Question

There are _______ independent shearing stresses.

(a) 2

(b) 3

(c) 6

(d) 8

I got this question during an interview for a job.

This interesting question is from Elasticity in portion Elements of Elasticity of Geotechnical Engineering I

Answer 1

Correct choice is (b) 3

Explanation: At a point there are six shearing stresses. At equilibrium of the elemental volume, moment about z-axis ∑Mz = 0.

∴ (τYX.dx.dz)dy = (τXY .dy.dz)dx

∴  τYX = τXY .

Similarly,

τYZ = τZY and τZX = τXZ.

Hence, out of six shearing stresses, there are only three independent shearing stresses.