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 = 30 kNABδ0.75 m0.75 m

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

P = 30 kNL = 1.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 7 kNδL = 3 m

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

P = 7 kNL = 3 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δ = mm
3.Medium
P = 2 kNABδ1 m3 m

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δP under the load.

P = 2 kNa = 1 mL = 4 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δP = mm
4.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 = 11 GPa (timber)I = 23 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 10 kN/mP = 5 kNδL = 1.5 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 = 5 kNw = 10 kN/mL = 1.5 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 4 kN/mABδ5 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 = 4 kN/mL = 5 mE = 11 GPa (timber)b = 100 mm
hreq = mm

Answer key

  1. 1. δmax = 1.199 mm
  2. 2. δ = 68.18 mm
  3. 3. δP = 5.929 mm
  4. 4. δmax = 20.1 mm
  5. 5. δmax = 1.094 mm
  6. 6. hreq = 277.2 mm

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