In the design of reinforced concrete structures, one of the most important decisions is how much reinforcement to place and how to distribute it. It's not just about "adding bars just in case," but about finding a precise balance between concrete, which resists compression, and steel, which handles tension. This balance ensures safety, economy, and above all, predictable and safe structural behavior.
The Role of Deformations: The Pivot Diagram
When a reinforced concrete beam or slab is subjected to bending, its upper fibers compress and the lower ones elongate. In between, there exists a neutral axis where deformation is zero. If we represent the deformations of steel and concrete at different points of the section, we obtain a linear diagram that tells us a lot about how the structure works.
Jiménez Montoya, in his classic book Reinforced Concrete, calls this graph the pivot diagram, because as the neutral axis changes position within the section, the deformation line "rotates" or "pivots" around a fixed point. Each position of the neutral axis represents a different way in which the material responds to the load.
The Five Deformation Domains
I Domain I – Simple Tension
Only the steel works in tension; the concrete is completely cracked. Not used in bending.
II Domain II – Bending with Elastic Steel
The steel begins to deform, but has not yet reached its yield limit. The concrete works without reaching its maximum deformation. This is an intermediate, elastic-plastic state.
III Domain III – Bending with Plasticized Steel
The steel has reached its yield deformation and the concrete is near its maximum deformation (≈3.5‰). This domain is the ideal for design, because failure is ductile: the steel deforms significantly before the concrete breaks, warning of failure. It is the point of maximum utilization of both materials.
IV Domain IV – Bending-Compression
The neutral axis rises so much that part of the steel also enters compression. Failure becomes brittle, as the concrete can crush without warning. Avoided in bending design.
V Domain V – Pure Compression
The entire section is compressed. Corresponds to columns or elements in simple compression.
Why Domain III is the Most Desired
Designing a reinforced concrete section in Domain III means achieving perfect balance: the steel works at maximum capacity (yields) and the concrete reaches its limit without breaking. Failure, if it occurs, is not sudden: the structure gives clear warning signs, such as cracking and visible deformations.
Conversely, if too much steel is placed (high reinforcement ratio), the neutral axis rises, the concrete crushes before the steel yields, and failure is brittle. On the other hand, if too little steel is placed, the element may crack excessively or fail before utilizing the concrete's load-bearing capacity.
The Perfect Balance
That's why the correct dimensioning of reinforcement doesn't depend solely on the bending moment or loads, but on the mechanical reinforcement ratio, which relates the steel area, steel strength, and concrete strength. It is this relationship that determines the working domain of the section.
At the boundary between Domains III and IV, when the concrete reaches its ultimate deformation (3.5‰) and the steel just yields (≈2‰), the neutral axis is located around 0.63·d (d = effective depth). This point marks the perfect balance: neither too much steel, nor too little.
In Summary
Reinforcement design is not an exercise in intuition, but in understanding. Knowing the deformation domains and using the pivot diagram allows us to understand how internal forces are distributed and how materials interact.
Working in Domain III guarantees an efficient, safe structure with predictable behavior, where steel yields before concrete breaks. That is the true essence of reinforced concrete: two materials that, together, compensate for each other's weaknesses to form something stronger than each one separately.