Interstorey Drift Ratio Research Articles

Numerical evaluation of the seismic performance of existing reinforced concrete buildings with corroded smooth rebars

Exposure to aggressive environments is one of the most critical problems of reinforced concrete (RC) structures, which can affect both their static and dynamic behaviour. In this paper, the linear and non-linear performance of existing corroded RC framed structures were studied through an advanced numerical model. Moreover, an extensive literature review of models and approaches used for the assessment of RC structures exposed to different levels of corrosion was presented. The numerical evaluation of an existing RC structure subjected to different exposures and degradation was considered. A new approach was presented for the evaluation of the ultimate capacity of RC elements. Such an approach has been compared and validated against a set of the experimental results from the literature. The results of comparative analyses showed that the proposed approach could predict the ultimate capacity of corroded RC components. Linear and non-linear analyses were performed using a refined Finite Element method; the seismic performance evaluated in terms of shear strength degradation, inter-storey displacements, ductility, and maximum base shear. The outcomes of the present study demonstrated that corrosion had a significant impact on the structural response of the existing building. Such an effect depended on the type of exposure. The elastic dynamic analyses of the building demonstrated that corrosion increased the fundamental periods and, changed the mass participation factor and the mode of vibration, i.e. the external exposure. Non-linear static analyses showed a significant reduction of the shear capacity and the translation ductility with the increase of the corrosion rate for all lateral loading patterns specified by the Eurocode. The results of the non-linear dynamic analyses illustrated that the damage and deterioration due to the corrosion attack increased the roof and the inter-storey drift-ratios, as well as a relevant decay of the base shear capacity and early collapse were noted for high-levels of corrosion. Comparisons between non-linear static and dynamic analyses were also provided in terms of roof drift-ratios and base shears.

A direct displacement-based seismic design method using a MDOF equivalent system: application to R/C framed structures

An improved version of the direct displacement-based design (DDBD) method for the seismic design of plane moment resisting frames in the framework of performance-based design approach is presented. The method employs a multi-degree-of-freedom equivalent system instead of the single-degree-of-freedom equivalent system used by the conventional DDBD method. Thus, the proposed method can take more rationally and with higher accuracy into account the higher mode and P-Δ effects than the conventional one. This is accomplished with the aid of the concept of deformation dependent equivalent modal damping ratios previously developed by the present authors for other purposes and the concept of the design modal displacements developed herein. These design modal displacements are determined on the basis of target inter-storey drift ratios for every performance level and the first few modes significantly contributing to the structural response. Thus, one can determine from the displacement spectrum with high amounts of viscous damping the required modal periods for known values of the design modal displacements. From those modal periods, the corresponding required modal stiffness and hence the modal base shear forces can be obtained. The final required design base shear can be obtained by a combination rule, like the SRSS rule. Numerical examples involving the seismic design of two moment resisting reinforced concrete plane frames are presented in detail for illustrating the proposed approach and demonstrating its merits over the conventional DDBD method and the force-based design method of Eurocode 8.

Seismic behaviour of stiffness irregular steel frames under mainshock–aftershock

Generally, the buildings located in earthquake-prone regions are subjected to a sequence of earthquakes. The sequence of earthquakes is termed as mainshock–aftershock (MS–AS). Most of the time the rehabilitation of structure before the occurrence of aftershock cannot be carried out due to a short interval of time between mainshock and aftershock results in additional damage to the structure. The irregular distribution of mass, stiffness and strength along the height of the building may exhibit the poor seismic performance of the structures. The present study examined the influence of stiffness irregularity on seismic demands of 3-, 6- and 9-storey steel moment-resisting frames by comparing the mean seismic demands on reference regular frames under mainshocks and MS–AS seismic sequences. Stiffness irregular frames are obtained by modifying the stiffness at three different locations (bottom, middle and top storey) along with the height of reference regular frame. MS–AS seismic sequences are generated by using a randomized approach. The comparison between reference and stiffness irregular frames shows that the effect of stiffness irregularity on the height-wise variation of interstorey drift ratio is significant. Results of the effect of MS–AS seismic sequence show that aftershock increases the structural responses of both reference regular and stiffness irregular frames.

Comparison of fully non-stationary artificial accelerogram generation methods in reproducing seismicity at a given site

Seismic input modelling is a crucial step when Non-Linear Time-History Analyses (NLTHAs) are performed, the seismic response of structures being highly responsive to the input employed. When natural accelerograms able to represent local seismicity are not available, the use of generated accelerograms is an efficient solution for input modelling. The aim of the present paper is to compare four methods for generating fully non-stationary artificial accelerograms on the basis of a target spectrum, identified using seven recorded accelerograms registered in the neighbourhood of the construction site during a single event, assumed as target accelerograms. For each method, seven accelerograms are generated and used to carry out NLTHAs on three RC structures, having irregular mass and stiffness distributions. The generation methods are evaluated in terms of both input modelling and seismic response of three RC structures. The results point out that maximum interstorey drift ratios are well reproduced only by generation methods based on spectrum-compatible criterion, while energy contained by the target set is only simulated by methods based on records of natural signals. Moreover, none of the method here investigated is able to reproduce the hysteretic energy dissipated by the structures subjected to the target accelerograms, in terms of both total amount and cumulative trend over the duration.

A Hybrid Seismic Design Method for Steel Irregular Space Moment Resisting Frames

ABSTRACT A performance-based hybrid force/displacement (HFD) seismic design method for space steel moment resisting frames irregular in plan view and in elevation is developed. Irregularity in elevation is either due to non-uniform distribution of mass or due to the presence of setbacks along the height of the frame. More specifically, 30 different frames irregular in plan view for the first case (plan-irregularities), 40 frames with setbacks (vertical stiffness irregularities) for the second case, and 18 frames with mass discontinuities (vertical mass irregularities) at the first, intermediate and top storey for the third case are considered. All these frames are designed according to Eurocodes 3 and 8 and subjected to 42 pairs of ordinary ground motions. Through nonlinear seismic analyses, seismic response databanks for these three types of irregular frames are generated corresponding to four performance levels. These databanks are then utilized for the development of simple expressions that determine the behavior (or strength reduction) factors of the frames. These are functions of frames geometrical/dynamic characteristics including measures of their irregularities as well as the target maximum interstorey drift ratio and member local ductility. The proposed design method, even though it is mainly a force-based design method, controls deformation and therefore damage through the proposed deformation-controlled behavior factors. Design examples are presented to validate the effectiveness of the method to account for the irregularity effects on the preliminary design stage while time-history analysis results demonstrate its advantages to control better the inelastic response of the frames over the conventional force-based seismic design method of Eurocode 8.

Mainshock‐aftershock state‐dependent fragility curves: A case of wood‐frame houses in British Columbia, Canada

SummaryDuring a mainshock‐aftershock (MSAS) sequence, there is no time to retrofit structures that are damaged by a mainshock; therefore, aftershocks could cause additional damage. This study proposes a new approach to develop state‐dependent fragility curves using real MSAS records. Specifically, structural responses before and after each event of MSAS sequences are used to obtain statistical relationships among the engineering demand parameter prior to the seismic event (pre‐EDP), the intensity measure of the seismic event (IM), and the engineering demand parameter after the seismic event (post‐EDP). The developed fragility curves account for damage accumulation, providing the exceeding probability of damage state (DS) given the IM of the event and the DS of the structure prior to the seismic excitation. The UBC‐SAWS model, which was developed for wood‐frame houses in British Columbia, Canada, is considered as a case study application. Results indicate that for the examined structural typology, state‐dependent fragility curves based on residual interstorey drift ratio (pre‐EDP), peak ground velocity (IM), and maximum inter‐storey drift ratio (post‐EDP) are the best choice to characterise the cumulative damage effect. An illustration of the developed fragility curves is provided by considering a hypothetical MSAS scenario of a Mw 9.0 Cascadia mainshock triggering a Mw 6.0 crustal event in the Leech River fault, affecting wooden houses in Victoria, Canada. The MSAS scenario increases Yellow tags (restricted access) by 12.3% and Red tags (no access) by 4.8%.

Optimal seismic retrofit method for reinforced concrete columns with wing walls

Seismic retrofit of reinforced concrete (RC) columns using wing walls can be used to improve the shear and flexural strength of the column through a relatively simple process. However, the feasibility and efficiency of the seismic retrofitting of RC frames with wing walls heavily depends on the selection of number of columns to be retrofitted, the cross-sectional dimensions of wing walls, and the quantity of re-bars of the wing wall. In this study, an optimal seismic retrofit design method is proposed to minimize not only the initial retrofit cost but also the earthquake-induced damage expected during the life cycle of the building. The seismic performance of structures before and after the application of the retrofit has been verified with the comparison of four response parameters: pushover curves, the inter-storey drift ratios, the energy dissipation capacities, and failure modes. The proposed retrofit method is applied to seismic retrofit of a six-storey RC building example and an actual RC building structure in use. For the retrofit of actual building structure, with an initial retrofit weight of 70.85 kN, which corresponds to 1.85% of the weight of the non-retrofitted building, the energy dissipation capacity was increase by 3.02 times and the life cycle cost (LCC) of the retrofit was reduced to 69.47% of the required LCC for the non-retrofitted building. In addition, it has been confirmed that no storey collapse occurred in collapse prevention level, which indicates the most severe failure mechanism of a structure due to an earthquake.

Effect of Lead Rubber Bearing on Seismic Response of Regular and Irregular Frames in Elevation

Base isolations are acknowledged as an effective seismic protective system for structural systems of buildings. This study investigates the effectiveness of lead rubber bearing (LRB) on the nonlinear response of the steel moment resisting frames subjected to real ground motions. To this aim, 12-storey regular and irregular steel frames in elevation upgraded with LRB were studied by evaluating the local and global deformations. LRB was modeled by considering three key parameters of isolation period, effective damping ratio, and stiffness ratio. Two-dimensional model of the base isolated frames were created and a series of time-history analyses were carried out by different earthquake ground motions. The seismic behaviour of the bare and isolated frames was measured by the variation of isolator displacement, acceleration, interstorey drift ratio, relative displacement, roof drift ratio, normalized base shear, base moment, and hysteretic curve. The supremacy of the base-isolated frames over the bare frames was discussed accordingly. It was found that the seismic response of the regular and irregular frames in elevation could be improved up to a certain degree by implementing LRB.

A comparison of three performance-based seismic design methods for plane steel braced frames

This work presents a comparison of three performance-based seismic design methods (PBSD) as applied to plane steel frames having eccentric braces (EBFs) and buckling restrained braces (BRBFs). The first method uses equivalent modal damping ratios (�k)referring to an equivalent multi-degree-of-freedom (MDOF) linear system, which retains the mass, the elastic stiffness and responds in the same way as the original non-linear MDOF system. The second method employs modal strength reduction factors (�𝑘) resulting from the corresponding modal damping ratios. Contrary to the behavior factors of code based design methods, both �k and �k account for the first few modes of significance and incorporate target deformation metrics like inter-storey drift ratio (IDR) and local ductility as well as structural characteristics like structural natural period, and soil types. Explicit empirical expressions of �k and �k, recently presented by the present authors elsewhere, are also provided here for reasons of completeness and easy reference. The third method, developed here by the authors, is based on a hybrid force/displacement (HFD) seismic design scheme, since it combines the force-base design (FBD) method with the displacement-based design (DBD) method. According to this method, seismic design is accomplished by using a behavior factor (qh), empirically expressed in terms of the global ductility of the frame, which takes into account both non-structural and structural deformation metrics. These expressions for qh are obtained through extensive parametric studies involving non-linear dynamic analysis (NLDA) of 98 frames, subjected to 100 far-fault ground motions that correspond to four soil types of Eurocode 8. Furthermore, these factors can be used in conjunction with an elastic acceleration design spectrum for seismic design purposes. Finally, a comparison among the above three seismic design methods and the Eurocode 8 method is conducted with the aid of non-linear dynamic analyses via representative numerical examples, involving plane steel EBFs and BRBFs.

A practical methodology for optimum seismic design of RC frames for minimum damage and life-cycle cost

The design criteria in current seismic design codes are mainly to control lateral displacements and provide adequate strength to sustain expected design load combinations. However, to achieve the most economic design solutions, the life-cycle total cost (TLCC), which includes both initial structural cost and expected damage cost, should be also considered for the probable earthquakes during the lifetime of the structure. In the present study, the TLCC of the buildings is used as the main objective function for optimum seismic design of reinforced concrete (RC) frames. First, it is demonstrated that the blind increase of the reinforcement ratios does not necessarily reduce the displacement demands and the damage costs. Subsequently, a practical methodology is developed for the optimum seismic design of RC frames based on the concept of uniform damage distribution (UDD). Using an adaptive iterative procedure, the distribution of inter-storey drifts and TLCC of the floors is modified along the height of the structure. To demonstrate the efficiency of the method, 5, 8 and 12 storey RC frames are optimized using the proposed algorithm. The results indicate that, while all predefined performance targets are satisfied, the maximum inter-storey drift ratio and TLCC of the frames are considerably reduced (up to 56% and 45%, respectively) only after a few steps. The proposed method should prove useful for more efficient performance-based design of RC frames in practice.

Comparative performance evaluation of RC frame structures using direct displacement-based design method and force-based design method

Force-based design (FBD) method has been practiced for a long time which focuses on the seismic force over the structure. Problems associated with FBD are assumed stiffness of structural elements, inappropriate R factors and others. Thus, a new alternative method is required to overcome these differences. Direct displacement-based design method (DDBD) provides an efficient alternative. It is more straightforward which aims to achieve a specified acceptable level of damage under the design earthquake. The main aim of DDBD is to define the target displacement profile for the structures. In this study, the performance of low- and medium-rise building is evaluated using FBD and DDBD method and results have been compared. Both structures are designed according to Indian standard loading in compliance with IS 1893 (part 1) 2016. Non-linear analyses have been carried out for evaluating structural performance like base shear, maximum displacement and inter-storey drift ratio (IDR%). From the study, it can be concluded that DDBD method is more effective than FBD method.

Seismic response of low-rise 3-D steel structures equipped with the seesaw system

The efficiency of the seesaw system when applied to low-rise 3-D steel structures is presented in this paper. This efficiency is judged by several seismic response results coming from inelastic seismic time-history analyses of 2-, 5- and 8-storey steel structures. These response results involve height wise distributions for peak interstorey drift ratios (IDR), peak residual interstorey drift ratios (RIDR) and plastic hinge formations in frame elements as well as peak forces to spiral strand ropes and viscous dampers of the seesaw system. For the foundation of the steel structures, different soil types are considered in order to assess the effects of soil-structure interaction (SSI). The seismic incident angle is also taken into account. From the results presented it is concluded that the seesaw system, essentially working always in tension, constitutes a bracing solution that can be potentially proposed by seismic codes as an alternative seismic force resisting system for low-rise steel structures.

Experimental Validation of a Radar-Based Structural Health Monitoring System

This paper presents a new structural health monitoring (SHM) method using frequency-modulated continuous wave (FMCW) radar. The method was developed to circumvent issues with SHM methods' need for displacement measurements, which can be difficult to obtain robustly through integrated accelerations, or through other displacement measurement methods. Instead, interstorey drift ratios (IDRs) were estimated through the direct measurement of interstorey displacement using FMCW radar. Simulation of this method using historical structural response data verified suitably accurate displacement measurements could be obtained using FMCW radar, and prompted the construction of a prototype system. Experimental validation of this prototype was carried out on a shake table. The precision of the system in terms of mean IDR was found to be 1.09 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . These results are encouraging for the future deployment of this SHM approach.

Seismic response of substandard RC frame buildings in consideration of staircases

During the seismic performance assessment of existing buildings, staircases are generally not taken into account as structural members but as dead load. Staircases, as secondary structural members, not only serve for connecting successive floors but also provide considerable amount of strength and stiffness to the building which can modify its seismic behaviour considerably. In this parametric study, the influence of staircases on the seismic response of substandard RC frame buildings which differ in number of storey and span, presence of staircase and its position has been examined. Modal Analyses and bidirectional Non-Linear Time History Analyses (NLTHA) were conducted to compare several engineering demand parameters (EDPs) such as inter-storey drift ratio (ISDR), floor accelerations, modal properties, member shear forces and plastic hinge distribution. Additionally, short column effect, variation in shear forces of columns that are attached to the staircase slab, failure and deformation in staircase models have also been investigated. As the staircase was considered in the analytical model, a different damage pattern can be developed especially in the structural components close to staircase.

Seismic Response of Steel Structures Equipped with the Seesaw System

ABSTRACTThis work provides seismic response results from non‐linear seismic analyses of low‐rise 3‐D steel structures equipped with the seesaw system. In particular, seismic response results involving height wise distributions for peak interstorey drift ratios (IDR) and peak residual interstorey drift ratios (RIDR) as well as plastic hinge formations are obtained for 2‐ and 8‐storey fixed‐base steel structures. Additionally, soil‐structure interaction is considered for these steel structures and its effect in the aforementioned seismic response results is discussed. It is concluded that the seesaw system constitutes an attractive solution for low‐rise 3‐D steel structures as buckling problems associated with common steel braces are eliminated and their damping capacity increases considerably.

Comparative evaluation of MFP and RBF neural networks’ ability for instant estimation of r/c buildings’ seismic damage level

The problem of the seismic damage prediction of reinforced concrete (r/c) buildings utilizing two types of Artificial Neural Networks (ANN) is investigated in the present paper. More specifically, the problem is formulated and solved in terms of the Function Approximation problem as well as of the Pattern Recognition problem using Multilayer Feedforward Perceptron Networks (MFP) and Radial-Basis Function (RBF) networks. The required training data-sets are created by means of Nonlinear Time History Analyses of 90 r/c buildings which are subjected to 65 earthquakes. The selected buildings differ in total height, in structural system, in structural eccentricity as well as the existence or not of masonry infills. The seismic damage index which is used to describe the seismic damage state is the Maximum Interstorey Drift Ratio. The influence of the parameters which are used for the configuration and the training of MFP and RBF networks on the reliability of their predictions is also investigated. The generalization ability of the best configured ANNs is examined by means of two categories of seismic scenarios. The most significant conclusion that turned out is that the trained ANNs can reliably and rapidly classify the r/c buildings into pre-defined damage classes provided they are appropriately configured.

Effect of friction pendulum bearing properties on behaviour of buildings subjected to seismic loads

This study investigates the influence of the friction pendulum bearing (FPB) isolator characteristics on the nonlinear response of the buildings under various seismic excitations. To represent a wide range of assessment, 3, 6, and 9-storey steel framed buildings with twenty seven different isolation models of FPB were studied by identifying the local and global deformations. Three important parameters such as isolation period T (as 2, 2.5, and 3 s), effective damping ratio ß (as 0.05, 0.15, 0.25), and yield strength ratio Fy/W (as 0.025, 0.05, and 0.10) were used in the modelling of FPB. Two-dimensional model of the base-isolated steel frames were created and the nonlinear time history analysis was performed through a number of earthquake ground motions. The behaviour of the isolated frames was measured by the variation of isolator displacement, roof drift ratio, relative displacement, interstorey drift ratio, absolute acceleration, base shear, base moment, hysteretic curve, and dissipated energy. The benefits obtained through the adoption of the base isolation system were discussed. It was found that the seismic response of the base-isolated frames could be estimated accurately by adjusting the proper isolation period, yield strength ratio, and effective damping ratio for the case studied structures.

Estimation of Inelastic Interstorey Drift for OSB/Gypsum Sheathed Cold-Formed Steel Structures under Collapse Level Earthquakes

In order to estimate the inelastic interstorey drift of cold-formed steel (CFS) framed structures under collapse level earthquakes, the deflection amplification factor ηp is employed in this paper to compute the maximum interstorey drift ratio (IDRmax) from an elastic analysis. For this purpose, a series of CFS wall specimens were tested under cyclic horizontal loads, and then the hysteresis model of the walls was put forward by test results. In terms of the hysteresis model, a large quantity of elastic-plastic time-history analysis of CFS building structures was conducted based on the storey shear-type model. Furthermore, the deflection amplification factor ηp for estimating IDRmax and the parameters were analyzed. The results indicate that the deflection amplification factor ηp is highly dependent on yielding coefficient of storey shear force ξy, storey number N, period of structure T, and ground acceleration records GA. Eventually, an approximate ξy-N-ηp relationship for estimating the deflection amplification factor ηp is proposed in this paper, which can be used for seismic design in practices.

Seismic response of SSSI system: surface structures and subway

The seismic response of an underground structure is analysed in the time domain by considering the non-linearity of soil and the structure–soil–underground structure interaction. A three-dimensional model that comprises a subway station and adjacent surface frame structure with a pile foundation and soft clay is established. The modified Davidenkov model is used to simulate the non-linearity of soft clay, which is then further developed using the commercial software Abaqus. This study focuses on the influence of adjacent surface frame structures on the seismic response of a subway station in the time domain. The interstorey drift ratio of the subway station is selected to evaluate the correlation effect in this complicated system. The influence factors, including the horizontal distance between the frame structures and subway station, length of the pile foundation, orientation of the frame structure and burial depth of the subway station, are discussed in the paper. Numerical results indicate that horizontal distance and burial depth are two of the key factors that may evidently amplify or attenuate the seismic response of an underground structure.

Prediction of the Seismic Response of Multi-Storey Multi-Bay Masonry Infilled Frames Using Artificial Neural Networks and a Bilinear Approximation

In order to test the reliability of neural networks for the prediction of the behaviour of multi-storey multi-bay infilled frames, neural network processing was done on an experimental database of one-storey one-bay reinforced-concrete (RC) frames with masonry infills. From the obtained results it is demonstrated that they are acceptable for the prediction of base shear (BS) and inter-storey drift ratios (IDR) in characteristic points of the primary curve of infilled frame behaviour under seismic loads. The results obtained on one-storey one-bay infilled frames was extended to multi-bay infilled frames by evaluating and comparing numerical finite element modelling(FEM) modelling and neural network results with suggested approximating equations for the definition of bilinear capacity by defined BS and IDRs. The main goal of this paper is to offer an interpretation of the behaviour of multi-storey multi-bay masonry infilled frames according to a bilinear capacity curve, and to present the infilled frame’s response according to the contributions of frame and infill. The presented methodology is validated by experimental results from multi-storey multi-bay masonry infilled frames.