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 = ?ABδ2.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 20 mm.

δ = 20 mmL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
P = kN
2.Easy
P = 9 kNδL = 4 m

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

P = 9 kNL = 4 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
P = 25 kNABδ1.5 m3.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δB at the free end B.

P = 25 kNa = 1.5 mL = 5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δB = mm
4.Medium
w = 2 kN/mδL = 8 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 = 8 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 17 kNP = 17 kNABδ1.333 m1.334 m1.333 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 17 kNL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 10 kN/mδL = 2 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 = 10 kN/mL = 2 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. P = 32.26 kN
  2. 2. δ = 17.14 mm
  3. 3. δB = 17.58 mm
  4. 4. δmax = 14.81 mm
  5. 5. δmax = 8.395 mm
  6. 6. Ireq = 34.09 × 10⁶ mm⁴

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