GATE 2025 AE – Question 59

Structures · Strength of materials: Transformation of stress and strain, Mohr's circle, combined loading and failure criteria · 2 marks · Numerical answer

A thin flat plate is subjected to the following stresses: $\sigma_{xx} = 160$ MPa; $\sigma_{yy} = 40$ MPa; $\tau_{xy} = 80$ MPa. Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is _____ (rounded off to two decimal places).

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Correct answer: 1.24 to 1.26

Explanation

For plane stress, $\sigma_{vm} = \sqrt{\sigma_{xx}^2 - \sigma_{xx}\sigma_{yy} + \sigma_{yy}^2 + 3\tau_{xy}^2} = \sqrt{25600 - 6400 + 1600 + 19200} = \sqrt{40000} = 200$ MPa. The factor of safety is $\frac{250}{200} = 1.25$.