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Abstract
In the present study, exterior beam column sub-assemblages are designed in accordance with the codal stipulations prevailed at different times prior to the introduction of modern seismic provisions, viz., i) Gravity load designed with straight bar anchorage (SP1), ii) Gravity load designed with compression anchorage (SP1-D), iii) designed for seismic load but not detailed for ductility (SP2), and iv) designed for seismic load and detailed for ductility (SP3). Comparative seismic performance of these exterior beam-column sub-assemblages are evaluated through experimental investigations carried out under repeated reverse cyclic loading. Seismic performance parameters like load-displacement hysteresis behavior, energy dissipation, strength and stiffness degradation, and joint shear deformation of the specimens are evaluated. It is found from the experimental studies that with the evolution of the design methods, from gravity load designed to non-ductile and then to ductile detailed specimens, a marked improvement in damage resilience is observed. The gravity load designed specimens SP1 and SP1-D respectively dissipated only one-tenth and one-sixth of the energy dissipated by SP3. The specimen SP3 showcased tremendous improvement in the energy dissipation capacity of nearly 2.56 times that of SP2. Irrespective of the level of design and detailing, energy dissipation is finally manifested through the damage in the joint region. The present study underlines the seismic deficiency of beam-column sub-assemblages of different design evolutions and highlights the need for their strengthening/retrofit to make them fit for seismic event.

Key Words
beam-column sub-assemblage; seismic design; ductile detailing; energy dissipation; strength degradation; shear deformation

Address
A. Kanchana Devi and K. Ramanjaneyulu: CSIR-Structural Engineering Research Centre, Chennai, 600113, Tamil Nadu, India A. Kanchana Devi and K. Ramanjaneyulu: Academy of Scientific and Innovative Research (AcSIR), Chennai, 600113, Tamil Nadu, India

Abstract
To overcome the difficulty of performing multi-point response spectrum analysis for engineering structures under spatially varying ground motions (SVGM) using the general finite element code such as ANSYS, an approach has been developed by improving the modelling of the input ground motions in the spectral analysis. Based on the stochastic vibration analyses, the cross-power spectral density (c-PSD) matrix is adopted to model the stationary SVGM. The design response spectra are converted into the corresponding PSD model with appropriate coherency functions and apparent wave velocities. Then elements of c-PSD matrix are summarized in the row and the PSD matrix is transformed into the response spectra for a general spectral analysis. A long-span high-pier bridge under multiple support excitations is analyzed using the proposed approach considering the incoherence, wave-passage and site-response effects. The proposed approach is deemed to be an efficient numerical method that can be used for seismic analysis of large engineering structures under SVGM.

Key Words
response spectral analysis; multiple support excitation; stochastic vibration analysis; high-pier railway bridge; seismic spatial variability

Address
Lanping Li, Yizhi bu, Hongyu Jia, Shixiong Zheng and Deyi Zhang: Department of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China Hongyu Jia: The Key Laboratory of Urban Security and Disaster Engineering, Beijing University of Technology, Beijing 100124, China Kaiming Bi: Center for Infrastructure Monitoring and Protection, School of Civil Engineering and Mechanics, Curtin University, Kent St, Bentley, WA 6102, Australia

Abstract
This work aims to analyze the thermo-viscoelastic interaction in an orthotropic solid cylinder. The medium is considered to be variable thermal conductivity and subjected to temperature pulse. Analytical solution based on dual-phase-lags model with Voigt-type for behavior of viscoelastic material has been effectively proposed. All variables are deduced using method of Laplace transforms. Numerical results for different distribution fields, such as temperature, displacement and stress components are graphically presented. Results are discussed to illustrate the effect of variability thermal conductivity parameter as well as phase-lags and viscoelasticity on the field quantities. Results are obtained when the viscosity is ignored with and without considering variability of thermal conductivity. A comparison study is made and all results are investigated.

Key Words
thermoviscelasticity; orthotropic medium; solid cylinder; temperature pulse; variable thermal conductivity; dual-phase-lags

Address
A.E. Abouelregal: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt A.M. Zenkour: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia A.M. Zenkour: Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

Abstract
Observations from past strong earthquakes revealed that near-fault ground motions could lead to the failure, or even collapse of electricity transmission towers which are vital components of an overhead electric power delivery system. For assessing the performance and robustness, a high-fidelity three-dimension finite element model of a long span transmission tower-line system is established with the consideration of geometric nonlinearity and material nonlinearity. In the numerical model, the Tian-Ma-Qu material model is utilized to capture the nonlinear behaviours of structural members, and the cumulative damage D is defined as an index to identify the failure of members. Consequently, incremental dynamic analyses (IDAs) are conducted to study the collapse fragility, damage positions, collapse margin ratio (CMR) and dynamic robustness of the transmission towers by using twenty near-fault ground motions selected from PEER. Based on the bending and shear deformation of structures, the collapse mechanism of electricity transmission towers subjected to Chi-Chi earthquake is investigated. This research can serve as a reference for the performance of large span transmission tower line system subjected to near-fault ground motions.

Key Words
long span transmission tower-line system; collapse simulation; near-fault ground motion; collapse fragility; collapse mechanism

Address
Li Tian, Haiyang Pan, Ruisheng Ma and Canxing Qiu: School of Civil Engineering, Shandong University, Jinan, Shandong, 250061, China Ruisheng Ma: Centre for Infrastructure Monitoring and Protection, School of Civil and Mechanical Engineering, Curtin University, Kent Street, Bentley, WA 6102, Australia

Abstract
One of the important phases of probabilistic performance-based methodology is establishing appropriate probabilistic seismic demand models (PSDMs). These demand models relate ground motion intensity measures (IMs) to demand measures (DMs). The objective of this paper is selection of the optimal IMs in probabilistic seismic demand analysis (PSDA) of the RC high-rise buildings. In selection process features such as: efficiency, practically, proficiency and sufficiency are considered. RC high-rise buildings with core wall structural system are selected as a case study building class with the three characteristic heights: 20-storey, 30-storey and 40-storey. In order to determine the most optimal IMs, 720 nonlinear time-history analyses are conducted for 60 ground motion records with a wide range of magnitudes and distances to source, and for various soil types, thus taking into account uncertainties during ground motion selection. The non-linear 3D models of the case study buildings are constructed. A detailed regression analysis and statistical processing of results are performed and appropriate PSDMs for the RC high-rise building are derived. Analyzing a large number of results it are adopted conclusions on the optimality of individual ground motion IMs for the RC high-rise building.

Key Words
RC high-rise building; probabilistic seismic demand model; intensity measure; optimality; nonlinear time-history analysis, regression analysis

Address
Jelena R. Pejovic, Nina N. Serdar and Radenko R. Pejovic: Faculty of Civil Engineering, University of Montenegro, Podgorica, Montenegro

Abstract
Fundamental period is one of the most critical parameters affecting the seismic design of buildings. In this paper, a very simple approach is presented for estimating the fundamental period of multiple-degree-of-freedom (MDOF) structures. The basic idea behind this approach is to replace the complicated MDOF system with an equivalent single-degree-of-freedom (SDOF) system. To realize this equivalence, a procedure for replacing a two-degree-of-freedom (2-DOF) system with an SDOF system, known as a two-to-single (TTS) procedure, is developed first; then, using the TTS procedure successively, an MDOF system is replaced with an equivalent SDOF system. The proposed approach is expressed in terms of mass, stiffness, and number of stories, without mode shape or any other parameters; thus, it is a very simple method. The accuracy of the proposed method is investigated by estimating the fundamental periods of many MDOF models; it is found that the results obtained by the proposed method agree very well with those obtained by eigenvalue analysis.

Key Words
fundamental-period estimation; seismic design; MDOF structures; TTS procedure; equivalent SDOF system

Address
Yan-Gang Zhao, Haizhong Zhang and Takasuke Saito: Department of Architecture, Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama 221-8686, Japan

Abstract
In this paper, dynamic response of the horizontal nanofiber reinforced polymer (NFRP) strengthened concrete beam subjected to seismic ground excitation is investigated. The concrete beam is modeled using hyperbolic shear deformation beam theory (HSDBT) and the mathematical formulation is applied to determine the governing equations of the structure. Distribution type and agglomeration effects of carbon nanofibers are considered by Mori-Tanaka model. Using the nonlinear strain-displacement relations, stress-strain relations and Hamilton\'s principle (virtual work method), the governing equations are derived. To obtain the dynamic response of the structure, harmonic differential quadrature method (HDQM) along with Newmark method is applied. The aim of this study is to investigate the effect of NFRP layer, geometrical parameters of beam, volume fraction and agglomeration of nanofibers and boundary conditions on the dynamic response of the structure. The results indicated that applied NFRP layer decreases the maximum dynamic displacement of the structure up to 91 percent. In addition, using nanofibers as reinforcement leads a 35 percent reduction in the maximum dynamic displacement of the structure.

Key Words
dynamic response; NFRP layer; seismic ground excitation; HDQM; Newmark method

Address
Sajad Shariati Rad and Mahmood Rabani Bidgoli: Department of Civil Engineering, Jasb Branch, Islamic Azad University, Jasb, Iran

Abstract
In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton\'s principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

Key Words
wave propagation; functionally graded beam; porosity; higher-order shear deformation beam theories

Address
Mourad Benadouda and Abdelouahed Tounsi: Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria Hassen Ait Atmane: 1) Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria 2) Département de genie civil, Faculté de genie civil et d\' architecture, Univesite Hassiba Benbouali de Chlef, Algerie Fabrice Bernard: INSA Rennes, Rennes, France S.R Mahmoud: Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia

Abstract
Base-isolation is now being adopted as a retrofitting strategy to improve seismic behaviour of reinforced concrete (r.c.) framed structures subjected to far-fault earthquakes. However, the increase in deformability of a base-isolated framed building may lead to amplification in the structural response under the long-duration horizontal pulses of high-magnitude near-fault earthquakes, which can become critical once the strength level of a fire-weakened r.c. superstructure is reduced. The aim of the present work is to investigate the nonlinear seismic response of fire-damaged r.c. framed structures retrofitted by base-isolation. For this purpose, a five-storey r.c. framed building primarily designed (as fixed-base) in compliance with a former Italian seismic code for a medium-risk zone, is to be retrofitted by the insertion of elastomeric bearings to meet the requirements of the current Italian code in a high-risk seismic zone. The nonlinear seismic response of the original (fixed-base) and retrofitted (base-isolated) test structures in a no fire situation are compared with those in the event of fire in the superstructure, where parametric temperature-time curves are defined at the first level, the first two and the upper levels. A lumped plasticity model describes the inelastic behaviour of the fire-damaged r.c. frame members, while a nonlinear force-displacement law is adopted for the elastomeric bearings. The average root-mean-square deviation of the observed spectrum from the target design spectrum together with a suitable intensity measure are chosen to select and scale near- and far-fault earthquakes on the basis of the design hypotheses adopted.

Key Words
seismic retrofitting; r.c. framed buildings; base-isolation system; fire scenarios; spectral matching; nonlinear dynamic analysis

Address
Fabio Mazza and Mirko Mazza: Dipartimento di Ingegneria Civile, Università della Calabria 87036 Rende (Cosenza), Italy

Abstract
Having the ability to keep on yielding stable solutions in problems involving high potential of instability, composite time integration methods have become very popular among scientists. These methods try to split a time step into multiple sub-steps so that each sub-step can be solved using different time integration methods with different behaviors. This paper proposes a new composite time integration in which a time step is divided into two sub-steps; the first sub-step is solved using the well-known Newmark method and the second sub-step is solved using Simpson\'s Rule of integration. An unconditional stability region is determined for the constant parameters to be chosen from. Also accuracy analysis is perform on the proposed method and proved that minor period elongation as well as a reasonable amount of numerical dissipation is produced in the responses obtained by the proposed method. Finally, in order to provide a practical assessment of the method, several benchmark problems are solved using the proposed method.

Key Words
simpson rule; newmark method; composite time integration; unconditional stability; numerical damping; period elongation

Address
K. Yasamani: Malek-ashtar University of Technology, Tehran, Iran S. Mohammadzadeh: 1) College of Engineering, School of Civil Engineering, University of Tehran, Tehran, Iran 2) Payam-Nour University of Urmia, West Azerbaijan, Iran

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