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
w = 10 kN/mABθ1.5 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 = 10 kN/mL = 1.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
θB = rad
2.Easy
P = 15 kNδL = 2.5 m

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

P = 15 kNL = 2.5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
w = 10 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 = 10 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 2 kN/mP = 27 kNABδ4 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 27 kNw = 2 kN/mL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴
δ = 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 = 11 kNABδ4 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 = 11 kNb = 1 mL = 5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. θB = 0.008971 rad
  2. 2. δ = 10.85 mm
  3. 3. δmax = 8.548 mm
  4. 4. δ = 76.19 mm
  5. 5. RB = 11.25 kN
  6. 6. δmax = 6.585 mm

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