Analyse and design a continuous beam

The continuous beam is the best structure to start learning analysis with. It is small enough to check by hand, yet it shows the key idea that makes real structures efficient: continuity. This tutorial uses the Continuous beam template — a strip of deck on two parallel continuous beams over pinned supports — and compares the results with the classic hand formulas.

#Why continuity matters

A simply supported beam of span L under a uniform load w has its largest moment at mid-span: M = wL²/8. Make the beam run continuously over several supports and it behaves differently: over each interior support it bends the other way (hogging, tension on top), and this hogging moment reduces the sagging moment in the spans. The beam is also much stiffer — the mid-span deflection of an interior span drops to about a fifth of the simply supported value.

Equal spans, uniform load w on all spans	Support moment	End span moment	Interior span moment
Simply supported (1 span)	0	0.125 wL²	—
2 spans	−0.125 wL²	0.070 wL²	—
3 spans	−0.100 wL²	0.080 wL²	0.025 wL²

#Step 1 — Pick the template

1. In the gallery choose Elements › Continuous beam.
2. The default is three 6 m spans with a 2 m wide strip of deck, in concrete, pinned at every support of both beams.

#Step 2 — Set the size

Parameter	Section	Default	Range
Spans	Span	3	1–8
Span length	Span	6 m	2–15 m
Strip width	Deck	2 m	0.5–5 m
Analysis divisions per span	More options	4	2–10

Each beam is one member from end to end; the divisions are analysis points along it, not joints. More divisions give smoother diagrams. Cross beams at every support tie the two beams, and the deck between them is a floor slab analysed as a plate, so each beam carries half the strip.

#Step 3 — Materials and sections

1. Pick the Design code. The template starts in concrete; switch to steel or timber to compare.
2. Set sections for Beams and Cross beams, and the Floor slabs thickness of the deck.
3. Try it once with Size members for me off, so you see the forces and checks for the section you chose.

#Step 4 — Supports and loads

1. The supports are pinned by the template. With pins on both beams, the pair cannot roll about its own axis.
2. Choose a Floor use and Finishes and services load for the deck.
3. Switch Wind off — for a floor beam it is not relevant (with no cladding it would act as drag on the members).

#Step 5 — Analyse and check by hand

Press Run analysis (F5). Then:

1. Show Moment for the Dead case. The diagram is drawn on the tension side: sagging below the beam in the spans, hogging above it over the supports. Peak values are labelled.
2. Compare with the table. Work out w for one beam: half the strip width × (slab weight + finishes) + beam self-weight. With a 200 mm slab (5 kN/m²), 1.5 kN/m² finishes and the 1 m half-width: about 6.5 kN/m plus the beam. Then the support moment ≈ 0.1 × w × 6² = 3.6 w.
3. Show Shear: the largest shear is at the first interior support, about 0.6 wL in a 3-span beam.
4. Show Displacement under the service combination and use Animate: the end spans deflect most.

Small differences from the table come from the cross beams and the deck plate, which share the load slightly differently from an ideal line load — exactly the kind of thing a 3D model captures.

#Step 6 — Design

1. Press Run design (F6). In concrete each beam is designed as a continuous beam line: bottom bars for the spans, top bars over the supports, stirrups for shear, and a deflection check. In steel, bending, shear, lateral-torsional buckling and deflection are checked.
2. Show Reinforcement bars (3D) to see the top bars over the supports and the stirrups closer together where shear is high.
3. Select a beam and open its Calculation report — the governing span's calculation is written out step by step.

#Things to try

• Set Spans to 1 and compare the mid-span moment with wL²/8 — and the deflection with 5wL⁴/384EI.
• Change the beam from concrete to steel and see the deflection change with the stiffness EI.
• Make one span much longer than the others: the short span's moment can turn hogging throughout, and its support may lift under pattern loading.

#Rules of thumb

• Concrete continuous beams: depth ≈ span / 15 (end spans) to span / 18 (interior).
• Steel continuous beams: depth ≈ span / 20 to span / 25.
• End spans of about 0.8× the interior spans balance the moments.