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 = 28 kNδL = 3 m

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

P = 28 kNL = 3 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 8 mm.

δ = 8 mmL = 5 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
P = kN
3.Medium
P = 22 kNABδ1.5 m3.5 m

A cantilever of length L is fixed at A and carries a point load P at a distance a = 1.5 m from A. Find the deflection δB at the free end B.

P = 22 kNa = 1.5 mL = 5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δB = mm
4.Medium
P = 21 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 = 21 kNa = 1 mL = 4 mE = 70 GPa (aluminium)I = 84 × 10⁶ mm⁴
δP = mm
5.Hard
w = 2.5 kN/mABδ6 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 = 6 mE = 11 GPa (timber)b = 125 mm
hreq = mm
6.Hard
P = 26 kNABδ3 m1 m

A simply supported beam carries a point load P at b = 1 m from support B. Find the maximum deflection δmax of the beam.

P = 26 kNb = 1 mL = 4 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 42.86 mm
  2. 2. P = 1.129 kN
  3. 3. δB = 46.41 mm
  4. 4. δP = 2.679 mm
  5. 5. hreq = 280.6 mm
  6. 6. δmax = 2.163 mm

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