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 = ?ABδ3 m3 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 6 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
P = kN
2.Easy
P = 11 kNδL = 3 m

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

P = 11 kNL = 3 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
3.Medium
P = 27 kNABδ2 m1 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δB at the free end B.

P = 27 kNa = 2 mL = 3 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δB = mm
4.Medium
w = 2 kN/mδL = 6 m

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

w = 2 kN/mL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 5 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 = 5 kN/mL = 1.5 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
P = 17 kNABδ5 m3 m

A simply supported beam carries a point load P at b = 3 m from support B. Find the deflection δmid at midspan.

P = 17 kNb = 3 mL = 8 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. P = 4.433 kN
  2. 2. δ = 11.79 mm
  3. 3. δB = 74.12 mm
  4. 4. δmax = 2.961 mm
  5. 5. Ireq = 1.13 × 10⁶ mm⁴
  6. 6. δmid = 36.03 mm

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