STRENGTH OF MATERIALS 279 



In this formula, L and K must be referred to in the same 

 unit of length, and A in the corresponding unit of area. Thus, 

 if L is in inches, K also must be in inches, and A must be in 

 square inches. 



EXAMPLE. A steel rod 10 ft. long and 2 sq. in. in cross- 

 section is stretched .12 in. by a weight of 54,000 Ib. What is 

 the tension modulus of elasticity of the material? 



SOLUTION. To apply the formula, the stress P = 54,000 Ib.; 

 L = 10 ft. = 120 in.; A =2 sq. in.; and K = .12 in. Therefore, 



54,000X120 



E = - 27,000,000 Ib. per sq. in. 



2X.12 



The relation E = p-S-l is true only when equal additions of 

 stress cause equal increases of strain. Previous to rupture, 

 this condition ceases to exist, and the material is said to be 

 strained beyond the elastic limit, which, therefore, is that 

 degree of stress within which the modulus of elasticity is nearly 

 constant and equal to the unit stress divided by the unit strain. 



The ultimate strength of a given material in tension, com- 

 pression, or shear is that unit stress which is just sufficient to 

 break it, and is equal to the maximum stress causing rupture 

 divided by the original area of the cross-section. The prece- 

 ding tables show the average ultimate strengths, in pounds per 

 square inch, of both metals and woods. 



Working stress is the maximum unit stress to which the parts 

 of a structure are to be subjected. 



Factor of safety is the ratio of the ultimate strength to working 

 stress. The factor of safety required for a structure depends 

 on the material and on the character of the loads applied that 

 is, whether the loads are quiescent or such that cause impact 

 and vibrations. For stone and brick, a factor of safety of from 

 10 to 30 is used; for timber, from 8 to 15; for cast iron, from 

 6 to 20; for reinforced concrete, from 4 to 6; and for structural 

 steel, from 3 to 6. 



It is obvious that structures subjected to loads causing 

 impact should be designed for a higher factor of safety than 

 those having to carry static loads. When a structure, as a 

 bridge, carries both dead and live loads, the modern prac- 

 tice favors the specifying of one working unit stress for both 



