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 = 12 kNδL = 8 m

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

P = 12 kNL = 8 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = 16 kNABδ2 m2 m

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

P = 16 kNL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 2 kN/mABθ5 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 = 2 kN/mL = 5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
θA = rad
4.Medium
P = 2 kNABδ1 m1 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 = 2 kNa = 1 mL = 2 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δB = mm
5.Hard
w = 2 kN/mP = 18 kNδL = 3 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 = 18 kNw = 2 kN/mL = 3 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 4 kN/mAB5 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a uniformly distributed load w over its whole length. EI is constant. Find the reaction RB at the prop.

L = 5 mw = 4 kN/m
RB = kN

Answer key

  1. 1. δ = 64 mm
  2. 2. δmax = 2.963 mm
  3. 3. θA = 0.01127 rad
  4. 4. δB = 17.83 mm
  5. 5. δmax = 5.098 mm
  6. 6. RB = 7.5 kN

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