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 = 4 kNδL = 5 m

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

P = 4 kNL = 5 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
2.Easy
P = 28 kNABδ1 m1 m

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

P = 28 kNL = 2 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴
δmax = mm
3.Medium
w = 20 kN/mABθ5 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 = 20 kN/mL = 5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
θA = rad
4.Medium
w = 15 kN/mP = 26 kNABδ3 m

A cantilever carries a uniformly distributed load w over its whole length and a point load P at its free end. Using superposition, find the deflection δ at the free end.

P = 26 kNw = 15 kN/mL = 3 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δ = mm
5.Hard
P = 10 kNABδ4 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 = 10 kNb = 1 mL = 5 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δmid = mm
6.Hard
w = 4 kN/mP = 12 kNδL = 1.5 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 = 12 kNw = 4 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. δ = 5.208 mm
  2. 2. δmax = 1.014 mm
  3. 3. θA = 0.0434 rad
  4. 4. δ = 16.08 mm
  5. 5. δmid = 8.404 mm
  6. 6. δmax = 1.318 mm

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