Elastic Equilibrium of Semi-Infinite Solid. 



37 



Siniilarlj' the second integral in (82) is 



Substituting tliese values and those found ])efore in the 

 formuke (59), we have for tlie stress 



rr 



27r'-VrV I 2ry.(ej— e2)(ei — e^) 



aa 



+ 



+ 



2 [îf(io-^j • [s-(^)-.d- '^'w":f' -] } 



// 



TT« 



-^(r<a) 

 {r>a)_ 



{)- + !i]r 



2« 



— (?• < (X) 



(85) 



-"■-(r>a) 

 _^ 2r ^ .1 



r<^f, 



r^— cr vrj^—ci}^^{v) 



ao. 



X4-a L' 



^ '^ *' ' ^ ^ r . 



I ^— (r <: a) 

 (r>«.) 



] 





Î5='(î;) 



// 



7t(X + //)«;• 



2« 



•).. 



(r >«.) 



(86) 



J I 



-_ //.? f (2a — 3are,)(-/^i + e,(o,) y^ — a^ ^ Vfj 



zz = 



TY \ 



77 (—('•<«) 1 



!î= (t\' 





TT« 



(' 



27rVr l2(e,-e,,)(e2-e.O ' 



r^ = 0, ^ = 0. 



(87) 

 (88) 



