Revisica
Sign in
ENGR5004 / Week 6
ENGR216 2021 Statics Q A2Past paperOld spec ENGR2162:227 marks32 min

ENGR216 Summer 2021 Statics Q A2[VALID] official answers

Consider the statically indeterminate beam with Young's modulus EE, cross sectional second area moment II past the neutral axis, and length LL depicted in Figure A2, subject to the constant distributed normal load w0w_0 along its entire length. The coordinate along the beam axis, denoted by xx, has origin at end A of the beam.

Figure A2: beam of length L fixed at A, roller at B, uniform load w0.
Figure A2: beam of length L fixed at A, roller at B, uniform load w0.
Formulas you may need
  • Elastic curve: EI d2ydx2=M(x)EI\,\dfrac{d^2y}{dx^2} = M(x) (learn this; on the 2025 sheet but not the 2026 one)
  • Load, shear and moment: dVdx=−w(x)\dfrac{dV}{dx} = -w(x), dMdx=V(x)\dfrac{dM}{dx} = V(x) (on the formula sheet)
  • Distributed load resultant P=∫w dxP = \int w\,dx at its centroid (on the formula sheet)
  • Equilibrium of a plane rigid body: ∑Fx=0\sum F_x = 0, ∑Fy=0\sum F_y = 0, ∑M=0\sum M = 0 (learn this)
  • Fixed-end conditions y=0y = 0, y′=0y' = 0; roller y=0y = 0, M=0M = 0 (learn this)
  1. (a)
    Sketch accurately the deformed longitudinal axis of the beam subject to the indicated load highlighting the geometric conditions imposed by the constraints, and draw the free body diagram of the loaded beam.
    [7]
  2. (b)
    List and count all unknown reactions, and the equations available to calculate all such unknown reactions.
    [6]Third
  3. (c)
    Knowing that the equation of the elastic curve of the beam subject to the given load is: y(x)=w0EI(−L2x216+5Lx348−x424)(2)y(x) = \frac{w_0}{EI}\left(-\frac{L^2 x^2}{16} + \frac{5 L x^3}{48} - \frac{x^4}{24}\right) \qquad (2) determine the magnitude of the maximum bending moment along the beam.
    [8]
  4. (d)
    Determine at which position along the beam the maximum magnitude of the shearing load occurs.
    [6]