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 = 5 m

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

P = 10 kNL = 5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ3 m3 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 6 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
P = kN
3.Medium
w = 6 kN/mδL = 4 m

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

w = 6 kN/mL = 4 mE = 200 GPa (steel)I = 57 × 10⁶ mm⁴
δ = mm
4.Medium
P = 22 kNABδ1 m2 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 = 22 kNa = 1 mL = 3 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δP = mm
5.Hard
w = 12 kN/mδL = 6 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 = 12 kN/mL = 6 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
w = 2.5 kN/mABδ4.5 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 = 4.5 mE = 11 GPa (timber)b = 100 mm
hreq = mm

Answer key

  1. 1. δ = 37.2 mm
  2. 2. P = 12.67 kN
  3. 3. δ = 16.84 mm
  4. 4. δP = 15.59 mm
  5. 5. Ireq = 173.6 × 10⁶ mm⁴
  6. 6. hreq = 213.3 mm

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