Seismic code provisions for asymmetric structures: a re-evaluation

Results of a parametric study on earthquake time history response of asymmetric single storey structures with one axis of symmetry modelled as two degree-of-freedom systems are compared with static seismic code provisions. A large number of such systems with a range of mass centre to rigidity centre eccentricities, a range of uncoupled lateral natural frequencies and a number of torsional to lateral frequency ratios Ω₀ were subjected to several earthquake acceleration records. Five percent damping was assumed in the two coupled modes. Maximum displacements at several locations along the roof deck were computed, normalized with respect to the symmetric case, averaged, and compared with code oriented static methods. The study shows that the static approach does not give reliable estimates for the response of frames in asymmetric buildings, even when the amplification factors provided by earthquake codes are incorporated into the formulation. In particular, code provisions often underestimate the response of frames located on the side of the rigidity centre away from the mass centre for small to moderate eccentricities when Ω₀² = 0.5, 1.0; whereas for systems with higher torsional rigidities (Ω₀² 2.0), the static approach appears to yield reasonable results. For members located on the opposite side of the roof, code provisions, including recent revisions, appear to overestimate the response with decreasing frequency ratio.     

Druckstrebentragfähigkeit torsionsbeanspruchter Stahlbetonbalken mit üblicher Betondeckung

Concrete struts bearing capacity of reinforced concrete beams in torsion with practical concrete cover The analysis of an experiment database according to DIN 1045‐1 provisions shows an overestimation of the strength of the concrete strut in torsion with increasing concrete cover. In addition significant differences can be detected when comparing international design codes in relation to the concrete covers contribution to the torsional resistance of a reinforced concrete beam. In this paper experimental as well as related theoretical investigations of the concrete struts bearing capacity of reinforced concrete beams in torsion with nowadays practical concrete cover are presented. With respect to the observed influences on the failure load an approach for a safe definition of the shear flow zone thickness on the basis of DIN 1045‐1 provisions but independent of the concrete cover is derived.     

Seismic response control of asymmetric buildings using tuned mass dampers

The aim of the present study is to investigate the efficiency of the torsional tuned mass dampers (T‐TMDs) in response control of asymmetric buildings under bidirectional earthquake ground excitations. The efficiency of the T‐TMDs is compared with bidirectional tuned mass dampers (BTMDs). The T‐TMDs are oriented to the rotation of the structures about vertical axis with a single torsional mass attached to spring–dashpot elements, whereas the BTMD connects a single mass to two orthogonal sets of spring–dashpot elements oriented to principal axes of the building. The buildings are idealized three‐dimensional models with two translational and one torsional degrees of freedom for each floor. Three different configurations (cruciform‐shaped, L‐shaped, and T‐shaped) of multistory buildings are considered. The 5‐, 15‐, and 20‐story buildings with and without the tuned mass damper schemes are subjected to bidirectional earthquake ground excitation. In order to evaluate the effectiveness of the T‐TMDs and BTMD, the rotation, displacement, acceleration, and base shear force responses are computed. Parametric studies are conducted for all the configurations installed with the T‐TMDs and BTMD by varying their mass ratio, damping ratio, and ground motions. It is concluded that the T‐TMDs are more effective in mitigating the torsional response of asymmetric buildings as compared with the BTMD.     

Zur Aussteifung von Biegeträgern durch Drehbettung und Schubsteifigkeit

Beams in bending restraint by rotational spring stiffness and shear stiffness of adjacent members. An exact but more extensive design check for lateral torsional buckling can be avoided if values for minimum restraints are fulfilled. Well known are values for minimum torsional restraints in the actual codes DIN 18800‐2 and DIN EN 1993‐1‐1. The values of DIN EN 1993‐1‐1 table BB‐1 are originally given in DIN 18800‐2 table 6 based on the lateral torsional buckling curve of DIN 18800‐2. They are newly calculated on the basis of the curves given in DIN EN 1993‐1‐1 chapte 6.3.2.3 and more load cases are taken into account. Different details are given in codes and literature concerning lateral restraints given by trapezoidally sheeting. Additional investigations are carried out with regard to the minimum shear stiffness (lateral restraint) S_min which limit the applicability of values S corresponding to eq. (5a) which is recommended in literature.     

Torsional coupling effects in the earthquake response of asymmetric buildings

This paper presents a detailed parametric study of the coupled lateral and torsional response of a partially symmetric single storey building model subjected to both steady state and earthquake base loadings. It is shown that the qualitative effects of the controlling parameters on the maximum translational and torsional responses of the coupled system are not affected by the nature of the loading. The maximum lateral edge displacement of the building arising from the combined response effects is investigated. The related lateral shear forces in vertical resisting elements located on the periphery of the structure may be significantly increased in comparison with the corresponding values for a symmetric building. It is concluded that for particular ranges of the key parameters defining the structural system, typical of the properties of many actual buildings, torsional coupling induces a significant amplification of earthquake forces which should be accounted for in their design.     

Effect of two horizontal components of earthquake on nonlinear response of torsionally coupled base isolated structures

Torsion in base‐isolated structures using bilinear rubber isolators effected by two horizontal components of earthquake simultaneously is investigated under various principal parameters including number of storeys; ratio of uncoupled torsional frequency to lateral frequency in the superstructure; ratio of uncoupled torsional frequency to lateral frequency in the isolation system; mass eccentricity in the superstructure and isolation system; and, in addition, the direction of eccentricity. Structure was supposed a shear structure and it was modeled by using concentrated mass and springs. Isolators are modelled by using nonlinear springs considering the interaction of isolator behaviour in two directions. The effect of variation in considered parameters on the behaviour of the superstructure and isolation system is investigated under seven ground motions. It is demonstrated that the parameters affect asymmetric structure behaviour with respect to symmetric one. The results of our investigations help us to understand the asymmetric structure behaviour under bidirectional earthquake by comparing it with a symmetric one. These results demonstrate that asymmetry in the superstructure or isolation system could have a significant effect on the torsional behaviour of isolated structures. In addition, the results show that the use of rigid superstructures and calculation of dynamic torsion by multiplying eccentricity by the dynamic base shear are unacceptable assumptions. Torsional effect on the isolated structural behaviour is amplified by considering two horizontal components of earthquake and comparing them with just one horizontal component. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of lateral‐torsional coupling in earthquake response of asymmetric multistory buildings

This paper presents a practical method for evaluating lateral‐torsional coupling in the elastic earthquake response of asymmetric multistory buildings. A transformation technique is first developed to shift the floor centers of mass of an asymmetric building to new reference positions where the sum of the squares of all floor rotations of the building due to lateral inertia loads is a minimum. By setting the locus of the floor centers of mass of the building at the new reference positions, a representative eccentricity and an effectively uncoupled system for the building can be established on the basis which an equivalent eccentric single mass system can be developed. The additional lateral translations caused by seismic torsional effects in the building can be analytically determined and expressed in terms of the representative building eccentricity and the uncoupled periods evaluated using the effectively uncoupled system. The effectiveness and practicality of the proposed method are illustrated with two 30‐story practical buildings. Copyright © 2013 John Wiley & Sons, Ltd.     

中美规范关于地震波的选择与框架-核心筒结构弹塑性时程分析

简述了中美两国抗震设计规范中有关地震波选择的相关条文,列举了工程实践中常用的选波方法,并对选出的地震波反应谱特性进行了比较。中美两国规范中建议的选波方法均要求选择能与规范的设计反应谱相一致的地震波,不同之处为中国规范是将地震波峰值加速度调幅至规范规定值,而美国规范是将某一周期范围内地震波反应谱调幅至与设计反应谱接近,调幅后的地震波峰值加速度无明显规律。按照中美两国抗震设计规范分别设计了两栋相似框架 核心筒结构,建立了两结构的弹塑性分析模型。根据中国规范建议方法选择出7组地震波,进行弹塑性时程分析。分析结果表明：在相应于中国8度罕遇地震的多组地震波作用下,中美两国规范设计方案在地震作用初期地震响应基本一致,在后期由于结构配筋形式与配筋数量等差异,结构损伤程度不同;按中国规范设计方案的最大层间位移角为按美国规范设计方案的1.03~1.17倍,连梁最大塑性变形为按美国规范设计方案的0.67~0.98倍,剪力墙应变沿层高的分布接近,美国规范设计结构纵筋的屈服应变是中国规范设计方案的1.2倍,按中国规范设计方案的剪力墙损伤程度重于按美国规范设计的剪力墙。     

抗震设计中的平扭耦联问题

偏心率、周期比(结构扭转为主的第1自振周期与平动为主的第1自振周期之比)和位移比(楼层最大水平位移(层间位移)与该楼层两端水平位移(层间位移)平均值之比)是平扭耦联问题中的三个关键参数。中美两国规范都把位移比大于1.2定义成平面不规则中的扭转不规则。但是,两国规范控制扭转效应的侧重点有所不同。美国规范不控制周期比,它对每层的动扭矩作了放大,以考虑扭转不规则对构件内力的影响,强调结构的地震反应和构件的内力;我国规范提出周期比不大于0.85~0.90的限值要求,强调结构的自振特性。本文详细地叙述了结构工程师关心的刚心和质心的定义和计算机求解方法,综合结构的自振特性和地震反应,以周期比、第1振型中的扭平分量比和位移比为控制指标,提出了结构动力规则性概念。明确指出结构的扭转不仅仅是几何规则性问题,本质上它更是一个动力规则性问题。结构可以是几何不规则的,但结构工程师要努力做到结构的动力特性是规则的。文中还列出了实现结构动力规则性的9     

Seismic response of multistory reinforced concrete frame with vertical mass and stiffness irregularities

Irregular buildings behave differently as compared with regular buildings. Seismic design codes have quantified the irregularities in terms of magnitude only ignoring the effect of irregularity location. In the present study, a single parameter to quantify mass, stiffness and strength irregularity in terms of both magnitude and location is proposed on the basis of the dynamic characteristics of the building. Furthermore, building models with different types of irregularity with variation in magnitude and location of irregularity are analyzed by subjecting them to an ensemble of 27 ground motions to create a seismic response databank. In the analysis, the torsional effects generated due to irregularities in the building systems (as per EC 8:2004 provisions) are included. On the basis of regression analysis conducted on this seismic response databank, equations to estimate seismic response parameters such as fundamental period, maximum roof displacement and maximum inter‐story drift ratio etc. are proposed for the irregular buildings in terms of the proposed irregularity index. Finally, applicability of the proposed equations is discussed in brief, and these equations are validated for 2D and 3D building models. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic performance of torsionally stiff and flexible multi‐story concentrically steel braced buildings

It is expected that application of torsion provisions in typical seismic codes shows different levels of efficiency for torsionally stiff and flexible buildings. This paper studies difference in performances of a range of code designed torsionally stiff and flexible five‐story building models. The models are classified in eight configurations to cover common range of buildings designed with the seismic provisions of Iranian Standard 2800 as a typical seismic design code. Seismic nonlinear dynamic time history behavior of eight building models subjected to seven horizontal bi‐directional design spectra compatible ground motions is investigated. These models cover a wide band of very torsionally stiff to very flexible buildings. Response parameters are element ductility demand and building story drift ratio. These criteria are appropriate indices for structural and nonstructural damages, respectively. The results indicate that the present linear static procedure of building codes such as the Iranian Standard 2800 is not generally adequate for structures with very low torsional stiffness. Copyright © 2012 John Wiley & Sons, Ltd.     

Elastic lateral buckling of cantilever Litesteel Beams under transverse loading

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using its patented dual electric resistance welding and automated continuous roll-forming technologies. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. Its flexural strength for intermediate spans is governed by lateral distortional buckling characterised by simultaneous lateral deflection, twist and web distortion. Recent research on LSBs has mainly focussed on their lateral distortional buckling behaviour under uniform moment conditions. However, in practice, LSB flexural members are subjected to non-uniform moment distributions and load height effects as they are often under transverse loads applied above or below their shear centre. These loading conditions are known to have significant effects on the lateral buckling strength of beams. Many steel design codes have adopted equivalent uniform moment distribution and load height factors based on data for conventional hot-rolled, doubly symmetric I-beams subject to lateral torsional buckling. The non-uniform moment distribution and load height effects of transverse loading on cantilever LSBs, and the suitability of the current design modification factors to include such effects are not known. This paper presents a numerical study based on finite element analyses of the elastic lateral buckling strength of cantilever LSBs subject to transverse loading, and the results. The applicability of the design modification factors from various steel design codes was reviewed, and suitable recommendations are presented for cantilever LSBs subject to transverse loading.     

高烈度地区框架-核心筒结构中美抗震设计方法对比

按照中美相关抗震设计规范分别对位于中国8度抗震设防区和美国典型高烈度区域（旧金山地区）的两栋层高与结构相似的钢筋混凝土框架 核心筒高层建筑结构进行了设计。介绍了抗震设计过程中根据中美相关抗震规范确定的地震作用参数与材料强度,比较了两国混凝土结构尤其是剪力墙结构抗震构造措施的异同。建立了两结构的空间弹性分析模型,采用振型分解反应谱法计算了两结构的弹性地震响应,比较了两结构自振周期、基底剪力、层剪力、结构层间变形、构件尺寸、配筋以及连梁受剪承载力等。计算结果表明：按照两国设计规范分别设计的结构,其设计地震作用水平相当;根据美国规范设计的结构连梁受剪承载力与中国规范设计方案相比偏低,约为中国规范设计方案的0.63~0.95倍;中美两国规范设计的剪力墙约束边缘构件的范围与配筋差异较大,中国规范设计方案剪力墙约束边缘构件内纵筋和箍筋集中在端部固定范围内,美国规范设计的箍筋约束范围大,对应端部固定范围的配筋比中国规范配筋量小。     

层状地基中单桩的扭转变形分析

研究了扭矩作用下单桩的扭转变形。采用积分变换和传递矩阵方法求解成层土在内部环形荷载作用下的基本解;利用此基本解并考虑桩土位移协调条件,提出了层状地基中单桩扭转变形的半解析方法;通过一匀质地基算例验证了该理论方法的正确性,并给出了双层地基模型的数值分析结果。     

Nonlinear Analysis of Torsionally Loaded Pile Groups

An empirical approach is developed to analyze the nonlinear torsional behavior of free-standing pile groups with rigid pile caps. In this approach, the lateral and torsional responses of individual piles in a pile group are modeled by p-y and τ-θ curves; the interaction among lateral resistances of the individual piles is predicted through Mindlin's elastic solutions; the interactions between the torsional and lateral resistances of the individual piles are described through Randolph's solution; and the coupling effect of lateral resistance on torsional resistance of the individual piles is quantified using an empirical factor “β”. The proposed approach is capable of capturing the most significant aspects of pile-soil-pile interactions and coupling effect in pile groups subjected to torsion. The proposed approach is verified using results of centrifuge model tests. In general, the applied torque-twist angle response and the transfer of applied torque in pile groups can be reasonably well predicted and are sensitive to the pile group configuration.     

A new approach to determine the base shear of steel frame structures

Base shear (V) is the maximum lateral force that will occur due to seismic ground motion at the base of a structure. Calculations of base shear depend on a lot of factors such as soil conditions, level of ductility, fundamental period of vibration of the structure, etc. A great number of methodologies have been developed to determine the dynamic responses of individual frameworks. However, there is no well established empirical solution of the dynamic response of the problem due to the base shear of the steel frames. In this study, a formulation based on NN to determine the dynamic response of both braced and unbraced plane steel frames are provided. The presented formulation is a function of number of stories (ns), bays of the frames (nb), and soil types (Z). The training and testing patterns of the proposed NN formulation are obtained from linear Finite Element Analysis (FEA) solution. The NN-based formulation results are compared with the results obtained from numerical and some current design codes. The NN- based formulation results are found to be more accurate.     

A simplified method for calculation of the natural frequencies of wall–frame buildings

A simple hand method is presented for the three-dimensional frequency analysis of buildings braced by frameworks, coupled shear walls, shear walls and cores. Lateral vibration is characterised by three types of deformation: the full-height ‘local’ bending of the individual columns/wall sections/shear walls/cores, the full-height ‘global’ bending of the frameworks/coupled shear walls, which is associated with the axial deformations of the columns/wall sections, and the shear deformation of the frameworks/coupled shear walls. Based on the stiffnesses associated with these three types of deformation, a closed formula is derived for calculation of the lateral frequencies. An analogy between bending and torsion is used to carry out the pure torsional frequency analysis. The coupling of the lateral and pure torsional modes is taken into account. The results of a comprehensive accuracy analysis covering 144 multi-storey structures demonstrate good agreement with the finite element solution, the maximum difference being 7%. A worked example with step-by-step instructions shows the easy use of the method.     

A statistical and experimental investigation into the accuracy of capacity reduction factor for cold-formed steel shear walls with steel sheathing

Buildings constructed of cold-formed steel members are increasingly used in many countries. In recent years, cold-formed steel shear walls with steel sheathing were introduced as lateral force resisting systems. Design provisions of these structures require that the shear strength of shear walls with a height to width aspect ratio (h/w) greater than 2:1 be reduced by the factor 2w/h for satisfying allowable story drift limit. In this research, the accuracy of the factor is investigated using the results of previous tests and the tests performed by the researcher. Results show that the reduction factor (2w/h) is conservative. Thus, a relation is proposed for the reduction factor.     

Comparison of Liquefaction-Induced Ground Deformation Between Results from Undrained Cyclic Torsional Shear Tests and Observations From Previous Model Tests and Case Studies

In order to investigate liquefaction-induced ground displacement, we conducted a series of undrained cyclic torsional shear tests on saturated Toyoura sand using a modified torsional apparatus capable of applying and measuring double amplitude shear strain up to about 100%. The limiting value of double amplitude shear strain, at which strain localization appears during undrained cyclic loading tests, was evaluated from the test results with reference to the change in the deviator stress during liquefaction. The limiting strain values, which increase with a decrease in the relative density of the specimen, were found to be consistent with the maximum amounts of liquefaction-induced ground displacement observed in the previous shaking table model tests and most of the relevant case studies. This feature is reasonable considering the reduction in the mobilized cyclic shear stress in liquefied soil due to the degradation of the shear resistance. As long as the liquefied soil layer remains in uniform deformation, these limiting strain values may be used in estimating the maximum amount of liquefaction-induced ground displacement.