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 = 10 kNδL = 4 m

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

P = 10 kNL = 4 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2 m2 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 8 mm.

δ = 8 mmL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
w = 20 kN/mδL = 2 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 20 kN/mL = 2 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δ = mm
4.Medium
w = 12 kN/mδL = 8 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 = 8 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 55 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 reaction RB at the prop.

L = 8 mP = 55 kN at 4 m
RB = kN
6.Hard
w = 15 kN/mP = 2 kNδL = 6 m

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δmax.

P = 2 kNw = 15 kN/mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 12.7 mm
  2. 2. P = 43.2 kN
  3. 3. δ = 63.8 mm
  4. 4. δmax = 57.14 mm
  5. 5. RB = 17.19 kN
  6. 6. δmax = 44.58 mm

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