Accidental Eccentricity Research Articles

Seismic Design of Symmetric Structures for Accidental Torsion

The paper presents an analytical estimation of the dynamic effects, caused by the shifting of the centre of mass with accidental eccentricity in symmetric structures. The approximate analytical solution proves, that even under small accidental eccentricities the symmetric structures exhibit “irregular behaviour” and the accidental torsional effects cannot be described properly by static application of torsional moments. The prescribed application rule by Eurocode 8 for multimodal analysis underestimates the accidental torsional effects up to 21% for 5% eccentricity for the structures considered in the paper. An expression for the correction of member responses is derived. It is proved by numerical simulations of the dynamic response of three-dimensional models of symmetric structures, that the proposed correction coefficient gives accurate results in cases of single-storey and multi-storey structures. It gives a convenient way for the design practice to estimate accurately the accidental torsional effects on planar and 3-D models of symmetric structures.

EVALUATION OF ACCIDENTAL ECCENTRICITY IN BUILDINGS DUE TO ROTATIONAL COMPONENT OF EARTHQUAKE

This study adopts a random procedure in the evaluation of the effect of the rotational component of earthquake on the accidental eccentricity of symmetric and asymmetric buildings. The spectral density function of the rotational component of earthquake acceleration (about the vertical axis) is obtained on the basis of the spectral density function of the horizontal component of earthquake acceleration. The rotational component of an earthquake can increase the response of the structure. The degree of the increase is highly dependent upon the dynamic characteristics of the system and the rotational component of the earthquake. To bring this increase under consideration, seismic codes represent a parameter referred to as accidental eccentricity, as a part of the design eccentricity. The purpose of the present study is to estimate the value of this increase and to make appropriate suggestions based on frequency domain analysis.

An investigation of torsionally irregular multi-story buildings under earthquake loading

It is well known that torsionally unbalanced buildings are more vulnerable to earthquake hazards than are the regular structural systems. In this paper, a parametric investigation is presented, in order to observe the amplification in the internal forces, when increased eccentricities are used instead of the ones corresponding to the 5% accidental eccentricity. A series of five, ten-story framed and walled structures, with rather high torsional irregularity coefficients, are selected and a numerical test procedure is applied. Numerical results show that the maximum amplification in the internal forces at the most critical beams and columns at the flexible sides of the structures is about 10%. It is concluded that, more serious measures in the codes are needed in the case of this rather dangerous type of irregularity.

INELASTIC SEISMIC TORSIONAL BEHAVIOUR OF ELEVATED TANKS

Torsional failure of elevated tanks has occurred in past earthquakes. The overall axisymmetric structural geometry and mass distribution of such structures may leave only a small accidental eccentricity between centre of stiffness and centre of mass. Such a small accidental eccentricity is not expected to cause a torsional failure. This paper studies the possibility of amplified torsional behaviour of elevated water tanks due to such small accidental eccentricity in inelastic range through detailed case studies; using two simple idealized systems with two coupled lateral–torsional degrees of freedom and, strength-deteriorating and elasto-plastic hysteresis models. The systems are capable of retaining the characteristics of two extreme categories of water tanks namely, (a) tanks on staging with less number of columns and panels and (b) tanks on staging with large number of columns and panels. The study shows that the presence of a small eccentricity may lead to localized unsymmetrical yielding in some of the reinforced concrete staging elements. This may lead to progressive strength deterioration through successive yieldings in same elements under cyclic loading during earthquakes. Such localized strength drop may increasingly develop large strength eccentricity resulting in large localized inelastic displacement and ductility demand, leading to failure. These observations are also verified for a real-life example elevated tank. The tanks supported on staging with fewer columns and panels are found to have greater torsional vulnerability. The tanks located near a fault are found to be vulnerable under near-fault pulses with a large duration compared to the lateral period of tank.

Seismic torsional vibration in elevated tanks

Some elevated water tanks have failed due to torsional vibrations in past earthquakes. The overall axisymmetric structural geometry and mass distribution of such structures may leave only a small accidental eccentricity between centre of stiffness and centre of mass. Such a small accidental eccentricity is not expected to cause a torsional failure. This paper studies the possibility of amplified torsional behaviour of elevated water tanks due to such small accidental eccentricity in the elastic as well as inelastic range; using two simple idealized systems with two coupled lateral-torsional degrees of freedom. The systems are capable of retaining the characteristics of two extreme categories of water tanks namely, a) tanks on staging with less number of columns and panels and b) tanks on staging with large number of columns and panels. The study shows that the presence of a small eccentricity may lead to large displacement of the staging edge in the elastic range, if the torsional-to-lateral time period ratio <TEX>$({\tau})$</TEX> of the elevated tanks lies within a critical range of 0.7< <TEX>${\tau}$</TEX> <1.25. Inelastic behaviour study reveals that such excessive displacement in some of the reinforced concrete staging elements may cause unsymmetric yielding. This may lead to progressive strength deterioration through successive yielding in same elements under cyclic loading during earthquakes. Such localized strength drop progressively develop large strength eccentricity resulting in large localized inelastic displacement and ductility demand, leading to failure. So, elevated water tanks should have <TEX>${\tau}$</TEX> outside the said critical range to avoid amplified torsional response. The tanks supported on staging with less number of columns and panels are found to have greater torsional vulnerability. Tanks located near faults seem to have torsional vulnerability for large <TEX>${\tau}$</TEX>.

Alternate tank staging configurations with reduced torsional vulnerability

The companion paper [Dutta SC, Jain SK, Murty CVR. Assessing the seismic torsional vulnerability of elevated tanks with RC frame-type staging. Soil Dynamics and Earthquake Engineering 2000;19(3):183–97] shows that many of the currently designed reinforced concrete elevated water tanks supported on frame-type stagings have the ratio of torsional and lateral natural periods, τ, in the critical range of 0.7–1.25. This may amplify the effect of small accidental eccentricity and cause large torsional vibration during translational ground shaking in earthquakes [Dutta SC. Torsional behaviour of elevated water tanks with reinforced concrete frame-type stagings during earthquakes. PhD thesis. Department of Civil Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India. 1995 and Dutta SC, Murty CVR, Jain SK. Torsional failure of elevated water tanks: the problems and some solutions. Paper No. 287. Eleventh World Conference on Earthquake Engineering. Acapulco, Mexico, 1996 June 23–28: Elsevier, Amsterdam, 1996]. It was seen that the period ratio ( τ) of the frame-type stagings cannot be changed appreciably by adjusting properties of the basic configuration, e.g. number of panels N p, number of columns N c, and the parameter K r related to the relative stiffness of columns and beams. Hence, alternate structural configurations are needed for such stagings so that τ lies outside the critical region. In this paper, approximate closed-form expressions are derived for lateral and torsional stiffnesses for a few alternate configurations. These expressions are used for studying the natural period ratio ( τ) for those alternate configurations. The alternate configurations are made by adding to the basic configuration (a) radial beams, (b) radial beams and a central column, (c) another concentric row of columns connected through radial and circumferential beams, and (d) diagonal braces. First three of these configurations have higher value of τ while the fourth configuration has a lower τ when compared with that of the basic configuration. The paper presents a limited parametric study to evaluate the effectiveness of each of these configurations in changing τ. A systematic stepwise approach is proposed for checking torsional vulnerability of the tanks and choosing a suitable configuration. Since the magnitude and direction of eccentricity for elevated water tanks is often not known, configuration-based solution may be preferable to the conventional increased strength design.

Multiple excitation effects on response of symmetric buildings

The behaviour of symmetric buildings subjected to spatially varying base excitations is studied. The spatial variation of ground motion is modelled by an empricial coherency loss function. A parametric study on the effects of coherency loss and phase shift between multiple input motions on base shear, torque and column shear forces is carried out. The adequacy of seismic code provisions on accidental eccentricity is discussed. It is found that the torsional response depends strongly on the ratio of torsional to lateral vibration frequencies W gq / w x Code provisions on accidental eccentricity are adequate for torsionally stiff structures in accounting for the spatially varying multiple excitations. For torsionally flexible structures, the accidental eccentricity provisions underestimate the multiple excitation effect on torque. It is also found that the effects of spatially varying multiple excitations on column shear forces are insignificant if the structure is flexible or its dimension is small. However, if the structure is stiff or its dimension is large such that its response is mainly quasistatic, considering only the uniform excitation-induced dynamic response greatly underestimates column shear forces.

Unreinforced loadbearing walls made of ceramic bricks and blocks

We present a method for the design of brick and ceramic blocks loadbearing walls. This methods is based on the verification of design stresses in critical points of the wall structure. The method considers the interaction and the connection among loadbearing and shear walls designed to carry imposed loads and lateral forces, taking into account the structural behaviour of each wall. Strength reduction factors due to slenderness and eccentricity, bending moments caused by floor loads, wall columns, stiffening walls, accidental eccentricities or the effect of lateral forces are analyzed. The basic mechanical properties of ceramic materials, compressive and shear strength are previous defined.

Evaluation of Seismic Torsional Provisions in Uniform Building Code

The main change in the torsional provisions of the 1991 edition of the \IUniform Building Code\N (UBC) from the 1979 UBC edition is the need to amplify the accidental eccentricity for torsionally flexible structural systems. This paper evaluates the consequences of the change on the strength design requirement and the ductility demand on the edge lateral force-resisting elements in torsionally unbalanced structural systems, which are designed based on the two editions of the UBC code. The major improvement of the 1991 UBC is its ability to limit the additional ductility demand on the stiff-edge element of a torsionally unbalanced system to an acceptable level, even when the system is torsionally flexible.

Influence of accidental eccentricity on inelastic seismic torsional effects in buildings

This paper aims, firstly to define, evaluate and compare a number of alternative interpretations of the application of code accidental torsional provisions. The extent to which the distribution of element design strength is affected by each approach adopted for the accidental component of the design eccentricity specified by seismic codes is examined. Secondly, the effectiveness of the protection given to the flexible-edge element in torsionally responding structures by a number of major code static torsional provisions is quantified and compared. Finally, a proposal is made with regard to a relevant interpretation of codified accidental eccentricity provisions, by which a minimum value is specified for laterally responding systems, with the remainder (if any) of the accidental eccentricity being incorporated into the allowance made in design for dynamic inelastic torsional effects. Evaluation of the results from inelastic dynamic analyses based on this proposal lead to the conclusion that all codes satisfactorily control the ductility demand for the flexible-edge element in torsionally unbalanced structures, and that the element deformation demand has a consistent relationship with variations of lateral period and static eccentricity, for all the codes considered. For the stiff-edge element in torsionally unbalanced systems, the previously noted deficiencies of codes which permit large reductions of design strength for this side of the structure have been confirmed by the presentation of some key results.

Accidental torsion in buildings due to base rotational excitation

AbstractThis investigation is concerned with accidental torsion in buildings resulting from rotational excitation (about a vertical axis) of the building foundations as a result of spatially non‐uniform ground motions. Because of this accidental torsion, the displacements and deformations in the structural elements of the building are likely to increase. This increase in response is evaluated using actual base rotational excitations derived from ground motions recorded at the base of 30 buildings during recent California earthquakes. Accidental torsion has the effect of increasing the building displacements, in the mean, by less than 5 per cent for systems that are torsionally stiff or have lateral vibration periods longer than half a second. On the other hand, short period (less than half a second) and torsionally flexible systems may experience significant increases in response due to accidental torsion. Since the dependence between this increase in response and the system parameters is complex, two simplified methods are developed for conveniently estimating this effect of accidental torsion. They are the ‘accidental eccentricity’ and the ‘response spectrum’ method. The computed accidental eccentricities are much smaller than the typical code values, 0.05bb or 0.1b, except for buildings with very long plan dimensions (b ≥ 50 m). Alternatively, by using the response spectrum method the increase in response can be estimated by computing the peak response to each base motion independently and combining the peak values using the SRSS rule.

Using accidental eccentricity in code‐specified static and dynamic analyses of buildings

AbstractThe differences between the increase in building response due to accidental eccentricity predicted by code‐specified static and dynamic analyses are studied for symmetric and unsymmetric single and multistorey buildings. The increase in response computed from static analysis of the building is obtained by applying the equivalent static forces at distance ea, equal to the storey accidental eccentricity, from the centre of mass at each floor. Alternatively, this increase in response is computed by dynamic analysis of the building with the centre of mass of each floor shifted through a distance ea from its nominal position. A parametric study is performed on single‐storey systems in order to evaluate the differences in response predicted by both analysis procedures. It is shown that these results are essentially the same as the ones obtained for a special class of multistorey systems. Upper and lower bounds for the differences in response computed from static and dynamic analyses are obtained for general multistorey systems. These differences in response depend primarily on the ratio of the fundamental torsional and lateral frequencies of the building. They are larger for small values of the frequency ratio and decrease to zero as the frequency ratio becomes large. Further, these discrepancies are in many cases of the same order as the code‐intended increase in response due to accidental eccentricity. This implies that the code‐specified static and dynamic analyses to account for accidental torsion should be modified to be mutually consistent.

Accidental eccentricity for strong ground motion

The Structural Design of Tall BuildingsVolume 3, Issue 2 p. 131-137 Short Communication Accidental eccentricity for strong ground motion Gary C. Hart, Gary C. Hart University of California, Los Angeles. Hart Consultant Group, Colorado Place, 2450 Broadway Avenue, Suite 560, Santa Monica, CA 90404, USASearch for more papers by this author Gary C. Hart, Gary C. Hart University of California, Los Angeles. Hart Consultant Group, Colorado Place, 2450 Broadway Avenue, Suite 560, Santa Monica, CA 90404, USASearch for more papers by this author First published: June 1994 https://doi.org/10.1002/tal.4320030205AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume3, Issue2June 1994Pages 131-137 RelatedInformation

Torsional Response of Unsymmetric Buildings to Incoherent Ground Motions

The behavior of unsymmetric buildings excited by incoherent seismic ground motions is studied, and the assessments and information reported make it possible to gain valuable insight into the resulting dynamic response. The effects of the ground motion incoherence and of the structural eccentricity are first considered independently of one another, and attempts are made to identify their relative importance. The torsional effects induced by the incoherence actions are interpreted in terms of normalized accidental eccentricities; and comparisons are made of these eccentricities with the value of 0.05 specified by design codes. Such comparisons form a frame of reference for the assessment of the importance of the torsional effects resulting from the ground motion incoherence. The coupled effects of incoherence and eccentricity are then considered, and it is reported that they can be approximately represented by proper combinations of the corresponding independent effects, under conditions that are of practic...

Re‐examination of Ylinen and Other Column Equations

In 1991, Ylinen's column equation was adopted for the design of wood columns in the United States. Ylinen originally derived this equation as a plastic buckling criterion, using a nonlinear compressive stress‐strain law as the starting point. The stress‐strain law contained a parameter c⩽1, which controlled the degree of nonlinearity. Linearity was achieved at c=1. This same parameter appeared in the final column equation. At c=1, the column equation reduced to elementary theory, i.e., to a perfectly plastic‐perfectly elastic failure criterion. Column design equations are viewed in this paper as interaction equations between two modes of failure: crushing and buckling. Ylinen's column equation is found to result from the addition of a cross‐product term to the linear interaction equation. This enables us to view c as measuring the degree of departure from the assumptions of elementary theory, including such phenomena as inhomogeneity of material, imperfections of shape, and accidental eccentricity of load...

Ultimate Strength of RC Wall Panels with Openings

Test results of 12 reinforced concrete (RC) wall panels with openings are presented. The panels have been subjected to in‐plane vertical loads applied at an eccentricity to represent possible accidental eccentricity that occurs in practice due to constructional imperfections. The 12 specimens consist of two identical groups of six panels each. One group of panels is tested in one‐way in‐plane action (i.e., supported at top and bottom edges against lateral displacement). The second group of panels is tested in two‐way in‐plane action (i.e., supported on all the four edges against lateral displacement). Openings in the panels represent typical door and window openings. Cracking loads, ultimate loads, crack patterns, and lateral deflections of the panels are studied. Empirical methods have been developed for the prediction of ultimate load. Also, lateral deflections, cracking loads, and ultimate loads of identical loads tested under one‐way and two‐way action are compared.

Ultimate Strength of R.C. Wall Panels in Two‐Way In‐Plane Action

Test results of 24 reinforced concrete wall panels in two-way action (i.e., supported on all the four sides) and subjected to in-plane vertical load are presented. The load is applied at an eccentricity to represent possible accidental eccentricity that occurs in practice due to constructional imperfections. Influences of aspect ratio, thinness ratio, slendemess ratio, vertical steel, and horizontal steel on the ultimate load are studied. Two equations are proposed to predict the ultimate load carried by the panels. The first equation is empirical and is arrived at from trial and error fitting with test data. The second equation is semi-empirical and is developed from a modification of the buckling strength of thin rectangular plates. Both the equations are formulated so as to give a safe prediction of a large portion of ultimate strength test results. Also, ultimate load cracking load and lateral deflections of identical panels in two-way action (all four sides supported) and oneway action (top and bottom sides only supported) are compared.

Accidental torsion in yielding symmetric structures

Building codes recognize a variety of sources of accidental eccentricity in buildings subjected to seismic excitation. This study examines the adequacy of code provisions for accidental eccentricity to account for torsion induced in nominally symmetric structures due to variation in the strength of elasto-plastic lateral load resisting elements or by unbalanced degradation in stiffness. The behaviour of an idealized single-storey structure subjected to different earthquake ground motions is examined, as well as the influence of torsional to translational frequency ratio Ω 0 and lateral period of vibration T o .

Rotational ground motion and seismic codes

The primary purpose of this paper is to discuss the separation of travelling wave effects from the mass center to resistance center eccentricity effects, and to propose means by which the torsional spectrum (or a torsional seismic factor) could be incorporated in the seismic provisions of the National Building Code of Canada. The paper begins the treatment of the subject matter by presenting a detailed review of previous work on the effects of torsional ground motion, emphasizing the methods which have been proposed to develop torsional response spectra. The travelling wave assumption is critically reviewed and the effective phase velocities applicable for design purposes are discussed. This is followed by a simple analysis showing how the torsional spectra can be derived directly from the corresponding translational response spectra. Formulae separating the torsional input effects from the accidental eccentricity effects are presented and discussed. Finally, it is shown how the torsional spectrum can be incorporated within the framework of the response spectrum procedure of the 1985 edition of the National Building Code of Canada. Key words: seismic, earthquake, structure, dynamic, rotation, code, torsion, foundation, eccentricity, response spectrum, acceleration, velocity, design.

Cladding influence on dynamics response of tall buildings

AbstractPrecast concrete panels form attractive facades for steel frame buildings and are generally regarded as non‐structural by structural engineers. However, panels have been found to add lateral stiffness until their capacity or that of their connections is exceeded. Consequently, the computed dynamic response based on a model of the structural framing alone may be quite different from that experienced by the actual structure.As a case study, the influence of precast concrete panels on lateral and torsional stiffness of a 25‐storey building was investigated. The effect of cladding on dynamic properties and linear seismic response was explored by varying panel stiffness. Cladding stiffness was added to the bare frame model until analytical frequency values matched vibration test results. Then, using the cladding stiffness values obtained, an accidental eccentricity between centres of mass and rigidity at each floor level was imposed and linear seismic response computed. Torsional response effects were increased substantially. Finally, a modified cladding panel connection was developed based on previously‐reported studies for panelized construction. The influence of the proposed connection on overall structural response was determined for different ground motion inputs.