Cantilever Beam with Uniform Load

Reference

The spread load cantilever: self weight, formwork overhangs, snow on a canopy. Everything hogs and everything meets at the wall.

The equation

Mwall = wL2/2
Vwall = wL
δtip = wL4/8EI
slope at the tip = wL3/6EI
  • w is the load per unit length, in kN per meter
  • L is the cantilever length, in meters
  • E and I are the modulus and second moment of area
  • δ is the tip deflection
w = 10 kN/mL = 3 mBending moment, sagging plotted upMwall = wL2 /2 = 45 kNm hoggingcalculatgeek.com
Moment grows with the square of the distance from the tip: the outer half of the span contributes only a quarter of the wall moment, and the wall sees four times what a simple span would carry at midspan.

Worked example

A 3 m cantilever carrying 10 kN/m with EI = 16000 kNm2. Wall moment is 10 × 32/2 = 45 kNm, wall shear 30 kN, and tip deflection 10 × 34/(8 × 16000) = 6.3 mm. For scale, a 3 m simple span under the same load would see just 11.25 kNm at midspan: the cantilever carries four times the moment for the same material.

When to use it

The same warning about real fixity as the point load case, doubled, because this is the construction stage workhorse: the formwork overhang and the scaffold bracket, where the load really is spread and the anchorage is often the weakest part of the story. Cantilever deflection limits usually run to span over 180, looser than floors, because nobody walks on the tip of most of them.

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