STRESS AND DEFORMATION 9 



If, now, the unit stress p produced by the impact lies below the 

 elastic limit, the total internal work of deformation is 



Internal work = 1 (Ap) AZ. 



In the case of a suddenly applied, or impact, load, like that due to 

 a train crossing a bridge at high speed, h = 0, and, equating the 

 expressions for the internal and external work, the result is 



whence p = 



A 



Comparing this with the expression for the stress produced by a 



W 



static load, namely, p = , it is evident that a suddenly applied 



A 



load produces twice the stress that would be produced by the 

 same load if applied gradually. 



8. Poisson's ratio. Experiment shows that when a bar is sub- 

 jected to tension or compression, its lateral, or transverse, dimen- 

 sions are changed, as well as its length. Thus, if a rod is pulled, it 

 increases in length and decreases in diameter ; if it is compressed, 

 it decreases in length and increases in diameter. 



It was found by Poisson that the ratio of the unit lateral defor- 

 mation to the unit change in length is constant for any given 



material. This constant is usually denoted by , and is called Pois- 1 



m 



son's ratio. Its average value for metals such as steel and wrought 

 iron is .3. Thus, suppose that the load on a steel bar produces a 

 certain unit deformation * lengthways of the bar. Then its unit 

 lateral deformation will be approximately .3s. Hence, the total 

 lateral deformation is found by multiplying this unit deformation 

 by the width, or diameter, of the bar. 



Values of Poisson's ratio for various materials are given in 

 Table I. 



9. Temperature stress. A property especially characteristic of 

 metals is that of expansion and contraction with rise and fall of 

 temperature. The proportion of its length which a bar free to move 

 expands when its temperature is raised one degree is called its 



