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 = 22 kNABθ6 m

A cantilever carries a point load P at its free end. Find the slope θB of the beam at the free end B, in radians.

P = 22 kNL = 6 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
θB = rad
2.Easy
P = 5 kNδL = 2 m

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

P = 5 kNL = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δ = mm
3.Medium
P = 15 kNABδ0.5 m1.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 0.5 m from A. Find the deflection δB at the free end B.

P = 15 kNa = 0.5 mL = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δB = mm
4.Medium
w = 6 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 = 6 kN/mL = 6 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 12 kN/mδL = 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 = 12 kN/mL = 5 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
P = 26 kNABδ3 m2 m

A simply supported beam carries a point load P at b = 2 m from support B. Find the maximum deflection δmax of the beam.

P = 26 kNb = 2 mL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. θB = 0.01238 rad
  2. 2. δ = 8.282 mm
  3. 3. δB = 3.72 mm
  4. 4. δmax = 3.164 mm
  5. 5. Ireq = 639.2 × 10⁶ mm⁴
  6. 6. δmax = 25.48 mm

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