Ductility:
The ability of a structure to deform plastically under load without fracture yet still fulfill a load carrying function. Example when considering dynamic loads, the energy absorbed during deformation becomes an important resistance characteristic. It is also generally accepted that the more ductile a structural form is the more robust it is.
It is relevant at component level and at structural system level. It is advantageous under static loading but is also key to structural response under dynamic loading, in which case it is linked with energy absorption.
In the absence of buckling, beams are robust under vertical load if they have strong connections and if they exhibit ductility. This is assured by codified rules.
Ductility is a sound attribute to have and achieving it is partly a matter of design and partly a matter of detailing. Without ductility, structures would be vulnerable to brittle failure and we could not rely on procedures such as slab yield line analysis or plastic design. At a simple level, ductility allows constant shear to be carried as in a real hinge and a sound objective of steelwork detailing is to allow shear connections to deform yet still carry normal loading even under working conditions.
Ductility at structural system level is implicitly linked with energy absorption capability. The details and the ductility of the structure and the type of connections will impact on the ability of a building to resist collapse during both the heating and the cooling phases.
Robustness is achieved by making the structure strong yet ductile with ductility having an importance comparable to strength. Joints are crucial to robust performance. Where reliance is placed on a single joint, special care is required.
Ties provide adequately robust structures preventing disproportionate collapse in real events. Tie effectiveness is probably limited by element ductility or more likely joint capacity/ductility. Whichever approach is adopted, the robustness of the structure will be improved by careful detailing to assure ductility and energy absorption and the other attributes.
Tie ductility can be improved by using higher ductility reinforcement, e.g. Class B or C. The maximum spacing of internal transverse ties is 1.5lr where lr is the greater spacing between columns. However, it is generally beneficial to adopt a lower spacing indeed the requirement for these ties to interact with column ties means that a practical maximum is the column spacing.
Minimum percentage of reinforcement in columns assures a minimal tensile capacity for what are supposedly compression members. Minimum link requirements in columns are defined to give a certain level of ductility at the column/floor connection. Connection detailing should be such that ductility is in-built so that inherent assumptions about load re-distribution can be realised.
It will be found that the concepts of ductility, energy absorption and rotational capacity and how these are achieved by design and detailing underlie many advanced studies of structural robustness.
The practice of adopting minimum sizes and minimum slenderness ratios assures a certain amount of construction robustness and many material codes give some guidance over minimum member sizes, minimum amounts of reinforcement, minimum connection capacities, minimum bearing lengths and so on.
Structural continuity and redundancy:
Structural engineering should never become a totally mathematical exercise. The real strength of structures is a function of their theoretical design, the quality of detailing and the quality of construction. There are uncertainties in each of those stages.
Redundancy means the structure has more load paths than it strictly needs robustness there is a second level of redundancy or spare capacity that can be exploited.
Ductility is a sound quality for a structure to have if it is to be robust. Most codes assure a level of useful ductility at component level by imposition of detailing rules. Structural ductility allows parts to deform yet still carry load it allows overloaded parts of the structure to yield and redistribute stress.
Catenary action which is a fundamental assumption of some survival strategies relies on the ability of connections and joints to deform without fracture and for example, reinforcing bars to elongate without fracture.
In routine design such ductility is not explicitly evaluated instead achievement has to be assured by good detailing which means using proven detailing techniques normally as recommended by relevant trade organisations.
The Building regulations and codified methods of imparting robustness implicitly rely on a level of ductility within the structure. Reinforcing bars to elongate without fracture. In routine design, such ductility is not explicitly evaluated instead achievement has to be assured by good detailing which means using proven detailing techniques normally as recommended by relevant trade organizations.
In general for routine building work it is not necessary to make any explicit calculations on ductility. Explicit calculations are used in seismic design and in blast resistant design for which specific detailing methods that assure high ductility in the context of system failure can be found in text books and codes.
With regard to fire safety:
The details and the ductility of the structure and the type of connections will impact on the ability of a building to resist collapse during both the heating and the cooling phases.
4.8 Methods of introducing ductility into RC structures
Displacement ductility:
It is essential that an earthquake resistant structure should be capable of deforming in a ductile manner when subjected to lateral loads in several cycles in the inelastic range. Let us take a single degree of freedom oscillator as shown in figure. In the elastic response, the oscillator has the maximum response at a. The area oab represents the potential energy stored when maximum deflection occurs. The energy is converted into kinetic energy when the mass returns to zero position. Figure shows the oscillator forming a plastic hinge at a much lower response when the deflection response continues along cd, d being the maximum response. The potential energy at the maximum response is now represented by the area ocde. When the mass returns to zero position, the part of the potential energy converted to kinetic energy is represented by fde, while the other energy under the area ocdf is dissipated by the plastic hinge by being transferred into heat and other forms of energy, which are irrecoverable.
It is thus evident that elastically the full potential energy is returned to kinetic energy, while elastoplastically a part of the energy is converted into kinetic energy. Hence, the potential energy stored in the elastoplastic structure may not be equal to that in elastic structure and the maximum deflection of the elastoplastic structure may not be equal to that of elastic structure.
The displacement ductility factor μ a measure of ductility of a structure is defined as the ratio of Δu, and Δy, where Δu, and Δy are the respective lateral deflections at the end of post elastic range and when the yield is first reached.
Thus, we have μ (with respect to displacement) = Δu / Δy
The values of displacement ductility factor should range from 3 to 5.
Elastic response
Elasto plastic response
Equal maximum deflection response Equal maximum potential energy response
Curvature ductility:
The curvature ductility factor μ is defined as the ratio of φu and φy, where φu and φy are the respective curvatures at the end of post elastic range and at the first yield point of tension steel as stipulated. Thus we have μ (with respect to curvature) = φu / φy. It should be noted that the curvature ductility factor is significantly different from the displacement ductility factor. At the start of yielding in a frame, the deformations concentrate at the positions of plastic hinge. Therefore when a frame is deflected laterally in the post elastic range then φu / φy ratio in a plastic hinge may be greater than Δu / Δy ratio.
Rotational ductility:
In a similar manner, the rotational ductility factor μ is defined as the ratio of θu and θy, where θu and θy are the respective rotations of at the end of post elastic range and at the first yield point of tension steel. Thus, we have μ (with respect to rotation) = θu / θy.Thus there are three methods of defining the ductility.
In general it can be stated that the ductility is the ratio of absolute maximum deformation at the end of post elastic range to the yield deformation. Accordingly the ductility can be defined with respect to strain, rotation, curvature or deflection. Rotation and curvature based ductility factors take into account shape and size of the member.