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 = 22 kNL = 2.5 mE = 200 GPa (steel)I = 84 × 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 25 mm.

δ = 25 mmL = 2 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴

P = kN

3.Medium

A cantilever of length L is fixed at A and carries a point load P at a distance a = 2 m from A. Find the deflection δ_B at the free end B.

P = 9 kNa = 2 mL = 2.5 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

δ_B = 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 = 23 kNw = 2 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

δ = mm

5.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 = 19 kNw = 4 kN/mL = 2.5 mE = 200 GPa (steel)I = 36 × 10⁶ mm⁴

δ_max = mm

6.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 = 12 kN/mL = 3 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

Answer key

1. δ = 6.82 mm
2. P = 2.372 kN
3. δ_B = 2.946 mm
4. δ = 6.802 mm
5. δ_max = 1.142 mm
6. I_req = 7.594 × 10⁶ mm⁴

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