In-plane floor flexibility effects on torsionally unbalanced systems

This paper presents the results of an analytical work addressed to understand the effects of in-plane floor flexibility on torsionally unbalanced (TU) systems subjected to bidirectional firm-soil earthquake records. The study uses a structural system consisting of a linear-elastic diaphragm supported by non-linear frames oriented along two orthogonal directions. The diaphragm is modelled with plane-stress finite elements and frames with stiffness-degrading flexural elements. Results indicate that an increase of in-plane diaphragm flexibility leads to a reduction of frame displacements for systems with initial lateral period of vibration T>0·4 s. For systems with T⩽0·4 s, in-plane floor flexibility can lead to significant frame displacement increments (50 per cent higher). Results show that these variations on displacements decrease for increasing values of both the seismic-force reduction factor and the system initial lateral period. Copyright © 1999 John Wiley & Sons Ltd.     

Inelastic seismic analysis of a building structure designed by argentine codes

A reinforced concrete frame-wall structure of a building designed in accordance to standard practice in Argentina was analysed by the procedures prescribed by current Argentine Codes. In addition, the inelastic step-by-step response of the structure to design spectrum-compatible accelerograms was studied by means of a special element for inelastic dynamic analysis of reinforced concrete frames. Results obtained by the different methods of analysis are presented.     

Pseudodynamic response of torsionally unbalanced two‐storey test structure

Two one‐way eccentric, two‐storey, one‐by‐one‐bay reinforced concrete (RC) structures are pseudodynamically tested under unidirectional ground motions. Theoretical considerations about the effect of torsional coupling on modal periods and shapes agree with modal results of the test structure, considering member stiffness is equal to the secant stiffness to yielding in skew‐symmetric bending. Modal periods of such an elastic structure are in fair agreement with effective periods inferred from the measured response at the beginning of a test of a thoroughly cracked structure and at the end of the test. A time‐varying stiffness matrix and a non‐proportional damping matrix fitted to the test results may be used to reproduce the measured response approximately by modal superposition and identify the role of the four time‐varying modes. Flexible side columns sustained very large drift demands simultaneously in the two transverse directions and suffered significant but not heavy, damage at lap‐splices. RC‐jacketing of the flexible side columns practically eliminated the static eccentricity between the floor centres of twist and mass as well as the torsional response. Inelastic time‐history analysis with point‐hinge member models, using as elastic stiffness the secant stiffness to yielding and neglecting post‐ultimate‐strength cyclic degradation of resistance in members with plain bars and poor detailing, predicted fairly well the response until the peak displacements and member deformations occurred. After that, it underestimated displacement peaks and the lengthening of the apparent period and missed the gradual drifting of the response towards a permanent offset. Copyright © 2007 John Wiley & Sons, Ltd.     

Inelastic seismic response of one-way plan-asymmetric systems under bi-directional ground motions

The static design requirements of some seismic codes, such as the Eurocode 8 and—in most cases—the Uniform Building Code, to allow for the effects of earthquake excitation acting in a direction other than the principal axes of the structure do not apply to one-way asymmetric systems. Therefore, with some exceptions, no specific provisions are considered for such systems to cover effects of structural asymmetry on the behaviour of elements located along the symmetric system direction. Aimed towards fulfilling this need, in this paper, a wide parametric study of the inelastic response of one-way asymmetric systems designed according to Uniform Building Code is carried out, considering two-component earthquake excitations. The analyses show that the maximum ductility demands on elements aligned along the asymmetric system direction are very close to, and even lower than, those obtained for symmetric reference systems. Conversely, the symmetric direction elements undergo significantly larger inelasticity than if they were located in symmetric reference systems. Subsequently, the overstrength needed by the symmetric direction elements to prevent such additional ductility demands for several stiffness and plan configurations is quantified. It is concluded that one-way asymmetry should be considered by seismic codes as an intrinsic system property, thus implying that specific provisions should be included for designing elements located along the symmetric system direction, in addition to those currently subscribed to design the asymmetric direction elements. © 1998 John Wiley & Sons, Ltd.     

Seismic displacements of torsionally unbalanced buildings

A parametric study is carried out to evaluate the seismic displacements at the flexible edge of torsionally unbalanced (TU) structural systems. Guidelines are provided to estimate these displacements so that they can be incorporated in the formulation of the displacement-based seismic design approach for the design of TU buildings. The ability of three code procedures to estimate the flexible-edge displacement is examined to show that not all procedures lead to conservative estimates. Finally, it is shown that elastic spectrum analysis incorporating accidental torsion effect is a viable means to estimate the flexible-edge displacements.     

Inelastic seismic response of simple eccentric structures

The maximum ductility demand and the edge displacement of a simple single mass eccentric model is evaluated when the system is subjected to ground motions represented by the El Centro 1940 and Taft 1952 earthquake records. The resisting elements are taken to be bilinear hysteretic. It is found that the ductility demand depends to a great extent on the energy content of the ground motions, particularly in the period range beyond the elastic period of the system. Unlike elastic response, the coincidence of uncoupled torsional and lateral frequencies does not lead to exceptionally high inelastic response. An increase by a factor of two in ductility demand is not uncommon for a system with large eccentricity as compared to a symmetrical system. Therefore, system eccentricity has a larger effect on ductility demand than earlier studies indicated. Using Clough's model to allow for stiffness degradation effect, results are found to be within 20 per cent of those calculated based on the bilinear hysteretic model.     

Laboratory tests of steel simple torsionally unbalanced models

The objective of this work is to obtain estimations of the amplification factors α and δ used for torsion design of buildings, from experiments. For this study, simple one‐storey torsionally unbalanced (TU) steel models were considered. Models consisted of a deck supported on four columns with a selected arrangement of hinges at column ends. Two theoretical structural eccentricities (e = 0.05 and 0.15) were considered. Models were excited with a simple long‐period pendulum consisting of a hanging platform with a forced‐vibration generator on it. Eight models were tested at several excitation levels (frequencies and force magnitudes) in both ranges of behaviour: elastic and inelastic. Experiments were conducted at three frequency ratios of excitation. Registered accelerations of the pendulum platform indicate that the experimental set‐up leads to excitations that resemble narrow‐band seismic ground motions. Frame shear force estimations, based on accelerations recorded at both deck sides, indicate that torsion design factors (α and δ) depend on eccentricity. Estimations of frame shears based on measurements indicate that for normalized eccentricities e ? 0.025, the amplification α can be between 2 and 3; while δ factor resulted between 0.0 and 1.6. Copyright © 2006 John Wiley & Sons, Ltd.     

Design of torsionally unbalanced structural systems based on code provisions I: Ductility demand

Using a three element single mass model, this paper presents the ductility demands on the elements of torsionally unbalanced systems when subjected to strong earthquake shaking. Torsionally unbalanced systems based on nine structural configurations are considered, ranging from torsionally stiff systems with the centre of rigidity (CR) centrally located to torsionally flexible systems with CR eccentrically located. The strength of the elements is designed based on the Canadian and New Zealand codes, and the Uniform Building Code (UBC) of the United States. It is shown that all three codes can limit the ductility demands on the elements to that of a similar but torsionally balanced system when the system is torsionally stiff. However, substantial additional ductility demands on the element at the stiff edge of the system exist for torsionally flexible systems when the New Zealand code or UBC is used. The large ductility demand is caused by the low strength of the stiff-edge element permitted by these codes.     

Design of torsionally unbalanced structural systems based on code provisions II: Strength distribution

This paper presents the results of an analytical study of the strength distribution of lateral load resisting elements in torsionally unbalanced systems designed based on codified torsional provisions. It is shown that the element strength can be expressed conveniently as the element strength of a similar but torsionally balanced system multiplied by a strength factor. This strength factor depends on three system parameters, namely, the location of the element relative to the centre of rigidity, and the torsional stiffness and eccentricity of the structure. In addition, it depends on the design coefficients of the code specified design eccentricity expressions. The influence of each of these factors on the element strength distribution is discussed. A new set of values for the design coefficients is proposed. By means of examples, it is shown that the proposed torsional provision is an improvement over those suggested in the National Building Code of Canada and the New Zealand code.     

Inelastic seismic response of one-storey,asymmetric-plan systems: Effects of system parameters and yielding

The inelastic response of one-storey, asymmetric-plan systems to two excitations is presented and analysed with the objective of identifying the influence of system parameters: uncoupled lateral vibration period, uncoupled torsional-to-lateral frequency ratio, stiffness eccentricity, relative values of the strength and stiffness eccentricities, and yield factor. Furthermore, the influence of yielding on the response of asymmetric-plan systems is examined. In particular, we determine whether the well known relationship between the response of yielding and elastic single-degree-of-freedom (SDF) systems is also applicable to asymmetric-plan systems.     

Inelastic seismic response of one-storey,asymmetric-plan systems: Effects of stiffness and strength distribution

The effects of plan-wise distribution of stiffness and strength-as determined by the number, location, orientation and yield deformations of resisting elements-on the inelastic response of one-storey systems are evaluated. In particular, various systems are investigated for wide ranges of parameters involved, with the objective of establishing how the response is influenced by: (i) the presence of resisting elements perpendicular to the direction of ground motion; (ii) the number of resisting elements along the direction of ground motion; (iii) the overstrength typical of code-designed buildings; (iv) the relative values of strength and stiffness eccentricities; and (v) whether the asymmetry of the system is due to eccentricity in stiffness or in mass. The results presented for a simple excitation make it possible to explain the inconsistencies in conclusions from various earlier investigations, and to evaluate their applicability to actual buildings.     

Inelastic dynamic analysis of tall buildings

The importance of inelastic action of frame structures subjected to strong ground motions has been recognized by engineers for many years. However, the dynamic analysis of buildings undergoing inelastic deformations requires the solution of many theoretical problems, as well as the development of computer software which makes such analyses economically feasible in a design office–in spite of the extraordinary amount of computation involved. In this paper, some of the principal theoretical problems are briefly described. These are the load-deformation relationship, yield capacity reduction, ductility, P– δ effect, viscous damping, panel zone distortions, numerical integration techniques, energy analysis and the effect of non-structural elements. Special consideration is given to questions associated with the practical implementation of this theory. These questions arose during the development of a computer program, called NLDYN, capable of analysing the non-linear dynamic behaviour of tall buildings in an engineering office environment. The capabilities of this computer program are illustrated with the results of the analysis of a 60 storey office building currently under construction in downtown Los Angeles.     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic seismic response of stiffening systems and development of demand spectrum: Application to MSSS bridges

A stiffening system is a system that increases its stiffness as it goes under large displacements. Such behavioural characteristic can result from constitutive behaviour or at the structural level often from closure of gaps between various components (sub‐systems) of the structure. An example of the latter situation is multi‐span simply supported (MSSS) bridges under horizontal earthquake ground motion. Unlike softening systems, stiffening systems have not been studied. In addition to the need for more understanding of the seismic response of stiffening systems, there is a need to develop response spectrum that can be used in design. Several parameters including gap size and ratios of sub‐systems stiffness, strength, and mass control the behaviour of a stiffening system. In this study, a simplified stiffening model is developed and over 367 000 cases are analysed to investigate the nonlinear stiffening behaviour and pounding. Parameters considered also include ground motion characteristic. Results are evaluated and compared in terms of displacement and dissipated hysteretic energy. Parameter study results show that, on average, the displacement response is lower for stiffening systems, however, they dissipates higher hysteretic energy, due to higher yield cycles and yield excursions, and can possibly sustain more damage than a bilinear, elastic–plastic system. Using parameter study database, design response spectrum for stiffening systems is also proposed and its practical application is demonstrated through its application to an MSSS bridge. Results of this study goes beyond MSSS bridges and will have application for many structural systems where response is characterized by a stiffening behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Non-linear seismic response analysis of soil-structure interaction systems

This paper presents an effective analysis procedure for the dynamic soil-structure interaction problem considering not only the sliding and separation phenomena but also the non-linear behaviour of soil by the finite element method. Soil is assumed to be an elasto-plastic material and the contact surface between the soil and structure is modelled by the joint element. The load transfer method is adopted to carry out dynamic non-linear response analysis. The method is applied to the response analysis of a nuclear reactor building resting on the ground surface. The effects of non-linear behaviour of soil on the safety against sliding of the structure are examined. The numerical computations reveal the following results: that the non-linear behaviour of soil reduces the response of the system and the magnitude of sliding of the structure, and that the safety against sliding obtained by the proposed method is higher than the safety obtained by classical methods. This implies the possibility of a more rational and economical design of large structures; it can be said that the proposed method provides useful information for the stability analysis of important and large structures.     

桩-土-结构动力相互作用的线弹性地震反应分析

采用集中质量法(简化模型)，用ANSYS软件作为桩—土—结构动力相互作用分析的工具，建立了小震下钢筋混凝土剪切型结构考虑桩—土—结构动力相互作用效应的计算模型，进行了桩—土—结构相互作用线性体系的模态分析，研究了考虑桩—土—结构相互作用体系的自振特性；进行了小展下桩—土—结构相互作用体系弹性地震反应时程分析，研究了土—结构动力相互作用效应对结构地震反应的影响；得出如下结论；考虑桩—土—结构相互作用效应后，结构体系的自振特性及结构的地震反应将有所改变。     

Elastk-plastic dynamic analysis of structures using known elastic solutions

A numerical method is shown to analyse the dynamic elastic-plastic responses of those structures with known elastic solutions. The displacement at one point at time t caused by a unit load applied at another point at zero time, called dynamic influence coefficient, is calculated from the known elastic solutions. Incremental plastic strain is accounted for by a set of additional incremental loads, so the stiffness matrix and the eigenvectors do not vary with time. From the incremental load including that caused by the incremental plastic strain, the displacement vs. time of the structure is obtained. This method is applied to simply supported beams with bilinear stress-strain relations with different strain-hardening rates and to a simply supported elastic-ideally plastic rectangular plate. This procedure can be extended to structures with no available known analytical elastic solutions. For these structures, the elastic solutions can be obtained by the finite element method.     

Inelastic response analysis of reinforced concrete structures using modified force analogy method

A modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi‐linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P‐Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non‐ductile RC bridge column, a two‐storey RC frame, and dynamic collapse test data of a non‐ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley & Sons, Ltd.     

Inelastic seismic response of code-designed multistorey frame buildings with regular asymmetry

Based on an asymmetric multistorey frame building model, this paper investigates the influence of a building's higher vibration modes on its inelastic torsional response and evaluates the adequacy of the provisions of current seismic building codes and the modal analysis procedure in accounting for increased ductility demand in frames situated at or near the stiff edge of such buildings. It is concluded that the influence of higher vibration modes on the response of the upper-storey columns of stiff-edge frames increases significantly with the building's fundamental uncoupled lateral period and the magnitude of the stiffness eccentricity. The application of the equivalent static torsional provisions of certain building codes may lead to non-conservative estimates of the peak ductility demand, particularly for structures with large stiffness eccentricity. In these cases, the critical elements are vulnerable to excessive additional ductility demand and, hence, may be subject to significantly more severe structural damage than in corresponding symmetric buildings. It is found that regularly asymmetric buildings excited well into the inelastic range may not be conservatively designed using linear elastic modal analysis theory. Particular caution is required when applying this method to the design of stiff-edge frame elements in highly asymmetric structures.     

Efficient analysis of dynamic response of linear systems

After reviewing briefly a recently proposed procedure for evaluating the dynamic transient response of a classically damped linear system from its corresponding steady-state response, a modified procedure is presented which also appears to be highly efficient for non-classically damped systems of the type encountered in studies of soil-structure interaction. The concepts involved are developed by reference to viscously damped single-degree-of-freedom systems, and numerical solutions are included to illustrate the accuracy and efficiency of the proposed procedure and its superiority over the classical Discrete Fourier Transform approach.