Question

Calculate Op3 and £p3 for plane stress and plane strain in the x-y plane.

Answer 1

Calalate and Eps. for plane Stress and Strain in X-y plane: plane stress: * Assume Zero stress Z-direction. ľ * is non- Z - strain Zero Valid for Components which Z dimension than x and у dimensions, in is Smaller * Optical thickness (Z-direction) allowed. plane Strain! * Assume Zero Strain in Z-direction. * non- Zero, Z-stress is Used for long, Constant Cross section structures. Valid for Components in which the Z-dimension larger than X and Y dimensions. 0.41 * is much Now in 20 Case Thin Bodies : Z 2 zz ZY Exx -r Syy E E E ~ Exy = cry or su Үху Cxy/G.

Ez a - G+yy) E > Vzx = Xyz Pyz = 0 Now, plane stress: Ya . Stresses: q=o, Txz =0, Tyz=0 have non-Zero Values. exy and Txy may Strains: Z Vazao , Yyz = 0 Ex, Ey, Ez and Yxy may have non-zero Values. How Plance strains: stresses: Ey Txz = 0 Ty2 = 0· and Txy may cx,y,cz have non-Zero Values Vxy strains! Ez=0, Vx2=0, Vyz = 0. Ex, Ey and Vxy may have non-Zero Values. Z