Question

The shearing strain component in Z-X plane is ________

(a) \(Γ_{xz} =\frac{∂w}{∂y}+\frac{∂v}{∂z} \)

(b) \(Γ_{xz} =\frac{∂v}{∂x}-\frac{∂w}{∂y} \)

(c) \(Γ_{xz} =\frac{∂u}{∂z}+\frac{∂w}{∂x} \)

(d) \(Γ_{xz} =\frac{∂v}{∂y}-\frac{∂w}{∂x} \)

I got this question in a national level competition.

This intriguing question comes from Strain Components and Compatibility Equations topic in division Elements of Elasticity of Geotechnical Engineering I

Answer 1

Correct option is (c) \(Γ_{xz} =\frac{∂u}{∂z}+\frac{∂w}{∂x} \)

Easiest explanation: In order to find the shearing strain component in Z-X plane, let us consider a plane lamina of size dx, dz in Z-X plane. If w is the displacement in z-direction and u is the displacement in x-direction, the shearing strain component is,

\(Γ_{xz} =\frac{∂u}{∂z}+\frac{∂w}{∂x}. \)