STRENGTH OF MATERIALS 



114. Thick cylinders built up of concentric tubes. From equa- 

 tions (77), it is evident that in a thick cylinder subjected to internal 

 pressure the stress is greatest on the inside of the cylinder, and 

 decreases toward the outside. In order to equalize the stress through- 

 out the cylinder and thus obtain a more economical use of material, 

 the device is resorted to of forming the cylinder of several concentric 

 tubes and producing an initial compressive stress on the inner ones. 

 For instance, in constructing the barrel of a cannon, or the cylinder 

 of an hydraulic press, the cylinder is built up of two or more tubes. 

 The outer tubes in this case are made of somewhat smaller diameter 

 than the inner tubes, and then each is heated until it has expanded 

 sufficiently to be slipped over the one next smaller. In cooling, the 

 metal of the outer tube contracts, thus producing a compressive stress 

 in the inner tube and a tensile stress in the outer tube. If. then, this 

 composite tube is subjected to internal pressure, the first effect of 

 the hoop tension thus produced is to relieve the initial compre- 

 stress in the inner tube and increase that in the outer tulc. Thus 

 the resultant stress in the inner tube is equal to the difference let 

 the initial stress and that due to the internal pressure, whereas the 

 resultant stress in the outer tube is the sum of these two. In this 

 way the strain is distributed more equally throughout the cylinder. 

 It is evident that the greater the number of tubes used in building 

 up the cylinder, the more nearly can the strain le equalized. 



The preceding discussion of the stress in thick tubes can also be 

 applied to the calculation of the stress in a rotating disk. For example, 

 a grindstone is strained in precisely the same way as a thick tul.e 

 under internal pressure, the load in this case being due to centrifugal 

 force instead of to the pressure of a fluid or gas. 



