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 = 26 kNABδ3 m3 m

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

P = 26 kNL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 14 kNδL = 2 m

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

P = 14 kNL = 2 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
3.Medium
w = 10 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 = 10 kN/mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 26 kNABδ1 m3 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δP under the load.

P = 26 kNa = 1 mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δP = mm
5.Hard
w = 10 kN/mAB3 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 = 3 mw = 10 kN/m
RB = kN
6.Hard
w = 10 kN/mδL = 5 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 = 5 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δmax = 19.9 mm
  2. 2. δ = 6.349 mm
  3. 3. δmax = 4.844 mm
  4. 4. δP = 2.172 mm
  5. 5. RB = 11.25 kN
  6. 6. Ireq = 83.71 × 10⁶ mm⁴

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