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 = 28 kNδL = 2 m

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

P = 28 kNL = 2 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 19 kNABδ3 m3 m

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

P = 19 kNL = 6 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 4 kN/mδL = 4 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 4 kN/mL = 4 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δ = mm
4.Medium
w = 20 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 = 20 kN/mL = 4 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 25 kNAB2 m2 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 4 mP = 25 kN at 2 m
MA = kN·m
6.Hard
w = 15 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 = 15 kN/mL = 3 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 3.111 mm
  2. 2. δmax = 53.11 mm
  3. 3. δ = 72.73 mm
  4. 4. δmax = 27.78 mm
  5. 5. MA = 18.75 kN·m
  6. 6. Ireq = 27.12 × 10⁶ mm⁴

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