8 STRENGTH OF MATERIALS 



Problem 12. How great a pull can a copper wire .2 in. in diameter stand with- 

 out breaking ? 



Problem 13. How large must a square wrought-iron bar be made to stand a 

 pull of 3000 lb.? 



Problem 14. A mild steel plate is in. thick. How wide must it be to stand a 

 pull of 1 ton ? 



Problem 15. A round wooden post is 6 in. in diameter. How great a load will 

 it bear ? 



11. Elastic law. Certain substances, notably cast iron, stone, 

 cement, and concrete, do not conform to Hooke's law, in that the 

 deformation is not proportional to the stress which produces it. 

 Consequently, for such substances the strain diagram is nowhere 

 a straight line, but is curved throughout, as shown in the curve 

 for cast iron in Fig. 2. In this case the modulus of elasticity 

 changes from point to point. It is customary, however, to retain 

 the formula 



which defines the modulus of elasticity at any point as the slope 

 of the chord joining that point to the origin. 



Numerous attempts have been made to determine the equation 

 of the strain curve for various materials which do not conform to 

 Hooke's law, and a corresponding number of formulas, or elastic laws. 

 have been proposed. The one which agrees best with experiment i> 

 the exponential law, expressed by the formula 



S = I'/'". 



where v and cr are constants determined by experiment. Fmm 

 Bach's experiments tlu* values of v and a were found to be 



for cast iron in tension, v = 138 | 700 , <r = 1.0663 ; 



for cast iron in compression, v = 1132700' a ~ 1-395 ; 



the unit stress p being expressed in atmospheres'(X atm. = 1 4.7 lb. 



However, all such elastic laws are at best merelv interpolation 

 formulas which are approximately true within the limits of tin- 

 experiments from which they were obtained. For this reason it is 

 best to carry out all investigations in the strength of materials 

 under the assumption of Hooke's law, and then modify the results 

 by a factor of safety, as explained in Article '21. 



