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 = ?ABδ4 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 8 mm.

δ = 8 mmL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
P = kN
2.Easy
P = 11 kNδL = 3 m

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

P = 11 kNL = 3 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
w = 20 kN/mδL = 3 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 = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 6 kN/mδL = 2 m

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

w = 6 kN/mL = 2 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δ = mm
5.Hard
w = 2 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 = 2 kN/mL = 4 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
P = 18 kNABδ5 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the maximum deflection δmax of the beam.

P = 18 kNb = 1 mL = 6 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. P = 3.15 kN
  2. 2. δ = 3.094 mm
  3. 3. δmax = 13.1 mm
  4. 4. δ = 47.43 mm
  5. 5. Ireq = 54.55 × 10⁶ mm⁴
  6. 6. δmax = 30.19 mm

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