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 = 5 kNL = 3 mE = 70 GPa (aluminium)I = 160 × 10⁶ mm⁴

δ = mm

2.Easy

A cantilever carries a point load P at its free end. Find the load P that makes the free end deflect by 12 mm.

δ = 12 mmL = 4 mE = 70 GPa (aluminium)I = 120 × 10⁶ mm⁴

P = kN

3.Medium

A cantilever carries a uniformly distributed load w over its whole length. Find the deflection δ at the free end.

w = 2 kN/mL = 1.5 mE = 11 GPa (timber)I = 57 × 10⁶ mm⁴

δ = mm

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 = 12 kNw = 2 kN/mL = 2.5 mE = 70 GPa (aluminium)I = 57 × 10⁶ mm⁴

δ = 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 = 6 mE = 70 GPa (aluminium)

I_req = × 10⁶ mm⁴

6.Hard

A simply supported timber beam of rectangular section, 125 mm wide, carries a uniformly distributed load w over its whole span. Its midspan deflection may not exceed span/250. Find the smallest depth h_req of the section.

w = 3 kN/mL = 6 mE = 11 GPa (timber)b = 125 mm

h_req = mm

Answer key

1. δ = 4.018 mm
2. P = 4.725 kN
3. δ = 2.019 mm
4. δ = 18.11 mm
5. I_req = 72.32 × 10⁶ mm⁴
6. h_req = 264 mm

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