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 = 28 kNδL = 1.5 m

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

P = 28 kNL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
P = 27 kNABδ0.75 m0.75 m

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

P = 27 kNL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 25 kNABδ3 m5 m

A simply supported beam carries a point load P at a = 3 m from support A. Find the deflection δP under the load.

P = 25 kNa = 3 mL = 8 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δP = mm
4.Medium
w = 6 kN/mP = 20 kNABδ4 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 20 kNw = 6 kN/mL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
w = 5 kN/mP = 2 kNδL = 4 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 = 2 kNw = 5 kN/mL = 4 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 12 kNABδ2.5 m1.5 m

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the maximum deflection δmax of the beam.

P = 12 kNb = 1.5 mL = 4 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 13.13 mm
  2. 2. δmax = 2.26 mm
  3. 3. δP = 9.766 mm
  4. 4. δ = 73.65 mm
  5. 5. δmax = 8.056 mm
  6. 6. δmax = 24.74 mm

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