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 = 2 kNδL = 2.5 m

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

P = 2 kNL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = 16 kNABδ3 m3 m

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

P = 16 kNL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 12 kNABδ1.5 m0.5 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 δP under the load.

P = 12 kNa = 1.5 mL = 2 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δP = mm
4.Medium
P = 27 kNABδ2.5 m1.5 m

A simply supported beam carries a point load P at a = 2.5 m from support A. Find the deflection δP under the load.

P = 27 kNa = 2.5 mL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δP = mm
5.Hard
w = 5 kN/mP = 18 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 = 18 kNw = 5 kN/mL = 6 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 5 kN/mδL = 2.5 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 = 5 kN/mL = 2.5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 4.134 mm
  2. 2. δmax = 6.316 mm
  3. 3. δP = 7.67 mm
  4. 4. δP = 6.878 mm
  5. 5. δmax = 5.168 mm
  6. 6. Ireq = 1.831 × 10⁶ mm⁴

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