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 = 6 kNδL = 2.5 m

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

P = 6 kNL = 2.5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 10 mm.

δ = 10 mmL = 2.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
P = kN
3.Medium
w = 2 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 = 2 kN/mL = 4 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 23 kNABδ6 m2 m

A simply supported beam carries a point load P at a = 6 m from support A. Find the deflection δP under the load.

P = 23 kNa = 6 mL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δP = mm
5.Hard
w = 12 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 size of the bending moment MA at the fixed end.

L = 4 mw = 12 kN/m
MA = kN·m
6.Hard
w = 10 kN/mδL = 6 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 10 kN/mL = 6 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 52.52 mm
  2. 2. P = 1.774 kN
  3. 3. δmax = 26.35 mm
  4. 4. δP = 5.75 mm
  5. 5. MA = 24 kN·m
  6. 6. Ireq = 144.6 × 10⁶ mm⁴

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