Two strain gauges fixed along the principal directions on a plane surface of a steel member recorded strain values of 0.0013 tensile and -0.0013 compressive respectively. Given that the value of E = 2 × 10⁵ MPa and μ = 0.3, the largest normal and shearing stress at this point are

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This question was previously asked in

ESE Mechanical 2015 Paper 2: Official Paper

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Answer 1

Concept: Major and minor Normal stress is given by

Where μ is the Poisson’s ratio, and ϵ₁ is the major principal strain, ϵ₂ is the minor principal strain and E is the modulus of elasticity

Calculation:

Given: ϵ₁ = 0.0013 and ϵ₂ = -0.0013, E =2 × 10⁵ MPa and μ = 0.3

So the Largest normal stress is 200 MPa