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 = 17 kNδL = 2.5 m

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

P = 17 kNL = 2.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2.5 m2.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 12 mm.

δ = 12 mmL = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
P = kN
3.Medium
w = 10 kN/mP = 11 kNABδ4 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 = 11 kNw = 10 kN/mL = 4 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
4.Medium
P = 22 kNABδ1.5 m2.5 m

A simply supported beam carries a point load P at a = 1.5 m from support A. Find the deflection δP under the load.

P = 22 kNa = 1.5 mL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δP = mm
5.Hard
P = 29 kNABδ6 m2 m

A simply supported beam carries a point load P at b = 2 m from support B. Find the maximum deflection δmax of the beam.

P = 29 kNb = 2 mL = 8 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 12 kN/mδL = 2.5 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 = 2.5 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 36.89 mm
  2. 2. P = 18.39 kN
  3. 3. δ = 48.65 mm
  4. 4. δP = 30.69 mm
  5. 5. δmax = 12.87 mm
  6. 6. Ireq = 79.9 × 10⁶ mm⁴

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