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 = 14 kNδL = 2.5 m

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

P = 14 kNL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
w = 8 kN/mABθ3 m

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θB of the beam at the free end B, in radians.

w = 8 kN/mL = 3 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
θB = rad
3.Medium
w = 2 kN/mδL = 4 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 2 kN/mL = 4 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 4 kN/mABθ6 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θA of the beam at support A, in radians.

w = 4 kN/mL = 6 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
θA = rad
5.Hard
P = 24 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 = 24 kNb = 1 mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 20 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 = 20 kN/mL = 4 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 8.681 mm
  2. 2. θB = 0.003214 rad
  3. 3. δmax = 71.3 mm
  4. 4. θA = 0.03896 rad
  5. 5. δmax = 9.036 mm
  6. 6. Ireq = 30 × 10⁶ mm⁴

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