According to the Maximum Shear Stress Theory (Tresca’s Theory), yielding occurs when the maximum shear stress in a material reaches
- AThe yield stress in axial tension.
- BHalf of the yield stress in axial tension.Correct
- CTwice the yield stress in axial tension.
- DThe ultimate tensile strength of the material.
Solution
Concept
Maximum Shear Stress Theory (Tresca's Theory)
Formula
τmax = σy / 2
Explanation
In a simple tension test, the maximum shear stress developed in the material is equal to half of the applied axial tensile stress. Therefore, according to Tresca’s theory, yielding begins when the maximum shear stress under any load condition reaches half of the material's yield stress in axial tension.
Common mistake
A common mistake is selecting Option A by equating the maximum shear stress directly to the yield stress in axial tension, forgetting that in a simple tension test, maximum shear stress is equal to half of the axial tensile stress. Another frequent error is selecting Option C by confusing the relationship and multiplying by two instead of dividing by two.
Correct answer: B) Half of the yield stress in axial tension.