Inter-story Displacement Research Articles

Performance-based seismic design of controlled rocking reinforced concrete frame with beam-end hinge

This study investigates the seismic performance of the Controlled Rocking Reinforced Concrete Frame with Beam-end Hinge (CR-RCFB) system. The novelty of our research lies in the development and validation of a finite element model that accurately predicts the dynamic response of CR-RCFB structures under various seismic conditions, specifically focusing on the innovative use of joint stiffness ratios and the integration of dampers. A finite element model was developed and validated through shaking table tests. The research examined the dynamic responses of the CR-RCFB under ten ground motion records, varying the node relative stiffness ratios. The interstory displacement amplification coefficient (α) was found to range between 1.08 and 1.20, while the earthquake-reduction coefficient (β) varied from 0.8 to 0.3 depending on the stiffness ratio. Results indicate that node stiffness ratios between 0.01 and 0.25 optimize performance, minimizing peak interstory displacement and base shear response. Additionally, integrating dampers increased the damping ratio from 14.48% to 30.51%, enhancing energy dissipation by shifting absorption from plastic deformation to damper yield. Pushover analysis was used to recalculate and validate the parameters α and β, demonstrating that the integration of dampers effectively controls displacement response. These findings suggest that the CR-RCFB system with integrated dampers offers enhanced seismic resilience by reducing displacement and base shear forces compared to traditional reinforced concrete frames.

Experimental and Numerical Research on a Sand Cushion Geotechnical Seismic Isolation System in Strong Earthquakes and Cold Regions

Masonry buildings in high-intensity seismic and cold regions of China face the dual challenges of frost heaving and seismic hazards. To explore the potential of a sand cushion instead of the frozen soil layer to deal with these problems, a cost-effective sand cushion-based Geotechnical Seismic Isolation System (GSI-SC) was developed in this study, where a sand cushion is introduced between the structural foundation and natural soil, while the space around the foundation is backfilled with sand. Shaking table tests on a one-story masonry structure equipped and non-equipped with the GSI-SC system were undertaken to investigate its effectiveness in seismic isolation, where the input wave adopted the north–south component of the EL Centro wave recorded in 1940, and the peak input acceleration (PIA) was set as 0.1 g, 0.2 g, and 0.4 g. It is found that the GSI-SC system significantly reduced the seismic response of the structure, effectively achieving seismic isolation. For a PIA of 0.4 g, the GSI-SC system reduced the acceleration of the roof panel and the inter-story displacement of the structure by 33% and 39%, respectively. Numerical simulations were performed to evaluate the seismic response of buildings equipped and non-equipped with the GSI-SC system. The simulation results matched well with the experimental results, verifying the effectiveness of the newly developed seismic isolation system. The GSI-SC system can provide the potential to reduce frost heave and earthquake disasters for buildings in high-intensity seismic and cold regions.

Transverse seismic analysis method of underground interchange prefabricated utility tunnel

The rapid development of underground utility tunnels has led to the formation of a large number of interchange utility tunnels. Due to significant differences in the lateral resisting stiffness in orthogonal directions, coupled with the close relationship between soil deformation and the depth of the utility tunnel, the seismic response mechanism of the interchange utility tunnel is complex. This paper proposes a method for transverse seismic analysis of the underground interchange utility tunnel based on the response displacement method. A load-structure analysis model of a certain underground cross-type interchange utility tunnel is first established. Then, the different conditions corresponding to maximum relative deformation between layers of the interchange node are discussed, and the proposed method is validated via the time-history analysis method. Based on the proposed analysis method in this paper, seismic response analysis is performed on the interchange utility tunnel considering the condition of vertical incidence of three different input seismic waves. Discussions are conducted in terms of internal forces, inter-story displacement angles, and damage responses under seismic excitations in different principal axis directions. The results show that under major earthquakes, the maximum inter-story displacement angle of the interchange node exceeds the standard limit by up to approximately 184 %, while the tensile damage can reach up to 0.985, significantly surpassing the tensile damage limit. Accordingly, the interchange node is the weakest part of the interchange utility tunnel. There exists deformation inconsistency between the interchange node and standard segments due to significant stiffness differences, with the influence range of the interchange node on internal forces, inter-story displacement angles, joint deformations and damage of the utility tunnel is approximately 7, 6, 8, and 6 prefabricated standard segments, respectively. Since the maximum relative deformation between layers of the interchange node does not occur simultaneously, for double-layered and multi-layered interchange utility tunnels, it is necessary to comprehensively consider the maximum inter-story displacement angle between each layer to determine their most unfavorable condition. The analytical method and related research conclusions presented in this paper can provide references for the transverse seismic design of interchange utility tunnels.

Numerical analysis of the seismic performance of existing steel frames with rigid connection with truss-beam-segments

Addressing the insufficient research on fully welded connection with truss-beam-segments (FWCT), this study conducts a comprehensive investigation into the seismic performance of FWCT and its associated steel frame. Primary parameters influencing the seismic performance of FWCT are examined through numerical analysis, and a design method for FWCT is provided. Subsequently, a time-history analysis of composite frames with FWCTs is proposed to investigate the effect of adding truss-beam-segments during rare earthquakes on the seismic performance of the structure as a whole, along with reinforcement recommendations. The study results show that the width of the truss-beam-segment (TS) should ideally be equal to the width of the beam flange, with a thickness equal to that of the beam flange. The net height should be less than or equal to 0.17 times the clear height of the steel beam. The horizontal angle of the external diagonal leg should be less than or equal to 40°, and the length of the horizontal short leg should be greater than the plastic deformation region length at the beam root. The axial compression ratio for the column should be less than 0.7 to prevent local buckling of the column. As the thickness of the composite slab increases, the initial stiffness and load-bearing capacity of the positive moment region gradually increase, while those of the negative moment region remain relatively constant. Time-history analysis indicates that the maximum story displacement and inter-story displacement of the composite frame with TSs are reduced by 4.7 %–5.3 % and 2.5 %–5.8 %, respectively, compared to the composite frame without TSs under seismic wave action. This implies an enhanced capacity of the composite frame with TSs to withstand lateral deformation. For a mid-to high-rise composite frame with n stories, the addition of TSs was recommended primarily for the first (n/2 + 1) floors where plastic regions occur, aiming for a more economically efficient retrofit design and enhanced seismic performance.

Torsional effect analysis of high-rise reinforced concrete space grid cassette multi-tube structure system

The manuscript introduces a new structural system called the reinforced concrete (RC) space grid cassette multi-tube structure for high-rise buildings. A case study building is analyzed using this system and compared to a conventional RC frame-core tube structure. Through modal analysis in the software “Midas Gen”, the torsional effect and control indices like inter-story displacement ratio, maximum displacement, etc. are compared between the two structural systems. The results show that the space grid cassette system has smaller displacement ratios, displacements, inter-story torsion angles, and thus better torsional resistance compared to the conventional frame-core tube system. Based on these analyses, the manuscript concludes that the RC space grid cassette multi-tube structural system has superior seismic performance and is more suitable for irregularly shaped high-rise residential buildings.

Seismic Response and Mitigation Analysis of a Subway Station in the Site with Weak Interlayers

Challenges related to seismic performance and seismic mitigation are more pronounced in the presence of weak interlayers compared to typical layered soil conditions. This study focuses on a double-layer double-span rectangular frame subway station structure. A coupled static–dynamic finite element analysis model of the soil-structure system is established by using the finite element software ABAQUS/CAE V 6.14. The research investigates the influence of factors such as interlayer thickness, location, and strength on the seismic response of subway station structures. Furthermore, in order to evaluate the effectiveness of FPB in mitigating seismic effects in the weak interlayer ground, two different schemes are proposed in this paper. One is the structure without FPB and the other is the structure with FPB on the top of the central column. The findings reveal that weak interlayers exert a significant influence on the seismic response of subway station structures, especially when these lower-strength weak interlayers are located within the central portion of the subway station structure and exhibit considerable thickness. The FPB on the top of the central column can reduce the overall lateral stiffness of the subway station structure. This, in turn, results in a slight increase in the deformation of sidewall and inter-story displacement angles, accompanied by a marginal exacerbation of sidewall damage. However, the implementation of FPB effectively reduces the deformation of the central column and substantially mitigates the extent of damage to the central column.

Assessment of the seismic failure of reinforced concrete structures considering the directional effects of ground motions

Seismic intensity measures at different levels significantly impact the seismic damage of building clusters. Reinforced concrete (RC) structures are a type of building widely used in different regions worldwide. A large amount of field seismic damage observation data indicates that within the same seismic intensity zone, the directional effects of varying ground motions lead to significant differences in damage to RC structures on different floors. However, relatively little research has been conducted on estimating the seismic fragility and vulnerability of RC structures considering the directional effects of seismic action. To further study the directional effect of seismic motion on the damage of different floors, this study conducted dynamic time history and spectral analyses on 1472,379 acceleration records in multiple directions obtained from monitoring at nine actual seismic stations during the 2008 Wenchuan earthquake in China. This paper innovatively reports on the actual damage features of RC structures during the Mw6.2 magnitude Jishishan earthquake in Gansu Province, China, on December 18, 2023 (the most severe destructive earthquake in China in 2023) and analyses the influence of earthquake directionality on the damage to different floors of RC structures. A three-dimensional numerical model of a four-story RC frame structure was established using numerical simulation and the finite element method. Different intensity measures were taken to input seismic excitations of different intensities into the RC structure in the 0°, 30°, 60°, and 90° directions, and damage simulation analysis was conducted. The nonlinear dynamic time history curves of structures under multiple directions of seismic excitation in different intensity zones have been developed. Using the interstory stiffness and interstory displacement angle as engineering demand parameters, damage assessment curves and stress clouds for RC structures with 1–4 floors considering different seismic directional effects were generated. The analysis results and major findings indicate that the seismic sequence in the 0° direction has a relatively heavy impact on the first floor of the RC structure in zone IX, which is consistent with the actual field observation results.

Seismic Performance of a Single-Story Timber-Framed Masonry Structure Strengthened with Fiber-Reinforced Cement Mortar.

Timber-framed masonry structures are widely used around the world, and their seismic performance is generally poor. Most of them have not been seismically strengthened. In areas with high seismic fortification intensity, there are great potential safety hazards. And it is urgent to carry out effective seismic reinforcement. However, due to the complicated construction process of the existing reinforcement technology, the poor durability of the reinforcement materials, and the significant disturbance to the life of the original residents, an efficient single-story timber-framed masonry structure reinforcement technology suitable for comprehensive promotion and application has not been explored. In this paper, a fiber-reinforced cement mortar (FRCM) material was proposed. A 1/2 scale model of a single-story timber-framed masonry structure was taken as the research object. The method of strengthening a single-story timber-framed masonry structure with FRCM layer was adopted. And the shaking table test of the model before and after reinforcement was carried out in turn. The dynamic characteristics, failure modes, acceleration response and displacement response of the FRCM layer-strengthened structure were analyzed through comparisons of the two cases. The experimental results showed that the FRCM layer significantly improved the seismic performance of the seismic-damaged single-story timber-framed masonry structures. The X- and Y-direction natural frequencies of the model structure were increased by 31.30% and 30.22%, respectively, after the structure was strengthened with FRCM. During a rare eight-degree earthquake, the inter-story displacement angles in the X- and Y-direction of the unreinforced model reached 1/98 and 1/577, respectively, and the structure was destroyed, while the inter-story displacement angle of the FRCM-reinforced model was only 1/2 of that the unreinforced model. During a rare nine-degree earthquake, the X-direction inter-story displacement angle of the model strengthened with FRCM reached 1/78 and the Y-direction inter-story displacement angle reached 1/178. At this time, the reinforced model structure was destroyed, but there was no collapse of the structural components, which met the seismic design objectives of "operational under the design minor seismic intensity, repairable damage under the design seismic precautionary intensity, and collapse prevention under the design rare seismic intensity", which proved that the FRCM layer was an effective and feasible way to strengthen the existing single-story wood-masonry rural building.

Analytical solution to 2D dynamic soil-tunnel-building interaction under seismic SH-wave excitation considering the influence of the stiffness of tunnel and building's foundation

This investigation examines the structure-soil-structure interaction (SSSI) problem between a tunnel and nearby aboveground building, considering the impact of the stiffness of tunnel and building's foundation. A two-dimensional (2D) model is utilized, which includes a flexible circular tunnel and a three-story building anchored by a flexible semi-circular foundation embedded in a homogeneous half-space. The response of the system to incident plane SH-wave excitation is solved analytically using the wave function expansion method. The analysis focuses on how the system response is affected by the stiffness of the tunnel and the building's foundation. Tunnel stiffness plays a leading role in tunnel response analysis. The model with a rigid tunnel and rigid foundation can offer a reasonable system response overall, but it fails to accurately represent tunnel deformation and stress distribution. Depending on the stiffness of the building's foundation, the maximum value of the inter-story displacement of the first floor can be overestimated by around 70 %, with even greater overestimations for higher floors. The results help understand observed seismic behaviors and provide insight into the effects of foundation and tunnel stiffness on the tunnel-building interaction system.

Study on Vibration Reduction Effect of the Building Structure Equipped with Intermediate Column–Lever Viscous Damper

Generally speaking, the traditional lever amplification damping system is installed between adjacent columns in a building, which occupies a significant amount of space in the building. In contrast to amplification devices in different forms, the damper displacement of the intermediate column damper system is smaller, and the vibration reduction efficiency is lower. In light of these drawbacks, this study proposes a new amplification device for energy dissipation and vibration reduction, which is based on an intermediate column–lever mechanism with a viscous damper (CLVD). Initially, a specific simplified mechanical model of CLVD is derived. Subsequently, an equivalent Kelvin mechanical model of CLVD is derived to intuitively reflect CLVD’s damping and stiffness effect. The damping ratio added by CLVDs to the structure is calculated according to that model; the additional damping ratio and additional stiffness are utilized to calculate the displacement ratio Rd and shear force ratio Rv of the structure with CLVDs to the structure without CLVDs. Rd and Rv are introduced to evaluate the vibration reduction effect of the structure with CLVDs, and the effects of various parameters (such as intermediate column position, beam’s bending line stiffness, lever amplification factor, damping coefficient, and earthquake intensity) on Rd and Rv are analyzed. The results indicate that when the ratio of the distance from the intermediate column to the edge column to the span of the beam is 0.5, CLVD owns the optimal vibration reduction effect. Increasing the beam’s bending line stiffness is beneficial for CLVD to control structural displacement and shear force; when the leverage amplification factor is too large, the CLVD provides the structure with stiffness as the main factor, followed by damping. Additionally, when the ratio of the displacement amplification factor to the geometric amplification factor satisfies fd/γ = 1/21−0.5α, the CLVD has the optimal displacement control effect on the structure. After that, measures are provided to optimize the CLVD in different situations in order to effectively control the inter-story displacement and the story shear force of the structure. Consequently, a nine-story frame is taken as an example to elaborate the application of CLVDs in the design for energy dissipation and vibration reduction. The results reveal that the CLVD scheme adopting the proposed optimization method can effectively enhance the displacement amplification ability of CLVDs, resulting in an additional damping ratio of up to 12%. At the same time, the inter-story displacement was reduced by almost 40% under fortification earthquakes. Through the research in this study, designers can obtain a new choice in structural vibration reduction design.

The Seismic Performance of Self-Centering Ribbed Floor Flat-Beam Frame Joints

To achieve rapid post-earthquake repair of self-centering ribbed floor flat-beam frame structures, a ductile hybrid joint consisting of dog-bone-shaped, weakened, energy-dissipating steel bars connected to the upper and lower column sections through high-strength threads is proposed based on the damage control design concept. By moving the ductile energy-dissipating zone out to the locally weakened section of the energy-dissipating steel bars and the locally unbonded prestressed steel bars in the core area, the residual deformation was limited and the seismic performance improved. Based on the working principle of hybrid joints, low cycle loading tests were conducted on two joint specimens to analyze the influence of lateral prestress on the seismic performance of the hybrid joints. Numerical modeling methods were used to compare the position of the energy-dissipating steel bars in the composite layer and the friction performance of the joints. The research results indicated that the hybrid joint had stable load bearing, deformation, and energy dissipation capabilities, with damage being primarily concentrated in the energy-dissipating steel bars. Even at an inter-story displacement angle of 5.5%, the upper and lower column segments remained elastic. After unloading, the connection seam at the joint was closed, and the self-centering performance was good. When the inter-story displacement angle reached 5.5%, the lateral prestress increased from 150 kN to 250 kN, the ultimate bearing capacity of the joint increased by 16.3%, and the cumulative energy consumption increased by 30.0%. The influence of the friction coefficient of the joint surface on the structural performance was set at a threshold of 0.7. When it was less than the threshold, the ultimate bearing capacity and initial stiffness of the joint increased with the increase in the friction coefficient. After reaching the threshold, the increase in the ultimate bearing capacity of the joint slowed down, and the rate of stiffness degradation gradually accelerated. This joint showed excellent seismic performance and can thus achieve post-earthquake repair of structures.

Influence of Empirical and Dynamic Periods on the Seismic Responses of Reinforced Concrete Buildings Braced by L-Shaped Shear Walls

The Algerian Seismic Regulation of 1999, version 2003 (RPA99/v2003), presents ambiguities and a lack of thorough explanations in certain articles, which has led to a diversity of readings and interpretations among various stakeholders in the field, particularly the control offices. This situation has caused significant disagreements, especially during the approval of civil engineering files, thus resulting in a negative impact on project progress. To ensure adequate seismic protection of civil engineering structures, this work aims to unify the interpretations of certain passages of the regulation, with a particular emphasis on verifying the fundamental period of the structure, the shear forces at the base, and inter-story displacements using seismic calculation methods prescribed by the RPA. The comparative study demonstrates that no correlation between the period determined by the equivalent static method and that calculated by the spectral modal analysis method has been observed. This justifies the conclusion that adjusting between the empirical period and the dynamic period is not necessary.

Study on the Damping Efficiency of a Structure with Additional Viscous Dampers Based on the Shaking Table Test

This study specifically focuses on the damping efficiency of a damped structure with additional viscous dampers. A two-layer steel frame structure with eight sets of viscous dampers is used to conduct a series of seismic simulation shaking table tests, including a non-damped structure without dampers and two damped structures with dampers placed at 1/2 and 1/6 of the beam span, respectively. By conducting these tests, the energy dissipation, force, and displacement of the damper, as well as the parameters of the structure such as floor displacement and acceleration, are obtained. The main damping efficiency indicators of the damped structure are calculated, including the additional damping ratio, inter-story displacement utilization rate, as well as the reduction rate of the vertex displacement and the base shear relative to the non-damped structure. The study shows that the viscous dampers exhibit full hysteresis loops and a strong energy dissipation capacity in the structure. The seismic response of the vertex displacement and base shear in the damped structure is significantly smaller than that in the non-damped structure. Under different seismic levels, including frequent earthquakes, occasional earthquakes, and rare earthquakes, the damping effect of the dampers placed at 1/2 of the beam span is significantly better than that placed at 1/6 of the beam span. For example, the additional damping ratio for the X-direction artificial wave REN is 19% and 11%, 20% and 13%, and 13% and 11%, respectively. The patterns for inter-story displacement utilization ratio, reduction rate of the vertex displacement, and reduction rate of the base shear are similar. The research findings strongly indicate that the damped structure with additional viscous dampers exhibits excellent damping efficiency. In future damping design, designers need to fully consider the placement of viscous dampers within the beam span.

Seismic performance investigation of irregular and complex connected structures based on the influence of ground fissure activity

To investigate the dynamic response of irregular and complex connected structure, the comprehensive soil and connected structure model was developed, which is considered the site condition of different foundation soils. This study explored on the deformation law of the connected structure, and analyzing the structural displacement, acceleration, and torsional response under various seismic conditions. The findings revealed that the presence of ground fissures significantly amplifies the dynamic response of connected structures, with a greater influence from the hanging wall. Additionally, the lag effect was observed in the generation of the peak ground acceleration (PGA) in the site model considering ground fissures, but the result surpassed those in ordinary sites. During the elastic-plastic loading stage, the study observed that the maximum inter-story displacement angle remained within the limits prescribed by specifications. Due to the varying distances between column bases of the main area and ground fissures, there is a significant magnification effect in inter-story torsional angle. The incorporation of sliding supports emerged as an effective measure in mitigating the relative displacement of connected structures, consequently reducing the translational-torsional coupling effect during rarely occurred earthquake. The research results provide reference for the seismic performance analysis of connected structures under complex site conditions.

Study of Panel Zone Behavior in Interior Beam–Column Joints with Reduced Beam Section (RBS)

Based on the post-earthquake investigation of the Beiling and Hanshen earthquakes, many welded rigid beam–column joints were found to exhibit brittle failure. The failure modes of the joint region and the overall steel frame structure under the action of the earthquake need to be studied. The seismic performance of different types of weakened beam-end interior joints was investigated. The finite element method was verified by high-strength steel beam–column joint tests conducted by our research team. Finite element modeling of weakened steel beam flanges and weakened steel beam web joints was carried out based on the validated finite element modeling method. The joints were studied and analyzed using seismic parameters such as joint stress clouds, equivalent story shear–inter-story displacement ratio curves, panel zone bending moment–shear ratio curves, ductility, stiffness, and energy dissipation. The results of this study showed that honeycomb open hole-type joints exhibit a better deformation and energy dissipation capacity compared to open circular web hole-type joints. However, their load carrying capacity is reduced, which is mainly due to the larger area of the web openings. Additionally, double reduced beam section (DRBS) joints exhibit superior seismic performance and plastic hinge outward movement characteristics compared to single reduced beam section (RBS) joints. It was also found that the deformation and energy dissipation of DRBS joints and steel beam honeycomb hole-type joints are mainly borne by the beams, with the panel zone’s participation in energy dissipation accounting for a smaller proportion of the energy.

Identification of full-field wind loads on buildings using a mechanism-inspired recursive convolutional neural network with partial structural responses

Indirect identification approaches through structural responses have proven effective for wind load estimation in real-world engineering. Currently, methods for identifying wind loads mainly rely on theoretical inverse identification, with rare research based on the mapping relationship between structural responses and wind loads through machine learning. In this paper, a scheme for identifying full-field wind loads using a recursive convolutional neural network (CNN) inspired by physical mechanisms is proposed. The recursive form of the network, as well as the inspiration for its inputs and outputs, is inspired by the spatial correlation and the mapping relationship between wind loads and structural responses. Thus, the network inputs comprise a fusion of structural acceleration and inter-story displacement responses, while the network outputs represent the independent wind loads on structures. Notably, mismatch test is employed by the network, wherein the training and testing datasets originate from entirely different sources. Specifically, during training, Gaussian white noises that simulate wind loads are utilized, while real wind load data are used for testing. The generalization of the proposed scheme is demonstrated through the identification of full-field wind loads generated by different stationary or non-stationary wind spectra of the 76-story wind-excited benchmark building. Furthermore, the proposed scheme is validated by identifying the full-field wind loads of a 67-story shear wall structure with wind tunnel test data.

Steel structure design and analysis of a modern extreme sports center

A modern extreme sports center consists of a three-story main structure and ancillary structures. The overall architectural shape is simple and elegant. In order to ensure that the center has the high strength, earthquake resistance, corrosion resistance and other characteristics required for extreme sports venues, while taking into account comfort and aesthetics, the building structure adopts a steel frame structure system. This article uses the PKPM2021-V2.1.1.1 version software to conduct an overall calculation and analysis of this steel structure project, and checks the floor displacement calculated by the elastic method under the action of wind load or frequent earthquake standard values. The results show that the vertical structure of this structure is The deformation of the axial members meets the requirements of the code; the displacement ratio and inter-story displacement ratio of the structure under the action of specified horizontal seismic forces considering the influence of accidental eccentricity are checked, and the results show that the structure does not belong to torsional irregularity; the overturning resistance of the structure is checked and The shear-to-weight ratio was calculated and the results showed that the stability of the structure met the specification requirements. It can be seen from the above calculation and analysis that this structure can meet the specification requirements under various working conditions, and the structural design is safe and reliable.

The Influence of Base Isolator on The Reinforced Concrete Structures at Sapadia Mataram Hotel Earthquake-Induced

Ring of Fire and at the intersection of three tectonic plates. Efforts are needed to minimize earthquake damage, one of which is the use of a base isolator system. This study aims to determine the effect of using High Damping Rubber Bearing (HDRB) with a diameter of 800 mm on the behavior of reinforced concrete structures in tall buildings under seismic loads. The research location is the 7-story Sapadia Hotel building in the city of Mataram. The research is conducted by analyzing a 3D model of the fixed base structure and the base isolator structure using numerical analysis. The results show an increase in the base displacement of the base isolator structure by 59% in the x-direction and 44% in the y-direction, while the inter-story displacement decreases by 36% in the x-direction and 69% in the y-direction. The use of base isolators can reduce the shear force by 35% in the x-direction and 15% in the y-direction. Based on the pushover analysis, the roof displacement values for the fixed base and base isolator structures are 0.159 m and 0.129 m respectively. These values can be used to determine the structural performance level according to ATC-40. The maximum drift value for the fixed base structure is 0.0055 m. For the base isolator structure, the maximum drift value is 0.0044 m, categorized as Immediate Occupancy (IO). This value can be used to determine the performance level of the structure based on ATC-40. The maximum drift value of the fixed base structure is 0.0055m. While in the base isolator structure, the maximum drift value is 0.0044 m which is included in Immediate Occupancy (IO). Thus, the use of base isolators in high-level buildings is able to reduce post-earthquake damage and the building is still safe to continue using.

Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs

Random vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pressure, and vibrations due to road asperity. Using random vibration analysis is possible, when the input is properly modeled as a stochastic process, to derive pieces of information about the structural response with a high quality (if compared with other tools), especially in terms of reliability prevision. Moreover, the random vibration approach is quite complex in cases of non-linearity cases, as well as for non-stationary inputs, as in cases of seismic events. For non-stationary inputs, the assessment of second-order spectral moments requires resolving the Lyapunov matrix differential equation. In this research, a numerical procedure is proposed, providing an expression of response in the state-space that, to our best knowledge, has not yet been presented in the literature, by using a formal justification in accordance with earthquake input modeled as a modulated white noise with evolutive parameters. The computational efforts are reduced by considering the symmetry feature of the covariance matrix. The adopted approach is applied to analyze a multi-story building, aiming to determine the reliability related to the maximum inter-story displacement surpassing a specified acceptable threshold. The building is presumed to experience seismic input characterized by a non-stationary process in both amplitude and frequency, utilizing a general Kanai–Tajimi earthquake input stationary model. The adopted case study is modeled in the form of a multi-degree-of-freedom plane shear frame system.

Analysis of Seismic Performance and Applicable Height of a Cooperative Modular Steel Building

Analysis of Seismic Performance and Applicable Height of a Cooperative Modular Steel Building