Aii-101 95 



Using tho values of |£ for the three layers listed in Appendix 

 '+(a) 5 wo havG 



' i <*': = po ^-^ f -< T-d 



z 



= p c 4'^, (T-z) T-d < z < T 



o ax ~ ~ 



= T < z 



Then 



g 1[ \ |£ dC ] dz = g --£il- |I [T-d + h ] 



J _h P (J 7 9x 1+cd ax 



cr 



^ 1 [^"^ e£ dC ] dz = gd ^^ + P ^ i 10- -^— 



j_^ P ^J2 9x ^"^ -"^^ ^-^ 3x ^ ax G -^ ^ cd+1 



1 [ |£ dC ]dz = 



-p P J 2 ^^ 



-) r] 



gp Ifl 1 ' 1 dz = g ^ -1-. [T-d+h] - g 1^ ^ log(-^.™) 

 •^o ax ( V. P 9x 1+cd ^ ax G cd+l 



+ g 9^ (t]-T). 



ax 



Let us put those values into (1) and at the same time 

 use 



ar _ _ P-o ari _ i an 



p. 



■o. 



and T = - ^^- C 



ax ~ Ap ax cd ax Ap 



. r "1 1 |£ dz = - g |a ™^ [T-d-h] + g 1^ -~i- [T-d+h] 



_^ p ax ax i+cd ax i+od 



- £ la - g P o 1 9 T] iog( 1 ) - g 1 |J1 log(--l ) 

 c ax A^p G ax cd+1 c ax cd+l 



