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 = 7 kNδL = 3 m

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

P = 7 kNL = 3 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ1.5 m1.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 20 mm.

δ = 20 mmL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
P = kN
3.Medium
w = 12 kN/mP = 7 kNABδ1.5 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 7 kNw = 12 kN/mL = 1.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δ = mm
4.Medium
P = 23 kNABδ1.5 m0.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δB at the free end B.

P = 23 kNa = 1.5 mL = 2 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δB = mm
5.Hard
w = 6 kN/mP = 26 kNδL = 3 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 = 26 kNw = 6 kN/mL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 19 kNABδ3 m2 m

A simply supported beam carries a point load P at b = 2 m from support B. Find the maximum deflection δmax of the beam.

P = 19 kNb = 2 mL = 5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 68.18 mm
  2. 2. P = 85.33 kN
  3. 3. δ = 24.67 mm
  4. 4. δB = 9.727 mm
  5. 5. δmax = 8.73 mm
  6. 6. δmax = 50.78 mm

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