A slab loads a beam, and the beam carries that load to its two end supports as reactions. Once you know the load shape the slab delivers, the reactions are pure statics: balance the load on the supports. A uniform load splits evenly, half to each end; an asymmetric load splits by the lever arm. StructLoads computes these reactions for each beam and passes them on as point loads to the columns.
Step 1: get the load on the beam
You cannot find a reaction until you know the load. A one-way slab puts a uniform line load on the beam, equal to the tributary width times the floor pressure, as set out in tributary width for a beam. A two-way slab puts a triangular or trapezoidal load on the beam instead, from how loads transfer from a slab to beams. The load shape is the input to the statics.
Step 2: balance it on the supports
For a simply supported beam, the two reactions must carry the whole load and keep the beam in balance. The split depends only on where the load sits.
| Load on the beam | Reaction split | Each reaction |
|---|---|---|
| Uniform over the span | Even | Half the total |
| Symmetric triangle or trapezoid | Even | Half the total |
| Asymmetric load | By lever arm | Total times distance from far support over span |
The first two rows cover most gravity cases, because slab loads are usually symmetric on a beam. The third row is the general rule. It works because any distributed load can be replaced by a single equivalent force whose magnitude is the area under the load diagram, acting through its centroid, the rule set out in the distributed loads chapter of Baker and Haynes’ open statics textbook; once the load is a single force, the two reactions follow from moment balance alone.
A worked uniform example
Take a beam carrying a uniform 15 kN per metre over a 6 metre span. The total load is 15 times 6, which is 90 kN. Because the load is uniform, each end reaction is half, so 45 kN at each support. The two reactions add to 90 kN, the conservation check that confirms the arithmetic. Those 45 kN reactions then sit on the columns at the beam ends.
When the load is not symmetric
If the load centroid is off centre, the supports do not share equally. Take a total load of 90 kN whose centroid sits 2 metres from the left support on a 6 metre span. The left reaction is 90 times (6 minus 2) over 6, which is 60 kN, and the right reaction is 90 times 2 over 6, which is 30 kN. They still add to 90 kN, but the support nearer the load carries more. This lever-arm split is how StructLoads handles triangular and trapezoidal beam loads.
From beam reaction to column load
A beam reaction is a point load on the column it lands on. Two beams framing into the same column add their reactions, and that sum joins the column’s own tributary load in the structural load takedown. So beam reactions are the link that carries slab load through the framing to the columns, rather than straight down.
Key takeaways: beam reactions from a slab
Find the load the slab puts on the beam, then balance it: uniform and symmetric loads split evenly, asymmetric loads split by the lever arm, and the reactions always add to the total. Those reactions become point loads on the columns. StructLoads computes them by statics from the tributary load as a preliminary model, confirmed by a qualified engineer for continuous or framed beams.
Quick answers
How do you calculate beam reactions from a slab?
First find the load the slab puts on the beam: the tributary width times the floor pressure for a uniform one-way load, or the triangular or trapezoidal shape for a two-way slab. Then balance that load on the two end supports by statics. A symmetric load gives each end half the total; an asymmetric load splits by the lever arm from the load centroid.
What is the reaction of a simply supported beam under a uniform load?
For a uniform line load over the full span, the total load is the line load times the span, and each end reaction is half of that. So a beam carrying 15 kN per metre over a 6 metre span has a total of 90 kN and a reaction of 45 kN at each end. The two reactions add up to the total load.
How do triangular and trapezoidal loads split to the supports?
By the position of the load centroid. A symmetric triangle or trapezoid splits evenly, because its centroid is at midspan. An asymmetric shape splits by the lever arm: the reaction at one end equals the total load times the distance from the other support to the centroid, divided by the span. The support nearer the centroid carries more.
When is a simple reaction calculation not enough?
A simply supported reaction is fine for a single span beam carrying gravity load. It is not enough for a continuous beam over several supports, which is statically indeterminate and needs analysis, or where moments are transferred, the beam is part of a frame, or lateral loads act. Use the simple split for the early takedown and full analysis for the detailed design.