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ENGR5004 / Week 1
Statics Session 2 Practice Problem ATutorialCurrent specThird6 min

ENGR5004 Statics session 2 worked example 3 (Appendix 2 practice problem A, slides 17-18) official answers

A horizontal steel rod (E=200E = 200 GPa) is fixed to a wall at A and is free at D. Going right from A it passes B and C. Axial loads act at three points: PB=350P_B = 350 kN at B to the right, PC=200P_C = 200 kN at C to the left and PD=130P_D = 130 kN at D to the right. Lengths: lAB=lBC=0.3l_{AB} = l_{BC} = 0.3 m, lCD=0.4l_{CD} = 0.4 m. Areas: AAB=ABC=5.8 cm2A_{AB} = A_{BC} = 5.8\ \mathrm{cm^2}, ACD=1.9 cm2A_{CD} = 1.9\ \mathrm{cm^2}.

Determine the internal force in each portion and the overall deformation of the rod.

Horizontal rod fixed to a wall at A; larger section from A to C (through B), smaller section from C to D. P_B to the right at B, P_C to the left at C, P_D to the right at the free end D.
Horizontal rod fixed to a wall at A; larger section from A to C (through B), smaller section from C to D. P_B to the right at B, P_C to the left at C, P_D to the right at the free end D.
Formulas you may need
  • Axial deformation of a stepped bar δ=∑iPiLiAiEi\delta = \sum_i \dfrac{P_i L_i}{A_i E_i} (learn this)
  • Internal force from a section FBD (take the free part, tension positive) (learn this)