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 = 27 kNABδ0.75 m0.75 m

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

P = 27 kNL = 1.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 19 kNδL = 4 m

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

P = 19 kNL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
w = 2 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 = 2 kN/mL = 6 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 4 kN/mδL = 5 m

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

w = 4 kN/mL = 5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
5.Hard
w = 6 kN/mAB6 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the reaction RB at the prop.

L = 6 mw = 6 kN/m
RB = kN
6.Hard
w = 5 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 = 5 kN/mL = 6 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δmax = 1.438 mm
  2. 2. δ = 56.3 mm
  3. 3. δmax = 1.406 mm
  4. 4. δ = 27.9 mm
  5. 5. RB = 13.5 kN
  6. 6. Ireq = 72.32 × 10⁶ mm⁴

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