Hooke's Law in shear relates shear stress tau and shear strain gamma via the modulus of rigidity G. The relationship between E, G, and Poisson's ratio nu is:

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Mechanical Engineering QUESTION #2495

Question 1

Hooke's Law in shear relates shear stress \(\tau\) and shear strain \(\gamma\) via the modulus of rigidity \(G\). The relationship between \(E\), \(G\), and Poisson's ratio \(\nu\) is:

\(E = G(1 + \nu)\)
\(E = 2G(1 - \nu)\)
\(E = 2G(1 + \nu)\)✔️
\(E = G/(2\nu)\)

Correct Answer Explanation

From elasticity theory, the three elastic constants are related by \(E = 2G(1+\nu)\). For steel: \(E \approx 207\) GPa, \(G \approx 79.3\) GPa, \(\nu \approx 0.292\).

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