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 = 2.5 m

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

P = 10 kNL = 2.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δ = mm
2.Easy
P = 19 kNABδ2 m2 m

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

P = 19 kNL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 10 kN/mABθ1.5 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 = 1.5 mE = 11 GPa (timber)I = 12 × 10⁶ mm⁴
θA = rad
4.Medium
w = 6 kN/mδL = 3 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 = 3 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmax = mm
5.Hard
P = 17 kNABδ6.5 m1.5 m

A simply supported beam carries a point load P at b = 1.5 m from support B. Find the maximum deflection δmax of the beam.

P = 17 kNb = 1.5 mL = 8 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δmax = mm
6.Hard
P = 14 kNABδ3 m1 m

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

P = 14 kNb = 1 mL = 4 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴
δmid = mm

Answer key

  1. 1. δ = 62 mm
  2. 2. δmax = 6.349 mm
  3. 3. θA = 0.01065 rad
  4. 4. δmax = 3.596 mm
  5. 5. δmax = 5.906 mm
  6. 6. δmid = 20.47 mm

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