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.     

Dynamic response of bilinear asymmetric structures

The inelastic behaviour of eccentric single-storey building structures subjected to sinusoidal ground excitation is examined. The Kryloff-Bogoliuboff method is employed to provide approximate solutions in the amplitude-frequency domain. Structural resisting elements are assumed to exhibit bilinear hysteretic behaviour and coupled response is investigated in terms of both system response as well as individual element ductility requirements. In addition to demonstrating the well-known softening property inherent in yielding systems, the importance of the principal parameters governing coupled response is evaluated in a consistent parametric fashion. Within the context of earthquake resistant building design, the results indicate the absence of amplified response when torsional and translational frequencies are close, in contrast to the much emphasized observation of internal resonance for linear elastic structures. Equally important, structural elements located on the stiff edge of eccentric buildings are found to be only marginally affected by the magnitude of the eccentricity, thus indicating that seismic building codes which reduce design requirements for these elements underestimate actual behaviour substantially.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

The effective period and damping of a class of hysteretic structures

This paper presents the results of a numerical investigation in which the maximum response of six hysteretic systems is calculated for an ensemble of twelve earthquakes. Inelastic response spectra are constructed for a range of response ductility. An effective linear period and damping are calculated for each system and ductility by determining those parameters which minimize an RMS response spectrum error. Conclusions are presented concerning the effects of deterioration, stiffness degradation, cracking and ductility on the effective linear system parameters.     

Base isolation systems for earthquake protection of multi-storey shear structures

This paper is a study of the effectiveness of a wide range of bilinear hysteretic isolation systems in shielding multistorey 2-D shear structures from earthquake excitations. Important parameters of the isolation system are identified and their effect on structure response noted. It is shown that isolation systems can be constructed which allow the structure proper to remain purely elastic even during very strong ground motions. It is further shown that the shear responses and base displacements of structures on these isolation systems can be accurately estimated from elastic response spectra of the forcing earthquakes. The philosophy of structure isolation is discussed and an introduction given to the physical devices currently available to provide it.     

Constant-ductility inelastic displacement ratios for displacement-based seismic design of self-centering structures

This paper focuses on constant-ductility inelastic displacement ratios of self-centering single-degree-of-freedom (SDF) systems with two different levels of energy dissipation capacity, in the presence of 5% viscous damping ratio. A statistical analysis is developed considering an earthquake database composed of 228 ground motions recorded in California with magnitudes greater than six and organized for NEHRP soil class, ground motion duration, and peak ground acceleration. The response of self-centering SDF systems with large variability of initial periods, ductility levels, and postyield stiffness ratios is investigated and compared with the responses of SDF systems with bilinear plastic, Clough, and Takeda hysteresis. The inelastic demand variation with soil class, initial period, postyield stiffness ratio, unloading stiffness degradation, ductility level, and hysteretic behavior is highlighted. Simple and conservative analytical estimates of constant-ductility inelastic displacement ratios for mean and 90th percentile values in terms of initial period, ductility level, and postyield stiffness ratio are proposed to allow the extension of the Displacement-Based Design via Inelastic Displacement Ratio (C_μDBD) to self-centering structural systems.     

Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity

This paper investigates the non-linear seismic behavior of structures such as slender unreinforced masonry shear walls or precast post-tensioned reinforced concrete elements, which have little hysteretic energy dissipation capacity. Even if this type of seismic response may be associated with significant deformation capacity, it is usually not considered as an efficient mechanism to withstand strong earthquakes. The objective of the investigations is to propose values of strength reduction factors for seismic analysis of such structures. The first part of the study is focused on non-linear single-degree-of-freedom (SDOF) systems. A parametric study is performed by computing the displacement ductility demand of non-linear SDOF systems for a set of 164 recorded ground motions selected from the European Strong Motion Database. The parameters investigated are the natural frequency, the strength reduction factor, the post-yield stiffness ratio, the hysteretic energy dissipation capacity and the hysteretic behavior model (four different hysteretic models: bilinear self-centring, with limited or without energy dissipation capacity, modified Takeda and Elastoplastic). Results confirm that the natural frequency has little influence on the displacement ductility demand if it is below a frequency limit and vice versa. The frequency limit is found to be around 2 Hz for all hysteretic models. Moreover, they show that the other parameters, especially the hysteretic behavior model, have little influence on the displacement ductility demand. New relationships between the displacement ductility demand and the strength reduction factor for structures having little hysteretic energy dissipation capacity are proposed. These relationships are an improvement of the equal displacement rule for the considered hysteretic models. In the second part of the investigation, the parametric study is extended to multi-degree-of-freedom (MDOF) systems. The investigation shows that the results obtained for SDOF systems are also valid for MDOF systems. However, the SDOF system overestimates the displacement ductility demand in comparison to the corresponding MDOF system by approximately 15%.     

Evaluation of the structural damage of high‐rise reinforced concrete buildings using ambient vibrations recorded before and after damage

Evaluation of the degrees of structural damage suffered by high‐rise residential buildings after being subjected to strong ground motions is extremely important to the development of life continuity planning for building residents. However, these evaluations cannot be based on strong‐motion records alone, because earthquake observation equipment is not installed in most such buildings in Japan. In this study, we propose simple equations for estimating the stiffness degradation rate and the peak inter‐story drift ratio (PIDR) by using ambient vibration records instead of strong‐motion records when high‐rise RC buildings are subjected to a severe earthquake. More specifically, we propose one equation that relates the square root of the stiffness degradation rate, which is the ratio of natural frequencies at the maximum response to the preliminary tremor response (elastic state), in strong‐motion records with the ratio of natural frequencies identified from ambient vibrations before and after damage was suffered. We also propose an equation that relates the PIDR with the stiffness degradation rate on the basis of the stiffness‐degrading bilinear restoring force characteristic derived from the strong‐motion records of 13 high‐rise buildings for the 1995 Hyogoken‐Nanbu Earthquake (Mw 6.9) and the 2011 Tohoku‐Oki Earthquake (Mw 9.0). Copyright © 2015 John Wiley & Sons, Ltd.     

Shaking table study and modelling of seismic behaviour of confined AAC masonry buildings

The response of autoclaved aerated concrete confined masonry buildings to seismic ground motion has been studied. Three 1:4 scale models of residential buildings with the same distribution of walls in plan but different types of floors and number of stories have been tested on a uni-directional shaking table. Lightweight prefabricated slabs have been installed in the case of the three-storey model M1, whereas reinforced concrete slabs have been constructed in the case of three-storey model M2 and four-storey model M3. Model M1 was subjected to seismic excitation along the axis of symmetry, whereas models M2 and M3 were tested orthogonal to it. Typical storey mechanism, characterised by diagonal shear failure mode of walls in the ground floor in the direction of excitation has been observed in all cases. Taking into consideration the observed behaviour, a numerical model with concentrated masses and storey hysteretic rules has been used to simulate the observed behaviour. Storey resistance curves calculated by a push-over method and hysteretic rules, which take into account damage and energy based stiffness degradation hysteretic rules, have been used to model the non-linear behaviour of the structure. Good agreement between the experimentally observed and calculated non-linear behaviour has been obtained.     

Investigation of story ductility demands of inelastic concrete frames subjected to repeated earthquakes

The present study focuses on the influence of repeated earthquakes on the maximum story ductility demands of three-dimensional inelastic concrete frames. A comprehensive assessment is conducted using generic frames with 3-, 6-, 12-, and 18-story structures. Each is assumed to have behaviour factors of 1.5, 2, 4, and 6 referring to Eurocode 8. Stiffness and strength degrading hysteresis rule to represent reinforced concrete structure is considered in the plastic hinge of members. Twenty ground motions are selected, and single, double, and triple events of synthetic repeated earthquakes are considered. Some interesting findings are provided showing that repeated earthquakes significantly increase the story ductility demand of inelastic concrete frames. On average, relative increment of maximum story ductility demand is experienced 1.4 and 1.3 times when double and triple events of repeated earthquakes are induced, respectively. Empirical relationships are also provided to predict these increments where their efficiency is presented examining characteristic 3- and 8-story reinforced concrete buildings.     

Inelastic torsional response of buildings to the 1985 Mexican earthquake: a parametric study

This study aims to determine the influence of torsional coupling on the inelastic response of a series of models representing typical structural configurations in real buildings. The lake bed (SCT) east-west component of the 1985 Mexico City earthquake was employed in the analysis, and is representative of a severe ground motion known to have induced large inelastic structural deformations in a high proportion of those buildings having asymmetrical distributions of stiffness and/or strength. Material non-linearity in lateral load-resisting elements has been defined using a hysteretic Ramberg-Osgood model. Structural eccentricities have been introduced into the building models by (i) asymmetrical distributions of stiffness and/or strength, (ii) asymmetrical configuration of lateral load-resisting elements, or (iii) varying post-elastic material behaviour in the resisting elements. The dynamic inelastic response of these models has been obtained by a numerical integration of the relevant equations of motion, expressed in a non-dimensional incremental form.

In the elastic range, the results correlate well with those of previous studies. In the inelastic range, it is concluded that the peak ductility demand of the worst-affected element increases with the ground excitation level across the range of building periods considered, and that the influence of torsional coupling on the key response parameters is model dependent. Most significantly, the strength eccentricity relative to the centre of mass has been shown to influence the peak edge displacement response more than conventionally employed stiffness eccentricity.     

A statistical approach to determine 2D optimal equivalent linear parameters with application to earthquake engineering

The equivalent linearization method approximates the maximum displacement response of nonlinear structures through the corresponding equivalent linear system.By using the particle swarm optimization technique,a new statistical approach is developed to determine the key parameters of such an equivalent linear system over a 2D space of period and damping ratio.The new optimization criterion realizes the consideration of the structural safety margin in the equivalent linearization method when applied to the performance-based seismic design/evaluation of engineering structures.As an application,equations for equivalent system parameters of both bilinear hysteretic and stiffness degrading single-degree-offreedom systems are deduced with the assumption of a constant ductility ratio.Error analyses are also performed to validate the proposed approach.     

Duration effect of near-fault pulse-like ground motions and identification of most suitable duration measure

The duration effect of near-fault pulse-like ground motions on structural demands and the identification of most suitable duration measure are systematically addressed in this paper. Firstly, the duration effect of the Mavroeidis & Papageorgiou (M&P) pulse on the normalized maximum displacement and normalized hysteretic energy of elastic-perfectly-plastic, bilinear and rigid-plastic (i.e., Newmark sliding block) single-degree-of-freedom (SDOF) systems is analyzed by using dimensional analysis. Particularly, an intrinsic length scale is proposed to present well the normalized responses. It is shown that the duration effect of M&P pulses on the normalized responses is affected by the frequency ratio and normalized yield displacement. Generally, the duration effect is significant on the normalized hysteretic energy, whereas it is not remarkable on the normalized maximum displacement of ordinary inelastic SDOF systems, except for the normalized sliding displacement of Newmark sliding blocks. Then, a set of 65 spectrally equivalent strongest near-fault ground motions is input to the aforementioned SDOF systems, and the correlation analysis between seismic responses and duration measures is conducted. It is shown that the associated results are consistent with those obtained by dimensional analysis. Moreover, the uniform duration generally presents the best correlation with seismic demands, and thus is identified as the most suitable duration measure. Finally, the correlation statements are further validated on three 5-, 10-, and 20-story shear frame buildings with strength and stiffness degradation under spectrally equivalent ground motions.     

Dynamic response of tipping core buildings

When subjected to major earthquakes, core-stiffened buildings may begin to tip. That is, the overturning moment on the core's footing becomes so large that the footing breaks contact with the ground and begins to rock. A method is described for including the effects of tipping in the analysis of multistorey core-braced structures. Curves are presented which summarize the maximum response to both pulse and earthquake excitations; these data are elucidated via a typical design example. By comparison to fixed-base behaviour, tipping greatly reduces the base shear and moment. This makes possible a more economical design. However, attention must be devoted to avoiding potential soil-mechanics problems associated with the wobbling behaviour of the tipping core.     

Hysteretic model development and seismic response of unbonded post‐tensioned precast CFT segmental bridge columns

The study investigated the cyclic behavior of unbonded, post‐tensioned, precast concrete‐filled tube segmental bridge columns by loading each specimen twice. Moreover, a stiffness‐degrading flag‐shaped (SDFS) hysteretic model was developed based on self‐centering and stiffness‐degrading behaviors. The proposed model overcomes the deficiency of cyclic behavior prediction using a FS model, which self‐centers with fixed elastic and inelastic stiffnesses. Experimental and analytical results showed that (1) deformation capabilities of the column under the first and second cyclic tests were similar; however, energy dissipation capacities significantly differed from each other, and (2) the SDFS model predicted the cyclic response of the column better than the FS model. Inelastic time‐history analyses were performed to demonstrate the dynamic response variability of a single‐degree‐of‐freedom (SDOF) system using both models. A parametric study, performed on SDOF systems subjected to eight historical earthquakes, showed that increased displacement ductility demand was significant for structures with a low period and low‐to‐medium yield strength ratio and reduced displacement ductility demand in these systems was effectively attained by increasing energy dissipation capacity. Copyright © 2008 John Wiley & Sons, Ltd.     

地震动滞回能量谱衰减规律研究

本文选用美国西部California州15次较大地震中的266条强地震动记录,利用衰减关系建立了滞回能量谱,分析了场地条件、延性系数、震级及距离等参数对滞回能量谱的影响。研究发现,场地条件对滞回能量谱影响很大,随着场地变软,滞回能量谱变大,与A B类场地相比,C类场地的滞回能量谱平均要高出70％左右,D类场地则要高出170％左右。随着延性系数的增大,滞回能量谱有增大的趋势,尤其是当延性系数由2变到4或6时更为明显,但当延性系数增加到一定程度时,滞回能量谱的差别不大,延性系数为4和6时的滞回能量谱差别不大,甚至在周期较大时,延性系数为6的滞回能量谱反而小于延性系数为4时的滞回能量谱。另外,研究结果表明,大的震级和小的距离对结构产生比较大的滞回能量需求。利用本文结果,可以估计未来地震中结构物所遭受滞回能量的大小。     

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.     

Residual displacement ratios for assessment of existing structures

Results of an analytical study aimed at evaluating residual displacement ratios, C_r, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.     

Cumulative damage‐based inelastic cyclic demand spectrum

The estimation of cyclic deformation demand resulting from earthquake loads is crucial to the core objective of performance‐based design if the damage and residual capacity of the system following a seismic event needs to be evaluated. A simplified procedure to develop the cyclic demand spectrum for use in preliminary seismic evaluation and design is proposed in this paper. The methodology is based on estimating the number of equivalent cycles at a specified ductility. The cyclic demand spectrum is then determined using well‐established relationships between seismic input energy and dissipated hysteretic energy. An interesting feature of the proposed procedure is the incorporation of a design spectrum into the proposed procedure. It is demonstrated that the force–deformation characteristics of the system, the ductility‐based force‐reduction factor R_μ, and the ground motion characteristics play a significant role in the cyclic demand imposed on a structure during severe earthquakes. Current design philosophy which is primarily based on peak response amplitude considers cyclic degradation only in an implicit manner through detailing requirements based on observed experimental testing. Findings from this study indicate that cumulative effects are important for certain structures, classified in this study by the initial fundamental period, and should be incorporated into the design process. Copyright © 2003 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.