Nonlinear Static Pushover Analysis Research Articles

Response Reduction Factor for Structures with Significant Irregularities on Different Soil Stratum

The ability of a structure to dissipate energy through inelastic behavior is reflected in the response reduction factor (R), which is influenced by redundancy, ductility, and overstrength. Accurate determination of R is crucial for seismic design. This study focuses on determining the response factor for reinforced concrete (RC) structures with various irregularities. Non-linear static pushover analysis using SAP2000 was employed for numerical simulations to assess the impact of soil-structure interaction (SSI). The analysis included elevational and in-plan irregularities, revealing that buildings with irregular vertical geometries have lower inelastic seismic capacities compared to regular buildings. Consequently, R should be reduced by 15–40% from the ECP 2020 standard before the design phase for such structures. Irregularity was found to have a significant impact on weak soil conditions (C), leading to a reduction in R of 20.3% and 13.1% for fixed and isolated supports, respectively, on loose soil. Additionally, stiffer base soils were associated with higher R values for the same structure. Doi: 10.28991/CEJ-2024-010-03-07 Full Text: PDF

Photogrammetry-aided numerical seismic assessment of historical structures composed of adobe, stone and brick masonry. Application to the San Juan Bautista Church built on the Inca temple of Huaytará, Peru

This research presents a cost-effective surveying methodology to assist the seismic assessment of complex heritage buildings, based on terrestrial structure-from-motion (SfM) photogrammetry. The method was applied to the study of the seismic performance of the church of San Juan Bautista – Inca temple of Huaytará, Peru, an emblematic case study due to its complex architecture and coexistence of different construction materials. The geometrical model for the seismic assessment was developed with an error of less than 2 % using SfM photogrammetry. Non-linear static pushover analyses were performed on 3D FEM models of the nave and the towers to evaluate their individual response under seismic loading. Mechanical properties of different structural materials of the church were evaluated based on laboratory experimental tests on mortar and adobe, contemporary and ancient fired brick, Inca stone, colonial stone and rubble stone units. Non-linear pushover analyses were conducted in four directions perpendicular to the perimeter walls, and the response of the structure was compared with the seismic demand specified in Peruvian Standards. The simulations show that damage-prone areas are the western and eastern facades, with cracking at the connections between orthogonal walls, as well as at the interface of adobe masonry with Inca stone masonry. The towers exhibit similar seismic response, with lower strength capacities compared to the main nave. In this case, flexural overturning mechanisms and cracking at the interface between stone and adobe masonry were observed. The displacement-based seismic assessment using the N2 method shows that a peak ground acceleration of 0.21 g could lead to the collapse of the north and south facades of the main nave. The towers showed a much smaller capacity with PGA leading to collapse of approximately 0.09 g. Overall, this study contributes to the understanding of the seismic performance of the Huaytará-Huancavelica church, highlighting vulnerabilities and providing valuable information for its preservation and future interventions. Future investigations should focus on on-site tests that will allow the estimation of the effect of existing damage on the structural response and their incorporation in the numerical model.

Seismic Resilience of Concrete Moment Frames with Fibrous Rubberized Beam-Column Joints

ABSTRACT Ensuring resilience through rapid buildings recovery in seismic zones has been placed at the forefront of recent studies. However, studies that compare the relative resilience of buildings constructed with different materials are lacking. This paper focuses on a comparative resilience analysis of concrete moment frames where beam-column connections are made with varying types of concrete mixtures. The connections are made with normal strength concrete (NSC), rubberized concrete (RbC), steel fiber rubberized concrete (STFRC), synthetic fiber rubberized concrete (SYFRC), and high strength concrete (HSC). Nonlinear static pushover and incremental dynamic analysis (IDA) are utilized to understand system response and the level of damage sustained following an earthquake. Subsequently, seismic fragility functions are constructed for the five considered frame types. The frames are subjected to different seismic scenarios, and the corresponding losses, recovery time, and resilience are quantified. A comparison between the five frame types is carried out to examine the optimal concrete mixture to be used to reduce damage probabilities, total direct losses, and recovery time and subsequently enhance resilience. The results show that rubberized concrete strengthened with steel and synthetic fibers can reduce economic losses by up to 19% and increase building resilience by up to 37% compared with the frames constructed with normal strength concrete.

Effect of masonry wall on Strength and Ductility in common RC frame low storey buildings

The Nepal National Building code (NBC) was promulgated in 2003 and is divided into four different parts in order to cover buildings constructed in Nepal. NBC 105 has undergone a major update in 2020 with its repercussions on existing prevalent buildings. So, in this paper effort has been made to understand municipal drawings submitted to municipalities constructed with current prevalent building construction practice with column size of 300mm x 300mm, 300mm x 230mm and 230mm x 230mm. Moreover, effects of masonry infill are considered with a separate model considering an equivalent strut as per IS 1893:2016. Ten sample buildings were selected after a rigorous sampling process of over 5000 municipal drawings to represent typical buildings. Non-linear static pushover analysis was conducted on those ten buildings and twenty models. There has been an increase in the over-strength factor of the buildings while there was reduction in ductility factor of the buildings. Equations are proposed based on non-linear regression analysis to determine the changes in over-strength and ductility factor of the buildings.

Seismic performance assessment of deficient RC structures retrofitted with different steel bracing systems

This paper discusses the use of concentric steel bracing systems as a global technique for retrofitting RC structures. A case study building with a five-story RC structure was retrofitted and tested using different types of bracing systems with different arrangements namely diagonal, X, and a combination between diagonal and X steel braces with tow arrangements. The main objective of the current study is to find out the most effective bracing system to upgrading the seismic behavior of deficient RC structures. The nonlinear static pushover and dynamic time-history analyses were carried out. The first method was applied by pushing the models until they arriving at a predefined target roof displacement. In the second method, a set of three natural earthquakes was employed to perform a dynamic time history analysis. The results indicate that the combined system of the diagonal and X braces using the second arrangement has the highest base shear and reaches the target roof displacement under pushover analysis. On the other hand, when using the response history analysis, it is the best system to reduce roof displacement compared to other techniques. However, steel braces cannot reduce the acceleration of the structure. The proposed combined system with the second arrangement is an effective retrofitting technique that has a much better seismic behavior and improves the ability to withstand even larger earthquake forces compared to other techniques.

Seismic collapse safety assessment of suspended zipper-braced frames

Seismic evaluation of suspended zipper-braced frames, which are an alternative to inverted-V-braced frames to improve their seismic behavior, is of greatest significance to determine the level of confidence in this type of seismic system during severe earthquakes. The arrangement and design parameters of these frames are mentioned in some references, but there is no probabilistic assessment of collapse risk based on various collapse uncertainties. To evaluate the probability of collapse and margin of safety, eighteen suspended zipper-braced frames with different geometry parameters in the most severe seismic design category (D max) have been designed. The designed frames were modeled in OpenSees software by considering the effect of gusset plate connections and evaluated by performing more than 15,800 dynamic and nonlinear static pushover analyses using FEMA P695 methodology. Total collapse uncertainty is considered in the evaluation of the probabilistic behavior of frames. The results show that the adjusted collapse margin ratio (ACMR) of designed frames by considering the total collapse uncertainty of 0.726 and 0.529 is 27% and 64% higher than the acceptance criteria, respectively. The results also indicate that a response modification coefficient of much more than 6 can be used for the economic design of long-period suspended zipper-braced frames.

Design of Vertical Evacuation Building at Painan City Using Results From Tsunami Propagation Modeling

Fault under the Mentawai Islands has high potential to cause a large earthquake and triggering tsunami. Painan City, is located near the fault. With geographical condition on a bay surrounded by hills in the upstream area, a tsunami may cause a flow channeling effect and increase the inundation distance. An alternative of mitigation effort is to build a Vertical Evacuation Building (VEB) to help the community to reach a safe elevation within the evacuation time. Therefore, VEB should be designed to withstand tsunami impacts and to resist large earthquakes. This study conducts the design and analysis of the performance of multi-functional VEB structures at Painan City. The tsunami propagation simulation was carried out, and parameters obtained were used for structural design. Three VEB models were developed, i.e., (i) model with walls under tsunami and earthquake loads, (ii) model without walls under tsunami and earthquake loads, and (iii) model without walls under earthquake load only as the lateral load. Non-linear static pushover analyses were later conducted to evaluate the structural performances. The study revealed that debris force affects the most compared to other tsunami force components. Structural openings also affect the tsunami load received by the structure. Column moment force for models designed with tsunami load is greater than that of earthquake, while the difference is less significant for beam. The internal force differences occur along the tsunami inundated depth, thus influence the component design. From the pushover analysis, all models were found to meet the performance targets for earthquake.

Displacement-based seismic performance of RC bridge pier

To correctly manage the road infrastructure before and after an earthquake, it is necessary to estimate and even predict the seismic performance of the bridge. The quantification of the bridge's seismic performance response was present in terms of displacement and also based on previous research of reinforced concrete bridge pier models. The displacement did define from a force lateral-displacement response diagram corresponding to the capacity curve, calculated through a non-linear static pushover analysis of the reinforced concrete bridge pier model for each limit state, from intact state to collapse. Thus, six defined displacements correspond to the cracking displacement, the yielding displacement, the spalling displacement, the crushing displacement, the buckling displacement, and the fracturing displacement. The six defined limit states correspond to the cracking limit state, the yielding limit state, the spalling limit state, the crushing limit state, the buckling limit state, and the fracturing limit state. Also, parametric analysis did carry out to evaluate the influence, relative importance, and trend of the input parameters in response to the seismic performance of the reinforced concrete bridge pier model. Eleven input parameters did analyze as the concrete compressive strength, the yield stress of reinforcing steel, the concrete cover thickness, the pier aspect ratio, the configuration of the transverse reinforcement, the spacing of the transverse reinforcing steel, the transversal diameter of the transverse reinforcing steel, the longitudinal reinforcement ratio, the transversal diameter of the longitudinal reinforcing steel, the axial load ratio, and coefficient of subgrade reaction.

Seismic and collapse behavior of existing high-rise steel buildings under long-period earthquakes

This work presented the experimental and numerical evaluation of the seismic and collapse behavior of Japanese existing high-rise steel buildings subjected to long-period ground motions (LPGMs). Initially, the experiment (E-Defense, 2008) was performed by the full-scale shaking table tests on a typical 21-story steel frame substructure. Accordingly, a nonlinear rotational spring model was used in the numerical modeling. In consideration of the stiffness/strength deterioration and fatigue fracture of beam-column connections, the cyclic pushover analysis was utilized to account for such effect using seismic response data from system-level testing. Subsequently, the numerical model parameters were derived and validated with the initial experiment on the high-rise steel frame substructure. Herein, a well agreement on the seismic failure behavior between simulation and experiment was found in this situation. Furthermore, both field-welded and shop-welded connections on the seismic performance were included for comparison. For the 21-story prototype steel building (built before 1970s), a series of numerical collapse analyses were performed. The above revised model using nonlinear static pushover analysis and time history analysis were conducted to simulate and compare the effects of connection details and composite slabs on the 21-story prototype building. Finally, a cyclic loading protocol for simulating LPGMs was proposed, and the related ultimate failure behavior of the high-rise building was analytically discussed. Critically, this work should provide a viable strategy to numerically simulate the seismic and collapse behavior of high-rise steel buildings in this progressing construction field.

Behavior And Performance Of Steel Frame Structures With X-Type Concentric Bracing System Due To Variations In Comparison Of Span Width To Story Height (L/H)

X-type bracing is the strongest bracing. The bigger ratio of the width of the span to the high level (L/H), the slope of the angle on the bracing will be more declivous. The analysis of the structure with the L/H ratio to determine the behavior of the structure using linear analysis of response spectrum and structural performance using the static nonlinear pushover analysis (ETABS 2016) to determine the displacement target that occurred in the structure. Structural modeling is done on 3D portals with levels of 3, 5, 8 and 10 floors with different L/H variations, including L/H=1; L/H=1.25; L/H=1.5; L/H=1.75; and L/H=2. Structural modeling is planned to be in the Surabaya area with moderate soil conditions. This study obtains data such as: (1) The largest maximum drift and floor drift are at type L/H=2, (2) The largest base shear force in the nonlinear pushover analysis at each story occurs at L/H=1, (3 ) In the yield condition type L/H=1 has the smallest percentage of structural stiffness, but in the ultimate condition type L/H=1 has the largest percentage of structural stiffness, and (4) The highest ductility value at each story occurs in type L/H=2 . Based on these results, it shows that the greater the type of L/H in the bracing structure, the greater the displacement target produced. If the angle of bracing becomes more sloping, then the displacement and target displacement that occurs increases.

Parameters Affect Flexural Mechanism to Prevent Progressive Collapse of RC Buildings

This study investigates the effect of spans length, reinforcement ratio and continuity of flexural reinforcement on the progressive collapse performance of double span beams over failed columns. The investigations focus on initial flexural resisting mechanism to prevent the progressive collapse. Detailed nonlinear finite element simulation of double span beam-column sub-assemblages subjected to residual gravity loads that initially carried by the failed column is adopted for the investigations. Nonlinear static pushover analysis is conducted in which capacity curves are derived and compared with demanded capacities. The effect of spans length, reinforcement ratio and number of continuous bottom flexural reinforcement on progressive collapse are considered in the investigations. Analysis results show that the strength to resist progressive collapse has decreased by 25.4 % and the ductility increased by 103 % following the increasing in span length from 5 m to 7 m. On the other hand, increasing reinforcement ratio of top flexural reinforcement from 0.447 to 1.089 leads to 26.27 % increasing in strength accompanied with a decrease in ductility equal to 16.42 %. In addition, extending all bottom bars rather than the minimum specified two bars resulted in 12 % increasing in strength and 40.28 % decreasing in ductility.

Investigation of effective parameters on seismic performance of steel frames with CFST columns

The seismic performance of steel frames with composite columns is evaluated by the seismic performance factors. Despite the essentiality of appropriate coefficient values, there are limitations in the building code regarding seismic performance factors of composite structures. These values have been presented in the regulations based on engineering judgment and comparison with similar steel and concrete structures. However, limited research exists on the determination of seismic performance factors for composite structures, where these coefficients are affected by numerous parameters. This article aims to cover the existing gaps and examine the parameters that have received inadequate attention in regulations and articles, despite their significance in the seismic design of composite structures. The present study conducts a nonlinear static pushover analysis of steel structures with concrete-filled tubular steel columns (CFST) to investigate the influential parameters in seismic performance factors. The variables studied in this research encompass the height of the structure, soil type, lateral force-resisting system, and structural irregularity. The findings demonstrate that changes in structural height influence the value of the response modification factor in all examined soil types for IMFs and SMFs. Also, the response modification factors provided in ASCE 7 prove to be conservative for the studied lateral force-resisting systems excluding SMFs in composite structures. In addition, the seismic performance of the studied models has dropped due to the geometric irregularity of the plan and the irregularity of non-parallel systems. Besides, the response modification factor values for composite structures surpass those specified for similar steel structures, while Eurocode 8 and ASCE 7 consider these values to be equal and similar to steel structures, respectively.

Effect of alternative load path design method on preventing progressive collapse and reducing the rehabilitation cost using FEMA-P58

The alternative load path (ALP) method is an important modern design approach to prevent progressive collapse of buildings by redesigning adjacent structural elements to provide an alternative load path in case of partial collapse. This may lead to tangible changes in the mass and stiffness of the building, which means a change in the seismic behavior of the building. This shows the fact that choosing and designing an alternative load path is not an easy task. Studying the improvement in the seismic behavior of the building, whether direct or indirect, as a result of using the ALP, is the main objective of this paper. To achieve this goal, this study examined approximately 96 models, including the study of the possibility of progressive collapse occurring, whether there is or isn't an alternative path for the loads using non-linear static and dynamic analysis, as well as evaluating the study models using various seismic evaluation methods, where both the nonlinear static pushover analysis method and the FEMA-P58 method were used and compared. The study models are divided into two sections, with and without (ALP). The study models are also categorized by building height using heights of 6, 9, 12 and 15 floors. The models were also divided based on the locations of weak points in the original design that may be susceptible to damage and lead to progressive collapse, whether they are internal, side, or corner weak columns. The findings from the examined models indicate that the efficiency of (ALP) systems is more prominent in low and mid-height buildings compared to tall buildings. Additionally, the results demonstrate that the FEMA-P58 method yields similar predictions regarding building behavior as traditional seismic assessment methods like pushover analysis, but in a simplified manner that benefits non-engineers by providing clear insights into the financial and temporal aspects of different structural system solutions.

An Open-Source Framework for Modeling RC Shear Walls Using Deep Neural Networks

Reinforced concrete (RC) shear walls macroscopic models are simplified strategies able to simulate the complex nonlinear behavior of RC shear walls to some extent, but their efficacy and robustness are limited. In contrast, microscopic models are sophisticated finite element method (FEM) models that are far more accurate and reliable. However, their elevated computational cost turns them unfeasible for most practical applications. In this study, a data-driven surrogate model for analyzing RC shear walls is developed using deep neural networks (DNNs). The surrogate model is trained with thousands of FEM simulations to predict the characteristic curve obtained when a static nonlinear pushover analysis is performed. The surrogate model is extensively tested and found to exhibit a high degree of accuracy in its predictions while being extremely faster than the detailed FEM analysis. The complete framework that made this study possible is provided as an open-source project. The project is developed in Python and includes a parametric FEM model of an RC shear wall in OpenSeesPy, the training and validation of the DNN model in TensorFlow, and an application with an interactive graphical user interface to test the methodology and visualize the results.

Assessment of seismic retrofitting interventions in reinforced concrete structures

Destruction of reinforced concrete (RC) structures, particularly non-ductile RC structures, in recent earthquakes demonstrate their vulnerability under lateral forces generated in an earthquake. Despite the extensive literature on the subject and the wide variety of strengthening techniques available, there is no consensus on the efficiency of these techniques in improving the seismic performance of RC structures. In this study, a five-storeyed RC-framed building is considered to evaluate its seismic performance through static non-linear pushover analysis. To examine the effect of various cases encountered in practice, the pushover analysis is carried out on the RC frame for various cases, i.e. a bare RC frame, an RC frame with masonry infills but with an open ground storey, and RC frames with shear walls with a variety of thicknesses and steel reinforcement ratios. Further, to investigate the effect of retrofitting, the RC frame is strengthened using local jacketing and bracings. From the results, it is observed that the initial stiffness and base shear of masonry infilled RC frame with an open ground storey exhibit an increase of 2.6%, and 19%, respectively, as compared to the bare frame. The use of shear walls increases the initial stiffness and base shears, and they increase by 6–14% and 8–20%, respectively, with an increase in the reinforcement ratio in the shear wall. Retrofitting with the use of both diagonal bracings causes the base shear to increase by a factor of 7.7 as compared to that of the open ground storey. Finally, the probability of damage to the RC frame in all cases was compared using seismic fragility curves.

EVALUASI KINERJA STRUKTUR RANGKA BETON BERTULANG BALOK LEBAR DENGAN DISTRIBUSI BEBAN PELAT SATU DAN DUA ARAH

A reinforced concrete frame building system using wide beams is a solution for buildings with limited heights to get a larger number of stories, a higher distance between stories, and flexibility in installing architectural elements and MEP. This analytical study was conducted to evaluate the behavior and performance of open-frame structures with wide beams for one-way and two-way slab system conditions. This study was carried out using a structural analysis program by applying linear and nonlinear analyzes to four models of a five-story structure with square columns, which varied in beam dimensions and slab systems. The variations considered are normal beam with one-way slab system (1wSN), normal beam with two-way slab system (2wSN), wide beam with one-way slab system (1wSW), and wide beam with two-way slab system (2wSW). All structural elements are designed to follow and meet the criteria of the Indonesian Building Codes, which are then followed by a non-linear static pushover analysis to obtain the performance of each structural model. The results of the analysis show that a structure with wide beams has greater deformation than a structure with normal beams with a faster achievement of collapse conditions so that the ductility of the structure also becomes lower. This is caused by the stiffness of the wide beam-column joints is lower than that of the normal beam-column joints. The use of one-way or two-way slab systems on structures with wide beams does not have a significant effect

Seismic performance of RC frames with self-centering precast post-tensioned connections considering the effect of infill walls

This paper presents the seismic performance evaluation of self-centering precast post-tensioned concrete (SCPPTC) frames with infill walls. The SCPPTC connection system consists of all-steel bamboo-shaped energy dissipaters (SBED) and prestressed tendons, which provide energy dissipation capacity and self-centering capability, respectively. Using modeling parameters calibrated with experimental tests, nonlinear numerical models of SBED, SCPPTC connection, infill walls, and 2D SCPPTC frames were developed in OpenSees, to compare the performance of the structures with different types of infill wall layouts. Nonlinear static pushover and incremental dynamic analysis (IDA) were performed to study the effect of infill walls on the overall response of SCPPTC frames, in terms of stiffness, strength, maximum interstory drift ratio,θmax, the maximum residual interstory drift ratio, θr,max, and the normalized post-tensioned force. Using the IDA results, the study also developed fragility curves and estimated the collapse margin ratios. The results demonstrated that the shear strength of the SCPPTC frame was improved from 4.19% to 12.2%, and the initial secant stiffness of the SCPPTC frame was augmented from 22.9% to 88.3% with increasing filling rate. The totally infilled SCPPTC frame (SCPPTC-ToI) exhibits a 19.86% lower θmax than that of pilotis-infilled SCPPTC frame (SCPPTC-PiI) under rare earthquakes, and the maximum prestress of SCPPTC-ToI was also 7.14% lower than that of SCPPTC-PiI. With the increase in filling rate, θr,max increased by a maximum of 120.45%. The pronounced soft layer led to the highest failure and collapse probabilities of SCPPTC-PiI among all SCPPTC frames at the same performance level.

Design Recommendations for Columns Made of Ultra-High-Performance Concrete and NiTi SMA Bars

The use of new materials in construction endows structures with better mechanical characteristics. The combination of ultra-high-performance concrete (UHPC) and nickel and titanium (NiTi) shape memory alloy (SMA) improves the behavior of building structures by increasing both their ductility and dissipation energy due to the low-damage and self-centering properties of NiTi SMA. Since UHPC and NiTi SMA are expensive materials and still scarce in distribution channels, this article tries to offer design recommendations to reduce the length of the column-beam connection in which these new materials should be introduced, leaving the rest of the column with conventional materials. To achieve this, a nonlinear static pushover analysis of columns using finite element software, SeismoStruct, was performed. This model was calibrated using experimental results. Next, a parametric analysis was carried out to propose the design recommendations. Results indicated that an adequate design for the column–beam connection, considering both economy and performance, should include a main zone with UHPC and SMA reinforcements, a transition zone with UHPC and steel reinforcements, and another zone with conventional reinforced concrete. The transition zone improved the hybrid column’s performance without excessively raising the cost. The main zone length, the transition zone length, and the strength of the concrete in the rest of the column must be determined to ensure that the critical section of the column was in the main zone to develop the maximum strength and ductility. The length of the main zone depended on the compressive strength of the conventional concrete, the relative axial load of the column, and the required ductility.

Seismic analysis of failure mechanisms in adjacent interacting stone masonry buildings via rigid block modeling

AbstractGroups of contiguous unreinforced stone masonry buildings are a common type of housing seen in old European downtowns. However, assessing their response to earthquakes poses several challenges to the analysts, especially when the housing units are laid out in compact configurations. In fact, in those circumstances a modeling technique that allows for the dynamic interaction of the units is required. The numerical study carried out in this paper makes use of a rigid block modeling approach implemented into in-house software tools to simulate the static behavior and dynamic response of an aggregate stone masonry building. Said approach is used to reproduce the results of bi-axial shake-table tests that were performed on a building prototype as part of the activities organized within the Adjacent Interacting Masonry Structures project, sponsored by the Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe. The experimental mock-up consisted of two adjacent interacting units with matching layout but different height. Two rigid block models are used to investigate the seismic response of the mock-up: a 3D model allowing for the limit analysis of the building on one hand, and a 2D model allowing for the non-linear static pushover and time-history analysis on the other. The 3D model was built for the blind prediction of the test results, as part of a competition organized to test different modeling approaches that are nowadays available to the analysts. The 2D model was implemented once the experimental data were made available, to deepen the investigation by non-linear static pushover and time-history analysis. In both models, the stonework is idealized into an assemblage of rigid blocks interacting via no-tension frictional interfaces, and mathematical programming is utilized to solve the optimization problems associated to the different types of analysis. Differences between numerical and experimental failure mechanisms, base shears, peak ground accelerations, and displacement histories are discussed. Potentialities and limitations of the adopted rigid block models for limit, pushover and time-history analyses are pointed out on the basis of their comparisons with the experimental results.

Degradation of the first frequency of an RC frame with damage levels

Damage in RC structures causes the degradation of stiffness and frequency parameters. In this study, the relationship between the two coefficients and damage severities is numerically investigated considering a three-dimensional (3D) reinforced concrete (RC) frame in which the concrete damage plasticity model (CDPM) and the elastoplastic model are selected to define concrete and reinforcement materials, respectively. Crack propagation of the frame is obtained utilizing a nonlinear static pushover analysis (NSPA). After the pushing procedure, according to the base shear force versus top displacement curve, the bending stiffness of the RC structure is determined rapidly. Thereafter, the degradation of the first frequency is obtained based directly on the nonlinear curve of stiffness. As a result, it is observed that the degradation of the first frequency of the RC frame is proportional to the severity of damage but not linearly. More significant damage, a more profound decrease in the modal characteristic. Particularly, the fundamental frequency of the RC frame reduces gradually until the base shear force reaches 70% of the ultimate value at which the parameter is about 60% of the counterpart at the intact stage. After that, the reduction gets more significant when the bending capacity approaches the ultimate value.