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 = ?ABδ2 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 5 mm.

δ = 5 mmL = 2 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴
P = kN
2.Easy
P = 8 kNδL = 1.5 m

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

P = 8 kNL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴
δ = mm
3.Medium
P = 12 kNABδ2 m1 m

A simply supported beam carries a point load P at a = 2 m from support A. Find the deflection δP under the load.

P = 12 kNa = 2 mL = 3 mE = 11 GPa (timber)I = 160 × 10⁶ mm⁴
δP = mm
4.Medium
w = 10 kN/mP = 18 kNABδ1.5 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 = 18 kNw = 10 kN/mL = 1.5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
P = 19 kNABδ4 m2 m

A simply supported beam carries a point load P at b = 2 m from support B. Find the deflection δmid at midspan.

P = 19 kNb = 2 mL = 6 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴
δmid = mm
6.Hard
w = 5 kN/mP = 18 kNδL = 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 = 18 kNw = 5 kN/mL = 5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. P = 21 kN
  2. 2. δ = 3.75 mm
  3. 3. δP = 3.03 mm
  4. 4. δ = 1.582 mm
  5. 5. δmid = 45.24 mm
  6. 6. δmax = 12.16 mm

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