In case of simple tension or compression, the maximum shear stress is equal to
- Athe applied stress and acts on planes at 45° to it
- Bone-half the applied stress and acts on planes at 45° to itCorrect
- Cthe applied stress and acts on planes at 60° to it
- Done-half the applied stress and acts on planes at 60° to it
Solution
Concept
Shear stress on an oblique plane
Formula
τ = (σ/2) sin 2θ
Step-by-step solution
1. τ = (σ/2) sin 2θ is largest at θ = 45°. 2. τmax = σ/2.
Explanation
In uniaxial stress the shear stress on a plane inclined at θ is (σ/2) sin2θ. Its maximum, σ/2, occurs on planes at 45° to the axis.
Why the other options are wrong
The shear stress cannot equal the applied stress, and at 60° it is only 0.433σ.
Shortcut
τmax = σ/2 at 45°.
Common mistake
Taking τmax = σ.
Correct answer: B) one-half the applied stress and acts on planes at 45° to it