Strength of Materials is the heading under which it is usual to discuss the elastic or resisting properties of the materials used in engineering or building operations (see ELASTICITY, also STRAIN AND STRESS). When a structure is being designed the engineer must know first of all the amount and character of the stresses (loads, wind-pressures, &c.) that will act upon the structure. He must then decide as to the size and shape of the pieces that are to compose the structure, so that they may easily stand these stresses. For this purpose he must know beforehand what 'strength of material' is possessed by the steel, iron, or wood that is to be used.
When any substance is strained beyond a certain limit it will break, and the greatest stress which the substance can bear without being torn asunder is called its ultimate strength. The value of this for any given piece of material will depend upon the kind of strain to which it is being subjected. But whatever this strain be, whether extension, compression, flexure, or twisting, there are two, or at most three, distinct kinds of ultimate strength which practically fall to be considered. The one is the ultimate tension or pressure applied in one direction, usually longitudinally; and the other is the ultimate shearing stress, such as comes into play in simple torsion. In certain cases, such as in steel, wrought-iron, and ductile metals generally, the strength under tension and that under longitudinal pressure—in other words, the tenacity and the resistance to crushing—are practically the same. In other cases, however, of which cast-iron is the most interesting instance, the resistance to crushing is much greater than the tenacity. The ultimate strength under shearing is generally less than that under tension or compression. For example, the ultimate tensile strength of steel varies from 30 to 45 tons' weight per square inch of section, while the ultimate shearing strength varies from 22 to 35. Cast-iron, again, which has a tensile strength of tons' weight per square inch, has a strength under crushing of 45 and a shearing strength of 12.
It is out of the question to make a structure in which the pieces are strained up to their ultimate limits. For, even though the limit is not exceeded and the material not torn asunder, the excessive straining to near the limit will produce a permanent deterioration in strength. In other words, the 'working strength' is much smaller than the ultimate strength, being obtained from it by dividing by a number known as the 'factor of safety.' In the case of steel this factor is about 6; so that in no structure should a hard steel rod be subjected to a greater tension than tons' weight per square inch. Experience is the sole guide as to the value of this factor, which must be taken large enough to provide a margin of strength for all possible contingencies. Now, in the first place, the ultimate strength of a material that is to be used in a bridge or roof is somewhat uncertain. It is obtained by testing a sample. But no two samples of the same material have ever quite the same strength. Again, although theoretically a long column should have the same tensile strength as a short one of the same material and section, practically it is not so. There is greater chance of there being weak places in the longer column, and at the weakest place the material will begin to yield. Thus a greater factor of safety must be used in estimating the working strength of the longer rod. Then, in the second place, the character of the stress to which the material is to be subjected must be considered. If it is to be a fluctuating and not a steady stress the factor of safety must be increased, and similarly a wider margin of strength must be provided if the material is to be subjected to sudden shocks or impacts. For example, a bridge which is strong enough to allow a train to rest on it or to crawl over it, may be unable to support the train dashing at full speed. In fact, under a stress which fluctuates between wide limits the ultimate strength is diminished; hence if the ultimate strength has been measured by testing a sample under a steady stress, and if the substance is to be subjected to a sudden shock, the factor of safety is doubled.
A very important part of the subject is the consideration of the form best suited to resist certain strains. A glance at any fine modern structure, such as the Forth Bridge, will show how the form is varied, according as the member is in compression or in extension. Here the question of flexibility enters in. For although the strengths under extension and compression may be the same, yet if a rod is taken too thin and subjected to a longitudinal pressure, it will bend long before the true compression limits are reached. This bending or buckling must be prevented, and the only way of doing so is to increase the section. Thus hollow tubes resist buckling better than rods of the same length and mass. Herein also lies the great virtue of the I-shaped rod, which if laid horizontally and supported by its ends bends under its own weight very slightly as compared with the bending of a solid cylindrical rod of the same length and mass.
See Todhunter and Pearson, A History of the Elasticity and Strength of Materials (1886-94); H. T. Bovey, Theory of Structures and Strength of Materials (New York and London, 1893); Barlow's Strength of Materials (6th ed. 1867); Fairbairn's Mechanical Properties of Steel (Brit. Assoc. Reports, 1867); Burr's Elasticity and Resistance of the Materials of Engineering (New York, 1883; new ed. 1889); and W. G. Kirkcaldy's Strength and Properties of Materials (New York, 1891).