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 = 24 kNδL = 2.5 m

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

P = 24 kNL = 2.5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2 m2 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 8 mm.

δ = 8 mmL = 4 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
w = 20 kN/mδL = 1.5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 20 kN/mL = 1.5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δ = mm
4.Medium
w = 10 kN/mδL = 4 m

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

w = 10 kN/mL = 4 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 20 kN/mP = 23 kNδL = 2 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 = 23 kNw = 20 kN/mL = 2 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 12 kNP = 12 kNABδ1.667 m1.666 m1.667 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 12 kNL = 5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 7.44 mm
  2. 2. P = 27.6 kN
  3. 3. δ = 9.588 mm
  4. 4. δmax = 25.25 mm
  5. 5. δmax = 60.61 mm
  6. 6. δmax = 57.62 mm

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