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 = ?ABδ4 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 5 mm.

δ = 5 mmL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
P = kN
2.Easy
P = 14 kNδL = 3 m

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

P = 14 kNL = 3 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
P = 27 kNABδ2 m1 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δB at the free end B.

P = 27 kNa = 2 mL = 3 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δB = mm
4.Medium
w = 10 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 = 10 kN/mL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 4 kN/mP = 3 kNδL = 4 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 = 3 kNw = 4 kN/mL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 65 kNAB2 m2 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 = 4 mP = 65 kN at 2 m
RB = kN

Answer key

  1. 1. P = 1.969 kN
  2. 2. δ = 71.59 mm
  3. 3. δB = 74.12 mm
  4. 4. δmax = 16.67 mm
  5. 5. δmax = 2.407 mm
  6. 6. RB = 20.31 kN

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