FRICTION AND LIMITING STRENGTH OF ROCKS 643 



We easily derive expressions for the principal shearing stresses 

 in the nickel-steel jacket. At points distant r' from the axis these 



are 



<r 1 c 2 /r' 2 — 1 



(i)' i\Fr>-zz'\=hP- 

 (ii)' ±\Fr>-6d'\=P 

 (iii)' l\fd'-zz'\=±P 



I — <r 1 + /8 c 2 /b 2 —l 

 a- 1 c 2 // 2 



I -or i+/8 c 2 /b 2 -l 



1 cV 2 + 1 



(4) 



1-0- i+y8c 2 /6 2 -i 



The radial displacement U' at the outer surface of the nickel-stee 

 jacket is given by 



c ix''c 2 ' i-b 2 /c 2 ' 1+0-' ' 5 ' 



By writing /x = o and therefore /3 = o, c = |, the foregoing give the 

 familiar results for stresses in a cylinder subject to internal hydro- 



CS|2 



lO 



(ii) 



(iii) 



Fig. i. — (Figure from this Journal, Vol. XX, No. 2 [February-March, 1912], 

 p. 123.) 



static pressure. The three principal shearing stresses given above 

 all take their maximum value (independent of sign) at the interior 



