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 20 mm.

δ = 20 mmL = 2.5 mE = 11 GPa (timber)I = 160 × 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 = 3 mE = 70 GPa (aluminium)I = 160 × 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 = 6 kN/mL = 5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

δ_max = mm

4.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 0.5 m from A. Find the deflection δ_B at the free end B.

P = 21 kNa = 0.5 mL = 2 mE = 11 GPa (timber)I = 36 × 10⁶ mm⁴

δ_B = 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 = 10 kN/mL = 2 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 = 25 kNw = 4 kN/mL = 2 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴

δ_max = mm

Answer key

1. P = 108.1 kN
2. P = 99.56 kN
3. δ_max = 4.36 mm
4. δ_B = 12.15 mm
5. I_req = 5.357 × 10⁶ mm⁴
6. δ_max = 7.974 mm

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