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 = 16 kNδL = 1.5 m

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

P = 16 kNL = 1.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ1.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 15 mm.

δ = 15 mmL = 1.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
P = 12 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 = 12 kNa = 2 mL = 3 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δB = mm
4.Medium
w = 20 kN/mδL = 2.5 m

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

w = 20 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 15 kN/mP = 14 kNδL = 1.5 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 = 14 kNw = 15 kN/mL = 1.5 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 26 kNP = 26 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 = 26 kNL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 3.913 mm
  2. 2. P = 61.33 kN
  3. 3. δB = 9.524 mm
  4. 4. δmax = 17.1 mm
  5. 5. δmax = 14.95 mm
  6. 6. δmax = 12.84 mm

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