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ENGR5004 / Week 5
Tutorial 2 Problem 1Exercise sheetCurrent spec2:120 min

ENGR5004 Statics Tutorial Sheet 2, Problem 1 official answers

The beam depicted in the left figure below is subject to two concentrated loads P1=60P_1 = 60 kN and P2=45P_2 = 45 kN, with points of application defined by the dimensions a=0.4a = 0.4 m, b=0.3b = 0.3 m. The beam features the hollow square cross section depicted in the right figure below. Consider section n-n, the position of which is defined by d=0.2d = 0.2 m. Determine:

Left: beam AB, pin at A, roller at B, P1 at a from A, P2 at a + b from A, span 2a + b, section n-n at d from A. Right: hollow square section 100 mm x 100 mm, wall 12 mm, point p at the inside top-left corner.
Left: beam AB, pin at A, roller at B, P1 at a from A, P2 at a + b from A, span 2a + b, section n-n at d from A. Right: hollow square section 100 mm x 100 mm, wall 12 mm, point p at the inside top-left corner.
Formulas you may need
  • Load-shear-moment relations and sign convention: dVdx=−w\dfrac{dV}{dx} = -w, dMdx=V\dfrac{dM}{dx} = V (on the formula sheet)
  • Rectangle second moment I=bh312I = \dfrac{bh^3}{12} (hollow section by subtraction) (on the formula sheet)
  • Parallel-axis theorem: I=Ic+Ad2I = I_c + Ad^2 (learn this)
  • Transverse shear stress: τ=VQIt\tau = \dfrac{VQ}{It}, Q=yˉ′A′Q = \bar y' A' (learn this; on the 2025 sheet but not the 2026 one)
  • Bending stress: σmax=∣M∣cI\sigma_{max} = \dfrac{|M|c}{I} (on the formula sheet)
  1. (a)
    the support reactions and the shearing load on section n-n;
  2. (b)
    the largest shear stress acting on section n-n;
  3. (c)
    the shear stress at point p on section n-n;
  4. (d)
    the largest normal stress on section n-n.