Fundamental Period Of Vibration Research Articles

Modal analysis of the 63 Square Building in Seoul, South Korea and its impact of subsidence and soil-structure interactions (SSI)

We conduct vibration analyses of 63 Building in Seoul, South Korea, using modal analysis and finite element modeling. The building is modeled as a solid structure having the shape of the real structure and with total weight and stiffness consistent with those of the real building. To better understand the fundamental periods of vibration of this structure and the associated mode shapes, we also consider structures with simplified geometry and perform modal analyses of them.

An Investigation into the Impact of Time-Varying Non-Conservative Loads on the Seismic Stability of Concrete-Filled Steel-Tube Arch Bridges

When the arch rib of the mid-bearing through and lower-bearing through arch bridges undergoes out-of-plane deformation, it is usually subject to the resilience force provided by the flexible hanger, which is known as the “non-conservative force effect” of the suspender. In contrast to the static condition, in the dynamic scenario, the time-varying non-conservative force exerted by the flexible suspender becomes more complex due to dynamic changes in external load. Moreover, the difference in fundamental frequency and vibration period between the bridge system and arch rib may influence the stress distribution within the arch rib during ground motion. This paper investigates the impact of time-varying non-conservative forces on the dynamic stability of arch ribs in concrete-filled steel tube (CFST) bridges under seismic loads. Specifically, it examines the influence of different seismic waveforms, frequency disparities between bridge slabs and arch ribs, and suspender stiffness on the non-conservative effect. The results reveal significant disparities in the impact of non-conservative forces exerted by the suspender during seismic events with identical intensity but varying frequency characteristics. The influence of non-conservative forces on the dynamic stability of bridges escalates as deck stiffness increases, while it remains relatively unaffected by changes in suspender stiffness.

The effect of superstructure properties on the re-centering capability of Friction Pendulum (PS) isolator

The re-centering capability after the seismic excitation is one of the fundamental properties of a seismic isolation system. This study examines the effects of superstructure properties on the re-centering capability of the Friction Pendulum (FP) isolator. To this end, a comprehensive parametric study is conducted using a two-degree-of-freedom (2DOF) model that accounts for the nonlinear behavior of the superstructure and isolator. This study evaluates the re-centering capability of the FP isolator by calculating the ratio of residual displacement (dres) to the maximum displacement (dmax). The effect of superstructure properties, including strength reduction ratio R, fundamental vibration period Ts, post-yield stiffness ratio αs, superstructure damping ratio ξs, and the ratio of superstructure mass to total mass of the system γm on the dres/dmax ratios is thoroughly analyzed. The findings suggest that while estimating the residual displacement of isolation systems, it is important to consider the impact of superstructure parameters. An analytical equation is proposed to predict dres/dmax ratio based on effective superstructure and isolator parameters.

Prediction of BLEVE loading on structures

In a previous study by the authors, rigid structure assumption, as commonly used in analysing blast wave interaction with structures, was adapted in investigating the Boiling Liquid Expanding Vapour Explosion (BLEVE) pressure wave interaction with structures to predict BLEVE loads on structures. However, real structures are not rigid and the duration of BLEVE wave is much longer than that from high explosives and may be in the order of structural natural vibration period. Neglecting structural deformation, therefore, may lead to inaccurate predictions of BLEVE loads acting on the structure because structural deformation during the action of BLEVE wave would change the wave and the structure interaction. In this study, intensive numerical simulations are carried out using a validated computer model to investigate the influences of structural stiffness and BLEVE wave duration on the reflected BLEVE pressure on the structure. Based on the numerical results, prediction charts are proposed as a function of the BLEVE wave duration and structural fundamental vibration period for reliable predictions of BLEVE loads on structures. The findings of this study can be used to predict explosion loads in structural design against BLEVE.

Prediction of the fundamental period of infilled RC framed structures considering the maximum inter-story drift at different design limit states

The fundamental period of vibration is a key parameter for the spectral approach to seismic design of structures, as it significantly affects the evaluation of the response spectra values. Even though infill elements can significantly increase a building's lateral stiffness, they are not always considered in the structural design process. This is particularly significant at the damage limitation states considered by the European (Eurocode 8) and Italian (NTC2018) seismic codes, where mostly elastic behaviour is expected. Non-structural elements, in fact, can influence the natural elastic period of buildings, determining spectral accelerations different from those evaluated by the simplified formulas provided by the seismic standards and related guidelines. This research aims to develop novel simplified period-height relationships to estimate the fundamental period of vibration of infilled Reinforced Concrete (RC) framed buildings more accurately at various limit states, as a function of inter-story drift value. To collect information about the fundamental period of structures in different damage conditions, several experimental campaigns involving more than 330 RC framed structures have been considered. Nonlinear numerical analyses have also been performed to integrate the database, especially for the Ultimate Limit State (ULS), considering different number of floors, infill distributions, and geometries. Collected data have been parametrized as a function of the damage level suffered by the considered structures, and different empirical period-height formulations have been defined for each limit state. The proposed relationships have been compared with those found in international, European, and national seismic codes, as well as with simplified formulations in previous literature studies. In particular, the results strongly suggested that the fundamental periods estimated according to the EC8 formulation, overestimates the experimental data, resulting in a potential underestimation of the seismic forces and therefore of damage to non-structural elements. To quantify the differences in spectral acceleration and spectral displacement at all design limit states, some examples have been proposed, considering different Italian seismic zones.

Investigating the seismic performance and developing the fragility curves of self-centering steel frames with augmented nonlinear viscous damping: A numerical simulation

This paper focuses on investigating the seismic performance of post-tensioned steel frames equipped with nonlinear viscous dampers. The aim is to increase the ductility and seismic energy dissipation capacity of these structures. Finite element (FE) models were created using the Abaqus software and validated against reference experimental data under cyclic loading. Two types of post-tensioned moment-resisting frames (PT-Frames) were developed: a conventional PT-Frame and a PT-Frame with two pairs of nonlinear viscous dampers acting as knee braces (each brace pair, contains two dampers connected in parallel, thus there are 4 dampers used in total). Various analyses, including modal analysis, cyclic loading, and incremental dynamic analysis (IDA), were conducted using earthquake records mentioned in FEMA P-695. Fragility curves were plotted based on the IDA results. The findings indicate that the augmented nonlinear viscous damping significantly increases the natural fundamental period of vibration in PT-Frames (133 % increase observed). It also enhances the absorption and dissipation of input seismic energy (800 % increase in cumulative dissipated seismic energy observed). Moreover, it reduces the probability of damage exceeding the damage index value for different performance levels (collapse prevention, life safety, and immediate occupancy) by average values of 115 %, 61.72 %, and 25.126 %, respectively. These improvements help mitigate damage to the structural components.

Estimation of the fundamental period of vibration of the dental clinics and the dental classroom of the Catholic University of Cuenca using environmental vibration recordings

In the Faculty of Dentistry of the Catholic University of Cuenca, located in the city of Cuenca, province of Azuay. The lecture hall and the clinics of the faculty are built. These structures were built during 2018 and 2019. Due to the seismic events occurred in recent years, monitoring was carried out to obtain the characterization of the dynamic behaviour. The two structures are formed by a structural system based on structural steel frames (beam-column), the structure for laboratory use has metal columns filled with concrete, while the structure for classroom use has metal columns without concrete filling. The main objective was to obtain the vibration periods experimentally from the recording of environmental vibrations and also to obtain them analytically with mathematical models elaborated in structural analysis programs and environmental vibration tests were performed. The results show that building 1, composed by the dentistry clinic, obtained a vibration period of 0.41 s in X and 0.33 s in Y (Analytical Model); and, in the environmental vibration test it showed a period of 0.46 s in X and, 0.30 in Y. Building 2, composed of the dental faculty classroom, obtained periods of 0.53 s in X and 0.29 s in Y (Analytical Model). While in the environmental vibration studies they gave values of 0.52 s in X and 0.26 in Y.

Response spectrum method for structures subjected to vertical ground motions: Absolute acceleration method

AbstractAlthough a wide variety of response spectrum methods have been developed to estimate peak horizontal building responses, much less attention has been devoted to study the applicability of those methods for the vertical direction or to develop new methods to estimate peak vertical building responses. Vertical building responses can be significant for structures located close to the earthquake rupture, and for buildings with fundamental period of vibration within the range of most energy content of the vertical component of the ground motion (typically 0.05 to 0.15 s). The frequency content of the vertical component is significantly different to that in the horizontal components; thus, it is not clear if previous methods are applicable. We present a new alternative response spectrum analysis (RSA) method to estimate absolute accelerations in the vertical direction, which is a modified version of a previously studied modal combination rule developed for the horizontal components of motion. This formulation is derived based on the use of modal absolute accelerations, and we compare it to the traditional complete quadratic combination (CQC). In the proposed method, we develop simplified equations to estimate the necessary correlation coefficients for the vertical direction which are calibrated to fit empirical correlations computed from the vertical response of single degree of freedom systems subjected to a set of 90 vertical components of recorded ground motions. We also compute these correlations by using an improved power spectral density (PSD) function, which is as an enhanced version of the modified Kanai‐Tajimi PSD to represent the frequency content in the vertical direction which differs from that in the horizontal direction. To evaluate the proposed modal combination rule, we compare the RSA results to those obtained using response history analyses (RHA) of peak responses for a simplified model consisting of a prismatic bar fixed only at one end, as well as for 2D frames. We show that the proposed modal combination rule can estimate peak building responses with higher accuracy than the commonly used CQC modal combination rule, for any general building configuration at any structural location.

Seismic response of multi-storied building with shear wall considering soil-structure interaction in Patna, India

The structural response of a building on soft or loose soil differs from that on hard and rocky soil. Investigating the behaviour of buildings with shear walls on such soft soil is essential. This study considers four structural models of the nine-storied building with and without infill walls. The modelled buildings represent the existing buildings in the Patna, India region. The frame was analysed in four different conditions: (1) Fixed base bare frame building, (2) Flexible base bare frame building, (3) Fixed base building with shear walls (4) Flexible base building with shear walls. Twenty-four pairs of scaled ground motion from the PEER Ground Motion Database were selected, and a nonlinear time history analysis was performed in SAP2000v20.0. Understanding that soil-structure interaction is paramount for building on soft soil, the study quantified the seismic response for the building in the Patna region, a region of high seismicity.Moreover, in current scenarios, multistorey buildings with an open ground storey and shear walls are prevalently found owing to their advantage for parking and enhancing the seismic capacity. The result shows that base flexibility significantly increases the peak floor displacement, total floor acceleration, inter-storey drift and displacement ductility for bare frame structures. At the same time, consideration of shear and infill walls only affects the flexible base structures. While shear and infill walls significantly affect the seismic behaviour of the fixed base structure. It was also found that the shear and infill walls increase the structure’s stiffness and thus reduce the fundamental vibration period of the structure. The study’s significant findings are (1) the shear and infill wall significantly reduces the seismic responses of the building, (2) base flexibility (SSI) increases the seismic vulnerability of the buildings, (3) the displacement ductility significantly depends on the aspect ratio (height/width) of the building, and (4) the inter-storey drift is relatively higher in the lower and mid storey of buildings.

Improving the Seismic Performance of Steel Frames under Mainshock–Aftershock Using Post-Tensioned Connections

In this study, the seismic responses of moment-resisting steel frames (MRSFs) with welded and post-tensioned connections under 28 artificial seismic sequences (mainshock–aftershock) are compared. For this aim, the mainshock are scaled at different ground motion intensity levels as a function of the spectral pseudo-acceleration corresponding to the fundamental period of vibration of the structure Sa(T1), whereas different intensity levels of the aftershocks are used for a percentage of the peak maximum acceleration of the mainshock. The seismic performance comparison of both structural systems is computed for the maximum, residual inter-story drift and hysteretic energy demands. The results show that post-tensioned frames significantly reduce the structural demands, especially in the case of residual inter-story drifts and hysteretic energy in comparison with moment-resisting steel frames with welded connections. The reductions in the structural response tend to be larger as the intensity of the aftershock tends to increase. Therefore, it is concluded that the use of post-tensioned connections is a great alternative to mitigate the seismic response of buildings subjected to seismic sequences.

Optimal Acceleration and Energy-Based Record Selection Using Artificial Intelligence Approaches and NP

ABSTRACT The new trend toward modern earthquake-resistant design of buildings based on nonlinear dynamic analysis accounting for peak and energy demands requires efficient ground motion record selection procedures. For this reason, in the present work, two record selection strategies based on acceleration and input energy spectrum considering the spectral shape via Np are presented. Furthermore, both record selection strategies are optimized by means of four artificial intelligence (AI) techniques: Genetic Algorithms (GA), Harmony Search (HS), Particle Swarm Optimization (PSO) and Vibrating Particle System (VPS). In particular, the effectiveness of each AI approach toward the best set of ground motion records for nonlinear dynamic analysis is compared. For this aim, spectral acceleration and input energy design spectra were considered, as well as 1024 seismic records obtained from the Pacific Earthquake Engineering Research Center. For all the AI or meta-heuristic approaches, the fitness function used is focused on minimizing the difference between the average spectrum of eleven ground motion records and the design spectrum using the well-known parameter Np, which represents the spectral shape in a range of periods. In addition, a penalization is included for those spectra with very large or low demands. Thus, 24 sets of eleven seismic records that can be used for nonlinear dynamic analysis of structures with a fundamental period of vibration of 0.6, 1.2 and 1.8 seconds were obtained and purposes. The results demonstrate the ability of the two records selection strategies analyzed and the four meta-heuristic procedures, achieving results quickly and simply regardless of the type of demands, intensities and periods considered. Finally, it is concluded that the VPS algorithm is better in comparison with GA, HS, and PSO since it obtains superior results in almost all the selected cases.

Ductility-strength and strength-ductility relations for a constant yield displacement seismic design procedure

The modern engineering approach to design of structures exposed to rare but intense earthquakes allows for their inelastic response. Models and tools to rapidly but accurately assess the extent of the inelastic response of the structure and control its performance are, therefore, essential. We develop a closed-form upmu -R^{*}-S_{d,y} relation between the ductility upmu and the strength reduction factor R*, as well as its approximate inverse R*-upmu -Sd,y relation, both functions of the SDOF oscillator yield displacement Sd,y, not its vibration period T. The fundamental vibration period of the structure varies during the iterative design process focused on modifying its strength. However, the yield displacement of the structure is practically invariant with respect to the strength of the structure, as it depends primarily on its geometry and material properties. We use these relations to formulate a constant yield displacement seismic design procedure and exemplify it. Noting the structure of the developed relations, we use dimensional analysis to formulate a version of the ductility-strength and strength-ductility relations that are dimensionless and independent of the seismic hazard intensity. These novel, dimensionless master relations are the upmu -R*-H/B-upkappa ductility-strength and the R*-upmu -H/B-upkappa strength-ductility relations.

Seismic Damage “Semaphore” Based on the Fundamental Period Variation: A Probabilistic Seismic Demand Assessment of Steel Moment-Resisting Frames

During strong earthquakes, structural damage usually occurs, resulting in a degradation of the overall stiffness of the affected structures. This degradation produces a modification in the dynamic properties of the structures, for instance, in the fundamental period of vibration (T1). Hence, the variation of T1 could be used as an indicator of seismic structural damage. In this article, a seismic damage assessment in four generic typologies of steel buildings was carried focused on verifying the variation of T1. To do so, several seismic damage states were calculated using the maximum inter-story drift ratio, MIDR, and following the Risk-UE guidelines. Then, a series of probabilistic nonlinear static analyses was implemented using Monte Carlo simulations. The probabilistic approach allows one to vary the main mechanical properties of the buildings, thus analyzing in this research 4000 buildings (1000 building samples for each of the four generic typologies). The variation of T1 was estimated using the capacity spectrum, and it was related to the MIDR for each damage state. As a main result of this study, the expected variation of T1 for several damage states is provided. Finally, a proposal for a seismic damage preventive “semaphore” and fragility curves are presented. These results may be useful as parameters or criteria in the evaluation of on-site structural monitoring for steel buildings.

Masonry infill in structural analysis: effects on seismic performance

In structural analysis, masonry infill is commonly regarded as a non-structural component. However, understanding the true behavior of a structure requires incorporating the effects of masonry infill in seismic evaluations. This paper reviews the effects of masonry infill on seismic performance through analyses including pushover analysis, time history analysis, response spectrum analysis, linear static analysis, and eigenvalue analysis. Ten research papers were reviewed, covering different aspects of masonry infill effects on structures of varying configurations and seismic zones. Results indicate that including masonry infill reduces the fundamental time period of vibration and storey displacement while increasing the base shear compared to bare frame structures. This comprehensive review underscores the importance of considering masonry infill in structural analysis to enhance seismic performance.

Seismic retrofit of an existing important building of the 60’s through a hybrid strategy

The paper deals with the seismic retrofit of an existing monumental building through a hybrid solution, applying an isolation system to a previously strengthened and stiffened structure. The case study was built in the Central Italy in the middle of the 1960s. The building is a mixed steel-concrete structure with a plan extension of about 2000m2, with an inner decentralized open court. At the first level, it is characterized by R.C. pillars and two shear walls not symmetrically placed in the plan. Upon it, there are two other levels made of steel frames. The first-floor level is a “floating plane”: consisting of a grid of steel beams, it bears loads transferred from the upper components. Through it, a structural continuity is ensured between portions having different stiffness, i.e. a wide upper steel part more deformable than the small lower R.C: lower. Resulting from a gravity-load design approach, without taking into account seismic actions, this monumental building is highly irregular at each level, with a noticeable asymmetry due to the shear walls distribution. These R.C. elements are the only ones having a certain horizontal stiffness at the upper levels, where the existing slender steel bracings are not placed in correspondence to the lower pillars. In this case, a hybrid solution for seismic retrofitting has been proposed. Considering the high deformability of the steel elements, not bearing seismic forces, the preventive strengthening actions refer mainly to R.C. components, including the strengthening of the existing shear walls and the introduction of other two ones, the structural consolidation of the SAP-type slabs. In addition, the strengthening of the existing slender steel bracings is expected. Working on such stiffened structure, the isolation system introduces anti-seismic devices below the floating plane, using 32 HDRBs (ϕ 600) and 8 sliders. This solution increases the fundamental vibration period from TFB= 0.563 s, valued for the fixed base, to TISO= 3.05 s, for the strengthened isolated solution, reducing the seismic action of 76%.

Comparative analysis and design of structure in accordance to Indian and American standards

Comparing and analyzing the seismic loads applied to Special Moment Resistant Frame (SMRF) structures is the study's main objective using Indian (IS: 456 and IS: 1893) and American Standard Codes (ASCE 7–10 and ACI 318). Additionally, both codes load factors and load combinations were examined. For this purpose, The SMRF building is analyzed according to both codes. In this study, an SMRF structure designed utilizing Indian (IS: 456–2000, IS: 1893–2016) and American main codes iscompared (ACI 318 2014 and ASCE 7–10 2014). This study compares seismic design regulations for reinforced concrete buildings in India (IS-1893–2016) and the United States (ASCE 7–10) based on the types of allowable analysis methods, zoning systems,fundamental vibration periods of the structures, important factors,response reduction factor, design response spectrum, and minimum design lateral forces. In order to analyze the seismic performance of building models, dynamic analysis was used to understand earthquake (EQ) considerations. Base shear coefficient (BSC), which displays EQ models, is used to compare seismic performance when the damping ratio is set at 0.05.

Hybrid strategy for the seismic retrofitting of existing buildings through Base Isolation System

A hybrid procedure for seismic retrofit of an existing R.C. structure by using base isolation system is discussed in this paper. The case study is a high school building in Naples, built at the end of 1970s, as result of a gravity-load design approach. It consists of three jointed R.C. portions, having different features in plan and elevation. In particular, “Building 1” and “Building 2” are characterized by resisting frames only in transversal direction. These ones support the actions transferred by the floors, whose load-bearing elements are warped longitudinally. Both the two buildings are characterized by some R.C. shear walls, in correspondence of (internal/external) staircases. The three portions are separated by tight joints, whose width is inappropriate to avoid pounding damages due to earthquake shaking. Considering that the structure has no resisting frames in longitudinal direction, this school building has low seismic capacity longitudinally and a high lateral deformability, with a fundamental vibration period of TAS-IS =1.37s. In this case, seismic retrofit by using base isolation system has been necessary to improve its seismic response. On the other hand, the main aspects of modern capacity design approach are not complied with between dissipative and no-dissipative components. So, it is assumed that the current structural system has no ductility reserves, on local and global scale. For the seismic retrofit of the existing structure an “all rubber” base isolation system (BIS) has been assumed by using ϕ600 HDRBs, allowing to reach a TISO = 4.0s. To maximize the effectiveness of BIS, the three bodies have been connected at each floor level and the upper structure has been strengthened previously, reducing to TFB=0.30s the fundamental period of the strengthened fixed base solution. The proposed hybrid solution for seismic retrofitting merges two conceptually opposite design strategies, opting for BIS applied to an existing structure, stiffened ad hoc by using shear walls.

Prediction of the Influence of Higher Modes on the Dynamic Response of High-Rise Buildings Subjected to Narrow-Banded Ground Motions

This paper presents the results of a study aimed at assessing the effects of higher modes of vibration on the nonlinear dynamic response of tall framed-buildings subjected to narrow-banded motions. For this purpose, analytical models of a 20-story building were developed under the consideration of two types of hysteretic behavior and subjected to 20 seismic excitations having a dominant period of motion of 1[Formula: see text]s. While the fundamental period of vibration of the building equals 2.7[Formula: see text]s, its second period is close to 1[Formula: see text]s; as a result, the selected seismic excitations over-stimulate the participation of the second mode in the overall dynamic response of the building. The circumstances under which the contribution of higher modes gives place to an excessive response of the upper stories are identified, and quantitative measures are presented. From an engineering point of view, parameters that predict an excessive response of higher-level floors are proposed.

A simplified formula for the determination of the fundamental period of mixed structures with vertical combination of different seismic resisting systems

Vertical combination of different seismic resisting systems, permitted in the seismic design codes such as ASCE/SEI7-16, is an effective choice for the structural design of mid- and high-rise buildings. In the seismic analysis of structures, according to the seismic codes, an estimate of the fundamental period of vibration is needed. On other hand, there is no simplified equation to compute the fundamental period of vibration of mixed buildings with vertical combination of different seismic resisting systems. In this study, by using the Rayleigh’s method, a simplified formula is proposed for determining the fundamental period of this type of structures. The proposed formula is verified by using the eigenvalue analysis of the mathematical model of the 11 building frames with different structural characteristics along their height. Also, two different mixed structures composed of steel and reinforced concrete moment-resisting frame (MRF) structures as well as of steel concentrically braced frame (CBF) and reinforced concrete MRF structures are examined. The fundamental period of a 3-dimensional (3D) vertically irregular 6-story building with setbacks is also determined to show the efficiency of the proposed method for vertically irregular structures. Furthermore, the proposed formula is verified by the period obtained from an experimental full-scale test of a structure. The results indicate that the proposed formula results in the fundamental period of the mixed structures with satisfactory accuracy. The largest and average errors in the fundamental period of the buildings under consideration, obtained by the proposed formula, are less than 10% and 6%, respectively, compared to the eigenvalue analysis. Therefore, the proposed formula can be used in the seismic evaluation process of existing buildings as well as in the design process of new ones.

The influence of multiple impedance contrasts on mHVSR site period estimates in the Canterbury Plains of New Zealand and implications for site classification

An experimental study of the fundamental period of vibration of geologic strata above multiple impedance contrasts is presented for the Canterbury Plains, a deep, complex sedimentary basin on the South Island of New Zealand. Microtremor Horizontal-to-Vertical Spectral Ratio (mHVSR) analysis was used at 152 locations to investigate the fundamental period of the strata above three significant impedance contrasts in the region: the Riccarton Gravel, the Banks Peninsula volcanic (BPV) rock, and the deep graywacke basement bedrock. Up to three mHVSR peaks were observed in many of the mHVSR curves, with the long-period (2–7 s) peaks controlled by the BPV and/or the underlying bedrock. As the thickness of the BPV increases, the response of the geologic strata above the basement bedrock was masked by the shallower BPV, effectively changing the definition of what constitutes the reference condition (i.e. engineering bedrock) for site response analyses. The mHVSR peaks matched the long-period amplification peaks observed in the response spectra calculated from ground motions recorded during the Canterbury Earthquake Sequence events, underscoring the importance of the identification and consideration of deep impedance contrasts in site classification.