Ductility

“The ductility of steel subjected to tension is its ability to deform under load without breaking, once the yield limit has been exceeded.”

“A ductile structure, when close to collapse, warns of its condition by undergoing significant deformations and substantial cracking.”

“If the structure is brittle, collapse occurs without warning, with small deformations and minimal cracking.”

A long time ago, it was observed that the actual load-bearing capacity of hyperstatic steel elements was much greater than that obtained through calculations based on the principles of linear theory.

It was also observed that, in this type of hyperstatic structures, starting from a certain point and near their collapse, very significant deformations occurred in response to small increases in loads, deviating from the linear behavior theoretically predicted. To explain this response of steel, confirmed in practice and different from what was expected, it was hypothesized that a certain phenomenon of creep or plasticity must occur within the material.

Subsequently, with more in-depth studies of the stress-strain relationships in steel, this non-linear behavior under certain conditions was confirmed. In 1965, Bulletin No. 52 of the CEB was published, outlining the basic principles of non-linear analysis.

Today, this issue has returned to the forefront due to the ability to address certain plastic calculations, thanks to advancements in knowledge on the subject, the capabilities of modern computers, and the inclusion in almost all standards of indirect plastic calculation methods based on stress redistribution criteria obtained through linear analysis. These approaches allow for more economical designs without compromising safety.

Resistance is a characteristic of steels required for calculation and outlined in the EHE Instruction, as steel plays an important role in the mechanical behavior of reinforced concrete. From the strength perspective, the Instruction reflects its requirements on two parameters: the yield strength, whose value is used to designate these types of steels, and the ultimate rupture load.

However, strength is a necessary but not sufficient characteristic for the behavior of steel for reinforced concrete to be adequate, as ductility requirements are also necessary. This is because concrete is a brittle material (it lacks ductility) and cannot be used in structural applications without the participation of steel. This is the reason behind the origin of reinforced concrete, or the combined use of concrete and steel.


GOOD
DUCTILITY
CHARACTERISTICS

WHAT DOES A STEEL
NEED TO HAVE GOOD
PERFORMANCE?

GOOD
STRENGTH
CHARACTERISTICS

The requirement for ductility in the structure, which concrete is unable to provide, must be fulfilled by steel. Therefore, it must have sufficient ductility so that each reinforced concrete section has adequate deformation capacity, and so that the structural elements possess this property.

“A DUCTILE STRUCTURE, WHEN CLOSE TO COLLAPSE, WARNS OF ITS CONDITION BY EXPERIENCING LARGE DEFORMATIONS AND SIGNIFICANT CRACKING.”

“IF THE STRUCTURE IS BRITTLE, COLLAPSE OCCURS WITHOUT WARNING, WITH SMALL DEFORMATIONS AND MINIMAL CRACKING.”

After many studies, it has become clear that the level of ductility of the steel influences and limits the rotation of the plastic spherical plain bearings.

In addition to strength and ductility requirements, reinforced concrete needs bonding characteristics so that concrete and steel can work together and cracking is controlled.

DUCTILITY is, therefore, a highly desirable characteristic of steel for reinforced concrete in all cases and essential in situations involving structures subjected to certain loads (seismic, dynamic, impact, etc.), or where, due to calculation hypotheses, significant stress redistributions are anticipated, or the loads cannot be assessed with the necessary precision, either due to the nature of these actions or the insufficient knowledge of their effects on the structure in question.

In the particular case of a reinforced concrete structure subjected to seismic loads, its behavior is closely related to the ductility of the steel, as in this situation more than any other, the structure’s ability to adapt to exceptional loads of this nature is crucial. In such cases, the elastic phases of the steel are likely exceeded, and the maximum possible energy reserve is required, which is provided by a high ductility of the steel.

Similarly, in the previously mentioned cases where the actions are difficult to quantify, it is desirable to design structures with the capacity to resist, exceptionally, loads that, although they greatly exceed the values used in the calculations, do not cause collapse without reaching significant deformation and cracking.
One of the reasons that exemplify the need for ductility is the possibility of redistributing moments in continuous bending elements such as beams and slabs, which allows for better utilization of concrete and steel, as the most stressed areas are able to transfer the load to adjacent, less stressed areas.
Moment redistribution means the ability to transfer negative moments to positive moments, or vice versa, and is addressed in the Structural Concrete Code EHE and in most codes (ACI, Eurocode 2, Model Code, etc).
Significant redistributions can only be achieved if the steel has high ductility.

The behavior of steels is characterized by their stress-strain diagram corresponding to the tensile test, in which the variations in deformation are shown as a function of load increments.

If a typical stress-strain curve of a steel is analyzed, two behaviors can be observed:

Elastic phase:

Deformations are proportional to the applied loads (straight branch) until the yield point is reached. The deformations are recoverable if the load is removed.

Plastic phase:

Once the yield point is exceeded, deformations are no longer proportional to the loads, with deformations increasing more rapidly than in the elastic phase, until reaching the maximum load value (curved branch). Most of the deformations are permanent, meaning they are not recoverable (only elastic deformation is recoverable). From this point, deformation continues with very small load increments until the specimen fractures.

During the course of the test, the initial section of the specimen decreases until it reaches the minimum at the point of fracture (necking).

In hot-rolled steels, the identification of the yield point on the diagram is very clear due to the presence of the “yield plateau,” which is a nearly horizontal section that marks the transition between elastic and plastic behavior.

STRESS-STRAIN DIAGRAM OF A HOT-ROLLED STEEL (B500SD).

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In contrast, the stress-strain diagrams of cold-rolled steels (drawn) lack this plateau, which prevents the direct determination of the yield point.


STRESS-STRAIN GRAPH OF A COLD-ROLLED STEEL (B500T).

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For this reason, the EHE Instruction considers a conventional yield point corresponding to the stress value that produces a permanent strain of 0.2%. Its determination on the diagram is made by drawing a parallel line to the elastic branch from this deformation value, and the intersection point of this line with the curve will have the corresponding stress value as the yield point.

Traditionally, the ductility of steel has been defined by two parameters obtained from the aforementioned stress-strain curve, which are outlined in the EHE Instruction:

1) Fracture stress-to-yield stress ratio (fs/fy)

It is a parameter that relates the collapse stress of the steel, which is usually the fracture or maximum stress (fs), with the stress corresponding to the limit of the actual elastic behavior, with the most commonly used being the yield stress of the steel (fy).

This parameter indicates the strength reserve of the steel once its plasticization has begun, and is sometimes referred to as work hardening.


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2) Fracture elongation (in %) based on 5 diameters (A5)

Traditionally, this is the parameter that indicates the deformation capacity of the steel and, until now, was adopted as the elongation after fracture measured over an initial specimen length equal to 5 ø. In other standards, the reference base is 10 ø.

The way to determine the value of the A5 parameter is:


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Once the tensile test of the steel has been performed and after fracture is reached, the two pieces of the specimen are joined together to measure the elongation experienced, considering the fracture area within the measurement.


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Currently, another deformation parameter alternative to A5 is used to define ductility, which is not included in the EHE Instruction but is present in multiple standards and codes (Eurocode, Model Code, etc.). It is called ε max (or ε u) and in steel terminology, “AGT.”


DETERMINATION OF AGT ON THE GRAPH

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It is defined as “ε max” or “AGT“, the uniform elongation experienced under maximum load, or the strain as a percentage corresponding to the maximum stress (fs), on the σ – ε diagram.

It is measured on the stress-strain graph by drawing a horizontal tangent to the curve. The point obtained has the maximum stress (fs) as the ordinate and the “AGT” value as the abscissa.

Thus, both the Eurocode and our EHE Instruction require minimum values for both parameters (fs / fy and ε max; fs / fy and A5, respectively) that must be verified simultaneously.

Currently, there is ongoing research to quantify ductility using a single parameter that allows the grading of steels based on this characteristic and the introduction of the concept of steels with equivalent ductility.


STRESS-STRAIN GRAPH OF THE “PLASTIC ENERGY FACTOR” OF A HOT-ROLLED STEEL.

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This area or “plastic energy factor” represents the remaining strength and deformation of the material after reaching its yield point, and therefore, it is a measure of the energy available once the material has plastified.

Ductility – Cold Drawing vs. Rolling

The limited ductility of concrete led it to be considered from the beginning as the limiting factor for plastic rotations. Until relatively recently, it was believed that the capacity for plastic rotation was independent of the type of steel used, as it was assumed that only the concrete limited it, and sufficient ductility was attributed to the steel so that it did not limit these rotations.

The explanation for this fact may be that, in the past, the steels used were of low strength and had very high ductility characteristics due to their chemical composition and manufacturing process. Later, other steels with much lower ductility and higher strengths were introduced, such as the so-called cold-drawn or cold-rolled steels, type “T”.

In this graph, it can be observed that as the cold deformation work increases, the yield strength increases dramatically at the expense of the deformation capacity, a circumstance that is evident from the reduced width of the curve. Furthermore, the behavior of the steel, described by the shape of the curve, also changes.

CORRUGATED WIRES:

Material obtained from a smooth product that has been hot-rolled (wire rod), whose geometric and mechanical characteristics are achieved through a second cold rolling process (drawing).


WIRE ROD
SMOOTH
ø 14 mm
Re = 380 MPa

WIRE ROD
CORRUGATED
ø 12 mm
Re = 520 MPs
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Didactic walk

Didactic




“THE DUCTILITY OF A STEEL SUBJECTED TO TENSION IS THE CAPACITY TO DEFORM UNDER LOAD WITHOUT BREAKING, ONCE THE ELASTIC LIMIT IS EXCEEDED.”


“A DUCTILE STRUCTURE, WHEN CLOSE TO COLLAPSE, ALERTS TO ITS SITUATION BY EXPERIENCING LARGE DEFORMATIONS AND SIGNIFICANT CRACKING.”
“IF THE STRUCTURE IS BRITTLE, COLLAPSE OCCURS WITHOUT PRIOR WARNING, WITH SMALL DEFORMATIONS AND REDUCED CRACKING.”

What is ductility?

Every reinforced concrete element, for example, a beam, is made up of two materials:


CONCRETE AND STEEL REINFORCEMENTS

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If we make the beam out of concrete without reinforcements (without bars), support it at both ends and at its center, and load it successively with weights on both sides, it may happen that:

  • When placing the first weight, the beam will deform slightly.
  • When placing the first weight, the beam will deform slightly.
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This happens because concrete is a brittle material; it lacks ductility.


BRITTLE = NOT DUCTILE


On the other hand, if we add steel bars to the concrete beam and proceed in the same way as in the previous case, the result would be as follows:

  • When placing weight 1, the beam deforms slightly.
  • When placing weight 2, the beam continues to deform.
  • When placing weight 3, the beam deforms a little more and small cracks appear.
  • When placing weight 4, the beam deforms further and larger cracks appear.
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In general, the beam will be more ductile the more ductile the steel is.

Advantages

In the event that we found ourselves in any of the following situations, we would certainly prefer the building to deform, even if it rendered it unusable, rather than collapse suddenly without the possibility of timely evacuation.

  • Seismic actions.
  • Acting with loads higher than those anticipated, such as:
    • For placing shelves with heavy loads in areas of floors designed for residential loads.
    • For the entry of heavy vehicles (trucks) into underground parking lots designed for cars.
    • Due to the flooding of a slab or rooftop.
    • Due to the foundation failure caused by nearby construction works, water leakage problems, etc.

“A ductile structure, when it is close to collapse, warns of its situation by experiencing large deformations and significant cracking.”

“If the structure is fragile, collapse occurs without warning, with small deformations and reduced cracking.”

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Parameters

So far we have seen what is required for a reinforced concrete beam to be ductile, then we will see that there are steels that have almost no ductility and, on the other hand, others are very ductile.

The behavior of a steel is defined by the stress–strain curve corresponding to the tensile test. To obtain it, a sample of a steel bar is taken and both ends are clamped by means of grips. The bar is then stretched at one end. As the bar is stretched, it lengthens. If we note the elongation that the bar undergoes for each force we apply, we obtain the stress–strain curve of that steel.

Broadly speaking, there are two types of stress-strain curves depending on whether the steel is cold-rolled, type “T” (brittle steel) or hot-rolled, types “S” and “SD” (ductile steels).

The parameters that define the degree of ductility of a steel are:

  • The yield stress to yield strength ratio, (fs / fy).
  • The elongation at break based on 5 diameters, A5. There is now an alternative deformation parameter to A5 for defining ductility, and it is called “AGT”. AGT” is defined as the uniform elongation reached under maximum load.

The Structural Concrete Instruction (EHE) requires minimum values of these parameters to be met simultaneously for each type of steel.

The higher the ratio (fs / fy) and the A5 (or “AGT”), the higher the ductility of the steel.

Ductility – Cold Drawn vs. Hot Rolled

Stress-strain curve of a cold-rolled steel. Type “T”.

  1. Elastic branch (Linear) . Al principio del ensayo cuando aplicamos una fuerza F1 la barra se alarga una longitud “l1“, si aplicamos el doble de fuerza F2=2 x F1, labarra se alarga el doble l2 = 2 x l1.

    Moreover, if we stop applying the force, the bar returns to its original length. This elastic behavior is reflected in this section of the curve until the yield limit (fy) of the steel is reached.

  2. Non-elastic branch. (Curve) . Una vez sobrepasamos el límite elástico, la deformación continúa para incrementos de carga muy pequeños hasta que se alcanza la tensión de rotura o carga máxima (fs), carga bajo la cual se produce la rotura de la probeta. Si dejamos de aplicar la carga sólo se recupera la deformación elástica. Durante el transcurso del ensayo, la sección inicial de la probeta disminuye hasta alcanzar la mínima sección cuando rompe.
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In a cold-rolled steel, the yield strength is difficult to visualize because it is very close to the breaking load.

The ratio (fs / fy) and the “AGT” are very small.

Tension-strain curve of a hot-rolled steel. Types “S” and “SD”.

The tension-strain curve of a hot-rolled steel has an elastic phase very similar to that of a cold-rolled steel, but the fundamental difference between both behaviors becomes evident once the yield strength is exceeded.

In this case, once the yield strength is reached, a deformation occurs that marks the transition between elastic and plastic behavior, which is represented in the curve by the “yield plateau.” Thus, the yield strength is clearly defined, unlike the previous case. From this point onward, for small increments in load, the deformation continues and is much greater than that experienced by a cold-rolled steel.

The parameters of ductility:

The ratio (fs / fy) and the “AGT” are much higher than those of a cold-rolled steel.

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Fatigue and cyclic loads

A load, always tensile, with a value lower than the steel’s yield strength can cause it to break if applied repeatedly. This phenomenon is known as fatigue.

This would be the case of the effect produced by significant moving loads, such as railways, crane bridges, etc.

Therefore, the new EHE Instruction requires that steels withstand 2,000,000 load cycles under specific conditions outlined in its provisions.


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Now we refer to those cases where the stresses in the steel repeatedly transition from tension to compression.

The behavior that steel experiences under this type of load, such as those caused by earthquakes, is very different from that of fatigue.

The alternation of tension and compression in the reinforcement produces a destructive effect on the steel that is much greater than that generated by fatigue.


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