Question

Problem Four: for the element shown, using the state of stress equation if, the element is oriented 60° clockwise. Answer the following 350 MPa 75 MPa 200 MPa

Answer 1

Normal stress $\sigma$ x=200 MPa

Normal stress $\sigma$ y=-350 MPa

Shear stress $\gamma$ xy=75 MPa

When the element is rotated 60° clockwise

$\theta$=-60°

$\sigma$x'=($\sigma$x+$\sigma$y)/2+($\sigma$x-$\sigma$y)/2*cos2$\theta$+$\gamma$xysin2$\theta$=(200+(-350))/2+(200-(-350))/2*cos(2*-60)+75*sin(2*-60)=-277.45 MPa

$\sigma$y'=($\sigma$x+$\sigma$y)/2-($\sigma$x-$\sigma$y)/2*cos2$\theta$-$\gamma$xysin2$\theta$=(200+(-350))/2-(200-(-350))/2*cos(2*-60)-75*sin(2*-60)=127.45 MPa

$\gamma$x'y'=-($\sigma$x-$\sigma$y)/2*sin(2$\theta$)+$\gamma$xy*cos(2$\theta$)=-(200-(-350))/2*sin(2*-60)+75*sin(2*-60)=173.21 MPa