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 = 5 kNδL = 2.5 m

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

P = 5 kNL = 2.5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = 2 kNABδ3 m3 m

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

P = 2 kNL = 6 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 16 kNABδ1.5 m4.5 m

A simply supported beam carries a point load P at a = 1.5 m from support A. Find the deflection δP under the load.

P = 16 kNa = 1.5 mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δP = mm
4.Medium
w = 12 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 = 12 kN/mL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 15 kN/mP = 24 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 = 24 kNw = 15 kN/mL = 3 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 6 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 = 6 kN/m
RB = kN

Answer key

  1. 1. δ = 4.429 mm
  2. 2. δmax = 1.071 mm
  3. 3. δP = 6.888 mm
  4. 4. δmax = 38.75 mm
  5. 5. δmax = 46.76 mm
  6. 6. RB = 9 kN

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