Reinforced Concrete Design / Analysis of reinforced-concrete structures
Moment redistribution
Moving moment away from a congested support — and the rotation you must pay for it.
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.
- Redistribution limits depend on material ductility, design basis and National Annex. The course 0.45 teaching limit must not be confused with balanced depth. Unequal support moments move the maximum positive moment away from midspan.
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 notesWhy this matters
Over the support of a continuous beam the hogging moment is large, the top steel is congested, and the column bars are in the way. Redistribution lets you reduce that moment and push the demand into the span, where there is room. It is one of the most useful tools in concrete design and one of the most misunderstood: it is not free, it is not a modelling convenience, and what it costs is ductility.
By the end of this lesson you should be able to
- Explain redistribution physically, as yielding and rotation
- Say why the span moment must rise when the support moment falls
- Apply the x/d restriction that the amount of redistribution imposes
- Judge when redistribution is worth using
What you should already know
- Ductility and the x/d limit (Module 4)
- Continuous beam analysis (Structural Analysis Fundamentals, Module 16)
- Plastic hinges (Structural Analysis Fundamentals, Module 9)
What actually happens
An elastic analysis says the support moment is, say, 200 kNm and the span moment 120 kNm. Suppose you deliberately provide only enough top steel for 160 kNm.
Load the beam. At about 80% of the design load, the support section reaches its capacity. It does not fail — it yields. The steel is on its plateau, so the section goes on carrying 160 kNm while rotating, like a stiff hinge.
Any further load cannot raise the support moment, so it all goes into the span. The beam behaves from that moment as though it were pinned at the support. When the design load is finally reached, the support is still at 160 kNm and the span has taken the rest.
The structure has redistributed the moment by yielding. It did not need permission, and it will do this whether or not you designed for it.
What the designer chooses is whether to anticipate it — and if you do, you must make sure the section can rotate far enough to complete the process before the concrete crushes.
From first principles
Why redistribution demands a shallow neutral axis
We want to show: To show that the amount of moment you may redistribute is limited by how far the section can rotate, and that this leads directly to a limit on x/d.
Redistribution needs the support section to act as a hinge: to hold its moment while turning through an angle. How far can a concrete section turn before it stops holding that moment? It turns until the concrete in the compression zone crushes. The rotation available is therefore governed by how much the steel can stretch before that happens — and that depends on how deep the compression zone is. A shallow compression zone means the steel is far from the neutral axis, so a given concrete strain corresponds to a large steel strain and a large rotation. A deep compression zone means the opposite: the concrete reaches its crushing strain while the steel has barely gone past yield, and there is almost no rotation available. So ductility and neutral-axis depth are the same statement, and the redistribution limit follows.
Worked example
Redistributing 20% at an interior support
Given
- Interior span of a continuous beam, elastic hogging moment 200 kNm at each support
- Elastic sagging moment at midspan 100 kNm
- Free bending moment wL²/8 = 200 kNm
- Redistribution of 20%, so δ = 0.80
Find
The redistributed moments, and the neutral-axis limit that now applies.
Assumptions
- Class B or C reinforcement
- k₁ = 0.4, k₂ = 1.0 — nationally determined, requiring verification
Practice
A support moment is redistributed by 25%. What is the maximum permitted x/d at that section? Take k₁ = 0.4 and k₂ = 1.0.
Practice
A beam has a free bending moment of 250 kNm and elastic support moments of 150 kNm at each end. After redistributing the supports by 20%, what is the span moment, in kNm?
Practice
For 40% redistribution, what value does (δ − 0.4)/1.0 give for x/d? This is an algebra exercise only: the stated δmin = 0.70 excludes that amount of redistribution.
Check yourself
Which check must still be carried out on the ELASTIC moments, not the redistributed ones?
Summary
- Redistribution happens by the support section yielding and rotating at constant moment
- The free bending moment is unchanged: what leaves the support arrives in the span
- Rotation capacity is set by neutral-axis depth, so δ and x/d are tied together
- x/d ≤ (δ − k₁)/k₂ — redistributing 30% caps x/d at 0.30
- There is a floor on δ: 40% redistribution is arithmetically fine and not permitted
- Serviceability is checked on the ELASTIC moments, because service load causes no yielding