Maximum Inter-story Drift Research Articles

Seismic Damage “Semaphore” Based on the Fundamental Period Variation: A Probabilistic Seismic Demand Assessment of Steel Moment-Resisting Frames

During strong earthquakes, structural damage usually occurs, resulting in a degradation of the overall stiffness of the affected structures. This degradation produces a modification in the dynamic properties of the structures, for instance, in the fundamental period of vibration (T1). Hence, the variation of T1 could be used as an indicator of seismic structural damage. In this article, a seismic damage assessment in four generic typologies of steel buildings was carried focused on verifying the variation of T1. To do so, several seismic damage states were calculated using the maximum inter-story drift ratio, MIDR, and following the Risk-UE guidelines. Then, a series of probabilistic nonlinear static analyses was implemented using Monte Carlo simulations. The probabilistic approach allows one to vary the main mechanical properties of the buildings, thus analyzing in this research 4000 buildings (1000 building samples for each of the four generic typologies). The variation of T1 was estimated using the capacity spectrum, and it was related to the MIDR for each damage state. As a main result of this study, the expected variation of T1 for several damage states is provided. Finally, a proposal for a seismic damage preventive “semaphore” and fragility curves are presented. These results may be useful as parameters or criteria in the evaluation of on-site structural monitoring for steel buildings.

A design method for seismic retrofit of reinforced concrete frame buildings using aluminum shear panels

Despite significant progress in research and development of aluminum shear panels in recent decades, their implementation for seismic retrofit of existing reinforced concrete (RC) buildings can still be significantly extended. Their application is limited by the general lack of relatively simple and effective design criteria and proper guidelines. This paper develops a design method for the seismic retrofit of reinforced concrete buildings using aluminum multi-stiffened shear panels as dampers. Both the nonlinearity in the structure and the dampers-structure interaction are considered to give an optimal distribution of the shear panels over the height of the building. The analytical laws refer to dissipative aluminum shear panels recently tested and analyzed by the authors. The proposed procedure has been described in detail. Its applicability has been demonstrated by analyzing two typical RC buildings having drift capacity-to-demand ratios ranging from 0.505 to 0.624. The design value of the panel-to-frame stiffness ratio has been found to range from 0.594 to 1.432 as a function of the lateral stiffness of the existing building. The verification of the proposed procedure has been carried out by checking the validity of the design assumptions. The first one (i.e., the mode shapes remain the same before and after retrofit) has been checked using the modal assurance criterion that gives values ranging from 0.992 to 0.998. The second one (i.e., uniform yield drift distribution over the building height) has been checked by comparing the yield drifts with their average value giving a standard deviation ranging from about 11 to 15%. The effectiveness of the design method has been finally validated through nonlinear time-history analysis for different seismic accelerograms and hysteresis models. The results show that the seismic retrofit design procedure is effective in significantly reducing inter-story drift (maximum inter-story drift ratio demands ranging from 1.04 to 2.07%) thus satisfying the acceptance criteria of the building, and avoiding drift concentration and consequential weak story collapse.

The Effect of Span-to-Height Aspect Ratio to The Damage Index Ratio of RC Buildings with Vertical Irregularity Setbacks

Many type irregularities exist in reinforced concrete frame buildings to accommodate the demand from architectural and aesthetic aspects. One of it is vertical irregularity setback. Its appearance affected the building seismic performance and the damage distribution. Previous researchers proposed equations to correlate between irregularity indices and damage index ratio of setback buildings. However, the aspect ratio between span and height were not included in the formula. This research presents the influence of span-to-height ratio to damage index ratio of the reinforced concrete buildings with setbacks. A set of 2D RC frames having setbacks are evaluated with nonlinear dynamic analyses under three seismic input motions. Several span-to-height aspect ratios were applied by changing the inter-story heights. The Park-Ang damage index was adopted to evaluate the damage index ratio between tower part and base part to represent the damage distribution and the inter-story drifts were observed to represent the building seismic performance. The result showed that under the same earthquake motions, the decrease in span-to-height ratio majorly increased the maximum inter-story drifts. The damage index ratio values between tower part and base part fluctuated, however the similar pattern of damage distributions between tower and base structure were obtained.

Life-cycle benefits estimation of self-centering building structures

Various self-centering structural systems were developed and investigated for reducing residual inter-story drifts of the traditional aseismic structural system by achieving full or partial self-centering behaviors under earthquakes in the past twenty years. However, limited research was conducted to investigate the life-cycle benefits of the full and partial self-centering structural systems on the life-cycle span, figuring out a more cost-effective solution for enhancing the building’s seismic resilience. This paper aims to comprehensively investigate the life-cycle benefits of full and partial self-centering structural systems compared to conventional buckling-restrained braced frames (BRBFs) using the life-cycle cost estimation method. The influences of the residual inter-story drift limit for demolition, the initial cost of emerging self-centering members, the value of building contents, and the discount rate were particularly investigated. To this end, three building structures with BRBFs and full and partial self-centering structural systems were designed to achieve the same capacity for controlling maximum inter-story drifts. Comprehensive dynamic analyses were performed to generate engineering parameters under different seismic intensities and the modeling uncertainties were properly considered through Monte Carlo simulation. The revised HAZUS loss calculation method was adopted to investigate the seismic annual loss (SAL) and life-cycle cost. The analysis results indicate that the partial self-centering behavior would be a better choice than the full self-centering behavior for developing the self-centering structural systems to achieve better life-cycle benefits. Moreover, it is essential and urgent to reduce the initial costs of self-centering structural members and control the floor acceleration responses for increasing the life-cycle benefits of self-centering structural systems and promoting their practical applications.

Seismic fragility and risk assessment of self-centering wall structures with traditional and sliding joint infill walls

Self-centering (SC) precast wall structures have emerged as earthquake-resilient structural systems with excellent seismic performances characterized by low damage as well as negligible post-earthquake residual deformation. However, research on SC wall systems often ignores infill walls for simplicity, which results in difficulty to achieve an integrated resilient structural system. To fill this gap, this paper presents a comprehensive assessment of SC precast concrete wall structures with three different types of infill walls and compares the results with that without infill walls. The maximum inter-story drift, the peak floor acceleration, and the damage index of the considered systems at different seismic intensities are calculated through incremental dynamic analysis. The assessment is then expanded from fragility to risk by evaluating the probabilities of exceeding each potential limit state throughout the service life. Results show that, despite merely no damage to the SC wall itself, the integral system could sustain significant damage due to the damage to the infills attached. What’s more, with stronger infill walls, severer damage to the integral system is likely to be. Among the three infills considered in this study, the one with sliding joints performs the best from the perspective of damage, resulting in a smaller likelihood of 21%∼60% exceeding various damage limits than that of traditional infills. However, the sliding joint infill’s benefit in damage is at the expense of larger drift and slightly higher acceleration responses compared with traditional infills. It is concluded that the infills considered in this paper all have their drawbacks and new infills that combine the sliding mechanism (to reduce damage) and higher damping (to reduce drift and acceleration) are encouraged to develop an integrated resilient system.

Machine learning-based seismic response and performance assessment of reinforced concrete buildings

Complexity and unpredictability nature of earthquakes makes them unique external loads that there is no unique formula used for the prediction of seismic responses. Hence, this research aims to implement the most well-known Machine Learning (ML) methods in Python software to propose a prediction model for seismic response and performance assessment of Reinforced Concrete Moment-Resisting Frames (RC MRFs). To prepare 92,400 data points of training dataset for developing data-driven techniques, Incremental Dynamic Analyses (IDAs) were performed considering 165 RC MRFs with two-, to twelve-Story elevations having the bay lengths of 5.0 m, 6.1 m, and 7.6 m assuming near-fault seismic excitations. Then, important structural features were considered in datasets to train and test the ML-based prediction models, which were improved with innovative techniques. The results show that improved algorithms have higher R2 values for estimating the Maximum Interstory Drift Ratio (IDRmax), and two improved algorithms of artificial neural networks and extreme gradient boosting can estimate the Median of IDA curves (M-IDAs) of RC MRFs, which can be used to estimate the seismic limit-state capacity and performance assessment of existing or newly constructed RC buildings. To validate the generality and accuracy of the proposed ML-based prediction model, a five-Story RC building with different input features was used, and the results are promising. Therefore, graphical user interface is introduced as user-friendly tool to help researchers in estimating the seismic limit-state capacity of RC buildings, while reducing the computational cost and analytical efforts.

Seismic performance of damaged frame retrofitted with self-centering and energy-dissipating rocking wall

This paper proposes the novel concept of retrofitting damaged reinforced concrete frame with self-centering and energy-dissipating rocking wall. Parametric studies were carried out base on pushover and time-history analysis. In both pushover and time-history analysis, the soft-story mechanism was effectively mitigated through the rocking wall retrofit of the damaged structures. The results demonstrated that the stiffness and bearing capacity of the retrofitted system were improved compare to its intact state. Additionally, the seismic response of the damaged frame retrofitted using rocking wall in combination with post-tension and shear-type damper fell within the relevant design limits. Pushover analysis of the rocking wall indicated that there is a linear relationship between the wall thickness and the initial stiffness of the retrofitted system. The addition of post-tension tendon to the rocking wall system enables the wall to self-center and increases lateral stiffness and bearing capacity of the retrofitted system. When the shear-type damper was installed, the energy dissipation of the system was increased, and the stiffness and bearing capacity of the retrofitted system were also improved. In the time-history analysis, it was found that the thickness of the rocking wall is directly related to the maximum inter-story drift and the distribution patterns of inter-story drift of the frame. As the post-tension was added to the system, the maximum inter-story drift under rare earthquake excitation improved significantly. With the addition of shear-type dampers, the overall drift magnitude of the retrofitted system was fundamentally decreased.

Direct displacement-based design of steel-timber hybrid structure with separated gravity and lateral resisting systems

Steel-timber hybrid structure can bring the benefits of timber and steel together in a more effective way. In this paper, a steel-timber hybrid structure with separated gravity and lateral resisting systems (ST-SGLRS) was proposed, and an iterative direct displacement-based design method was developed for this type of structure. Design examples revealed that the direct displacement-based design method with appropriate iterative steps is feasible for the design of steel-timber hybrid structures with separated gravity and lateral resisting systems. Furthermore, four steel-timber hybrid structures were designed based on the proposed design method, including 6-story, 9-story, 12-story structures with deformable steel-timber connections and a 9-story structure with rigid steel-timber connections, and corresponding OpenSees structural models were generated. Static and dynamic analyses were performed on the models to calibrate the structural performance. Comparing with the analytical result, it is found that the post-yield stiffness of the structure with deformable steel-timber connections decreased less than the structure with rigid steel-timber connections. As the earthquake intensity increased, the inter-story drift of the structure with rigid steel-timber connections increased rapidly. Besides, the residual inter-story drift of the structure with rigid steel-timber connections was generally larger than that of the structure with deformable steel-timber connections, indicating that the deformable connections contribute to the structure's ability to recover after a large earthquake. Finally, the seismic performance of the calibrated structures considering far-field and near-field earthquakes and impulse effect was evaluated via the probabilistic seismic demand analysis method. It is found that the maximum inter-story drift and the residual inter-story drift exceedance probabilities of the structures under near-field pulse-like earthquakes were larger than those under near-field no-pulse and far-field earthquakes. The research outcome aims to provide a fundamental basis for the design and engineering application of steel-timber hybrid structures with separated gravity and lateral resisting systems.

Two-Parameter–Based Damage Measure for Probabilistic Seismic Analysis of Concrete Structures

Traditional seismic fragility analysis defines the structural damage measure (DM) as a single parameter based on either strength, displacement, damage, or energy to evaluate the postearthquake performance of the structure, thus it is difficult to fully catch the behavior characteristics of the structures, e.g., both the maximum deformation capacity and the repairability of the structure. In this paper, we developed a multiparameter-based DM (mDM) index (here actually two parameters) for the probabilistic seismic analysis of reinforced concrete (RC) structures to capture a more comprehensive view of structural performance. Two parameters (i.e., the maximum interstory drift ratio θmax and the maximum residual interstory drift ratio θr,max) are combined to represent the overall structural performance, and different combination rules are investigated. To verify the superiority of the proposed mDM, the fragility analysis of three different structures is conducted, i.e., ordinary RC structure, aging RC structure, and new self-centering structure. The fragility curves derived from single DM and mDM are compared, and it is found that fragility curves with mDM can reflect both the maximum displacement and residual displacement features of the structure, thus mDM gives a more comprehensive and synthesis assessment of the postearthquake performance of the structure, which is beneficial for informed decision-making.

Predicting seismic interaction effect between soil and structure group using convolutional neural network

Quantifying the influence of seismic interaction between soil and structure group (SSGI) is of great significance to seismic design, retrofit, and damage assessment of structures in densely built urban areas. To this end, this study proposes a one-dimensional convolutional neural network (1D-CNN) model to rapidly predict the influence of adjacent structures on the maximum inter-story drifts and base shears of RC frame structures. Based on an experimentally validated three-dimensional finite element method, 890 pairs of soil-single structure versus soil-structure group systems under different earthquake loadings are simulated. The dataset comprising 890 groups of input (i.e., soil and structure group parameters, ground motion acceleration) and output data (i.e., changes in maximum inter-story drift and base shear) is constructed to train the machine learning model. Subsequently, sensitivity analysis is performed to identify optimal hyperparameters for training the 1D-CNN model, whereas a back propagation artificial neural network (BP-ANN) model is established to compare the model performance. Results indicate that compared with the BP-ANN model, the 1D-CNN model has a more stable and robust architecture and features superior prediction accuracy. In particular, the developed 1D-CNN model has a mean absolute error of less than 2.3% and an absolute error of less than 5.4% for 90% of cases in the testing set. The superior performance of the 1D-CNN model makes it an effective and efficient tool to be applied to predict the seismic responses of RC frame buildings under the SSGI effect.

Site dependent response estimation by holistic record selection and bagging algorithm

An efficient two-step method is proposed for site-specific structural response estimation of buildings at multiple sites with different seismicity. In the first step, holistic record sets that cover a range of seismic characteristics are constructed for a few intensity measure levels. Next, using the holistic sets and their associated responses, any required response measure (e.g., structural collapse) is calculated using a bagging algorithm. The proposed method has two advantages to many similar suggested processes in this regard. Because the proposed process works directly with record selection methods and a computational method, it can consider the effect of different ground motion intensity measures and works for all engineering demand parameters. The performance of the proposed method is investigated using two 4 and 8-story steel moment-resisting frames in six cities with different seismicity. The collapse fragility curve, maximum inter-story drift ratio (MIDR), and peak floor acceleration (PFA) are considered for performance assessment. It was observed that when the number of selected records is about twice the common required number of records for response assessment, the proposed method, on average, leads to equal or better efficiency for collapse fragility estimation compared to conventional single site-building analysis. Also, the results indicate an efficiency similar to utilizing about 10–20 ground motion records at each IM level for MIDR and PFA response estimation.

Hybrid Test of Precast Concrete Frame with Energy-Dissipation Cladding Panel System

To investigate the influence of an energy-dissipation cladding panel system (EDCPS) on the dynamic responses of a precast concrete (PC) frame structure, a six-story, three-span planar frame structure with an EDCPS (called “damping structure”) and a counterpart planar bare frame structure (called “bare frame structure”) were designed. The middle span and bottom two stories of the frame were selected as the test substructures, whereas the rest were considered using the numerical substructure. Hybrid tests were conducted on the two structures under four earthquake levels. The test results indicated that the damage evolution characteristics of the PC frame were not affected by the introduction of EDCPS. The dampers in the EDCPS successfully yielded and dissipated seismic energy under the four earthquake levels. Moreover, the maximum inter-story drift ratio of the damping structure was reduced by 12.59%, 17.68%, and 10.34% under the design-basis earthquake, maximum considered earthquake, and very rare earthquake, respectively, exhibiting a satisfactory damage-control effect. The cladding panels remained intact under the four earthquake levels, indicating that this structure effectively prevents damage to the cladding panels. Finally, a numerical simulation method is recommended according to the damage characteristics of the damping structure and is validated against the test data.

Comparison of seismic fragility of RC moment-resisting frame structures designed according to Chinese and Indian code

Seismic fragility analysis is a method used to evaluate the vulnerability experienced by structures when subjected to earthquakes. In this study, the seismic performance of 18 reinforced concrete moment-resisting frame structures designed according to Chinese code and Indian code is analyzed. A parametric study is conducted by varying the height of the building and the type of soil on which the building is constructed. Nonlinear time history analyses are conducted to develop fragility curves for four different damage levels: fully operational, operational, repairable, and collapse prevention. Linear regression analysis is conducted to correlate the engineering demand parameter (maximum inter-story drift) and the intensity of an earthquake (peak ground acceleration). The results show that the structures designed according to the Indian code experience higher story drift than those designed according to Chinese code, making them more vulnerable to the same earthquake intensity.

Vibration control of seismic forces using viscous dampers and buckling restrained braces in irregular composite buildings

This study addresses the effectiveness of buckling restrained braces (BRBs) and viscous dampers (VDs) in dissipating seismic energy and increasing the seismic performance of irregular composite buildings during earthquake events. The seismic response of steel-concrete composite moment resisting frames of 15 stories with concrete filled steel tubes (CFST) as columns and composite beams was examined with and without seismic protection devices by employing ETABS software using the response spectrum method as per IS 1893:2016 for seismic zone V. Regular and irregular plans characterised the structures. The plan irregular buildings include C and L-shaped buildings. The BRBs and VDs were installed on all the buildings in two configurations: corner bays and centre bays throughout the height. The results showed BRBs and VDs excellent energy dissipation capabilities. VDs contributions were 5%-8% more than BRBs and, therefore, more efficient. Centre bays placement of VDs was most efficient for regular buildings reducing time-period by 60%, maximum story displacement by 57%, base shear by 37%, and maximum interstory drift ratio by 70%. Corner bays placement of VDs was most efficient for C and L-shaped buildings reducing time-period by 55%-60%, maximum story displacement by 63%-65%, base shear by 30% and 13%, and maximum interstory drift ratio by 78%-80%, respectively, making viscous dampers an excellent choice for midrise composite buildings.

Experimental and numerical investigations on the similitude effect of scaled lead rubber bearings for shaking table test

Small scaled lead rubber bearings (SLRBs) are widely used for shaking table tests in isolated tall buildings. Notably, research on the similitude effect of such bearings has rarely been conducted at the component and overall structural levels. Thus, two types of SLRBs with a diameter of 95 mm were designed according to the post-yield stiffness (i.e., SLRB95-A) and equivalent stiffness (i.e., SLRB95-B) to evaluate the existing design principle for the SLRB in the shaking table tests. At the component level, the mechanical characteristics of the two types of SLRBs were evaluated through vertical compression tests and compression-shear tests, and the effects of critical factors on the mechanical parameters were identified. A more desirable and stable performance was realized for SLRB95-B than for SLRB95-A. At the overall structural level, the seismic performance of the prototype structure and scaled structure using the two types of SLRBs were compared. A better agreement was observed between the distributions of the maximum inter-story drift ratio of the prototype structure and scaled structure using SLRB95-B compared to SLRB95-A. Based on these results, the SLRB is recommended to be designed based on the equivalent stiffness. The research outcome will provide a useful reference for the design of scaled lead rubber bearings for shaking table tests.

Controlling interstory drift ratio profiles via topology optimization strategies

An approach to control the profiles of interstory drift ratios along the height of building structures via topology optimization is proposed herein. The theoretical foundation of the proposed approach involves solving a min–max optimization problem to suppress the maximum interstory drift ratio among all stories. Two formulations are suggested: one inherits the bound formulation and the other utilizes a p-norm function to aggregate all individual interstory drift ratios. The proposed methodology can shape the interstory drift ratio profiles into inverted triangular or quadratic patterns because it realizes profile control using a group of shape weight coefficients. The proposed formulations are validated via a series of numerical examples. The disparity between the two formulations is clear. The optimization results show the optimal structural features for controlling the interstory drift ratios under different requirements.

Seismic performance evaluation of steel buckling-restrained braced frames including SMA materials

The permanent deformation of the building after seismic excitations can be determined by the Maximum Residual Interstory Drift Ratio (MR-IDR), which may be used for measuring the damage states. Low-post yield stiffness of the steel buckling-restrained braced frame (BRBF) makes this system vulnerable to large MR-IDR after a severe earthquake event. To overcome this issue, this paper investigates the seismic limit state performances of low- to mid-rise BRBFs with two- to eight-story levels (i.e. 2-Story, 4-Story, 6-Story, and 8-Story) adopting different lateral force-resisting systems using Viscous Dampers (VDs) and Shape Memory Alloys (SMAs). For this purpose, BRBFs improved with different implementation of SMAs and VDs, and Incremental Dynamic Analyses (IDAs) were performed based on Maximum Interstory Drift Ratio (M-IDR) and MR-IDR demands. Results showed that VDs and SMAs can decrease the values of maximum moment and rotation of hinges of structural members. Implementing both SMAs and VDs can significantly improve the seismic performance level and collapse failure probability of BRBFs more effectively than using one of the VDs or SMAs; then, it can be recommended to control the MR-IDR of BRBFs. To use the results, graphical user interface has been developed to estimate the improvements in the M-IDR and MR-IDR demands.

Fragility curves for reinforced concrete frames characterised by different regularity

This paper presents a comparison between fragility curves developed for regular and non-regular reinforced frames. Three 3D reinforced concrete multi-story frames characterised by different regularity are analysed. These fragility curves are developed through the “Cloud Analysis“ procedure, which evaluates the structural response via Non-Linear Time History Analysis (NLTHA).Both maximum inter-story drift and maximum chord-rotation demand/capacity ratio are used as Engineering Demand Parameters, in which the chord-rotation capacity is calculated according to the Italian Code. To fully develop the fragility curves, both structure-independent and structure-dependent scalar intensity measures are selected among the most referred in practice and literature.This work shows the influence of regularity on the damage levels of the three buildings. Furthermore, it shows the uncertainties caused by the selection criteria for EDP thresholds, which are necessary for a correct representation of the Limit State.

Story-wise assessment of seismic behavior and fragility analysis of R/C frames considering the effect of masonry infills

The present paper investigates the story-wise damage response and the seismic fragility of planar multistory R/C buildings with various masonry infills' distributions. In order to fulfil this purpose, six planar R/C buildings (three moment frames and three dual structural systems consisting of frames and walls) are studied. For each structure several different masonry infills' distributions are taken into account. Then, the buildings are subjected to a set of appropriately chosen real earthquake records for which nonlinear time history analyses are conducted and the story-wise IDA curves for each building and infill distribution are constructed. The quantification of the expected seismic damage state is accomplished through the calculation of the maximum interstory drift ratio. Subsequently, based on the results of the IDA curves, the fragilities of each buildings' story as well as of the whole buildings are calculated. The results of this study demonstrate the role of masonry infills on the story-wise seismic damage of R/C buildings. The presence of the masonry infills cannot be ignored, since they can signifficantly modify the damage response and the seismic fragility of buildings depending on the structural system and on the infills' distribution.

Seismic performance of precast concrete frame with energy dissipative cladding panel system: Half-scale test and numerical analysis

An energy dissipative cladding panel system was proposed for large precast concrete cladding panels in multi-story buildings. A six-story, three-span planar prototype frame structure with energy dissipative cladding panel was designed to evaluate the seismic performance and damage control effects of the precast concrete frame with the proposed energy dissipative cladding panel system. The bottom two stories of the middle span were selected as the test substructure and were tested under cyclic loading. The damage evolution mode and seismic performance of this structure were identified. A numerical simulation method was recommended for such a structure based on the damage characteristics observed in the two-story substructure, and validated against the test results. The seismic responses of the six-story prototype frame structure with and without the energy dissipative cladding panel were then compared through nonlinear time-history analyses under near- and far-field ground motions. The analysis results indicated that the maximum inter-story drift ratios of the precast concrete frame with energy dissipative cladding panel were 23.8%–35.2% and 19.8%–41.6% lower than those of the bare precast concrete frame under far- and near-field ground motions, respectively. The maximum inter-story drift ratios of the precast concrete frame with energy dissipative cladding panel under near-field motions were 1.72 and 1.76 times those under far-field motions under the maximum considered and very rare earthquakes, respectively.