Uniformly Distributed Load vs Point Load on Beams

Every load on a structure has to be described before it can be designed for, and the two simplest descriptions are the point load and the uniformly distributed load. A point load acts at a single spot, like a column landing on a beam. A uniformly distributed load, usually shortened to UDL, is spread evenly along a length or over an area, like the self-weight of a slab or a layer of screed across a floor.

The distinction is not academic. The same total weight produces very different bending moments, shear forces and deflections depending on how it is spread. This article explains the intuition, gives the standard formulas for a simply supported beam, works through a direct comparison, and covers the mistakes people make when they convert real loads into design loads.

The intuition: concentrated versus spread out

Imagine a plank spanning between two bricks. Stand in the middle and it sags noticeably. Now lie down along its full length: your weight has not changed, but the plank sags less. When you stand, your whole weight acts at the point where it does the most harm, at midspan, as far from both supports as possible. When you lie down, much of your weight is close to the supports, where it can travel into them without bending the plank much at all.

That is the essence of the difference. A point load concentrates its effect, while a uniformly distributed load shares it along the span. For a given total weight on a simply supported beam, a central point load produces twice the maximum bending moment of the equivalent UDL and noticeably more deflection.

Real loads are rarely perfectly either. A wall sitting on a beam is distributed along part of its length; a heavy safe on a floor is effectively a point load; a crowd of people is idealised as a uniform load over the floor area. Engineers choose the description that represents the load fairly, and codes give standard values for both.

How loads are expressed

A point load is a force, written P and measured in kilonewtons (kN). A line UDL is a force per unit length, written w and measured in kN/m. An area load, such as an imposed floor load or a finish, is a force per unit area in kN/m². To turn an area load into a line load on a beam, multiply it by the width of floor that the beam supports, called its tributary width. A beam carrying 3 m of floor either side at 5 kN/m² receives a UDL of 5 × 3 = 15 kN/m.

Loads also come in different kinds: permanent loads from the structure and finishes, variable or imposed loads from occupants and contents, and environmental loads such as wind. Our guide to types of structural loads explains these categories. In Singapore, buildings are designed to the Eurocodes with Singapore National Annexes, which set characteristic imposed loads for each category of use and the partial factors applied to them.

Uniformly distributed load and point load formulas

For a simply supported beam of span L, the key results are:

UDL w over the full span: support reactions R = w·L/2; maximum shear V = w·L/2 at the supports; maximum bending moment M = w·L²/8 at midspan; maximum deflection δ = 5·w·L⁴/(384·E·I).
Point load P at midspan: reactions R = P/2; maximum shear V = P/2, constant between support and load; maximum bending moment M = P·L/4 under the load; maximum deflection δ = P·L³/(48·E·I).

The shapes of the diagrams differ too. Under a UDL the shear force varies linearly from +wL/2 to −wL/2, and the bending moment diagram is a parabola. Under a central point load the shear diagram is a pair of flat steps and the bending moment diagram is a triangle peaking under the load. The sibling article on shear force and bending moment diagrams shows how to draw both.

A worked comparison

Take a 6 m simply supported beam carrying a total load of 60 kN, first as a UDL and then as a single central point load.

As a UDL, w = 60 / 6 = 10 kN/m. The reactions are 30 kN each. The maximum bending moment is 10 × 6² / 8 = 45 kNm.

As a central point load, P = 60 kN. The reactions are again 30 kN each. The maximum bending moment is 60 × 6 / 4 = 90 kNm.

The reactions and maximum shear are the same, because the total load and its centre of gravity are unchanged. But the bending moment has doubled. Deflection rises too: with W as the total load, the UDL deflection is 5WL³/384EI and the point-load deflection is WL³/48EI, which is 8/5 or 1.6 times larger. So a heavy item placed at midspan of a floor beam can be considerably more demanding than its weight spread over the floor, even though the supports feel no difference.

The reverse lesson matters as well. If you place the same 60 kN point load near a support rather than at midspan, the bending moment falls sharply but the reaction and shear at that nearer support rise towards the full 60 kN. Position changes which check governs.

Real-building examples

Most of the load on a typical floor is a uniformly distributed load: the slab’s self-weight, screed, tiles, ceilings and services, plus the imposed load for occupancy. Beams supporting that floor see a UDL from it. Point loads arise when a column from above lands on a transfer beam, when a beam frames into another beam, or when heavy equipment sits on a small footprint. Water tanks on roofs, plant, bank vaults, compactus filing systems, large aquariums and stone kitchen islands are common examples in homes and offices.

A partition wall running across a slab is a line load: uniform along its length, but concentrated across the slab’s span. On a one-way slab, a wall running parallel to the span is far less onerous than one running perpendicular to it across midspan. When a renovation adds heavy walls, a raised floor or a large planter, this is exactly what the engineer checks. Our article on what a structural engineer does describes how these checks fit into a typical assessment.

Common mistakes

Treating a heavy item as part of the floor’s imposed load. Code imposed loads are averages over an area. A single concentrated item can exceed what the slab can take locally even if the average is within limits. Codes therefore also specify a concentrated load check.
Mixing units. kN/m² is an area load, kN/m a line load and kN a point load. Multiplying a floor load by span instead of tributary width, or forgetting to convert kg to kN (roughly 1 kN per 100 kg), produces errors of an order of magnitude.
Assuming equal total load means equal effect. As the example shows, the distribution matters as much as the magnitude for bending and deflection.
Using simply supported formulas for continuous beams. Continuous and fixed-ended beams redistribute moment to the supports and need their own coefficients.
Forgetting self-weight. The beam’s own weight is itself a UDL and must be included.

Frequently asked questions

What is a uniformly distributed load?

A uniformly distributed load is a load spread evenly along the length of a member or over an area, expressed in kN/m for a beam or kN/m² for a slab. Typical examples are the self-weight of a slab, a floor finish and the code-specified imposed load for occupants and contents.

Is a point load or a UDL worse for a beam?

For the same total weight on a simply supported beam, a point load at midspan is worse for bending and deflection: it produces twice the maximum bending moment and 1.6 times the deflection of the equivalent UDL. The support reactions and maximum shear are the same in both cases.

How do I convert a floor load to a beam load?

Multiply the area load in kN/m² by the tributary width of floor that the beam supports, in metres. The result is a line load in kN/m. For a beam supporting half the span of slabs on each side, the tributary width is the sum of those two half-spans.

Is a wall on a floor a point load or a distributed load?

It is a line load, uniform along the wall’s length but concentrated across its narrow width. Its effect on the slab depends on its direction relative to the slab’s span and on where it sits, so heavy masonry walls added in renovations should be checked by an engineer.

Why do the reactions stay the same for both load types?

Support reactions depend on the total load and the position of its centre of gravity. A UDL over the full span and a point load at midspan both have their resultant at the centre, so each support carries half the load in both cases, even though the internal bending differs.

Adding heavy items, walls or equipment to an existing floor? Talk to our consultancy or get in touch.