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 = 5 kNABθ1.5 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 = 5 kNL = 1.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
θB = rad
2.Easy
P = 8 kNδL = 2.5 m

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

P = 8 kNL = 2.5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
3.Medium
w = 6 kN/mδL = 2 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 6 kN/mL = 2 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = mm
4.Medium
P = 20 kNABδ0.5 m5.5 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 = 20 kNa = 0.5 mL = 6 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δB = mm
5.Hard
w = 8 kN/mP = 17 kNδL = 2 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 = 17 kNw = 8 kN/mL = 2 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 7 kNP = 7 kNABδ2 m2 m2 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 = 7 kNL = 6 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. θB = 0.003309 rad
  2. 2. δ = 7.086 mm
  3. 3. δ = 1.429 mm
  4. 4. δB = 15.78 mm
  5. 5. δmax = 11.36 mm
  6. 6. δmax = 4.792 mm

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