Old spec Statics Session 11 Example 2 (ENGR5004)

Old spec Statics Session 11 Example 2TutorialOld spec ENGR2162:28 min

ENGR216 (old spec) Statics session 11 worked example 2 (slides 9-10) official answers

A cantilever AB of length $2L$ and flexural rigidity $EI$ , fixed at A, carries a downward concentrated load $P$ at its midpoint C ( $AC = CB = L$ ).

You may use the result for a cantilever of length $L$ with an end load $P$ : $\theta(x) = \dfrac{1}{EI}\left[-PLx + \dfrac{Px^2}{2}\right]$ , $y(x) = \dfrac{1}{EI}\left[-\dfrac{PLx^2}{2} + \dfrac{Px^3}{6}\right]$ .

Cantilever AB of length 2L fixed at A; downward load P at the midpoint C, AC = CB = L.

Formulas you may need

Elastic curve: $\dfrac{d^2y}{dx^2} = \dfrac{M(x)}{EI}$ , slope $\theta = \dfrac{dy}{dx}$ (learn this; on the 2025 sheet but not the 2026 one)
Unloaded segment: $M = 0$ , so it stays straight (rigid rotation), small angles $y_B \approx y_C + L\theta_C$ (learn this)

(a)
Sketch the deformed shape of the beam.
(b)
Calculate the maximum deflection of the beam.