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 = 20 kNδL = 1.5 m

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

P = 20 kNL = 1.5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ3 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 8 mm.

δ = 8 mmL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
P = kN
3.Medium
P = 4 kNABδ2 m1 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δB at the free end B.

P = 4 kNa = 2 mL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δB = mm
4.Medium
P = 17 kNABδ2 m6 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 17 kNa = 2 mL = 8 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δP = mm
5.Hard
w = 20 kN/mδL = 6 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 = 6 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
w = 6 kN/mP = 26 kNδL = 4 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 = 26 kNw = 6 kN/mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 3.125 mm
  2. 2. P = 7.467 kN
  3. 3. δB = 2.222 mm
  4. 4. δP = 6.071 mm
  5. 5. Ireq = 1841 × 10⁶ mm⁴
  6. 6. δmax = 13.7 mm

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