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 = 9 kNABδ3 m3 m

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

P = 9 kNL = 6 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 8 kNδL = 3 m

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

P = 8 kNL = 3 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
P = 25 kNABδ2.5 m0.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2.5 m from A. Find the deflection δB at the free end B.

P = 25 kNa = 2.5 mL = 3 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δB = mm
4.Medium
w = 10 kN/mδL = 5 m

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

w = 10 kN/mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 8 kN/mδL = 1.5 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 = 8 kN/mL = 1.5 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
P = 14 kNABδ3 m1 m

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

P = 14 kNb = 1 mL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. δmax = 10.15 mm
  2. 2. δ = 10 mm
  3. 3. δB = 15.11 mm
  4. 4. δmax = 4.844 mm
  5. 5. Ireq = 1.808 × 10⁶ mm⁴
  6. 6. δmid = 1.782 mm

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