SPHERES AND CYLINDERS 



125 



The actual stress in a thin cylinder, due to the combination of these 

 two stresses and based on a value of Poisson's ratio = .3, is then 

 found to be* 



(182) 1>=.425 . 



h 



II. Thick Cylinder. Lame's Formula. In article 76 the maxi- 

 mum stress in a thick cylinder under uniform internal pressure is 

 given by equation (176) in terms of the radii a and b. If the internal 

 and external diameters of the tube are denoted by d and D respec- 

 tively, then d = 2 6, D = 2 a, and the formula becomes 



(183) 



P = 



D 2 - d 



III. Barlow's Formula. This formula, which is widely used 

 because of its simplicity, assumes that the area of cross section of 

 the tube remains constant under the strain, and that the length 

 of the tube also remains unaltered. As neither of these assump- 

 tions is correct, the formula can give only approximate results. 

 In the notation previously used Barlow's formula is 



(184) 



P = 



wD 



It is therefore of the same form as the formula for the hoop stress 

 in a thin cylinder, except that it is expressed in terms of the out- 

 side diameter D inside of the inside diameter. 



From the results of their experience in the manufacture and 

 testing of tubes, the National Tube Company asserts that for any 



ratio of -- < .3 Barlow's formula " is best suited for all ordinary 



calculations pertaining to the bursting strength of commercial tubes, 

 pipes, and cylinders." 



For certain classes of seamless tubes and cylinders, however, and 

 for critical examination of welded pipe, where the least thickness 

 of wall, yield point of the material, etc. are known with accuracy, 

 and close results are desired, they recommend that the following for- 

 mulas, due to Clavarino and Birnie, be used rather than Barlow's. 



* Slocum and Hancock, Strength of Materials, Revised Edition, p. 156. 



