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 = 4 kNδL = 6 m

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

P = 4 kNL = 6 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ1 m1 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 25 mm.

δ = 25 mmL = 2 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
w = 8 kN/mP = 22 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 = 22 kNw = 8 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
4.Medium
P = 3 kNABδ0.5 m4.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 0.5 m from A. Find the deflection δB at the free end B.

P = 3 kNa = 0.5 mL = 5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δB = mm
5.Hard
P = 4 kNP = 4 kNABδ1.333 m1.334 m1.333 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 4 kNL = 4 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 30 kNABδ5 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the maximum deflection δmax of the beam.

P = 30 kNb = 1 mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 25.71 mm
  2. 2. P = 59.4 kN
  3. 3. δ = 2.662 mm
  4. 4. δB = 3.046 mm
  5. 5. δmax = 68.84 mm
  6. 6. δmax = 11.3 mm

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