Answer to Question #297675 in Mechanical Engineering for Harsh

Question

Direct stresses of 120 N/mm^2 (tension) and 90 N/mm^2 (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(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 using Mohr's circle

Answer 1

$\sigma_x=120$

$\sigma_y=-90$

$\sigma_1=100$

Let allowable value of shear stress be denoted $\tau_{xy}$

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

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

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

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

=-10

=10N/mm² compressive force.