Figure from:Static pushover versus dynamic collapse analysis of RC buildings

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Fig. 14. Differences between the three lateral load patterns. Despite the fact that all load shapes do not represent the actual distribution of relative inertia forces during the dynamic analysis, almost an identical response is observed in the first group of buildings between the dynamic analysis best-fit envelopes and the static response obtained from the triangular and the multimo- dal distributions. On the other hand, the uniform load overestimates the initial stiffness and the maximum base shear in the four buildings. Table 6 illustrates graphically the differences between the results of the static pushover analysis for the triangular and the uniform load patterns on one side, and the incremental dynamic analysis (average for eight records) on the other, at global col- lapse limit state. Since the triangular load shape is simple and show very close results with the multimodal load pattern, it was decided to exclude the latter from this comparison. It is clear that the uniformly distributed load is unconservative in predicting collapse limit states (underestimates the drift and overestimates the strength). The overall prediction of collapse using the triangular load is significantly better. Although it slightly under- In contrast to the first group of buildings, the results of the static pushover of the 12-storey group, illustrated in Fig. 12, show discrepancies with the dynamic response envelope in the post-elastic range. While the static pushover results of the triangular and the multimo- dal load pattem show a good agreement with the dynamic results best fit in the elastic range, both give a conservative prediction of the maximum lateral strength, as also shown in Table 6 for the triangular load. How- ever, in the four buildings the triangular load response is higher than the lower limit envelopes obtained from dynamic analyses employing natural and artificial rec- ords. On the other hand, the capacity curve obtained from the uniformly distributed load overestimates the response in the elastic range. However, it gives better prediction of the ultimate strength. It is also clear from Fig. 12 that the triangular load shape gives good predic- tion of the deformation at collapse, while the uniform load underestimates the collapse limit state in the four buildings. It is concluded for this group of buildings that the triangular distribution is again the most suitable load pattern given that the uniform load, which is rec- — Figure 14 Differences between the three lateral load patterns. Despite the fact that all load shapes do not represent the actual distribution of relative inertia forces during the dynamic analysis, almost an identical response is observed in the first group of buildings between the dynamic analysis best-fit envelopes and the static response obtained from the triangular and the multimo- dal distributions. On the other hand, the uniform load overestimates the initial stiffness and the maximum base shear in the four buildings. Table 6 illustrates graphically the differences between the results of the static pushover analysis for the triangular and the uniform load patterns on one side, and the incremental dynamic analysis (average for eight records) on the other, at global col- lapse limit state. Since the triangular load shape is simple and show very close results with the multimodal load pattern, it was decided to exclude the latter from this comparison. It is clear that the uniformly distributed load is unconservative in predicting collapse limit states (underestimates the drift and overestimates the strength). The overall prediction of collapse using the triangular load is significantly better. Although it slightly under- In contrast to the first group of buildings, the results of the static pushover of the 12-storey group, illustrated in Fig. 12, show discrepancies with the dynamic response envelope in the post-elastic range. While the static pushover results of the triangular and the multimo- dal load pattem show a good agreement with the dynamic results best fit in the elastic range, both give a conservative prediction of the maximum lateral strength, as also shown in Table 6 for the triangular load. How- ever, in the four buildings the triangular load response is higher than the lower limit envelopes obtained from dynamic analyses employing natural and artificial rec- ords. On the other hand, the capacity curve obtained from the uniformly distributed load overestimates the response in the elastic range. However, it gives better prediction of the ultimate strength. It is also clear from Fig. 12 that the triangular load shape gives good predic- tion of the deformation at collapse, while the uniform load underestimates the collapse limit state in the four buildings. It is concluded for this group of buildings that the triangular distribution is again the most suitable load pattern given that the uniform load, which is rec-

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Fig. 1. Plane and cross sectional elevation of the buildings: (a) 8-storey irregular frame buildings; (b) 12-storey regular frame buildings; (c) 8- storey regular frame-wall buildings.

Definition of the structural systems under analysis Table il

Fig. 2. The overlay technique considered and description of the beam-column joint modelling. Reinforced concrete column-section and T-section are utilised for modelling of columns and beams, respect- ively. Both sections, taken from ADAPTIC library, allow the geometrical definition of the section as well as that of the confined concrete region within it. Taking into account the available cross sections in ADAPTIC library, a reasonable approximation is made to replace the original U-shaped section of the core of the frame- wall structures by a T-section, with the same stiffness properties. The approximation may be justified in the light of the two-dimensional modelling which neglects torsion and the regularity of the structure both in terms of stiffness and strength. Reinforcement patterns are varied for each section as a function of stirrup spacing in accordance with those specified in the design. Con- finement factors are evaluated as described in Eurocode 8, and varied along the member length according to the arrangement of transverse reinforcements. The effective slab width participating in beam deformation is taken as The structural mesh utilises three elements for beam- column members, the lengths of which are determined on the basis of the critical member lengths. These lengths are determined according to EC8 provisions for different ductility classes. The ends of horizontal elements within the beam-column joints are considered rigid. Consequently, two elements are added to each beam at its extremities. Furthermore, shear spring con- nection elements are introduced to represent the shear stiffness of the beam-column connection. To simplify calculations of the shear stiffness of the joint, the force- deformation relationship for both concrete and steel reinforcement within the joint is assumed to be linear elastic. Despite the simplicity of the joint modelling, glo- bal structural response obtained have been extensively compared and checked with analyses performed by Sal- vitti and Elnashai [17] and Panagiotakos and Fardis [18]. These show a good conceptual agreement with the cur- rent modelling results since the drift values are on the whole higher than the values by Salvitti and Elnashai [17] where no provision for beam-column connection behaviour was made. For the sake of brevity, only some results of the comparison are shown in Fig. 3. The results of the current study, for two of the 12-storey frame

Fig. 3. Verification of modelling assumptions (a) RF-H030 building and (b) RF-L015 building (average for four artificial accelerograms)

Fig. 4. Acceleration spectra for the artificial accelerograms (5% damping).

Earthquake IF-buildings RF-buildings FW-buildings Average

Characteristics of records used in analysis Table 2

Fig. 5. Elastic spectra for the long. component of the natural records (5% damping).

Fig. 6. Dynamic collapse analysis results for the irregular frame structures.

Fig. 7. Dynamic collapse analysis results for the regular frame structures.

Observed response at global collapse for the eight records @ Location where interstorey drift collapse criterion is observed for the eight ground motions. Table 4

Fig. 8. Dynamic collapse analysis results for the frame-wall structures.

Fig. 9. Elastic and inelastic (at the design and twice the design ground acceleration) predominant response periods of the buildings — average for the eight seismic actions.

Fig. 10. Fourier amplitude spectra for the input accelerograms (scaled to 0.30 g) and the average inelastic period of the buildings

Fig. 11. Static and dynamic pushover analysis results for the irregular frame structures.

Fig. 12. Static and dynamic pushover analysis results for the regular frame structures.

Results at global collapse limit state for the three load patterns

Fig. 13. Static and dynamic pushover analysis results for the frame-wall structures.

Differences between static and dynamic pushover analysis at global collapse limit state Table 6 ever wall response) the amplification of the base shear during the dynamic analysis is difficult to predict by pushover analysis. However, the triangular load profile shows good correlation in the elastic range, conservative predictions of the ultimate strength and reasonable esti- mations of the collapse limit state (underestimates the drift by about 8%). Hence, it may be employed for esti- mating the seismic capacity and collapse limit state.