Old spec Statics Session 11 Example 1 (ENGR5004)

Old spec Statics Session 11 Example 1TutorialOld spec ENGR216Third8 min

ENGR216 (old spec) Statics session 11 worked example 1 (slides 7-8) official answers

A cantilever AB of length $L$ and flexural rigidity $EI$ , fixed at A, carries a downward concentrated load $P$ at its free end B. Take $x$ from A along the beam and $y$ upwards.

Cantilever AB of length L, fixed at A (left), with a downward load P at the free end B.

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)
Fixed end: $y = 0$ and $\theta = 0$ (learn this)
Bending moment by the method of sections, positive sagging (on the formula sheet)

(a)
Sketch the elastic curve of the beam.
(b)
Calculate the slope $\theta(x)$ and deflection $y(x)$ of the elastic curve.
(c)
Calculate the maximum deflection of the beam.