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 = 16 kNδL = 4 m

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

P = 16 kNL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 22 kNABδ1.5 m1.5 m

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

P = 22 kNL = 3 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 12 kN/mδL = 3 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 = 3 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
4.Medium
w = 15 kN/mδL = 2 m

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

w = 15 kN/mL = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 8 kN/mAB4 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 = 4 mw = 8 kN/m
RB = kN
6.Hard
w = 15 kN/mP = 11 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 = 11 kNw = 15 kN/mL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 14.22 mm
  2. 2. δmax = 20.8 mm
  3. 3. δ = 16.88 mm
  4. 4. δmax = 3.382 mm
  5. 5. RB = 12 kN
  6. 6. δmax = 28.67 mm

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