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 = 18 kNδL = 2 m

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

P = 18 kNL = 2 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ4 m4 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 = 8 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
P = kN
3.Medium
P = 3 kNABδ4 m1 m

A simply supported beam carries a point load P at a = 4 m from support A. Find the deflection δP under the load.

P = 3 kNa = 4 mL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δP = mm
4.Medium
w = 10 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 = 10 kN/mL = 6 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 4 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 = 4 kN/mL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 5 kNP = 5 kNABδ2 m2 m2 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 = 5 kNL = 6 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 36.36 mm
  2. 2. P = 3.375 kN
  3. 3. δP = 1.27 mm
  4. 4. δmax = 28.7 mm
  5. 5. δmax = 1.014 mm
  6. 6. δmax = 2.282 mm

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