RC Moment Frames Research Articles

Method to identify if torsional mode of a building is its first mode

Torsionally flexible buildings (that have torsional mode as fundamental mode) twist during earthquake shaking, and may collapse partially or completely depending upon the direction and level of shaking. The problem is aggravated when the building is torsionally unsymmetrical. Some design codes (like Eurocode, Indian Code) explicitly prohibit the design of such buildings. This paper presents a simple approximate method to identify torsionally flexible RC Moment Frame and RC Structural Wall buildings at the initial proportioning stage itself without carrying out a detailed structural analysis. It is possible to identify whether or not the first mode is torsional mode of a building (i.e., torsionally flexible building) if Natural Period Ratio τ>1 by modelling the building with rigid diaphragm and distribution of mass & stiffness along the height of building, and estimating: (1) radius of gyration of rotational mass rm of each floor plan geometry by lumping the masses of slabs, beams and all vertical elements at each nodes, (2) radius of gyration of twisting stiffness rKθ of all vertical elements using their translational and torsional stiffnesses (considering flexibility of adjoining beams and vertical elements accounting for both flexural and shear deformations), and (iv) τ (=rm/rKθ). The method is validated with 3D Modal Analysis (using τ =Tθ/T, where Tθ is Uncoupled Torsional Natural Period and T Uncoupled Translational Natural Period) of hypothetical buildings using a commercial structural analysis software. Also, parameters are identified that lead to τ>1, and solutions suggested to avoid torsional flexibility in buildings. Further, the method helps identify vertical stiffness irregularity in buildings. Draft provisions are suggested for inclusion in seismic codes. Also, poor performance of multi-storey building (with τ>1) is demonstrated using nonlinear static and nonlinear time history analyses.

Performance-based versus conventional seismic design: comparative assessment on a 4-story RC moment frame

AbstractFive different design approaches are compared on a single mid-rise reinforced concrete building, pitting two performance-based designs against three conventional methods in delivering a solution that satisfies different sets of performance objectives. Two of the conventional designs stem from the literature, and they represent 2003 IBC compatible solutions. Another employs the yield point spectra to deliver a code-like solution, satisfying the design norms without needing iterations. The final two are based on the yield frequency spectra to offer a design that can satisfy more detailed performance objectives in a single step. Overall, all five methods are shown to deliver what is expected. Conventional methods can safely capture the code requirements, yet they are disadvantaged when treading in beyond-life-safety territory, where Immediate Occupancy or Collapse Prevention objectives cannot be easily satisfied, a problem that is not shared by performance-based approaches.

Impact of diaphragm flexibility on dynamic properties and seismic design parameters of irregular buildings in plan

One of the established conditions of structural regularity in modern Mexican seismic codes is that a rigid and strong diaphragm has to be provided at each story. However, this condition is one of the least rigorously reviewed in the design of buildings in Mexico. During the past 15–20 years, a modern version of flatslab floor systems are being dominantly used in new building construction in Mexico City. However, their ability to transmit and carry adequately important seismic loads has not been demonstrated. In this paper, the authors present a study where two buildings irregular in plan using a cast-in-place flatslab system lightened with large Styrofoam (EPS) blocks were designed according to Mexican codes as done by most engineers: assuming a rigid and strong diaphragm. Then, the diaphragm flexibility was evaluated using detailed finite element models, as well as equivalent solid slabs with orthotropic modeling and struts models to account for the diaphragm flexibility. It was found that when modeling the diaphragm flexibility, lateral displacements increased from 2.1 to 3.4 times those of the rigid diaphragm assumption. When modeling the diaphragm flexibility, the natural periods of vibration increased, due to the decrement of the effective lateral stiffness for the buildings. It was found that the effective lateral stiffness for the buildings decreased by 54.3% for a subject 8-story confined masonry building and by 66.7% for a subject 15-story RC moment frame building. Switching of dominant mode shapes between the rigid and the flexible diaphragm assumption was also observed.

Modeling of RC Moment Frame Retrofit with Mortar Walls Reinforced with Steel Wire Mesh

Current construction codes require detailed analyses for structural retrofitting, which must consider performance during seismic events. Therefore, the computational models used to evaluate existing infrastructure require nonlinear structural analysis and damage estimates. For structural retrofitting, nonlinear computational modeling must represent the connectivity between existing and new elements. This study proposes recommendations on structural modeling based on fiber elements to represent reinforced concrete (RC) moment frames retrofitted with mortar walls reinforced with steel wire mesh. For this purpose, capacity curves of moment frames retrofitted with mortar walls were calculated by hand with the Bernoulli–Euler beam theory, moment–curvature analyses, and a plastic hinge model. Then, these capacity curves were used to calibrate the connectivity and constraint conditions in fiber models between the existing frame and the new wall required to capture the performance of the retrofitted structure. The study found that, for a single wall connected with top and bottom frame border elements, the capacity curves from fiber models underestimate stiffness, maximum strength, and residual strength. These estimation issues are reduced by including intermediate connectivity nodes between the top and bottom frame where rigid link constraints connect the existing frame with the new wall.

Seismic Performance of RC Moment Frame Buildings Considering SSI Effects: A Case Study of the New Venezuelan Seismic Code

The Soil–Structure Interaction (SSI) effect has been widely evidenced during several earthquakes around the world. In the Venezuelan context, the seismic event in Caracas in 1967 showed the significant consequences of designing buildings without considering the SSI effect. Nevertheless, limited research on the seismic performance of concrete moment frames (commonly used as structural systems in office and residential buildings in Venezuela and Latin America) considering the SSI effects has been developed, although there have been continuous updates to the Venezuelan Seismic Code. In this research, the influence of the SSI on the seismic performance of RC moment frame buildings designed according to the New Venezuelan Seismic Code was studied. An extensive numerical study of 3D buildings using concrete moment frames supported by mat foundations on sandy and clayey soils was performed. The response spectrum method, non-linear static analysis, and non-linear dynamic analysis were used to assess the seismic response of the archetypes studied. The results show that SSI effects can have a significant impact on the seismic response of RC moment frame buildings, increasing the interstory drift ratio and decreasing the shear forces. As is shown in fragility curves, the probability of collapse increases for cases with flexible bases in comparison to the cases of models with fixed bases. Additionally, in the 24-story archetype, the fixed-base model reached a maximum probability of collapse. Finally, a new proposal for the reduction of the strength-reduction factor (R) must be incorporated into the Venezuelan Seismic Code to improve the safety of the structures. Limitations in the use of RC moment frames must be incorporated for high-rise buildings since, as the present work demonstrates, for high-period structures, the normative provisions are not reached.

Corrigendum to Seismic resilience of typical code-conforming RC moment frame buildings in Canada. Earthquake Spectra. Epub ahead of print 13 January 2023. DOI: 10.1177/87552930221145455

Corrigendum to Seismic resilience of typical code-conforming RC moment frame buildings in Canada. Earthquake Spectra. Epub ahead of print 13 January 2023. DOI: 10.1177/87552930221145455

Scaled Shaking Table Tests Simulating the Damage of the School Gymnasium in the 2016 Kumamoto Earthquake

The transverse out-of-plane response of the RC moment frame on the arena floor damaged a school gymnasium that was expected to function as a natural disaster shelter. It was composed of heavy RC substructure and a light steel roof, which partially collapsed, resulting in the facility's permanent destruction in the 2016 Kumamoto earthquake. This study describes scaled shaking table tests that simulate out-of-plane response-induced damage to the RC moment frame of the school gymnasium during the 2016 Kumamoto earthquake and verifies the damage mechanism proposed by the previous numerical simulation and the efficiency of a response control by the friction damper support. Furthermore, the study validates two methods for evaluating the response of the RC moment frame and the overall buckling strength of the roof truss member with semi-rigid joints.

Cyclic Lateral Load Test for RC Moment Frames Retrofitted with External Steel Frames

Cyclic Lateral Load Test for RC Moment Frames Retrofitted with External Steel Frames

Machine learning-aided scenario-based seismic drift measurement for RC moment frames using visual features of surface damage

This paper presents a novel computer vision-based methodology for assessment of the seismic damage in reinforced concrete moment frames using visual characteristics of surface damage following an earthquake. An extensive collected database comprising 974 images associated with 256 cyclic-loaded damaged beam-column joints, providing a set of cracking and crushing progression with increasing the evolution of damage level, is collected and used for the development and validation of the methodology. Employing image processing techniques, the characteristics of the surface damage, including the cracking length and crushing areas, are measured and used in a scenario-based assessment for the seismic peak drift prediction. Based on the availability of the structural information, four scenarios are proposed using input parameters among cracking length, crushing areas, concrete compressive force, and the aspect ratio of the joint. The machine learning regression method is employed for developing nonlinear regression models for each scenario. The proposed models measure the seismic peak drift ratio during the earthquake excitation based on the visual damage features at the external surface of the components. Finally, the seismic peak drift ratio obtained by the proposed methodology of this paper can be used as an input engineering demand parameter in the existing seismic loss measurement frameworks. An example specimen at various drift ratios is also presented as a case study to evaluate the predicted versus actual experimental drift ratio.

Influence of ground motion frequency content on the nonlinear response and seismic performance of RC moment frame structures

Several parameters may affect the response of structures to seismic excitation. These include features of the structures, properties of imposed ground motion and geological specifications of building location. This research has been conducted to investigate the effects of the frequency content of earthquakes as an important property of ground motion on the seismic performance and nonlinear response of reinforced concrete moment frame (RCMF) structures. To this end, forty-two earthquake records have been selected from the stations on site classes A and B based on ASCE7-10. These input excitations have been classified into three groups based on PGA to PGV ratios namely: Low, Intermediate, and High frequency motions. Three RCMFs with 2, 6, and 10 stories have been designed according to ACI318-14 and ASCE7-10. Finally, utilizing OpenSEES platform, based on the FE method a numerical model has been built to perform incremental dynamic analysis (IDA). After interpreting the results of the IDA, fragility curves have been obtained as a function of PGA for pre-defined damage states. The results showed that the associated PGA with the median of the fragility curve is in ascending order Low, Intermediate and High frequency motions. Accordingly, it is concluded that in the same PGA level, Low frequency motions are more probable to reach a damage threshold than Intermediate and High frequency motions. Similarly, Intermediate frequency motions is more capable reaching the damage threshold in comparison to High frequency motions.

Effect of Mainshock–Aftershock Excitations on Seismic Energy Dissipation Mechanism of RC Frames

Four RC moment frames (RCMFs) with 4–20 stories are designed, modeled, and subjected to IDA procedures by considering various levels of prior damage caused by mainshock (MS). The collapse of the structures is then identified by gradual scale-up of the aftershock until dynamic instability is observed. The percentage of the energies dissipated by various parts of the structures and via different modes is next studied at three states during the collapse-inducing excitation. These states include the final residual state, the maximum drift state, and the maximum kinetic energy state. While an almost constant contribution of around 30% is provided by the inherent damping of the nodal masses, the share of beams’ hysteretic energy varies between 10% in the low-rise shear-dominated frame and 30% in the high-rise flexure-dominated RCMFs. The contribution of the columns’ hysteresis also changes in a reverse manner so that the sum of ratios provided by the beams and columns hysteresis is kept constant and equal to around 70%. The prior damage caused by the MS also leads to changes in the contribution of various elements and stories due to the deterioration MS induces to the strength of the members.

Seismic resilience index for RC moment frames of school buildings using neuro-fuzzy approach

Seismic resilience index for RC moment frames of school buildings using neuro-fuzzy approach

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.