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 = 30 kNδL = 4 m

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

P = 30 kNL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 13 kNABδ2.5 m2.5 m

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

P = 13 kNL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 12 kNABδ2 m1 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 12 kNa = 2 mL = 3 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δP = mm
4.Medium
P = 28 kNABδ1 m5 m

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δP under the load.

P = 28 kNa = 1 mL = 6 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δP = mm
5.Hard
P = 30 kNABδ3 m2 m

A simply supported beam carries a point load P at b = 2 m from support B. Find the maximum deflection δmax of the beam.

P = 30 kNb = 2 mL = 5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 12 kN/mδL = 8 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 = 8 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 26.67 mm
  2. 2. δmax = 13.43 mm
  3. 3. δP = 21.08 mm
  4. 4. δP = 1.62 mm
  5. 5. δmax = 6.614 mm
  6. 6. Ireq = 411.4 × 10⁶ mm⁴

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