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A cubic shape body is subjected to stress as shown in the figure below. Both are stresses are equal in magnitude but opposite in direction. Calculate the shear stresses on black plane and green plane.

A cubic shape body is subjected to stress as shown in the figure below. Both are stresses are equal in magnitude but opposite in direction. Calculate the shear stresses on black plane and green plane. Correct Answer Black=σ, green=σ/2

In the case of black plane, stress acting in the right direction will create stress of σ/2 on the black plane; the stress acting in the upward direction is parallel to the black plane so its contribution in shear stress will be zero. So, total shear stress will 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 will also create stress σ/2 in the same direction. So net resultant will be σ/2 + σ/2 = σ.

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