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 slope θ_B of the beam at the free end B, in radians.

P = 25 kNL = 1.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴

θ_B = rad

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 = 2 kN/mL = 3 mE = 70 GPa (aluminium)I = 8.5 × 10⁶ mm⁴

θ_B = rad

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 = 12 kNw = 5 kN/mL = 1.5 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴

δ = mm

4.Medium

A simply supported beam carries a point load P at a = 1 m from support A. Find the deflection δ_P under the load.

P = 21 kNa = 1 mL = 8 mE = 200 GPa (steel)I = 23 × 10⁶ mm⁴

δ_P = 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 = 7 kNw = 2 kN/mL = 3 mE = 11 GPa (timber)I = 23 × 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 = 5 mE = 200 GPa (steel)

I_req = × 10⁶ mm⁴

Answer key

1. θ_B = 0.006114 rad
2. θ_B = 0.01513 rad
3. δ = 3.623 mm
4. δ_P = 9.321 mm
5. δ_max = 23.9 mm
6. I_req = 23.44 × 10⁶ mm⁴

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