GeneralizedHooksLaw

GeneralizedHooksLaw - Generalized Hook’s Law(Multiaxial...

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Unformatted text preview: Generalized Hook’s Law (Multiaxial stress case) _ E £X:O'x V(:y+02) 0X=W[(l—V)8X+V(Sy+52)] _. E 8y:0y V(1:fz+0'x) ay:W[(l—v)gy+v(gz+gx)] O'z-V ax+o— : E _ El 2 (E y) 02 (1+V)(1_2V) [(1 V)EZ +v(5x +£y)] Aft? Txy=G7xy 7” =2” Tyz = Gm 715:: 119Gb where E Young’s Modulus/Elastic Modulus G = Shear Modulus v = Possion’s Ratio E — = l+V ZG Hook’s Law 1 09/30/2008 Hook’s Law (Plane Stress: 0'2 =0, r“ = 0 and ryz = 0) 5 *Ox—VO-y 0' = E (5 +149) r_ E x 1_V2 x y oy—vo-X E g): )E 0'y=1_V2(8y+V8x) g :—v(0'x+0'y) 02:0 2 E r 7,, = Txy =G7ry n50 rxz=0 yyzzo TyZZO Hook’s Law 2 09/30/2008 Hook’s Law (Biaxial Stress*: 02 = 0 and r” 2 TH = rfl = 0),: 0 —v0 E = X y a = a +vg 8X E x X y) 01—1/0; _ E 8y: ’ E O'y~1_v2(8y+vgx) _ (ax +ay) _ g_ 2 0 — O ‘ E m = 0 rxy = 0 yXZ : 0 TXZ : 0 yyz : 0 Iyz : 0 *a special case of Plane Stress ~> X Hook’s Law 3 09/30/2008 5X: x O-XZEEX E _VO"X — 5y: E O’y—O 52:_V0-‘ 02:0 E yr):0 Txy:0 yxz:0 TXZ:0 yyZZO TyZZO Similarly, the corresponding equations for plane strain can be obtained by setting the following conditions in the equations of Generalized Hook’s Law: Hook’s Law 4 09/30/2008 ...
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This note was uploaded on 11/04/2008 for the course CE 207 taught by Professor Elghandour during the Spring '06 term at Cal Poly.

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GeneralizedHooksLaw - Generalized Hook’s Law(Multiaxial...

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