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Question

In a strained body, the three principal stresses at a point are denoted by σ1,σ2andσ3 such that σ1>σ2>σ3.. If σ0 denoted yield stress, then according to the maximum shear stress theory

A

σ1σ2=σ0

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B

σ1σ3=σ0

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C

σ2σ3=σ0

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D
σ1σ32=σ0
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Solution

The correct option is B

σ1σ3=σ0


As per maximum shear stress theory, for no failure maximum shear stress should be less than half of yield stress.

Max[(σ1σ22),(σ2σ32),(σ3σ12)]σ02

Given that σ1>σ2>σ3

σ1σ32=σ02


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