Continuous Beam Explained: How Multi-Span Beams Work

A continuous beam is a beam that runs unbroken over three or more supports, rather than stopping and starting at each one. Most reinforced concrete floors in real buildings behave this way, because the bars and the concrete are cast through the supports as a single piece. Understanding how such a beam shares load between its spans explains a great deal about why structural drawings look the way they do.

This article sets out the intuition first, then the key results in plain-text formulas, a worked example, the common mistakes we see on site and in renovation work, and the point at which a professional engineer has to take over.

The intuition: a beam that helps its neighbours

Start with a single plank resting on two bricks. Load it and it sags in the middle; the ends simply rotate on the bricks. This is the simply supported beam, and every span works alone.

Now lay one long plank across three bricks. Press down on the left span and the plank over the middle brick tries to rotate, lifting the right span slightly. The two spans are now talking to each other. Over the middle support the top of the plank stretches and the bottom compresses, the opposite of what happens at mid-span. That reversal is the defining feature of a continuous beam: it bends downwards (sagging) within each span and upwards (hogging) over the interior supports.

The practical consequence is that each span is stiffer and carries less mid-span moment than it would on its own. The price is a new, often larger, moment over the supports that must be designed for, and reinforcement that has to sit in the top of the section where many people do not expect it.

Sagging, hogging and the shape of the bending moment diagram

The bending moment in such a beam swings between positive and negative values along its length. A simply supported span under a uniform load produces a single smooth curve with its peak at mid-span. A multi-span beam produces the same parabola, but it is pulled down at the supports by the hogging moments, so the curve crosses zero at two points within each span. These are the points of contraflexure, where the beam changes from curving one way to curving the other.

For a uniformly distributed load w on a span L, the familiar results are:

Simply supported span: maximum moment = wL²/8 at mid-span.
Two equal continuous spans: hogging moment over the middle support = wL²/8; maximum sagging moment in each span ≈ 0.070wL².
Interior span of a long run of equal spans: hogging at supports ≈ wL²/12; sagging at mid-span ≈ wL²/24.

These are textbook elastic values for idealised cases. Real beams have unequal spans, patterned imposed loads and supports that are not perfectly rigid, so the engineer analyses the actual arrangement rather than relying on the coefficients.

A worked example

Consider a reinforced concrete beam running over two equal 6 m spans, carrying a total factored uniform load of 30 kN/m. If each span were simply supported, the mid-span moment would be 30 × 6² / 8 = 135 kNm.

Made continuous over the middle column, the picture changes. The moment over the middle support becomes 30 × 6² / 8 = 135 kNm hogging, and the maximum sagging moment in each span falls to about 0.070 × 30 × 36 ≈ 76 kNm. The reaction at the middle support also rises: it carries roughly 1.25wL, or about 225 kN, compared with 180 kN if the two spans were separate and simply sat on it. The end supports carry correspondingly less.

Three lessons follow. The beam needs top bars over the middle support sized for 135 kNm. The bottom bars can be lighter than for a simply supported span. And the middle column and its foundation must be designed for the increased reaction, which is easy to miss if someone sizes the column by sharing the load equally between supports.

Why engineers design continuous beams

Continuity is rarely a deliberate choice in reinforced concrete; it is the natural result of monolithic casting. But it brings real advantages that engineers exploit:

Lower deflection. A continuous span is markedly stiffer than an equivalent simply supported one, so a shallower section can satisfy the deflection limits.
Economy of material. Moments are spread between support and span regions instead of concentrated at mid-span, which generally allows a lighter section overall.
Robustness. Continuity gives a structure alternative ways to carry load if one element is damaged. Codes deliberately require ties and continuity reinforcement for this reason.
Moment redistribution. Ductile reinforced concrete can shed some moment from the supports to the spans as it cracks. Codes permit limited redistribution, which helps the engineer balance top and bottom reinforcement.

The disadvantages are sensitivity to support settlement, more complex analysis, and the need for careful detailing of laps and anchorage at the supports. In steel frames, continuity has to be built in through moment-resisting connections, since a simple bolted end plate behaves more like a pin.

Common mistakes with continuous beams

In our consulting work, most problems with multi-span beams arise not in the original design but in what happens to the beam afterwards.

Removing or weakening an interior support

Taking out a column or wall that supports a continuous beam does not just remove one support. It doubles the effective span, roughly quadruples the moment and changes the sign of the moment where top bars were placed. A beam detailed for hogging over a support may have little bottom steel there, exactly where the new sagging moment peaks.

Cutting top bars or coring near supports

Chasing services across the top of a slab or beam near a support can sever the very bars that resist hogging. Cracks across the top surface over supports are a warning sign worth investigating, and our guide to types of concrete cracks explains how to read them.

Ignoring pattern loading

The worst sagging moment in a span often occurs when that span is loaded and its neighbours are empty. Designing only for full load everywhere can underestimate span moments.

Assuming equal reactions

As the example shows, interior supports take a larger share of the load. Columns and footings sized on equal shares can be overstressed.

How continuous beams are analysed

Historically, engineers used methods such as the three-moment equation and moment distribution to solve multi-span beams by hand. Today the analysis is normally carried out with frame or finite element software, but the hand methods remain valuable as checks. Reinforced concrete design in Singapore is based on the Eurocodes with Singapore National Annexes, which also give simplified moment coefficients for beams and slabs with roughly equal spans and predominantly uniform loads.

Whichever method is used, the engineer must consider several load arrangements, check shear near the supports where it is highest, verify deflection and cracking, and detail curtailment so that top bars extend far enough beyond the points of contraflexure. These are judgements that combine analysis with experience of how beams behave once built. For a broader overview of beam forms, see our guide to types of beams.

Why you need an engineer

A continuous beam is a system, not a set of separate spans. Any change to one part, such as removing a support, adding a heavy load, coring an opening or extending a span, alters the forces everywhere else in the run. That is why changes to beams in existing buildings in Singapore must be assessed and endorsed by a Professional Engineer and approved by the Building and Construction Authority before work starts.

If you are planning alterations that touch beams, columns or walls, an early review by an experienced structural consultancy will establish how the existing structure actually carries load and what can safely change.

Frequently asked questions

What is the difference between a continuous beam and a simply supported beam?

A simply supported beam spans between two supports and is free to rotate at each end, so each span works independently and bends only downwards. A continuous beam runs unbroken over three or more supports, so adjacent spans restrain each other, producing hogging moments over the interior supports and smaller sagging moments within the spans.

Why does a continuous beam need top reinforcement over supports?

Over an interior support a continuous beam curves upwards, which puts the top of the section into tension. Concrete is weak in tension, so steel bars are placed in the top of the beam over the support to resist this hogging moment and to control cracking there.

Is a continuous beam always better than simply supported spans?

Not always. Continuity usually reduces deflection and material, but it makes the beam sensitive to differential settlement, temperature movement and changes to supports. On poor ground or where movement is expected, engineers sometimes prefer simply supported spans with movement joints.

Can I remove a column under a continuous beam during renovation?

Only after a Professional Engineer has assessed the structure and designed a replacement load path, and with the necessary BCA approval. Removing an interior support changes both the size and the direction of the bending moment in the beam, and the existing reinforcement is very unlikely to suit the new condition.

Need accountable advice on beams, columns or alterations in an existing building? Talk to our structural engineering consultancy or get in touch to discuss your project.