Question

The shearing strain component in X-Y plane is ________

(a) \(Γ_{xy}=\frac{∂v}{∂x}+\frac{∂u}{∂y} \)

(b) \(Γ_{xy}=\frac{∂v}{∂x}-\frac{∂u}{∂y} \)

(c) \(Γ_{xy}=\frac{∂v}{∂y}+\frac{∂u}{∂x} \)

(d) \(Γ_{xy}=\frac{∂v}{∂y}-\frac{∂u}{∂x} \)

The question was asked by my college director while I was bunking the class.

My question is based upon Strain Components and Compatibility Equations in chapter Elements of Elasticity of Geotechnical Engineering I

Answer 1

Right choice is (a) \(Γ_{xy}=\frac{∂v}{∂x}+\frac{∂u}{∂y} \)

For explanation: In order to find the shearing strain component in X-Y plane, let us consider a plane lamina of size dx, dy in X-Y plane. If u is the displacement in x-direction and v is the displacement in y-direction, the shearing strain component is,

\(Γ_{xy}=\frac{∂v}{∂x}+\frac{∂u}{∂y} \).