Question

The equation of deformation is derived to be \( y = x^2 - xL \) for a beam shown in the figure. 

Hint:

The curvature of a beam is the second derivative of the deformation equation with respect to \( x \).

Answer 1

Correct Answer: 2

The curvature of a beam is given by the second derivative of the deformation equation with respect to \( x \). The deformation equation is: \[ y = x^2 - xL. \] Taking the first derivative: \[ \frac{dy}{dx} = 2x - L. \] Taking the second derivative to find the curvature: \[ \frac{d^2y}{dx^2} = 2. \] Thus, the curvature of the beam at the mid-span is \( \boxed{2} \).