794 Dr. Cbree on the Stresses in the Earth's Crust 



axis of z being along tbe prismatic axis, the stresses and stress- 

 difference are given by 



(29) 



§ 10. Hollow right circular cylinder outer radius a, inner a', 

 exposed to pressures p and P over its external cylindrical 

 surface and flat ends respectively. 



The stresses are 



7r = -X(l-«V)/(« 2 -a ,2 )n 



^ = - i? a 2 (l + a> 2 )/(a 2 -a' 2 ) J j- . . (30) 

 ?z = -P. J 



At a given distance r from the axis the maximum stress 

 difference may according to circumstances be any one of the 

 three following : — 



Si = r^~&j> = 2pa?a h2 + r\a?-a' 2 ), 1 



5 2 = 7r- ?z = V-pa' 2 (l-a ,2 /r 2 )/(a?-a ,2 ) i L (31) 



5 3 = £-$4> = -?+pa 2 (l+a'*/r i )f(a?-a'' 2 ).J 



But for the greatest value of S there are only two options, 

 both referring to the inner surface, of the cylinder, viz. : — 



s 2 = p. J 



When a' /a is very small, a close approximation is 



Si = 2/> (33) 



§ 11. Solid sphere of radius a exposed to uniform surface- 

 pressure p. 



The solution is 



u/r = du/dr = — p/(3m — n),") 

 7r=66=-p, > . . . (34) 



s = o. J 



§ 12. Spherical shell outer radius a, inner a\ exposed to 

 uniform pressure p over the outer surface. 



