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 = ?ABδ1.5 m

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 25 mm.

δ = 25 mmL = 1.5 mE = 200 GPa (steel)I = 8.5 × 10⁶ mm⁴
P = kN
2.Easy
P = 12 kNδL = 3 m

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

P = 12 kNL = 3 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴
δ = mm
3.Medium
w = 10 kN/mδL = 3 m

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 10 kN/mL = 3 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴
δ = mm
4.Medium
w = 4 kN/mP = 14 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 = 14 kNw = 4 kN/mL = 1.5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴
δ = mm
5.Hard
w = 2 kN/mδL = 6 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 = 6 mE = 200 GPa (steel)
Ireq = × 10⁶ mm⁴
6.Hard
P = 17 kNP = 17 kNABδ1.667 m1.666 m1.667 m

A simply supported beam carries two equal point loads P at its third points (L/3 from each support). Using superposition, find the midspan deflection δmax.

P = 17 kNL = 5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴
δmax = mm

Answer key

  1. 1. P = 37.78 kN
  2. 2. δ = 42.86 mm
  3. 3. δ = 3.164 mm
  4. 4. δ = 1.088 mm
  5. 5. Ireq = 10.13 × 10⁶ mm⁴
  6. 6. δmax = 3.143 mm

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