Module 3 · Lesson 3.1
Idealisation, spans and load patterns
The decisions made before the analysis starts, which affect the answer more than the analysis does.
Why this matters
By the time you press solve, the answer has largely been decided. It was decided when you chose where the span is measured from, which loads to put on which spans, and whether the connection is a pin or a moment connection. Analysis software will faithfully compute the consequences of those choices and tell you nothing about whether they were right. This lesson is about the choices.
By the end of this lesson you should be able to
- Define the effective span and calculate it
- Explain why a span error is amplified in the moment
- List the load patterns for a continuous beam and what each governs
- Take a support moment at the face of a monolithic support
What you should already know
- Combinations of actions (Module 2)
- Bending moment diagrams for continuous beams (Structural Analysis Fundamentals, Module 16)
Where does the span begin?
A steel beam sits on a bearing and the span is obvious. A concrete beam is cast into a 400 mm column, and the answer is genuinely unclear — the beam does not stop at a line, it merges into the column over a finite width.
The convention is the effective span: the clear distance between support faces, plus a small addition at each end.
The addition is the lesser of half the support width and half the member depth. The second limit is the interesting one: it says the reaction cannot be assumed to act further into a wide support than the member is deep. A 200 mm slab on a 900 mm wall does not span to the middle of the wall, because the slab cannot reach that far in to find its support.
What it calculates: The span to be used in analysis.
- ln
- Clear distance between support FACES (mm)
- ti
- Width of support i (mm)
- h
- Overall depth of the member (mm)
This assumes
- The support is monolithic or a bearing wide enough to develop the reaction
- A true bearing on a narrow pad is measured to the bearing centre instead
In plain terms: Between the clear span and the centre-to-centre span, and usually much closer to the clear span. The distinction is not pedantry: moment goes with the square of span, so a 7% span error becomes a 15% moment error, always in the direction of over-design.
Worked example
The cost of measuring the span wrongly
Given
- A 300 mm deep slab spanning between 800 mm wide walls
- Clear distance between wall faces: 5.0 m
- Ultimate load 12 kN/m²
Find
The design moment using the effective span, and using centre-to-centre instead.
Assumptions
- Simply supported for this comparison
- Monolithic construction, so the effective-span rule applies
Which spans carry the imposed load?
Permanent load is on every span, always. The variable load is variable in position as well as magnitude, and the arrangement that maximises one effect minimises another.
There are three families, and each exists for a reason:
- All spans loaded. Maximises the total reaction, and usually the shear at internal supports.
- Alternate spans loaded. Maximises the sagging moment in the loaded spans. An unloaded neighbour offers less restraint, so the loaded span sags more freely.
- Two adjacent spans loaded. Maximises the hogging moment at the support between them. Both spans push down on the same support, and neither has an unloaded neighbour to relieve it.
The last is the one most often forgotten, and it is the one that sizes the top steel over the supports.
Predict first
For a three-span continuous beam, which imposed-load arrangement gives the largest hogging moment over the first internal support?
Taking the moment at the support face
An analysis of a line diagram reports the moment at the support centreline, where the two members meet as points. The real support is 400 mm wide, and over that width the reaction is spread out rather than concentrated.
Where the support is monolithic, the design moment may be taken at the support face:
What it calculates: The design hogging moment, reduced from the centreline value.
- Moment from the analysis, at the support centreline (N·mm)
- Design support reaction (N)
- t
- Support width (mm)
This assumes
- The support is monolithic with the member — not a bearing
- The reaction is distributed across the support rather than concentrated
In plain terms: For a 400 kN reaction on a 400 mm column this removes 20 kNm, which on a 200 kNm support moment is a 10% reduction. It is legitimate, it is free, and it is routinely left on the table.
Practice
A 250 mm slab spans between 400 mm walls with a clear distance of 4.6 m. What is the effective span, in m?
Practice
A continuous beam has a design support moment of 180 kNm at the centreline of a 350 mm wide column carrying a reaction of 320 kN. What is the design moment at the column face, in kNm?
Check yourself
A four-span continuous beam. How many imposed-load patterns must be examined in total?
Summary
- Effective span = clear span + min(t/2, h/2) at each end
- A span error is squared in the moment, and is always conservative — so nothing reveals it
- All spans loaded: maximum reactions and shear
- Alternate spans: maximum sagging moments
- Adjacent pairs: maximum hogging at the support between them — the forgotten one
- A monolithic support permits the moment to be taken at its face
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint