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 = 17 kNδL = 1.5 m

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

P = 17 kNL = 1.5 mE = 11 GPa (timber)I = 160 × 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 5 mm.

δ = 5 mmL = 1.5 mE = 11 GPa (timber)I = 8.5 × 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 = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
4.Medium
P = 4 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 = 4 kNa = 1 mL = 3 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
δP = mm
5.Hard
w = 8 kN/mδL = 4 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 = 8 kN/mL = 4 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
P = 18 kNABδ5 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the maximum deflection δmax of the beam.

P = 18 kNb = 1 mL = 6 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 10.87 mm
  2. 2. P = 6.649 kN
  3. 3. δ = 7.445 mm
  4. 4. δP = 13.47 mm
  5. 5. Ireq = 34.29 × 10⁶ mm⁴
  6. 6. δmax = 47.44 mm

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