Principal Stresses and Strains MCQ with answer and solution

Concept

Maximum shear stress in uniaxial loading

Formula

τ_max = σ/2

Step-by-step solution

1. Uniaxial stress creates both normal and shear stresses on planes inclined to the loading axis. 2. Maximum shear stress occurs on planes inclined at 45 degrees to the applied uniaxial stress direction. Answer: B

Explanation

In a pure uniaxial stress state, the principal stresses are the applied stress σ and zero. The maximum shear stress is given by half the difference between the principal stresses, which evaluates to σ divided by two. This maximum shear stress occurs on planes inclined at 45 degrees to the loading axis, making option B correct.

Why the other options are wrong

A) Maximum shear stress in uniaxial loading is half the applied normal stress, not double. C) Dividing the applied stress by four gives one-quarter of the stress value rather than the maximum shear stress.

Shortcut

For uniaxial loading, max shear stress occurs at 45 degrees and equals half the applied axial stress (σ / 2).

Common mistake

Assuming maximum shear stress is equal to the applied axial stress and selecting option D.