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 simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 12 mm.

δ = 12 mmL = 2 mE = 11 GPa (timber)I = 8.5 × 10⁶ mm⁴

P = kN

2.Easy

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 5 mm.

δ = 5 mmL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴

P = kN

3.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 = 22 kNw = 15 kN/mL = 2 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

δ = mm

4.Medium

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

w = 8 kN/mL = 6 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

δ_max = mm

5.Hard

A simply supported beam carries a uniformly distributed load w. Its deflection may not exceed span/360. Find the smallest second moment of area I_req that meets this limit.

w = 5 kN/mL = 4 mE = 70 GPa (aluminium)

I_req = × 10⁶ mm⁴

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 = 22 kNw = 4 kN/mL = 2 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴

δ_max = mm

Answer key

1. P = 6.732 kN
2. P = 170.7 kN
3. δ = 10.56 mm
4. δ_max = 33.83 mm
5. I_req = 21.43 × 10⁶ mm⁴
6. δ_max = 7.177 mm

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