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 = 18 kNABδ2 m2 m

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

P = 18 kNL = 4 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm
2.Easy
P = 5 kNδL = 2.5 m

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

P = 5 kNL = 2.5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
δ = mm
3.Medium
w = 8 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 = 8 kN/mL = 4 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 10 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 = 10 kN/mL = 3 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴
θA = rad
5.Hard
w = 2 kN/mδL = 4 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 = 2 kN/mL = 4 mE = 11 GPa (timber)
Ireq = × 10⁶ mm⁴
6.Hard
w = 5 kN/mP = 2 kNδL = 3 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 = 2 kNw = 5 kN/mL = 3 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δmax = 28.57 mm
  2. 2. δ = 2.325 mm
  3. 3. δmax = 42.53 mm
  4. 4. θA = 0.02841 rad
  5. 5. Ireq = 54.55 × 10⁶ mm⁴
  6. 6. δmax = 68.43 mm

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