• Earthquakes and Structures
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• v.6 no.2
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• pp.201-216
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• 2014

Many building codes use the empirical equation to determine fundamental period of vibration where in effect of length, width and the stiffness of the building is not explicitly accounted for. Also the equation, estimates the fundamental period of vibration with large safety margin beyond certain height of the building. An attempt is made to arrive at the simple empirical equations for fundamental period of vibration with adequate safety margin, using soft computing technique of Genetic Programming (GP). In the present study, GP models are developed in four categories, varying the number of input parameters in each category. Input parameters are chosen to represent mass, stiffness and geometry of the buildings directly or indirectly. Total numbers of 206 buildings are analyzed out of which, data set of 142 buildings is used to develop these models. It is observed that GP models developed under B and C category yield the same equation for fundamental period of vibration along X direction as well as along Y direction whereas the equation of fundamental period of vibration along X direction and along Y direction is of the same form for category D. The equations obtained as an output of GP models clearly indicate the influence of mass, geometry and stiffness of the building over fundamental period of vibration. These equations are then compared with the equation recommended by other researcher.

• Wind and Structures
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• v.29 no.3
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• pp.209-223
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• 2019

The assessment of wind-induced vibration for tall reinforced concrete (RC) buildings requires the accurate estimation of their dynamic properties, e.g., the fundamental vibration periods and damping ratios. In this study, RC frame-shear wall systems designed under gravity and wind loadings have been evaluated by utilising 3D FE modelling incorporating eigen-analysis to obtain the elastic periods of vibration. The conducted parameters consist of the number of storeys, the plan aspect ratio (AR) of buildings, the core dimensions, the space efficiency (SE), and the leasing depth (LD) between the internal central core and outer frames. This analysis provides a reliable basis for further investigating the effects of these parameters and establishing new formulas for predicting the fundamental vibration periods by using regression analyses on the obtained results. The proposed constrained numerically based formula for vibration periods of tall RC frame-shear wall office buildings in terms of the height of buildings reasonably agrees with some cited formulas for vibration period from design codes and standards. However, the same proposed formula has a high discrepancy with other cited formulas from the rest of design codes and standards. Also, the proposed formula agrees well with some cited experimentally based formulas.

• Earthquakes and Structures
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• v.16 no.5
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• pp.611-623
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• 2019

A set of mid-rise bare and uniformly infilled reinforced-concrete frame buildings are analyzed for two different seismic intensities of ground-motions (i.e., 'Design Basis Earthquake' and 'Maximum Considered Earthquake') to study their floor response. The crucial parameters affecting seismic design force for acceleration-sensitive non-structural components are studied and compared with the guidelines of the European and the United States standards, and also with the recently developed NIST provisions. It is observed that the provisions of both the European and the United States standards do not account for the effects of the period of vibration of the supporting structure and seismic intensity of ground-motions and thereby provides conservative estimates of the in-structure amplification. In case of bare frames, the herein derived component amplification factors for both the design basis earthquake and the maximum considered earthquake exceeds with their recommended values in the European and the United States standards for non-structural components having periods in vicinity of the higher modes of vibration, whereas, in case of infilled frames, component amplification factors exceeds with their recommended value in the European standard for non-structural components having periods in vicinity of the fundamental mode of vibration, and only for the design basis earthquake. As a consequence of these observations, as well as capping on the design force (in case of United states standard and NIST provisions), in case of the design basis earthquake, the combined amplification factor is underestimated for non-structural components having periods in vicinity of the higher modes of vibration of bare frames, and also for non-structural components having periods in vicinity of the fundamental mode of vibration of infilled frames. At the maximum considered earthquake demand, excepting non-structural components having periods in vicinity of the higher modes of vibration of bare frames, all provisions generally provide conservative estimates of the design floor accelerations.

• Earthquakes and Structures
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• v.19 no.2
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• pp.119-128
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• 2020

In seismic design of a pylon supporting transmission lines in an overhead electricity transmission system, an estimation of the fundamental periods of the pylon in two orthogonal vertical planes is necessary to compute the seismic forces required for sizing pylon members and checking pylon deflections. In current practice, the fundamental periods of a pylon in two orthogonal vertical planes are typically obtained from eigenvalue analyses of a model consisting of the pylon of interest as well as some adjacent pylons and the transmission lines supported by these pylons. Such an approach is onerous and numerically inconvenient. This research focused on development of a simplified method to determine the fundamental periods of pylons. The simplified method is rooted in Rayleigh's quotient and is based on a single-pylon model. The force vectors that can be used to generate the shape vectors required in Rayleigh's quotient are presented in detail. Taking three pylons selected from representative overhead electricity transmission systems having different design parameters as examples, the fundamental periods of the chosen pylons predicted from the simplified method were compared with those from the rigorous eigenvalue analyses. Result comparisons show that the simplified method provides reasonable predictions and it can be used as a convenient surrogate for the tedious approach currently adopted.

• Earthquakes and Structures
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• v.26 no.6
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• pp.417-431
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• 2024

The fundamental period of vibration is one of the most critical parameters in the analysis and design of structures, as it depends on the distribution of stiffness and mass within the structure. Therefore, building codes propose empirical equations based on the observed periods of actual buildings during seismic events and ambient vibration tests. However, despite the fact that infill walls increase the stiffness and mass of the structure, causing significant changes in the fundamental period, most of these equations do not account for the presence of infills walls in the structure. Typically, these equations are dependent on both the structural system type and building height. The different values between the empirical and analytical periods are due to the elimination of non-structural effects in the analytical methods. Therefore, the presence of non-structural elements, such as infill panels, should be carefully considered. Another critical factor influencing the fundamental period is the effect of Soil-Structure Interaction (SSI). Most seismic building design codes generally consider SSI to be beneficial to the structural system under seismic loading, as it increases the fundamental period and leads to higher damping of the system. Recent case studies and postseismic observations suggest that SSI can have detrimental effects, and neglecting its impact could lead to unsafe design, especially for structures located on soft soil. The current research focuses on investigating the effect of infill panels on the fundamental period of moment-resisting and eccentrically braced steel frames while considering the influence of soil-structure interaction. To achieve this, the effects of building height, infill wall stiffness, infill openings and soil structure interactions were studied using 3, 6, 9, 12, 15 and 18-story 3-D frames. These frames were modeled and analyzed using SeismoStruct software. The calculated values of the fundamental period were then compared with those obtained from the proposed equation in the seismic code. The results indicate that changing the number of stories and the soil type significantly affects the fundamental period of structures. Moreover, as the percentage of infill openings increases, the fundamental period of the structure increases almost linearly. Additionally, soil-structure interaction strongly affects the fundamental periods of structures, especially for more flexible soils. This effect is more pronounced when the infill wall stiffness is higher. In conclusion, new equations are proposed for predicting the fundamental periods of Moment Resisting Frame (MRF) and Eccentrically Braced Frame (EBF) buildings. These equations are functions of various parameters, including building height, modulus of elasticity, infill wall thickness, infill wall percentage, and soil types.

• Structural Monitoring and Maintenance
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• v.4 no.4
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• pp.351-364
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• 2017

In this study effects of various parameters like a number of bays, the stiffness of the structure along with the height of the structure was examined. The fundamental period of vibration T of the building is an important parameter for evaluation of seismic base shear. Empirical equations which are given in the Indian seismic code for the calculation of the fundamental period of a framed structure, primarily as a function of height, and do not consider the effect of number of bays and stiffness of the structure. Building periods predicted by these expressions are widely used in practice, although it has been observed that there is scope for further improvement in these equations since the height alone is inadequate to explain the period variability. The aim of this study is to find the effects of a number of bays in both the directions, the stiffness of the structure and propose a new period equation which incorporates a number of bays, plan area, stiffness along with the height of the structure.

• International Journal of High-Rise Buildings
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• v.3 no.1
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• pp.49-64
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• 2014

Natural vibration period is an important parameter for high-rise building, Based on 414 high-rise buildings completed or passed over-limit approval in China, the distribution law of natural vibration periods is analyzied. In order to satisfy the design requirements, such as global stability, story drift limit and minimum shear-gravity ratio, the reference ranges of fundamental periods $T_1$ are $0.3{\sqrt{H}}{\sim}0.4{\sqrt{H}}$ when the structural heights $H{\geq}250m$, when 150 m ${\leq}$ H < 250m, $T_1=0.25{\sqrt{H}}{\sim}0.4{\sqrt{H}}$, when 100 m ${\leq}$ H < 150 m, $T_1=0.2{\sqrt{H}}{\sim}0.35{\sqrt{H}}$, when 50 m $ {\leq}$ H < 100m, $T_1=0.15{\sqrt{H}}{\sim}0.3{\sqrt{H}}$. These can provide reference data for controlling mass and rigidity of high-rise buildings.

• Earthquakes and Structures
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• v.14 no.4
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• pp.305-312
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• 2018

Significant research efforts were undertaken to evaluate seismic performance of vertically irregular buildings on flat ground. However, there is scarcity of study on seismic performance of buildings on hill slopes. The present study attempts to investigate seismic behaviour of reinforced concrete irregular stepback building frames with different configurations on sloping ground. Based on extensive regression study of free vibration results of four hundred seventeen frames with varying ground slope, number of story and span number, a modification is proposed to the code based empirical fundamental time period estimation formula. The modification to the fundamental time period estimation formula is a simplified function of ground slope and a newly introduced equivalent height parameter to reflect the effect of stiffness and mass irregularity. The derived empirical formula is successfully validated with various combinations of slope and framing configurations of buildings. The correlation between the predicted and the actual time period obtained from the free vibration analysis results are in good agreement. The various statistical parameters e.g., the root mean square error, coefficient of determination, standard average error generally used for validation of such regression equations also ensure the prediction capability of the proposed empirical relation with reasonable accuracy.

• Earthquakes and Structures
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• v.3 no.1
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• pp.17-35
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• 2012

Simplified equations for fundamental period of vibration of skeletal structures provided by most seismic design provisions suffer from the absence of any associated confidence levels and of any reference to their empirical basis. Therefore, such equations may typically give a sector of designers the false impression of yielding a fairly accurate value of the period of vibration. This paper, although not addressing simplified codes equations, introduces a set of mathematical equations utilizing the theory of error propagation and First-Order Second-Moment (FOSM) techniques to determine bounds on the relative error in theoretically calculated fundamental period of vibration of skeletal structures. In a complementary step, and for verification purposes, Monte Carlo simulation technique has been also applied. The latter, despite involving larger computational effort, is expected to provide more precise estimates than FOSM methods. Studies of parametric uncertainties applied to reinforced concrete frame bents - potentially idealized as SDOF systems - are conducted demonstrating the effect of randomness and uncertainty of various relevant properties, shaping both mass and stiffness, on the variance (i.e. relative error) in the estimated period of vibration. Correlation between mass and stiffness parameters - regarded as random variables - is also thoroughly discussed. According to achieved results, a relative error in the period of vibration in the order of 19% for new designs/constructions and of about 25% for existing structures for assessment purposes - and even climbing up to about 36% in some special applications and/or circumstances - is acknowledged when adopting estimates gathered from the literature for relative errors in the relevant random input variables.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1999.10a
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• pp.375-382
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• 1999

The fundamental vibration period of a shearwall apartments cannot estimate accurately by means of empirical formulas specified in present codes, The objective of this paper is to estimate the period of a shearwall apartments by microtremor measurement. A micretremor is the continuous small oscillation of the ground cause by traffic and operation machinery. Microtremors are extensively studied primarily in Japan to estimate conveniently subsurface structures of soil deposits and building vibrations. It is obtained the results that the fundamental periods estimated by microtremor measurement are shorter than those values by dynamic analysis of building.