RC Moment Research Articles

On advantages of the “Substitute Frame” model for incremental dynamic analysis: Integration of speed and accuracy

The “Substitute Frame” (SF) model, which is a simplified MDOF system consisting of a one-bay multistory frame, has recently been introduced by the authors to predict the static and dynamic response of RC building frames, especially in terms of Interstory Drift Ratio (IDR) and plastic hinge rotation. It is known that incremental dynamic analysis (IDA) is one of the most accurate nonlinear seismic analyses that is of course a time-consuming method, having a high computational cost. Hence, this paper aims to focus on the accuracy and speed of the Substitute Frame (SF) as a simplified frame model in performing IDA, fragility analysis, and other probabilistic analyses. If the desired result is achieved, this can be promising to perform extensive probabilistic analysis efficiently. To this end, three 8-, 12-, and 20-story benchmark RC moment frames were selected and the corresponding simplified SF models were generated. To accurately perform the required analyses, the OpenSEES software by implementing modified Ibarra-Medina-Krawinkler springs with deteriorating peak-oriented behavior was used to apply Nonlinear Time-History Analysis (NTHA) using the Hunt-Fill algorithm for IDA analyses. The results showed that the SF model can be reliably applied to perform IDA analyses and developing fragility curves and it is computationally efficient and robust. The selected OpenSEES example files for the present study, are shared through the link “https://web.nit.ac.ir/~h.hamidi/software_data.htm”.

Seismic Strengthening of RC Structures Using Wall-Type Kagome Damping System

In this study, the Kagome truss damper, a metallic wire structures, was introduced and its mechanical properties were investigated through theoretical analyses and experimental tests. The yield strength of the Kagome damper is dependent on the geometric shape and diameter of the metallic wire. The Kagome damper has higher resistance to plastic buckling as well as lower anisotropy. Cyclic shear loading tests were conducted to investigate the energy dissipation capacity and stiffness/strength degradation by repeated loadings. The hysteretic properties obtained from the tests suggest that a modification of the ideal truss model with a hinged connection could be used to predict the yield strength and stiffness of the damper. For seismic retrofitting of a low-rise RC moment frame system, a wall-type Kagome damping system (WKDS) was proposed. The effectiveness of the proposed system was verified by conducting cyclic loading tests using a RC frame with/without the WKDS (story drift ratio limit 1.0%). The test results indicated that both the strength and stiffness of the RC frame increased to the target level and that its energy dissipation capacity was significantly enhanced. Nonlinear static and dynamic analyses were carried out to validate that the existing building structure can be effectively retrofitted using the proposed WKDS.

A seismic fragility model accounting for torsional irregularity in low‐rise non‐ductile RC moment‐resisting frames

AbstractBuildings characterized by torsional irregularity are notorious for their vulnerability to earthquakes. However, most fragility/vulnerability models used for regional seismic risk assessment fail to distinguish between buildings with torsionally balanced and unbalanced configurations. The present study aims to develop a seismic fragility model sensitive to torsional irregularity for low‐rise non‐ductile RC moment frame buildings. To this end, a numerical investigation centred on 13 three‐storied plan‐asymmetric models, each characterized by a distinct combination of normalized stiffness eccentricity, torsional radius to mass radius of gyration ratio and normalized strength eccentricity, is presented. Using high‐dimensional model representation (HDMR), a metamodel for the maximum inter‐storey drift under bi‐directional seismic action is calibrated, considering average spectral acceleration and the above trio of torsional irregularity descriptors (TIDs) as the predictor variables. Carrying out numerical simulations on limit state functions formulated using the above demand model and appropriate capacity thresholds, the seismic fragility is estimated. The parameters of a lognormal fragility function compatible with the above estimates are determined using the method of maximum likelihood. A strong correlation is observed between the TIDs and the fragility function parameters. This reinforces the importance of accounting for all three TIDs while rating the seismic fragility of a building. Using least‐square error minimization technique, a functional relationship is established between the fragility model parameters and the TIDs. The framework described herein provides a simple, yet rational means to develop the next generation of seismic fragility models accounting for one of the most critical factors governing seismic behaviour––‘torsional irregularity’.

Column-to-beam flexural strength ratio for performance-based design of RC moment frames

The concept of strong column – weak beam is frequently used in seismic design to secure the safety of framed buildings, and for RC special moment frames, current design codes require the minimum column-to-beam flexural strength ratio at joints to reduce the likelihood of yielding in columns. However, the requirement for the strength ratio may not be satisfactory to prevent column hinging due to inelastic moment distributions and higher mode effects of dynamic response. In the present study, to investigate the required strength ratio, a numerical study was performed considering various parameters (plastic rotations of beams and columns, design earthquake loads and vertical distributions, gravity loads, stiffness ratios, design methods for beam strength, joint locations, and frame heights). The numerical study results showed that the strength ratio varies with the parameters and its vertical distribution is generally in a wine-glass shape along the frame height. On the basis of the numerical investigation, a design method for the strength ratio was developed as a function of the height ratio for performance-based design. For verification, nonlinear static and dynamic analyses were performed for regular and irregular frames designed by the developed method, and the results showed that the use of the developed method can improve seismic performance in a more economical way.

Effect of bidirectional excitation on seismic performance of regular RC frame buildings designed for modern codes

The existing practice to estimate seismic performance of a regular building is to carry out nonlinear time history analysis using two-dimensional models subjected to unidirectional excitations, even though the multiple components of ground motion can affect the seismic response, significantly. During seismic shaking, columns are invariably subjected to bending in two orthogonal vertical planes, which leads to a complex interaction of axial force with the biaxial bending moments. This article compares the seismic performance of regular and symmetric RC moment frame buildings for unidirectional and bidirectional ground motions. The buildings are designed and detailed according to the Indian codes, which are at par with the other modern seismic codes. A fiber-hinge model, duly calibrated with the biaxial experimental results, is utilized to simulate the inelastic behavior of columns under bidirectional bending. A comparison of the estimated seismic collapse capacity is presented, illustrating the importance of considering the bidirectional effects. The results from fragility analysis indicate that the failure probabilities of buildings under the bidirectional excitation are significantly higher as compared to those obtained under the unidirectional excitation.

Seismic Response of RC Moment Frame Including Topography–Soil–Structure Interaction

AbstractThe reflections of waves collide with the slope, and the reduction in the ground lateral stiffness in the areas near the slope crest affects buildings. In this research, using the three-dim...

Evaluation of RC Moment Frames Designed Based on Proposed Energy-Based Design Method

AbstractThis study presents an energy-based procedure for the design of RC frames under earthquake strong motions. For this purpose, three RC frames having 4, 8, and 12 stories that were used in FE...

General Substitute Frame Model (GSF) for efficient estimation of seismic demands of steel and RC moment frames

This paper proposes an approach to simplify 2D moment-resisting frames (with equal or non-equal bay lengths) to an equivalent single-bay framed MDOF model. This model, named the General Substitute Frame (GSF), is a promising development of the recently introduced Substitute Frame (SF) model by the authors that was restricted to equal-bay moment frames. The proposed GSF model which resolves the limitation of the SF model is applicable for both the steel and RC moment frames from low-rise to high-rise buildings. In order to evaluate the accuracy of the GSF model rigorously, a combination of 24 full-frame 2D moment frames including 4-, 12-, and 20-story buildings was designed and the results of nonlinear dynamic analyses were compared with their corresponding GSF models in terms of engineering demand parameters. In addition, modal and pushover analyses were also performed. Earthquake ground motions employed in this study include mild far-fault, moderate far-fault, and severe near-fault records selected by the Conditional Spectrum method. To accurately perform the required analyses, OpenSEES software was used, and 3600 runs of nonlinear time history analysis have been carried out. Based on the results of the analyses, it was demonstrated that the GSF model could predict the seismic response of moment frames well enough into both the linear and nonlinear ranges with high accuracy and can be a reliably practical substitution for moment-resisting frames. Moreover, the GSF model can be easily extracted from the primary full-frame based on the proposed equations.

Design of RC moment frame buildings consistent withearthquake resistant design philosophy

Earthquake Resistant Design Philosophy seeks (a) no damage, (b) no significant structural damage, and (c) significant structural damage but no collapse of normal buildings, under minor, moderate and severe levels of earthquake shaking, respectively. A procedure is proposed for seismic design of low-rise reinforced concrete special moment frame buildings, which is consistent with this philosophy; buildings are designed to be ductile through appropriate sizing and reinforcement detailing, such that they resist severe level of earthquake shaking without collapse. Nonlinear analyses of study buildings are used to determine quantitatively (a) ranges of design parameters required to assure the required deformability in normal buildings to resist the severe level of earthquake shaking, (b) four specific limit states that represent the start of different structural damage states, and (c) levels of minor and moderate earthquake shakings stated in the philosophy along with an extreme level of earthquake shaking associated with the structural damage state of no collapse. The four limits of structural damage states and the three levels of earthquake shaking identified are shown to be consistent with the performance-based design guidelines available in literature. Finally, nonlinear analyses results are used to confirm the efficacy of the proposed procedure.

Challenges in Evaluating Seismic Collapse Risk for RC Buildings

The development of fragility functions that express the probability of collapse of a building as a function of some ground motion intensity measure is an effective tool to assess seismic vulnerability of structures. However, a number of factors ranging from ground motion selection to modeling decisions can influence the quantification of collapse probability. A methodical investigation was carried out to examine the effects of component modeling and ground motion selection in establishing demand and collapse risk of a typical reinforced concrete frame building. The primary system considered in this study is a modern 6-story RC moment frame building that was designed to current code provisions in a seismically active region. Both concentrated and distributed plasticity beam–column elements were used to model the building frame and several options were considered in constitutive modeling for both options. Incremental dynamic analyses (IDA) were carried out using two suites of ground motions—the first set comprised site-dependent ground motions, while the second set was a compilation of hazard-consistent motions using the conditional scenario spectra approach. Findings from the study highlight the influence of modeling decisions and ground motion selection in the development of seismic collapse fragility functions and the characterization of risk for various demand levels.

Seismic Debris Field for Collapsed RC Moment Resisting Frame Buildings

AbstractThe debris field of earthquake-induced building collapse can block or reduce the capacity of adjacent sidewalks and roads, hinder emergency and evacuation operations, and therefore adversel...

Gaussian Kernel Methods for Seismic Fragility and Risk Assessment of Mid-Rise Buildings

Seismic fragility functions can be evaluated using the cloud analysis method with linear regression which makes three fundamental assumptions about the relation between structural response and seismic intensity: log-linear median relationship, constant standard deviation, and Gaussian distributed errors. While cloud analysis with linear regression is a popular method, the degree to which these individual and compounded assumptions affect the fragility and the risk of mid-rise buildings needs to be systematically studied. This paper conducts such a study considering three building archetypes that make up a bulk of the building stock: RC moment frame, steel moment frame, and wood shear wall. Gaussian kernel methods are employed to capture the data-driven variations in the median structural response and standard deviation and the distributions of residuals with the intensity level. With reference to the Gaussian kernels approach, it is found that while the linear regression assumptions may not affect the fragility functions of lower damage states, this conclusion does not hold for the higher damage states (such as the Complete state). In addition, the effects of linear regression assumptions on the seismic risk are evaluated. For predicting the demand hazard, it is found that the linear regression assumptions can impact the computed risk for larger structural response values. However, for predicting the loss hazard with downtime as the decision variable, linear regression can be considered adequate for all practical purposes.

Impact of the Lead Rubber Base Isolators on Reinforced Concrete Building

Civil engineering infrastructures are prone to natural disasters like earthquakes, floods, and hurricanes. Dissipation energy plays the main role in design of structures under Earthquake loads and controls the behavior of buildings when it bears the lateral loads and transfers them to the foundation. To resist the vibrations in the structure, it is important to use a high technology like Base isolation which reduces base frequency of building vibration and reaching it to a lower value. In other words, seismic isolation has the main objective to protect structure during earthquake events. Base isolation is a flexible layer between foundation and superstructure thus decoupling the structure from damaging effect of ground motion. This edits the dynamic characteristics of the structural system. A comparative study is conducted of seismic performance on three types of thickness (100mm,200mm, 300mm) in which M1T1, M2T1, M3T1, M1T2, M2T2, M3T2, M1T3, M2T3, M3T3, M1T4, M2T4, and M3T4 has been analyzed of isolators namely Lead Rubber Base Isolators (LRBI). For this evaluation, an 8-story structure has been analyzed by using (ETABS) finite element program where Models have ordinary RC moment- resisting frames with square column cross- sections. Parameters like drift, displacement, story acceleration, frequency, and story velocity have been analyzed and it has been found that due to the presence of Lead Rubber Isolators the story drift, story accelerations, base shear, lateral shear forces, and velocity are greatly reduced and story displacement is increased in both X and Y directions compared for various thickness of lead rubber base isolation systems under near and far-field earthquakes. Most importantly it has been established that the transmission of the high energy seismic waves to the superstructure is greatly reduced by introducing base isolators in between the top of the footing and the bottom of the superstructure. The base isolator with thickness 100mm for the concrete grade M20, M30, M40 performed more efficiently than other thicknesses. In conclusion, the deformation and transmissibility ratio must be minimized to introduce as a solution for absorbing the vibrations where the engineer should consider this effect for adequate design.

Peak Velocity of Viscous Dampers for Direct Displacement Based Design of RC Moment Resisting Frames

ABSTRACT Previous researchers have extended the direct displacement-based design (DDBD) procedure, to design reinforced concrete moment-resisting frame (RC-MRF) buildings with linear viscous dampers (LVDs). In those studies, the viscous damper forces are found to be larger than the design viscous damper forces because the actual relative structural velocity is different from the pseudo-velocity and also due to higher-mode effects. In the present study, a damper velocity correction factor is introduced along the height of the RC-MRF with LVDs, to calculate the corrected velocity of the LVD from the design velocity of the LVD, when the DDBD procedure is used. The damper velocity correction factor is proposed using the results of nonlinear response history analysis (NLRHA) for a set of RC-MRFs with LVDs, which are designed using the DDBD procedure. The DDBD procedure is then used to design RC-MRFs with nonlinear viscous dampers (NLVDs) making use of the proposed damper velocity correction factor, by calculating the NLVD characteristics using the equal energy (EE) dissipation approach or the equal power (EP) consumption approach. The accuracy of the proposed damper velocity correction factor is evaluated by carrying out NLRHA of two sets of RC-MRFs with NLVDs, one set where the damper velocity correction factor is not used, and the other set where it is used. When the damper velocity correction factor is used; the design LVD forces either agree with NLRHA results or are slightly more conservative, the design NLVD forces are close to the NLRHA results, and the maximum value of peak inter-story drift ratio (IDR) along the height of the RC-MRF from NLRHA is close to the design IDR limit. There is no significant difference in the peak story shear forces whether the damper velocity correction factor is used or not.

Seismic performance assessment of multi-story RC buildings with soft-story collapse mechanism equipped with gapped inclined bracing (GIB)

Gapped inclined bracing (GIB) is an innovative retrofit system for buildings with soft-story collapse mechanism. The system consists of a brace with gap element that activates before the structure approaches post-capping negative stiffness and collapse, providing supplemental plastic deformation and enhancing ductility of the system. This technique is also a resilient solution as the damage is controlled at the retrofitted soft-story, reducing the cost and time of repair. The paper presents a numerical study to verify the application of GIB systems for modern RC buildings, where masonry infill panels may be removed from lower stories due to functional requirements for more open spaces. Based on nonlinear static analysis, a novel and efficient design method is proposed to determine the GIB design parameters. To verify the performance of the retrofitting methodology, 12 configurations of RC moment frames with 4 and 8 stories are designed according to modern seismic codes and subjected to nonlinear static and incremental dynamic analyses. The results are then used to conduct fragility analysis to assess classical performance levels including immediate occupancy, life-safety, and collapse prevention. The results show that using the proposed design of GIB elements, the ultimate drift capacity corresponding to the collapse of soft-structures are increased by a factor of two. Also, the probability of collapse is reduced by 50% increase in the median collapse hazard intensity. These highlight significant improvements in the safety and resilience of buildings with soft-stories.

Experimental research methodology for the deformation of RC frame under instantaneous loss of column

In recent years, numerous experimental and especially numerical studies have been conducted in order to study the mechanisms of the resistance of reinforced concrete building frames to progressive collapse during the instantaneous removal of one of the columns. Analysis of these researches shows that almost all study deals with strength performance of RC structural elements under quasi static or instantaneous loss of column. At the same time, a number of numerical and analytical studies of the progressive collapse behaviour of steel moment frames as well as fragments of RC moment frames indicates that loss of bearing capacity of structures can be associated with buckling behaviour. Therefore, using the theory of functional similarity, a physical model of the reinforced concrete frame of a multi-storey building and a methodology for experimental studies of the buckling and fracture of this structural system under instantaneous loss of the corner column are proposed.

Characterization of ground motion intensity for the seismic fragility assessment of plan-irregular RC buildings

The identification of ground motion intensity measures (IMs) that are characterized by virtues such as efficiency, sufficiency, scaling robustness and hazard computability, has been the subject of extensive research over the past several years. In the process, there have evolved, numerous non-structure specific as well as structure specific descriptors of ground shaking severity. Most of the studies that investigated the optimality of such descriptors were, however, restricted to the seismic response of single or multi-storey planar frame buildings under unidirectional excitation. The study herein aims to examine, the efficiency and sufficiency of a wide spectrum of IMs, in predicting the maximum interstorey drift demands on plan-irregular RC moment frame buildings subjected to bi-directional ground motion. This is accomplished through a cloud analysis-based framework that integrates nonlinear response history analysis and statistical regression analysis. Further, the use of scalar bi-directional shaking intensity measures (BSIMs) derived from a vector of intensities corresponding to each horizontal component of ground motion using popular combination schemes such as geometric averaging, arithmetic averaging, SRSS and use of envelope values, is examined from the perspective of their ability to predict drift demands. Observations from the study reveal that IMs based on the geometric averaging of spectral ordinates over a range of periods are superior to the other descriptors considered, in terms of the aforementioned attributes and that combining the intensities of the two orthogonal components by geometric averaging leads to an optimal BSIM that could be used in place of vector IMs. The heteroscedasticity in the maximum interstorey drift response under different levels of the BSIM is further investigated using a Multiple Stripe Analysis framework. The optimal BSIM is observed to perform reasonably well at all target intensity levels, making it an excellent candidate to base fragility and vulnerability functions upon.

Performance-Based Seismic Design of RC Moment Resisting Frames with Friction-Damped Self-Centering Tension Braces

ABSTRACT This paper presents a performance-based seismic design method of RC moment resisting frame with friction damped self-centering tension braces (FSTB-Frame). The structural configuration and theoretical model of FSTB is introduced, and the numerical model of FSTB is established and validated through cyclic loading tests of a FSTB specimen. Based on the equivalent linear method, the seismic design procedure is developed and verified through 3-, 6-, 9-, and 12-story structures with different design performance objectives. Numerical models of FSTB-frames are established and used to verify whether the design performance targets are achieved through nonlinear dynamic analyses using the design-basis earthquake (DBE) ground motions. The research results show FSTB-frames can achieve the intended performance levels in terms of story drift, residual story drift and base shear, and the maximum and residual story drift of RC frames can be significantly decreased after equipping FSTBs.

Cyclic Response of Steel Fiber Reinforced Normal Strength Concrete Exterior Beam-Column Joint Under Reversed Cyclic Load

Failure investigation studies on a large number of buildings exposed to earthquake loads revealed that Beam-Column Joint (BCJ) is the most critical structural regions in any moment resisting RC structure. The structural response of RC moment resting frame system under the earthquake loads mainly depends on the behavior and performance of the BCJ. It should be designed and detailed properly to ensure safety and serviceability of the structure under various earthquake loads. In the present Experimental work, Normal Strength Concrete (NSC) Fiber Reinforced Beam-Column Joint specimens are cast and are subjected to Cyclic loading. Proportions of steel fibers used are 0%, 0.5% and 1%. Load response curves have been plotted to demonstrate change in the Energy absorption, Stiffness Degradation and Ductility factors.

Progressive collapse behaviour of compressed-bent rods of RC moment frames at sudden column removal

Due to the increasing incidence of disproportionate destruction of structural elements after the sudden removal of any supporting element, the number of studies of the resistance of structural systems to progressive collapse has grown significantly. However, among the research results presented in the scientific literature, there are practically no such studies in which an analysis of the resistance of compressed and compressed-curved reinforced concrete elements to disproportionate destruction would be performed. Therefore, in this paper, using the step-iteration method (Lira-CAD software) and non-linear stability analysis, we analyzed the behavior of the frame model when the column of the outer row was suddenly removed. In order to solve this problem, the analytical dependences are obtained for evaluating the stiffness of sections of compressed and compressed-curved elements. It has been established that the disproportionate fracture mechanism of compressed-bent elements of frame model is associated with a loss of stability.