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 = 20 kNδL = 2.5 m

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

P = 20 kNL = 2.5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ2.5 m2.5 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 = 5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
P = kN
3.Medium
w = 4 kN/mδL = 2 m

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

w = 4 kN/mL = 2 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
4.Medium
P = 20 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 = 20 kNa = 1 mL = 3 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δP = mm
5.Hard
P = 17 kNP = 17 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 = 17 kNL = 6 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 2 kN/mP = 3 kNδL = 1.5 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 = 3 kNw = 2 kN/mL = 1.5 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 3.255 mm
  2. 2. P = 8.832 kN
  3. 3. δ = 4.706 mm
  4. 4. δP = 3.527 mm
  5. 5. δmax = 54.31 mm
  6. 6. δmax = 3.666 mm

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