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 = 15 kNABδ1.25 m1.25 m

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

P = 15 kNL = 2.5 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 26 kNδL = 1.5 m

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

P = 26 kNL = 1.5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δ = mm
3.Medium
w = 10 kN/mP = 13 kNABδ2 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 13 kNw = 10 kN/mL = 2 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
4.Medium
w = 10 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 = 10 kN/mL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 2 kN/mP = 19 kNδL = 2 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 = 19 kNw = 2 kN/mL = 2 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 22 kNABδ2.5 m1.5 m

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the maximum deflection δmax of the beam.

P = 22 kNb = 1.5 mL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 19.3 mm
  2. 2. δ = 49.16 mm
  3. 3. δ = 32.16 mm
  4. 4. δmax = 39.68 mm
  5. 5. δmax = 38.32 mm
  6. 6. δmax = 3.748 mm

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