Residual Drift Demands Research Articles

Estimating inelastic drift demands for wood portal frame systems considering accumulated damages

SummaryAs one key to the implementation of the performance‐based design methodologies for wood structures, the performance objectives and their corresponding limit state criteria are usually correlated with the peak (maximum) interstory drift demands. This paper evaluates the inelastic drift demands including the peak drift and the residual drift for the prototype timber portal frame structural elements. Analytical 2D‐framed model representative of the study‐case were subjected to a suite of 50 pulse‐type earthquake ground motions. In addition, an accumulated damage index is added to the inputs of the nonlinear analyses to account for the damage caused by the previous ground excitations. Larger accumulated damages lead to larger inelastic drifts. Strong correlation is revealed among the drift demands, the peak ground accelerations, and the variables characterizing the nonlinear system behavior. Finally, estimation formulas for the peak and residual drift demands are proposed and validated with the simulated results from nonlinear time‐history analyses. Based on the presented formulas, the resilience ratio and the effective elastic drift are further derived to comprehend the nonlinear behavior of such timber made structures.

Response to seismic sequences of short-period structures equipped with Buckling-Restrained Braces located on the lakebed zone of Mexico City

As part of an ongoing research program, this paper presents the results of a numerical study of steel frames with and without Buckling-Restrained Braces (BRBs), representative of essential buildings (e.g. hospitals). The aim of this study is to understand the effects of seismic sequences on this type of structures when located on the soft soil of Mexico City. For that purpose, three-, six-, and nine-storey frames were designed under diverse criteria and analysed under artificial sequences to understand the influence of BRBs on the peak and residual inter-storey drifts demands. The results showed that the effect of aftershocks is very significant when their intensity, in terms of peak-ground velocity, is similar to that of the mainshock. It is also shown that, although aftershock effects may not be eliminated, a proper design based on the concept of dual systems could help to mitigate aftershock effects. Based on the analytical results, expressions to estimate the magnitude of peak and residual inter-storey drift demands under mainshocks and the sequence mainshock-aftershock are offered as a helpful guide to structural designers.

Seismic assessment of concrete buildings reinforced with shape memory alloy materials in different stories

SummaryShape memory alloy (SMA) is a unique material with many beneficial characteristics such as superelasticity and excellent resistance against corrosion. However, the high expenses related to the material costs and difficulties associated with implementation of SMAs in reinforced concrete (RC) structures may limit their usage. To decrease the costs related to SMA installation, this paper investigates the seismic performance of RC moment‐resisting frames with the intention of specifying the optimal stories for SMA utilization. To this end, RC frames with 3, 5, 7, and 9 stories are modeled and various cases are considered for SMA locations in different story levels. For each building, 4 different cases are considered including a frame with regular steel reinforcement (Steel), a frame with SMAs in all story levels (full SMA), and 2 remaining cases consist of frames with SMAs in bottom and middle story levels only. In the first part, nonlinear dynamic time history analyses are conducted to evaluate the base shear, roof displacement, interstory, and residual drift demands of the structures using 10 ground‐motion records. In the second part, the incremental dynamic analysis is employed to assess the entire range of structural dynamic behavior. By using the generated data from incremental dynamic analysis procedure, fragility evaluation is conducted on multiple limit states to provide a comprehensive performance assessment for each case. The results indicate that frames with SMA in their lower story levels performed similar to frames equipped with SMA in all story levels. However, the fragility assessments show the better performance of frames with SMA in their bottom stories versus other cases. On this basis, the costs associated with SMA fabrication could be reduced noticeably (nearly two‐thirds) without sacrificing the overall performance of the frame and its post‐earthquake serviceability.

Influence of modeling assumptions and aftershock hazard level in the seismic response of post-mainshock steel framed buildings

Seismic response under strong aftershocks has become an important topic in performance-based earthquake engineering recently. This paper examines the influence of the modeling approach in the response of a case-study four-story steel framed building designed with modern seismic provisions when subjected to two sets of aftershocks representing different aftershock-hazard levels. It was assumed that the building models experienced specific post-mainshock residual drifts prior of being subjected to the aftershocks. Results shown that including additional sources of stiffness and strength (i.e. inclusion of the interior gravity framing and participation of the slab in the beams) in the building analytical model lead to a different response under aftershocks in terms of maximum and residual interstory drifts than that of the analytical model commonly used in previous studies. Particularly, additional overstrength and post-yield stiffness ratio help to constrain residual drift demands under strong aftershocks, and decrease the probability of imminent demolition due to excessive post-mainshock residual drifts.

Fragility analysis of self-centering prestressed concrete bridge pier with external aluminum dissipators

A novel self-centering prestressed concrete pier with external energy dissipators has been developed to realize seismic resilient performance and enhanced corrosion-resisting property. Self-centering capacity of the pier is provided by the unbonded post-tensioned tendons and damage is mostly concentrated on the replaceable dissipators. To investigate the seismic behavior of the proposed pier, a detailed analytical model considering interface opening and dissipator deformation was developed and verified through existing cyclic load tests. Based on the proposed model, a prototype reinforced concrete pier and a self-centering prestressed concrete pier with similar backbone curves are designed, and fragility analyses are conducted on the two piers through incremental dynamic analysis. One maximum drift-based performance limit state (i.e. collapse prevention) and two residual drift-based performance limit states (i.e. emergent usage and reconstruction) are defined for seismic capacity evaluation. Fragility curves indicate that the self-centering prestressed concrete pier has a slightly higher peak drift demand owing to its inferior dissipating capacity as compared with the reinforced concrete pier, while sustains a much lower residual drift demand due to its inherent self-centering characteristic.

Probabilistic seismic demand assessment of residual drift for Buckling-Restrained Braced Frames as a dual system

The main drawback of Buckling-Restrained Braced Frames (BRBFs) is low post-yield stiffness of steel cores that leads to concentrate large residual drift in a story after earthquakes. Residual drifts not only cause serviceability issues but also increase the potential damage during aftershocks or future events. In this study seismic demands of low and mid-rise BRBFs and Dual-BRBFs were studied using the Probabilistic Seismic Demand Analysis (PSDA). By comparing demand hazard curves of frames it was concluded that using of BRBFs as a dual system could reduce the residual drift demand significantly. It can improve the revival capacity of such structures after earthquakes with low repairing cost. In the other part of this study, two different nonlinear models including a deteriorating model and a non-deteriorating model were used to explore the effect of degradation on Dual-BRBFs seismic demands. It was observed that the residual deformations are more sensitive to degradation than maximum deformations. Although the deterioration is not serious because of large BRBs stiffness which keeps MRFs in low range of nonlinearity.

Evaluation of approximate methods to estimate residual drift demands in steel framed buildings

SummaryThis paper presents the evaluation of two approximate methods recently proposed in the literature to estimate residual (permanent) drift demands at the end of earthquake excitation for seismic assessment of buildings. Both methods require an estimate of the peak (maximum) interstory drift demand and the corresponding drift demand at significant yielding of the building. Additionally, an approximate method is proposed as part of this study. The introduced method follows a coefficient‐based approach similar to the Coefficient Method included in several US documents. For evaluating the approximate methods, five moment‐resisting steel framed buildings having different number of stories were analyzed under four sets of earthquake ground motions. Quantification of the accuracy of the approximate methods to estimate residual drift demands with respect to results from nonlinear time‐history analyses was performed through error measures computed for each building and each set of earthquake ground motions. Results show that the mean standard error tends to increase as the seismic hazard level increases. Between the two methods, the method introduced by Erochko et al. seems more effective in predicting residual drift demands than that proposed in the FEMA P‐58 recommendations in the USA. It is demonstrated that including additional sources of stiffness and strength in the modeling approach constrains the amplitude of residual drift demands. As a beneficial consequence, the accuracy of both approximate methods in predicting residual drift demands is significantly improved (i.e., mean standard error decreases). The introduced method also provides similar accuracy than the approximate methods available in the literature. Copyright © 2015 John Wiley & Sons, Ltd.

Aftershock seismic assessment taking into account postmainshock residual drifts

SummaryThis paper introduces and evaluates a methodology for the aftershock seismic assessment of buildings taking explicitly into account residual drift demands after the mainshock (i.e., postmainshock residual interstory drifts,RIDRo). The methodology is applied to a testbed four‐story steel moment‐resisting building designed with modern seismic design provisions when subjected to a set of near‐fault mainshock–aftershock seismic sequences that induce five levels ofRIDRo. Once the postmainshock residual drift is induced to the building model, a postmainshock incremental dynamic analysis is performed under each aftershock to obtain its collapse capacity and its capacity associated to demolition (i.e., the capacity to reach or exceed a 2% residual drift). The effect of additional sources of stiffness and strength (i.e., interior gravity frames and slab contribution) and the polarity of the aftershocks are examined in this study. Results of this investigation show that the collapse potential under aftershocks strongly depends on the modeling approach (i.e., the aftershock collapse potential is modified when additional sources of lateral stiffness and strength are included in the analytical model). Furthermore, it is demonstrated that the aftershock capacity associated to demolition (i.e., the aftershock collapse capacity associated to a residual interstory drift that leads to an imminent demolition) is lower than that of the aftershock collapse capacity, which mean that this parameter should be a better measure of the building residual capacity against aftershocks. Copyright © 2014 John Wiley & Sons, Ltd.

Probabilistic assessment of strain hardening ratio effect on residual deformation demands of Buckling-Restrained Braced Frames

In this study the effect of steel core strain hardening ratio of Buckling-Restrained Braces (BRBs) on residual drift demands of Buckling-Restrained Braced Frames (BRBFs) was assessed by using Probabilistic Seismic Demand Analysis (PSDA) methodology. Results show that by mere 1% change in strain hardening ratio, the residual drift demands of low and medium-rise studied frames experienced significant increment and restoring ability of BRBFs reduced meaningfully. On the other hand, maximum drift demands were approximately independent from strain hardening ratio. Given that, the large permanent drifts can make serious serviceability issues after earthquakes, accurate material tests play an important role in structural safety.

Effect of seismic sequences in reinforced concrete frame buildings located in soft-soil sites

On September 19 and 20, 1985, two strong subduction interface earthquakes struck Mexico City leading to a large stock of damaged, or even collapsed, reinforced concrete (RC) building structures located in soft soil sites of the former lake-bed zone. The aim of this study is to gain further understanding on the effects of soft-soil seismic sequences on the seismic response of RC framed-buildings. This investigation employed artificial sequences since only two real sequences were gathered during the 1985 earthquakes. The nonlinear response, in terms of peak and residual lateral inter-story drift demands of four RC buildings having 4, 8, 12, and 16 stories, was evaluated. Results show that the relationship of the damaged period of the building (i.e. period of the building after the mainshock) to the predominant period of the aftershock, which is a measure of its frequency content, has a significant impact in the building response.

Residual drift demands in moment‐resisting steel frames subjected to narrow‐band earthquake ground motions

SUMMARYThis paper presents the main results of the evaluation of residual inter‐story drift demands in typical moment‐resisting steel buildings designed accordingly to the Mexican design practice when subjected to narrow‐band earthquake ground motions. Analytical 2D‐framed models representative of the study‐case buildings were subjected to a set of 30 narrow‐band earthquake ground motions recorded on stations placed in soft‐soil sites of Mexico City, where most significant structural damage was found in buildings as a consequence of the 1985 Michoacan earthquake, and scaled to reach several levels of intensity to perform incremental dynamic analyses. Thus, results were statistically processed to obtain hazard curves of peak (maximum) and residual drift demands for each frame model. It is shown that the study‐case frames might exhibit maximum residual inter‐story drift demands in excess of 0.5%, which is perceptible for building's occupants and could cause human discomfort, for a mean annual rate of exceedance associated to peak inter‐story drift demands of about 3%, which is the limiting drift to avoid collapse prescribed in the 2004 Mexico City Seismic Design Provisions. The influence of a member's post‐yield stiffness ratio and material overstrength in the evaluation of maximum residual inter‐story drift demands is also discussed. Finally, this study introduces response transformation factors, Tp, that allow establishing residual drift limits compatible with the same mean annual rate of exceedance of peak inter‐story drift limits for future seismic design/evaluation criteria that take into account both drift demands for assessing a building's seismic performance. Copyright © 2013 John Wiley & Sons, Ltd.

Reduction of Maximum and Residual Drifts on Posttensioned Steel Frames with Semirigid Connections

The aim of this paper is to study the seismic performance of self-centering moment-resisting steel frames with posttensioned connections taking into account nonlinear material behavior, for better understanding of the advantages of this type of structural system. Further, the seismic performance of traditional structures with rigid connections is compared with the corresponding equivalent posttensioned structures with semirigid connections. Nonlinear time history analyses are developed for both types of structural systems to obtain the maximum and the residual interstory drifts. Thirty long-duration narrow-banded earthquake ground motions recorded on soft soil sites of Mexico City are used for the analyses. It is concluded that the structural response of steel buildings with posttensioned connections subjected to intense earthquake ground motions is reduced compared with the seismic response of traditional buildings with welded connections. Moreover, residual interstory drift demands are considerably reduced for the system with posttensioned connections, which is important to avoid the demolition of the buildings after an earthquake.

On the influence of strong-ground motion duration on residual displacement demands

This paper summarizes results of a comprehensive analytical study aimed at evaluating the influence of strong ground motion duration on residual displacement demands of single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. For that purpose, two sets of 20 earthquake ground motions representative of short-duration and long-duration records were considered in this investigation. While the influence of strong ground motion duration was evaluated through constantstrength residual displacement ratios, Cr, computed from the nonlinear response of elastoplastic SDOF systems, its effect on the amplitude and height-wise distribution of residual drift demands in MDOF systems was studied from the response of three one-bay two-dimensional generic frame models. In this investigation, an inelastic ground motion intensity measure was employed to scale each record, which allowed reducing the record-to-record variability in the estimation of residual drift demands. From the results obtained in this study, it was found that long strong-motion duration records might trigger larger median Cr ratios for SDOF systems having short-to-medium period of vibration than short strong-motion duration records. However, taking into account the large record-to-record variability of Cr, it was found that strong motion duration might not be statistically significant for most of the combinations of period of vibration and levels of lateral strength considered in this study. In addition, strong motion duration does not have a significant influence on the amplitude of peak residual drift demands in MDOF systems, but records having long strong-motion duration tend to increase residual drift demands in the upper stories of long-period generic frames.

Evaluation of drift demands in existing steel frames under as-recorded far-field and near-fault mainshock–aftershock seismic sequences

This paper presents results of a study aimed at evaluating the effect of aftershocks in steel framed buildings. For that purpose, three frame models representing existing steel moment-resisting frames were subjected to a set of as-recorded mainshock–aftershock seismic sequences. For this purpose, 64 as-recorded seismic sequences registered as a consequence of the 1994 Northridge and 1980 Mammoth Lakes earthquakes were considered in this study. In particular, this investigation employed 14 seismic sequences recorded in 7 accelerographic stations in the near-fault region. An examination of the as-recorded seismic sequences shows that the frequency content of the mainshock and the main aftershock is weakly correlated. The response of the frame models was measured in terms of the peak and residual (permanent) drift demands at the end of the earthquake’s excitation. From the results of this investigation, unlike previous results based on artificial seismic sequences, it was found that as-recorded aftershocks do not significantly increase peak and residual drift demands since the predominant period of the aftershocks (i.e. frequency content) is very different from the period of vibration of the frame models. In addition, it was shown that artificial seismic sequences could significantly overestimate median peak and residual drift demands as well as the record-to-record variability.

Probabilistic estimation of residual drift demands for seismic assessment of multi-story framed buildings

This paper presents the implementation of a probabilistic approach to estimate residual drift demands (e.g. residual roof, residual drift at specific stories, and maximum residual drift over all stories) during the seismic performance-based assessment of existing multi-story buildings. The approach combines residual drift demand fragility curves obtained from an inelastic intensity measure, incorporates explicitly the aleatory uncertainty (i.e. record-to-record variability) inherent in the estimation of residual drift demands at the end of the seismic excitation, with maximum inelastic displacement seismic hazard curves to obtain site-building-specific residual drift demand hazard curves which express the mean annual frequency of exceeding residual drift demands. Recognizing the evolution of central tendency and dispersion of residual drift demands with changes in the ground motion intensity, this procedure makes use of functional models that capture that variation. It is shown that the relationship between transient (maximum) and residual (permanent) drift demands depends on the mean annual frequency of exceedance and the building’s number of stories for a similar lateral load resisting system.

Evaluation of residual drift demands in regular multi-storey frames for performance-based seismic assessment

This paper summarizes results of a comprehensive analytical study aimed at evaluating the amplitude and heightwise distribution of residual drift demands in multi-storey moment-resisting frames after earthquake excitation. For that purpose, a family of 12 one-bay two-dimensional generic frame models was subjected to an ensemble of 40 ground motions scaled to different intensities. In this investigation, an inelastic ground motion intensity measure was employed to scale each record, which allowed reducing the record-to-record variability in the estimation of residual drift demands. The results were statistically processed in order to evaluate the influence of ground motion intensity, number of stories, period of vibration, frame mechanism, system overstrength, and hysteretic behaviour on central tendency of residual drift demands. In addition, a special emphasis was given to evaluate the uncertainty in the estimation of residual drift demands. Results of incremental dynamic analyses indicate that the amplitude and heightwise distribution of residual drift demands strongly depends on the frame mechanism, the heightwise system structural overstrength and the component hysteretic behaviour. An important conclusion for performance-based assessment is that the evaluation of residual drift demands involves significantly larger levels of uncertainty (i.e. record-to-record variability) than that of maximum drift demands, which suggests that this variability and corresponding uncertainty should be explicitly taken into account when estimating residual drift demands during performance-based seismic assessment of frame buildings. Copyright © 2006 John Wiley & Sons, Ltd.