• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.679-705
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• 2005

This paper presents a practical method to evaluate the effective length factors for columns in multi-storey unbraced frames based on the concept of storey-based elastic buckling by means of decomposing a multi-storey frame into a series of single-storey partially-restrained (PR) frames. The lateral stiffness of the multi-storey unbraced frame is derived and expressed as the product of the lateral stiffness of each storey. Thus, the stability analysis for the multi-storey frame is conducted by investigating the lateral stability of each individual storey, which is facilitated through decomposing the multi-storey frame into a series of single-storey PR frames and applying the storey-based stability analysis proposed by the authors (Xu and Liu 2002) for each single-storey PR frame. Prior to introducing decomposition approaches, the end rotational stiffness of an axially load column is derived and rotational stiffness interaction between the upper and lower columns is investigated. Three decomposition approaches, characterized by means of distributing beam-to-column rotational-restraining stiffness between the upper and lower columns, are proposed. The procedure of calculating storey-based column effective length factors is presented. Numerical examples are then given to illustrate the effectiveness of the proposed procedure.

• Earthquakes and Structures
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• v.12 no.4
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• pp.437-448
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• 2017

Soft or extreme soft storeys in multi-storied buildings cause localized damage (and even collapse) during strong earthquake shaking. The presence of such soft or extremely soft storey is identified through provisions of vertical stiffness irregularity in seismic design codes. Identification of the irregularity in a building requires estimation of lateral translational stiffness of each storey. Estimation of lateral translational stiffness can be an arduous task. A simple procedure is presented to estimate storey stiffness using only properties of fundamental lateral translational mode of oscillation (namely natural period and associated mode shape), which are readily available to designers at the end of analysis stage. In addition, simplified analytical expressions are provided towards identifying stiffness irregularity. Results of linear elastic time-history analyses indicate that the proposed procedure captures the irregularity in storey stiffness in both low- and mid-rise buildings.

• Earthquakes and Structures
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• v.11 no.1
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• pp.1-23
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• 2016

Numerous buildings have been damaged or destroyed in previous earthquakes by developing soft storey. Almost all the seismic codes have provisions to prevent soft storey in structures, most of them have recommended the ratio of stiffness between adjacent storeys, but none of them has proposed the method to calculate the storey stiffness. On the other hand a great number of previous researches on stiffness have been focused on approximate methods and accurate methods by using analytical softwares have been almost neglected. In this study, six accurate methods for calculating the storey stiffness have been studied on 246 two-bay reinforced concrete frames. It is shown with the results of the statistical study and structural analysis that method 3 in which there is no modification of the original model and the forces with triangular distribution similar to seismic forces are applied to the center of mass of all storeys has acceptable accuracy and desirable efficiency for designing and controlling structures.

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.19-33
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• 2015

Open ground storey (OGS) buildings are characterized by the sudden reduction of stiffness in the ground storey with respect to the upper infilled storeys. During earthquakes, this vertical irregularity may result in accumulated damage in the ground storey members of OGS buildings without much damage in the upper storeys. Hence, the structural design of OGS buildings needs special attention. The present study suggests a modification of existing displacement-based design (DBD) procedure by proposing a new lateral load distribution. The increased demands of ground storey members of OGS buildings are estimated based on non-linear time history analysis results of four sets of bare and OGS frames having four to ten storey heights. The relationship between the increased demand and the relative stiffness of ground storey (with respect to upper storeys) is taken as the criterion for developing the expression for the design lateral load. It is also observed that under far-field earthquakes, there is a decrease in the ground storey drift of OGS frames as the height of the frame increases, whereas there is no such reduction when these frames are subjected to near-field earthquakes.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.9-17
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• 2018

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

• Earthquakes and Structures
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• v.25 no.5
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• pp.359-367
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• 2023

High-rise structures are considered as symbols of economic power and leadership. Developing countries like India are also emerging as centers for new high-rise buildings (HRB). As the land is expensive and scarce everywhere, construction of tall buildings becomes the best solution to resolve the problem. But, as building's height increases, its stiffness reduces making it more susceptible to vibrations due to wind and earthquake forces. Several systems are available to control vibrations or deflections; however, outrigger systems are considered to be the most effective systems in improving lateral stiffness and overall stability of HRB. In this paper, a 42-storey RCC HRB is analyzed to determine the optimum position of outriggers of different materials. The linear static analysis of the building is performed with and without the provision of virtual outriggers of reinforced cement concrete (RCC) and pre-stressed concrete (PSC) at different storey levels by response spectrum method using finite element based Extended3D Analysis of building System (ETABS) software for determining responses viz. storey displacement, base shear and storey drift for individual models. The maximum allowable limit and percentage variations in earthquake responses are verified using the guidelines of Indian seismic codes. Results indicate that the outriggers contribute in significantly reducing the storey displacement and storey drift up to 28% and 20% respectively. Also, it is observed that the PSC outriggers are found to be more efficient over RCC outriggers. The optimum location of both types of outriggers is found to be at the mid height of building.

• Earthquakes and Structures
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• v.11 no.6
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• pp.1101-1121
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• 2016

Base isolation, one of the popular seismic protection approaches proven to be effective in practical applications, has been widely applied worldwide during the past few decades. As the techniques mature, it has been recognised that, the biggest issue faced in base isolation technique is the challenge of great base displacement demand, which leads to the potential of overturning of the structure, instability and permanent damage of the isolators. Meanwhile, drain, ventilation and regular maintenance at the base isolation level are quite difficult and rather time- and fund- consuming, especially in the highly populated areas. To address these challenges, a number of efforts have been dedicated to propose new isolation systems, including segmental building, additional storey isolation (ASI) and mid-storey isolation system, etc. However, such techniques have their own flaws, among which whipping effect is the most obvious one. Moreover, due to their inherent passive nature, all these techniques, including traditional base isolation system, show incapability to cope with the unpredictable and diverse nature of earthquakes. The solution for the aforementioned challenge is to develop an innovative vibration isolation system to realise variable structural stiffness to maximise the adaptability and controllability of the system. Recently, advances on the development of an adaptive magneto-rheological elastomer (MRE) vibration isolator has enlightened the development of adaptive base isolation systems due to its ability to alter stiffness by changing applied electrical current. In this study, an innovative semi-active storey isolation system inserting such novel MRE isolators between each floor is proposed. The stiffness of each level in the proposed isolation system can thus be changed according to characteristics of the MRE isolators. Non-dominated sorting genetic algorithm type II (NSGA-II) with dynamic crowding distance (DCD) is utilised for the optimisation of the parameters at isolation level in the system. Extensive comparative simulation studies have been conducted using 5-storey benchmark model to evaluate the performance of the proposed isolation system under different earthquake excitations. Simulation results compare the seismic responses of bare building, building with passive controlled MRE base isolation system, building with passive-controlled MRE storey isolation system and building with optimised storey isolation system.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.1-17
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• 2013

In this study, the modified finite element- transfer matrix methods are proposed for free vibration analysis of asymmetric structures, the bearing system of which consists of shear wall-frames. In the study, a multi-storey structure is divided into as many elements as the number of storeys and storey masses are influenced as separated at alignments of storeys. The shear walls and frames are assumed to be flexural and shear cantilever beam structures. The storey stiffness matrix is obtained by formulating the governing equation at the center of mass for the shear walls and the frames in the i.th floor. The system transfer matrix is constructed in the dimension of $6{\times}6$ by transforming the obtained stiffness matrix. Thus, the dimension, which is $12n{\times}12n$ in classical finite elements, is reduced to the dimension of $6{\times}6$. To study the suitability of the method, the results are assessed by solving two examples taken from the literature.

• Structural Engineering and Mechanics
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• v.70 no.4
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• pp.421-429
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• 2019

This paper presents an analytical model for the estimation of initial lateral stiffness of steel moment resisting frames with masonry infills. However, rather than focusing on the single bay-single storey substructure, the developed model attempts to estimate the global stiffness of multi-storey and multi-bay frames, using an assembly of equivalent springs and taking into account the shape of the lateral loading pattern. The contribution from each infilled frame panel is included as an individual spring, whose properties are determined on the basis of established diagonal strut macro-modeling approaches from the literature. The proposed model is evaluated parametrically against numerical results from frame analyses, with varying number of frame stories, infill openings, masonry thickness and modulus of elasticity. The performance of the model is evaluated and found quite satisfactory.

• Structural Engineering and Mechanics
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• v.46 no.2
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• pp.245-267
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• 2013

During preliminary design of a RC building located in a seismic area, having quick but reliable analytical measurement of interstory drifts and storey stiffnesses might be helpful in order to check the fulfillment of damage limit state and stiffness regularity in elevation required by seismic design codes. This paper presents two approximate methods, strongly interrelated each other, and addressed to achieve each of these two purposes for frame buildings. A brief description of some already existing methods addressed to the same aims is included to compare the main differences in terms of general approaches and assumptions. Both new approximate methods are then applied to 9 'ideal' frames and 2 'real' buildings designed according to the Italian seismic code. The results are compared with the 'exact' values obtained by the code-based standard calculation, performed via FEM models, showing a satisfactory range of accuracy. Compared with those by the other methods from literature, they indicate the proposed procedures lead to a better approximation of the objective structural parameters, especially for those buildings designed according to the modern 'capacity design' philosophy.