EQUILIBRIUM OF AN ISOTROPIC ELASTIC ROD OF CIRCULAR SECTION. 911 



1 



a-* 7r/x(8 - v) 



2__ V2-20./+92 



a-' \ ^ 7r//(8 - v) 37r/^(8 - v)2 



Thus the permanent terras of the solution are 



"P ={l('- 'f + ^'(« - ^'y I cos (a, - <o'), 

 «. = { - -3(^ - 2')3 + ^{z - .')p2 } sin (o> - a,'), 



with the rigid body rotation 



Up = {z- Z) COS (to - O)'), \ 



/ '\ ■ / /\ 1(4-" '^ 



Mo, = - (Z - 2 ) sin (o) - OJ ), I . ^, -I - 

 Uz= - p cos (w - (1)'), 



Transverse traction. 7 (3). 



- i^^ 12.^8 -V)'- i ^'^ ~ ''^ - '^' - ^^ ^^ - '^^ ^'' ^"^ - "''^ 'J 



^ = a^~r8^){-6(^-^')^^-^<^-^V}(-)cos(.-.') 

 In terms of displacements, 



"p = I 3(2 - 2? + ^"(2 - 2>- } sin (o, - 0)'), 



-.= { -^(-^? + ^>-^V }(-)cos(.-co'), I . i ^^^^ 



Mz= "j - (2 - z')V + ^pH "^^ «V I sin(aj-oj'), 



with the rigid body rotation 



Up= -{z- z') sin ((o - oV), 



v2 - 20./ + 92 



-92) 



Longitudinal traction. 8 (3). 



^43|(^){^^^-^')^^-8-^1^«^('^--') 



^=i-:^^tU(-^T.-Jp^} sin (.-.') 



a^ 7r/x(8-v) ( 2' 



- ^ 12.^8 -v^) { ^' - '')^''' - ''^ + (7 - 5.)(8 - V) I p sin (. - .'). 

 TRANS. ROY. SOC. EDIN., VOL. XLIX. PART IV. (NO. 17). 



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