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 = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = 17 kNABδ1.25 m1.25 m

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

P = 17 kNL = 2.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 22 kNABδ1.5 m3.5 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 = 5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δP = mm
4.Medium
w = 20 kN/mδL = 2 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 = 2 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 20 kN/mP = 13 kNδL = 2.5 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 = 13 kNw = 20 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 4 kN/mδL = 3 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 = 4 kN/mL = 3 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 12.3 mm
  2. 2. δmax = 1.387 mm
  3. 3. δP = 16.84 mm
  4. 4. δmax = 44.56 mm
  5. 5. δmax = 5.716 mm
  6. 6. Ireq = 46.02 × 10⁶ mm⁴

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