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

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

P = 5 kNL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴

δ = mm

2.Easy

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 12 mm.

δ = 12 mmL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴

P = kN

3.Medium

A simply supported beam carries a uniformly distributed load w over its whole span. Find the maximum deflection δ_max, at midspan.

w = 10 kN/mL = 5 mE = 200 GPa (steel)I = 84 × 10⁶ mm⁴

δ_max = mm

4.Medium

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 = 12 kNw = 10 kN/mL = 2 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

δ = mm

5.Hard

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 δ_max.

P = 18 kNL = 5 mE = 70 GPa (aluminium)I = 23 × 10⁶ mm⁴

δ_max = mm

6.Hard

A simply supported beam carries a uniformly distributed load w and a point load P at midspan. Using superposition, find the midspan deflection δ_max.

P = 13 kNw = 20 kN/mL = 3 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴

δ_max = mm

Answer key

1. δ = 22.41 mm
2. P = 2.678 kN
3. δ_max = 4.844 mm
4. δ = 13.03 mm
5. δ_max = 49.6 mm
6. δ_max = 33.82 mm

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