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 = 3 kNL = 1.5 mE = 70 GPa (aluminium)I = 12 × 10⁶ mm⁴

δ = mm

2.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 = 8 kN/mL = 4 mE = 200 GPa (steel)I = 160 × 10⁶ mm⁴

θ_B = rad

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 = 15 kNa = 2 mL = 2.5 mE = 70 GPa (aluminium)I = 36 × 10⁶ mm⁴

δ_B = 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 = 8 mE = 70 GPa (aluminium)I = 120 × 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 = 5 mE = 200 GPa (steel)

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 = 10 kNw = 12 kN/mL = 4 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

δ_max = mm

Answer key

1. δ = 4.018 mm
2. θ_B = 0.002667 rad
3. δ_B = 21.83 mm
4. δ_max = 50.79 mm
5. I_req = 14.65 × 10⁶ mm⁴
6. δ_max = 13.37 mm

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