A beam is designed for a load per metre, so the first step is turning the floor pressure into one. The uniform line load, or UDL, on a beam is its tributary width times the floor pressure, plus the beam’s own self weight. For a 3 metre tributary width under 5 kN per square metre, that is 15 kN per metre. StructLoads collects this strip onto each beam, and the method below is quick by hand.
From pressure to line load
A floor load is a pressure in kN per square metre, but a beam carries a line load in kN per metre. The bridge between them is the tributary width: the strip of floor the beam collects, half the spacing to the parallel member on each side. Multiply the width by the pressure and the units work out to a load per metre. The tributary width itself is covered in tributary width for a beam.
The calculation
UDL equals tributary width times floor pressure, plus beam self weight.
| Input | Value | Contribution |
|---|---|---|
| Tributary width | 3.0 m | times pressure |
| Floor pressure | 5.0 kN/m2 | gives 15 kN/m |
| Beam self weight | about 1.0 kN/m | added on top |
| Total UDL | about 16 kN/m |
So the beam is designed for roughly 16 kN per metre. The self weight is small but real, and forgetting it slightly under-loads the beam. Keep dead and live contributions separate within the UDL so the load factors can act on each.
Why uniform, and when
A one-way floor spans onto the beam evenly along its length, so the strip it delivers is the same intensity everywhere: a genuine UDL. That is the usual and correct model for one-way framing. A two-way panel is different, which is the main exception below. For the uniform case, the UDL is all you need to find the beam’s bending and, by statics, its end reactions.
From UDL to reactions
A uniform load over a simply supported span splits evenly: each end reaction is half the total. A 16 kN per metre UDL over a 6 metre span totals 96 kN, so each support takes 48 kN. If you want the shear and moment along the span, not just the ends, David Roylance’s MIT OCW notes on the statics of bending walk through building the diagrams from exactly this kind of distributed load, one free body cut at a time. Those reactions become point loads on the columns, continuing the load path, the step set out in how to calculate beam reactions from a slab. The UDL is the input; the reactions are the output.
The two-way exception
When the slab spans two ways, the beam does not receive a uniform strip; it receives a triangle on a short edge or a trapezoid on a long edge, from the 45 degree distribution in how loads transfer from a slab to beams. For quick design you can convert that shape to an equivalent UDL that gives the same peak bending moment, using standard factors, or analyse the real shape. The equivalent UDL is a convenience, not the true load, so use it knowingly.
Point loads are separate
A UDL models an evenly spread floor strip. It does not model a concentrated load, such as a column landing on the beam, a heavy item of plant, or a secondary beam framing in. Those are point loads, added to the UDL and analysed separately, and they often govern the local shear. So a real beam may carry a UDL from its floor strip plus one or more point loads from the framing.
Key takeaways: UDL on a beam
The UDL is tributary width times floor pressure, plus self weight: a few kN per metre that drives the beam’s bending and reactions. It is exact for one-way framing, an equivalent approximation for two-way panels, and never the model for concentrated loads. StructLoads builds the line load on each beam as a preliminary figure a qualified engineer confirms.
Quick answers
How do you calculate the UDL on a beam from tributary area?
Multiply the beam’s tributary width by the floor pressure, then add the beam’s self weight. A beam with a 3 metre tributary width under a 5 kN per square metre floor load carries 15 kN per metre from the floor, plus perhaps 1 kN per metre of self weight, giving 16 kN per metre. That uniform line load is the input for the beam’s bending and reactions.
What is a UDL?
A UDL is a uniformly distributed load, spread evenly along a member and measured in force per length, such as kN per metre. On a beam it represents the floor strip the beam collects, turned from a pressure into a line load. Uniform means the same intensity at every point along the span, the usual model for a one-way floor on a beam.
How do you turn a triangular or trapezoidal load into a UDL?
For a two-way panel the beam load is a triangle or trapezoid, not uniform. For quick design you convert it to an equivalent UDL that gives the same maximum bending moment, using standard factors, or analyse the real shape directly. The equivalent UDL is a convenience; the true shape is more accurate for reactions and shear.
When is a UDL not the right model for a beam?
A UDL is not right when the load is genuinely concentrated, such as a column landing on the beam, a heavy point of equipment, or another beam framing in. Those are point loads, analysed separately. A two-way slab also gives a triangle or trapezoid rather than a uniform load. Use a UDL for an evenly spread one-way floor strip.