Mohr’s Circle
In the element shown, what is the max in-plane shear stress in MPa?
Expand Hint
Mohr's Circle:
$$$R=\sqrt{(\frac{\sigma _{x}-\sigma_{y}}{2})^{2}+\tau_{xy}^{2}}$$$
Hint 2
$$\sigma_x$$
,
$$\sigma_y$$
, and
$$\tau_{xy}$$
are defined as:
From a constructed Mohr's Circle, the max in-plane shear stress occurs when
$$\tau_{max}=R$$
$$$R=\sqrt{(\frac{\sigma _{x}-\sigma_{y}}{2})^{2}+\tau_{xy}^{2}}$$$
Thus, the max in-plane shear stress is:
$$$R=\sqrt{\left ( \frac{300-150}{2} \right )^{2}+50^{2}}=\sqrt{75^2+2,500}$$$
$$$=\sqrt{5,625+2,500}=\sqrt{8,125}=90.14\:MPa$$$
90.14 MPa
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