US: Tel: 1-206-279-3300
EU: Tel: +30 6986 007 252

Eurocode 8 aims to ensure the protection of life during a major earthquake simultaneously with the restriction of damages during more frequent earthquakes. The standard allows the receipt of seismic forces either with damping energy (ductile behavior) or without damping energy (elastic behavior). Nevertheless it is distinguished a preference towards the first approach.

Ductility is defined as the ability of the structure or parts of it to sustain large deformations beyond the yield point without breaking. In the field of applied seismic engineering, the ductility is expressed in terms of demand and availability. The ductility demand is the maximum ductility level that the structure can reach during a seismic action, that is a function of both the structure and the earthquake. The available ductility is the maximum ductility that the structure can sustain without damage and it is an ability of the structure. So, a great part of the standard aims to ensure the existence of a stable and trustworthy model of absorbing energy in predefined critical areas that restrict no inertial loading that appears in other parts of the structure. The designing rules achieve to develop the wanted ductility in these critical areas, with the benefits of the reduced no inertial loading, that are received by more strict construction arrangements and designing rules (Elghazouli, 2009). In the case of reinforced concrete structures, this behavior can be achieved only through the reduction of capacity through delay circles from suitable construction arrangements of such critical zones to ensure stable plastic behavior that  it is not undermined by brittle modes of failure such as concrete shearing, concrete crushing, or reinforcement bending.

This leads to the adaptation of three levels of absorbing energy:

• Low (Ductility class low (DCL)) that does not require delayed ductility and the resistanse to seismic loading is achieved through the capacity of the structure (q=1.5).
• Medium (DCM) that allowes high levels of ductility and there are responsive design demands (1.5
• High (DCH) that allowes even higher levels of ductility and there are responsive strict and complicated design demands (q>4).

The Ductility Class Low (DCL) predicts the design of the members with the seismic loading that occurs from the design seismic action (of the 475 years) with a behavior factor of q=1.5 and reinforcement calculations like in the case of usual, non-seismic actions, with some material restrictions (the minimum concrete quality that can be used is C16/20 etc). EC8 suggests that the design with DCL should be limited only in areas with low earthquake activity (i.e. in areas with maximum ground design acceleration less than 0.10g). In areas of medium or high earthquake activity, the buildings designed with DCL are not supposed to be financially efficient. In addition, because of the low ductility, it is likely that they would not have a sufficient security level against an earthquake bigger than the design seismic action.

In the two higher ductility classes (DCM and DCH) the design ensures the existence of a stable and trustworthy model of absorbing energy in predefined critical areas and uses a behavior factor q>1.5. These two ductility classes differ in:

• Geometrical restrictions and materials (steel strain)
• The design loadings
• The rules of capacity design and local ductility

The behavior factor can vary in different horizontal directions of the structure, even if the ductility class is the same in all directions.

These two classes are equivalent regarding the performance of the structure under the design seismic action. The design with DCM is easier to be executed on spot and can have a better result in medium seismic actions. The design with DCH seems to provide higher security levels from DCM against local or total collapse under earthquakes greater than the design seismic action. EC8 does not connect the choice of the two higher ductility classes with the seismic actions of the area or the importance of the structure, nor sets any kind of limit for the use of it. It is up to the state-members to define the different areas and the different structure types, or even better to leave the option of choice to the designer.

If the design forces are calculated according to ductile response demand, then it is necessary to ensure that the structure will fail in a ductile way. This demand is the main idea of the capacity design.

The capacity design contents:

• Ensurance of formation of plastic hinges on the beams and not on the columns.
• Providing of sufficient shear reinforcement (dense steel stirrups).
• Ensurance that the steel objects fail far away from the connection points.
• Avoidence of big structural irregularities.
• Ensurance that the tensile capacity will exceed the shear capacity.

The easiest way to define the ductility is in terms of displacements, as the maximum displacement divided with the displacement during the first yield:

The yield of the structure has as a result the reduction of the maximum load that can be sustained. Usually (as well in EC8) this reduction is being applied through the behavior factor, q:

where

F_el is the maximum strength that would be developed if the system had an elastic response to the seismic action, and F_y is the yield strength of the system.

It is acceptable that, for big periods (>Τ_C, where Τ_C is the upper limit of the period of the constant spectral acceleration branch), yielding and elastic structures are subjected to almost the same displacements. Next, for these structures, the force reduction is equal to the ductility. For lower periods, the force reduction that is achieved for a certain ductility is reduced. EC8 uses the following equations: (EC8 § 5.2.3.4(3))

 

The first of these equations expresses the rule of equal displacements.(Elghazouli, 2009).

Figure 1: Equivalence of ductility and behavior factor,  assuming equal elastic and inelastic displacements (Elghazouli, 2009).