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 = 24 kNδL = 2 m

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

P = 24 kNL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
2.Easy
P = 10 kNABδ1 m1 m

A simply supported beam carries a point load P at midspan. Find the midspan deflection δmax.

P = 10 kNL = 2 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 8 kNABδ1 m1.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1 m from A. Find the deflection δP under the load.

P = 8 kNa = 1 mL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δP = mm
4.Medium
w = 8 kN/mABθ3 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θA of the beam at support A, in radians.

w = 8 kN/mL = 3 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
θA = rad
5.Hard
w = 8 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 = 8 kN/mL = 2.5 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
P = 29 kNABδ7 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 = 29 kNb = 1 mL = 8 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 13.91 mm
  2. 2. δmax = 4.209 mm
  3. 3. δP = 1.569 mm
  4. 4. θA = 0.005294 rad
  5. 5. Ireq = 8.371 × 10⁶ mm⁴
  6. 6. δmax = 6.922 mm

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