WORK DONE ON BARS. 247 



so that the work done on the bar is 

 W = m. n. a. 



= 5 x - x 17-48, 



= 58 '30 inch-tons; 



and the work done per cubic inch of the original volume 

 of the bar is 



w; 



IA 



58-30 



= 10 x 0-788 

 = 7 '39 inch-tons, 



where I is the original length of the bar, and A is the area 

 of the original cross section. 



The same result may be obtained by making use of 

 the approximate formula suggested by Dr. Kennedy,* and 

 based on the assumption that the semi-plastic curve is a 

 parabolic one. In this formula 



P is the maximum load in tons, 

 e is the total extension in inches, 

 and r is the ratio of limit to maximum. 



The formula gives the total work done on the bar as 



and the work done per cubic inch is 



- P e ( r + 



In the present instance the values of the symbols 

 already given are 



P = 21-90 tons, 



e = 3 '06 inches, 



I = 10 inches, 

 A = 0*788 square inches, 



< = = 0-594. 



From which the result is obtained that 



(' 



21-9 x 3-06 /0-594 + 2 



w = - 



10 x 0-788 

 = 7'34 inch-tons per cubic inch. 



See Inst. Mecfc. Eng. Froc., 1886, p. 68. 



