## Ductile walls coupled and uncoupled

The main type of wall according to Section 5 is the ductile wall, designed and detailed to dissipate energy in a flexural plastic hinge only at the base and to remain elastic throughout the rest of its height, in order to promote - or even force - a beam-sway plastic mechanism: for a flexural plastic hinge with high ductility and dissipation capacity to develop at the base, the ductile wall should be fixed there so that relative rotation of its base with respect to the rest of the structural system is prevented. Moreover, the zone just above the base of the ductile wall should be free of openings or large perforations that might jeopardize the ductility of the plastic hinge.

Two or more individual ductile walls connected through - more or less - regularly spaced beams meeting special ductility conditions ('coupling beams') may be considered as a single element termed a 'coupled wall', provided that their connection through the coupling beams reduces by at least 25% the sum of bending moments at the base of the individual walls, compared with the case when they are working separately. It is noted that the total bending moment at the base of a coupled wall is equal to the sum of the base moments of the individual walls plus the couple moment of the axial forces that develop in the individual walls due to the coupling beams. (The shear forces in the string of coupling beams above the base accumulate into axial forces in the individual walls connected by them, positive in one of the walls, negative in the other; the couple moment of these axial forces is the contribution of the coupling beams to the total bending moment of the coupled wall.) Strictly speaking, to check whether an ensemble of walls meets the criteria of a coupled wall, the analysis of the structural system for the horizontal design seismic action should be repeated, with the coupling beams removed from the model. Moreover, if there are several candidate coupled walls in the building, this exercise has to be performed separately for each of them. Conclusions are not expected to change if the characterization of the walls as coupled or not is based on a single analysis of the structural system including the coupling beams and a comparison of the sum of the resulting bending moments at the base of the individual walls to 75% of the total bending moment at the base of the candidate coupled wall (sum of the base moments of the individual walls plus the moment of their axial forces with respect to the centroid of the section of the candidate coupled wall). After all, and notwithstanding the significant enhancement of wall ductility brought about by the coupling, the characterization of the walls as coupled has minor impact on the design. The only practical consequence is linear envelope m for low-rise that the q factor of structural systems in which more than 65% of the seismic base shear is resisted by walls (the wall system, see Section 5.3) is reduced by 10-20%, if more than 50% of the wall resistance is provided by uncoupled rather than by coupled walls.

Because in coupled walls more energy is normally dissipated in the coupling beams than in the plastic hinges at the base of the individual walls, the coupling beams are equally important as these walls, and Section 5 has special dimensioning and detailing provisions for them. (In fact, the couple moment of the axial forces in the individual walls, on which a lower limit of 25% of the total bending moment of the individual walls is placed for the wall to be considered as coupled, is simply the sum of bending moments at the two ends of all coupling beams, transferred from the face of the individual walls to their axes.) No special rules are given for the individual walls, though. Despite their action as a system, these walls are dimensioned in bending and shear as if they were separate. However, the values of the bending moment and the axial force for which the vertical reinforcement is dimensioned do of course reflect the coupling, at least as far as this is captured by the elastic analysis. It should be noted that, because the axial force in the individual walls from the analysis for the design seismic action is large, there is often a large difference between the absolutely maximum and minimum axial forces in the individual walls in the seismic design situation (including the axial force due to gravity loads). As the vertical reinforcement at the base of each individual wall is controlled by the case in which the bending moment from the analysis, MEd0, is combined with the minimum axial compression (or maximum axial tension), the flexural capacity when the maximum axial compression is considered at the base, MRdo, is much larger than MEdo. This has serious repercussions on the design of walls of Ductility Class High (DCH) in shear, as in these walls the capacity design magnification factor e applied to shear forces from the analysis, VEd, depends on the ratio MRdo/MEdo (see equations (D5.17) and (D5.18)). In some cases the value of e may become so high that the verification of the individual walls in shear (especially against failure due to diagonal compression) may be unfeasible. The (up to 30%) redistribution of bending moments MEdo from the individual wall with the low axial compression (or net axial tension) to the one with the high axial compression, as recommended for coupled walls in clause 5.4.2.4(2) of EN 1998-1, may be used to advantage; however, the advantage is limited by the need to redistribute shear forces from the analysis along with the bending moments. So, if the moment acting on the wall together with the low axial compression is reduced to 0.7MEdo and that on the wall with the high axial compression is increased to 1.3MEdo, the flexural capacity will decrease to MRd0 < MRdo, and the magnification factor e, which depends on M^do/1.3MEdo, will decrease even more. The reduced magnification factor will be applied, though, on 1.3FEd, and the benefit to the shear verification will be limited.

The conclusion is that, despite the generally recognized enhancement of seismic performance brought about by coupling the walls, the current provisions in Section 5 do not offer real incentives for the use of coupled walls, especially in buildings of DCH.

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### Responses

• Elsa
What is coupled and uncoupled wall?
4 years ago
• Barbara Gutierrez
What is a coupled walls structural?
7 months ago
• susanna
What is coupled and uncopled plan building?
1 month ago