• Structural Engineering and Mechanics
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• v.67 no.6
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• pp.671-682
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• 2018

The effect of earthquake induced torsion, due to mass eccentricities, is investigated with the objective of providing practical design guidelines for minimizing the torsional response of building structures. Current code provisions recommend performing three dimensional static or dynamic analyses, which involve shifting the centers of the floor masses from their nominal positions to what is called an accidental eccentricity. This procedure however may significantly increase the design cost of multistory buildings, due to the numerous possible spatial combinations of mass eccentricities and it is doubtful whether such a cost would be justifiable. This paper addresses this issue on a theoretical basis and investigates the torsional response of asymmetric multistory buildings in relation to their behavior when all floor masses lie on the same vertical line. This approach provides an insight on the overall seismic response of buildings and reveals how the torsional response of a structure is influenced by an arbitrary spatial combination of mass eccentricities. It also provides practical guidelines of how a structural configuration may be designed to sustain minor torsion, which is the main objective of any practicing engineer. A parametric study is presented on 9-story common building types having a mixed-type lateral load resisting system (frames, walls, coupled wall bents) and representative heightwise variations of accidental eccentricities.

• 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.

• Steel and Composite Structures
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• v.5 no.6
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• pp.443-458
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• 2005

Steel angles are widely used in roof trusses as web and chord members and in lattice towers. Very often angle members are connected eccentrically. As a result, not only an angle member is under an axial force, but it is also subject to a pair of end eccentric moments. Moreover, the connection at each end provides some fixity so neither pinned nor the fixed end represents the reality. Many national design codes allow for the effects due to eccentricities by modifying the slenderness ratio and reducing the compressive strength of the member. However, in practice, it is difficult to determine accurately the effective length. The concept behind this method is inconsistent with strength design of members of other cross-sectional types such as I or box sections of which the buckling strength is controlled by the Perry constant or the initial imperfection parameters. This paper proposes a method for design of angle frames and trusses by the second-order analysis. The equivalent initial imperfection-to-length ratios for equal and unequal angles to compensate the negligence of initial curvatures, load eccentricities and residual stresses are determined in this paper. From the obtained results, the values of imperfection-to-length ratios are suggested for design and analysis of angle steel trusses allowing for member buckling strength based on the Perry-Robertson formula.

• International Journal of Concrete Structures and Materials
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• v.10 no.3
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• pp.393-406
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• 2016

Axially loaded reinforced concrete columns are hardly exist in practice due to the development of some bending moments. These moments could be produced by gravity loads or the lateral loads. First, the current paper presents a detailed analysis on the overall structural behavior of 15 eccentrically loaded columns as well as one concentrically loaded control one. Columns bent in either single curvature or double curvature modes are tested experimentally up to failure under the effect of different end eccentricities combinations. Three end eccentricities ratio were studied, namely, 0.1b, 0.3b and 0.5b, where b is the column width. Second, an expression correlated the decay in the normalized axial capacity of the column and the acting end eccentricities was developed based on the experimental results and then verified against the available formula. Third, based on the equivalent column concept, the equivalent pin-ended columns were obtained for columns bent in either single or double curvature modes. And then, the effect of end eccentricity ratio was correlated to the equivalent column length. Finally, a simplified design procedure was proposed for eccentrically loaded braced column by transferring it to an equivalent axially loaded pin-ended slender column. The results of the proposed design procedure showed comparable results against the results of the ACI 318-14 code.

• Journal of the Earthquake Engineering Society of Korea
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• v.17 no.5
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• pp.237-243
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• 2013

In the Korean Building Code (KBC), the Design Eccentricity involves the torsional amplification factor (TAF), and the inherent and accidental eccentricities. When a structure of less than 6-stories and assigned to seismic design category C or D is designed using equivalent static analysis method, both KBC-2006 and KBC-2009 use the TAF but apply different calculation methods for the of design eccentricity. The design eccentricity in KBC-2006 is calculated by multiplying the sum of inherent eccentricity and accidental eccentricity at each level by a TAF but that in KBC-2009 is calculated by multiplying only the accidental eccentricity by a TAF. In this paper, the damage indices of a building with planar structural irregularity designed by different design eccentricities are compared and the relationship between the earthquake damage and design eccentricity of the building is evaluated. On the basis of this study, the increment of design eccentricity results in the decrement of final eccentricity and global damage index of structure. It is observed that design eccentricity in KBC-2006 reduces the vulnerability of torsional irregular building compared to design eccentricity in KBC-2009.

• Wind and Structures
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• v.11 no.2
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• pp.153-178
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• 2008

Based on the empirical formulas for power spectra of generalized modal forces and local fluctuating wind forces in across-wind and torsional directions, the wind-induced lateral-torsional coupled response analysis of a representative rectangular tall building was conducted by setting various parameters such as eccentricities in centers of mass and/or rigidity and considering different torsional to lateral stiffness ratios. The eccentricity effects on the lateral-torsional coupled responses of the tall building were studied comprehensively by structural dynamic analysis. Extensive computational results indicated that the torsional responses at the geometric center of the building may be significantly affected by the eccentricities in the centers of mass and/or rigidity. Covariance responses were found to be in the same order of magnitude as the along-wind or across-wind responses in many eccentricity cases, suggesting that the lateral-torsional coupled effects on the overall wind-induced responses can not be neglected for such situations. The calculated results also demonstrated that the torsional motion contributed significantly to the total responses of rectangular tall buildings with mass and/or rigidity eccentricities. It was shown through this study that the framework presented in this paper provides a useful tool to evaluate the wind-induced lateral-torsional coupled responses of rectangular buildings, which will enable structural engineers in the preliminary design stages to assess the serviceability of tall buildings, potential structural vibration problems and the need for a detailed wind tunnel test.

• Journal of the Earthquake Engineering Society of Korea
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• v.16 no.5
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• pp.33-40
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• 2012

To reduce the vulnerability of torsional irregular buildings caused by seismic loads, the torsional amplification factor was introduced by the seismic code. This factor has been applied differently in a variety of seismic codes. In this study, the final static eccentricity, and the lateral and torsional stiffness ratios of buildings designed with different design eccentricities were compared. The increment of the torsional amplification factor resulted in a decrement of the final static eccentricity of the building. However, after reaching the maximum value of this factor, the final static eccentricity of the building increased again. The final static eccentricity of the building designed by multiplying the sum of the inherent and accidental eccentricity by the torsional amplification factor was zero or had a minus value, depending to the position of the vertical element.

• Steel and Composite Structures
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• v.32 no.4
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• pp.521-536
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• 2019

The mechanical response of concrete-filled steel tubular (CFST) columns subjected to pure compression or uniaxial bending was studied in depth over the last decades. However, the available research results on CFST columns under biaxial bending are still scarce and the lack of experimental tests for this loading situation is evident. At the same time, the design provisions in Eurocode 4 Part 1.1 for verifying the stability of CFST columns under biaxial bending make use of a simplistic interaction curve, which needs to be revised. This paper presents the outcome of a numerical investigation on slender CFST columns subjected to biaxial bending. Eccentricities differing in minor and major axis, as well as varying end moment ratios are considered in the numerical model. A parametric study is conducted for assessing the current design guidelines of EN1994-1-1. Different aspect ratios, member slenderness, reinforcement ratios and load eccentricities are studied, covering both constant and variable bending moment distribution. The numerical results are subsequently compared to the design provisions of EN1994-1- 1, showing that the current interaction equation results overly conservative. An alternative interaction equation is developed by the authors, leading to a more accurate yet conservative proposal.

• Structural Engineering and Mechanics
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• v.26 no.3
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• pp.297-313
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• 2007

A preliminary performance-based seismic design methodology is proposed. The top yield displacement of the system is computed from these of the components, which are assumed constant. Besides, a simple procedure to evaluate the top yield displacement of frames is developed. Seismic demands are represented in the form of yield point spectra. The methodology is general, conceptually transparent, uses simple calculations based on first principles and is applicable to asymmetric systems. To consider a specific situation two earthquake levels, occasional and rare are considered. The advantage of an arbitrary assignment of strength to the different components to reduce eccentricities and improved the torsional response of the system is addressed. The methodology is applied to an asymmetric five story building, and the results are verified by push-over analysis and non linear dynamic analysis.

• 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.