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 = ?ABδ3 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 5 mm.

δ = 5 mmL = 3 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
P = kN
2.Easy
P = 27 kNδL = 2.5 m

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

P = 27 kNL = 2.5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
P = 15 kNABδ5 m1 m

A simply supported beam carries a point load P at a = 5 m from support A. Find the deflection δP under the load.

P = 15 kNa = 5 mL = 6 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δP = mm
4.Medium
w = 10 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 = 10 kN/mL = 3 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
w = 12 kN/mP = 30 kNδL = 2 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 = 30 kNw = 12 kN/mL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 12 kN/mδL = 4 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 = 12 kN/mL = 4 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. P = 3.267 kN
  2. 2. δ = 19.53 mm
  3. 3. δP = 4.529 mm
  4. 4. δ = 76.7 mm
  5. 5. δmax = 1.63 mm
  6. 6. Ireq = 18 × 10⁶ mm⁴

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