70 APPLIED MECHANICS 
If w is the weight of a unit volume of the bar, then the weight of the 
bar will be Vw. Let % equal the height through which this weight must 
fall in order to accumulate an amount of energy equal to the resilience of 
the bar, then Vf? ft 
Vwh = OE” and h= TE 
The resilience of a bar is a measure of its power to resist a blow or 
shock without taking a permanent set. . 
Suppose a bar AB (Fig. 81) of length 7 and area 7% 
of cross section @ to be suspended from one end, and : 
let it have a weight W threaded on it as shown. If 
the weight is allowed to fall freely through a heighth 5 
before striking the head formed on the lower end of | 
the bar, the bar will lengthen an amount #, and the i 
total fall of the weight will be h+a. At the end j=] |p 
of the fall the resistance offered by the bar to i 
further stretching will be af, where f is the maxi- 
mum stress. The diagram of work done on the bar, 
assuming that it is not strained beyond the elastic «af - 1 
limit, will be a triangle whose area 3a/x will equal Fiq. 81. 
the work done in stretching the bar, and this must 
equal the work done by the falling weight. 
ke--00 - 
Therefore W(h+2) = _. but «= _ ; 
SO afl 
Hence w(h + rt) a) vy 
si JW? + 2WEath. 
' Solving this quadratic equation, f= — 
hid 
al 
If = 0,.thon fae 
When the load at is applied gradually, as when the bar is stretched 
in a testing machine, the maximum stress, when the load is all on, 
becomes Ss but if the full load is put on at once the maximum stress, as 
shown above, is = . The effect of a suddenly applied load is therefore 
to produce a stress double that produced when the load is applied 
gradually. 
Exercises VIa. 
1. A steel wire 0°08 inch diameter and 50 feet long is subjected to tension 
by a load of 112 lbs. Determine (1) the stress in lbs. per square inch, (2) the 
elongation in inches, (3) the strain, and (4) the work done, in inch-lbs., in pro- 
ducing the strain. E=30,000,000 lbs. per square inch. 
2. A steel piston-rod 2 inches diameter is subjected to a pull and thrust alter- 
nately. The tensile and compressive stresses are each 8000 Jbs. per square inch. 
Two points A and B on the axis of the rod are 4 feet apart when the rod is 
unloaded. Determine (1) the effective load on the piston, (2) the difference 
between the greatest and least distances between A and B, E=30,000,000 Ibs. 
per square inch. 
