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 = 8 kNABδ3 m3 m

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

P = 8 kNL = 6 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 2 kNδL = 4 m

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

P = 2 kNL = 4 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δ = mm
3.Medium
w = 15 kN/mδL = 2.5 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 15 kN/mL = 2.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 19 kNABδ1 m2 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 = 19 kNa = 1 mL = 3 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δP = mm
5.Hard
w = 5 kN/mδL = 2 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 = 5 kN/mL = 2 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
P = 16 kNABδ4 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the maximum deflection δmax of the beam.

P = 16 kNb = 1 mL = 5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 20.45 mm
  2. 2. δ = 26.5 mm
  3. 3. δmax = 5.78 mm
  4. 4. δP = 14.19 mm
  5. 5. Ireq = 2.679 × 10⁶ mm⁴
  6. 6. δmax = 18.28 mm

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