10 RESISTANCE OF MATERIALS 



coefficient of linear expansion, and will be denoted by C. Values 

 of this constant for various materials are given in Table I. 



If a bar is prevented from expanding or contracting, then change 

 in temperature produces stress in the bar, called temperature stress. 

 Thus, let I denote the original length of a bar, and suppose its 

 temperature is raised a certain amount, say T degrees. Then, if C 

 denotes the coefficient of linear expansion for the material, and AZ 

 the amount the bar would naturally lengthen if free to move, 



we have 



AZ = CTl, 



and consequently the unit deformation is 



Therefore, if p denotes the unit temperature stress, 



APPLICATIONS 



1. A 5-in. copper cube supports a load of 75 tons. Find its change in volume. 

 Solution. Area of one face = 5 x 5 = 25 in. 2 Unit compressive stress p on 



this area is then p = = 6000 lb./in. 2 Modulus of elasticity for copper 



E = 15,000,000 lb./in. 2 Therefore unit vertical contraction s = = ; total 



vertical contraction AZ = Z s =5- = in. Since Poisson's ratio for copper 



1 340 

 is = .340, the unit deformation laterally is .340 s > and the total lateral 



m 2500 



340 

 deformation is 5 x = .00068 in. The three dimensions of the deformed cube 



are therefore 5.00068, 5.00068, 4.998 ; its volume is 124.984 in. 8 , and the decrease 

 in volume is .016 in. 8 



2. A |-in. wrought-iron bolt has a head jj in. deep. If a load of 4 tons is applied 

 longitudinally, find the factors of safety in tension and shear. 



Solution. Area of body of bolt at root of thread = .442 in. 2 Unit tensile stress 



in bolt is p = - = 18,000 lb./in. 2 Factor of safety in tension = . = 2 .7. 



442 18,000 



Area in shear = TT . ? . 5 = 1.47 in. 2 Unit shearing stress is - ^22 = 5440 lb./in. 2 



Factor of safety in shear = i = 7.3. 



