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 = 26 kNδL = 1.5 m

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

P = 26 kNL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
w = 6 kN/mABθ5 m

A cantilever carries a uniformly distributed load w over its whole length. Find the slope θB of the beam at the free end B, in radians.

w = 6 kN/mL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
θB = rad
3.Medium
w = 6 kN/mδL = 6 m

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

w = 6 kN/mL = 6 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 26 kNABδ2 m0.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δB at the free end B.

P = 26 kNa = 2 mL = 2.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
δB = mm
5.Hard
w = 10 kN/mAB3 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 = 3 mw = 10 kN/m
RB = kN
6.Hard
P = 35 kNAB3 m3 m

A propped cantilever is fixed at A and simply supported (propped) at B. It carries a point load P at midspan. EI is constant. Find the size of the bending moment MA at the fixed end.

L = 6 mP = 35 kN at 3 m
MA = kN·m

Answer key

  1. 1. δ = 34.82 mm
  2. 2. θB = 0.003906 rad
  3. 3. δmax = 76.7 mm
  4. 4. δB = 56.08 mm
  5. 5. RB = 11.25 kN
  6. 6. MA = 39.38 kN·m

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