Seismic response of slender MDOF structures with self‐centering base shear and moment mechanisms

As the amplification of seismic force demands due to higher‐mode effects on tall buildings is increasingly recognized as a design challenge, a number of high‐performance systems have been proposed to limit such effects through combined base shear‐limiting and moment‐limiting dual mechanisms. To better understand the influence of these dual base systems on the overall seismic behavior of tall buildings, this paper presents a study on the seismic response of Multi‐Degree‐of‐Freedom (MDOF) systems incorporating combined base shear‐limiting and moment‐limiting mechanisms. For an MDOF system with a given initial period and base strength level, the base shear‐limiting mechanism is defined by a shear strength factor, an inelastic stiffness parameter, and an energy‐dissipation parameter, while the base moment‐limiting mechanism is defined by a moment strength factor. To determine the influence of these parameters on the overall seismic responses of MDOF structures, a comprehensive parametric study was conducted, and the results were presented and discussed in terms of base displacement and rotation demands, seismic force demand amplification at the base and along the height, peak floor acceleration, peak roof drift, and absorbed energy. The numerical modeling methodology used in the parametric study was validated against 200 small‐scale shaking table tests of a scaled MDOF specimen with a base shear and moment dual‐mechanism system and was used to model MDOF structures that are representative of tall buildings with initial periods ranging from 1.0 to 10 s and having various base‐mechanism properties. The parametric study was then conducted using an ensemble of 20 Ground Motions (GM) scaled to three code‐specified seismic hazard levels for Los Angeles, California. The results of this study can be used to facilitate the design of base shear and moment dual‐mechanism systems for mitigating higher‐mode effects and enhancing the seismic resilience of tall buildings.


INTRODUCTION
The contribution of higher modes of vibrations to the dynamic response of slender MDOF structures has been recognized as an important challenge in the seismic design of tall buildings, especially for tall buildings relying on lateral force resisting systems consisting of slender shear walls that are intended to yield in flexure at their base. 1,2 These types of structures have been observed, following past earthquakes, to have experience excessive damage in the designated base plastic hinge locations and even a few stories above the base plastic hinges in some cases. [3][4][5][6] While poor ductile detailing was identified in earthquake reconnaissance reports as one of the main causes of the observed damage, extensive research over the past few decades has also revealed that simplified methods in typical seismic design codes underestimated the seismic demands in these slender shear wall structures, primarily because of inadequate consideration of the amplified dynamic response due to higher modes of vibrations that are not controlled by the designated base plastic hinging mechanism in these structures. 1,2 To address this issue, extensive research efforts have focused on developing and validating more advanced analysis approaches to account for higher-mode effects in the design of conventional slender shear walls. [7][8][9][10][11][12][13] In parallel, several high-performance systems have also been proposed that mitigate higher-mode effects through a more robust control of seismic demands induced by these effects. Rather than relying solely on the base plastic hinging mechanism for the seismic design of these structures, concepts of multiple flexural plastic hinging mechanisms along the height of the structure, 12,13 and of dual base-mechanism systems that provide a designated shear-limiting mechanism in addition to the plastic hinging mechanism at the base of a structure [14][15][16][17][18] have been suggested. Numerical results obtained from these studies [12][13][14][15][16][17][18] demonstrated that these shear-limiting mechanisms mitigated higher-mode effects and the corresponding inelastic responses along the height of tall buildings. Among these dual base-mechanism systems, the concept previously proposed by the authors 18 enabled uncoupled flexural and shear response at the base of tall buildings with full recentering capability, utilizing the rocking podium concept that was first developed in Russia [19][20][21][22] as free-standing kinematic base isolation for low to mid-rise structures and has been further investigated in recent years by an increasing number of researchers to improve its practical application, as summarized by Zhong and Christopoulos. 23 As illustrated in Figure 1, this concept, termed the Shear-Controlling Rocking-Isolation Podium (SCRIP) system, incorporates a rocking podium designed to displace laterally (through the nonlinear elastic rocking response of rocking columns) during the seismic response and recenter the structure after the earthquake, and energy-dissipating devices designed to yield and dissipate energy as the rocking podium moves. On top of the rocking podium is a rocking core wall designed to control the base-moment demands and recenter the superstructure while uncoupling the flexural response of the superstructure from the lateral response of the rocking podium. The higher-mode mitigating capability and self-centering characteristics of the SCRIP system have been validated through numerical case studies of a benchmark tall building 18 and shaking table tests of a scaled specimen, 24 demonstrating enhanced seismic resilience of structures equipped with the proposed system. This paper presents a first extensive numerical study on the seismic response of slender MDOF structures with selfcentering base shear and moment mechanisms considering a wide range of superstructure properties and base mechanism characteristics. The main objective of this study is to provide some insights on the response of slender MDOF structures with different fundamental periods and base mechanism characteristics. The numerical modeling scheme developed for the parametric study is first validated against a dataset of shaking table tests on a scaled slender tower with the SCRIP F I G U R E 1 Schematics of the benchmark tall building with the SCRIP base system NOVELTY • A numerical modeling methodology for MDOF structures using base shear and moment mechanisms as  their seismic force-resisting system, with validation against 200 shaking table tests both deterministically and  statistically.  • A comprehensive parametric study (using the validated model) on 1920 MDOF structures of different heights and periods, and having various base shear and moment mechanism properties. • Insights into the influence of different base mechanism parameters on the overall seismic responses of MDOF structures including higher-mode effects. • General design recommendations on the base shear and moment dual-mechanisms for enhancing the seismic performance of MDOF structures.
F I G U R E 2 Schematics of the shaking table specimen for the dataset system and is then applied to the modeling of six slender MDOF structures that are representative of tall buildings, with initial periods ranging from 1.0 to 10 s and having various base-mechanism properties defined in this paper. Nonlinear Response History Analyses (NLRHA) were carried out using an ensemble of 20 selected ground motions scaled to three code-prescribed seismic hazard levels: Service-Level Earthquake (SLE), Design Earthquake (DE), and Maximum Considered Earthquake (MCE), with detailed discussions focusing on the responses at MCE-Level to investigate the ultimate response of the structures that would control their seismic design. While the parametric study was conducted based on structural systems that are equipped with base mechanisms similar in behavior to that of the SCRIP system, the results of this study can also be extended to structures with other shear and flexural dual base-mechanism systems that were cited above, that rely on separately limiting both the maximum shear and OTM demands at the base of tall and slender structures to mitigate higher-mode effects and associated seismic demands above the base.

VALIDATION OF NUMERICAL MODELING SCHEME
This section briefly describes how the experimental dataset created by Zhong and Christopoulos 25 was used for the validation of the numerical modeling scheme that was utilized in the parametric study discussed in this paper. A detailed description of the experimental setup and test procedure is discussed in Zhong and Christopoulos. 24,26 This dataset was selected for numerical validation as it provided shaking table test results of a slender, higher-mode sensitive MDOF specimen with a scaled shear and flexural dual base system (i.e., the SCRIP system) under a large number of spectrally compatible ground motions, enabling both deterministic and statistical validations of the numerical modeling scheme. The scaled shaking table specimen (shown in Figure 2) was designed based on the 42-story benchmark building (shown in Figure 1) studied as part of the case study for the development and numerical validation of the SCRIP system, 27 following F I G U R E 3 Numerical modeling scheme of the shaking table specimen a scaling procedure that maintained the dynamic response characteristics of the slender superstructure including highermode effects. 24,26 A total of 100 shaking table tests using synthesized ground motions were performed for the specimen with the scaled SCRIP base system shown in Figure 2 and were repeated for the specimen with a free-standing rocking base mechanism for comparison purposes. Both test series were used in this section for the numerical model validations.

Numerical modeling
A number of modeling techniques have been previously studied to simulate the seismic rocking response of structures, from simple stick models that either use a lumped-plasticity element 28 to capture the hysteretic behavior only or a multispring element 29 to represent the rocking contact interface, to more complex finite element 30 or discrete element 31 models that explicitly simulate the rocking and friction-sliding mechanisms of the rocking interface for more accurate predictions on the rocking responses at the expense of higher computational cost. [30][31][32] For this study, a two-dimensional (2D) elastic stick model with lumped-plasticity elements at the base was used to model the shaking table specimen in OpenSees, 33 as illustrated in Figure 3. The main objectives of this simplified model were to provide a generalized representation of the dual base mechanisms being investigated and to maximize the computational efficiency to enable the execution of the extensive numerical parametric study presented in the subsequent sections. The use of an elastic stick model of the superstructure is justified by the fact that the superstructure of the tested specimen remained elastic during all shaking table tests, 24 and the superstructure of real applications of the SCRIP system is also expected to be designed for minimum inelastic response. 18,24 The superstructure of the tested specimen (i.e., the aluminum HSS tower) was modeled using elastic beam-column stick elements with a constant flexural rigidity, , based on the nominal properties of the aluminum HSS tower. The seismic mass, , at each story level was assigned to the horizontal Degree-of-Freedom (DOF) based on the nominal properties of the steel plates attached to the tower as seismic masses in the shaking table specimen. The freestanding rocking base mechanism was modeled using a lumped-plasticity rotational spring at the base of the stick model and was assigned an elastic-bilinear moment-rotation relation that has been previously shown to be able to represent the free-rocking behavior at the base of flexible rocking structures. 28 Second-order geometric (i.e., P-Delta) effects were accounted for in the stick model to approximate the overall slight negative post-rocking stiffness of the specimen, which was shown to closely represent the experimental behavior within the range of the rocking rotations expected as shown in Figure 3B. The shear base mechanism of the scaled SCRIP system was simulated using a lumped-plasticity translational spring at the base of the stick model connecting to the same node as the rotational spring. A generalized self-centering material model available in OpenSees was used to define the behavior of the translational spring, based on experimentally determined properties of the scaled SCRIP system used in the shaking table tests, as presented in the bottom plot of Figure 3B. A Rayleigh damping ratio of 1.6% was assigned to the elastic stick model based on the experimentally obtained damping ratio of the aluminum HSS tower, whereas the model excluded the lumped-plasticity rotational and translational

Motion-by-motion comparison
The results obtained from the numerical model presented above were first evaluated against the experimentally obtained results motion-by-motion for both the case with the free-standing rocking base and with the SCRIP base system, as presented by the scatter plots in Figure 4. If the experimental results and the corresponding numerical predictions were identical, the points would fall on the diagonal line of the scatter plots. The Mean Absolute Percentage Error (MAPE) was included in each plot, which can be used as an indicator of the accuracy of the numerical prediction that measures the average deviation of the scatter plots from the diagonal line. The coefficient of correlation (r) was also reported to quantify the linear relationship between the experimental and numerical results. Figure 4A shows the comparison of the test and numerical results for the structure with the free-standing rocking base. Considering the MAPE, the OTM demands at the base and mid-height were generally well-predicted (with MAPE below 10%) as these parameters were controlled by the rocking base, which also suggested that the lumped-plasticity rotation spring with the assigned moment-rotation relation was capable of capturing the force-limiting mechanism of the free-standing rocking base. Shear force demands at the base and mid-height were less well-predicted since shear force demands along the height of the structure were not limited by the base plastic hinging mechanism of the rocking base 2 and thus were more sensitive than the OTM demands. The maximum Interstory Drift Ratio (IDR) showed a good correlation between the experimental and numerical results, as IDR for this structure was mostly influenced by the elastic stiffness of the superstructure that was designed to experience relatively large elastic deformations under the scaled GM excitations in order to better emulate the effects caused by higher mode vibrations. 26 The peak roof accelerations and the maximum rocking uplifts were both more dispersed than the other parameters, probably owing to rocking-impact and friction-sliding responses during rocking action that are not accounted for with the rotational spring model. Similar observations were made based on the r values, except that a low r value was reported for the base OTM demands, as a result of the discrepancies between the experimental and numerical rocking and non-rocking cases (cases where rocking occurred during tests but no-rocking was predicted numerically, and vice versa). Figure 4B presents the comparison of the structure with the SCRIP base system. With the addition of a shear-limiting mechanism at the base, improved predictability (for both the MAPE and the r value) was observed among all parameters being considered, which also suggests that a better controlled seismic response is achieved with the SCRIP base system (that limits both the shear and moment demands at the base) compared to the free-rocking base (which only limited the moment demands at the base). Since the lateral response of the SCRIP base was dominated by the combined lateral resistance of the rocking podium and the friction braces and was less affected by the impact and sliding response of the rocking columns, the translational spring with the self-centering hysteresis captured the lateral response of the SCRIP base with good accuracy. As the SCRIP base responded inelastically to limit the shear force transfer to the structure, the rocking response of the free-rocking base above was moderated, which in turn reduced the effect of rocking impact and sliding response of the rocking base on the overall behavior and predictability of the structure. Although the discrepancies between the numerical and experimental maximum rocking uplift (of the rocking base) and maximum lateral displacement (of the SCRIP base) were still apparent when compared to other parameters, some studies on the predictability of free-rocking structures have suggested that a statistical model evaluation approach may be more appropriate when evaluating the displacement demands of free rocking response, since the displacement parameters are expected to be more sensitive to model assumptions and imperfections, as well as input GM excitations. 27,33,34 Therefore, the following section compares the numerically predicted results against experimentally obtained results in a statistical manner to provide further insight into the performance and appropriateness of the numerical modeling approach used in this study.

Statistical comparison
Following the motion-by-motion comparison, the numerical and experimental results of the shaking table dataset were revisited with a focus on the statistical comparison of the Cumulative Distribution Function (CDF) of key response parameters that were discussed previously. The concept of statistical validation using the CDF plots has been applied to modelling of rocking structures that showed predictable rocking responses in the statistical sense. 30-32,35-38 Figure 5 presents the CDF plots used for the statistical comparison in this section. The numerical and experimental CDF plots were compared based on the Kolmogorov-Smirnov (K-S) distance 39,40 (i.e., the maximum vertical distance between the experimental and numerical CDF plots) and the relative errors ( , defined as the absolute error between the experimental and numerical values divided by the experimental value) at the maximum horizontal distance, as well as at median and 90 th percentile of the experimental CDF plots, as listed in Table 1, and within each plot of Figure 5.
For the shear and OTM demands, similar observations as those in the deterministic evaluations were made, that both the rotational and translational springs with their assigned hysteretic relations were capable of simulating the seismic response of the base rocking and SCRIP-system mechanisms in the shaking table tests. The predictability of shear force demands at the base and mid-height showed improvements with the use of the SCRIP system to control the shear force transfer at the base. The relative errors of the roof acceleration predictions were also lowered, which was not as F I G U R E 5 Statistical comparison of the test and numerical results: (A) Specimen with a free-standing rocking base, and (B) specimen with the SCRIP base system obvious in the deterministic evaluation. Although the relative errors of the CDF plots for the maximum rocking uplift in the structure with the free-standing rocking base were up to 86.6%, as shown in Figure 5A, this error occurs at an experimental rocking uplift amplitude of around 1.5 mm (i.e., the absolute difference between the numerical and experimental rocking uplift was less than 1.5 mm). The relative errors were reduced for the maximum rocking uplift in the structure with the SCRIP system. In addition, the relative errors for the maximum lateral displacement were further reduced, agreeing with previous observations and discussions in the deterministic evaluation. Despite some relative errors (for rocking uplift and lateral displacement) that appeared large, the overall shapes of CDF plots presented in Figure 5B showed good agreement between the experimental results and the predictions using the numerical model constructed and discussed in the previous section. Considering the inherently stochastic nature of the seismic rocking response, the numerical modeling approach was deemed appropriate for the modeling of the tested slender MDOF structure with the SCRIP system and was extended to perform the subsequent parametric study on the seismic response of slender MDOF structures with the SCRIP system or other self-centering base shear and moment mechanisms exhibiting similar dynamic characteristics.

PARAMETRIC STUDY
The parametric study presented in this section focuses on the seismic response of tall shear wall buildings ranging in height from 45 to 600 m, with the SCRIP system (i.e., self-centering shear and moment dual base system) at the base. The fundamental periods, 1 , of these buildings are listed in Table 2 with their corresponding structural height, , total seismic weight, , and flexural stiffness, . The fundamental periods of these buildings are within the common period range for their structural heights, based on a study conducted by Xu et al. 41 on 414 completed tall buildings. For each building considered, the mean base shear and OTM demands under Service-Level Earthquake (SLE) excitations were determined (as presented in Table 2), based on analysis results from an ensemble of 20 GMs scaled to the code-specified SLE hazard level having a 50% probability of being exceeded in 30 years for Los Angeles, California. Of the 20 GMs selected, eight pulse-like GMs were included to reflect a pulse fraction of 0.38 for the Los Angeles site considered. 42 All GMs selected were recorded from earthquakes of magnitudes ranging from 6 to 9 on soil type C sites. Table 3 lists the GM ensemble with the corresponding Record Sequence Number (RSN) used to identify the selected GMs and their basic information from the PEER NGA-West2 database. 43 The average of the maximum-direction spectra of the 20 GMs was amplitude matched to the corresponding SLE-level and MCE-level response spectra by minimizing the square of the error at the following period values: = 0.  Table 3. The target MCE-level response spectrum, as well as the mean, mean-plus-standard-deviation, and mean-minus-standard-deviation spectral values of the 20 scaled GMs were plotted in Figure 6, with the spectral values of each individual scaled GM included in grey.
For each building listed in Table 2, the strength level of the base mechanism was designed based on the mean baseshear and OTM demands at the SLE level, which are typically the minimum strengths required for the design to ensure a primarily elastic response at the SLE-level earthquake events. The base-shear strength factor, , corresponds to the ratio of the shear strength of the base mechanism to the mean base-shear demands at the SLE level. Similarly, the base OTM strength factor, , is the ratio of the flexural strength of the base mechanism to the mean base OTM demands at the SLE level. In addition, the self-centering hysteretic model of the SCRIP system is fully adjustable and can be defined using the response parameters, and , where is the inelastic stiffness coefficient expressed as a fraction of the initial stiffness, and is the energy dissipation coefficient expressed as a fraction of the design shear strength at the base. The values of and considered in the parametric study are listed in Table 2. Values of ranged from 0 to 0.2, where a lower bound of = 0 was selected to produce a system with zero inelastic stiffness. Negative inelastic stiffness was not considered in this parametric study since it is generally not recommended for the practical design of self-centering systems. 23 Values of ranged from 0 to 2.0, where 1.0 represents the upper bound for a self-centering system with full-recentering capability, and a value of 2.0 corresponds to an equivalent elastoplastic hysteretic system with no self-centering capability. The  Table 3, resulting in a total of 38400 time-history analyses at each hazard level for the parametric study. Figure 7 provides a schematic overview of the model parameters considered in the parametric study. Throughout the study, a damping ratio of 2.5% was assigned to modes 1 and 3 for the superstructure.

RESPONSES OF SLENDER MDOF STRUCTURES WITH SHEAR AND MOMENT BASE SYSTEMS
While the parametric study was carried out for all three hazard levels, minor inelastic response was observed for SLE-level results, and the DE-level results were lower in amplitude but similar in trends to those at the MCE-level. Therefore, this section focuses on the MCE-level results in order to provide insights into the ultimate response of the structures that would govern the seismic design of their shear and moment dual base systems. Discussions on selected key response parameters are presented in terms of their mean values over the ensemble of GMs for each of the 1920 structures analyzed. The mean values of the base rotation demands are shown in Figure 8. For all values of the fundamental period 1 , the mean base rotation demands generally decrease for increasing values of the base OTM strength factor and decreasing values of the base-shear strength factor . Increasing the inelastic stiffness coefficient of the shear mechanism also increases the mean base rotation demands since the peak base-shear strength increases as increases. As the base-shear strength continues to increase, its influence on the mean base rotation demands would gradually diminish when it eventually reaches the level where its shear strength is similar to that of a base plastic-hinging-only structure. Under lower values of and , increasing the energy dissipation coefficient tends to reduce the mean base rotation demands, which is more apparent for structures with longer fundamental periods 1 . In addition, structures with shorter fundamental periods 1 tend to experience larger base rotation demands under the same set of key parameters for the base mechanisms.
The mean values of base lateral displacement demands Δ are plotted in Figure 9. Similar to the base rotation demands, the mean base lateral displacement demands for all values of the fundamental period 1 decrease as values of the baseshear strength factor or the inelastic stiffness coefficient increase, and as the values of the base OTM strength factor decrease. As the base OTM strength increases to a value where the base shear required to activate the inelastic moment mechanism is larger than the base-shear strength of the system, the influence of the base OTM strength on the overall dynamic response of the structure then becomes minimum, since the inelastic moment mechanism would not be activated. For the majority values of and where the shear mechanism remains active under GM excitations, increasing the energy dissipation coefficient would reduce the mean base lateral displacement demands. As opposed to the relation between base rotation demands and fundamental periods, in this case, structures with shorter fundamental periods 1 experience smaller mean base lateral displacements demands under the same set of key parameters for the base mechanisms, although the differences in ratios are not as significant as the base rotation demands. Figure 10 presents the mean values of the base shear overstrength, ∕ , , where is the maximum baseshear strength obtained during a time-history analysis and , is the design base-shear strength (equivalent to in F I G U R E 8 Mean base rotation demands for different base mechanism properties Figure 7). The values of base shear overstrength are mainly dependent on two parameters, the inelastic stiffness coefficient and the base lateral displacement demands Δ (plotted in Figure 9). A larger value corresponds to a larger overstrength increase per unit lateral displacement, whereas a larger Δ corresponds to a larger overstrength for a given value. As expected, structures with smaller values and larger values (i.e., more lateral displacement demands) exhibit more significant base shear overstrength. This suggests that for the design of a base mechanism with lower strength levels, a smaller value should be used to avoid large base shear overstrength which might limit the effectiveness of the force-limiting objective of the base mechanism. As for controlling the base lateral displacement demands Δ , a larger value would be preferable over a larger value. To further evaluate the force-limiting capability of the base mechanisms not only at the base of the structures but also along its height, the mean ratios of the shear force demands at 1/4, 1/2, and 3/4 height of the structure to the design base-shear strength were computed. Similar trends were observed when looking at changes in the ratios of the shear force demands at 1/4, 1/2, and 3/4 of the height of the structure to the design base-shear strength; therefore, the results at mid-height of the structure are reported in this section to provide a representative measurement on the effect of the base mechanism in controlling seismic force demands and reducing higher-mode effects along the height of the structures. As shown in Figure 11, the mean ratios of the shear force demand at mid-height to the design base-shear strength, F I G U R E 9 Mean base lateral displacement demands for different base mechanism properties ∕ , , tend to increase for increasing values of the base OTM strength factor and decreasing values of the baseshear strength factor . A larger base OTM strength factor indicates more of a contribution of first-mode response, thus higher ∕ , values under the same base-shear strength level. It is interesting to point out that for a value of unity, most structures considered in the parametric study show ∕ , values of larger than unity but less than 2. Although the shear force demands at mid-height (and along the height) of the structures are lower in the case of = 1 than = 2, the distribution of shear force demands is less desirable for the case of = 1 because of the amplification of shear force demands above the base shear-limiting mechanism. Although this could be partially attributed to large MCE-to-SLE demand ratios for the site used in the parametric study (i.e., a peak spectral acceleration ratio of 5.6), it still implies a potential constraint to be considered in the design of a base shear-limiting mechanism with low values (that result in base shear strength levels close to the elastic base-shear demands at SLE-level), in addition to the constraint of large base lateral displacement demands Δ that need to be accommodated.
Similarly, since the ratios of the OTM demands at 1/4, 1/2, and 3/4 height of the structure to the design OTM strength have similar trends with respect to changes in the base mechanism properties, the mean ratios of the OTM demand at midheight to the design OTM strength, ∕ , , were also used for this assessment. As plotted in Figure 12 for the base mechanisms for structures with longer 1 (i.e., 1 = 6, 8, and 10 s), and closer or smaller for structures with shorter 1 (i.e., 1 = 1, 2, and 4 s). This suggested that the shear force demands are better controlled using base mechanisms for structures with longer fundamental periods 1 , whereas the OTM demands are better controlled for structures with shorter fundamental periods 1 . Figure 13 plots the mean values of peak accelerations for different sets of key parameters. In general, the mean values of peak accelerations reduce as the energy dissipation coefficient for the base shear-limiting mechanism increases, although the rate of reduction gradually decreases as increases. The differences in the mean values of peak accelerations between a value of 1.0 (i.e., with full self-centering hysteresis) and a value of 2.0 (i.e., with elastoplastic hysteresis) was minimal for almost all plots in Figure 13. The values of the inelastic stiffness coefficient , however, have less influence on the mean values of peak accelerations. When comparing the response of structures with different fundamental periods 1 , higher values of the mean peak accelerations are observed for structures with shorter 1 , which is likely influenced by the shapes of the response spectra shown in Figure 6 that have higher spectral accelerations at shorter periods.
The mean values of peak roof drift ratios are presented in Figure 14. For lower values of the base-shear strength factor , the peak roof drifts generally decrease for increasing values of the energy dissipation coefficient and decreasing values of the inelastic stiffness coefficient . These trends are less apparent for cases with higher where the peak roof drift ratios become more constant. Since the superstructures above the base mechanisms are designed for primarily elastic response, the peak roof drift ratios (as well as the peak IDRs) are relatively small in all cases, as shown in Figure 14.
Values of the mean absorbed energȳ, as shown in Figure 15, are normalized as fractions of the corresponding seismic weight of the structure in each case. This response parameter is an indicator of potential structural damage in the base shear-limiting mechanism (in the case of the SCRIP system, it is a measure of cumulative inelastic action only in the energy-dissipating devices, since the rocking columns of the SCRIP system respond to seismic demands mainly through nonlinear-elastic rocking actions). The mean absorbed energȳgenerally increases for decreasing values of fundamental periods 1 and increasing values of the energy dissipation coefficient . In addition, similar to the base lateral displacement demands Δ , The mean absorbed energȳincreases for decreasing values of the base-shear strength factor and increasing values of the base OTM strength factor . The differences in the mean absorbed energȳis most apparent when a structure changes from a full self-centering base-shear mechanism (i.e., = 1) to an elasto-plastic base-shear mechanism (i.e., = 2), and as the values of fundamental periods 1 decrease, such differences become even more significant. While considering self-centering base-shear mechanisms only, the differences in the mean absorbed energȳbetween a mechanism with = 0.6 and with = 1 are minimal in most cases, suggesting that structures with = 0.6 exhibit similar energy dissipating capacity as structures with = 1.0. If base lateral displacement demands Δ in both cases can be practically designed for, structures with = 0.6 are preferable as they have more of a reserve in F I G U R E 1 2 Mean ratios of OTM demands at mid-height to design OTM strength at the base for different base mechanism properties their self-centering capacities in order to offset any potential discrepancies in the actual self-centering forces provided by the structure due to differences in the assumed and actual properties of the structure (i.e., seismic weight, geometry, and material strength, etc.), whereas structures designed with = 1.0 could lead to an actual value that is greater than 1.0, which signifies that the structures would not have full self-centering capabilities.

DISCUSSION AND CONCLUDING REMARKS
This paper presents a numerical investigation into the seismic response of slender MDOF structures incorporating base shear-limiting and moment-limiting dual mechanisms. The numerical modeling approach used for this study was validated both deterministically and statistically against a dataset of 200 shaking table tests on a scaled slender tower with the SCRIP system, and was extended to model MDOF structures that are representative of tall buildings with initial periods ranging from 1.0 to 10 s and having various base-mechanism properties. For an MDOF structure with a given initial period and base strength level, the incorporated base shear-limiting mechanism is defined by a base-shear strength factor , an inelastic stiffness coefficient , and an energy-dissipation coefficient , while the moment-limiting mechanism is defined by a base OTM strength factor , resulting in a total of 1920 systems. All systems were subjected to an F I G U R E 1 3 Mean peak acceleration for different base mechanism properties ensemble of 20 GMs, amplitude scaled to three corresponding code-prescribed seismic hazard levels for Los Angeles, California, USA. Among these results, the MCE-level results were presented and discussed in detail with respect to changes in base rotation and displacement demands, seismic force demand amplifications at the base and along the height, peak accelerations, peak roof drifts, and absorbed energy. While the parametric study was conducted based on structural systems that are equipped with base mechanisms similar in behavior to that of the SCRIP system, the results of this study may be extended to structures with other physical embodiments of shear and flexural dual base-mechanism systems that rely on limiting both the maximum shear and OTM demands at the base to resist earthquake loading. The results presented in this study may also be used for the preliminary design of tall and slender structures incorporating systems to mitigate higher-mode effects, as it provides insights on the impact of the base shear and flexure mechanism properties on the global response of these structures, which are summarized as follows: • The base rotation demands in the moment-limiting mechanism were reduced for increasing values of the base OTM strength factor , decreasing values of the base-shear strength factor and the inelastic stiffness coefficient , • The base lateral displacement demands in the shear-limiting mechanism were reduced as values of the base-shear strength factor or the inelastic stiffness coefficient increased, and as the values of the base OTM strength factor decreased. Increasing the energy dissipation coefficient reduced base lateral displacement demands in the F I G U R E 1 4 Mean peak roof drift ratio for different base mechanism properties shear-limiting mechanism for almost all cases, whereas its reduction to base rotation demands in the moment-limiting mechanism was effective only for structures with shorter fundamental periods 1 and lower base-shear strength factor . • The base-shear strength was better controlled with smaller values of the inelastic stiffness coefficient , especially considering the variation in the base lateral displacement demands Δ under different GM excitations as the overstrength caused by was directly proportional to Δ . Therefore, in cases where reduced base lateral displacement demands were required, it was preferable to increase the values of as opposed to increasing the value of , in order to avoid large seismic force amplification at the base and along the height of the structures with base mechanisms.
• The ratios of the shear force demand at mid-height to the design base-shear strength of the structure, ∕ , , increased for increasing values of the base OTM strength factor and decreasing values of the base-shear strength factor , so were the ratios of the OTM demands at mid-height to the design OTM strength of the structure, ∕ , . However, in cases where reduced seismic force demands are required, the values of should not be set too low to avoid a shear or moment overstrength ratio above the base mechanism that is larger than unity.
• The base mechanisms in general were more effective in controlling shear force demands for structures with longer fundamental periods 1 , and inversely, the OTM demands were more effectively controlled for structures with shorter • The peak accelerations reduced (at a decreasing rate) as the energy dissipation coefficient for the base shear-limiting mechanism increases. The peak accelerations of a structure with a full self-centering base shear-limiting mechanism were only slightly higher than the structure with a comparable elastoplastic base shear-limiting mechanism. The values of the inelastic stiffness coefficient had less influence on the mean values of peak accelerations. • For structures with lower values of the base-shear strength factor , their peak roof drift generally decreased for increasing values of the energy dissipation coefficient and decreasing values of the inelastic stiffness coefficient . Such observations were less apparent for structures with higher where the peak roof drift ratios became more constant. • The mean absorbed energȳwas, as expected, always less for structures with a self-centering base shear-limiting mechanism than with a comparable elastoplastic base shear-limiting mechanism. However, for structures incorporating the SCRIP systems, this parameter was of less importance since it is an indicator of potential cumulative damage only in the designated energy-dissipating devices while the rest of the structure responds to seismic loading primarily in the elastic range.

A C K N O W L E D G M E N T
The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

D ATA AVA I L A B I L I T Y S TAT E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.