16 RESILIENCE. <Art. 19. 



E s , the shear modulus, may also be determined theoretically 

 from the cases shown in Figs. 5 or 12, if Poisson's ratio is known. 

 This theoretic relation is, 

 # g = JL rf* = -I- E, when ??i =4 or Poisson's ratio equals - 



19. Work Done in Deforming a Body. Resilience. Sir re 

 work is measured by the product of the force acting and the 

 distance through which it acts, the work done in elongating a 

 steel bar, for example, is equal to the elongating force times the 

 elongation. If the force is gradually applied, it increases from 

 zero to the final value W, and its mean value is y 2 W. If the 

 accompanying elongation is 8L, the total work done is y 2 W8L; 

 if this be divided by the volume AL, we have, 



Work done per unit volume = s 8 



If s does not exceed the elastic limit, this will also represent 

 the potential energy in the bar per unit volume, or the energy 

 restored when the load is taken off or when the bar springs back, 

 and is called the resilience. 

 Resilience per unit volume 



= i s $ = i > f rom e( l- 2 > P a ge .7. (4) 



The term resilience is also applied to designate the work 

 done on a body stressed beyond the elastic limit (21). 



The work done by an instantaneously applied force W would 

 be W 8 L, and hence it will produce twice the stress, on the same 

 bar, that a gradually applied force produces. If the stress is 

 doubled, the deformation is also momentarily doubled (within 

 the elastic limit). This has been of importance in selecting 

 working stresses. 



If the load is applied with impact by a weight W falling 

 through a height h, the work done at the instant of im- 

 pact, will equal Wh, and it will be spent upon the falling weight, 

 the body struck, and its supports ; how much is spent on the body 

 struck would be difficult to determine 



The resilience is a good measure of the shock-resisting qual- 

 ities of a material. To compare various materials in this respect, 



