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 = 30 kNδL = 3 m

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

P = 30 kNL = 3 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
2.Easy
P = 27 kNABδ1.5 m1.5 m

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

P = 27 kNL = 3 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 4 kN/mδL = 2.5 m

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

w = 4 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 5 kN/mP = 3 kNABδ4 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 = 3 kNw = 5 kN/mL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
5.Hard
w = 15 kN/mP = 23 kNδL = 8 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 = 23 kNw = 15 kN/mL = 8 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 12 kN/mδL = 4 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 = 12 kN/mL = 4 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 58.7 mm
  2. 2. δmax = 8.629 mm
  3. 3. δmax = 2.422 mm
  4. 4. δ = 31.11 mm
  5. 5. δmax = 62.22 mm
  6. 6. Ireq = 51.43 × 10⁶ mm⁴

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