SPHERES 



CYLINDEKS 



123 



m 1 



m 1 wr 



m m 2 h 



If the value of m is assumed to be 3J, this expression for p e becomes 



(63) p e = 



IT 



Problem 127. How great is the stress in a copper sphere 2 ft. in diameter and 

 .25 of an inch thick, under an internal pressure of 175 Ib /in. 2 ? 



106. Hoop tension in hollow circular cylinder. In the case of a 

 cylindrical shell, its ends hold the cylindrical part together in such 

 u way as to relieve the hoop tension at either extremity. Suppose, 

 then, that the portion of the cylinder considered is so far removed 

 from either end that the influence of the 

 end constraint can be assumed to be zero. 



Suppose the cylinder cut in two by a 

 plane through its axis, and consider a sec- 

 tinn cut out of either half cylinder by two 

 1*1 a nes perpendicular to the axis, at a dis- 

 tance apart equal to c (Fig. 90). Then the 

 resultant internal pressure P on the strip 

 under consideration is P = 2 crw, and the resultant hoop tension is 

 2 chp, where the letters have the same meaning as in the preceding 

 article. Consequently, 2 crw = 2 chp ; whence 



FIG. 90 



(64) 



rw 

 ~JT 



If the longitudinal stress is zero, p e = />. 



This result is applicable to shells under both inner and outer pres- 

 sure, if P is taken to be the excess of the internal over the external 

 pressure. 



Problem 128. A cast-iron water pipe is 24 in. in diameter and 2 in. thick. 

 What i.s the greatest internal pressure which it can withstand? 



107. Longitudinal stress in hollow circular cylinder. If the ends 

 of a cylinder are fastened to the cylindrical part, the internal pres- 

 sure against the ends produces longitudinal stresses in the side walls. 

 In this case the cylindrical part is subjected both to hoop tension 

 and to longitudinal tension. 



