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 = 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 = 36 × 10⁶ mm⁴
δ = mm
2.Easy
P = 30 kNABδ1.25 m1.25 m

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

P = 30 kNL = 2.5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 25 kNABδ1 m3 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 = 25 kNa = 1 mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δP = mm
4.Medium
w = 4 kN/mδL = 3 m

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

w = 4 kN/mL = 3 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 28 kNABδ4.5 m1.5 m

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

P = 28 kNb = 1.5 mL = 6 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmid = mm
6.Hard
w = 20 kN/mδL = 1.5 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 = 20 kN/mL = 1.5 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 11.61 mm
  2. 2. δmax = 1.356 mm
  3. 3. δP = 4.699 mm
  4. 4. δmax = 3.196 mm
  5. 5. δmid = 7.734 mm
  6. 6. Ireq = 28.76 × 10⁶ mm⁴

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