Old spec Statics Session 11 Example 3 (ENGR5004)

Old spec Statics Session 11 Example 3TutorialOld spec ENGR2162:210 min

ENGR216 (old spec) Statics session 11 worked example 3 (slides 11-12) official answers

A simply supported beam AB of length $L$ and flexural rigidity $EI$ (pin at A, roller at B) carries a uniform distributed load $w$ over its whole length. Take $x$ from A and $y$ upwards.

Simply supported beam AB of length L (pin at A, roller at B) under a uniform downward load w.

Formulas you may need

Elastic curve: $EI\dfrac{d^2y}{dx^2} = M(x)$ , slope $\theta = \dfrac{dy}{dx}$ (learn this; on the 2025 sheet but not the 2026 one)
Boundary conditions for a simply supported beam: $y = 0$ at each support (learn this)

(a)
Sketch the deformed shape.
(b)
Calculate the slope $\theta(x)$ and deflection $y(x)$ of the elastic curve.
(c)
Calculate the maximum deflection and the rotation of end A.