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ENGR5004 / Week 3
Old spec Statics Session 7 Problem 1TutorialOld spec ENGR2162:210 min

ENGR216 (old spec) Statics session 7 worked example 1 (Problem 1, slides 5-8) official answers

Beam AC is simply supported (pin at A, roller at C) with span 9 m. It carries a uniformly distributed load of 20 kN/m over the 6 m length AB; the remaining 3 m, BC, is unloaded.

Simply supported beam AC, pin at A, roller at C; 20 kN/m downward over AB = 6 m, BC = 3 m unloaded.
Simply supported beam AC, pin at A, roller at C; 20 kN/m downward over AB = 6 m, BC = 3 m unloaded.
Formulas you may need
  • Load, shear and moment: dVdx=−w\dfrac{dV}{dx} = -w, dMdx=V\dfrac{dM}{dx} = V and their integral forms (on the formula sheet)
  • Maximum bending stress σmax=∣M∣cI=∣M∣S\sigma_{max} = \dfrac{|M|c}{I} = \dfrac{|M|}{S} with section modulus S=I/cS = I/c (on the formula sheet: ∣M∣c/I|M|c/I; SS learn this)
  1. (a)
    Draw the shear and bending moment diagrams of the beam.
  2. (b)
    Determine the location of the section where the maximum normal stress due to bending occurs and, assuming an elastic section modulus S=1270 cm3S = 1270\ \mathrm{cm^3}, the magnitude of that stress.