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ENGR5004 / Week 9
Old spec Statics Session 18 ProblemTutorialOld spec ENGR2162:212 min

ENGR216 (old spec) Statics session 18 worked example (Problem, slides 10-12) official answers

A 2 m long pin-ended steel column of solid circular cross section has E=200E = 200 GPa and allowable normal stress σall=100\sigma_{all} = 100 MPa. Using a factor of safety k=2.5k = 2.5 on Euler's critical load for buckling, determine the cross-section radius needed if the column is to safely support:

Formulas you may need
  • Euler load for a pinned-pinned column Pcr=π2EIminL2P_{cr} = \dfrac{\pi^2 E I_{min}}{L^2} (Le=LL_e = L) (on the formula sheet)
  • Solid circle A=πr2A = \pi r^2, I=πr44I = \dfrac{\pi r^4}{4} (on the formula sheet)
  • Design: Pcr≥kPP_{cr} \ge kP and σ=P/A≤σall\sigma = P/A \le \sigma_{all}; the larger radius governs (learn this)
  1. (a)
    a 380 kN load;
  2. (b)
    an 800 kN load.