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 = 9 kNδL = 2.5 m

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

P = 9 kNL = 2.5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 15 kNABδ2.5 m2.5 m

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

P = 15 kNL = 5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 26 kNABδ0.5 m5.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 0.5 m from A. Find the deflection δP under the load.

P = 26 kNa = 0.5 mL = 6 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δP = mm
4.Medium
P = 30 kNABδ1 m1 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δB at the free end B.

P = 30 kNa = 1 mL = 2 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δB = mm
5.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
6.Hard
w = 10 kN/mP = 27 kNδL = 6 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 = 27 kNw = 10 kN/mL = 6 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 1.953 mm
  2. 2. δmax = 65.65 mm
  3. 3. δP = 1.821 mm
  4. 4. δB = 2.976 mm
  5. 5. Ireq = 46.02 × 10⁶ mm⁴
  6. 6. δmax = 72.74 mm

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