In a strained body- the three principal stresses at a point are denoted by -1-2 and -3 such that -1-2 - -3- If -0 denoted yield stress- then according to the maximum shear stress theory

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Strength of Materials

Maximum Shear Stress Theory

In a strained...

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In a strained body, the three principal stresses at a point are denoted by $σ_{1}, σ_{2} a n d σ_{3}$ such that $σ_{1} > σ_{2} > σ_{3} .$ . If $σ_{0}$ denoted yield stress, then according to the maximum shear stress theory

$σ_{1} - σ_{2} = σ_{0}$

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$σ_{1} - σ_{3} = σ_{0}$

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$σ_{2} - σ_{3} = σ_{0}$

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\frac{σ_{1} - σ_{3}}{2} = σ_{0}

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Solution

The correct option is B
$σ_{1} - σ_{3} = σ_{0}$

As per maximum shear stress theory, for no failure maximum shear stress should be less than half of yield stress.
$M a x [(\frac{σ_{1} - σ_{2}}{2}), (\frac{σ_{2} - σ_{3}}{2}), (\frac{σ_{3} - σ_{1}}{2})] \leq \frac{σ_{0}}{2}$

Given that $σ_{1} > σ_{2} > σ_{3}$

$\frac{σ_{1} - σ_{3}}{2} = \frac{σ_{0}}{2}$

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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

The correct option is B σ1−σ3=σ0 As per maximum shear stress theory, for no failure maximum shear stress should be less than half of yield stress. Max[(σ1−σ22),(σ2−σ32),(σ3−σ12)]≤σ02 Given that σ1>σ2>σ3 σ1−σ32=σ02

In a strained body, the three principal stresses at a point are denoted by $σ_{1}, σ_{2} a n d σ_{3}$ such that $σ_{1} > σ_{2} > σ_{3} .$ . If $σ_{0}$ denoted yield stress, then according to the maximum shear stress theory