In building structures designed for energy dissipation and ductility, the value of the behaviour Clause 5.2.2.2 factor q, by which the elastic spectrum used in linear analysis is reduced, depends on the type of lateral-force-resisting system and on the ductility class selected for the design. As we will see in Section 5.6.3.2 the value of the q factor is linked, directly or indirectly, to the local ductility demands in members and hence to the corresponding detailing requirements.
As in DCL buildings, overstrength of materials and elements is presumed to correspond to a q factor of 1.5, already built into the q factor values given for buildings of DCM or DCH. In addition, overstrength of the structural system due to redundancy is explicitly included in the q factor, through the ratio ajav This is the ratio of the seismic action that causes development of a full plastic mechanism to the seismic action at the formation of the first plastic hinge in the system - both in the presence of the gravity loads considered to act simultaneously with the seismic action. If ax is considered as a multiplicative factor on seismic action effects from the elastic analysis for the design seismic action, the value of a1 may be computed as the lower value over all member ends in the structure of the ratio (MRd - My)IMv_, where Mm is the design value of the moment capacity at the member end and Me and Mv are the bending moments there from the elastic analysis for the design seismic action and for the gravity loads included in the load combination of the seismic design situation. The value of au may be found as the ratio of the base shear on development of a full plastic mechanism according to a pushover analysis to the base shear due to the design seismic action (Fig. 5.2). Gravity loads considered to act simultaneously with the seismic action should be maintained constant in the pushover analysis, while lateral forces increase. For consistency with the calculation of av the moment capacities at member ends in the pushover analysis should be the design values, MRd. If the mean values of moment capacities are used instead, as customary in pushover analysis, the same values should also be used for the calculation of av
In most cases the designer will not consider it worthwhile performing iterations of pushover analyses and design based on elastic analysis, just for the sake of computing the ratio au/a1 that may enter into the determination of the q factor. For this reason, Section 5 gives default values of this ratio. For buildings regular in plan, the default values are:
• ajo-i = 1.0 for wall systems with just two uncoupled walls per horizontal direction
8 ajcti = 1.1 for (1) one-storey frame or frame-equivalent dual systems and (2) for wall systems with more than two uncoupled walls per direction
• ajax = 1.2 for (1) one-bay multi-storey frame or frame-equivalent dual systems, (2) wall-equivalent dual systems and (3) coupled-wall systems
9 olJo-x = 1.3 for multi-storey multi-bay frame or frame-equivalent dual systems.
In buildings which are not regular in plan, the default value of ajax is the average of (1) 1.0 and (2) the default values given above for buildings regular in plan.
Values higher than the default ones may be used for ajax up to a maximum of 1.5, provided that the higher value is confirmed through a pushover analysis, after design with the resulting q factor.
For concrete buildings regular in elevation, Section 5 specifies the values of the q factor given in Table 5.1.
Inverted-pendulum systems are assigned very low q factors: the value for DCM does not exceed that considered available due to overstrength alone without any design for ductility. The low q factor values are due to concerns for potentially large P—A effects or overturning moments and reduced redundancy. In view of the q factors of 3.5 for bridges with concrete (single-)piers and more than 50% of the mass at the level of the deck, inverted-pendulum buildings may seem unduly penalized. For this reason, Section 5 allows the value of q0 of inverted-pendulum systems to be increased, provided that it is shown that a correspondingly higher energy dissipation is ensured in the critical regions.
The values of q in Table 5.1 are called basic values, q0, of the q factor. They are the ones to be used for the estimation of the curvature ductility demands and for the detailing of the 'critical regions' of elements (see equations (D5.ll) in Section 5.6.3.2). For the purposes of calculation of seismic action effects from linear analysis, the value of q may be reduced with respect to q0 as follows:
Fig. 5.2. Definition of factors au and a, on the basis of base shear versus top displacement diagram from pushover analysis (Vb is the base shear and Vbd is the design base shear)
Lateral-load-resisting structural system |
DCM |
DCH |
Inverted-pendulum system |
1.5 |
2 |
Torsionally flexible structural system |
2 |
3 |
Uncoupled-wall system, not belonging in one of the two categories above |
3 |
4 ajat |
Any structural system other than the above |
3 ajai |
4.5 ajal |
• In buildings which are irregular in elevation, the q factor value is reduced by 20%.
• In wall, wall-equivalent dual or torsionally flexible systems, the value of q is the basic value qa (reduced by 20% in the presence of irregularity in elevation) multiplied by a factor which assumes values between 0.5 and 1 and is otherwise equal to (1 + a0)/3, where a0 is the (mean) aspect ratio of the walls in the system (sum of wall heights, hvll, divided by the sum of wall cross-sectional lengths, /w). This factor reflects the adverse effect of a low shear span ratio on the ductility of walls. It is equal to 1 if a0 is at least equal to 2, and equal to 0.5 when a0 is less than 0.5. Given that in walls with such a low aspect ratio the shear span (moment-to-shear ratio at the base) is about equal to two-thirds of the wall height /iw, the (1 + a0)/3 factor is less than 1.0 when the mean shear span ratio of the walls in the system is less than 1.33; these are really squat walls with not so ductile behaviour.
Regardless of the above reductions of q, DCM and DCH buildings are permitted a final q factor value of at least 1.5, which is considered to be always available owing to overstrength alone.
Systems of large lightly reinforced walls can only belong to DCM. Therefore, the basic value of their q factor is 3 (or 2, if there is only one large wall in the horizontal direction of interest) to be multiplied by (1 + a0)/3 if the mean aspect ratio of their walls, a0, is less than 2. Normally, such systems are not irregular in elevation, so their q factor is not reduced any further.
A building which is not characterized as an inverted-pendulum system or as torsionally flexible may have different q factors in the two main horizontal directions, depending on the structural system and its vertical regularity classification in these two directions, but not due to the ductility class, which should be chosen to be the same for the whole building.
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