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 = ?ABδ2.5 m2.5 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 12 mm.

δ = 12 mmL = 5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
2.Easy
P = 12 kNδL = 3 m

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

P = 12 kNL = 3 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
3.Medium
w = 4 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 = 4 kN/mL = 5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 12 kN/mδL = 2.5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 12 kN/mL = 2.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δ = mm
5.Hard
w = 5 kN/mP = 19 kNδL = 6 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 = 19 kNw = 5 kN/mL = 6 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 10 kN/mδL = 6 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 = 10 kN/mL = 6 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. P = 21.2 kN
  2. 2. δ = 63.53 mm
  3. 3. δmax = 38.75 mm
  4. 4. δ = 33.29 mm
  5. 5. δmax = 7.078 mm
  6. 6. Ireq = 144.6 × 10⁶ mm⁴

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