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Thrust & Pressure

In an elastic...

Question

In an elastic material, the principal stresses are $σ_{1}$ (tensile), 2 $σ_{1}$ (tensile) and $σ_{1}$ (compressive), Maximum shear stress developed in the member is ______ $σ_{1}$
1.5

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Solution

The correct option is A 1.5
Maximum shear- stress = $M a x i m u m o f ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{2 σ_{1} - σ_{1}}{2} = \frac{σ_{1}}{2} \frac{σ_{1} + σ_{1}}{2} = σ_{1} \frac{2 σ_{1} + σ_{1}}{2} = \frac{3}{2} σ_{1} \end{matrix}$
= $\frac{3}{2} σ_{1} = 1.5 σ_{1}$

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