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 = 10 kNABδ1.5 m1.5 m

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

P = 10 kNL = 3 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δmax = mm
2.Easy
w = 15 kN/mABθ2 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 = 15 kN/mL = 2 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
θB = rad
3.Medium
w = 12 kN/mδL = 3 m

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

w = 12 kN/mL = 3 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 23 kNABδ1 m4 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 = 23 kNa = 1 mL = 5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δB = mm
5.Hard
w = 15 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 = 15 kN/m
RB = kN
6.Hard
P = 25 kNP = 25 kNABδ1.333 m1.334 m1.333 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 = 25 kNL = 4 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 4.261 mm
  2. 2. θB = 0.003401 rad
  3. 3. δmax = 2.751 mm
  4. 4. δB = 63.89 mm
  5. 5. RB = 16.88 kN
  6. 6. δmax = 7.888 mm

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