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ENGR5004 / Week 6
Old spec Statics Session 12 Example 1TutorialOld spec ENGR2162:120 min

ENGR216 (old spec) Statics session 12 worked example 1 (slides 6-9) official answers

A cantilever ABC of length 3a3a and flexural rigidity EIEI is fixed at A. Portion AB (0≤x≤2a0 \le x \le 2a) carries a uniform distributed load ww acting UPWARDS; portion BC (2a≤x≤3a2a \le x \le 3a) is unloaded, and a downward concentrated load P=23waP = \tfrac{2}{3}wa acts at the free end C. Take xx from A and yy upwards.

Cantilever fixed at A, length 3a: upward uniform load w on AB (length 2a), downward load P = (2/3)wa at the free end C (BC = a).
Cantilever fixed at A, length 3a: upward uniform load w on AB (length 2a), downward load P = (2/3)wa at the free end C (BC = a).
Formulas you may need
  • Elastic curve: EId2ydx2=M(x)EI\dfrac{d^2y}{dx^2} = M(x), slope θ=dydx\theta = \dfrac{dy}{dx}, two constants per segment; boundary and continuity conditions (learn this; on the 2025 sheet but not the 2026 one)
  • Equilibrium ∑Fy=0\sum F_y = 0, ∑MA=0\sum M_A = 0; fixed support gives a force and a couple (learn this)
  • Bending moment by the method of sections; dMdx=V\dfrac{dM}{dx} = V (on the formula sheet)
  1. (a)
    Calculate the deflection and rotation of the free end C.
  2. (b)
    Sketch M(x)M(x) and y(x)y(x).
  3. (c)
    Calculate the maximum deflection of the beam.