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 kNδL = 1.5 m

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

P = 30 kNL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ6 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 10 mm.

δ = 10 mmL = 6 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
P = kN
3.Medium
w = 4 kN/mABθ3 m

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θA of the beam at support A, in radians.

w = 4 kN/mL = 3 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
θA = rad
4.Medium
w = 6 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 = 6 kN/mL = 4 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δmax = mm
5.Hard
w = 10 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 = 10 kN/mL = 6 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴
6.Hard
P = 8 kNP = 8 kNABδ1.667 m1.666 m1.667 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 8 kNL = 5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 14.06 mm
  2. 2. P = 4.444 kN
  3. 3. θA = 0.002557 rad
  4. 4. δmax = 7.937 mm
  5. 5. Ireq = 144.6 × 10⁶ mm⁴
  6. 6. δmax = 56.61 mm

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