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Abstract
This study explores the inelastic behavior of systems with flexible base. The use of a single degree of freedom system (ESDOF) with equivalent ductility to represent the response of flexible base systems is discussed. Two different equations to compute equivalent ductility are proposed, one which includes the contribution of rigid body components, and other based on the overstrength of the structure. In order to asses the accuracy of ESDOF approach with the proposed equations, the behavior of a 10-story regular building with reinforced concrete (RC) moment resisting frames is studied. Local and global ductility capacity and demands are used to study the modifications introduced by base flexibility. Three soil types are considered with shear wave velocities of 70, 100 and 250 m/s. Soil-foundation stiffness is included with a set of springs on the base (impedance functions). Capacity curves of the building are computed with pushover analysis. In addition, non linear time history analysis are used to asses the ductility demands. Results show that ductility capacity of the soil-structure system including rigid body components is reduced. Base flexibility does not modify neither yield and maximum base shear. Equivalent ductility estimated with the proposed equations is fits better the results of the numerical model than the one considering elastoplastic behavior. Modification of beams ductility demand due to base flexibility are not constant within the structure. Some elements experience reduced ductility demands while other elements experience increments when flexible base is considered. Soil structure interaction produces changes in the relation between yield strength reduction factor and structure ductility demand. These changes are dependent on the spectral shape and the period of the system with fixed and flexible base.

Key Words
dynamic soil structure interaction; inelastic behavior; ductility demands; equivalent single degree of freedom model; RC buildings

Address
Luciano R. Fernandez-Sola and Juan E. Huerta-Ecatl: Departamento de Materiales, Universidad Autónoma Metropolitana-Azcapotzalco, San Pablo #180 Z.C. 02200, Mexico

Abstract
The design of seismically isolated structures considering the stochastic nature of excitations, base isolators\' design parameters, and superstructure properties requires robust reliability analysis methods to calculate the failure probability of the entire system. Here, by applying artificial neural networks, we proposed a robust technique to accelerate the estimation of failure probability of equipped isolated structures. A three-story isolated building with susceptible facilities is considered as the analytical model to evaluate our technique. First, we employed a sensitivity analysis method to identify the critical sources of uncertainty. Next, we calculated the probability of failure for a particular set of random variables, performing Monte Carlo simulations based on the dynamic nonlinear time-history analysis. Finally, using a set of designed neural networks as a surrogate model for the structural analysis, we assessed once again the probability of the failure. Comparing the obtained results demonstrates that the surrogate model can attain precise estimations of the probability of failure. Moreover, our proposed approach significantly increases the computational efficiency corresponding to the dynamic time-history analysis of the structure.

Key Words
seismic reliability; neural network; base isolation; friction pendulum; sensitivity analysis; equipment protection

Address
Hesamaldin Moeindarbari and Touraj Taghikhany: Civil and Environmental Engineering Department Amirkabir University of Technology, Tehran, Iran

Abstract
Computational cost is one of the major obstacles for detailed risk analysis of structures. This paper puts forward a methodology for efficient probabilistic seismic loss assessment of structures using the Endurance Time (ET) analysis and the first-order reliability method (FORM). The ET analysis efficiently yields the structural responses for a continuous range of intensities through a single response-history analysis. Taking advantage of this property of ET, FORM is employed to estimate the annual rate of exceedance for the loss components. The proposed approach is an amalgamation of two analysis approaches, ET and FORM, that significantly lower the computational costs. This makes it possible to evaluate the seismic risk of complex systems. The probability distribution of losses due to the structural and non-structural damage as well as injuries and fatalities of a prototype structure are estimated using the proposed methodology. This methodology is an alternative to the prevalent risk analysis framework of the total probability theorem. Hence, the risk estimates of the proposed approach are compared with those from the total probability theorem as a benchmark. The results indicate a satisfactory agreement between the two methods while a significantly lower computational demand for the proposed approach.

Key Words
seismic risk; loss; life-cycle cost; endurance time method; reliability method; FORM

Address
Mohammad Ch. Basim: Department of Civil Engineering, Sahand University of Technology, Tabriz, Iran Homayoon E. Estekanchi and Mojtaba Mahsuli: Department of Civil Engineering, Sharif University of Technology, Tehran, Iran

Abstract
Earthquakes have shown the vulnerability of unreinforced masonry (URM) structures. The aim of this research is to study a technique for in-plane seismic retrofitting of URM walls in which both diagonal and vertical steel strips are added to a single side of a URM wall. Specimens have been tested under quasi-static cyclic lateral load in combination with constant vertical load. The tests show that vertical and diagonal strips cause a significant increase in seismic capacity in terms of both strength (about 200%) and displacement at maximum (about 20%). Furthermore, this technique caused the failure modes of URM walls were influenced.

Key Words
seismic retrofit; clay brick; URM walls; vertical and diagonal steel strips; lateral strength and ductility

Address
Abbas Darbhanzi: College of Engineering, Vali-e-Asr University of Rafsanjan, Iran Mohammad S. Marefat, Mohammad Khanmohammadi, Amin Moradimanesh and Hamid Zare: School of Civil Engineering, College of Engineering, University of Tehran, Iran

Abstract
Reducing response of buildings during earthquakes by mass dampers, has been examined in many articles and books. Nowadays, many researchers are trying to realistically examine this type of dampers by new methods of performance. In this paper, for the better study of tuned mass damper (TMD), two schematic models are presented for a passive TMD with softening stiffness (softening TMD) and a passive TMD with hardening stiffness (hardening TMD). Then by modeling and analysis of the damper on a single degree of freedom (SDOF) structure and an 11-story steel building, the dampers performance was evaluated. State space was used for damper and structure modeling and to solve nonlinear equations, the Newton-Raphson method was used. The results show that when the structure is subjected to the Chi-Chi earthquake, response of the sixth floor in the system without TMD reduces 54.0% in comparison to the structure with softening TMD. This percentage of reduction for hardening TMD is 55.0%. Also for the Tabas earthquake, reduction in the RMS acceleration of the sixth floor in the system with hardening TMD is 96.2% more than the structure without TMD. This percentage of reduction for hardening TMD is 96.3%.

Key Words
softening damper; hardening damper; tuned mass damper; geometrically nonlinear behaviour; nonlinear analyses

Address
Mohammad Khalil Khalili and Karim Badamchi: Department of Civil Engineering, University of Tabriz, 29 Bahman Blvd, Tabriz 51666-16471, Iran

Abstract
The seismic vulnerability of skewed bridges had been observed in many past earthquakes. Researchers have found that the in-plane rotation of the girders was one of the main reasons for the vulnerability of these types of bridges. To date, not many experimental works have been done on this topic, especially those including pounding between adjacent structures. In this study, shake table tests were performed on a bridge-abutment system consisting of a straight, 30o, and 45o bridge with and without considering pounding. Skewed bridges with the same fundamental frequency and those having the same girder mass as the straight bridge were studied. Under the loadings considered, skewed bridges with the same frequency as the straight tend to have smaller responses than those with the same mass. The average maximum bending moment developed in the piers of the 30o bridge with the same mass as that of the straight when pounding was not considered was 1.6 times larger than when the frequencies were the same. It was also found that the NZTA recommendations for the seat lengths of skewed bridges could severely underestimate the relative displacements of these types of bridges in the transverse direction, especially when pounding occurs. In the worst case, the average transverse displacement of the 45o bridge was about 2.6 times the longitudinal displacement of the straight, which was greatly over the limit suggested by the NZTAof 1.25 times.

Key Words
skewed bridge; pounding; shake table testing; girder unseating; bridge-abutment system

Address
Chern Kun, Ziqi Yang and Nawawi Chouw: Department of Civil and Environmental Engineering, Faculty of Engineering, The University of Auckland, 20 Symonds Street, Auckland 1010, New Zealand

Abstract
Recently, the adaptive nonlinear static analysis method has been widely used in the field of performance based earthquake engineering. However, the proposed methods are almost deterministic and cannot directly consider the seismic record uncertainties. In the current study an innovative Stochastic Adaptive Pushover Analysis, called \"SAPA\", based on equivalent hysteresis system responses is developed to consider the earthquake record to record uncertainties. The methodology offers a direct stochastic analysis which estimates the seismic demands of the structure in a probabilistic manner. In this procedure by using a stochastic linearization technique in each step, the equivalent hysteresis system is analyzed and the probabilistic characteristics of the result are obtained by which the lateral force pattern is extracted and the actual structure is pushed. To compare the results, three different types of analysis have been considered; conventional pushover methods, incremental dynamic analysis, IDA, and the SAPA method. The result shows an admirable accuracy in predicting the structure responses.

Key Words
Bouc-Wen model; stochastic adaptive pushover; stochastic linearization; extreme value

Address
Mohammad Jafari and Masoud Soltani: Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran

Abstract
With the further increase of span length, the cable-stayed bridge tends to be more slender, and becomes more susceptible to the seismic action. By taking a super long-span cable-stayed bridge with main span of 1400m as example, structural response of the bridge under the E1 horizontal and vertical seismic excitations is investigated numerically by the multimode seismic response spectrum and time-history analysis respectively, the seismic behavior and also the effect of structural nonlinearity on the seismic response of super long-span cable-stayed bridge are revealed. Furthermore, the effect of structural parameters including the girder depth and width, the tower structural style, the tower height-to-span ratio, the side-tomain span ratio, the auxiliary piers in side spans and the anchorage system of stay cables etc on the seismic performance of super long-span cable-stayed bridge is investigated numerically by the multimode seismic response spectrum analysis, and the favorable earthquake-resistant structural system of super long-span cable-stayed bridge is proposed.

Key Words
super long-span cable-stayed bridge; seismic performance; multimode seismic response spectrum analysis; time-history analysis; structural parameters

Address
Xin-Jun Zhang, Chen-Yang Zhao and Jian Guo: College of Civil Engineering & Architecture, Zhejiang University of Technology, Hangzhou 310023, P.R. China

Abstract
Static pushover analyses of typical existing reinforced concrete frames, designed according to the previous generations of design codes in Greece, have established these structures\' inelastic characteristics, namely overstrength, global ductility capacity and available behaviour factor q, under planar response. These were compared with the corresponding demands at the collapse limit state target performance point. The building stock considered accounted for the typical variability, among different generations of constructed buildings in Greece, in the form, the seismic design code in effect and the material characteristics. These static pushover analyses are extended, in the present study, in the time history domain. Consequently, the static analysis predictions are compared with Incremental Dynamic Analysis results herein, using a large number of spectrum compatible recorded base excitations of recent destructive earthquakes in Greece and abroad, following, for comparison, similar conventional limiting failure criteria as before. It is shown that the buildings constructed in the 70s exhibit the least desirable behaviour, followed by the buildings constructed in the 60s. As the seismic codes evolved, there is a notable improvement for buildings of the 80s, when the seismic code introduced end member confinement and the requirement for a joint capacity criterion. Finally, buildings of the 90s, designed to modern codes exhibit an exceptionally good performance, as expected by the compliance of this code to currently enforced seismic provisions worldwide.

Key Words
existing RC buildings; seismic design code; comparative analysis; nonlinear dynamic analysis; performance evaluation; ductility; behaviour factor

Address
Christos A. Zeris: Department of Civil Engineering, National Technical University of Athens, University Campus, Zografou 15780, Greece Constantinos C. Repapis: Department of Civil Engineering, University of West Attica, 250 Thivon and Petrou Ralli Str., Egaleo 12244, Greece

Abstract
This study presents a new beam-column model comprising material nonlinearity and joint flexibility to predict the nonlinear response of reinforced concrete structures. The nonlinear behavior of connections has an outstanding role on the nonlinear response of reinforced concrete structures. In presented research, the joint flexibility is considered applying a rotational spring at each end of the member. To derive the moment-rotation behavior of beam-column connections, the relative rotations produced by the relative slip of flexural reinforcement in the joint and the flexural cracking of the beam end are taken into consideration. Furthermore, the considered spread plasticity model, unlike the previous models that have been developed based on the linear moment distribution subjected to lateral loads includes both lateral and gravity load effects, simultaneously. To confirm the accuracy of the proposed methodology, a simply-supported test beam and three reinforced concrete frames are considered. Pushover and nonlinear dynamic analysis of three numerical examples are performed. In these examples the nonlinear behavior of connections and the material nonlinearity using the proposed methodology and also linear flexibility model with different number of elements for each member and fiber based distributed plasticity model with different number of integration points are simulated. Comparing the results of the proposed methodology with those of the aforementioned models describes that suggested model that only uses one element for each member can appropriately estimate the nonlinear behavior of reinforced concrete structures.

Key Words
material nonlinearity; joint flexibility; spread plasticity; lateral load; gravity load

Address
Mehdi Izadpanah: Department of Civil Engineering, Kangavar Branch, Islamic Azad University, Kangavar, Iran AliReza Habibi: Department of Civil Engineering, Shahed University, Tehran, Iran

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