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CONTENTS
Volume 10, Number 5, May 2016
 

Abstract
The structural dynamic behavior and yield strength considering both ductility and strain rate effects are analyzed in this article. For the single-degree-of-freedom (SDOF) system, the relationship between the relative velocity and the strain rate response is deduced and the strain rate spectrum is presented. The ductility factor can be incorporated into the strain rate spectrum conveniently based on the constant-ductility velocity response spectrum. With the application of strain rate spectrum, it is convenient to consider the ductility and strain rate effects in engineering practice. The modal combination method, i.e., square root of the sum of the squares (SRSS) method, is employed to calculate the maximum strain rate of the elastoplastic multiple-degree-of-freedom (MDOF) system under uniform excitation. Considering the spatially varying ground motions, a new response spectrum method is developed by incorporating the ductility factor and strain rate into the conventional response spectrum method. In order to further analyze the effects of strain rate and ductility on structural dynamic behavior and yield strength, the cantilever beam (one-dimensional) and the triangular element (two-dimensional) are taken as numerical examples to calculate their seismic responses in time domain. Numerical results show that the permanent displacements with and without considering the strain rate effect are significantly different from each other. It is not only necessary in theory but also significant in engineering practice to take the ductility and strain rate effects into consideration.

Key Words
strain rate effect; ductility effect; multiple-support earthquake excitations; strain rate spectrum; response spectrum method

Address
Guohuan Liu, Jijian Lian, Chao Liang: State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, 300072, Tianjin, China

Guohuan Liu, Jijian Lian, Chao Liang: School of Civil Engineering, Tianjin University, 300072, Tianjin, China

Mi Zhao: College of Architecture and Civil Engineering, Beijing University of Technology, 100124, Beijing, Chin

Abstract
Several historical earthquakes demonstrated that local amplification and soil nonlinearity are responsible for the uneven damage pattern of the structures and lifelines. On April 25th 2015 the Mw7.8 Gorkha earthquake stroke Nepal and neighboring countries, and caused extensive damages throughout Kathmandu valley. In this paper, comparative studies between equivalent-linear and nonlinear seismic site response analyses in five affected strategic locations are performed in order to relate the soil behavior with the observed structural damage. The acceleration response spectra and soil amplification are compared in both approaches and found that the nonlinear analysis better represented the observed damage scenario. Higher values of peak ground acceleration (PGA) and higher spectral acceleration have characterized the intense damage in three study sites and the lower values have also shown agreement with less to insignificant damages in the other two sites. In equivalent linear analysis PGA varies between 0.29 to 0.47 g, meanwhile in case of nonlinear analysis it ranges from 0.17 to 0.46 g. It is verified from both analyses that the PGA map provided by the USGS for the southern part of Kathmandu valley is not properly representative, in contrary of the northern part. Similarly, the peak spectral amplification in case of equivalent linear analysis is estimated to be varying between 2.3 to 3.8, however in case of nonlinear analysis, the variation is observed in between 8.9 to 18.2. Both the equivalent linear and nonlinear analysis have depicted the soil fundamental period as 0.4 and 0.5 sec for the studied locations and subsequent analysis for seismic demands are correlated.

Key Words
site response analysis; structural damage; EERA; NERA; seismic demand; Gorkha Earthquake; Kathmandu valley

Address
Dipendra Gautam: Structural and Earthquake Engineering Research Institute, Kathmandu, Nepal

Giovanni Forte: DICEA Department, Università degli Studi di Napoli Federico II, Naples, Italy

Hugo Rodrigues: RISCO, School of Technology and Management, Polytechnic Institute of Leiria, Leiria, Portugal

Abstract
An analytical solution based on the neutral surface concept is developed to study the free vibration behavior of simply supported functionally graded plate reposed on the elastic foundation by taking into account the effect of transverse shear deformations. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain obtained by using a new refined shear deformation theory. The foundation is described by the Winkler-Pasternak model. The Young´s modulus of the plate is assumed to vary continuously through the thickness according to a power law formulation, and the Poisson ratio is held constant. The equation of motion for FG rectangular plates resting on elastic foundation is obtained through Hamilton´s principle. Numerical examples are provided to show the effect of foundation stiffness parameters presented for thick to thin plates and for various values of the gradient index, aspect and side to thickness ratio. It was found that the proposed theory predicts the fundamental frequencies very well with the ones available in literature.

Key Words
functionally graded material; analytical solution; free vibration analysis; neutral surface concept; elastic foundation

Address
Rabia Benferhat, Mohamed Said Mansour: Laboratoire de Géomatériaux, Département de Génie Civil, Université de Chlef, Algérie

Tahar Hassaine Daouadji, Lazreg Hadji: Département de Génie Civil, Université Ibn Khaldoun, BP 78 Zaaroura, 14000 Tiaret, Algérie

Abstract
An approximate analysis is presented for multi-story setback buildings subjected to ground motions. Setback buildings with mass and stiffness discontinuities are common in modern architecture and quite often they are asymmetric in plan. The proposed analysis provides basic dynamic data (frequencies and peak values of base resultant forces) and furthermore an overview of the building response during a ground excitation. The method is based on the concept of the equivalent single story system, which has been introduced by the author in earlier papers for assessing the response of uniform in height buildings. As basic quantities of the dynamic response of elastic setback buildings can be derived by analyzing simple systems, a structural layout of minimum elastic rotational response can be easily constructed. The behavior of such structural configurations, which is basically translational into the elastic phase, is also examined into the post elastic phase when the strength assignment of the various bents is based on a planar static analysis under a set of lateral forces simulating an equivalent ´seismic loading´. It is demonstrated that the almost concurrent yielding of all resisting elements preserves the translational response, attained at the end of the elastic phase, to the post elastic one.

Key Words
setback buildings; modal analysis; eccentric structures; modal centre of rigidity; inelastic analysis

Address
George K. Georgoussis: Department of Civil Engineering, School of Pedagogical and Technological Education (ASPETE), N. Heraklion 14121, Attica, Greece

Abstract
In this paper, a decoupled proportional-integral-derivative (PID) control approach for seismic control of smart structures is presented. First, the state space equation of a structure is transformed into modal coordinates and parameters of the modal PID control are separately designed in a reduced modal space. Then, the feedback gain matrix of the controller is obtained based on the contribution of modal responses to the structural responses. The performance of the controller is investigated to adjust control force of piezoelectric friction dampers (PFDs) in a benchmark base isolated building. In order to tune the modal feedback gain of the controller, a suitable trade-off among the conflicting objectives, i.e., the reduction of maximum modal base displacement and the maximum modal floor acceleration of the smart base isolated structure, as well as the maximum modal control force, is created using a multi-objective cuckoo search (MOCS) algorithm. In terms of reduction of maximum base displacement and story acceleration, numerical simulations show that the proposed method performs better than other reported controllers in the literature. Moreover, simulation results show that the PFDs are able to efficiently dissipate the input excitation energy and reduce the damage energy of the structure. Overall, the proposed control strategy provides a simple strategy to tune the control forces and reduces the number of sensors of the control system to the number of controlled stories.

Key Words
seismic control; smart base isolated structures; piezoelectric friction dampers; multiobjective cuckoo search; PID controller

Address
Sadegh Etedali: Department of Civil Engineering, Birjand University of Technology, P.O. Box 97175-569, Birjand, Iran

Saeed Tavakoli: Faculty of Electrical and Computer Engineering, University of Sistan and Baluchestan, Zahedan, Iran

Mohammad Reza Sohrabi: Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran

Abstract
Modified two-surface model (M2SM) is one of the steel elasto-plastic hysteretic constitutive models that consider both analysis accuracy and efficiency. However, when M2SM is used for complex strain history, sometimes the results are irrational due to the limitation of stress-strain path judgment. In this paper, the defect of M2SM was re-modified by improving the judgment of stress-strain paths. The accuracy and applicability of the improved method were verified on both material and structural level. Based on this improvement, the nonlinear time-history analysis was carried out for a deck-through steel arch bridge with a 200 m-long span under the ground motions of Chi-Chi earthquake and Niigata earthquake. In the analysis, we compared the results obtained by hysteretic constitutive models of improved two-surface model (I2SM) presented in this paper, M2SM and the bilinear kinematic hardening model (BKHM). Results show that, although the analysis precision of displacement response of different steel hysteretic models differs little from each other, the stress-strain responses of the structure are affected by steel hysteretic models apparently. The difference between the stress-strain responses obtained by I2SM and M2SM cannot be neglected. In significantly damaged areas, BKHM gives smaller stress result and obviously different strain response compared with I2SM and M2SM, and tends to overestimate the effect of hysteretic energy dissipation. Moreover, at some position with severe damage, BKHM may underestimate the size of seismic damaged areas. Different steel hysteretic models also have influences on structural damage evaluation results based on deformation behavior and low cycle fatigue, and may lead to completely different judgment of failure, especially in severely damaged areas.

Key Words
hysteretic constitutive model; modified two-surface model; steel arch bridge; fiber model; seismic response; damage evaluation

Address
Tong Wang, Xu Xie, Zhanzhan Tang: College of Architecture & Civil Engineering, Zhejiang University, Hangzhou 310058, China

Chi Shen: International Project Group, Chodai Co., Ltd., Ibaraki 305-0812, Japan

Abstract
To study seismic performance of steel frame-bent structure, one specimen with one-tenth scale, three-bay, and five-story was tested under reversed cyclic lateral load. The entire loading process and failure mode were observed, and the seismic performance indexes including hysteretic loops, skeleton curve, ductility, load bearing capacity, drift ratio, energy dissipation capacity and stiffness degradation were analyzed. The results show that the steel frame-bent structure has good seismic performance. And the ductility and the energy dissipation capacity were good, the hysteresis loops were in spindle shape, which shape were full and had larger area. The ultimate elastic-plastic drift ratio is larger than the limit value specified by seismic code, showing the high capacity of collapse resistance. It can be helpful to design this kind of structure in high-risk seismic zone.

Key Words
steel; frame-bent structure; cyclic lateral load; seismic performance; ductility

Address
Jiongfeng Liang, Lian S.Gu and Ming H. Hu: Faculty of Civil & Architecture Engineering, East China Institute of Technology, Nanchang 330013, China

Jiongfeng Liang: Guangxi Key Laboratory of Disaster Prevention and Structural Safety, Guangxi University, Nanning 530004, China

Abstract
The direct displacement based design (DDBD) approach is spreading in the field of seismic design for many types of structures. This paper is carried out to present a robust approach for the DDBD procedure for single degree of freedom (SDOF) concentrically braced frames (CBFs). Special attention is paid to the choice of an equivalent viscous damping (EVD) model that represents the behaviour of a series of full scale shake table tests. The performance of the DDBD methodology of the CBFs is verified by two ways. Firstly, by comparing the DDBD results with a series of full-scale shake table tests. Secondly, by comparing the DDBD results with a quantified nonlinear time history analysis (NLTHA). It is found that the DDBD works relatively well and could predict the base shear forces (Fb) and the required brace cross sectional sizes of the actual values obtained from shake table tests and NLTHA. In other words, when comparing the ratio of Fb estimated from the DDBD to the measured values in shake table tests, the mean and coefficient of variation (CV) are found to be 1.09 and 0.12, respectively. Moreover, the mean and CV of the ratios of Fb estimated from the DDBD to the values obtained from NLTHA are found to be 1.03 and 0.12, respectively. Thus, the DDBD methodology presented in this paper has been shown to give accurate and reliable results.

Key Words
concentrically braced frames; displacement based design; shake table tests; nonlinear time history analysis; seismic design; equivalent viscous damping

Address
Suhaib Salawdeh and Jamie Goggins: Civil Engineering, College of Engineering & Informatics, National University of Ireland, Galway, Ireland

Suhaib Salawdeh and Jamie Goggins: Centre for Marine and Renewable Energy Ireland (MaREI), Galway, Ireland

Jamie Goggins: Ryan Institute, Galway, Ireland

Abstract
Offshore wind turbines are considered as a fundamental part to develop substantial, alternative energy sources. In this highly flexible structures, monopiles are usually used as support foundations. Since the monopiles are large diameter (3.5 to 7 m) deep foundations, they result in extremely stiff short monopiles where the slenderness (length to diameter) may range between 5 and 10. Consequently, their elastic deformation patterns under lateral loading differ from those of small diameter monopiles usually employed for supporting structures in offshore oil and gas industry. For this reason, design recommendations (API and DNV) are not appropriate for designing foundations for offshore wind turbine structures as they have been established on the basis of full-scale load tests on long, slender and flexible piles. Furthermore, as these facilities are very sensitive to rotations and dynamic changes in the soil-pile system, the accurate prediction of monopile head displacement and rotation constitutes a design criterion of paramount importance. In this paper, the Fourier Series Aided Finite Element Method (FSAFEM) is employed for the determination of static impedance functions of monopiles for OWT subjected to horizontal force and/or to an overturning moment, where a non-homogeneous soil profile has been considered. On the basis of an extensive parametric study, and in order to address the problem of head stiffness of short monopiles, approximate analytical formulae are obtained for lateral stiffness KL, rotational stiffness KR and cross coupling stiffness KLR for both rough and smooth interfaces. Theses expressions which depend only on the values of the monopile slenderness L⁄Dp rather than the relative soil/monopile rigidity Ep ⁄Es usually found in the offshore platforms designing codes (DNV code for example) have been incorporated in the expressions of the OWT natural frequency of four wind farm sites. Excellent agreement has been found between the computed and the measured natural frequencies.

Key Words
semi-analytical FE analysis; laterally loaded short monopiles; monopile head stiffnesses; offshore wind turbines; natural frequency

Address
Younes Abed, Djillali Amar Bouzid: Department of Civil Engineering, Faculty of Technology, University Saad Dahled of Blida, Route de Soumaa, Blida 09000, Algeria

Subhamoy Bhattacharya: Department of Civil and Environmental Engineering, Tomas Telford Building, University of Surrey, Surrey GU2 7HX, UK

Mohammed H. Aissa: Department of Material Engineering, Faculty of Sciences and Technology, University of Médéa, Quartier Ain
D´hab, Medea 26000, Algeria

Abstract
Fragility and loss functions are developed to predict damage and economic losses due to earthquake loading in Reinforced Concrete (RC) structural components with smooth rebars. The attention is focused on external/internal beam-column joints and ductile/brittle weak columns, designed for gravity loads only, using low-strength concrete and plain steel reinforcing bars. First, a number of damage states are proposed and linked deterministically with commonly employed methods of repair and related activities. Results from previous experimental studies are used to develop empirical relationships between damage states and engineering demand parameters, such as interstory and column drift ratios. Probability distributions are fit to the empirical data and the associated statistical parameters are evaluated using statistical methods. Repair costs for damaged RC components are then estimated based on detailed quantity survey of a number of pre-70 RC buildings, using Italian costing manuals. Finally, loss functions are derived to predict the level of monetary losses to individual RC components as a function of the experienced response demand.

Key Words
fragility functions; damage states; RC frame buildings; beam-column joints; weak columns; smooth reinforcing bars; repair methods; repair costs; loss functions; FEMA P-58

Address
School of Engineering, University of Basilicata, Viale Ateneo Lucano 10, 85100 Potenza, Italy

Abstract
This paper investigates the response of nonstructural components in the presence of nonlinear behavior of the primary structure considering the near-fault pulse-like ground motions. A database of 81 near-fault pulse-like ground motions is used to examine the effect of these ground motions on the response of nonstructural components. For comparison, a database of 573 non-pulse-like ground motions selected from the PEER database is also employed. The effects of peak ground velocity (PGV), maximum incremental velocity (MIV), primary structural degrading behavior and damping of nonstructural components are evaluated and discussed statistically. Results are presented in terms of amplification factor which quantifies the effect of inelastic deformations of the primary structure on subsystem responses. The results indicate that the near-fault pulse-like ground motions can significantly increase the amplification factors of nonstructural components with primary structural period and the magnitude of increase can reach 17%. The effect of PGV and MIV on amplification factors tends to increase with the increase of primary structural ductility. The near-fault pulse-like ground motions are more dangerous to components supported by structures with strength and stiffness degrading behavior than ordinary ground motions. A new simplified formulation is proposed for the application of amplification factors for design of nonstructural components for near-fault pulse-like ground motions.

Key Words
floor response spectra; nonstructural components; near-fault pulse-like ground motions; inelastic seismic behavior; seismic design

Address
Chang-Hai Zhai, Zhi Zheng, Shuang Li, Xiaolan Pan and Li-Li Xie: School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China

Chang-Hai Zhai, Shuang Li: Key Lab of Structures Dynamic Behavior and Control (Harbin Institute of Technology), Ministry of Education, Heilongjiang, Harbin, 150090, China

Li-Li Xie: Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China

Abstract
In this paper, it is aimed to determine the stochastic response of a suspension bridge subjected to spatially varying ground motions considering the geometric nonlinearity. Bosphorus Suspension Bridge built in Turkey and connects Europe to Asia in Istanbul is selected as a numerical example. The spatial variability of the ground motion is considered with the incoherence, wave-passage and site-response effects. The importance of site-response effect which arises from the difference in the local soil conditions at different support points of the structure is also investigated. At the end of the study, mean of the maximum and variance response values obtained from the spatially varying ground motions are compared with those of the specialised cases of the ground motion model. It is seen that each component of the spatially varying ground motion model has important effects on the dynamic behaviour of the bridge. The response values obtained from the general excitation case, which also includes the site-response effect causes larger response values than those of the homogeneous soil condition cases. The variance values calculated for the general excitation case are dominated by dynamic component at the deck and Asian side tower. The response values obtained for the site-response effect alone are larger than the response values obtained for the incoherence and wavepassage effects, separately. It can be concluded that suspension bridges are sensitive to the spatial variability of ground motion. Therefore, the incoherence, the wave-passage and especially the site-response effects should be considered in the stochastic analysis of this type of engineering structures.

Key Words
suspension bridge; spatially varying ground motion; incoherence effect; wave-passage effect; site-response effect; geometric nonlinearity

Address
Süleyman Adanur, Ahmet C. Altunisik, Alemdar Bayraktar: Department of Civil Engineering, Karadeniz Technical University, Trabzon, Turkey

Kurtuluş Soyluk: Department of Civil Engineering, Gazi University, Ankara, Turkey

A. Aydin Dumanoglu: Department of Civil Engineering, Canik Başar


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