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 kNABδ2 m2 m

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

P = 10 kNL = 4 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 5 kNδL = 2.5 m

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

P = 5 kNL = 2.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δ = mm
3.Medium
w = 5 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 = 5 kN/mL = 3 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 8 kN/mδL = 6 m

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

w = 8 kN/mL = 6 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
w = 12 kN/mP = 20 kNδL = 4 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 = 12 kN/mL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 2.5 kN/mABδ5 m

A simply supported timber beam of rectangular section, 125 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/360. Find the smallest depth hreq of the section.

w = 2.5 kN/mL = 5 mE = 11 GPa (timber)b = 125 mm
hreq = mm

Answer key

  1. 1. δmax = 22.41 mm
  2. 2. δ = 5.661 mm
  3. 3. δmax = 8.411 mm
  4. 4. δ = 77.14 mm
  5. 5. δmax = 2.778 mm
  6. 6. hreq = 233.8 mm

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