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 = 10 kNδL = 2 m

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

P = 10 kNL = 2 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
P = 9 kNABδ1.5 m1.5 m

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

P = 9 kNL = 3 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 20 kN/mδL = 2.5 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δmax, at midspan.

w = 20 kN/mL = 2.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 29 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 = 29 kNa = 1 mL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δP = mm
5.Hard
P = 15 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 = 15 kNb = 1 mL = 8 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 11 kNP = 11 kNABδ1.333 m1.334 m1.333 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 = 11 kNL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 31.75 mm
  2. 2. δmax = 2.978 mm
  3. 3. δmax = 16.22 mm
  4. 4. δP = 5.37 mm
  5. 5. δmax = 65.09 mm
  6. 6. δmax = 29.75 mm

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