Seismic performance of R/C frames with overstrength discontinuities in elevation

The paper presents the results of a research study concerning the seismic response and design of r/c frames with overstrength discontinuities in elevation. The discontinuities are obtained assigning overstrengths either to the beams or to the columns of a “regular frame” (assumed as reference). Two “regular frames” are designed: one according to the Eurocode 8 (EC8) medium ductility class (DCM) rules and the other one according to the EC8 high ductility class (DCH) rules. For all frames the criteria of vertical strength irregularity of many international seismic codes are applied. Non linear static and dynamic analyses are performed; mechanical non linearity is concentrated at the element ends. These analyses are carried out according to EC8 provisions: for non linear static analysis the N2 method is applied; in the case of non linear time-history analyses, seven real earthquakes, selected in order to fit on average the elastic design spectrum, are used as input. The seismic response of frames characterised by the assigned overstrength is not very different with respect to the “regular frame” one; furthermore all the frames satisfy the Ultimate Limit State, verified by the application of non linear static and dynamic analyses. This demonstrates that the sensitivity of frames, designed according to EC8 medium and high ductility classes, to overstrength vertical variations is low. Consequently, international code provisions on vertical strength regularity should be reviewed.     

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. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comparison between non-linear dynamic and static seismic analysis of structures according to European and US provisions

Several procedures for non-linear static and dynamic analysis of structures have been developed in recent years. This paper discusses those procedures that have been implemented into the latest European and US seismic provisions: non-linear dynamic time-history analysis; N2 non-linear static method (Eurocode 8); non-linear static procedure NSP (FEMA 356) and improved capacity spectrum method CSM (FEMA 440). The presented methods differ in respect to accuracy, simplicity, transparency and clarity of theoretical background. Non-linear static procedures were developed with the aim of overcoming the insufficiency and limitations of linear methods, whilst at the same time maintaining a relatively simple application. All procedures incorporate performance-based concepts paying more attention to damage control. Application of the presented procedures is illustrated by means of an example of an eight-storey reinforced concrete frame building. The results obtained by non-linear dynamic time-history analysis and non-linear static procedures are compared. It is concluded that these non-linear static procedures are sustainable for application. Additionally, this paper discusses a recommendation in the Eurocode 8/1 that the capacity curve should be determined by pushover analysis for values of the control displacement ranging between zero and 150% of the target displacement. Maximum top displacement of the analyzed structure obtained by using dynamic method with real time-history records corresponds to 145% of the target displacement obtained using the non-linear static N2 procedure.     

Static versus modal analysis: influence on inelastic response of multi-storey asymmetric buildings

The paper investigates the influence of design procedures on the seismic response of multi-storey asymmetric buildings. To this end, some structures are designed according to methods based on either static or modal analysis, with or without design eccentricities. The seismic response of these systems is determined by means of inelastic dynamic analyses and the design is thoroughly examined in order to explain the results of the dynamic analyses. Attention is basically focused on the ability of design methods to prevent asymmetric buildings from experiencing ductility demands much larger than those of the corresponding torsionally balanced systems. Numerical analyses underline that while design procedures based on either static or modal analysis are suitable for the design of torsionally rigid structures only those based on modal analysis lead to the satisfactory performance of torsionally flexible buildings. Furthermore, the study highlights the qualities of a design method proposed by the Authors. Its application does not require any explicit calculation of design eccentricities and leads to proper seismic response of both torsionally rigid and flexible asymmetric buildings.     

Seismic code analysis of multi-storey asymmetric buildings

Static torsional provisions in most seismic codes require that the lateral force at each floor level be applied at some distance from the reference centre at that floor. However, codes do not specify how to determine the locations of these centres. As a result, several different definitions of the reference centres are being used to implement the code analysis. This investigation examined how the results using various reference centres differ and which of these centres would lead to results that are in agreement with those of dynamic analysis. For this purpose three different buildings ranging form torsionally stiff to torsionally flexible were analysed. It was shown that for the class of buildings studied in this investigation that although the locations of the reference centres were quite different, the results were very similar and nearly independent of the reference centre. Comparison of results calculated from static code equivalent lateral force procedures and results from dynamic response spectrum analyses showed that the static code procedures led to design forces very close (flexible wall) or slightly conservative (stiff wall) when compared to the dynamic analysis for the torsionally stiff building. However, the static code procedures significantly underestimated the design forces of the stiff walls and significantly overestimated the design forces of the flexible walls for the torsionally flexible buildings. © 1998 John Wiley & Sons, Ltd.     

An experimental and numerical investigation into the seismic performance of a multi-storey concentrically braced plan irregular structure

In this investigation, the seismic torsional response of a multi-storey concentrically braced frame (CBF) plan irregular structure is evaluated numerically and experimentally through a series of hybrid tests. CBF structures have become popular in seismic design because they are one of the most efficient types of steel structures to resist earthquake loading. However, their response under plan irregular conditions has received little focus mostly in part due to their complex behaviour under seismic loading conditions. The majority of research on the seismic response of plan irregular structures is based purely on numerical investigations. This paper provides much needed experimental investigation of the seismic response of a CBF plan irregular structure with the aim of characterising the response of this class of structure. The effectiveness of the Eurocode 8 torsional effects provision as a method of designing for low levels of mass eccentricity is evaluated. Results indicate that some of the observations made by purely numerical models are valid in that; torsionally stiff structures perform well and the stiff side of the structure is subjected to a greater ductility demand compared to the flexible side of the structure. The Eurocode 8 torsional effects provision is shown to be adequate in terms of ductility and interstorey drift however the structure performs poorly in terms of floor rotation. Importantly, stiffness eccentricity occurs when the provision is applied to the structure when no mass eccentricity exists and results in a significant increase in floor rotations.     

Importance of seismic design accidental torsion requirements for building collapse capacity

Seismic ground motions induce torsional responses in buildings that can be difficult to predict. To compensate for this, most modern building codes require the consideration of accidental torsion when computing design earthquake forces. This study evaluates the influence of ASCE/SEI 7 accidental torsion seismic design requirements on the performance of 230 archetypical buildings that are designed with and without accidental torsion design provisions, taking building collapse capacity as the performance metric. The test case archetypes include a broad range of heights, gravity load levels, and plan configurations. Results show that the ASCE/SEI 7 accidental torsion provisions lead to significant changes in collapse capacity for buildings that are very torsionally flexible or asymmetric. However, only inconsequential changes in collapse capacity are observed in the buildings that are both torsionally stiff and regular in plan. Therefore, the study concludes that accidental torsion provisions are not necessary for seismic design of buildings without excessive torsional flexibility or asymmetry. Copyright © 2013 John Wiley & Sons, Ltd.     

Inelastic seismic response of torsionally unbalanced systems designed using elastic dynamic analysis

This paper evaluates the inelastic seismic response of torsionally unbalanced structural systems with strength distributed using elastic response spectrum analysis. The structural model is a single mass torsionally unbalanced system with lateral load resisting elements spanning in two principal directions. The element strength is distributed based on elastic response spectrum analysis and three different approaches to incorporate accidental torsion are considered: (a) without incorporating accidental torsion; (b) by applying static floor torques; (c) by shifting the location of the centre of mass. The seismic input is bidirectionally applied at the base of the model. It is shown that the inelastic responses depend strongly on the torsional stiffness of the system. For a torsionally stiff system, the torsional response leads to a decrease in the stiff edge displacement; however, for a torsionally flexible system, it tends to increase the stiff edge displacement. Using response spectrum analysis without including accidental torsion may lead to excessive additional ductility demand on the stiff edge element. With accidental torsion effect incorporated, the response spectrum analysis will give a strength distribution such that there will be no excessive additional ductility demands on the lateral load resisting elements.     

Accidental design eccentricity: Is it important for the inelastic response of buildings to strong earthquakes?

To deal with earthquake-induced torsion in buildings due to some uncertain factors, difficult to account for directly in design, modern codes have introduced the so-called accidental design eccentricity (ADE). This provision has been based primarily on elastic investigations with special classes of multi-story buildings or with simplified, one-story inelastic models. In the present paper, the effectiveness of this provision is investigated using inelastic models, both of the typical one-story, 3-DOF type, and the more sophisticated MDOF, frame idealizations of the plastic hinge type. One, three and five story, realistic, frame buildings with different natural eccentricities were designed for different ADEs, including those specified by the EC8 and IBC codes. The evaluation is made using mean peak ductility factors of the edge frames as measures of their inelastic response, obtained from dynamic analyses for ten pairs of semi-artificial earthquake motions. The simplified models indicate that the accidental design eccentricity is very effective in reducing ductility demands, especially for very stiff systems. However, this is not confirmed by the more accurate and detailed plastic hinge building models, which show that designs accounting for accidental eccentricity do not exhibit any substantial reduction or better distribution of ductility demands, compared to designs in which accidental eccentricity has been entirely ignored. These findings suggest that the ADE provisions in codes, especially the more complicated ones as in the IBC, should be re-examined, by weighting their importance against the additional computational work they impose on designers. In the cases examined herein this importance can be characterized as marginal. Obviously additional studies are required, to include more building types and earthquake motions, in order to arrive at firm conclusions and recommendations for code modifications.     

Evaluation of seismic response of bridges under asynchronous excitation and comparisons with Eurocode 8-2 provisions

The paper aims to evaluate the way Eurocode 8 treats the consideration of asynchronous earthquake ground motion during the seismic design of bridges, and to discuss alternative solutions for cases wherein existing provisions do not lead to satisfactory results. The evaluation of EC8-2 new provisions and simplified methods is performed through comparison with a more refined approach whereas an effort is made to quantitatively assess the relative importance of various design and analysis assumptions that have to be made when spatial variability of ground motion is taken into consideration, based on the study of the dynamic response of 27 different bridges. It is concluded that, despite the complexity of the problem, there are specific cases where EC8 provisions can be safely and easily applied in practice, while in other cases ignoring the effect of asynchronous excitation or performing simplified calculations can significantly underestimate the actual seismic demand.     

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.     

Assessing the seismic response of existing RC buildings using the extended N2 method

Extensive studies have confirmed the good performance of the N2 method, recommended by Eurocode8, when performing pushover analyses in regular structures. However, this procedure shows lack of accuracy in predicting the torsional motion of plan-asymmetric buildings. In order to overcome this problem, Peter Fajfar and his team have proposed an extension of the method based on a combination of a pushover analysis and of an elastic response spectrum analysis. Since definitive answers about this topic have not yet been reached, this paper intends to proceed the study applying the extended N2 method to real existing RC buildings. Three real plan-asymmetric buildings with three, five and eight storeys were assessed. The results obtained with the extended N2 method were compared with the ones evaluated by means of the original N2 and with the nonlinear dynamic analysis through the use of semi-artificial ground motions. The analyses were performed for different seismic intensities in order to evaluate the torsional response of the building through different stages of structural inelasticity. The results obtained show that the extended N2 method generally reproduces in a very good fashion the real torsional behavior of the analyzed buildings. The conclusions herein outlined, added to the ones already published by the aforementioned authors, seem to confirm that the extended N2 method can be introduced in the next version of Eurocode8 as a nonlinear static procedure capable of accurately predicting the torsional response of plan-asymmetric buildings.     

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

The 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 e_a, 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 e_a 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.     

AN OPTIMIZED PROCEDURE FOR SEISMIC DESIGN OF TORSIONALLY UNBALANCED STRUCTURES

This paper develops an optimized procedure for the design of torsionally unbalanced structures subjected to earthquake loading, considering both the serviceability and the ultimate limit states. An optimal design eccentricity expression, in the form of design charts, and an optimal overstrength factor equation, are proposed. Results show that the recommended design procedure can result in nearly equal performance of both the rigid edge and the flexible edge elements. For a wide combination of primary system parameters, the responses of both edge elements are consistently lower than, or in the neighbourhood of, the response of the corresponding torsionally balanced reference model. The proposed procedure retains simplicity and can be easily implemented (with certain limitations) in design practice. It also has the added advantages of requiring the structure to be analysed only once for each limit state in each principal direction (as opposed to twice, in existing code torsional provisions), and results in a significantly lower overstrength factor, compared with the overstrength factors corresponding to the torsional provisions of seismic codes in the United States and Canada. The proposed procedure is also applicable to torsionally unbalanced structures with and without transverse resisting elements. © 1997 John Wiley & Sons, Ltd.     

Torsionally coupled dynamic performance analysis of asymmetric offshore platforms subjected to wave and earthquake loadings

The dynamic equations of motion of asymmetric offshore platforms under three different environmental conditions:seismic action,wave action and their combination are established in this paper. In establishing these motion equations,three typical eccentricity types including mass eccentricity,rigidity eccentricity and their combination were considered,as are eccentricities that occur un-idirectionally and bi-directionally. The effects of the eccentricity type,the dynamic characteristics and the environmental conditions on the torsional coupling response of platforms are investigated and compared. An effort has also been made to analyze the inffluence of accidental eccentricity on asymmetric platforms with different eccentricity in two horizontally orthogonal directions. The results are given in terms of non-dimensional parameters,accounting for the uncoupled torsional to lateral frequency ratio. Numerical results reveal that the eccentricity type has a great inffluence on the torsionally coupled response under different environmental conditions. Therefore,it is necessary to consider the combination of earthquake and wave action in the seismic response analysis of some offshore platforms.     

Evaluation of dynamic eccentricities obtained using a probabilistic approach,response spectrum methods and modern building codes

In this paper a probabilistic approach has been adopted to study both the effects of uncertainty in earthquake frequency content and the correlation between earthquake frequency content and ground motion intensity on the response of a single-storey torsionally coupled elastic structure. The earthquake ground motion has been assumed to be a Gaussian, zero mean, stationary random process which is fully characterized by a power spectrum. The ground acceleration power spectrum is idealized as a probabilistic normalized power spectrum computed from actual earthquake records. The advantage of such an idealization is that it enables the effect of the natural frequency as a controlling structural parameter in torsional coupling to be assessed. Comparisons of the dynamic amplifications of eccentricity with those obtained from modern codes of practice and conventional response spectrum analyses have been made. The results of this study have shown that the variation in the frequency content has a significant effect on the response of low frequency structures, while the correlation between the frequency content and the intensity of seismic ground motion is insignificant for the wide range of structures considered. The structure natural frequency has been shown to be an important controlling parameter in the torsionally coupled response of structures subject to seismic loading. The frequency dependence of the dynamic amplification of eccentricity was found not to be reflected in the response spectrum analysis and the torsional provisions of modern building codes.     

Re-evaluation of seismic torsional provisions

Traditionally, seismic torsional provisions have been evaluated based on the assumption that the strength of the lateral load resisting elements can be adjusted without changing their stiffness. There is an important class of elements that a change of their lateral strength implies a corresponding change of stiffness, as exemplified by reinforced concrete flexural walls. This would imply that when torsional provisions are applied to adjust the strengths of these elements, the stiffness distribution, and also the eccentricity of the system, will change. This paper re-evaluates the consequences of applying the torsional provisions of the Uniform Building Code (UBC, 1997) and also the Eurocode (Eurocode 8, 1994) to single mass eccentric systems supported by elements having such characteristics. In conjunction with the results based on the traditional assumption, the effectiveness of the two provisions to mitigate torsional effects is discussed from a broader perspective. Copyright © 1999 John Wiley & Sons, Ltd.     

Accidental torsion in buildings due to base rotational excitation

This 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.     

A modified static procedure for the design of torsionally unbalanced multistorey frame buildings

Seismic building codes include design provisions to account for the torsional effects arising in torsionally unbalanced (asymmetric) buildings. These provisions are based on two alternative analytical procedures for determining the design load for the individual resisting structural elements. A previous study has shown that the linear elastic modal analysis procedure may not lead to conservative designs, even for multistorey buildings with regular asymmetry, when such structures are excited well into the inelastic range of response. The equivalent static force procedure as recommended by codes may also be deficient in accounting for additional ductility demand in the critical stiff-edge elements. This paper addresses the non-conservatism of existing static torsional provisions and examines aspects of element strength distribution and its influence on inelastic torsional effects. A recommendation is made for improving the effectiveness of the code-type static force procedure for torsionally unbalanced multistorey frame buildings with regular asymmetry, leading to a design approach which estimates conservatively the peak ductility demand of edge elements on both sides of the building. The modified approach also retains the simplicity of existing code provisions and results in acceptable levels of additional lateral design strength. It has recently been adopted by the new Australian earthquake code, which is due to be implemented early in 1993.     

Evaluation of structural walls designed according to Eurocode 8 and SIA 160

For earthquake action the new design provisions of Eurocode 8 are in the process of replacing the European national earthquake codes. The paper treats the design and behaviour of multi-storey structural walls in view of the new provisions. For structural walls the provisions of the Eurocode 8 are compared with those of a national code which it is going to replace. As the national code the current Swiss earthquake standard SIA 160 is chosen. Basic design rules of both codes are introduced and compared by means of examples comprising buildings which are regular in plan and elevation and which use structural walls for lateral resistance. The height of the buildings is varied from a from four to eight storeys. In the example, both the SIA and the Eurocode design provisions are based on the static equivalent force method, and a triangular distribution of the lateral force. However, most other design provisions differ between the two codes. The structures designed are modelled numerically and subjected to non-linear time-history analysis. At first, both the SIA and Eurocode designed structures are subjected to ground motions compatible to the design spectra in the respective codes. Then all structures are subjected to a recorded ground motion. The results are discussed in view of assumptions made at the design phase. Conclusions and recommendations are provided. © 1998 John Wiley & Sons, Ltd.