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 = ?ABδ4 m4 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 8 mm.

δ = 8 mmL = 8 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
P = kN
2.Easy
P = 25 kNδL = 2.5 m

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

P = 25 kNL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
3.Medium
w = 12 kN/mδL = 6 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 12 kN/mL = 6 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 4 kNABδ1 m2 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 = 4 kNa = 1 mL = 3 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δB = mm
5.Hard
w = 4 kN/mP = 6 kNδL = 2 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 = 6 kNw = 4 kN/mL = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 26 kNABδ5 m3 m

A simply supported beam carries a point load P at b = 3 m from support B. Find the maximum deflection δmax of the beam.

P = 26 kNb = 3 mL = 8 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. P = 1.275 kN
  2. 2. δ = 15.5 mm
  3. 3. δmax = 8.438 mm
  4. 4. δB = 3.313 mm
  5. 5. δmax = 2.183 mm
  6. 6. δmax = 55.46 mm

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