GATE 2026 ME – Question 52

Mechanics of Materials · Transformation of stress and strain, Mohr circle · 2 marks · Numerical answer

A welded square plate of 1 m $\times$ 1 m is subjected to biaxial stress of magnitude 6.5 MPa and 25 MPa, as shown in the figure below. The ratio of the normal stress acting in the perpendicular direction of the weld to the shear stress of the weld is ________ (*rounded off to 2 decimal places*).

A square plate with a weld along its diagonal. A 6.5 MPa compressive stress acts on the left and right edges, and a 25 MPa tensile stress acts on the top and bottom edges.

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Correct answer: 0.58 to 0.60

Explanation

Take the stresses as $\sigma_x = -6.5$ MPa (compression) and $\sigma_y = 25$ MPa (tension). The weld is along the diagonal, so its normal makes 45° with the axes. At 45° the normal stress is $\frac{\sigma_x + \sigma_y}{2} = 9.25$ MPa, and the shear stress has magnitude $\frac{|\sigma_x - \sigma_y|}{2} = 15.75$ MPa. The ratio is $\frac{9.25}{15.75} = 0.59$.