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 = 17 kNABδ3 m3 m

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

P = 17 kNL = 6 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 21 kNδL = 4 m

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

P = 21 kNL = 4 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
w = 20 kN/mδL = 8 m

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

w = 20 kN/mL = 8 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 20 kN/mδL = 2 m

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

w = 20 kN/mL = 2 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δ = mm
5.Hard
w = 12 kN/mP = 16 kNδL = 3 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 = 16 kNw = 12 kN/mL = 3 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 70 kNAB2 m2 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the reaction RB at the prop.

L = 4 mP = 70 kN at 2 m
RB = kN

Answer key

  1. 1. δmax = 10.63 mm
  2. 2. δ = 39.3 mm
  3. 3. δmax = 63.49 mm
  4. 4. δ = 63.8 mm
  5. 5. δmax = 34.54 mm
  6. 6. RB = 21.88 kN

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