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GATE 2026 CE (CE2) – Question 38

Structural Analysis · Influence lines and moving loads · 2 marks · Multiple choice

A simply supported, linearly elastic, homogeneous, prismatic beam of length $L$ and flexural rigidity $EI$ is shown in the figure.

[Figure: A simply supported beam with a pin support at A on the left and a roller support at B on the right, span L. A downward unit load acts at a distance x from A. The deflected shape is drawn with the end rotation at B marked as theta B of x.]

The expression for the Influence Line Diagram (ILD) of the rotation $\theta_B(x)$ at the support B is

Diagram for GATE 2026 CE (CE2) question 38
  1. $\frac{1}{6EI}(x^2 - L^2)$
  2. $\frac{1}{6EIL}(x^3 - L^2x)$
  3. $\frac{1}{3EI}(x^2 - Lx)$
  4. $\frac{1}{3EIL}(x^3 - L^2x)$

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Show answer and explanation

Correct answer: (B) $\frac{1}{6EIL}(x^3 - L^2x)$

Explanation

By Maxwell's reciprocal theorem, the rotation at B due to a unit load at $x$ equals the deflection at $x$ due to a unit moment applied at B. For a unit end moment at B that deflection is $\frac{x(L^2 - x^2)}{6EIL}$. So $\theta_B(x)$ has the magnitude $\frac{L^2x - x^3}{6EIL}$, which is option B up to the sign convention for the rotation. Options A and C have the wrong powers of $x$, and option D has twice the correct magnitude.