ELASTIC PROPERTIES OF MATERIALS 13 



stresses are produced in the body called temperature stresses. Thus 

 suppose a bar of length / is rigidly fastened to immovable supports 

 and its temperature is then raised a certain amount. Let A/ be the 

 amount the bar would naturally lengthen under this rise in temper- 

 ature if left free to move. Then the stress necessary to produce a 

 shortening of this amount is the temperature stress. 

 I f the temperature of the bar is raised T degrees, 



A/ = LIT, 



and consequently s = = LT. 



Therefore, if p denotes the unit temperature stress, 



The temperature of metals also has a marked influence upon 

 their ultimate strength. Experiments along this line show that at 

 -296 F. the tensile strength- <>f iru and steel are about twice as 

 as at ordinary temperatures.* 



Problem 16. A \\T. .uirht-in.n bar is 20 ft long at 32 F. How long will it be at 

 '.>:, I 



Problem 17. A rast-inm pii*- 1> ft. lmi: is placed between two heavy walls. 

 What will b- the stress in the pipe if the temperature rises 2:> ? 



Problem 18. Stn-1 railroad rails, each 80 ft. Inn::, an- l;ii<l at a temperature of 

 40 F. What space must be left betwi-m th-m in <nlrr that their mils shall just 



Problem 19. In th prvo-iling problem, if the rails an- laid with their ends in 

 hat will be the temperature stress in them at 100 I 



20. Effect of length, diameter, and form of cross section. When 



rnal force is tirst applied to a bdy the internal stress is dis- 



tributed uniformly throughout the body and, consequently, all parts 



are equally deformed. When ih. m passes the elastic limit 



thi> is in. lunger true, and certain portions ,f the body begin to mani- 



fest greater dr for mat ion than others. For instance, consider a bar of 



Heel under ten -ion. As the stress increases from zero to the 



limit the bar gradually lengthens and its cross section dimin- 



,ill parts h.-inr e.juallv affected. When the stress passes beyond 



the elastie limit the .- ,,n at some particular point of the bar, 



* Everett. ' m </ Unit*, p 



