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 kNABδ2 m2 m

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

P = 16 kNL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 13 kNδL = 8 m

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

P = 13 kNL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
w = 10 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 = 10 kN/mL = 2 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 8 kN/mP = 2 kNABδ3 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 = 2 kNw = 8 kN/mL = 3 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
w = 2 kN/mP = 14 kNδL = 5 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 = 14 kNw = 2 kN/mL = 5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 8 kN/mAB3 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 = 3 mw = 8 kN/m
RB = kN

Answer key

  1. 1. δmax = 2.963 mm
  2. 2. δ = 69.33 mm
  3. 3. δmax = 1.578 mm
  4. 4. δ = 4.125 mm
  5. 5. δmax = 4.708 mm
  6. 6. RB = 9 kN

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