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 = 11 kNABθ3 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 = 11 kNL = 3 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
θB = rad
2.Easy
P = 11 kNδL = 6 m

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

P = 11 kNL = 6 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
w = 4 kN/mδL = 2.5 m

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

w = 4 kN/mL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δ = mm
4.Medium
P = 20 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 δB at the free end B.

P = 20 kNa = 1 mL = 2.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δB = mm
5.Hard
w = 10 kN/mP = 20 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 = 20 kNw = 10 kN/mL = 2 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 17 kNABδ3.5 m2.5 m

A simply supported beam carries a point load P at b = 2.5 m from support B. Find the maximum deflection δmax of the beam.

P = 17 kNb = 2.5 mL = 6 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. θB = 0.0375 rad
  2. 2. δ = 70.71 mm
  3. 3. δ = 11.49 mm
  4. 4. δB = 2.579 mm
  5. 5. δmax = 2.149 mm
  6. 6. δmax = 29.26 mm

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