GATE 2025 AE – Question 55

Structures · Strength of materials: stress and strain, stress-strain curves, trusses, bars, beams and shafts, determinate and indeterminate · 2 marks · Numerical answer

A 1 m long rod of 1 cm $\times$ 1 cm cross section is subjected to an axial tensile force of 35 kN. The Young's modulus of the material is 70 GPa. The cross-section of the deformed rod is 0.998 cm $\times$ 0.998 cm. The Poisson's ratio of the material is ________ (rounded off to one decimal place).

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Correct answer: 0.39 to 0.41

Explanation

The axial stress is $\sigma = \frac{35000}{10^{-4}} = 3.5 \times 10^8$ Pa, so the axial strain is $\varepsilon = \frac{3.5 \times 10^8}{70 \times 10^9} = 0.005$. The lateral strain is $\frac{0.998 - 1}{1} = -0.002$. So $\nu = \frac{0.002}{0.005} = 0.4$.