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 = ?ABδ3 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 5 mm.

δ = 5 mmL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
P = kN
2.Easy
P = 2 kNδL = 5 m

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

P = 2 kNL = 5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
w = 6 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 = 6 kN/mL = 8 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 20 kN/mδL = 1.5 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 = 1.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
P = 3 kNP = 3 kNABδ2.667 m2.666 m2.667 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 3 kNL = 8 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 4 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 = 4 kN/m
RB = kN

Answer key

  1. 1. P = 4.667 kN
  2. 2. δ = 20.89 mm
  3. 3. δmax = 28.57 mm
  4. 4. δ = 1.507 mm
  5. 5. δmax = 33.86 mm
  6. 6. RB = 9 kN

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