Beam deflection worksheet with answers

Free printable Beam deflection worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
P = 8 kNABδ1.25 m1.25 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 8 kNL = 2.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 26 kNδL = 2.5 m

A cantilever carries a point load P at its free end. Find the deflection δ at the free end.

P = 26 kNL = 2.5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
w = 12 kN/mδL = 5 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 12 kN/mL = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 24 kNABδ3 m2 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 3 m from A. Find the deflection δB at the free end B.

P = 24 kNa = 3 mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δB = mm
5.Hard
w = 10 kN/mAB8 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the reaction RB at the prop.

L = 8 mw = 10 kN/m
RB = kN
6.Hard
P = 75 kNAB4 m4 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 8 mP = 75 kN at 4 m
MA = kN·m

Answer key

  1. 1. δmax = 2.818 mm
  2. 2. δ = 4.232 mm
  3. 3. δmax = 24.48 mm
  4. 4. δB = 25.71 mm
  5. 5. RB = 30 kN
  6. 6. MA = 112.5 kN·m

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