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ENGR5004 / Week 1
Statics Session 2 Practice Problem BTutorialCurrent spec2:212 min

ENGR5004 Statics session 2 worked example 4 (Appendix 3 practice problem B, slides 19-21) official answers

The horizontal rigid bar BDE is supported by two vertical pin-ended links. Link AB (aluminium, E=70E = 70 GPa, area 500 mm2500\ \mathrm{mm^2}, length 0.3 m) hangs from a fixed pin A down to B; link CD (steel, E=200E = 200 GPa, area 600 mm2600\ \mathrm{mm^2}, length 0.4 m) hangs from a fixed pin C down to D. BD=0.2BD = 0.2 m and DE=0.4DE = 0.4 m, and a downward force of 30 kN acts at E. Treat bar BDE as rigid.

Determine the vertical deflection of (a) B, (b) D and (c) E.

Rigid bar BDE hung from two vertical links: AB (0.3 m) above B and CD (0.4 m) above D, both pinned to a fixed support. BD = 0.2 m, DE = 0.4 m; 30 kN downward at E.
Rigid bar BDE hung from two vertical links: AB (0.3 m) above B and CD (0.4 m) above D, both pinned to a fixed support. BD = 0.2 m, DE = 0.4 m; 30 kN downward at E.
Formulas you may need
  • Equilibrium of a rigid body: ∑MB=0\sum M_B = 0, ∑MD=0\sum M_D = 0 (learn this)
  • Axial deformation δ=FLAE\delta = \dfrac{FL}{AE} (learn this)
  • Rigid bar: displaced points stay on a straight line (similar triangles) (learn this)
  1. (a)
    Deflection of B (give the direction).
  2. (b)
    Deflection of D (give the direction).
  3. (c)
    Deflection of E (give the direction).