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 = 25 kNABδ3 m3 m

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

P = 25 kNL = 6 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 3 kNδL = 2.5 m

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

P = 3 kNL = 2.5 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
3.Medium
P = 25 kNABδ4.5 m3.5 m

A simply supported beam carries a point load P at a = 4.5 m from support A. Find the deflection δP under the load.

P = 25 kNa = 4.5 mL = 8 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δP = mm
4.Medium
w = 2 kN/mP = 20 kNABδ2.5 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 = 20 kNw = 2 kN/mL = 2.5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
w = 5 kN/mP = 22 kNδL = 5 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 = 22 kNw = 5 kN/mL = 5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 12 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 = 12 kN/mL = 6 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δmax = 15.63 mm
  2. 2. δ = 1.371 mm
  3. 3. δP = 35.89 mm
  4. 4. δ = 4.747 mm
  5. 5. δmax = 4.083 mm
  6. 6. Ireq = 173.6 × 10⁶ mm⁴

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