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 = 15 kNδL = 2.5 m

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

P = 15 kNL = 2.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δ = mm
2.Easy
P = 21 kNABδ1.25 m1.25 m

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

P = 21 kNL = 2.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 10 kNABδ1.5 m1.5 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 = 10 kNa = 1.5 mL = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δB = mm
4.Medium
P = 11 kNABδ1.5 m2.5 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 = 11 kNa = 1.5 mL = 4 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δP = mm
5.Hard
P = 18 kNP = 18 kNABδ1.667 m1.666 m1.667 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 = 18 kNL = 5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 15 kN/mP = 29 kNδL = 3 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 = 29 kNw = 15 kN/mL = 3 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 19.58 mm
  2. 2. δmax = 5.179 mm
  3. 3. δB = 17.47 mm
  4. 4. δP = 5.156 mm
  5. 5. δmax = 60.5 mm
  6. 6. δmax = 38.25 mm

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