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 = 4 m

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

P = 26 kNL = 4 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = 30 kNABδ3 m3 m

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

P = 30 kNL = 6 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 15 kN/mδL = 4 m

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

w = 15 kN/mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
P = 14 kNABδ1.5 m4.5 m

A simply supported beam carries a point load P at a = 1.5 m from support A. Find the deflection δP under the load.

P = 14 kNa = 1.5 mL = 6 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δP = mm
5.Hard
w = 2.5 kN/mABδ3.5 m

A simply supported timber beam of rectangular section, 100 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/300. Find the smallest depth hreq of the section.

w = 2.5 kN/mL = 3.5 mE = 11 GPa (timber)b = 100 mm
hreq = mm
6.Hard
w = 10 kN/mδL = 8 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 = 8 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 17.33 mm
  2. 2. δmax = 56.25 mm
  3. 3. δmax = 8.503 mm
  4. 4. δP = 22.01 mm
  5. 5. hreq = 165.9 mm
  6. 6. Ireq = 120 × 10⁶ mm⁴

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