What Is a Tributary Region? Drawing Them on a Floor Plan

A tributary region is the part of a floor that loads one wall or beam. How to draw them on a real plan, check they add up, and turn them into kN/m loads.

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A tributary region is the part of a floor or roof whose load is carried by one particular wall, beam or post. For a floor that spans one way between two walls, you split each span at midspan and give each half to the wall it bears on. The width of that strip is the loaded width, and area load × loaded width gives the line load on the wall in kN/m.

Drawing the regions on the plan is the first step of any load takedown. If they are right, the rest is arithmetic.

Tributary areas explained: which walls carry the floor?0:58

How do you draw tributary regions on a floor plan?

Work one floor at a time, on the plan:

1. Mark the span direction of every floor zone. Timber joists, beam and block and precast planks all span one way, from wall to wall.
2. Find the supports at each end of each span. Walls running parallel to the joists are not supports for that floor.
3. Draw the dividing line at midspan for a simple span. For continuous joists and cantilevers the line moves, as shown further down.
4. Give each piece to its wall and label it with the loaded width and area.
5. Check the areas add up to the floor area. Nothing should be left over or counted twice.

On a rectangle this takes seconds. Real houses are rarely rectangles, so here is an L-shaped first floor.

The front range is 10.0 × 4.0 m with joists spanning 4.0 m from the front wall W1 to the back walls W2 and W3. The rear wing is 5.0 × 4.0 m with joists spanning 5.0 m across it, from W4 to W6.

The floor is 10.0 × 4.0 + 5.0 × 4.0 = 60 m², so the regions balance.

Two things on this plan catch people out. W4 is one wall with two loaded widths: nothing along the front range, where the joists run parallel to it, and 2.5 m along the wing. And W3 is an internal wall that only picks up floor from one side, because the wing joists run parallel to it.

How do you turn a tributary region into a line load?

Multiply the area load by the loaded width:

Line load (kN/m) = area load (kN/m²) × loaded width (m)

Keep permanent (dead) and variable (imposed) loads separate, so you can apply the right factor to each later. For a typical UK timber first floor, take 0.6 kN/m² permanent and 1.5 kN/m² imposed, plus 0.8 kN/m² for movable partitions (the cautious band; light timber studs fall in the 0.5 band). These are typical values; check them with a competent engineer and against the actual build-up. Typical UK floor and roof loads explains where they come from.

For W4 along the wing:

Loaded width          = 5.0 / 2 = 2.5 m
Permanent   Gk        = 0.6 × 2.5 = 1.5 kN/m
Variable    Qk        = (1.5 + 0.8) × 2.5 = 5.75 kN/m
Characteristic total  = 1.5 + 5.75 = 7.25 kN/m
Design (1.35G + 1.5Q) = 1.35 × 1.5 + 1.5 × 5.75 = 10.7 kN/m

The characteristic figure is the one you carry down to check bearing pressure. The design figure is for sizing the wall or a beam. Characteristic vs design loads covers which to use where.

W1 works the same way: 2.0 m × 2.9 kN/m² = 5.8 kN/m, along its full 10.0 m.

Does the dividing line always fall at midspan?

Only for a simple span, where each joist sits on two supports and nothing else. Two other cases are common in houses.

Continuous over an internal wall. If joists run unbroken over a middle wall, that wall attracts more than half of each span. For two equal spans, the middle wall takes 1.25 × the span (5.0 m of floor for two 4.0 m spans) and each end wall takes 0.375 × the span (1.5 m). Many engineers use the simple split for timber joists, then check the internal wall with this allowance if it is close to its limit.

Cantilever. When a floor runs past a wall to form a balcony or bay, the wall under the overhang carries more than the overhang plus half the back span. With back span L and overhang c:

Inner wall (under the overhang) = (L + c)² / (2L)
Far wall                        = (L² − c²) / (2L)

L = 4.0 m, c = 1.0 m:
Inner wall = 5.0² / 8.0         = 3.125 m
Far wall   = (16.0 − 1.0) / 8.0 = 1.875 m
Check      = 3.125 + 1.875     = 5.0 m of floor ✓

The far wall gets lighter as the overhang grows, and it can lift if the overhang is loaded and the back span is not. One-way spans works through the same case in kN/m.

What about slabs that span two ways?

A concrete slab supported on all four sides, and less than about twice as long as it is wide, spans both ways. Its tributary regions are drawn with 45° lines from each corner: a triangle to each short wall and a trapezoid to each long wall. The 45° rule for two-way slabs has the formulas and a worked panel. Timber joists never span two ways, however square the room.

What is the tributary area of a post or column?

For a point support, the tributary region is the area halfway to each neighbouring support in both directions. A post under a beam that spans 4.0 m on each side, with the beam carrying a 3.0 m strip of floor, has a tributary area of (4.0 / 2 + 4.0 / 2) × 3.0 = 12 m². At 2.9 kN/m² that is 34.8 kN characteristic, delivered as a point load. Steel post point loads follows that load down to a pad.

Common mistakes

• Giving floor load to walls parallel to the joists. They carry the roof or wall above, and their own weight, but no floor (W5 and W7 above).
• Forgetting the second side of an internal wall. Where floors span onto a wall from both sides, add both loaded widths.
• Smearing a stair or void. A void removes floor from some walls, but the trimmers around it collect load and put point loads where they bear.
• One loaded width for a whole wall. If the floor changes along the wall, as at W4, split the wall into lengths.
• Not checking the total. If the regions do not add up to the floor area, something is missing or counted twice. The six quick checks start with exactly this.

FAQ

What is the difference between a tributary region and a loaded width?

The tributary region is the area of floor a support carries, drawn on the plan. The loaded width is its width measured at right angles to the wall. For a rectangular strip, line load = area load × loaded width, and total load = area load × tributary area.

Is tributary area the same as tributary region?

Yes. Both mean the part of a floor or roof whose load a given support carries. "Tributary area" is more common for posts and columns, where you want a total in kN. "Region" is often used for walls, where the shape matters as much as the size.

Do walls parallel to the joists take any floor load?

Very little. They may carry a narrow strip of boarding next to them, which is usually ignored. They still carry their own weight, anything bearing on them from above, and any load from a different floor zone that spans onto them.

Do I use characteristic or design loads with tributary regions?

The region is the same either way. Multiply it by characteristic loads for bearing pressure checks, and by design loads (1.35G + 1.5Q) for sizing walls and beams. Keep the two in separate columns.

In LoadTakedown you trace walls and spans over the architect's PDF, and the tributary regions show as coloured areas on the plan, so you can see which wall each part of the floor loads.

For the next step, see loaded width and the foundation load from a wall worked example. Try it on your own drawings at LoadTakedown.