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 = ?ABδ1.25 m1.25 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 20 mm.

δ = 20 mmL = 2.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
P = kN
2.Easy
P = 13 kNδL = 4 m

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

P = 13 kNL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
3.Medium
P = 7 kNABδ2 m2 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 δP under the load.

P = 7 kNa = 2 mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δP = mm
4.Medium
w = 5 kN/mP = 9 kNABδ2 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 9 kNw = 5 kN/mL = 2 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
5.Hard
P = 28 kNABδ3 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the maximum deflection δmax of the beam.

P = 28 kNb = 1 mL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 2 kNABδ4.5 m3.5 m

A simply supported beam carries a point load P at b = 3.5 m from support B. Find the deflection δmid at midspan.

P = 2 kNb = 3.5 mL = 8 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. P = 245.1 kN
  2. 2. δ = 11.56 mm
  3. 3. δP = 3.175 mm
  4. 4. δ = 13.49 mm
  5. 5. δmax = 1.087 mm
  6. 6. δmid = 5.227 mm

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