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 = 14 kNδL = 2.5 m

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

P = 14 kNL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 12 mm.

δ = 12 mmL = 5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
P = kN
3.Medium
w = 5 kN/mδL = 4 m

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

w = 5 kN/mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 12 kNABδ7 m1 m

A simply supported beam carries a point load P at a = 7 m from support A. Find the deflection δP under the load.

P = 12 kNa = 7 mL = 8 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δP = mm
5.Hard
w = 6 kN/mAB5 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 = 5 mw = 6 kN/m
RB = kN
6.Hard
w = 8 kN/mP = 25 kNδL = 4 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 = 25 kNw = 8 kN/mL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 28.94 mm
  2. 2. P = 1.693 kN
  3. 3. δmax = 2.834 mm
  4. 4. δP = 1.458 mm
  5. 5. RB = 11.25 kN
  6. 6. δmax = 13.04 mm

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