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Reinforced Concrete Design / Analysis of reinforced-concrete structures

Idealisation, spans and load patterns

The decisions made before the analysis starts, which affect the answer more than the analysis does.

Lesson review: expert verification remains open

This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.

Checks needed for project use

  • A concrete-design reviewer must check the stated first-generation clauses, National Annex choices, detailing rules and factor sets. Numerical agreement alone does not establish code compliance.
  • The distinction between support-face moments and the Ft/8 reduction has been corrected here. Related beam examples still need checking. Loading-pattern coverage also requires review; the six teaching patterns do not cover every case.

These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.

Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.

Read the lesson register and outstanding review notes

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.

Effective span
leff=ln+a1+a2,ai=min⁡ ⁣(ti2, h2)l_{eff} = l_n + a_1 + a_2, \qquad a_i = \min\!\left(\frac{t_i}{2},\ \frac{h}{2}\right)

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 overestimate gives about a 15% moment overestimate in this simply supported UDL model. Underestimating span gives the opposite error.

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.

    Load path from slab through beam and column to foundationslabbeamcolumnpadload → slab → beam → column → pad → ground
    Every load pattern is a statement about where the imposed load is at one moment. Permanent load never moves; imposed load can be anywhere, and must be assumed to be wherever is worst for the effect being checked.

    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.

    For a monolithic support, assess the moment at its face under the applicable EC2 rule. The separate reduction below applies to a continuous member over a support offering no rotational restraint, with the analysis span measured between support centrelines:

    Support-moment reduction over a rotationally unrestrained support
    MEd,face=MEd,cl−FEd,sup t8M_{Ed,face} = M_{Ed,cl} - \frac{F_{Ed,sup}\, t}{8}

    What it calculates: The design hogging moment, reduced from the centreline value.

    MEd,clM_{Ed,cl}
    Moment from the analysis, at the support centreline (N·mm)
    FEd,supF_{Ed,sup}
    Design support reaction (N)
    t
    Support width (mm)

    This assumes

    • The member is continuous over a support with no rotational restraint, and the analysis uses centre-to-centre spans
    • 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. Apply this reduction only when its support and analysis assumptions are met.

    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 beam is continuous over a 350 mm wide support that offers no rotational restraint. A centre-to-centre span analysis gives a hogging support moment of 180 kNm and reaction of 320 kN. Using the stated Ft/8 reduction, what reduced design support moment is obtained, in kNm?

    Check yourself

    The simplified teaching set contains one all-loaded case, two alternate-span cases and one adjacent-pair case at each internal support of a four-span beam. How many cases are in that set?

    Summary

    • Effective span = clear span + min(t/2, h/2) at each end
    • In the simply supported UDL model, moment scales with span squared; an underestimated span can be unconservative
    • 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