The three-dimensional state of stress at a point is given by σ = [[10, 0, 0],[0, 40, 0],[0, 0, 0]] MPa. The maximum shear stress at the point is

20 MPa
15 MPa
5 MPa
25 MPa

Correct answer: 20 MPa

Solution

The matrix is diagonal, so principal stresses are 40, 10 and 0 MPa. Maximum shear stress = (sigma_max - sigma_min)/2 = (40 - 0)/2 = 20 MPa, not 25 MPa.

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