantilevers and knees and state amount of thrust coming on the wall. Looking carefully at the drawing we see that the machine sets on four pads, two resting on each beam; such being the case one-fourth of the total weight will come on each foot or a load of iisf, which for conven- ience we may call 115/; such loads fall respectively THE ACTION OF ELEMENTARY FORCES. I17 12" and 36" from the wall center; as these beams are to be supported by a knee at the outer end we will deal with them as simple beams, supported at both ends, and since we have two beams, one-half the total load will be distributed by means of two concentrated loads on each beam, hence a design for one beam will be suffi- FlG. 44. cient, using the same design a second time for the other beam. Reaction will be taken by the knee, while will be taken by the wall; applying the solutions already presented we have: 42i?,= (36Xiis) + (i2Xiis) ii8 MATERIALS AND CONSTRUCTION. assumed to act at extreme end of beam JR^ = i3i+ call this 135 and 42i?2=(ii5X3o) + (iisX6) or R.^=gg call this 100 The sum of actual loads is 224^ but due to the slight changes made for convenient calculation we deal with 235#- The next step, finding the maximum bending mo- ment, and working out we have: Mb = 100X12 = 1200 M6= (100X36) - (115X24) =840 By inspection of these values we see that lies under the load nearest the wall and is i2oo#". We know (see p. 48 and resume of notations) that Mr = Su^ and hence to be safe Su — = 1200^" must hold true. Looking at Table No. 4 dealing with factors of safety we will use twelve as a factor of safety, because such equipment is apt to produce shocks. The material we are using is weaker in tension, being about 50,000^ per sq. in.; see Table 2, and using a factor of twelve we 50000 may use for 5^ = = 41 66#, which we will call 4100/; 12 substituting values we have : I I 4100 4100X =1200 or — = = 3-41 Cn Cn 1200 the section modulus. THE ACTION OF ELEMENTARY FORCES. 119 Looking at Table 8 we see that a 4" heavy I-beam has a sec. mod. of 3.6, hence we will use this for the main beam. As to stress in the knee we have, applying the trian- gle of forces: — = cos 45° X or 135 . , ■ = rt; = stress m knee. cos 45° Looking at a table of co-sines we find cos 45° = . 707, hence I -7 f = ;t;= 191/ which we will call 2oo#. .707 This knee is really a column and could be designed as such, but this is not a common practice on small jobs, it being taken as mentioned on p. 114. An angle would be used for such a brace, and looking at Table 10 we see that a 3X3X1/2" angle will give a sectional area of about 3/4 that of the beam, and such a proportion would be a wise selection because the load will cause shock. Two angles would give a neater design, hence we may use 2 1/2X2 1/2X3/8" angles, placed one each side of the I-beam web. As to thrust on the wall if we apply the triangle of forces to the stress in the knee, we will find it to be i35#, which should be taken by an iron plate of sufficient area to insure remaining inside the unit shearing strength of brickwork (see Table 5) and attached to both the plate and I-beam by a riveted joint designed along ines presented in the chapter on riveted joints. For I20 MATERIALS AND CONSTRUCTION. method of holding an iron plate to brick or masonry, see Kidder's Architects Pocket Book under the head- ing of expansion bolts. The Weight of the Members in a Structure. — A feature to be remembered in any extensive design or framework, is the weight of the various parts of the structure itself. In designing small structures there is no necessity for such consideration as a rule, but if the work is extensive this factor should not be neglected. The method of introduction is to add the weight of the beam or column to the actual applied load; let us assume that we are to design a steel beam to carry a uniform load of 150/ per ft. 10 ft. long. Formula is Cn o Use factor of safety of 3 we may make 5^ = i6ooo# + and inserting numerical values we have : ^ / I 10000 = X 1500X120 Cn 8 or , I I 10000 =22500 =1-4 from which we select a 3" light I-beam. The weight of this beam is 5.5/ per ft. hence considering the weight of beam we will have for weight per ft. 155.5^ which we will use as i56# and hence Pt = i56o#. Introducing numerical values we have: / I 16000 == X 1560X 120 = 1.46 Cn 8 and we find that a 3" I-beam is still safe. If the beam carries one or more concentrated loads, THE ACTION OF ELEMENTARY FORCES. 121 instead of being uniformly loaded, its weight may be treated as a concentrated load, applied at the center of its span. Distribution of Load on Floor Joists. — In the dis- tribution of loads on floor joists, it is not a certainty Fig. 4s. just what load will come on the whole floor; for this reason it is customary to design floors for certain pur- poses to carry a definite load and table #19, A, gives val- ues used to a considerable extent as an average guide, though of course any building may be designed for a specific floor load varying from this. A floor is constructed as shown in fig. 45, with joists resting on sills and the load assumed as coming on any joist is that laying between two successive joists; to illustrate: We have in the figure a floor which we will 122 MATERIALS AND CONSTRUCTION. assume to be 15 ft. wide, and the distance between joist centers 15" or i 1/4 ft. The joist A then will carry the load which falls on 15 X" = — = i8^~ sq. ft. of area 4 4 4 and if we are designing a shop store room this joist must support: 18.75 X 120 = 2250^ as a uniformly distributed load, all floor joists being the same size. The student should make a careful study of fig. 45 that he may know the parts of a common framework when they are mentioned. Lag Screws. — Lag screws are much used in shops and buildings; Table 21, B, gives the loads necessary to pull out certain sizes ; factors of safety must not be forgotten when using these values. Rope. — ^Table #20, will be of assistance when select- ing rope for any given loading, the approximate diameters given serving as a guide in selecting blocks. Rope is specified by "girth" or circumference rather than diameter however, and if you planned to use a rope about 7/8" diameter it would be ordered as so many feet of hemp or cotton, or manilla rope 2 3/4" girth. CHAPTER VIII. RIVETED JOINTS. Study Table i6 carefully in connection with this chapter. The purpose of this section is to cover riveted joints as applied in the construction of tanks used as oil or water storage and air receivers of low pressure; we will then become acquainted with the riveted joint, method of its construction, and the relation of its various elements one to the other. A riveted joint may fail in one of several ways, or by a combination of these ways : ABC D Fig. 46. The plate may pull apart along the line of the joint as indicated at A, fig. 40 or by crushing the metal of the plate and rivet as at B of the same figure or by splitting out the sheet as at C of the same figure or 123 124 MATERIALS AND CONSTRUCTION. by simply shearing off the rivet as at 46 D and again in failing the rivet may shear, plate crush and pull apart and possibly split slightly, in which case we have failure due to the several weaknesses combined. Before taking up the details of joint design we must consider briefly the construction of a tank in order that we may be familiar with the position of the various (fhtrtl Fig. 47. riveted joints; looking at fig. 47, we see one joint running parallel with the axis of the tank, while others are made up around the circumference; those running parallel with the axis are known as the longitudinal seams, while those around the tank are technically termed "girth" or "ring" seams, and such joints are put up in all the types available, dependent on the requirements of the design; at A in the same figure we see what is known as the spiral joint, which has become common in pipe work during recent years. RIVETED JOINTS. 125 Joint Classification. — ^Joints are broadly divided into two classes, single riveted and double riveted; a single riveted joint is understood to have but one row of rivets, while a double riveted has two rows of rivets holding the plates in place; single and double riveted joints are shown at B, fig. 47 (single riveted), and C (double riveted) . Under each of these general types of joints we have the lap joint, butt joint with single cover plate and butt joint with double cover plate; at fig. 47, B, we see the single riveted lap joint and at C a double riveted joint of the same type. The lap joint has an important undesirable feature in that when it Fig. 49. Fig. so. fails there is a tendency not only to cut the rivet off, but to bend it and the plate as well, as illustrated in fig. 47, D, where we see the rivet pulled and distorted, while the plate is bent about point P. To overcome such action, the butt joint in its two types, one with a single and the other with a double cover plate was devised; no figure is shown of the joint with a single cover plate, such an arrangement giving the same con- struction as in fig. 49, except that one plate, the outside one is used, and the inside one omitted; a study of fig. 49 brings out the fact that the bending action of both 126 MATERIALS AND CONSTRUCTION. plate and rivet are largely eliminated, placing the rivet directly in double shear; in this figure we have what is technically known as a single riveted butt joint with two cover plates, while in fi^. 50 there is presented a double riveted butt joint with two cover plates; there are a great many other arrangements of joints possible, to meet varied conditions, but those presented are the fundamental types; for the average run of tank work the lap joint in some of its forms is satisfactory, Fig. si. unless pressures approach 75 pounds or more, when the butt joint with double cover plates may well be considered. Arrangement of Rivets.— In making up riveted joints the rivets may be placed in a row the proper distance apart, and relative to the edge of the plate both in the case of lap and butt joints; such placing is known as CHAIN riveting and is shown at A, fig. 51 (single chain) and at B (double chain), as applied to a lap joint; same specifications as above hold true for the butt joint as RIVETED JOINTS. 127 to rivet arrangement. At C of the same figure we see what is known as staggered riveting, where, instead of the second row rivet standing directly back of that in the first row, as at B, it is set diagonally, half way be- tween the rivets of the first row. Girth seams are commonly put up single riveted. Joint Efficiency. — ^The efficiency of the joint is a very important element in the process of design, since it tells us directly the relation of the strength of the joint to that of the solid plate which we must use in our construction; e.g., if a piece of the solid plate from which we build a tank sustains an ultimate stress of 2o,ooo# and we take a joint involving a piece of the same size as that tested and find it will carry a load of but io,ooo# before breaking at the joint, then the joint is but half as strong as the plate, or its efficiency is 50%. Reasoning from the above simple calcula- tion, we may deduce a definition for joint efficiency as follows: The efficiency of a riveted joint is the ratio of the strength of the joint to strength of the solid plate. Numerical Values of Joint Efficiencies. — ^In testing the efficiency of two samples of the same joint they will vary to some extent; again, different authorities give unlike values for this item, so that the best one can do is to select an average as a guide, and such is the pur- pose of presenting the following in this connection: Single riveted lap joint, 55%. Single riveted butt joint, with single cover plate, 55%. Double riveted lap joint, 65%. Double riveted butt joint, two cover plates, 70%. The single riveted butt joint with one cover plate is 128 MATERIALS AND CONSTRUCTION. not recommended for practice, since it adds to expense, without great increase of efficiency over a lap joint, while the double riveted butt shown adds but a com- paratively small amount in cost over the single riveted butt, and gives a marked increase in efficiency over any other type of joint. Design of Joints. — ^The design of joints for tank and receiver work must take up the consideration of other features than the ultimate breaking of the joint, since it is entirely possible to so construct a joint that it will not actually fail, but still not hold a fluid sub- stance without leaking. The efficiency values just pre- sented will assist us in selecting the type of joint for any given case, and known pressures will enable us to select the proper thickness of plate; on this selection of plate the other elements of the joint are based, working along well defined lines, as to size of hole in plate, size of rivet, and features of spacing. Rivet Sizes. — Certain sizes of rivets are considered satisfactory for the various thicknesses of plates, and designers use a table of plate and rivet sizes in selecting to meet the requirements for any given problem; the holes are made somewhat larger than the rivet is, so that the rivet may be easily and quickly placed when it is hot, while the process of heading up is assumed to fill the hole as well as form the rivet head; Table No. 22, which is taken from Button's Mechanical Engineering of Power Plants, serves as a guide in this work. Pitch of Rivets. — The pitch of a rivet is the distance from the center of one rivet to the center of the next measured parallel with the seam; this feature must be considered in designing, and like other factors, there RIVETED JOINTS, 129 is considerable variation in practice, hence following proportions are presented as a guide, from which one may find a wide departure at times. The pitch is usually related to the diameter of the rivet, which in turn is related to the thickness of plate. For single rivet lap joint, and butt joint with single cover plate we may take the pitch as 21/4 times the diameter of the rivet. Fig. 52.— D = Diam. of rivet. A=i 1/2 D. For a double riveted lap joint use 33/4 times the diameter of the rivet. For double riveted butt joints with two cover plates use 4 times the diameter of the rivet. The distances between the two lines of rivets as well as the distance a rivet must be set from the edge of the plate are shown in fig. 52. Solution of Problem Illustrating Application of Text to Riveted Joints. Prob. #14 of Following Series. (See fig. 53.) Since this is low pressure work, nothing but single riveted lap joints will be necessary; as the barrel is 9 MATERIALS AND CONSTRUCTION. but 4 ft. long, no girth seams are necessary, as I can purchase a plate 4 ft. wide and simply roll it up. My first step is to select size of rivet; as the steel is 5/16" thick I see by Table 12 that I must use a rivet 11 /16" diam. and the holes must be 3 / 4" diameter, and accord- ing to text on p. 129 they should be spaced i 1/2" apart; again looking at fig. 52 to guide me I find that the rivets must be set i" from edge of plate. As to method of holding bottom in place, assuming that I have no means of flanging, I will use an angle, bending it to the required shape; the pressure on such a part is Fig. S3. not easily determined, and judgment is relied upon to guide one; these heads must support a shaft, however, so I want a reasonably strong joint; I will make the ring half the thickness of the shell, which calls for 5 /3 2" ; the nearest thickness of angle listed is 3/16", and fol- lowing the Table No. 1 2 as a guide, I will use 1/2" diam. rivets spaced i 1/2" apart; as distance from center of rivet to edge of steel angle must be at least 3/4" (see fig. 52) I must use i 1/2" angle, and the rivet holes will be 9/16". Select rivets and spacing of same for inside angles by applying rules and proportions given above, as illustrated in connection with the angle used for holding bottom in place. RIVETED JOINTS. PROBLEMS. Note. — All tank work given is low pressure, that is less, than 75# □"• I. Fig. 54 shows the rough sketch of a shelter shed to be built, the load assumed on the roof is 4o# □ ft. Select, size of rafters, if spaced 24" apart, size of plate P, posts A, B, C, and braces D. (Load is assumed vertical on roof; its perpendicular component is not considered.) Sketch your own design of the various joints as you would have them made. Fig. S4. 2. A motor which develops 15 H. P. running at 1200 R. P. M. having a 6" pulley is to be carried on a timber framework 8 ft. high; the machine weighs i5oo#; if framework must have four timber posts, and be braced with counters, get out full design, giving size of timbers; state the pull tend- ing to tip the stand over, assuming belt runs horizontally. 3. Fig. 55 shows the arrangement for a tank support; this tank will be filled with water; design the main header A, columns B, small header C and counters at D, all in timber. 132 MATERIALS AND CONSTRUCTION. 4. Fig. 56 shows the essential parts of a tank support, built into the wall; beam A is to be a steel I-beam and braces B ' are to be steel angles; select the proper size of each to carry the load and also area of foot plate C, so that suffi- cient area of wall may be covered to safely take thrust of brace. Fig' 57 shows the construction of a support for a water tank in a factory. Design the columns, headers A and C, also the counters B. Fig. ss- 6. A wash tank 48" deep, 60" long and 36" wide is to be built for factory use; the pressure is not great, and i /4" sheet steel is selected for the stock. Design the riveted joints at the comers, and edges of tank, presenting sketches showing arrangement of parts at these places. 7. The sprinkler system in a factory required the use of an open tank, 15 ft. long, 8 ft. wide and 5 ft. deep; it was made of 1/2" steel, with i 1/2" steel angles 3/8" thick riveted lengthwise, and across ends horizontally to prevent bulging. Design the riveted joints, and spacing of rivets on the horizontal braces; present sketches illustrating your designs. RIVETED JOINTS. 8. An acid tank used in a factory has a steel shell 3/8" thick; it is 12 ft. long, 6 ft. wide, and 4 ft. deep; i 1/4" steel ± L- Fig. 5 7. angles 1/4" thick are used as braces on sides and ends; give full specifications for riveted joints and bracing rivets. 9. A cylindrical oil storage tank is to be made of 1/4" steel; 134 MATERIALS AND CONSTRUCTION. design the lengthwise and girth seam riveting, presenting sketches of joint arrangement. 10. A cooHng tank used in a hardening room is to be made of 5/16" steel; it is 4 ft. long, 4 ft. wide, and 4 ft. high. Design the riveting for all joints, and illustrate your design with sketches. 11. A tank used in a drip system is of cylindrical form, 5 ft. long, 3 ft. diam. and made of 3/8" steel. Design all joints, illustrating with sketches. 12. In the protection system of a factory it is decided to make some large semi-circular guards for gears, of 3/16" steel; such guards are 30" radius and 15" long. Give your specifications for the riveted joints, and illustrate with sketches. 13. A coal truck body is made of 1 1 ^" steel; it is 6 ft. long, 5 ft. wide and 24" deep; this size necessitates riveted joints in the bottom, and at the edges; present your design of these joints. 14. A tumbling drum used in a factory is to be 4 ft. long, and 3 ft. diam. of 5/ 16" steel; it has steel heads and inside of it are riveted 3" steel angles 1 1 ^" thick; design the longitudinal seam, riveting for inside angles, and riveting for holding bottom in place. Present necessary sketches. Answered as an illustrative problem. 15. A small tank 24" deep and 30" square is made of 1 1 ^" steel for use in a glue heating device. Design tht corner joints. 16. Design the riveted joints necessary for holding steel angles to I-beam and wall plate called for in problem 4 of this set. CHAPTER IX. REINFORCED CONCRETE. Reinforced concrete is a combination which has come to the industries in comparatively recent years; con- crete and cement have been used a great deal for many years past in foundations and similar work; but the placing of steel rods in concrete to take up stress in tension, which is the arrangement of reinforced con- crete, is comparatively new; the greatest common error on the part of many persons who have had more or less to do with this material has been the belief that no skill was necessary in putting up concrete construction; no assumption could be more misleading; concrete must be composed of the proper ingredients, carefully mixed, and applied in the successive steps in such a way that there is certainty of a uniting of all the parts 'into one solid structure; forms must be carefully placed, and the supports for such forms properly designed; further these forms must not be removed until the material is fully able to bear its own weight, while if the concrete is placed in cold weather care of materials in the way of heating before and after placing must be particularly observed. Before proceeding with the study of reinforced concrete, the matter already presented in an earlier chapter on cement and concrete should be reviewed, because all the truths pre- 135 136 MATERIALS AND CONSTRUCTION. sented hold with equal force in the handling of concrete in the reinforced form. In reinforced concrete work the steel is introduced and so placed that it will take up any load causing tension, or bending, while the concrete itself carries the compression, so we see that we are dealing with a composite structure, made up of two entirely different kinds of materials. The position and amount of steel used in such construction bears a very important rela- tion to the strength of the work in hand; at the same time we are dealing with a material which in actual practice, lends itself but little to nicety of calculation, so design has developed along practical lines, using Fig. 58. certain formulas which have been deduced, and a liberal factor of safety. Actual experiment shows a marked variation from the results which might be expected if we use even the most complicated formulas, so it is customary with many engineers to use a simple formula, giving results which have been found service- able in practice; the formulas given in this section are taken or adapted largely from the book entitled "Concrete"^ by Edward Godfrey, M. Am. Soc. C. E. Steel in Reinforced Concrete. — ^The steel used as rein- forcement for concrete is not usually of a simple square or round form, because it is apt to slip in the concrete when stress is applied ; the bars are variously 1 Published by the author, Monongahela Bank Building, Pittsburg, Pa. REINFORCED CONCRETE. shaped, but a twisted square bar as shown in fig. 58, does very effective work, and is the only deformed bar which we will consider in this book. Placing Reinforcement in Forms. — ^The method of placing the steel in concrete is to fasten it in place by means of wires to the forms so that the reinforcement is in exactly the required position within the forms, after these forms are carefully set. The method is shown in fig. 59, the sketch at A showing the method for supporting the reinforcing on a beam and that at B and C" illustrating it for a column; the notes on the plate make the details of setting clear; after the reinforcing is thus placed, the concrete is put in the forms, and when it is sufficiently set such forms are removed; as already mentioned in connection with plain concrete these forms should not be removed in less than one or two weeks for walls, about three weeks for columns and beams, while arch forms should stay in place about a month, assuming that the weather is good; if cold or damp weather is experienced the forms should remain in place for a longer period; concrete should not be subject to its full load in less than from sixty to ninety days after it is completed; after removal of the forms the supporting wires which have been used to carry the reinforcement are cut off close to surface of the concrete. Columns may be reinforced by using a number of small rods set vertically, and surrounded by "spirals" of wire or rings as shown in fig. 61. The horizontal and vertical reinforcing should be tied together by several turns of binding wire about 1/16" diam. In the case of cylindrical coluinns, the reinforcing is set in the form REINFORCED CONCRETE. of a circle, while in the case of square column the reinforcement is set to a square form; proportions for such reinforcement will be taken up later; on the larger jobs, the reinforcing surrounding the vertical bars of i i hack ofhaT, Vl/e<^So = 35oo# 'If /\ / \ wt. of cu.ms.mft. onecu. ft. of cone. MATERIALS AND CONSTRUCTION. This should be added to the total beam load of 25,000^ and beam calculations checked, for the new load, and then we will have for (e) g2^2_ 4X^8.5ooXi44 354X8 BD'=S199* (58oo#) we now see that the size of the beam must be increased, and we will find 15 X 20 when tried for BD^ = 6ooo and will be chosen. The reinforcement may now be considered; the total area of such steel reinforcement (see p. 142), is 1.25% of beam area; 1.25% of 15X20 = 3 3/4n" of steel; the square reinforcing bar already mentioned will be used ; requirements for placing this reinforcement may be fiilled thus : let N represent the necessary number of bars for reinforcement, and knowing the width of the beam, which in this case is 15", we may deduce a formula which can be used in determining the number of bars to be used as follows: SD X N + (2X1.5^) = 15 Distance between corresponding faces of adjacent rein- forcing bars. Number of reinforc- ing bars. Distance of rod faces from beam faces. Width of beam we are con- sidering. We may SDN substitute + or 3D this = 15. formula until the two members balance, first and we have Suppose we try a 1" sq. bar for the 5XiXA^ + 3Xi = iS or 5A^-^3 = IS .... 8A^=is REINFORCED CONCRETE. N=i 7/8, and it is evident we cannot use a fraction of a bar, so we call N=2. Two bars, each i" in diam. will not, however, give us sufficient steel reinforcement, since we will have but 2 and according to calculations we should have 3 3/4 two bars i 1/2" diam. will give us a total steel area of 4.5 and we are ready to specify the location; under directions of p. 142 these must not be nearer to each other than 4X1.5 =6", nor nearer to the beam faces than 1.5X1.5 = 2.25". If we go over the dimensions we have for total measure- ment over rods: 6" + 3" = 9" Distance Twice between diam. of rods. one rod. 15" ~ 9" = 6" or we have 3" between Total width face of beam and face of of beam. each rod. hence we are within all limitations. We must now find out whether or not the beam is safe in shear; the reaction at each end of the beam is 6.5 tons, or 13,000/, and this is the load tending to shear the member. Applying the formula p. 144, for the safe shearing load to which this beam may be subject we have 2 Z = -X5oXi5X2o= io,ooof. 3 Our design is not sufficiently large to care for shear, so we must increase the area as it approaches the columns, MATERIALS AND CONSTRUCTION. which we may do by increasing the depth at these points until we have 2 13,000 = -X so X 15 X depth, 3 or depth must be 26". The beam will take the form shown at b, fig. 65. The distance of the reinforcing rods from the bottom of the beam should be 1/8X20" = 2.5", and carried di- rectly across the beam as indicated by the dotted lines in b, fig. 65. As we have 25 T supported on four columns it is evident that each column will carry a load of 6 1/4 T = i2,5oo#; we will design these on a basis of diameter equal to 1/15 of length, and have: 1/15X15 = 1 ft. = 12" diam. of longer column and 1/15X10 = 10/15 ft. = 8'' diameter of shorter column. Design on a stress of 400/ per sq. in., and each of these columns will carry 12 X 12 X4oo = 57,6oo# and 8X8X400 = 25, 6oo# safely. We may proceed directly with the reinforce- ment, as the columns are safe, so far as compressive stresses are concerned. The reinforcing rings will be square and each : 7/8X12 = 10 1/2" and 7/8X8" = 7" having the proper lap. (see fig. 62). The diameter of stock from which these rings will be made is i/4oXi2 = .3" or 5/16" and 1/40X8 = .2" or 1/4". . REINFORCED CONCRETE. 153 When calculated values are determined, it is customary- practice to take the nearest sixteenth inch size, hence 5/ 1 6" = .3 1 2'' and 1/4" = .2 50" come nearest to the calculated values above; for lengthwise reinforcement, the diameter of rods will be the same as for the rings in each case, eight rods being used as shown at fig. 60, placed inside the rings ; the vertical distance between the reinforcing rings is i/8Xi2" = i 1/2" 1/8X8 =1" respectively. (If a coil is used this will be the pitch of the "spiral" to which coil is wound.) Fig. 64. Rods can be purchased on the market, which are 10 ft. and 15 ft. long without difficulty, hence, no lapping of reinforcement will be necessary. The column footings are the next features to be consid- ered, and as this work was placed on firm earth, we may assume a loading of i 1/2 T per sq. ft. Each column carries 6 i /4 T, hence area at bottom of footing must be 154 MATERIALS AND CONSTRUCTION. 25 3 r. =4.1 sq. ft. 4 2 which we may call 4 sq. ft. for practical purposes. Making the footing 2 ft. sq. the overhang in each case will be: 6" in the case of 12" column and 8" in the case of 8" column. Height of footing according to formula p. 146 is: /i-. 56X6X1. 5 = 5-04" or 5 1/4" and h-.56X8X 1.5 = 6.72" or 6 3/4". "1 r J" Fig. 6s. Fig. 66. As to reinforcement of footings, formulas p. 147 give us 1/50X6 = . 12" or 1/8" and 1/50X8 = . 16" or 3/16'' as rod diameters. These rods will be spaced respectively: 8.5Xi/8 = i"( + ) for 12" column and 8.5X3/16" = 1.6" or I 5/8" for 8" column. • Such rods should be located 1/8X5 1/4 = 5/8" ( + ) and TABLES. 1/8X63/4=7/8" (-) from bottom of footing. These footings made square, with two layers of reinforcing, one above the other, and sides standing at an angle of 60° with the horizontal, giving a top smaller than bottom; as the beam A, fig. 64, is 15" wide and columns 8'' and 12", it is evident that the columns must be "flared" at the top to give a support over the whole bottom of the beam; the design of one bent is shown complete in fig. 66. Any of the problems involving columns or beams which have been presented may be used for practice in reinforced concrete, since it is somewhat a matter of choice as to what materials shall be used in these constructions. Elastic Limits of Materials. TABLE I. (Largely from Trautwine's "Civil Engineers' Pocket-book,' Trautwine Company, Philadelphia, Pa.) Material. Ash 4Soo#D" White or yellow pine 33oo# □" Spruce 33oo#D" Cast brass 6ooo# Drawn brass (may be used for rolled brass) i6ooo#n" Cast copper 6300/ Drawn copper (may be used for rolled copper) ioooo#n" Cast iron 45oo#D" Wrought iron 3oooo#n" Steel 39ooo#n" 156 MATERIALS AND CONSTRUCTION. TABLE 2. Ultimate strength in lbs. per sq. in. of metals. Taken largely from "Mechanics of Engineering" by Irving P. Church, C. E. Pub. by John Wiley and Sons, New York. Material. Tension. Com- pression. Shear. 80,000 130,000 30,000 45,000 200,000 90,000 40,000 70,000 go,ooo f quite 10,000 < ^ variable 50,000 Where no definite information as to compressive strength of a material such as steel or wrought iron is available it may be assumed as about 2/3 of tensile strength. Malleable iron 30,000^, 50,000/, io,oooyf. TENSILE STRENGTH OF STEEL. Bessemer-Structural and bar 50,000 Open hearth structural and bar 50,000 ■ Cold rolled steel 75,000 Crucible 95, 000 Tool steel 130,000 When you are not certain just what kind of steel you will use in a design, base calculation on general entries of soft and hard as in first section of table. If class is definitely known use second section for steel. TABLES, TABLE 2 A. Values of Su for use in gearing. Speed of teeth 100 in feet per or 200 300 600 900 1200 1800 2400 minute less 8000 6000 4800 4000 3000 2400 2000 1700 20000 1 5000 12000 10000 7500 6000 5000 4300 From Kent's Engineer's Pocket Book. John Wiley and Sons, N. Y. TABLE 3. Ultimate strength of various woods in lbs. per square inch. From Mechanical Engineer's Pocket Book, by William Kent, M. Am. Soc. M. E. John Wiley and Sons, New York. Wood Tensile strength Crushing strength endwise Crushing strength crosswise Shearing strength with grain Shearing strength across grain Ash 12000 6800 3000 Soo 6200 Oak 1 1000 7000 4000 800 4400 Yellow pine. . . 13000 8500 2600 300 SSoo 10000 4SOO 1200 250 3200 Hemlock 7200 4000 1000 400 2700 Note. — Values in all instances are in whole numbers, rather than as exactly given in table; hemlock is a particularly unreliable wood as sold in the market. MATERIALS AND CONSTRUCTION, TABLE 4. Factors of Safety. Cast iron, 4 for a dead load. 6 for a live load. 1 5 for a load producing shocks. Steel, 3 for a dead load. 5 for a live load. 12 for a load producing shocks. Timber, 7 for a dead load. 10 for a live load. 20 for a load producing shocks. Brickwork, 20 for a dead load. 30 for a live load. Stonework same as brickwork. Malleable iron and brass same as cast iron. Wrought iron same as steel. Reinforced concrete, 4 for a dead load. Reinforced concrete, 5 for a live load. Plain concrete, 10 for a dead load. Plain concrete, 15 for a live load. TABLES. TABLE 5. Ultimate strength of brickwork, stonework and concrete. All entries are for work which is 3 Ultimate crush- months old. ing strength in tons per sq. ft. Common brick laid in lime mortar, 60 Common brick laid in Rosendale cement 100 mortar, Common brick laid in Portland cement 150 mortar, Rubble walls (stone), Portland cement 30 mortar. Dimension sandstone, Portland cement 100 mortar, Dimension granite, Portland cement mortar 200 Portland cement concrete, 144 Terra cotta (dense), ^ One half that given for brick- work. Terra cotta (porous), Three tenths that given for brick- work. Ultimate tensile strength of brick and stonework laid in lime mortar may be taken at about 1.5 tons per sq. ft.; and shearing strength about 1/2 of tensile strength. The workmanship is supposed to be well done for these allowances. Ultimate tensile strength of concrete about i/io of compressive strength and shearing strength may be taken about equal to tensile. * National Fire Proofing Co., N. Y. City, issues descriptive pamphlets. i6o MATERIALS AND CONSTRUCTION. TABLE 6. Common standard sizes of timber. In section. Two inches by 4//_6"_8"-i o"-i 2 "-1 ^"-16" Two and one-half inches by i2"-i4"-i6" Three inches by 6"-8"-io"-i2"-i4"-i6" Four inches by 4"-6"-8''-io"-i2"-i4" Six inches by 6''-8"-io"-i2"-i4"-i6" Eight inches by 8"-io"-i2"-i4" Ten inches by io"-i2"-i4"-i6" Twelve inches by i2"-i4"-i6" Fourteen inches by i4"-i6" In length. 10 ft. 12 ft. 14 ft. 16 ft. 1 64 MATERIALS AND CONSTRUCTION. TABLE 8. — Continued PROPERTIES OF STANDARD I-BEAMS. of Beam. SVeight per Foot. )f Section Thickness of Web. of Flange. Moment of Inertia Axis I-I. Depth Area c Width d A t b I Inches lbs. Sq. Ins. In. Ins. Ins. 4 9 21 .OO 6.31 .29 4.33 84.9 9 25.00 7.3s .41 4.4s 91.9 9 30-00 8.82 .57 4.61 loi .9 9 35. 00 10. 29 .73 4.77 III. 8 lO 25.00 7.37 .31 4.66 122 . 1 lO 30.00 8.82 .45 4.80 134.2 lO 35.00 10. 29 .60 4.95 146.4 lO 40.00 11.76 .75 S.io 158.7 12 31.50 9. 26 .35 S .00 215.8 12 3S.OO 10.29 .44 5-09 228.3 I 2 40 . 00 II .76 .56 5.21 24s. 9 IS 42 .00 12 .48 .41 5.50 441 .8 IS 45.00 13 .24 .46 S.5S 4S5.8 IS 50.00 14.71 .56 5.65 483 -4 IS 55. 00 16.18 .66 S.7S 511 .0 IS 60 . 00 17.65 • 75 5. 84 538. 6 Ins.' = 1 Ins. 18.9 20 .4 22 . 6 24.8 24.4 26.8 29.3 31.7 36.0 38.0 41 . o 58.9 60.8 64 S 68.1 71.8 3.67 3.54 3 .40 3 .30 4.07 3.90 3.77 3.67 4.83 9.50 4.71 10.07 4.S7 10.95 S.9S 5. 87 5. 73 S.62 5. 52 "Cambria Steel," prepared by George E. Thackray, C. E. i66 MATERIALS AND CONSTRUCTION. TABLE 9. — Continued. PROPERTIES OF STANDARD CHANNELS. Depth of Channel Weight per Foot Area of Section Thick- ness of Web Width of Flange Moment of Inertia Axis i-i Section Modulus Axis i-i d A t b I S Inches Pounds Sq. Ins. Inch Inches Inches* Inches' 9 9 9 9 10 10 10 10 10 12 1 2 12 1 2 1 2 IS IS IS IS IS IS 13 -as IS -oo 20 . 00 25 .00 IS -oo 20 . 00 25 .00 30.00 35 .00 20.50 25 .00 30.00 35.00 40 . 00 33.00 35. 00 40 . 00 45 .00 SO. 00 55. 00 3.89 4.41 5.88 7.35 4.46 5.88 7.35 8.82 10 . 29 6.03 7-35 8.82 10.29 11 . 76 9.90 10 . 29 11 . 76 13 24 14.71 16.18 .23 . 29 •45 .61 .24 .38 ■ S3 .68 .82 .28 ■39 .51 .64 .76 .40 • 43 • 52 .62 • 72 .82 2^43 2.49 2 .65 2.81 2 . 60 2.89 3 .04 3.i8 2.94 3.05 3-17 3 30 3 ^42 3 ^40 3 ^43 3 ^52 3 62 3^72 3^82 47^3 SO. 9 60.8 70.7 66.9 78 . 7 91 . 0 103 .2 115.5 128. 1 144.0 161 .6 179-3 196.9 312-6 319-9 347. S 37S-I 402 . 7 430.2 10. 5 11.3 13-5 1S.7 13-4 15.7 18.2 20 . 6 23 ■ I 21 .4 24 . 0 26 . 9 29.9 32.8 41.7 42.7 46.3 SO-o 53-7 57-4 " Cambria Steel," prepared by George E. Thackray, C. E. 1 68 MATERIALS AND CONSTRUCTION. TABLE lo. — Continued. PROPERTIES OF STANDARD ANGLES. Thick- ness Inch "Weight per Foot Pounds 2- 5 3- 2 4.0 4- 7 5- 3 6.0 3- 1 4- 1 5- o 5-9 6.8 7-7 8.S 4.9 6.r 7.2 8.3 9-4 I0.4 11-5 12. s Area of Section Sq. Ins. .72 • 94 i.i6 1 .36 I.S6 1.75 .91 1. 19 1.47 1.74 2 . 00 2.2S 2.50 1.44 1.78 2. II 2.44 2.7S 3 .06 3.36 3.66 Moment of Inertia Axis i-i Inches* .27 • 35 .42 .48 • 54 .59 • 55 .70 .85 .98 I . II 1.23 1-34 1 . 24 1-51 1 . 76 1.99 2 . 32 2.43 2.62 2.81 Section Modulus Axis i-i Inches' .19 .25 • 30 • 35 .40 .45 .30 .39 .48 .57 .65 .72 .80 .58 .71 .83 .95 1 .07 1. 19 1.30 1 .40 Cambria Steel," prepared by George E. Thackray, C. E. 170 MATERIALS AND CONSTRUCTION. TABLE 12. PROPERTIES AND PRINCIPAL DIMENSIONS OF STANDARD T-RAILS. Axis i-l. Weight A rpa b d k X per ^^3,rci Moment Section of Inertia. !M[odulus. Pounds. Sq. Ins. Inches. Inches. Inches. Inches. I S 8 0 78 li li n 0 75 0 23 0.31 12 I 18 ij li 0 92 0 55 0.58 16 I 57 2i 2i li I I I I 0.95 20 2 00 2i 2i If I 2 I 7 1-3 25 2 5 2i 2i li I 3 2 6 1.8 30 2 9 3 3 if 1 4 3 6 2.3 35 3 4 3i 3i li I 6 4 9 3.9 40 3 9 3i 3i il I 7 6 6 3.6 4S 4 4 3JJ 3}g 3 1 8 8 I 4-2 SO 4 9 3i 3i 2j I 9 9 8 4-9 SS S 4 4l"6 . 1 4l6 2i 2 0 1 2 2 5-9 60 S 9 4i 4i 2-8" 2 I 14 7 6.7 6S 6 4 4 IS 4t^s 2ii 2 2 17 0 7-4 70 6 9 4i 4l 2l\ 2 2 20 0 8.4 75 7 4 4li 4 IB 2ji 2 3 23 0 9.1 80 7 8 5 5 2i 2 4 26 7 10. 1 8S 8 3 Sis 5t% 215 2 5 30 S 1 1 . 2 90 8 8 Si Sf 2i 2 6 34 4 12.3 9S 9 3 Sl°e 5lB 2 7 38 6 13 -3 100 9 8 Si Si 2i 2 8 43 4 14-7 ISO 14 7 6 6 4i 3 0 69 3 23 • I All sections from 40 lbs. to 100 lbs. both inclusive are Am. Soc. C. E. Standard. "Cambria Steel," prepared by George E. Thackray, C. E. TABLES. 171 TABLE 13. DIMENSIONS OF BOLTS AND NUTS. Franklin Institute Standard. Bolts and Threads. Rough Nuts and Heads . Diameter at Root of Thread. Area of Diameter 1 nreaas Area of Bolt at 1 hicjcness 1 1 hicKness 01 ijOlt. per Inch. ooiL rjoay. Root of of Nuts. of Heads. Inches. No. Inches. Sq. Ins. Sq. Ins. Inches. Inches. i 20 .18s .049 . 027 i i i8 . 240 .077 ■ 04s 10 1 16 .294 . 110 .068 3 1 1 32 7 I6 14 • 344 .ISO .093 7 16 36 ei 13 .400 . 196 . 1 26 7 16 9 10' 12 .454 .249 . 162 64 1 1 1 .507 ■ 307 . 202 s i 10 .620 .442 .302 i f i 9 • 731 .601 .420 i 1 8 .837 .785 .550 I li 7 .940 • 994 .694 ij u li 7 1 .06s 1 . 227 .893 li I 1? 6 1 . 160 1.48s 1 .057 if ii'2 li 6 1 . 284 I . 767 1.29s li I IB If si 1.389 2.074 1.51S If lii if s I -490 2.405 1.744 li if I 8^ 5 1 .615 2.761 2 . 048 li iM 2 4i 1.712 3 • 142 2.302 2 Irs 2i 4i 1 . 962 3.976 3 .023 2i li 4 2.I7S 4.909 3.715 2i i}§ 2i 4 2.42s 5-940 4.619 2f 2i 3 3i 2 . 629 7 . 069 5.428 3 2 A 3i 3i 2.879 8.296 6.510 3i 2i 3i 3i 3 . 100 9.621 7.548 3i 2 IB 3i 3 3.317 11.045 8.641 3l 2| 4 3 3 .567 12.566 9.993 4 3 IS 4i 2i 3.798 14. 186 II .329 4i 3i Ai 2| 4 . 028 15.904 12.743 4* 3 IS 4i 2i 4.255 17.721 14 . 220 4i 3f S 2-i 4 .480 19.63s IS. 763 5 3U Si 2i 4.730 21 .648 17.572 Si 4 si 2t 4.953 23.758 19 . 267 Si 4is si 2t 5.203 25.967 21 . 262 si 4* 6 2i 5. 423 28 . 274 23 .098 6 4/s "Cambria Steel," prepared by George E. Thackray, C. E. Bolts and nuts are put on the market in standard sizes ; a study of this table shows us that for a given diameter there are a certain number of threads per in. used, that the body of the bolt and section at bottom of thread have certain areas, and heads of bolts as well as nuts have given standard thicknesses; all of these values are necessary in design involving use of bolts and nuts in construc- tive work. 172 MATERIALS AND CONSTRUCTION. TABLE 14. UPSET SCREW ENDS FOR ROUND BARS. Diameter of Bar. Area of Body of Bar. Diameter of Screw. Length of Upset. Area at Root of Thread. Number of Threads per Inch. A B G Inch. Sq. Ins. Inches. Inches. Sq. Ins. 1 . X96 I 4i .30a 10 Iff .249 f 4i .302 10 i .307 i 4* .420 9 ih .371 4i .550 8 1 • 44a 4i • S50 8 ii .519 ij 4i .694 7 i .601 li 4i .893 7 if .690 li 4f .893 7 .78s i| S 1.057 6 .887 if S 1. 057 6 Ii .994 li S 1.29s 6 1. 108 14 s 1.295 6 li 1.227 Ii 5i 1.515 si I-3S3 il si 1 . 744 5 I* 1.48s 1} si 1.744 5 1.623 ij si 2.048 s li 1.767 2 si 2.302 4i 1. 918 2 si 2.302 4i If 2.074 2i si 2.650 4i lU 2.237 2i si 2.650 4i li 2.40s ai si 3.023 4i iM 2.580 2i si 3.023 4i li 2.761 2i 6 3.419 4i i}g 2.948 2i 6 3.71S 4 2 3.142 6 3.715 4 3-341 2i 6i 4-155 4 3 .547 6i 4.1SS 4 3.758 2i 6i 4-619 4 2i 3.976 2i 6i S.108 4 TABLES. 173 TABLE 14. — Continued. UPSET SCREW ENDS FOR ROUND BARS. ■ Diameter of Bar. A Area of Body of Bar. Diameter of Screw. Length of Upset. Area at Root of Thread. Number of Threads per Inch. B C Inch. Sq. Ins. Inches. Inches. Sq. Ins. 6 2is 4 . 200 2i 6J S . 108 4 2t 4-430 3 6i S.428 3h 2 1 If 4.666 3i 6J S.9S7 3i 2i 4.909 3i 6i S-9S7 zh Si's S.IS7 3i 6i 6.510 3i 2f S.412 3i 6i 6.510 3i S.673 3f 7 7.087 3* 2i S.940 3f 7 7.087 3* 2}| 6. 213 3i 7 7.548 3i 2i 6.492 3l 7i 8.171 3i 2}g 6.777 3f 7i 8. 171 3i 3 7.069 3i 7i 8.641 3 " Cambria Steel, " prepared by George E. Thackray, C. E. These bars are used in places to take tension; they may be used in small cranes, and as " counterbraces " in stands or platform supports; both round and square type are available, and may be made in the forge shop or purchased on the market. 174 MATERIALS AND CONSTRUCTION. TABLE 15. UPSET SCREW ENDS FOR SQUARE BARS. Side of SQU,a.re Bar. Area of Body of Bar. Diameter of Screw. T of Upset. Area at Root of Thread. Number of Threads per Inch. A Q Inch. Sq. Ins. Inches. Inches. S Ins ns. . 250 i 4i .302 10 .316 i 4i .420 9 S • 391 I 4i .550 8 ik • 473 I 4i .550 8 f • 563 li 4f .694 7 ii .660 li 4f .893 7 i .766 I* 5 1 .057 6 Tii .879 i|- S 1.0S7 6 I I . 000 li 5 1 . 295 6 1.129 if 5i 1 .515 si li 1 . 266 if si 1.515 si 1 .410 if Si 1 • 744 s li 1 .563 I* si 2 . 048 5 1.723 i-l si 2 .048 S If 1. 891 2 5i 2 .302 4i lj\ 2 . 066 2i Si 2.650 4i li 2 . 250 2i si 2 .650 4i li% 2.441 2i si 3 .023 4i If 2 . 641 2| 6 3 .419 4i lli 2.848 2f 6 3.419 4i ij 3 .063 6 3.715 4 3.28s 2i 6i 4-155 4 ll 3.516 2t 6i 4. IS5 4 3.754 2i 6i 4.619 4 2 4 . 000 2i 6i 5.108 4 2i's 4.254 2i 6i 5.108 4 2j 4.516 3 6i 5.428 3i 2lB 4.78s 3J 6i S.9S7 3i 2i 5 .063 3i 6i 5.957 3i TABLES. 175 TABLE 15. — Continued. UPSET SCREW ENDS FOR SQUARE BARS. Side of Area of Body of Bar. Diameter Length of XJpset. Area at Root of Thread. Number of Threads per Inch. A G Inch. Sq Ins. Inches. Inches. Sq. Ins. 5-348 3i 6i 6.510 si 2 "8" 5-641 3t 7 7-087 3i 2r5 5-941 3i 7 7.087 3i 2i 6.250 3i 7 7-548 3l 2 16 6.566 3i 7i 8. 171 3i 2S 6.891 3i 7i 8. 171 3i 2l5 7-223 3i 7i 8.641 3 2i 7-563 3l 7i 9-30S 3 2 IB 7.910 3i 7i 9-30S 3 2i 8.266 4 7i 9-993 3 2li 8.629 4i 7i 10. 706 3 3 9 . 000 4i 7i 10. 706 3 " Cambria Steel, " prepared by George E. Thackray, C. E. These bars are used in places to take tension; they may be used in small cranes, and as " counterbraces " in stands or platform supports; both round and square type are available, and may be made in the forge shop or purchased on the market. 176 MATERIALS AND CONSTRUCTION. TABLE 16. LENGTH OF RIVETS REQUIRED FOR VARIOUS GRIPS IN- CLUDING AMOUNT NECESSARY TO FORM ONE HEAD. Grip >W ^ Grip- -Length Diameter of Rivet in Inches. • T 1, in XncxiGS- i" 4" S" i" 4" i" li" It 15 I* iir 2 as ai 5 ? » 1 IS 1* if _ 7 1* 2 ai ai af 3 % _ 1 It i4 li 2 ai ai af 24 i If If ,7 a* ai ai a4 2i It It 2 ai 2| a4 ai a} -1 I* If I* 24 ai at 2i 2i a4 It IJ 2 2i 24 at ai a4 3 If ^\ 2i 2I 2t a4 3 3 3i _ 1 15 2 24 ai 3 3i 34 3i 18 2i ai 24 3i 3i 3i 34 2i 24 2f 3 3i 3i 34 3i 2i aj 3i 3f 34 3i 3I 2 2i ai 3i 3f 34 3S 3i 3I 2i 2i 3i 34 3S 3i 34 4 2i 3 3f 3f 3i 34 4 4i 2# •^8 ^8 OB 3 z ot 3s 4 A it 45 4t 2i 3 3i 3f 34 4 4i 4i 4i 2f 3j 34 3J 4 4i 4i 4i 44 2i 3i 3f 3i 4i 4i 4i 44 4i a* 3i 3i 4 4i 4i 44 4i 4f 3 34 3i 4i 4i 44 4S 4i 44 3i 3S 4 4i 44 4i 4i s s 3i 3l 4i 4i 4l 44 s si si 3f 3i 4i 44 44 s si si si 34 4 4i 4i S si si si s4 3i 4i 44 4i Si si si s4 si 3i 4i 4f 4f 44 si si s4 si si 34 4i s Sf s4 si si s4 4 44 4i si s4 si si s4 6 4i 4f S si si si . s4 6 6i 4i 4i si s4 si 54 6 6i 6i 4f 4i si sf s4 6 6i 6i 6i 44 5 si sf 6 6i 6i 6i 64 REINFORCED CONCRETE. 177 TABLE 16. — Continued. LENGTH OF RIVETS REQUIRED FOR VARIOUS GRIPS IN- CLUDING AMOUNT NECESSARY TO FORM ONE HEAD. Diameter of Rivet in Inches. Rivet in Inches. i" f" i" f" f" 7 // 1" i4" 4i si Si si 6i 6i 61 6i 61 4f si si 6 6i 6i 6f 6i 6i 4l si si 61 6i 6f 6i 61 65 5 si si 6i 61 6i 61 ' 7 7 Si si 6 61 6i 6J 7 7i 7i si si 6i 6i 6* 7 7i 7i 7i sf s* 6i 61- 7 7i 7i 7-1- 7l s4 6 6i 6i 7i 7i 7f 7i 7i sf 6i 6i 6-J 7i 7f 7i 7i- 7f si 6i 6i 7 7 s 7l 7l 7i 7i si 6i 6i 7i 7i 7i 7i 7l 75 6 6i 7 7i ll ll 8 8i Amount in Inches to be subtracted from above lengths for Countersunk Heads. i i "Cambria Steel," prepared by George E. Thackray, C. E. The beginner is at a loss to know what rivet length he should select to hold a certain thickness of plate in joint, and have it " head up " properly. This table gives such information for button and countersunk heads. 178 MATERIALS AND CONSTRUCTION. TABLE 17. WEIGHTS OF VARIOUS SUBSTANCES. The Basis for Specific Gravities is Pure Water at 63 Degrees Fah., Barometer 30 Inches. Weight of One Cubic Foot, 62.355 Pounds. Average Weight of One Cubic Foot. Pounds. Air, atmospheric at 60 degrees F., under pressure of one atmosphere, or 14.7 pounds per square inch, weighs sisth as much as water Aluminum Anthracite of Penna Anthracite, broken, of any size, loose Anthracite, broken, moderately shaken Anthracite, broken, heaped bushel, loose, 77 to 83 pounds. . Anthracite, broken, a ton loose occupies 40 to 43 cubic feet . . Antimony, cast Antimony, native Ash, perfectly dry Ash, American White Ashes of soft coal, solidly packed Asphaltum, i to 1.8 Brass (copper and zinc), cast Brass, rolled Brick, best pressed Brick, common and hard Brick, soft inferior Brickwork, pressed brick, fine joints Brickwork, medium quality Brickwork, coarse, inferior, soft Brickwork, at 125 pounds per cubic foot, i cubic yard equals 1.507 tons, and 17.92 cubic feet equal i ton Bronze, copper 8, tin i (gun metal) Cement, hydraulic. American, Rosendale, ground and loose Cement, hydraulic. American, Rosendale, U. S. struck bush., 70 pounds Cement, hydraulic. American, Rosendale, Louisville bushel 62 pounds Cement, hydraulic. American, Cumberland, ground, loose. Cement, hydraulic. American, Cumberland, ground, thor- oughly shaken .0765 162 93. S 52 to 56 56 to 60 418 416 47 38 40 to 45 87.3 S04 524 ISO I2S 100 140 125 100 529 56 REINFORCED CONCRETE. 179 TABLE 17. — Continued. WEIGHTS OF VARIOUS SUBSTANCES.— Continued. The Basis for Specific Gravities is Pure Water at 62 Degrees Fah., Barometer 30 Inches. Weight of One Cubic Foot, 63.355 Pounds. Average Weight of One Cubic Foot. Pounds. Cement, hydraulic. English Portland (U. S. struck bushel, 100 to I 28) Cement, hydraulic. English Portland, a barrel, 400 to 430 pounds Cement, hydraulic. American Portland, loose Cement, hydraulic. American Portland, thoroughly shaken. Charcoal of pines and oaks Chalk Cherry, perfectly dry Clay, potters', dry Clay, dry in lump, loose Coal, bituminous, solid Coal, bituminous, solid, Cambria Co., Pa Coal, bituminous, broken, of any size, loose Coal, bituminous, moderately shaken Coal, bituminous, a heaped bushel, loose, 70 to 78 Coal, bituminous, i ton occupies 43 to 48 cubic feet Coke, loose, good quality Coke, loose, a heaped bushel, 35 to 42 Coke, I ton occupies 80 to 97 cubic feet , Corundum, pure, 3.8 to 4. , Copper, cast , Copper, rolled Cork, dry Earth, common loam, perfectly dry, loose Earth, common loam, perfectly dry, shaken Earth, common loam, perfectly dry, rammed Earth, common loam, slightly moist, loose Earth, common loam, more moist, loose Earth, common loam, more moist, shaken , Earth, common loam, more moist, packed Earth, common loam, as soft flowing mud Earth, common loam, as soft flowing mud well pressed Elm, perfectly dry Flint 81 to 102 no IS to 30 IS6 42 119 63 84 79 to 84 47 to 52 SI to 56 23 to 32 542 SSS IS 72 to 80 82 to 92 90 to 100 70 to 76 66 to 68 75 to 90 90 to 100 1 04 to 112 1 10 to 120 35 162 i8o MATERIALS AND CONSTRUCTION. TABLE 17. — Continued. WEIGHTS OF VARIOUS SUBSTANCES.— Continued. The Basis for Specific Gravities is Pure Water at 62 Degrees Fah., Barometer 30 Inches. Weight of One Cubic Foot, 62.355 Pounds. Average Weight of One Cubic Foot. Pounds. Glass Glass, common window Gneiss, common Gneiss, in loose piles Gold, cast, pure or 24 karat Gold, pure, hammered Granite Greenstone Gypsum, plaster of Paris Hickory, perfectly dry Ice Iron Iron, grey foundry, cold Iron, grey foundry, molten Iron, wrought Lead, commercial Lignumvitae (dry) > Limestone and marble Lime, quick Lime, quick, ground, well shaken, per struck bushel 80 pounds Lime, quick, ground, thoroughly shaken, per struck bushel 93 J pounds Locust Mahogany, Spanish, dry Mahogany, Honduras, dry Maple, dry Marble (see Limestone) . Masonry of granite or limestone, well-dressed Masonry of granite, well-scabbled mortar rubble, about 5 of mass will be mortar Masonry of granite, well-scabbled dry rubble Masonry of granite, roughly scabbled mortar rubble, about i to ^ of mass will be mortar Masonry of granite, scabbled dry rubble 186 IS7 168 96 1204 1217 170 187 141 6 S3 57 4 446 4SO 433 480 709 6 41 to 83 164 4 95 64 75 44 S3 35 49 i6s 154 138 150 12s REINFORCED CONCRETE. TABLE 17. — Continued. WEIGHTS OF VARIOUS SUBSTANCES.— Continued. The Basis for Specific Gravities is Pure Water at 62 Degrees Fah., Barometer 30 Inches. Weight of One Cubic Foot, 62.355 Pounds. Average Weight of One Cubic Foot. Pounds. Masonry of sandstone, J less than granite. Masonry of brickwork (see Brickwork). Mercury, at 32 degrees Fah Mica, 2.75 to 3. 1 Mortar, hardened Mud, dry, close Mud, wet, moderately pressed Mud, wet, fluid Oak, live, perfectly dry, (see note below) . Oak, Red, Black, perfectly dry Petroleum Pitch Poplar, dry (see note below) . Platinum Quartz Rosin Salt, coarse, (per struck bushel, Syracuse, N. Y., 56 pounds) . Sand, of pure quartz, perfectly dry and loose Sand, of pure quartz, voids full of water Sand, of pure quartz, very large and small grains, dry Sandstone Sandstone, quarried and piled, i measure solid makes if (about) piled Snow, fresh fallen Snow, moistened, compacted by rain Sycamore, perfectly dry (see note below) Shales, red or black Silver Slate Soapstone Steel Sulphur Tallow Tar Tin, cast 849 183 103 80 to 1 10 1 10 to 130 104 to 120 59-3 32 to 45 S4-8 71.7 29 1342 165 68.6 45 90 to 106 118 to 129 117 iSi 86 5 to 12 IS to so 37 162 6SS I7S 170 490 I2S 58.6 62.3SS 459 l82 MATERIALS AND CONSTRUCTION. TABLE 17. — Continued. WEIGHTS OF VARIOUS SUBSTANCES. The Basis for Specific Gravities is Pure Water at 62 Degrees Fah., Borometer 30 Inches. Weight of One Cubic Faat, 62-355 Pounds. Average Weight of One Cubic Foot, Pounds. Walnut, Black, perfectly dry (see note below) Water, pure rain, distilled, at 32 degrees F., Bar. 30 inches. Water, pure rain, distilled, at 62 degrees F., Bar. 30 inches . . Water, pure rain, distilled, at 212 degrees P., Bar. 30 inches. . 38 62 .417 62.355 59.7 64.08 437.5 "Cambria Steel," prepared by George E. Thackray, C. E. Note. — Green timbers usually weigh from one-fifth to nearly one-half more than dry; ordinary building timbers, tolerably seasoned, one-sixth more. TABLE 18. Values of B for use in column formulas. Gray Iron Wrought Iron Structural or Open hearth steel Crucible Machine Steel Timber I I I I I 6400 36000 22000 14000 3000 From Carpenter's Mechanics of Engineering. Wiley and Son's N. Y. REINFORCED CONCRETE. 183 TABLE 19. • Formulas for Polar Moment of Inertia (Ip) . From "Mechan- ics of Engineering" by I. P. Church, C. E. John Wiley and Sons, N. Y. City. For a solid circular shaft. For a hollow circular shaft. 7p = j7r(ri*-r2*) For a solid square shaft. T —ih* TABLE 19 A. Table giving average values of floor load in pounds per sq. ft. for particular classes of buildings: Approximate, Rooms in dwelling houses and schools 50 Offices... 75 Garages, stables and foot bridges 70 Shops and store rooms 120 to 150 184 MATERIALS AND CONSTRUCTION. TABLE 20. Giving approximate strength of hemp rope. Diameters approximate. Diam. Circumference Ultimate strength in lb. 1" 2f" 4000 li" 31" 8000 li" 1 2000 li" sh" 16000 2" 6" - 20000 2i" 7" 28000 Cotton rope about two-thirds as strong as hemp. Manila rope about 50 per cent, stronger than hemp rope. TABLE 20 A. Resume of general notations used in formulas. H.P Horse power. Mg . . . . I Simple moment. Mb Bending moment. Mb Maximum bending moment. Mr Resisting moment. A'^= Rev. per minute. Pt Total uniform load. Pu A unit load. Li Length in inches. Lf Length in feet. Su Unit fiber stress as used in beam and column formula. / Rectangular moment of inertia. Ip Polar moment of inertia. Cn Distance from neutral axis to outer fiber of an element. REINFORCED CONCRETE. 185 TABLE. 20 A. — Continued. Pc A concentrated load. Pe An eccentric load. R A reaction. Rs A resultant. Safe unit fiber stress in shear. W Width in inches. V Surface speed in feet per min. Ac Arc of contact in degrees. r Radius of gyration. Pm A combined load treated as a single load. Sk Safe fiber stress in direct tension or comp. in eccentric column formula. d Distance of resultant of loads from column center. A Sectional area in sq. ins. Ts Radius of a shaft. TABLE 21. Shafting Speeds. Iron working shops 150 R. P. M. Wood working plants 275 R. P. M. Clothing factories and cloth mills in general. 3 50 R. P. M. Tx\BLE 21 A. Horse-power required for various machines, average values. Machine H. P. 20" Engine lathe J for metal turning. 15" Stroke shaper f for metal planing. 36" II ft. stroke planer i for metal planing. Drill press; capacity from i" to i" "1 ■■ r ,1 1 J .„ > It for metal work, dnll J * 10" Stroke slotter J for metal work. Brown and Sharpe milling machine 1 , ^ , , . T,j r o \. 1 j^g^al work. No. I J * 20" Swing horizontal boring mill i for metal work. 24" Planer 3 for wood work. MATERIALS AND CONSTRUCTION. TABLE 2 1 A. — Continued. Saw bench carrying a saw 23" diam. 3 J for wood work. Band saw, 34" wheel i for wood work. Grindstone for general use. Emery wheel i for general use. Adapted from Kent's Engineer's Pocket Book. Wiley and Sons, N. Y. TABLE 21 B. Holding power of lag. screws. Diam. of screw Diam. of bit used to bore hole Length of thread screwed in wood Load at which screw pulled out I" f" 3" 590o# v 11" 1 6 3" ¥' ¥' 3" 6ooo# ¥' 2." 5" 9000# i" t" 4¥' 7ooo# i" ¥' 4" 6ooo# V ¥' 3¥' 35oo# ¥' 2" i900# \" 3 // 1^ i" 7oo# TABLE 22. From Hutton's Mech. Eng. of Power Plants. Relation between thickness of plate, diameter of rivet and diameter of hole for riveted joints. 1 1 5 1 7 1 e i Diam. of rivet t 11 1 6 a 4 la 1 6 i i 1 0 I H INDEX OF TABLES. Angles, properties, 167 Average floor loads for buildings, 183 Bolts and nuts, dimensions, 171 Channels, properties, 165, 166 Elastic limit of materials, 155 Factors of safety, 158 Fiber stress values (Su) for gearing, 157 Formulas for polar moment of inertia, 183 for properties of sections, 161, 162 Holding power of lag screws, 186 Horse-power required for machines, 185 Properties of standard I-beams, 163 Relation between plate thickness, 186 diameter of rivet, 186 of rivet hole, 186 Resume of notation, 184 Rivets, length required for grips, 176 Shafting speeds, 185 Standard sizes of timber, 160 Strength of hemp rope, 184 T-Bars, properties, 169 T-rails, properties and dimensions, 170 Ultimate strength of brickwork, stonework, concrete, and terra-cotta, 159 of metals, 156 of woods, 157 Upset screw ends for round bars, 172 for square bars, 174 Values of B for use in column formulas, 182 Weight of electrical machinery, 187 Weights of substances, 178 189 INDEX OF SUBJECTS. Aggregate, 25 Application of column iormulas, 78 of text to joint design, 129 Arc of contact, 93, 94 Area, unit of, 6 Ashler, 20 Axis, longitudinal, 4 Beam design, 59-61 Beams, method of loading, 36 simple, 37 uniformly loaded, 63 Bearing power of soil and masonry, 145 Belting, 91 formulas, 92 Bending moments, 59 Bricks, 22 arch, hard, 22 red, well burned, 22 salmon, soft, 22 Broken stone, 19 Calculations, elementary, 34 Cantilever design, 67 Cantilevers, 38, 66 Cast iron, 29 Cement, 23, 24 Column and beam design in concrete — illustrative problem, 150 classification, 73 design, re-inforced, 147 formulas and notation, 72, 75 191 192 INDEX OF SUBJECTS. Columns, 71 eccentric loading, 75 formulas for, 76 in re-inforced concrete, 144 problem illustrating solution for eccentric loading, 8 r Compression, 3 Concentrated loads, 37 Concrete, 25 amount of water per bag of cement when mixing, 27 forms for, 25 mixing, 25 number of turns of mechanical mixer, 2 7, producing satisfactory surface appearances, 25 proportions of ingredients, 27 re-inforced, 135 slushed, 25 strength of, 28 Counterbracing, 114 Crowning pulleys, 95 Dead and live loads, 11 Deformation, 2, 3 Design calculations for re-inforced concrete beams, 142 process of, in re-inforced beams, 144 Dimension stone, 2 1 Eccentric loading of columns, 75 Elastic limit, 8 Elasticity, 7 Elongation, 3 Factor of safety, 10 formula, 10 Fiber stress, 46 Footing proportions, re-inforced, 146 re-inforced design, 145 Forms for concrete, 25 Grading lumber, 29 INDEX OF SUBJECTS. Gravel, 22 Gravity axis, 41 Horse-power of belting, 90 Illustration of column and beam design in re-inforced con- crete, 148 Joint classification, 125 design, 128 application of text, 129 efficiency, 127 numerical values, 127 Lag screws, 122 Lime, 23 Load, distribution of on floor joist, 121 uniformly distributed, 37 Loads, dead and live, 1 1 producing shocks, 11 Location of greatest shear, 60 Longitudinal axis, 4 Lumber grading, 29 Malleable iron, 30 Materials, 19 for re-inforced concrete, 140 Maximum bending moment formula for uniformly loaded beams, 64 Metals, 29 Moment, 34 formulas, 35 of inertia, 44 polar, 45 rectangular, 44 positive and negative, 35 rule for, 34 value of, 34. 13 194 INDEX OF SUBJECTS. Neutral axis, 40 to outer fiber (distance,) 43 line, 40 plane, 40 Notes on setting forms in re-inforced concrete, 141 Pitch of rivets, 128 Positive and negative moments, 35 Principles, elementary, i Properties of sections, 38 Proportions of reinforcement in beams, 142 in columns, 147 Pull on support (determining,) 97 Pulley crowning, 95 Reaction, 38 Reactions, determination of, 50 Re-inforced column design, 147 footings, 144 concrete, 135 materials for, 140 footing design, 145 joints, tieing of, 140 Re-inforcement, amount of steel in concrete beams, 142 in columns, proportions, 147 placing of, informs, 137 Resilience, 9 Resisting and bending moment compared, 59 moment, 48 formula, 48 in re-inforced concrete beams, 143 Rip-rap, 19, 21 Rivet arrangement, 126 pitch, 128 sizes, 128 Riveted joints, 123 Rope, 122 Rubble, 19, 21 specification for, 21 INDEX OF SUBJECTS. Run of crusher stone, 21 Sand, 23 Section area, transverse, 5 modulus, 45 transverse, 5 Sectional area, uniform, 6 Sections, properties of, 38 Shaft couplings, 98, 99 Shafting formula, 90 Shape, change of, 2 Shear, 4 distribution, 60 in beams, 60 in concrete beams, 143 Sieve classification, 24 Simple beam, 37 stress in, 39 Small tool design, stress calculations, 102 Spacing of re-inforcing in concrete beams, 142 Speed of pulleys and gears, calculating, 97 Steel, 31 in re-inforced concrete, 136 meaning of terms used in manufacture of, 32 re-inforcement, amount of in beams, 142 Stone dust, 19 trade classification in, 21 Stonework, grouted, 19 Strain, 3 Strength of gear teeth, 100 ultimate, 9 Stress, allowable, 8 compound, 3 defined, 2 kinds of, 3 per unit area, rules and formula for, 6 simple, 3 torsional, 4 units of, 4 196 INDEX OF SUBJECTS. Tension, 4 Terra cotta, 24 Tieing of re-inforcing joints, 140 Timber, 28 Torsion, 87 Total area subject to load, formula, 7 load, formula for, 6 Trade classifications, 2 1 Transverse section, 5 sectional area, 5 Triangle of forces, 112 Ultimate strength, 9 Uniform sectional area, 6 Uniformly distributed load, 37 loaded beams, 63 Unit of area, 6 Units of stress, 4 Weight of members in a structure, 120 Wrought iron, 30 Yield point, 8 Date Due — ^ ■ ' ' '-'} -^—i L. B. CAT. NO. 1187