Design Principles for Minimum Torsional Response of Wall-Frame Concrete Structures

A seismic design procedure is described incorporating the well-accepted property that the stiffness of reinforced concrete elements is strength dependent and the requirement that the method of assigning strength to elements should be aiming at minimum torsional phenomena. Such a response allows a direct comparison with the findings of a static nonlinear analysis, which may provide the limits of story drifts and the induced plastic rotations in potential plastic hinges. The requirement of a practically translational response implies that the element strength assignment should be based on planar considerations and the initially elastic response should be of minimum torsion.     

Nonlinear Static and Dynamic Behavior of a 16-Story Torsionally Sensitive Building Designed According to Eurocodes

A 16-story building under construction in Bucharest has been designed according to the provisions of EC2 and EC8, using elastic spectral modal analysis. Considering that the building is torsionally sensitive in the nonlinear range, it was further checked and verified using nonlinear dynamic and static procedures, using a detailed space-frame model. Specifically, time-history analysis for seven different excitations, as well as respective inelastic static analysis taking into account torsional effects were performed. The results are examined regarding structural (global) and member (local) response and various issues concerning the adequacy of the original elastic design and the applicability of advanced analysis methods are discussed.     

Displacement-Controlled Behavior of Asymmetrical Single-Story Building Models

Displacement controlled behavior is a feature of low to moderate seismicity areas where the peak displacement demand on structures could be limited despite significant structural strength and stiffness degradation. In this article, the extension of the displacement controlled phenomenon to torsionally unbalanced framing systems is investigated. It is shown that the displacement demand of critical elements within a building can be insensitive to changes in eccentricity and torsional stiffness properties. While torsional actions is a well-researched topic, the incorporation of displacement controlled phenomenon into the analysis is original and represents a new development.     

Simple Models for Inelastic Seismic Analysis of Asymmetric Multistory RC Buildings

A simple stick model is presented for the inelastic seismic analysis in 3D of two-way eccentric multistory RC buildings. It has 3 DoFs per floor, point hinges at the ends of the vertical elements connecting floors, elastic story stiffness derived from the corresponding story force-interstory deformation relations of the elastic 3D structure under inverted-triangular floor loading (by torques for torsional stiffness, by horizontal forces for the lateral ones), story yield forces derived from the total resistant shear of the story vertical elements, but no coupling between lateral and torsional inelasticity. It is evaluated on the basis of comparisons of response histories of floor displacements to those from full nonlinear models in 3D of four actual buildings. Alternative locations of the story vertical element with respect to the floor mass center are examined: (a) the floor “center of twist” of the elastic 3D building under inverted-triangular floor torques; (b) the story “effective center of rigidity,” through which application of inverted triangular lateral forces does not induce twisting of floors; (c) the centroid of the secant stiffness of the story vertical members at yielding and (d) the centroid of the lateral force resistance of story vertical elements. Among alternatives (a)–(d), the floor “center of twist” provides the best agreement with floor displacement response-histories from full 3D nonlinear models. This means that the static eccentricity that matters for torsional response may be taken as that of the floor “center of twist.” The center of resistance comes up as the second-best choice.     

Effect of AAC Infill Walls on Structural System Dynamics of a Concrete Building

The effect of autoclaved aerated concrete (AAC) infill walls on the structural system dynamics of a two-story reinforced concrete building is investigated using its finite element structural model, which is calibrated to simulate the acceleration-frequency response curves from its forced vibration test. The model incorporating the AAC infill walls by equivalent diagonal struts captures the increase in lateral stiffness of the building and the torsional motions induced due to the asymmetrically placed AAC infill walls. A higher strut width coefficient than in ASCE/SEI 41-06 is recommended to model the stiffness of the AAC infill walls in the elastic range.     

Retrofit Design Methodology for Substandard R.C. Buildings with Torsional Sensitivity

Recent earthquakes have revealed the susceptibility of non-ductile reinforced concrete (R.C.) buildings with deficiencies related to stiffness and/or mass irregularities in plan and elevation. This paper proposes a design methodology for the seismic upgrading of rotationally sensitive substandard R.C. buildings. The methodology aims to first eliminate the effect of torsional coupling on modal periods and shapes and then modify the lateral response shape of the building in each direction so as to achieve an optimum distribution of interstory drift along the building height. A case study is used to illustrate practical application of the proposed methodology.     

Fragility-Based Performance Evaluation of Asymmetric Single-Story Buildings in Near Field and Far Field Earthquakes

Previous studies have shown that both distribution and intensity of response parameters in asymmetric buildings are dependent on their stiffnesses and strength distributions. The locations of centers of strength and rigidity relative to the center of mass provide suitable metrics for strength and stiffness distributions. In general, the proper locations of these centers are a function of earthquake ground motion characteristics and the level of building's nonlinear responses. In this article, using nonlinear response evaluation of single-story building models with a wide range of uncoupled torsional to lateral frequencies subjected to near field and far field earthquake excitations the proper location of building centers is studied . Diaphragm rotation, interstory drift, hinge plastic rotation, and ductility demand are selected as damage measure parameters. To compare the performance of models in each limit state, fragility representation of responses is used. It is concluded that proper configuration of building centers in a torsionally stiff building fundamentally depends on the chosen demand parameter. The proper configuration of centers in a torsionally stiff building for a specific demand parameter can converge the probability and distribution of related damages to those in the symmetric building counterpart. When the critical demand parameter for a case is identified, its corresponding arrangements of centers for a suitable seismic behavior may also be recognized. By rearranging the configuration of centers based on the attained configuration, the adverse effects of asymmetry can be avoided.     

DESIRABLE STRENGTH DISTRIBUTION FOR ASYMMETRIC STRUCTURES WITH STRENGTH-STIFFNESS DEPENDENT ELEMENTS

Recent studies have shown that for many reinforced concrete lateral force-resisting elements (LFRE) stiffness is dependent on strength, and as a result strength assign-ment to these elements would affect both the strength and stiffness distributions in a structure. As a consequence, stiffness distribution cannot be considered known prior to strength assignment. This implies that in assigning strength to LFRE, the designer has the ability not only to prescribe the strength distribution, but also indirectly control the stiffness distribution in the structure. In this paper, a study is made on the seis-mic performance of a number of single-story structures to reconfirm that the “balanced CV-CR location” criterion, previously suggested by the writers, constitutes a desirable strength/stiffness distribution for minimising torsional response of asymmetric reinforced concrete structures.     

A Simple Model for Estimating Shocks in Unrestrained Building Contents in an Earthquake

Building contents that include cabinets housing electronic equipment are typically not rigidly secured to the floor, nor to the adjacent wall except in regions of high seismic activities. The behavior of unrestrained building contents in an earthquake is a cause of concern because of the consequence of damage to certain equipment or other forms of fragile items. Much of the research reported in the literature has been devoted to studying the rocking and sliding motion behavior of base-excited rigid objects and their risks of overturning. In contrast, this paper is concerned with estimating the impact acceleration that can be generated by the pounding of the rocking object onto the floor. Algebraic expressions for predicting the acceleration level, which can be translated into dynamic force values, are derived and illustrated by case studies. Importantly, the proposed expressions have been verified by comparisons with results from both simulated and physical experiments. In illustrating the use of the proposed analytical procedure, a parametric experimental study has been undertaken on a cushion material to study the sensitivity of its static and dynamic stiffness to changes in the boundary conditions of the cushion. The proposed calculation procedure, while simple to apply, can be used as a means of predicting shock and the dynamic forces that can be generated in an object in the course of the response to an earthquake.     

Simplified Seismic Sidesway Collapse Capacity-Based Evaluation and Design of Frame Buildings with Linear Viscous Dampers

This article describes a simplified procedure for estimating the seismic sidesway collapse capacity of frame building structures incorporating linear viscous dampers. The proposed procedure is based on a robust database of seismic peak displacement responses of viscously damped nonlinear single-degree-of-freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed procedure is assessed by comparing its collapse capacity predictions on 272 different building models with those obtained from incremental dynamic analyses. A straightforward collapse capacity-based design procedure is also introduced for structures without extreme soft story irregularities.     

故宫灵沼轩的动力特性及抗震性能研究

故宫灵沼轩是我国最早建造的钢铁-砌体组合结构之一,具有重要的历史、艺术和科学价值。为了评估灵沼轩在地震作用下的结构安全状况,建立了灵沼轩结构的三维有限元模型,并对其进行了动力特性和地震时程分析,得出了其固有频率、模态振型、地震位移响应和地震应力响应。结果表明:灵沼轩整体结构布置对称性较高,扭转刚度较大,对抗震较为有利;在8度多遇地震、设防地震和罕遇地震作用下,灵沼轩的金属结构部分及砌体结构部分的顶点位移和层间位移角均符合现行规范要求,砌体结构部分的第三主应力响应均小于材料的抗压强度,不存在压溃风险。在8度多遇地震和设防地震作用下,砌体结构部分的第一主应力响应均小于材料的抗拉强度,结构不会发生拉裂。但在8度罕遇地震作用下,砌体结构的部分位置拉应力超过材料的抗拉强度,这些位置存在开裂危险。最后,综合动力特性和抗震性能分析的结果,提出了灵沼轩的抗震加固建议。     

Confidence Factor?

Eurocode 8 Part 3 (EC8-3) is devoted to assessment and retrofitting of existing buildings. In order to take into account the uncertainty in the knowledge of structural properties, EC8-3 defines, analogously to the ordinary material partial factors, an adjustment factor, called “confidence factor (CF),” whose value depends on the level of knowledge (KL) of properties such as geometry, reinforcement layout and detailing, and materials. This solution is plausible from a logical point of view but it cannot yet profit from the experience of its use in practice, hence it needs to be substantiated by a higher level probabilistic analysis accounting for and propagating epistemic uncertainty (i.e., incomplete knowledge of a structure) throughout the seismic assessment procedure. This article investigates the soundness of the format proposed in EC8-3. The approach taken rests on the simulation of the entire assessment procedure and the evaluation of the distribution of the assessment results (distance from the limit state of interest) conditional on the acquired knowledge. Based on this distribution, a criterion is employed to calibrate the CF values. The obtained values are then critically examined and compared with code-specified ones. The results pinpoint a number of deficiencies that appear to somewhat invalidate the approach. The methodological significance of the work extends beyond the assessment procedure in EC8-3, since similar factors appear in other international guidelines (e.g., the knowledge factor of FEMA356).     

Optimum Design Approaches for Improving the Seismic Performance of 3D RC Buildings

In this article, a number of design approaches for 3D reinforced concrete (RC) buildings are formulated in the framework of structural optimization problems and are assessed in terms of their performance under earthquake loading. In particular, three design approaches for RC buildings are considered in this study. In the first, the initial construction cost is considered as the objective function to be minimized. The second one is formulated as a minimization problem of the torsional response, while a combined formulation is also examined as the third design approach. The third approach is considered with two distinctive formulations. According to the first approach, the torsional behavior is minimized by minimizing the eccentricity between the mass and rigidity centers, while the second one is achieved by minimizing the eccentricity between the mass and strength centers. It is shown that the optimized designs obtained according to the minimum eccentricity of the rigidity center behave better in frequent (50/50 hazard level) and occasional (10/50 hazard level) earthquakes, while the designs obtained according to the minimum eccentricity of the strength center formulation was found better in rare (2/50 hazard level) events. Designs obtained through a combined formulation seem to behave equally well in the three hazard levels examined.     

西藏坚塞颇章宫的结构计算分析

本研究以全国重点文物保护单位西藏罗布林卡三大宫殿之一的坚塞颇章宫为实例,分析藏式古建筑的结构特点,探讨计算分析方法,并针对静力荷载工况和地震组合工况下的结构性能进行了讨论。本研究区别于以往藏式结构的研究方法,主要在于:在计算分析中将墙体建入整体结构模型,考虑墙体对结构的影响;考虑墙体和木柱的“收分”造型的影响;将楼板和屋面的密布木檩等刚度转化为单向板考虑;同时考虑构件已存的变形缺陷影响。计算结果表明:西藏坚塞颇章宫在静力荷载工况作用下,整体状态良好,梁柱墙及节点均满足承载力要求;在地震组合工况作用下,部分柱和墙不满足抗震承载力要求。在地震作用下,该建筑刚度较小的木结构构件首先发生振动。结构薄弱部位是中部四根二层通高木柱。这四根通高木柱长细比较大,刚度较小,一旦发生较大的变形,将直接影响整体结构安全。木柱与墙体之间的变形差异较大,两者变形协调性较差。此外,存在变形缺陷的中部通高木柱所在梁柱节点的抗震承载力不满足要求,应注意加强防护。研究涉及的计算分析方法及相关计算结论对藏式建筑结构的深入研究具有重要的参考价值。     

Identification of Suitable Limit States from Nonlinear Dynamic Analyses of Masonry Structures

Performance-based earthquake engineering, developed over the last decades for the design and assessment of other structures, can also be applied for masonry structures if the particularities of masonry are incorporated into the procedure. According to this methodology, structural performance can be assessed according to damage states which are identified through displacement/damage indicators. While various methods for the identification of limit states from the results of nonlinear static analyses exist, the identification of damage states from the results of nonlinear dynamic analyses is still uncertain. This article investigates a number of criteria allowing to identify the attainment of significant limit states from the results of time history analyses, in terms of appropriately identified response quantities. These criteria are applied to five building prototypes and their results are compared. A comparison with the limit states derived from nonlinear static analyses is also made.     

Nonlinear Static Procedure for Multi-Story Asymmetric Frame Buildings Considering Bi-Directional Excitation

The present article focuses on a nonlinear static procedure (NSP) for a multi-story asymmetric frame building with regular elevation subjected to bi-directional ground motion. In this procedure, two simplified models—an equivalent single-story model and an equivalent single-degree-of-freedom (SDOF) model—are used to predict the peak response of multi-story asymmetric buildings. The peak response is predicted through pushover analysis of an equivalent single-story model considering the effect of bi-directional excitations and an estimation of the nonlinear response of equivalent SDOF models. The predicted results are compared with the nonlinear dynamic analysis results, and satisfactory predictions can be obtained by the proposed procedure.     

Point-to-Surface Pounding of Highway Bridges with Deck Rotation Subjected to Bi-Directional Earthquake Excitations

Post-earthquake survey of several strong earthquakes demonstrated that pounding between the neighboring civil infrastructures, such as building and highway bridge, would induce significant structural damage, even collapse, of the structures. This article presents a pounding experiment of highway bridge, especially focused on the point-to-surface pounding of bridge decks due to torsional rotation, when subjected to extreme bi-directional earthquake excitations. To experimentally investigate the point-to-surface pounding between the neighboring bridge segments, a base-isolated highway bridge model, in which the mass centers of the bridge decks do not strictly coincide with the corresponding stiffness centers, is manufactured. A series of shaking table tests of the highway bridge model are carried out for the structural model with large and small separations of the expansion joint to investigate the dynamic responses of the bridge model with and without including the pounding effects, respectively. An analytical model of the highway bridge, in which the point-to-surface pounding is represented by using a modified contact-friction element, is also established based on the lump mass model with three degrees of freedom for each segment. Based on the test results, the model parameters of the modified contact-friction element are identified, and the analytical responses of the highway bridge model with pounding effects are compared with the experimental data. The results show that the highway bridge is vulnerable to the deck rotation, and point-to-surface pounding should be considered in the structural design to lighten the pounding damage of the highway bridge under strong earthquake excitations.     

TORSIONAL EFFECTS IN THE PUSHOVER-BASED SEISMIC ANALYSIS OF BUILDINGS

The general trends of the inelastic behaviour of plan-asymmetric structures have been studied. Systems with structural elements in both orthogonal directions and bi-axial eccentricity were subjected to bi-directional excitation. Test examples include idealised single-storey and multi-storey models, and a three-storey building, for which test results are available. The response in terms of displacements was determined by nonlinear dynamic analyses. The main findings, limited to fairly regular and simple investigated buildings, are: (a) The amplification of displacements determined by elastic dynamic analysis can be used as a rough, and in the majority of cases conservative estimate in the inelastic range, (b) Any favourable torsional effect on the stiff side, which may arise from elastic analysis, may disappear in the inelastic range. These findings can be utilised in the approximate pushover-based seismic analysis of asymmetric buildings, e.g. in the N2 method. It is proposed that the results obtained by pushover analysis of a 3D structural model be combined with the results of a linear dynamic (spectral) analysis. The former results control the target displacements and the distribution of deformations along the height of the building, whereas the latter results define the torsional amplifications. The proposed approach is partly illustrated and evaluated by test examples.     

SEISMIC DESIGN REGULATION CODES: CONTRIBUTION OF K-NET DATA TO SITE EFFECT EVALUATION

The purpose of this study is to compare the site effect section of building codes (EC8 and UBC97) with the set of data provided by the Kyoshin network. In order to obtain a set of site coefficients and spectral shapes, we have first deduced an attenuation law for both horizontal and vertical motion. Site conditions are represented by the shear velocity averaged over the upper 30 m (V _s ³⁰). Our site classification (4 categories similar to those proposed in the new ECS and the UBC97) is based on borehole investigations at every station. This classification has permitted to distinguish clearly four response spectra which demonstrates the efficiency of V _s ³⁰ as characterising site conditions. Our law is then used to test site coefficients and spectral shapes of building codes ECS and UBC97. Concerning spectral shapes and site coefficients, our results are found to be in good agreement with EC8 and UBC97 only if category B (400<V _s ³⁰<800 m/s) is taken as reference. We also conclude that a site which is characterised as “rock” on geological criteria can not generally be classified in category A (V _s ³⁰>800 m/s). This suggests that classification in category A should be based only on field measurements. Concerning vertical motion, our analysis of the K-NET data shows that the ratio av/ah (vertical peak ground acceleration over horizontal peak ground acceleration) is between 0.50 and 0.68.