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 = 25 kNδL = 3 m

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

P = 25 kNL = 3 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = 19 kNABδ1 m1 m

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

P = 19 kNL = 2 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 15 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 = 15 kN/mL = 2 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δ = mm
4.Medium
w = 8 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 = 8 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 12 kN/mP = 27 kNδL = 6 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 = 27 kNw = 12 kN/mL = 6 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 3 kN/mABδ4.5 m

A simply supported timber beam of rectangular section, 150 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 = 3 kN/mL = 4.5 mE = 11 GPa (timber)b = 150 mm
hreq = mm

Answer key

  1. 1. δ = 7.031 mm
  2. 2. δmax = 1.967 mm
  3. 3. δ = 17.05 mm
  4. 4. δmax = 4.844 mm
  5. 5. δmax = 28.93 mm
  6. 6. hreq = 210.4 mm

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