Question

The state of plane stress in an element is shown in the figure.

The maximum shear stress in the element is ______ \(\text{N/mm}^2\).

• A. 0
• B. 5
• C. 10
• D. 25

Hint:

Both given faces have zero shear, so sigma x and sigma y are already the principal stresses.

Answer 1

The Correct Option is B

This question tests the direct formula for maximum in-plane shear stress from two known normal stresses acting with no shear on the given faces.

1. 0: This would only hold if the two normal stresses were equal, but here they differ, 20 versus 30, so shear stress must exist on some other plane.
2. 5: With sigma x equal to 20 and sigma y equal to 30, and zero shear on the given faces, these two values are already the principal stresses. Half their difference, 30 minus 20 over 2, gives 5, the maximum in-plane shear stress. This is correct.
3. 10: This equals the full difference of the two stresses instead of half of it, a common slip when the factor of 2 is dropped.
4. 25: This is close to an average of the two normal stresses, not their half-difference, so it does not represent a shear stress here.

The correct choice is (B): the maximum shear stress works out to 5 N/mm squared, using half the difference of the two principal stresses.