Question

If u is the displacement in x-direction, the linear strain component in is defined by __________

(a) \(ε_X=\frac{∂u}{∂x}\)

(b) \(ε_X=\frac{∂x}{∂u}\)

(c) \(ε_X=\frac{dx}{du}\)

(d) εX=x+u

I got this question in final exam.

I need to ask this question from Strain Components and Compatibility Equations topic in section Elements of Elasticity of Geotechnical Engineering I

Answer 1

The correct option is (a) \(ε_X=\frac{∂u}{∂x}\)

Explanation: The strain is the ratio of change in dimension of an object to its original dimension. Therefore, the linear strain component in is defined by,

\(ε_X=\frac{∂u}{∂x}\). Where, u is the displacement in x-direction.