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ENGR5004 / Week 10
Tutorial 4 Problem 1Exercise sheetCurrent spec2:28 min

ENGR5004 Statics Tutorial Sheet 4, Problem 1 official answers

A compression member of 510 mm effective length consists of a solid aluminium rod of diameter D=24D = 24 mm. To reduce the weight of the member by 25%, the solid rod is replaced by a hollow rod of internal diameter d=12d = 12 mm. Determine

Solid circular section of diameter D and hollow circular section of outer diameter D and inner diameter d.
Solid circular section of diameter D and hollow circular section of outer diameter D and inner diameter d.
Formulas you may need
  • Euler critical load: Pcr=π2EIminLe2P_{cr} = \dfrac{\pi^2 E I_{min}}{L_e^2} (on the formula sheet)
  • Solid circle I=πr44I = \dfrac{\pi r^4}{4}, hollow circle I=π(r24−r14)4I = \dfrac{\pi(r_2^4 - r_1^4)}{4} (on the formula sheet)
  1. (a)
    the percent reduction in the critical load,
  2. (b)
    the value of the critical load for the hollow rod. Use E=70E = 70 GPa.