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 = 1.5 m

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

P = 14 kNL = 1.5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δ = mm
2.Easy
P = 30 kNABδ1.5 m1.5 m

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

P = 30 kNL = 3 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 4 kNABδ3 m3 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 3 m from A. Find the deflection δB at the free end B.

P = 4 kNa = 3 mL = 6 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δB = mm
4.Medium
w = 10 kN/mδL = 6 m

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

w = 10 kN/mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 10 kN/mδL = 3 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 = 3 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
w = 15 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 = 15 kN/m
RB = kN

Answer key

  1. 1. δ = 26.47 mm
  2. 2. δmax = 1.48 mm
  3. 3. δB = 55.9 mm
  4. 4. δmax = 28.7 mm
  5. 5. Ireq = 6.328 × 10⁶ mm⁴
  6. 6. RB = 33.75 kN

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