• Structural Engineering and Mechanics
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• v.19 no.1
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• pp.55-71
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• 2005

In several design codes and specifications, simplified formulae and diagrams are given for determining the buckling lengths of frame columns. It is shown that these formulae may yield rather erroneous results in certain cases. This is due to the fact that, the code formulae utilise only local stiffness distributions. In this paper, a simplified procedure for determining approximate values for the buckling loads of multi-storey frames is developed. The procedure utilises lateral load analysis of frames and yields errors in the order of 10%, which may be considered suitable for design purposes. The proposed procedure is applied to several numerical examples and it is shown that all the errors are in the acceptable range and on the safe side.

• Structural Engineering and Mechanics
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• v.51 no.3
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• pp.487-502
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• 2014

In buildings structures, the flexural stiffness reduction of beams and columns due to concrete cracking plays an important role in the nonlinear load-deformation response of reinforced concrete structures under service loads. Most Seismic Design Codes do not precise effective stiffness to be used in seismic analysis for structures of reinforced concrete elements, therefore uncracked section properties are usually considered in computing structural stiffness. But, uncracked stiffness will never be fully recovered during or after seismic response. In the present study, the effect of concrete cracking on the lateral response of structure has been taken into account. Totally 120 cases of 3 Dimensional Dynamic Analysis which considers the real and accidental torsional effects are performed using ETABS to determine the effective structural system across the height, which ensures the performance and the economic dimensions that achieve the saving in concrete and steel amounts thus achieve lower cost. The result findings exhibits that the dual system was the most efficient lateral load resisting system based on deflection criterion, as they yielded the least values of lateral displacements and inter-storey drifts. The shear wall system was the most economical lateral load resisting compared to moment resisting frame and dual system but they yielded the large values of lateral displacements in top storeys. Wall systems executes tremendous stiffness at the lower levels of the building, while moment frames typically restrain considerable deformations and provide significant energy dissipation under inelastic deformations at the upper levels. Cracking found to be more impact over moment resisting frames compared to the Shear wall systems. The behavior of various lateral load resisting systems with respect to time period, mode shapes, storey drift etc. are discussed in detail.

• Coupled systems mechanics
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• v.8 no.2
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• pp.169-184
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• 2019

This research work presents a study that aims to assess the dynamic structural behaviour and also investigate the human comfort levels of a reinforced concrete building, when subjected to nondeterministic wind dynamic loadings, considering the effect of masonry infills on the global stiffness of the structural model. In general, the masonry fills most of the empty areas within the structural frames of the buildings. Although these masonry infills present structural stiffness, the common practice of engineers is to adopt them as static loads, disregarding the effect of the masonry infills on the global stiffness of the structural system. This way, in this study a numerical model based on sixteen-storey reinforced concrete building with 48 m high and dimensions of $14.20m{\times}15m$ was analysed. This way, static, modal and dynamic analyses were carried out in order to simulate the structural model based on two different strategies: no masonry infills and masonry infills simulated by shell finite elements. In this investigation, the wind action is considered as a nondeterministic process with unstable properties and also random characteristics. The fluctuating parcel of the wind is decomposed into a finite number of harmonic functions proportional to the structure resonant frequency with phase angles randomly determined. The nondeterministic dynamic analysis clearly demonstrates the relevance of a more realistic numerical modelling of the masonry infills, due to the modifications on the global structural stiffness of the building. The maximum displacements and peak accelerations values were reduced when the effect of the masonry infills (structural stiffness) were considered in the dynamic analysis. Finally, it can be concluded that the human comfort evaluation of the sixteen-storey reinforced concrete building can be altered in a favourable way to design.

• Nuclear Engineering and Technology
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• v.31 no.6
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• pp.586-594
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• 1999

To limit both the large displacement and acceleration response of the structure efficiently, the relationships between acceleration and displacement responses of the structure under several earthquakes are investigated for various horizontal stiffness of the base isolation system to determine the effective stiffness of the base isolation system in this paper. An example structure is a five-storey steel frame building as the primary structure and the secondary structures are assumed to be located on the fifth floor of the primary structure. Input motions used in the structural analysis are El Centre 1940, Taft 1952, Mexico 1985, San Fernando 1971 Pacoima Dam, and artificially generated earthquakes. The relationships of the absolute peak acceleration and the displacement at the top of the structure are calculated for various natural periods of base isolators under various earthquakes. The peak acceleration response of the fifth floor in the base isolated structure is significantly reduced by a factor of 2.1 through 6.25. Also, the relative displacement response of the floor to the base of the superstructure is very small. The results of this study can be utilized to determine the effective stiffness of the base isolation system.

• Earthquakes and Structures
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• v.27 no.3
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• pp.227-237
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• 2024

The incidence angle of seismic excitation relative to the two orthogonal major axes of structures has been a subject of considerable research interest. Previous studies have primarily focused on single-storey symmetric and asymmetric structures, suggesting a minimal effect of incidence angle on structural behavior. This research extends the investigation to multi-storey structures, including vertically irregular configurations, using a comprehensive set of 20 near fault and 20 far field seismic excitation. The study employs nonlinear time-history analysis with a bidirectional hysteresis model to capture inelastic deformations accurately. Various structural models, including one-storey and two- storey regular structures (R1, R2) and vertically irregular structures with setbacks in one direction (IR1) and both directions (IR2), are analysed. The analysis reveals that the incidence angle has no discernible impact over the response of regular multi-storey structures. However, vertically irregular structures exhibit notable responses at corner columns, which decrease towards central columns, irrespective of the incidence angle. This response is attributed to the inherent mass distribution and stiffness irregularities rather than the angle of seismic excitation. The findings indicate that for both near fault and far field seismic excitation, the incidence angle's impact remains marginal even for complex structural configurations. Consequently, the study suggests that the angle of incidence of seismic excitation need not be a primary consideration in the seismic design of both regular and vertically irregular structures. These conclusions are robust across various structural models and seismic excitation characteristics, providing a comprehensive understanding the impact of incidence angle on seismic response.

• Earthquakes and Structures
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• v.6 no.1
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• pp.89-110
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• 2014

Nonlinear dynamic analyses are carried out to investigate the influence of the pinching hysteretic response of the exterior RC beam-column joints on the seismic behavior of multistory RC frame structures. The effect of the pinching on the local and global mechanisms of an 8-storey bare frame and an 8-storey pilotis type frame structure is evaluated. Further, an experimental data bank extracted from literature is used to acquire experimental experience of the range of the real levels that have to be considered for the pinching effect on the hysteretic response of the joints. Thus, three different cases for the hysteretic response of the joints are considered: (a) joints with strength and stiffness degradation characteristics but without pinching effect, (b) joints with strength degradation, stiffness degradation and low pinching effect and (c) joints with strength degradation, stiffness degradation and high pinching effect. For the simulation of the beam-column joints a special-purpose rotational spring element that incorporates the examined hysteretic options developed by the authors and implemented in a well-known nonlinear dynamic analysis program is employed for the analysis of the structural systems. The results of this study indicate that the effect of pinching on the local and global responses of the examined cases is not really significant at early stages of the seismic loading and especially in the cases when strength degradation in the core of exterior joint has occurred. Nevertheless in the cases when strength degradation does not occur in the joints the pinching may increase the demands for ductility and become critical for the columns at the base floor of the frame structures. Finally, as it was expected the ability for energy absorption was reduced due to pinching effect.

• Structural Engineering and Mechanics
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• v.15 no.4
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• pp.381-394
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• 2003

While constructing multistorey buildings with reinforced concrete framed structures it is a common practice to provide parking space for vehicles at the ground floor level. This floor will generally consist of open frames without any infilled walls and is called an open-storey. From a post disaster damage survey carried out, it was noticed that during the January 26, 2001 Bhuj (Gujarat, India) earthquake, a large number of reinforced concrete framed buildings with open-storey at ground floor level, suffered extensive damage and in some cases catastrophic collapse. This has brought into sharp focus the need to carry out systematic studies on the seismic vulnerability of such buildings. Determination of vulnerability requires realistic structural response estimations taking into account the stochasticity in the loading and the system parameters. The stochastic finite element method can be effectively used to model the random fields while carrying out such studies. This paper presents the details of stochastic finite element analysis of a five-storey three-bay reinforced concrete framed structure with open-storey subjected to standard seismic excitation. In the present study, only the stochasticity in the system parameters is considered. The stochastic finite element method used for carrying out the analysis is based on perturbation technique. Each random field representing the stochastic geometry/material property is discretised into correlated random variables using spatial averaging technique. The uncertainties in geometry and material properties are modelled using the first two moments of the corresponding parameters. In evaluating the stochastic response, the cross-sectional area and Young' modulus are considered as independent random fields. To study the influence of correlation length of random fields, different correlation lengths are considered for random field discretisation. The spatial expectations and covariances for displacement response at any time instant are obtained as the output. The effect of open-storey is modelled by suitably considering the stiffness of infilled walls in the upper storey using cross bracing. In order to account for changes in soil conditions during strong motion earthquakes, both fixed and hinged supports are considered. The results of the stochastic finite element based seismic analysis of reinforced concrete framed structures reported in this paper demonstrate the importance of considering the effect of open-storey with appropriate support conditions to estimate the realistic response of buildings subjected to earthquakes.

• Structural Engineering and Mechanics
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• v.8 no.3
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• pp.243-256
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• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• Steel and Composite Structures
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• v.28 no.2
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• pp.123-138
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• 2018

Eccentrically braced frames (EBF) represent an optimal structural solution for seismic prone areas, being able to provide high dissipative capacity and good elastic stiffness, to withstand strong seismic events without significant loss of bearing capacity and to avoid damage to non-structural elements in case of low and moderate earthquakes. The accurate knowledge of the cyclic behaviour of the dissipative links, characterizing the whole performance of EBFs, is required to optimize the structural properties and to refine the design techniques adopted for multi-storey buildings' analysis. Reliable numerical models for the links, at the same time requiring a limited computational effort, are then needed. The present work shows the results of a wide experimental test campaign executed on real-scale one storey/one bay frames with horizontal and vertical links, together with the elaboration of a simple semi-analytical model for the quick representation of the cyclic behaviour of shear links.

• Earthquakes and Structures
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• v.10 no.3
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• pp.589-611
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• 2016

This paper presents an analytical study aimed at evaluating the seismic performance of steel moment resisting frames (MRFs) retrofitted with different approaches. For this, 3, 6 and 12 storey MRFs having four equal bays of 5 m were selected as the case study models. The models were designed with lateral stiffness insufficient to satisfy code drift and hinge limitations in zones with high seismic hazard. Three different retrofit strategies including traditional diagonal bracing system and energy dissipation devices such as buckling restrained braces and viscoelastic dampers were used for seismic upgrading of the existing structures. In the nonlinear time history analysis, a set of ground motions representative of the design earthquake with 10% exceedance probability in fifty years was taken into consideration. Considering the local and global deformations, the results in terms of inter-storey drift index, global damage index, plastic hinge formations, base shear demand and roof drift time history were compared. It was observed that both buckling-restrained braces and viscoelastic dampers allowed for an efficient reduction in the demands of the upgraded frames as compared to traditional braces.