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ENGR5004 / Week 3
Statics Session 2 Problem (rods CE and DF)TutorialCurrent spec2:118 min

ENGR5004 Statics session 2 problem set for week 4 (slide 14, with answers), worked in old-spec Statics session 7 Problem 2 (slides 9-13) official answers

Rod CE and rod DF are attached to the rigid horizontal bar ABCD, which is pinned at B. Distances along the bar: AB=338AB = 338 mm, BC=225BC = 225 mm, CD=150CD = 150 mm. Both rods hang vertically down from the bar to fixed supports at E and F: rod CE has length 450 mm and diameter 10 mm; rod DF has length 562 mm and diameter 15 mm. Both rods are steel with E=200E = 200 GPa. A vertical downward load of 100 kN is applied at end A of the bar.

Determine:

Rigid bar ABCD pinned at B; 100 kN downward at A, 338 mm left of B. Rod CE (450 mm long) and rod DF (562 mm long) run down from C and D to fixed supports E and F; BC = 225 mm, CD = 150 mm.
Rigid bar ABCD pinned at B; 100 kN downward at A, 338 mm left of B. Rod CE (450 mm long) and rod DF (562 mm long) run down from C and D to fixed supports E and F; BC = 225 mm, CD = 150 mm.
Formulas you may need
  • Equilibrium of a rigid body: ∑MB=0\sum M_B = 0, ∑Fy=0\sum F_y = 0 (learn this)
  • Axial deformation δ=FLAE\delta = \dfrac{FL}{AE}, circle A=πd2/4A = \pi d^2/4 (learn this; circle area on the formula sheet)
  • Rigid bar rotating about B: displacements proportional to distance from B (similar triangles) (learn this)
  • Bending moment by the method of sections; dMdx=V\dfrac{dM}{dx} = V (on the formula sheet)
  1. (a)
    the internal force in each rod;
  2. (b)
    the vertical displacements of bar ends A and D;
  3. (c)
    the maximum absolute value of the bending moment in the bar, and where it occurs.