Revisica
Sign in
ENGR5004 / Week 5
Tutorial 1 Problem 4Exercise sheetCurrent spec2:120 min

ENGR5004 Statics Tutorial Sheet 1, Problem 4 official answers

Consider a simply supported beam subject to the linear distributed load sketched below.

Beam AB of length L, roller at A (left), pin at B (right), triangular load rising from zero at A to w0 at B; x along the beam from A, y up.
Beam AB of length L, roller at A (left), pin at B (right), triangular load rising from zero at A to w0 at B; x along the beam from A, y up.
Formulas you may need
  • Distributed load resultant: P=∫w dxP = \int w\,dx, position xP=∫x w dx∫w dxx_P = \dfrac{\int x\,w\,dx}{\int w\,dx} (on the formula sheet)
  • Load-shear-moment relations: dVdx=−w(x)\dfrac{dV}{dx} = -w(x), dMdx=V(x)\dfrac{dM}{dx} = V(x) (on the formula sheet)
  • Maximum bending stress: σmax=∣M∣cI\sigma_{max} = \dfrac{|M|c}{I}, rectangle I=bh312I = \dfrac{bh^3}{12} (on the formula sheet)
  • Maximum transverse shear stress, rectangle: τmax=3V2A\tau_{max} = \dfrac{3V}{2A} (learn this; on the 2025 sheet but not the 2026 one)
  1. (a)
    Determine the equations of shearing load V(x)V(x) and bending moment M(x)M(x) as a function of the position xx, the value of the distributed load w0w_0 at the right end of the beam, and the beam length LL;
  2. (b)
    plot V(x)V(x) and M(x)M(x) along the beam axis;
  3. (c)
    determine the position along the beam where the maximum normal stress occurs and, knowing that the cross section is square and has length aa, calculate the value of such maximum normal stress as a function of w0w_0, aa and LL;
  4. (d)
    determine the position along the beam where the maximum shear stress occurs and the value of such maximum shear stress as a function of w0w_0, aa and LL.