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ENGR5004 / Week 6
Old spec Statics Session 12 Example 2TutorialOld spec ENGR2162:118 min

ENGR216 (old spec) Statics session 12 worked example 2 (slides 10-16) official answers

A beam AB of length LL and flexural rigidity EIEI is fixed at A and supported by a roller at B. It carries a uniform downward load ww over its whole length. Take xx from A and yy upwards.

Propped cantilever: beam AB of length L, fixed at A (left), roller at B (right), uniform downward load w.
Propped cantilever: beam AB of length L, fixed at A (left), roller at B (right), uniform downward load w.
Formulas you may need
  • Equilibrium ∑Fx=0\sum F_x = 0, ∑Fy=0\sum F_y = 0, ∑M=0\sum M = 0; a fixed support gives two forces and a couple, a roller one force; degree of indeterminacy = unknown reactions minus independent equilibrium equations (learn this)
  • Elastic curve: EId2ydx2=M(x)EI\dfrac{d^2y}{dx^2} = M(x), slope θ=dydx\theta = \dfrac{dy}{dx} (learn this; on the 2025 sheet but not the 2026 one)
  • Fixed end y=0y = 0, θ=0\theta = 0; roller y=0y = 0 (learn this)
  1. (a)
    Determine the reactions of the supports.
  2. (b)
    Sketch the elastic curve.
  3. (c)
    Determine the position of the maximum deflection.