If a body carries two unlike principal stresses, what is the maximum shear stress?

Half the difference of magnitude of the principal stresses

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Half the sum of the magnitude of principal stresses

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Difference of the magnitude of principal stresses

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Sum of the magnitude of principal stresses

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Solution

The correct option is B Half the sum of the magnitude of principal stresses
$τ_{max} = \frac{σ_{1} - σ_{2}}{2} (m a g n i t u d e)$
The principal stress given are unlike i.e. if one of tensile, other is compressive. Let $σ_{1}$ be tensile and $σ_{2}$ be compressive, then
$τ_{max} = \frac{σ_{1} - (- σ_{2})}{2} = \frac{σ_{1} + σ_{2}}{2}$

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