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 = 29 kNδL = 1.5 m

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

P = 29 kNL = 1.5 mE = 200 GPa (steel)I = 12 × 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 = 11 GPa (timber)I = 120 × 10⁶ mm⁴
P = kN
3.Medium
P = 8 kNABδ0.5 m1.5 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 = 8 kNa = 0.5 mL = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δB = mm
4.Medium
w = 2 kN/mδL = 5 m

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

w = 2 kN/mL = 5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
w = 15 kN/mP = 28 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 = 28 kNw = 15 kN/mL = 1.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 2 kN/mδL = 6 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 2 kN/mL = 6 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 13.59 mm
  2. 2. P = 7.92 kN
  3. 3. δB = 1.139 mm
  4. 4. δ = 18.6 mm
  5. 5. δmax = 2.241 mm
  6. 6. Ireq = 10.13 × 10⁶ mm⁴

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