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 kNδL = 3 m

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

P = 10 kNL = 3 mE = 11 GPa (timber)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = 19 kNABδ2.5 m2.5 m

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

P = 19 kNL = 5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
3.Medium
P = 15 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 = 15 kNa = 2 mL = 2.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δB = mm
4.Medium
w = 8 kN/mδL = 2 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 = 2 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
w = 10 kN/mδL = 5 m

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area Ireq that meets this limit.

w = 10 kN/mL = 5 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
w = 2.5 kN/mABδ3.5 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 = 3.5 mE = 11 GPa (timber)b = 125 mm
hreq = mm

Answer key

  1. 1. δ = 68.18 mm
  2. 2. δmax = 58.9 mm
  3. 3. δB = 11.96 mm
  4. 4. δ = 17.32 mm
  5. 5. Ireq = 532.7 × 10⁶ mm⁴
  6. 6. hreq = 163.7 mm

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