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A cubic shape body is subjected to stresses as shown in the figure below. If both are stresses are equal in magnitude, calculate the shear stresses on black and green planes.

A cubic shape body is subjected to stresses as shown in the figure below. If both are stresses are equal in magnitude, calculate the shear stresses on black and green planes. Correct Answer Black=σ/2, green=0

The stress of magnitude σ will generate the shear stress of σ/2 on the plane which is at 45 degrees with principal stress direction. In the case of black plane, stress acting in the right direction will create stress of σ/2 on the plane. The stress acting in the upward direction is parallel to the black plane, so its contribution to shear stress will be zero. So, total shear stress in this black plane is σ/2. In the case of green plane, stress acting in the right direction will create stress of σ/2 on the green plane; the stress acting in the upward direction also create stress σ/2, but in the opposite direction. So the net result will be zero stress in the green plane.

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