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 uniformly distributed load w over its whole length. Find the slope θ_B of the beam at the free end B, in radians.

w = 15 kN/mL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

θ_B = rad

2.Easy

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 8 mm.

δ = 8 mmL = 8 mE = 200 GPa (steel)I = 8.5 × 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 = 10 kNw = 15 kN/mL = 1.5 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

δ = 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 = 11 kNa = 0.5 mL = 2.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴

δ_B = 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 = 3 kNw = 6 kN/mL = 2 mE = 11 GPa (timber)I = 120 × 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 = 6 kN/mL = 8 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

Answer key

1. θ_B = 0.01905 rad
2. P = 1.275 kN
3. δ = 2.469 mm
4. δ_B = 5.117 mm
5. δ_max = 1.326 mm
6. I_req = 72 × 10⁶ mm⁴

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