The major and minor principal stresses at a point are 3MPa and -3MPa respectively. The maximum shear stress at the point is

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GATE CE 2010 Official Paper

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Answer 1

Concept:

When two stress are acting at a point, the maximum shear stress(τ_max) is given by

\({\tau _{max}} = \frac{{{σ _1} - {σ _3}}}{2}\)

σ₁ = Major principal stress

σ₃ = Minor principal stress

Calculation:

Given:

σ1 = 3 MPa

σ3 = -3 MPa

\({\tau _{max}} = \frac{{{3} - {(-3)}}}{2}\)

⇒ 3 MPa