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EVALUATION OF CONVENTIONAL AND ADAPTIVE PUSHOVERANALYSIS II: COMPARATIVE RESULTSVassilis K. Papanikolaoua; Amr S. Elnashaib; Juan F. Parejac

a Laboratory of Reinforced Concrete and Masonry Structures, Civil Engineering Department, AristotleUniversity of Thessaloniki, Thessaloniki, Greece b Willet Professor, Director Mid-America EarthquakeCenter University of Illinois, Urbana, Illinois, USA c University of Illinois, Urbana, Illinois, USA

To cite this Article Papanikolaou, Vassilis K. , Elnashai, Amr S. and Pareja, Juan F.(2006) 'EVALUATION OFCONVENTIONAL AND ADAPTIVE PUSHOVER ANALYSIS II: COMPARATIVE RESULTS', Journal of EarthquakeEngineering, 10: 1, 127 — 151To link to this Article: DOI: 10.1080/13632460609350590URL: http://dx.doi.org/10.1080/13632460609350590

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EVALUATION OF CONVENTIONAL AND ADAPTIVE PUSHOVER ANALYSIS 11: COMPARATIVE RESULTS

VASSILIS K. PAPANIKOLAOU

Labomtory of Reinforced Concrete and Masonm Structures Civil Engineering Department, Arlstotle University of Thessaloniki

P.O. Box 482, Thessaloniki, 54124, Greece

AMR S. ELNASHAI

Willet Professor, Director Mad-Amerlca Earthquake Center University of Zllinois, 205 N w t h Mathews

Urbana, Illinoas, 61 801, USA

JUAN ,F. PAREJA

University of Illinois, 205 North Mathews, Urbana, Illinois, 61 801, USA

Received 20 December 2004 Reviewed 24 June 2005 Accepted 3 August 2005

In this the methodology for evaluation of conventional and adaptive pushover analysis presented in a companion paper is applied to a set of eight different reinforced concrete buildings, covering various levels of irregularity in plan and elevation, structural ductility and directional effects. An extensive series of pushover analysis results, monitored on various levels is presented and compared to inelastic dynamic analysis under various strong motion records, using a new quantitative measure. It is concluded that advanced (adaptive) pushover analysis often gives results superior to those from conventional pushover. However, the consistency of the improvement is unreliable. It is also emphasised that global response parameter comparisons often give an incomplete and sometimes even misleading impression of the performance.

Keywords: Pushover analysis; incremental dynamic analysis; seismic assessment.

1. In t roduct ion

During the last few years, the significant increase in the use of inelastic static (pushover) analysis as a more realistic means of assessing the deformational state in structures subjected to strong ground motion (compared to simple linear or equivalent linear analysis still applying in a design office environment), has resulted not only in the inclusion of static inelastic methods in official assessment guidance notes and modern design codes, but also in boosting research towards the develop ment of more advanced pushover procedures. These procedures are mainly focused to capture, at a much lower computational cost, the dynamic characteristics of inelastic dynamic analysis. The latter is deemed to be the most accurate but still a numerically expensive method. These dynamic characteristics include higher mode

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128 V. K. Papanikolaou, A . S. Elnashai 8 J . F . Paeja

effects [Paret et al., 1996; Sasaki et d., 1998; Moghadarn and Tso, 2002; Chopra and Goel, 20021 and variation of the modal properties during the inelastic process by applying the so-called adaptive pushover procedures [Bracci et al., 1997; Lefort, 2000; Gupta and Kumath, 2000; Papanikolaou, 2000; Albanesi et al., 2002; Antoniou, 2003; Antoniou and Pinho, 20041. Nevertheless, previous research, with few exceptions, has focused only on development of advanced pushover techniques without assessing their performance comprehensively.

For this reason, a general methodology for the evaluation of conventional and adaptive pushover methods was suggested in a companion paper [Papanikolaou and Elnashai, 20051. The basis of this evaluation procedure is a percentile measure, namely Capacity Curve Discrepancy Factor (CCDF), which quantifies the difference between the response derived from pushover analysis and a reference response emanating from inelastic incremental dynamic analysis [Mwafy and Elnashai, 2001; Vamvatsikos and Cornell, 20021. This comparison is performed on various structural levels, namely global, storey (first and middle) and section levels (Fig. 1).

Eight different structural systems covering various degrees of irregularity, structural ductility and directional effects were analysed using conventional pushover,

Conventional and Adaptive CCDF Calculation Incremental Dynamic Analysis Pushover

m.

Global Level Storey Level Section Level

Global Level Results Storey Levei Results Section Level Results

Fig. 1. Outline of the suggested methodology.


Evaluation of Conventional and Adaptive Pushover Analysis II: Comparative Results 129

adaptive pushover and inelastic dynamic analysis, under four different strong motion records in terms of origin and frequency content. Structural and strong motion characteristics have already been described in detail in the companion paper. The analysis results presented in the subsequent sections are expected to answer, at least in part, the critical question of whether pushover analysis of various levels of complexity is capable of replacing dynamic analysis as a reliable assessment and design tool and therefore, what are the limits of applicabiIity of conventional and adaptive pushover methods in terms of structural and input motion characteristics.

2. Analysis Resul t s

This section presents an extensive review of the obtained results for each of the eight analysed structures. A complete presentation of all results can be found in Papanikolaou et al. [2005]. All analyses were performed using the finite element package ZEUS-NL [Elnashai et aL, 2002-20051, which is the analysis and simulation platform of the Mid-America Earthquake Center.

2.1. Regular structures

Figure 2 summarises the percentile difference (CCDF) values for conventional and adaptive pushover methods compared to dynamic analysis, for high (left) and low (right) ductility regular structures at all structural levels (global, first storey, middle storey, section) and under all four strong motion records.

At the global level, the adaptive pushover, in general, improves the quality of results since it always produces'lower CCDF values compared to conventional ones, both for high and low ductility structures. In Fig. 3 it is observed that adaptive pushover is closer to the dynamic response when the structure is in the elastic range and the initial part of the inelastic response (up to 2% global drift), while for higher levels of inelastic response, there is no further improvement. This is due to the fact that in the high inelastic range, the analysis solver is unable to find real solutions to

Gbbal level Fin1 stcq lwel W l s slo~y lwd S e c i h lmd Gbbal lwei Fd stnry I d Middle stmy lwd Sscticn level

Fig. 2. CCDF results summary for regular structures.


130 V. K. Papanikolaou, A. S. Elnashai B J . F. Pareja

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Fig. 3. Response at the global level for the high ductility regular structure.

the eigenvdue problem and hence, the load vector cannot be updated in the subsequent steps. Therefore, no improvement in the results is introduced using the adaptive pushover. Larger differences are observed for both methods when the structures are subjected to artificial records compared to natural ones. There is also a trend for both pushover approaches to underestimate the dynamic response especially when the structure enters the high inelastic range. The same trends apply for the low ductility structure, indicating that for this type of bi-dimensional regular structures, ductility is not a factor that modifies the behaviour trends at the global level.

At the first storey level, as shown in Fig. 2, adaptive pushover again performs slightly better for both types of structures. Figure 4 shows a comparison between pushover curves and dynamic analysis for the high ductility regular structure. It is clear that the correspondence between the dynamic analysis and the pushover curves is better for natural records. Considering pushover curves as indicators of

Fig. 4. Response at the first storey level for the high ductility regular structure.


Evaluation of Conventional and Adaptive Pushover Analysis 11: Compamtiue Results 131

structural capacity, results show that the adaptive method produces less conservative results than the conventional onel especially in the inelastic range. There is not a big difference; however, it is an indicator of how the adaptive procedure produces a resultant of lateral forces closer to the base of the structure than that of the one produced by the fixed triangular pattern. The same trends are observed for the low ductility structure as well.

Contrary to the response at the global and a t the first storey levels, a t the middle storey level adaptive pushover appears to lose its superiority. As is shown in Figs. 2 and 5, the adaptive pushover produces higher CCDF values than the conventional one and shows a lower structural capacity which is too conservative when compared to dynamic analysis. For the high ductility structure, adaptive pushover shows that the middle storey softens in a brittle way reaching a lower total deformation, which is not reflected in the dynamic response. This trend is also observed in the low ductility structure but in this case, the failure is more gradual.

The above results suggest that the adaptive pushover procedure imposes higher inelastic deformations at the middle storey level and therefore, has a tendency to overestimate the structural damage. This behaviour has also been observed in Antoniou and Pinho [2004]. In order to explain the reasons behind these results, the methodology used to combine the modal forces for updating the lateral load profile should be considered. Since the SRSS and the CQC rules are unable to represent the sign inversion in the force vector modal decomposition, the resulting augment in the applied lateral forces is not necessarily realistic and sometimes produces higher loads especially in the intermediate stories. As is suggested by Antoniou and Pinho [2004], a more refined methodology of modal force combination should be employed in future developments; for example, a weighted vectorial addition of each mode contribution.

At the section'leveE, both pushover methods and dynamic analysis results react almost identically for both regular structures (high and low ductility) under all

Fig. 5. Response at the middle storey level for the high ductility regular structure.


132 V. K. Papanikolaou, -4. 5. EElnoshai 8 J . F. Pareja

Fig. 6. Response at the section level for the high ductility regular structure.

strong motion records (Fig. 6). Since the relation between moment and curvature is a property of the section, any dserence between the dynamic analysis and pushover curves, is due to the applied IDA methodology which uses the maximum moment versus maximum curvature. Nevertheless, these results are used to show how the static analyses handle a similar level of axial forces which is the only factor able to modify this relation for a fued section.

It has to be noted that the above section curves refer to the first storey column lying on the opposite side of which pushover loads are applied. However, if the column at the same side with load application was monitored instead, the difference between pushover and dynamic analysis would appear much larger. This is due to second order tensile forces, which dominate the local element behaviour. Therefore, it is proposed that whether second order effects are included in the analysis, static pushover should be undertaken for each direction of loading and the worst case actions and deformations are used for design and/or assessment.

2.2. Shear wall structu~es

Figure 7 summarises the difference (CCDF) values for conventional and adaptive pushover methods compared to dynamic analysis, for high and low ductility structures under all strong motion records and structural levels.

At the global level, as in regular structures, adaptive pushover shows lower difference values compared to its conventional counterpart. Figure 8 shows a detailed view of the response a t the global level for the high ductility structure.

Several trends, already identified for regular structures are again detected:

In the same way that in regular structures, adaptive pushover is less conservative than the conventional one. In capacity terms it shows a slightly stiffer structure, suggesting a lower application point of the lateral load resultant.

0 There is again a better correspondence between the dynamic analyses performed with natural records that with the ones executed with artificial ones.



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Gk-M level first slmy lave1 M W story level Sec(ion lml Gbbal lml First sm?j levd MWdle story level Ssction leva

Fig. 7. CCDF results summary for shear wall structures.

Fig. 8. Response at the globai level for the high ductility shear wall structure.

In the higher inelastic range, both pushover approaches underestimate the dynamic response. However, the adaptive pushover shows a slightly better approximation. It is also clear that adaptive procedure converges to a fixed load pattern for the high inelastic response since the difference between both pushover approaches is stabilised. As previously stated, for regular structures, this is due to the impossibility of the program to find solutions to the eigenvalue problem.

The same comments applying at the global level also fit the response at the first s t m y level. However, at the middle storey level, Fig. 9 shows that both pushover 'analyses almost converge to the same results. It is also not apparent whether natural records produce better results than artificial ones.

In order to explain the response at this level, it is important to consider the influence of the beam to column stiffness ratio (p ) of the structure. As is described in Chopra [1995], this parameter is based on beam and column properties of the storey closest to the middle of the frame. For an ideal p = 0 the frame behaves as a flexural beam, while for p = oo the structure behaves as a shear


Fig. 9. Response at the middle storey level for the high ductility shear wall structure.

beam with its columns in double curvature in each storey. This structure, due to shear w a s , is going to have a lower value of p than the regular structures and hence, its behaviour.will be closer to a flexural beam. As pointed out by Chopra [1995], the higher mode response is negligible for frames responding like shear beams and maximises for buildings deforming like flexural beams. It is not very clear if this type of structure is more sensitive to the higher mode response .when there is aImost no difference between both pushover approaches at this level, especially when considerable variations were already observed in the response of the regular frame.

Nevertheless, this question can be answered considering the process used to update the Iateral load in the adaptive pushover and also the damage distribution along the height of the structure. It can be inferred from the formulations presented in the companion paper that any significant changes in the Iateral load vector emanate from the alterations in the modal shapes produced by the reduc- tion in the structural stiffness, when the damage starts to concentrate in several localised areas of the structure. Ln the adaptive pushover there is always an increase in the applied load, which is not reahtic, because the direction of the modal forces are not taken into consideration. In t h s case, the damage is localised in the base of the structure and according to the above results; it seems that there are not big alterations between the modal shapes calculated in each load step. Hence, the lateral load vector shape remains similar to the fundamental mode since the structure is just suffering stiffness degradation only a t lower storeys. For a better visuali- sation, Fig. 10 presents the variation of the normalised modal scaling vector used to distribute the forces in the adaptive pushover. It is clear that the initial modal vector is very similar to the fundamental mode and damage is concentrated at the base of the structure. The graph also confirms that the applied loads remain almost constant at the middle level of the structure and adaptive pushover does not offer a consistent improvement in the resdts. Consequently, at this level of response, benefits from adaptive pushover analysis are marginal.


Evaluation of Conventional and Adaptive Pushover Analysis II: Compamtive Results 135

Load Patterns Wall - High ductility - - - . ..... - . . y..... :

Fig. 10. Variation on the modal scaling vector for different load factors.

a I I

3 -

Fig. 11. Response at the section level for the high ductility shear wail structure.

t load factor 0.1

.-*..load factor 0.4

- - - load factor 0.90

Figure I1 shows the response at the section level for the high ductility shear wall structure. These results show the same trend detected in the regular frame whch rerate to the comparable level of axial forces in both pushover approaches and dynamic analysis. This can be inferred from the fact that maximum moment in the dynamic analysis coincide with the maximum moment obtained in the pushover analyses. Consequently, adaptive pushover does not introduce any especial advan- tage in the estimation of the response a t the section level.

j - j

2.3. Imgular structures

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

Nomallzed modal scaling vector

Figure 12 summarises the difference (CCDF) values for conventional and adaptive pushover methods compared to dynamic analysis, for the high and low ductility


136 V. K. Papanikolaou, A. S. Elnashai Ed J. F. Pareja

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Fig. 12. CCDF results summary for irregular structures.

Fig. 13. Response at the global level for the low ductility irregular structure.

irregular structures. Figure 13 depicts the response of the low ductility irregular structure at the global level.

It seems that the same trends observed for the regular and shear wall structures are present. However, for the low ductility structure, an important stiffness degradation process is observed in the pushover curves, which at first glance differs from the results obtained with the incremental dynamic analysis. Nevertheless, this strength degradation does not imply a bad performance of the pushover approaches since the maximum value of the base shear is approximately equal in the pushover analyses and in the dynamic calculations. On the other hand, it is clear that for this case, the use of the adaptive pushover does not introduce any additional benefit in the estimation of the structural raponse at the global level for the low ductility structure, which exhibits a brittle behaviour. This non-ductile performance is not odd if the characteristics of the structure are considered; irregular geometry and low ductility design. However, as was previously mentioned, the dynamic analysis



does not show this decay in the structural strength. Two main factors can explain this difference:

The criteria used to plot the IDA points, using the absolute maxima. As it is observed in Fig. 13, in the inelastic range, IDA points appear almost in a horizon- tal line that coincides with the peak base shear of the pushover curves. However, since each point is plotted against the maximum displacement, it is very difficult to visualise a process of strength degradation. It is important to consider that the monotonic Ioad application produces a conservative estimation of the structural capacity due to the faster increment in the localised damage. In the case of the adaptive pushover, as was stated by Antoniou and Pinho [2004], there is a trend to exaggerate the inelastic deformations in the locations of damage, and in this way, sometimes extremely conservative results can be obtained.

It is also interesting to consider that in the case of the low ductility structure, almost immediately after the structure has reached its peak resistance, both pushover techniques produce almost the same results. This means that this structure has a brittle behaviour and the formation of the failure mechanism is produced almost immediately after the structure enters into the inelastic range. T h s implies that the eigensolver can no longer find real solutions and therefore, the lateral load vector remains unchanged.

In the same way that the regular and shear wall structures responded, at the first storey level adaptive pushover produces slightly better results than the conventional one, especially in the case of the high ductility irregular structure. On the other hand, for the low ductility irregular frame, there is almost no difference in the results provided by both pushover approaches. Since the main differences between the conventional pushover and the adaptive one occur in the post-elastic range, this coincidence in the results suggests a brittle behaviour in the structural response. It is interesting to observe, according to the pushover results, that the brittle behaviour of the structure is not localised at this level, contrary to the expected effect of the induced soft storey. It appears that for this case, the pushover approaches do not supply a correct estimation of the interstorey drift and shear distribution along the height of the building. Here it is interesting to note that Antoniou and Pinho [2004] have reported cases where the totally inadequate predictions of these parameters were made by the pushover techniques with adaptive and fixed load distributions.

At the middle storey level, as in the regular structures, the adaptive pushover loses its superiority over the conventional one. Both pushover approaches are too conservative in the estimation of the structural response at this level, predicting a very low structural capacity, especially in the low ductility irregular frame. In fact, Fig. 14 explains why at the global and first storey levels, both pushover approaches show the same results in the inelastic range for the low ductility frame: There is a brittle failure mechanism that generates a fast degradation in


138 V. K. Papanikolaou, A . S. Elnashai J . F. Pareja

Fig. 14. Response at the middle storey level for the low ductility irregular structure.

the stiffness of the structure, creating problems to update the iaterd load vector in the adaptive procedure. In order to explain this behaviour the following factors should be considered:

0 As was mentioned before, the combination of load forces using the SRSS or the CQC method seems to produce extremely conservative results. Especially since at this level, the sign reversal in the different modal loads is not taken into account. Since in an irregular frame structure the damage tends to be distributed in a less localized way than, for instance, a structure with shear walls, the alterations in the stiffness matrix of the structure will generate higher changes in the modal shapes. Hence, this can lead to wrong estimations of the structural capacity with the adaptive technique, due to the excessive increasing in the lateral forces applied in the damaged locations.

Another interesting observation is that the conventional pushover seems to be a better estimator of the response at the middle storey level. As is -shown in Fig. 15, which presents the variation of the modal scaling vector through different lateral load factors together with a comparison with the fixed triangular pattern, it is clear how the adaptive pushover concentrates the forces increment in the lower middle of the structure and applies higher forces than the fixed pattern in the stories where the damage is concentrated. This inferior level of forces at the lower storeys allows the conventional pushover to reach higher level of deformations that supply slightly better estimations of the interstorey drift and shear.

Identical to the regular structures, at the section level, both pushover analyses produce basically the same results. No substantial improvement is produced applying the adaptive pushover technique. However, the maximum moment estimated with dynamic analysis is very similar to the maximum moment predicted by the pushover methods. It can be inferred that the level of axial loads are comparable between these methodologies. As previously mentioned, these differences are due


Evaluation of Conventional and Adaptive Pwhover Analysis 11: Cornpamtive Results 139

Load Patterns Irregular frame - Low ductility

- =- load factor 0.94

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

Normallzed modal sullng vector

Fig. 15. Variation on the modal scaling vector, for different load factors.

more to the method employed to plot the IDA points than to the inaccuracy of the static pushover techniques.

2.4. ICONS bare frame

Figure 16 summarises the difference (CCDF) values for conventional and adaptive pushover methods compared to dynamic analysis for the ICONS bare frame. At the global level, difference values strongly increase compared to the previously analysed structural systems and both pushover procedures appear very conserw tive compared to dynamic analysis, as shown in Fig. 17. It appears that for this type of weak and irregular structure, both pushover approaches fail completely to approach the dynamic response. Still, the adaptive pushover shows a marginal better approximation.

Global level First story level Middle story lwel Section level

Fig. 16. CCDF results summary for the ICONS bare frame.


140 V. K. Papanikolaou, A. S. Elnashai d J. F. Pareja

Fig. 17. Response at the global level for the ICONS bare frame

Fig. 18. Response at the middle storey level for the ICONS bare frame.

At the first storey level the situation does not improve, showing a very high discrepancy between pushover and dynamic analysis. At the middle storey level, as shown in Fig. 18, although both pushover approaches are again very consem- tive in the prediction of the structural capacity, the conventional pushover gives better results than the adaptive technique. As was stated before, this behaviour is explained by the lower level of forces applied by the conventional pushover in the lower floor levels of the structure where the damage is concentrated.

At the section level, the same trends observed in the previous analyses are again detected. There is no significant improvement using the adaptive pushover technique, and basically both pushover approaches produce the same results.


Evaluation of Conventional and Adaptive Pwhower Analysis II: Comparative Results 141

2.5. SPEAR 3 0 frame

Figure 19 summarises the difference (CCDF) values for conventional and adaptive pushover methods compared to dynamic analysis: for this three-dimensional, irregular both in plan and elevation structure.

Contrary to the trends already observed, conventional pushover analysis performs for the f i s t time consistently better than the adaptive one at the global level, although there are large differences between both pushover procedures and dynamic analysis. However, as it is shown in Fig. 20, the maximum base shear predicted by the dynamic analyses is very similar to the peak base shear observed in the pushover curves. The main difference is the fast strength degradation observed in the pushover curves in the inelastic range which is not suggested by incremental dynamic analysis.

According to the trends observed in 2D structures, when the structure starts to develop considerable damage which is not concentrated at its base, pushover

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Fig. 19. CCDF results summary for the ICONS bare frame.

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- - --

Fig. 20. Response at the global level for the SPEAR 3D frame.


142 V. K. Papanikolaou, A . S. Elnoshaa d J . F. Pareja

analyses have a tendency to underestimate the structural capacity and this observation is even more notorious in the adaptive pushover. According to its characteristics, this structure is susceptible to experiment this behaviour since it was designed accordihg to outdated design codes and with no seismic design provisions. Weak concrete and smooth bars were used, and additionally it has heavily imbal- anced stiffness in the two orthogonal directions, as well as large eccentricity in plan and irregularity in elevation that coupled produce high sensitivity to the torsional effects. Keeping in mind these considerations, the following observations about the performance of pushover techniques for this irregular 3D structure can be made:

Despite both pushover approaches show a strong process of structural stiffness degradation in the inelastic range, it is interesting to observe that with the a d a p tive procedure, the structural peak resistance is reached a t a lower level of global deformation. Additionally, the graphs illustrate that with conventional pushover, the transition between the elastic and the inelastic range is slightly more gradual. These observations imply that a higher concentration of force is present at the damage locations when the adaptive procedure is employed. This confirms the fact that when structural damage is irregularly spread, the performance of the pushover techniques is diminished.

0 As was mentioned for the irregular 2D structures, the methodology used to plot the IDA points makes it difficult to visualise a process of stiffness degradation since the maximum force is plotted against the maximum displacement. However, according to the dynamic analysis results, both pushover procedures seems to predict in a good way the maximum capacity of the structure at the global level.

r The inclusion of torsional effects in the analysis generates higher alterations in the stiffness matrix, producing problems of damage concentration and lateral load vector updating in the adaptive procedure. Fajfar [2002] has reported these problems in the application of the pushover technique to asymmetric and tor- sionally flexible structures. The use of effective eccentricities has been suggested in order to improve the results of the pushover analysis. In this study, the lateral loads were applied in a conventional way since the main objective is to measure the improvement in the results produced by the adaptive technique. However,

'

this is an issue that requires further investigation.

As can be inferred from Figs. 19 and 21, the adaptive pushover does not introduce any significant improvement in the estimation of the response at the first storey level. It is also observed that, contrary to the response at the global level, at the first storey level the structure does not show any brittle behaviour. As shown in Fig. 22, at the middle storey level, adaptive pushover completely fails in the estimation of structural response and the conventional pushover pro- vides a more acceptable estimation in terms of strength and ductility for all the considered ground motions. Nevertheless, in this case, the lower differences in the adaptive procedure are clearly produced by the lack of comparison points, and for this reason they do not represent an improvement in the results accuracy.


Evaluation of Conventional and Adaptive Pwhover Analysis II: Compamtave Results 143

Fig. 21. Response at the first storey level for the SPEAR 3D frame.

Fig. 22. Response at the middle storey level for the SPEAR 3D frame.

It is important to say that the results presented in Fig. 22 correspond to the second storey of the middle frame of the building. Considering that this structure is subjected to torsion effects due to its sti&less imbalance, even worst results should be obtained in the frames located in the perimeter of the building. Figure 23 was produced in order to verify the force concentration at the middle storey level that occurs in the adaptive procedure and the variation of the lateral loads in the three frames of the building. In this figure, the variation in the normalised modal scaling vector for several load factors in each one of the three frames of the structure is depicted. The idhence of torsion is evident when the load distributions between frames 1 and 3 are compared. However, it seems that adaptive pushover procedure overestimates the forces applied to the middle frame. They are even higher at the initial load stages than the ones applied in the frame 3, which should have higher solicitations produced by torsion effects. This observation confirms why


144 V. K. Papanikolaou, A. S. Elnashai & J. F. Pareja

Load Patterns Spear 3D frame - Frame 'i

Normalized modal scaling v~ector

Load Patterns S ~ e a r 38 fra

. .

0.00 0.'10 0.20 0.30 0.40 0.50 0.60 0.70

Normalized modal scaling vector

Load Patterns Spear 3 0

Normalized modal scaling vector

Fig. 23. Variation on the modal scaling vector, for different load factors in the three SPEAR frames.


Evaluation of Conventional and Adaptive Pushover Analysis 11: Comparative Results 145

Fig. 24. Response at the section level For the SPEAR 3D frame.

further research is required in order to determine the optimum point to apply the . lateral loads when asymmetric 3D structures are evaluated using simplified static procedures.

Figure 24 proves that conventional pushover produces better results at the section level, especially in the estimation of the structural peak response. On the other hand, adaptive procedure strongly underestimates the sectional capacity. As mentioned before, since the moment-curvature relation is an intrinsic property of the section (under the same axial load), these results suggest that in this case a higher level of axial loads is present in the adaptive procedure.

3. Generaf Evaluation

3.1. Responae at the global level

Figure 25 shows an overall comparison of the CCDF values obtained using conventional and adaptive pushover procedures at the global level, for each one of the eight structures considered in this study. It is clear that for bi-dimensional structures in general, the adaptive pushover produces better results than the conventional one. It is also interesting that when the structure is weak and irregular (ICONS), both pushover approaches fail to approach the dynamic response. For the 3D structure (SPEAR) both pushover techniques are unable to predict, with reasonable accuracy, the response at the global level and, in fact, the adaptive pushover had a worse performance than the conventional one. Finally, it is important to highlight the f a d that adaptive procedure improved the results basically at the initial stages of the inelastic response. For higher inelastic deformations, a d a p tive pushover downgrades to conventional, since the analysis solver is not able to find real solutions for the eigenvalue problem.


146 V. K. Papanikolaou, A. S. Elnaahai b J. F. Pareja

Fig. 25. Overall comparison of the response at the global level.

3.2. Response at the first storey level

Figure 26 confirms that the same observations and trends of the global level also apply at the first storey level. It is clear that for bi-dimensional structures that adaptive pushover produces better results opposing to the highly irregular structures (ICONS and SPEAR) where there is no benefit from applying the adaptive pushover procedure. In fact, as was described in the previous sections, it seems that for irregular structures both pushover approaches produce almost the same results. This implies that the updating of the lateral load vector in the adaptive process stops almost immediately after the structure reaches its peak resistance, due to the presence of a brittle failure mechanism that degenerates the stiffness matrix introducing problems in the solution of the eigenvalue problem.

3.3. Response at the middle storey level

The main drawback in the performance of the adaptive pushover was detected at the middle storey level. With the exception of the shear wall structures, for all other cases the adaptive pushover was conservative in the estimat'ion of the structural response, exaggerating concentration of damage at this level (Fig. 27). This problem is mainly produced by the difficulties faced by the adaptive procedure to model the sign reversal in the modal load vectors. For this reason, more rehed methods to combine the decomposed modal forces are required in order to improve the performance of the adaptive technique.

3.4. Response at the section level

Figure 28 shows a summary of response at the section level for all analysed structures. It is observed that there is practically no gain from applying the advanced


Evaluation of Conventzonal and Adap twe Pushover Analysis II: Comparative Results 147

Fig. 26. Overall comparison of the response at the first s torey level.

Fig. 27. Overall comparison of the response at the middle s torey level.

pushover procedure when the section behaviour is evaluated. Nevertheless, it is important to point out that at the section level, the differences between the dynamic analyses and the pushover curves are expected to be negligible because the moment versus curvature diagram is an intrinsic characteristic of a reinforced concrete section under the same axial loading. Since both pushover approaches produce basically the same results for each one of the considered structures and predict almost the same peak capacity of the section observed in the dynamic analysis, the differences quantified through CCDF are generally due to the applied IDA approach, using


148 V. K. Papanikolaou, .-I. S. Elnashai €9 J. F. Pareja

Fig. 28. Overall comparison of the response at the section level.

DyMmic Max Curvature n Max Moment

15 DyMmic Max Moment vs brrespondlng Gnatwe 10 - AdapWe i v e e r

..---. Conventional Pushover rad

0 0.1 0.2 0.3 0.4 0.5 0.6

Fig. 29. Comparison between different methodologies to plot the dynamic analyses resdts.

the maximum moment against the maximum curvature, although these two values are not simultaneous. In order to clarify this concept, Fig. 29 shows a moment versus curvature diagram complemented with the incremental analysis results plotted using the maximum moment versus its corresponding curvature and also for the maximum curvature versus its corresponding moment. From this figure, it is clear that the response maxima approach is not always adequate, and therefore this is an issue of further discussion and research.

4. Conclusions

The main conclusions obtained from the present study are summarised below:

0 Pushover analysis yields close results to dynamic analysis as long as the structural systems under consideration are free from irregularities in plan and elevation. As


Evaluation of Conventional nnd Adaptive Pushover Analysis II: Comparative Results 149

these irregularities become more important, higher discrepancies are observed. Moreover, there is a trend for natural records to produce lower differences between dynamic and pushover analysis as opposed to artificially generated ones. The latter records may include unrealistic frequency content and number of peaks, leading to larger dynamic energy dissipation not captured by static analysis. The overall assessment of the extensive results from this study indicates that the adaptive pushover in general does not provide major advantages over the traditional methodology. Despite the apparent enhancement in the assessment of the response at the global level from adaptive pushover results, it is also clear that it presents serious defi- ciencies in the estimation of the structural response at the local level, especially for the intermediate storeys. Careful assessment of the local response is necessary before an assessment method is used with confidence; globa1 results comparisons may be misleading.

0 It is clear that the adaptive procedure presents a problem of excessive force concentration at the locations of the structure where the damage is concentrated. This is a consequence of the approach used to combine the modal forces using the SRSS or CQC methodologies, since the sign reversals in the Ioad vectors are not included. Hence, more refined methodologies are required to compute the normalised scaling load vector. In the adaptive pushover procedure updating of the lateral Ioad vector is directly related to the calculation of the vibration modes for each of the load steps. There- fore, when the structure reaches very hlgh inelastic deformations or presents a brittle failure the benefits generated with the application of the adaptive methodology are eliminated because the load vector is no longer updated, since the mode shapes include imaginary components.

0 The results obtained for the 3D SPEAR frame show that pushover techniques still require further refinement in order to provide reliable estimates of the dynamic response of 3D asymmetrical structures. Torsional effects are not adequately r e p resented in pushover analysis. The methodology used to plot the dynamic (pushover) analysis results using tem- porally coincident maxima of force/moment and deformation/ curvature yields in general a conservative estimate of the capacity. It has, however, drawbacks that generate difficulties in the comparisons with the results of the pushover curves. The option of comparing the results of the pushover curves with those of the dynamic analyses plotted using the maximum force/moment versus the corresponding displacement/curvature and with the force/moment corresponding to the maximum displacement/curvature may provide a better understanding of the differences between the static and the dynamic procedures. The Capacity Curve Discrepancy Factor (CCDF) used in this study should be considered a primary and simplistic approach to quantify the difference between dynamic analysis and pushover curves, since it applies to the common range of deformations between pushover and dynamic analysis. Additionally, the


150 V. K. Papanikolaou, A. S. Elnashai 8 J. F. Pareja

drawbacks in the representation of IDA mentioned in the previous paragraph require that this parameter has to be interpreted with judgment and careful consideration. Further research is required in order to validate the adaptive and other forms of advanced pushover techniques as a viable (or even enhanced) tool to replace the estimation of the dynamic response through inelastic time-history analyses.

Acknowledgement

The work described in the paper was funded by the Mid-America Earthquake Center at the University of Illinois at Urbana-Champaign.

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