• Earthquakes and Structures
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• v.1 no.2
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• pp.163-175
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• 2010

The vertical axis through the modal center of rigidity (m-CR) is used for interpreting the code torsional provisions in the design of eccentric multi-story building structures. The concept of m-CR has been demonstrated by the author in an earlier paper and the particular feature of this point is that when the vertical line of the centers of mass at the floor levels is passing through m-CR, minimum base torsion is developed. For this reason the aforesaid axis is used as reference axis for implementing the code provisions required by the equivalent static analysis. The study examines uniform mixed-bent-type multistory buildings with simple eccentricity, ranging from torsionally stiff to torsionally flexible systems. Using the results of a dynamic response spectrum analysis as a basis for comparisons, it is shown that the results of the code static design are on the safe side in torsionally stiff buildings, but unable to predict the required strength of bents on the stiff side of systems with a predominantly torsional response. Suggestions are made for improving the code provisions in such cases.

• Structural Engineering and Mechanics
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• v.40 no.4
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• pp.489-500
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• 2011

The elastic seismic response of plan-asymmetric multi storey steel-frame buildings is investigated under earthquake loading with particular emphasis on forward-rupture directivity and fling records. Three asymmetric building systems are generated with different torsional stiffness and varying static eccentricity. The structural characteristic of these systems are designed according to UBC 97 code and their seismic responses subjected to a set of earthquake records are obtained from the response history analysis (RHA) as well as the linear static analysis (LSA). It is shown that, the elastic torsional response is influenced by the intensity of near-fault ground motions with different energy contents. In the extreme case of very strong earthquakes, the behaviour of torsionally stiff buildings and torsionally flexible buildings may differ substantially due to the fact that the displacement envelope of the deck depends on ground motion characteristics.

• Wind and Structures
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• v.6 no.1
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• pp.23-40
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• 2003

The steady state response of a torsionally coupled system with tuned mass dampers (TMDs) to external wind-induced harmonic excitation is presented. The torsionally coupled system is considered as one-way eccentric system. The eccentricity considered in the system is accidental eccentricity only. The performance of single tuned mass damper (TMD) optimally designed without considering the torsion is investigated for the torsionally coupled system and found that the effectiveness of a single TMD is significantly reduced due to torsion in the system. However, the design of TMD system without considering the torsion is only justified for torsionally stiff systems. Further, the optimum parameters of a single TMD considering the accidental eccentricity are obtained using numerical searching technique for different values of uncoupled torsional to lateral frequency ratio and aspect ratio of the system. The optimally designed single TMD system is found to be less effective for torsionally coupled system in comparison to uncoupled system. This is due to the fact that a torsionally coupled system has two natural frequencies of vibration, as a result, at least two TMDs are required which can control both lateral and torsional response of the system. The optimum damper parameters of different alternate arrangements such as (i) two identical TMDs placed at opposite corners, (ii) two independent TMDs and (iii) four TMDs are evaluated for minimum response of the system. The comparative performance of the above TMDs arrangements is also studied for both torsionally coupled and uncoupled systems. It is found that four TMDs arrangement is quite effective solution for vibration control of torsionally coupled system.

• Earthquakes and Structures
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• v.9 no.2
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• pp.391-413
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• 2015

Damage of torsionally coupled buildings situated on soil sites has been reported in literature, however no site-specific studies are available for torsionally coupled buildings having site characteristics as a parameter. Effect of torsion is being accounted in seismic codes by the provision of design eccentricity where the dynamic to static eccentricity ratio is a parameter. In this paper, a methodology to determine dynamic to static eccentricity ratio of torsionally coupled buildings has been demonstrated for Delhi region for two torsionally coupled buildings on three soil sites. The variations of average and standard deviations of frame shears for stiff and flexible edges are studied for four eccentricity ratios for the two buildings for the three sites. From the limited studies made, it is observed that the dynamic to static eccentricity ratios observed for site-specific earthquakes are different from Indian seismic code specified value, hence a proposal is made to include a comment in Indian seismic code. Methodology proposed in this paper can be adopted for any region, for the estimation of dynamic to static eccentricity ratio for site specific earthquake.

• Earthquakes and Structures
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• v.9 no.1
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• pp.145-171
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• 2015

Due to earthquakes, many structures suffered extensive damages that were attributed to the torsional effect caused by mass, stiffness or strength eccentricity. Due to this type of asymmetry torsional moments are generated that are imposed by means of additional shear forces developed at the vertical resisting structural elements of the buildings. Although the torsional effect on the response of reinforced concrete buildings was the subject of extensive research over the last decades, a quantitative index measuring the amplification of the shear forces developed at the vertical resisting elements due to lateral-torsional coupling valid for both elastic and elastoplastic response states is still missing. In this study a reliable index capable of assessing the torsional effect is proposed. The performance of the proposed index is evaluated and its correlation with structural response quantities like displacements, interstorey drift, base torque, shear forces and upper diaphragm's rotation is presented. Torsionally stiff, mass eccentric single-story and multistory structures, subjected to bidirectional excitation, are considered and nonlinear dynamic analyses are performed using natural records selected for three hazard levels. It was found that the proposed index provides reliable prediction of the magnitude of torsional effect for all test examples considered.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.505-530
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• 2008

This paper proposes the application of active multiple tuned mass dampers (AMTMD) for translational and torsional response control of a simplified two-degree-of-freedom (2DOF) structure, able to represent the dynamic characteristics of general asymmetric structures, under the ground acceleration. This 2DOF structure is a generalized 2DOF system of an asymmetric structure with predominant translational and torsional responses under earthquake excitations using the mode reduced-order method. Depending on the ratio of the torsional to the translational eigenfrequency, i.e. the torsional to translational frequency ratio (TTFR), of asymmetric structures, the following three cases can be distinguished: (1) torsionally flexible structures (TTFR < 1.0), (2) torsionally intermediate stiff structures (TTFR = 1.0), and (3) torsionally stiff structures (TTFR > 1.0). The even distribution of the AMTMD within the whole width and half width of the asymmetric structure, thus leading to three cases of installing the AMTMD (referred to as the AMTMD of case 1, AMTMD of case 2, AMTMD of case 3, respectively), is taken into account. In the present study, the criterion for searching the optimum parameters of the AMTMD is defined as the minimization of the minimum values of the maximum translational and torsional displacement dynamic magnification factors (DMF) of an asymmetric structure with the AMTMD. The criterion used for assessing the effectiveness of the AMTMD is selected as the ratio of the minimization of the minimum values of the maximum translational and torsional displacement DMF of the asymmetric structure with the AMTMD to the maximum translational and torsional displacement DMF of the asymmetric structure without the AMTMD. By resorting to these two criteria, a careful examination of the effects of the normalized eccentricity ratio (NER) on the effectiveness and robustness of the AMTMD are carried out in the mitigation of both the translational and torsional responses of the asymmetric structure. Likewise, the effectiveness of a single ATMD with the optimum positions is presented and compared with that of the AMTMD.

• Earthquakes and Structures
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• v.2 no.2
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• pp.109-126
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• 2011

The inelastic earthquake response of non-symmetric, braced steel buildings, designed according to the EC3 (steel structures) and EC8 (earthquake resistant design) codes, is investigated using 1, 3 and 5-story models, subjected to a set of 10, two-component, semi-artificial motions, generated to match the design spectrum. It is found that in these buildings, the so-called "flexible" edge frames exhibit higher ductility demands and interstory drifts than the "stiff" edge frames. We note that the same results were reported in an earlier study for reinforced concrete buildings and are the opposite of what was predicted in several other studies based on the over simplified, hence very popular, one-story, shear-beam type models. The substantial differences in such demands between the two sides suggest a need for reassessment of the pertinent code provisions. In a follow up paper, a design modification will be introduced that can lead to a more uniform distribution of ductility demands in the elements of all building edges. This investigation is another step towards more rational design of non-symmetric steel buildings.

• Earthquakes and Structures
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• v.2 no.2
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• pp.127-147
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• 2011

In a companion paper as well as in earlier publications, it has been shown that in asymmetric frame buildings, designed in accordance with modern codes and subjected to strong earthquake excitations, the ductility demands at the so called "flexible" edges are consistently and substantially higher than the ductility demands at the "stiff" edges of the building. In some cases the differences in the computed ductility factors between elements at the two opposite building edges exceeded 100%. Similar findings have also been reported for code designed reinforced concrete buildings. This is an undesirable behavior as it indicates no good use of material and the possibility for overload of the "flexible" edge members with a consequent potential for premature failure. In the present paper, a design modification will be introduced that can alleviate the problem and lead to a more uniform distribution of ductility demands in the elements of all building edges. The presented results are based on the steel frames detailed in the companion paper. This investigation is another step towards more rational design of non-symmetric steel buildings.

• Earthquakes and Structures
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• v.8 no.2
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• pp.463-484
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• 2015

Modern codes for earthquake resistant building design require consideration of the so-called accidental design eccentricity, to account for torsional response caused by several factors not explicitly considered in design. This provision requires that the mass centres in the building floor be moved a certain percentage of the building's dimension (usually 5%) along both the x and y axes and in both positive and negative directions. If one considers also the spatial combinations of the two component motion in a dynamic analysis of the building, the number of required analyses and combinations increases substantially, causing a corresponding work load increase for practicing structural engineers. Another shortcoming of this code provision is that its introduction has been based primarily on elastic results from investigations of oversimplified, hence questionable, one story building models. This problem is addressed in the present paper using four groups of eccentric braced steel buildings, designed in accordance with Eurocodes 3 (steel) and 8 (earthquake design), with and without accidental eccentricities considered. The results indicate that although accidental design eccentricities can lead to somewhat reduced inelastic response demands, the benefit is not significant from a practical point of view. This leads to suggestions that accidental design eccentricities should probably be abolished or perhaps replaced by a simpler and more effective design provision, at least for torsionally stiff buildings that constitute the vast majority of buildings encountered in practice.

• Earthquakes and Structures
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• v.11 no.3
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• pp.421-443
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• 2016

When conducting seismic assessment of an asymmetric building, it is essential to carry out three-dimensional analysis considering all the possible directions of seismic input. For this purpose, the author proposed a simplified procedure is to predict the largest peak seismic response of an asymmetric building subjected to horizontal bidirectional ground motion acting in an arbitrary angle of incidence in previous study. This simplified procedure has been applied to torsionally stiff (TS) asymmetric buildings with regular elevation. However, the suitability of this procedure to estimate the peak response of an asymmetric building with vertical irregularity, such as an asymmetric building with setback, has not been assessed. In this article, the pushover-based simplified procedure is applied to estimate the peak response of asymmetric buildings with bidirectional setback. Nonlinear dynamic (time-history) analysis of two six-storey asymmetric buildings with bidirectional setback and designed according to strong-column weak beam concept is carried out considering various directions of seismic input, and the results compared with those estimated by the proposed method. The largest peak displacement estimated by the simplified method agrees well with the envelope of the dynamic analysis response. The suitability assessment of the simplified procedure to analysed building models is made as well based on pushover analysis results.