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 = 19 kNL = 1.5 mE = 200 GPa (steel)I = 12 × 10⁶ mm⁴

δ = mm

2.Easy

A simply supported beam carries a point load P at midspan. Find the load P that makes the midspan deflect by 15 mm.

δ = 15 mmL = 2 mE = 11 GPa (timber)I = 84 × 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 = 15 kNw = 4 kN/mL = 1.5 mE = 11 GPa (timber)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 = 11 kNa = 1 mL = 5 mE = 11 GPa (timber)I = 23 × 10⁶ mm⁴

δ_P = 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 = 15 kN/mL = 8 mE = 70 GPa (aluminium)

I_req = × 10⁶ mm⁴

6.Hard

A simply supported timber beam of rectangular section, 100 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/300. Find the smallest depth h_req of the section.

w = 2 kN/mL = 6 mE = 11 GPa (timber)b = 100 mm

h_req = mm

Answer key

1. δ = 8.906 mm
2. P = 83.16 kN
3. δ = 76.7 mm
4. δ_P = 46.38 mm
5. I_req = 514.3 × 10⁶ mm⁴
6. h_req = 264 mm

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