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 load P that makes the free end deflect by 20 mm.

δ = 20 mmL = 2 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴

P = kN

2.Easy

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

P = 11 kNL = 2.5 mE = 200 GPa (steel)I = 120 × 10⁶ mm⁴

δ = mm

3.Medium

A simply supported beam carries a uniformly distributed load w over its whole span. Find the slope θ_A of the beam at support A, in radians.

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

θ_A = rad

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 = 6 kNw = 15 kN/mL = 1.5 mE = 11 GPa (timber)I = 23 × 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 = 5 kNw = 20 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 57 × 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 = 8 kN/mL = 4 mE = 70 GPa (aluminium)

I_req = × 10⁶ mm⁴

Answer key

1. P = 4.463 kN
2. δ = 2.387 mm
3. θ_A = 0.008506 rad
4. δ = 64.2 mm
5. δ_max = 2.957 mm
6. I_req = 34.29 × 10⁶ mm⁴

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