LIST OF FOLDING PLATES

PLATE

I. PLATE WEB GIRDER BRIDGE FOR DOUBLE LINE OF RAILWAY

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CHAPTER I.

STRENGTH, ELASTICITY, ENDURANCE, AND SAFE WORKING STRESS IN IRON AND STEEL.

THE strength of a structure, such as a roof or a bridge, depends not only upon its form and dimensions, but also upon the material used in its manufacture. The load or loads which a structure is designed to carry produce stresses in the various members, which may be tensile, compressive, shearing, and occasionally torsional; the stresses develop resistances in the material, which are generally accompanied by slight alterations in form, such as an elongation or shortening of the member in question. The elongation or compression, as the case may be, is termed the "strain," which must not be confounded with the stress producing it. The stresses produced in the various parts of a structure depend upon the form and dimensions of the structure and the loads which it carries; but, in arranging the sections of the various members to resist the stresses developed in them, it is necessary to know the physical properties of the materials used, such as the tensile, shearing, and compressive strengths, elasticity, ductility, rate of expansion by heat, etc. In order to design a structure in an economical manner we require to know many other things, such as, in the case of wrought iron and steel, the ordinary and maximum sizes of plates and bars, and their relative cost; how best to connect the various members together, so that they may have the necessary strength and otherwise fulfil their purpose efficiently; what portions are best made of cast iron, and how such castings should be designed. If stone, brick, or concrete is used in the structure, such as for abutments and piers of bridges, it will be necessary to know how to dispose these

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materials to resist the stresses developed in them, and to limit the pressure on the foundations, etc. It is proposed to deal with the principles which govern the design of structures in iron, steel, and timber, and to work out examples in details of the most common of these, such as the engineer is frequently called upon to construct.

In the first place, the strength and elasticity of iron, steel, and timber will be considered. Our knowledge of the physical properties of materials is derived chiefly from experiments made with the testing-machine, which at the present time, in some form or other, finds a place in every engineering laboratory. The most important testing-machines used in England and Europe are based on the constructive principle first adopted by Mr. David Kirkaldie—that, namely, of applying the load by water-pressure, and measuring it by means of weights and levers. In some of the larger testing-machines in America, and generally in smaller machines, spur-gearing and screws are used to apply the load. It should, however, be mentioned that a large and accurate testing-machine was designed by Mr. A. H. Emery for the Watertown Arsenal, in which the power is applied by means of a hydraulic press, supplied by a set of pumps driven by a steam-engine through an accumulator. The stresses are measured by scale-beams, to which they are transmitted through a set of diaphragms and cells containing a mixture of alcohol and glycerine, and which operate as a frictionless reducing mechanism. The machine, once standardized, is said to be almost absolutely accurate. Its capability of recording accurately large and small stresses was shown when it was first used for breaking a bar of iron 5 inches in diameter, and afterwards a single horsehair. It has been since used for a variety of most valuable tests, which are recorded in the reports published each year by the United States Government.

In using a testing-machine for the determination of the tensile strength, elasticity, and ductility of a specimen of metal, it should be accurately prepared to a suitable form, such as in Figs. 1, 2, and 3; the exact sizes, however, will depend upon the machine and the method of holding the specimen.

If the specimen under consideration be iron, and it be desired to test the elasticity, it will be necessary to attach to it a piece of apparatus for measuring the small extensions.

produced, such as a screw micrometer or Kennedy's extensometer, which latter consists of a light lever multiplying 100 to 1. On applying the load, it will be at once observed, if the apparatus be sufficiently delicate, that the specimen stretches, and that with a load of 1 ton per square inch the stretch will be about 12000 part of the length of the specimen under test. In Figs. 1, 2, and 3, which have a test length of 10 inches, the stretch would be 12 of an inch. With a load of 2 tons per square inch, the elongation will be of an inch; and with 3, 4, 5, 6, 7, 8 tons, the elongations will be 3, 4, 5, 6, 7, and 8 times of an inch respectively, and generally the elongations are sensibly proportional to the loads producing them. In other words, the specimen is said to be perfectly elastic for these loads; which is shown by releasing the pressure, when

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the specimen springs back to its original length of 10 inches. But this so-called elasticity has a limit, which in wrought iron is about 12 tons, and in mild steel about 18 tons, per square inch, after which the elongations increase much more rapidly than the loads producing them, and the material behaves as if it were plastic until the specimen fractures, which generally occurs at from 20 to 24 tons per square inch for iron, and from 24 to 30 tons per square inch for mild steel; the elongations at the point where the material apparently ceases to be elastic being about of an inch, whereas the total elongation at fracture will be from 1 to 1 inch for ordinary iron, and from 2 to 3 inches for mild steel, measured on a length of 10 inches. The apparatus used for measuring the small elongations is removed after the elastic limit has been determined, otherwise

it might be injured when the specimen fractures. The ductility of the specimen is measured by the total percentage of elongation, and the percentage of contraction of the fractured area.

The term "modulus of elasticity" is used to denote the result found by multiplying the stress per square inch by the original length of the specimen, and dividing by the elongation. Thus it has been stated that a stress of 1 ton per square inch will produce an elongation of 1200 of an inch on a length of 10 inches, which gives the modulus of elasticity 26,880,000 lbs. per square inch. The modulus of elasticity may also be defined as the ideal stress which would be capable of stretching a perfectly elastic bar to double its length; it may be calculated from the following formula :

This is Young's modulus, or the coefficient of direct elasticity. The coefficient of transverse elasticity is derived from experiments on loaded beams, and will be referred to in connection with the deflection of beams. The modulus of elasticity is an important factor in all calculations where the stress is determined from the strain, and it will be used in connection with the deflection of beams, continuous girders, and arched ribs. For its exact determination, very delicate instruments are necessary; the same remark applies to the determination of the elastic limit, which will now be considered more closely. The method described for testing a piece of iron or steel and determining its so-called elastic limit is that usually adopted in the commercial testing of materials; what is really found is better defined as the "yield-point." It is well known that the yield-point can be raised by mechanical means, that the application of a stress greater than the yield-point raises the yieldpoint, and that it may be artificially raised almost to the breaking-point. With very delicate instruments a permanent set is observable with stresses well within the yield-point, and the stress fixed upon as the elastic limit depends upon the

See Unwin, "The Testing of the Materials of Construction."