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 = 12 kNδL = 4 m

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

P = 12 kNL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ0.75 m0.75 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 15 mm.

δ = 15 mmL = 1.5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
P = kN
3.Medium
P = 25 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 = 25 kNa = 1 mL = 3 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δP = mm
4.Medium
w = 4 kN/mδL = 4 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 = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
P = 14 kNP = 14 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 = 14 kNL = 5 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 15 kN/mδL = 2.5 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 = 15 kN/mL = 2.5 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 30.48 mm
  2. 2. P = 126.9 kN
  3. 3. δP = 43.92 mm
  4. 4. δ = 15.24 mm
  5. 5. δmax = 47.06 mm
  6. 6. Ireq = 5.493 × 10⁶ mm⁴

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