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 = 23 kNδL = 2 m

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

P = 23 kNL = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = 5 kNABδ2 m2 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 5 kNL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 4 kN/mδL = 3 m

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

w = 4 kN/mL = 3 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
4.Medium
w = 15 kN/mP = 5 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 = 5 kNw = 15 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
5.Hard
w = 10 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 = 10 kN/mL = 6 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
w = 2 kN/mP = 11 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 = 11 kNw = 2 kN/mL = 4 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 66.38 mm
  2. 2. δmax = 1.671 mm
  3. 3. δ = 5.625 mm
  4. 4. δ = 18 mm
  5. 5. Ireq = 920.5 × 10⁶ mm⁴
  6. 6. δmax = 8.466 mm

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