A beam is subjected to the uniform load W_e per unit length and M_A, V_A & V_B are the reactions as shown in the figure. The expression for shear force V(x) and Bending moment M(x) is given by

Question

Question

This question was previously asked in

ISRO Scientist Mechanical 7 Jan 2024 Official Paper

Attempt Online

Answer 1

Concept:

The beam is subjected to a uniformly distributed load (UDL) of intensity \(W_e\) N/m over its length.

Let \(x\) be the distance from the fixed support A.

Shear Force Calculation:

Consider a section at distance \(x\) from A.

Upward force due to support A = \(V_A\)

Downward load from 0 to x = \(W_e \cdot x\)

So, shear force at distance x is:

\(V(x) = V_A - W_e \cdot x\)

Bending Moment Calculation:

Bending moment due to:

So, bending moment at distance x is:

\(M(x) = M_A + V_A x - \frac{W_e x^2}{2}\)

Final Expressions:

\(V(x) = V_A - W_e x\)

\(M(x) = M_A + V_A x - \frac{W_e x^2}{2}\)