Answer to Question #298699 in Mechanical Engineering for Harsh

Question

Direct stresses of 120 N / mm ^{2}N/mm2 (tension) and 90 N / mm ^{2}N/mm2 (compression) are applied at a particular point in an elastic material on two mutually perpendicular planes. The principal stress in the material is limited to 100 N / mm ^{2}N/mm2 (tension). Calculate the allowable value of shear stress at the point on the given planes. Determine also the value of the other principal stress and the maximum value of shear stress at the point. Verify your answer using Mohr’s circle.

Answer 1

$\sigma_x=120$

$\sigma_y=-90$

$\sigma_1=100$

$\sigma_1=\frac{1}{2}[(\sigma_x+\sigma_y)+\sqrt{(\sigma_x-\sigma_y)^2+4\tau_{xy}^2}$

$100=\frac{1}{2}[(120-90)+\sqrt{(120+90)^2+4\tau_{xy}^2}$

$100=120+2\tau_{xy}$

$\tau_{xy}=\frac{-20}{2}$

=-10

=10N/mm² Compressive force.