Fundamental Period Of Vibration Research Articles

Investigation of a Base-Isolator System’s Effects on the Seismic Behavior of a Historical Structure

The earthquake performance of structures with seismic isolation is much better than that of fixed-base structures, and the application of seismic insulation ensures both structural integrity and the protection of the items present in the structures. The base-isolation system is used to extend the fundamental period of vibration of the structure and to obtain higher value from base-isolated structures relative to the fixed-base structure. Historical masonry mosques could be strengthened using a base-isolation technique. In this study, a historical masonry mosque was organized and modelled using SAP2000 software. Nonlinear Time History analyses were carried out for the historical masonry structure, firstly for the fixed-base mosque and secondly for the base-isolated mosque with lead rubber bearing (LRB). The use of a base-isolator system caused an increase in the historical mosque’s period, reducing the displacements, acceleration, and force applied on the mosque and the resulting structural deformation; the results of the analysis indicate a significant improvement in the seismic behavior. The modelling results show that such historical masonry buildings (especially those with high and delicate minarets) can be vulnerable to major earthquakes, and it may be useful to examine strengthening strategies for these buildings.

A New Relationship to Determine Fundamental Natural Period of Vibration for Irregular Buildings in Height Using Artificial Neural Network

One of the most important structural features is fundamental vibration period which depends significantly on the inherent characteristics of structures. Seismic codes and some researchers estimate experimentally and mathematically fundamental vibration period using the number of stories or the overall height of the building. The consequences of evaluating the various relationships have been resulted based on structural height, mass, stiffness and number of stories. As the overall height and the number of stories do not make difference between regular and irregular structures, so it seems that mass and stiffness of each story is so important in zone of building vibration period. Considering the importance of irregular buildings, a new relationship proposed to determine fundamental natural period of vibration for elastic regular and irregular buildings in height using artificial neural network. The accuracy of the proposed relationship is perfectly validated and confirmed by numerical calibrations and matrix analyses.

A new evolutionary polynomial regression technique to assess the fundamental periods of irregular buildings

AbstractThe main seismic design codes propose simplified formulations to evaluate the fundamental period of regular structures based on the total height. Indeed, the fundamental period depends on several parameters directly connected to the mass and stiffness of the structure and on its geometrical characteristics, including also irregularities.This paper proposes a set of mathematical formulations to evaluate the longitudinal and transversal fundamental period of vibration of 3D Reinforced Concrete (RC) frames, which have various vertical and plan irregularities and for different mechanical and geometrical design parameters.Several types of Reinforced Concrete Bare Moment Resisting Frame (RC‐BMRF) buildings have been designed according to the different versions of the Italian codes starting from 1916 to nowadays and then used as case studies. Modal analysis is performed on the entire building dataset to assess the fundamental periods in both longitudinal and transversal directions. Then, cluster analysis is carried out to classify the buildings based on similar design characteristics and construction details. Finally, a robust Evolutionary Polynomial Regression (EPR) technique is used to find the optimal polynomial forms of the natural period. Numerical results show a better performance of the proposed formulation compared with the existing methodologies available in the literature.

A period-height relationship for newly constructed mid-rise reinforced concrete buildings in Turkey

The fundamental period is an essential parameter in the force-based design of buildings as it defines the spectral acceleration and thus the base shear force to which the building should be designed. The fundamental period can be computed based on modeling or utilizing simplified empirical relationships defined in seismic design codes. Previous studies show that the simplified equations should be region-specific and should represent the general design and the construction characteristics of the region. In this study, ambient vibration measurements were carried out on 24 newly constructed, mid-rise reinforced concrete (RC) buildings in Eskisehir, Turkey. The relationships between the fundamental periods and the building heights were examined. Through regression analysis, a simple equation was derived to estimate the elastic fundamental vibration period of mid-rise RC buildings with respect to building height. The proposed relationship was compared to the equation defined in the new Turkey Building Earthquake Code (TBEC-2018) and with the other simplified equations in different design codes and the related literature. The results showed that the fundamental period estimates of the TBEC-2018 equation are much longer than the fundamental periods of the measured buildings in this study. This overestimation may lead to unconservative base shear forces. Therefore, the proposed equation can be used in the force-based design of mid-rise RC frame buildings for conservative estimates of the fundamental period. The contribution of infill walls to the lateral stiffness of the buildings was also investigated, and some preliminary suggestions are made for the related parts in TBEC-2018.

Seismic performance evaluation of crumb rubber concrete frame structure using shake table test

The research work presented in this paper has been carried out to investigate the dynamic characteristics and seismic performance parameters of reinforced concrete frame structure built in crumb rubber. Two test specimens were fabricated in reduced scale 1:3 and tested under seismic loading using the shake table. One of the test models was made of normal reinforced concrete, which was used as a reference. The second model was fabricated of reinforced concrete having rubber crumb; replacing the volume of fine aggregates partially by crumb rubber particles. The test specimens were subjected to free vibration test followed by dynamic testing having multiple base excitations using Northridge 1994 accelerogram to explore the dynamic characteristics and seismic response parameters, respectively. The results demonstrated that the partial inclusion of rubber crumb in concrete reduces compressive strength, density, and yield strength. Fundamental period of vibration and damping ratio were increased for crumb in concrete frame. Damage pattern of both the frames was observed and recorded. These results suggested that fine aggregates in concrete can be confidently replaced partially by crumb rubber particles in structures subjected to seismic loadings.

Modelling of soil-structure interaction in OpenSees: A practical approach for performance-based seismic design

In this paper, a numerical tool based on the Monkey-tail fundamental lumped parameter model is proposed for the simulation of dynamic soil-structure interaction (SSI). The proposed model has been implemented in the OpenSees finite element environment where the input parameters are merely function of the soil properties. The ease of use, accuracy and versatility of the proposed model is demonstrated in order to encourage its use within, among others, the practicing engineers’ community. Furthermore, the influence of the SSI and local soil conditions (i.e., site effect) on the seismic response of two 5-storey steel moment-resisting frame buildings has been investigated. Preliminary results shed light on the influence of these two geotechnical aspects on the structural seismic response where peak floor displacements and inter-storey drifts considering the SSI are even larger in the lower stories than those of the fixed base case. Furthermore, the results revealed the dependence of the soil amplification factor on the fundamental period of vibration, seismic intensity level and soil stiffness which are not taken into account by the current European design codes.

Prediction equation for the fundamental vibration period of concrete gravity dams with impounded water

The design of dam structures requires advanced analysis techniques due to the dam body’s complicated interaction with its surroundings. Consequently, most of the time, it is a must to perform response history analysis during the design and assessment of dam structures. The target fundamental vibration period is necessary to generate ground motion histories compatible with the site-specific response spectrum. In this study, an equation was developed to predict the fundamental vibration period of concrete gravity dams based on an extensive database. First, a wide range of parameters to describe gravity dams’ three-dimensional (3D) geometry and their valleys are determined. A total of 19,440 different 3D numerical models with fluid and solid elements were formed, and the fundamental vibration period values were determined to create the necessary database. Then, multiple nonlinear regression analysis was conducted to propose an equation to predict the fundamental vibration period. The proposed equation could be used to accurately estimate the required fundamental vibration period during the preliminary design stage or the implementation of simplified procedures or during the spectrum matching operations.

Numerical Modelling of CFS Three-Story Strap-Braced Building under Shaking-Table Excitations.

In recent research activities, shake-table tests were revealed to be useful to investigate the seismic behavior of cold-formed steel (CFS) buildings. However, testing full-scale buildings or reduced-scale prototypes is not always possible; indeed, predicting tools and numerical models could help designers to evaluate earthquake response. For this reason, numerical modelling of two strap-braced prototype buildings, recently tested on shake-table at University of Naples Federico II in cooperation with Lamieredil S.p.A. company, was developed. The models were validated trough the comparison between experimental and numerical results, in term of dynamic properties (fundamental period of vibration and modal shapes), peak roof drift ratios and peak inter-story drift ratios. Although dynamic properties of mock-ups were captured with accuracy by the developed models, the comparison highlighted the need to consider accumulation of damage and rocking phenomenon in the modelling to capture with good accuracy the seismic behavior of CFS strap-braced building, subjected to high intensity records.

Experimental Estimation of Period of Vibration for Multistory RC Frame Buildings (Dept.C)

At the present lime most current building codes specify equations to be used for the calculation of the base shear and lateral loads. For the determination of these lateral loads, it is necessary to determine first the period of vibration of the building. As is known, the period of vibration of buildings can be determined theoretically or experimentally. The theoretical design values of the period ol' vibration are different from the experimental ones. Significant differences have been observed for RC multistory frame buildings and in a lesser degree for other building types such as: masonry, stone, large-paneled, and large-brains buildings. The natural periods of vibration of 53 multistory RC frame buildings have been measured by the station of Engineering-Seismometer Services (ESS). These 53 buildings have different number of stories, different dimensions in.plan (with different plan length to width ratios) and effected on different soil conditions. On the basis of these data an improved simple empirical equation relating the period of vibration and the number of stories of the building is proposed 113 estimate the fundamental period of vibration of RC multistory frame buildings. In this paper the effect of soil condition and the divisions of the building in plan on the period of vibration have been studied. Comparison of periods determined using the proposed relationships and the adopted ones shows rather well agreement.

Optimum position of outrigger-belt system in a high-rise RCC building through pushover analysis

This study aims to investigate the behaviour of high-rise RCC buildings with core and outrigger-belt system, and to find the optimum position for the outrigger-belt system in that building. For this purpose, Pushover Analysis is used to capture the seismic response for the buildings of 10, 15, 20, 25, and 30 storeys with varying positions outrigger-belt system. Pushover analysis is a static procedure which uses a simplified nonlinear technique to calculate seismic structural deformations. The position of outrigger-belt arrangement changes from the first storey to top storey of the 3D building models, which gives the data regarding the behaviour of the building models with the change in position of that arrangement throughout its height. The analysis of these building models is performed in two different directions using two different load patterns in each direction. The results depict the optimum positions of the outrigger-belt system depending on lateral load patterns, the direction of loading, and the height of a building. It also shows how the optimum position of an outrigger-belt system can affect the performance of the buildings, which is measured in terms of roof displacement, storey shear, the fundamental period of vibration, base shear, and performance point of the buildings.

Response spectrum-based seismic response of bridge embankments

A single degree of freedom model is presented for calculating the free-field seismic response of bridge embankments due to horizontal ground shaking using equivalent linear analysis and a design response spectrum. The shear wave velocity profile, base flexibility, 2D shape, and damping ratio of the embankment are accounted for in the model. A step-by-step procedure is presented for calculating the effective cyclic shear strain of the embankment, equivalent homogeneous shear modulus and damping ratio, fundamental period of vibration, peak crest acceleration, peak shear stress profile, peak shear strain profile, equivalent linear shear modulus profile, and peak relative displacement profile. Model calibration and verification of the proposed procedure is carried out with linear, equivalent linear, and nonlinear finite element analysis for embankments with fundamental periods of vibration between 0.1 and 1.0 s. The proposed model is simple, rational, and suitable for practical implementation using spreadsheets for a preliminary design phase of bridge embankments.

A practice-oriented method for estimating elastic floor response spectra

A practice-oriented modal superposition method for setting elastic floor acceleration response spectra is proposed in this paper. The approach builds on previous contributions in the literature, making specific recommendations to explicitly consider floor displacement response spectra and accounts for uncertainty in modal characteristics. The method aims to provide reliable predictions which improve on existing code methods but maintain simplicity to enable adoption in practical design. This work is motivated by recent seismic events which have illustrated the significant costs that can be incurred following damage to secondary and nonstructural components within buildings, even where the structural system has performed well. This has prompted increased attention to the seismic performance of nonstructural components with questions being raised about the accuracy of design floor acceleration response spectra used in practice. By comparing floor acceleration response spectra predicted by the proposed method with those recorded from instrumented buildings in New Zealand, it is shown that the proposed approach performs well, particularly if a good estimate of the building’s fundamental period of vibration is available.

Influence of Wind-Induced Antenna Oscillations on Radar Observations and Its Mitigation

AbstractAs Typhoon Goni (2015) passed over Ishigaki Island, a maximum gust speed of 71 m s−1 was observed by a surface weather station. During Typhoon Goni’s passage, mountaintop radar recorded antenna elevation angle oscillations, with a maximum amplitude of ~0.2° at an elevation angle of 0.2°. This oscillation phenomenon was reflected in the reflectivity and Doppler velocity fields as Typhoon Goni’s eyewall encompassed Ishigaki Island. The main antenna oscillation period was approximately 0.21–0.38 s under an antenna rotational speed of ~4 rpm. The estimated fundamental vibration period of the radar tower is approximately 0.25–0.44 s, which is comparable to the predominant antenna oscillation period and agrees with the expected wind-induced vibrations of buildings. The reflectivity field at the 0.2° elevation angle exhibited a phase shift signature and a negative correlation of −0.5 with the antenna oscillation, associated with the negative vertical gradient of reflectivity. FFT analysis revealed two antenna oscillation periods at 0955–1205 and 1335–1445 UTC 23 August 2015. The oscillation phenomenon ceased between these two periods because Typhoon Goni’s eye moved over the radar site. The VAD analysis-estimated wind speeds at a range of 1 km for these two antenna oscillation periods exceeded 45 m s−1, with a maximum value of approximately 70 m s−1. A bandpass filter QC procedure is proposed to filter out the predominant wavenumbers (between 40 and 70) for the reflectivity and Doppler velocity fields. The proposed QC procedure is indicated to be capable of mitigating the major signals resulting from antenna oscillations.

Estimating Fundamental Period of Corrugated Steel Plate Shear Walls

Corrugated steel plate shear walls (CoSPSWs), which consist of corrugated infill steel wall panels and steel boundary frames, could be used as lateral force-resisting systems for mid- to high-rise buildings. In seismic design, the fundamental vibration period is generally estimated by empirical formulae corresponding to different types of lateral force-resisting systems. However, both the formulae in various design specifications and improved formulae proposed recently for steel shear walls with flat wall panels were not suitable and accurate for CoSPSWs since the difference in the load-carrying mechanism of steel shear walls with flat and corrugated wall panels respectively. Eigenvalue frequency analyses were conducted on a total of 60 validated CoSPSW finite element models with varying geometries, and results showed that fundamental periods estimated by current formulae were shorter than periods from the analyses, which might lead to the over-conservative and uneconomic design. Improved empirical formula was proposed for the fundamental period of CoSPSWs based on regression analyses. Simplified calculation method for calculating the fundamental period of CoSPSWs after the first trial design was proposed using the shear-flexure cantilever formulation, and validated through finite element analyses. Furthermore, influences of major geometric properties of CoSPSWs on the fundamental period was investigated.

Unified Shear-Flexural Model for Vibration Control of Buildings Using Passive Dynamic Absorbers

A unified design model is proposed for various kinds of passive dynamic absorbers (PDAs) attached to buildings with different lateral resisting systems. A total of five different PDAs are considered in this study: (1) tuned mass damper (TMD), (2) circular tuned sloshing damper (C-TSD), (3) rectangular tuned sloshing damper (R-TSD), (4) two-way liquid damper (TWLD), and (5) pendulum tuned mass damper (PTMD). The unified model consists of a coupled shear-flexural (CSF) discrete model with equivalent tuned mass dampers (TMDs), which allows the consideration of intermediate modes of lateral deformation. By modifying the nondimensional lateral stiffness ratio, the CSF model can consider lateral deformations varying from those of a flexural cantilever beam to those of a shear cantilever beam. The unified model was applied to a 144-meter-tall building located in the Valley of Mexico, which was subjected to both seismic and along-wind loads. The building has similar fundamental periods of vibration and different nondimensional lateral stiffness ratios for both translational directions, which shows the importance of considering both bending and shear stiffness in the design of PDAs. The results show a great effectiveness of PDAs in controlling along-wind RMS accelerations of the building; on the contrary, PDAs were ineffective in controlling peak lateral displacements. For a single PDA attached at the rooftop level, the maximum possible value of the PDA mass efficiency index increases as the nondimensional lateral stiffness ratio decreases; therefore, there is an increase in the vibration control effectiveness of PDAs for lateral flexural-type deformations.

Seismic Control of Cable-stayed Bridge Using Negative Stiffness Device and Fluid Viscous Damper under Near-field Ground Motions

ABSTRACT Under near-field ground motions, fluid viscous dampers (FVDs) are effective in controlling deck longitudinal displacement but lead to the increase of bending moment and shear force at tower base. Negative stiffness (NS) devices are introduced in combination of FVDs for the bridge. The NS devices lengthen the fundamental vibration period of the bridge to reduce the spectrum acceleration whereas FVDs introduce extra damping to the bridge system to reduce the deck displacement. After implementing NS devices, designers have more options of designing FVDs for seismic control of the cable-stayed bridges while maintaining the design requirements under near-field seismic excitations.

EXPERIMENTAL INVESTIGATION OF SEISMIC RESPONSE PARAMETERS OF RUBBERISED AGGREGATE CONCRETE FRAME STRUCTURE

This paper presents the results of experimental investigations on a reduced-scale, reinforced, rubberised, aggregate concrete frame structure for the evaluation of seismic response parameters. The considered frame has twenty percent scrap-tyre rubber (crumb) replacing fine aggregates. A one-third reduced scale model of a two-storey single-bay frame was fabricated using the mix ratio of 1:1.68:1.72 (cement: sand: aggregate) and water/cement of 0.48, replacing twenty percent of fine aggregates via waste rubber (crumb) by volume. The model frame was subjected first to a free vibration test for evaluation of dynamic characteristics (frequency/period, elastic viscous damping). It was subjected to simulated multiple base excitations using 1994 Northridge earthquake time history for the evaluation of seismic response parameters (ductility factor, overstrength factor, and response modification factor). Seismic response curve (lateral displacement versus peak base acceleration) was developed for the model to assess the viability of crumb in concrete in areas of active seismicity. The fundamental period of vibration and damping were calculated as 0.75 sec and 10.85 percent, respectively using records of free vibration tests. The ductility, overstrength and response modification factors, and maximum acceleration resisted were computed using multiple base excitations which came out to be 3.10, 2.16, 6.70 and 0.72g, respectively.

Machine learning and nonlinear models for the estimation of fundamental period of vibration of masonry infilled RC frame structures

In this work, the estimation of the fundamental period of vibration of masonry infilled RC frame structures is achieved using both Machine Learning techniques and concise nonlinear formulas. The data used are extracted from a recently published extensive database that associates the period with relevant information, such as the height of the structure, the span length between columns, the wall opening ratio, and the masonry wall stiffness. It is shown that, as compared to the utilized data, the proposed methods produce excellent results at the cost of various levels of complexity.

Experimental evaluation of permeable cable-supported façades subjected to wind and earthquake loads

In building engineering, non-structural components represent a significant cost of the overall budget of a construction project. However, in many cases their design is essentially based on architectural criteria rather than on structural performance mainly because the structure stability does not necessary rely on them. Among nonstructural elements, façades are one of the most visible and expensive components where innovation is very popular. Permeable cable-supported façades are a recent frontage proposal designed to allow not only flexible exterior finishes, but also the flow of natural light and the apparent building transformation according to the daytime and light; however, their structural performance for wind and earthquake loads is still a subject of research. This paper, for the first time, experimentally evaluates the wind and seismic behavior of these type of façades. A five-step comprehensive approach is proposed for the evaluation of cable-supported masonry facades including field and laboratory tests. In the first step, the individual capacity of the connections and materials of the system is evaluated under standardized and non-standardized procedures. The next step consisted in quantifying the fundamental vibration periods and the modal shapes of the façade system including the effect of the border and hanging conditions. The following phase is to estimate the wind load using computational fluid dynamics (CFD). In order to understand the effect of the wind at the different scales of the structure, simulations are performed starting with few bricks and progressively increasing the size of the computational model until assessing the entire building. These analyses allow understanding how the micro and macro components distribution and geometry can affect the wind in-and-out-flow and the possibility of vortexes. Then, a full-scale experimental sub-assembly specimen of a representative module of the façade is subjected to uniformly distributed pressures; the setup considered the border conditions, tension loads, and actual materials. Finally, the seismic assessment phase includes a simplified non-linear procedure to calculate critical accelerations at the building roof, and shaking-table tests of full-scale specimens subjected to these demands. The proposed methodology is apply to a case study consisting on a 40-m height permeable façade of the 12-story Santafe Foundation Hospital located in Bogota (Colombia). The main conclusions of this study are: (1) the dynamic properties of the system mainly rely on the cable tensioning and mass of the system; (2) fundamental vibration frequencies of the façade are much higher than wind demands, so no wind-related amplifications are expected; (3) the façade porosity avoids that high wind pressures may be developed; and (4) for design level earthquakes no major damage is expected. Overall, results show an appropriate performance of this type of façades.

Dynamic Identification for Representative Building Typologies: Three Case Studies from Bucharest Area

The paper presents results from an experimental program implemented for three representative buildings in Bucharest metropolitan area and aimed to explore the potential of various dynamic identification methods in providing information about building state changes. The objective is to establish reference values of potential use in rapid earthquake damage detection systems. Each of the selected buildings was designed according to a different seismic code, in force at the time of its construction. The methods employed for this study were: the analysis of Fourier spectra, the analysis of the transfer function and the random decrement technique. To validate the results, the fundamental periods of vibration determined experimentally were compared with the corresponding values predicted by the empirical formulas specified in the corresponding editions of the Romanian seismic code. The results revealed consistent values for both the fundamental period and the damping ratio of the buildings. However, small variations of the two parameters were identified, depending on the time the recordings were performed, noise sources and levels and building occupancy. The results, in terms of validated data on the dynamic characteristics of Romanian building stock and of assessment of methods performance, add up to the information pool needed for the development of countrywide pre- and post-earthquake assisted decision tools.