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 = 4 m

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

P = 10 kNL = 4 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
2.Easy
P = ?ABδ1.25 m1.25 m

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 25 mm.

δ = 25 mmL = 2.5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
P = kN
3.Medium
w = 2 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 = 2 kN/mL = 4 mE = 11 GPa (timber)I = 84 × 10⁶ mm⁴
δmax = mm
4.Medium
w = 10 kN/mABθ4 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 = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
θA = rad
5.Hard
w = 10 kN/mP = 25 kNδL = 2 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 = 25 kNw = 10 kN/mL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
6.Hard
w = 5 kN/mδL = 8 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 = 5 kN/mL = 8 mE = 70 GPa (aluminium)
Ireq = × 10⁶ mm⁴

Answer key

  1. 1. δ = 8.889 mm
  2. 2. P = 135.2 kN
  3. 3. δmax = 7.215 mm
  4. 4. θA = 0.006683 rad
  5. 5. δmax = 1.359 mm
  6. 6. Ireq = 171.4 × 10⁶ mm⁴

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