Shock and Vibration Digest (17413184)32(1)pp. 67-67
The use of uniform hazard spectra for obtaining the seismic design forces is being considered for the next version of the national building code of Canada. Such spectra provide the spectral accelerations of a single-degree-of-freedom system for a range of periods but for a uniform level of hazard. One of the issues that needs to be resolved before uniform hazard spectra are used in design is the adjustment required in the base shear to account for the higher mode effects present in a multi-degree-of-freedom system. This issue is examined through analytical studies of the response of idealized multistorey building frames to ground motions representative of the seismic hazard in east and west Canada.
Institute of Physics Conference Series (09513248)180pp. 25-34
Geometry has a ritual origin and utilisation of Sacred Geometry by man goes back many centuries. Certain specific ratios can be found in the design of lifeforms in nature Traditional civilisations regarded architecture as a sacred means by which the heavens were manifested. Persian architecture utilised proportions comprehensively and by means of Sacred Geometry measured the proportions of heaven and reflected them in the dimensions of buildings on Earth. In this paper, the design of a number of Persian historical buildings by the use of the science of geometry will be presented. The geometric factors upon which the design of these buildings is made, from both architectural and structural viewpoints, will be discussed and common design laws between Persian monuments and creatures in nature will be explained.
Advances in Earthquake Engineering (1361617X)13pp. 157-165
Iranian traditional domes are of the most notable samples of traditional construction in Iran spanning thousands of years, many of which have been standing on seismic parts of the country for many centuries. Structurally, Iranian domes can be categorised into single, double and triple-shell domes. Single-shell domes are the earliest type of domes. The single-shell is the main load bearing part. Double-shell domes consist of two shells, and they are divided into continuous and discontinuous types. In continuous double-shell domes the distance between the two shells is small and shells are connected by brick connectors. In discontinuous double-shell domes there is a considerable distance between the two shells. For the structural stability of some domes meridional walls or stiffeners are built in the space between the two shells. There are also a few domes with three shells. In this paper, structural systems of a number of Iranian historical domes made of masonry materials will be discussed and their structural strength and stability due to dynamic effects of earthquakes will be presented. The document will also explain the structural role of meridional stiffeners in double-shell domes.
International Journal of Rock Mechanics and Mining Sciences (13651609)41(SUPPL. 1)
There are various structural and geological stratigraphies in study area. The main lithology includes the shale, marl, limestone and dolomite that belong to the Cambrian to upper Cretaceous besides Quaternary deposits. To identify the engineering and geotechnical characteristics of the rock mass along the tunnel route, the results of laboratory and in situ tests, geophysical explorations (geoelectrical methods), field observations and borehole logging charts have been used. The well-known rock mass classification systems for tunnelling purposes (RMR, GSI and Q-system) have been used. Using the GSI classification system for rock mass, the modified Hock- Brown criterion parameters of the rock mass for typical section were determined. The RMR was used to determine the required support for the entire length of tunnel. Also the Q system was used to compare the required support from Q system with the RMR system. Finally rock-support interaction analysis was conducted for a typical cross section of the tunnel. Using the above empirical and analytical methods, the required supports were compared for a typical section. © 2004 Elsevier Ltd.
International Journal for Numerical Methods in Engineering (00295981)64(4)pp. 427-460
In this part of paper we shall extend the formulation proposed by Babuška and co-workers for robustness patch test, for quality assessment of error estimators, to more general cases of patch locations especially in three-dimensional problems. This is performed first by finding an asymptotic finite element solution at interior parts of a problem with assumed smooth exact solution and then adding a correction part to obtain the solution near a kinked boundary irrespective of other boundary conditions at far ends of the domain. It has been shown that the solution corresponding to the correction part may be obtained in a spectral form by assuming a suitable proportionality relation between the nodal values of a mesh with repeatable pattern of macro-patches. Ha ving found the asymptotic finite element solution, the performance of error estimators may be examined. Although in this paper we focus on the asymptotic behaviour of error estimators, the method described in this part may be used to obtain finite element solution for two/ three-dimensional unbounded heat/elasticity problems with homogeneous differential equations. Some numerical results are presented to show the validity and performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering (00295981)64(4)pp. 461-502
In this part of the paper we shall use the formulation given in the first part to assess the quality of recovery-based error estimators using two recovery methods, i.e. superconvergent patch recovery (SPR) and recovery by equilibrium in patches (REP). The recovery methods have been shown to be asymptotically robust and superconvergent when applied to two-dimensional problems. In this study we shall examine the behaviour of the recovery methods on several three-dimensional mesh patterns for patches located either inside or at boundaries. This is performed by first finding an asymptotic finite element solution, irrespective of boundary conditions at far ends of the domain, and then applying the recovery methods. The test procedure near kinked boundaries is explained in a step-by-step manner. The results are given in a series of tables and figures for various cases of three-dimensional mesh patterns. It has been experienced that the full superconvergent property is generally lost due to presence of boundary layer solution and the definition of the recoveries near boundaries though the results of the robustness test is still within an acceptable range. Copyright © 2005 John Wiley & Sons, Ltd.
Building and Environment (03601323)40(10)pp. 1413-1427
Nature displays profound preference for certain specific ratios to design her life-forms. These are geometric relationships that are transcendent and originated from Sacred Geometry. The view that geometry had a ritual origin is a part of a wider view that civilisation itself had a ritual origin, and therefore the history of utilisation of Sacred Geometry by man goes back to many centuries ago. The Pythagorean tradition, and the Egyptian and Babylonian sciences from which it derived, and Persian mathematics, a part of which reflects a Pythagorean intellectuality, are based on the sacred conception of numbers and their symbolism. In the traditional world, geometry was inseparable from the other sciences of the Pythagorean Quadrivium, namely arithmetic (numbers), music and astronomy. Traditional geometry is related to the symbolic configurations of space. Geometric forms such as the triangle, square and various regular polygons, the spiral and the circle are seen in the traditional perspective to be, like traditional numbers, as aspects of the multiplicity of the Unity. Architecture itself has always had a sacred meaning to all traditional civilisations through millennia, by which means man has tried to provide for himself a manifestation of heavens. Persian architecture always emphasised on Beauty, and by means of Sacred Geometry Persians measured the proportions of heaven and reflected them in the dimensions of buildings on the earth. A comprehensive utilisation of proportions in Persian architecture, such as in the design of plans, elevations, geometric and architectural patterns, and mechanical and structural features, can be proved through geometrical analysis of Persian historical buildings. In this paper, the sacred conception of geometry and its symbolism in the Pythagorean tradition, and Sacred Geometry and proportions in natural life-forms will be explained. The use of the science of geometry in design of a number of Persian historical buildings will be presented. The geometric factors upon which the design of these buildings, from both architectural and structural viewpoints, is made will be discussed. © 2004 Elsevier Ltd. All rights reserved.
Advances in Architecture Series (13681435)20pp. 503-512
The use of wood as a building material in Iran has a long history which dates back to the first millennium. At that time wood was used to make the roofs, beams and columns of some buildings. The extensive use of wood in the construction of large wooden buildings came into practice in the seventeenth century A.D. In that era, huge wooden structures were introduced to the world, some of which are still in existence. A typical example of such buildings is the wooden structure of the Ali Qapu building in Isfahan, Central Iran. The main part of the building, which supports the wooden structure, is made of masonry materials and it was repaired and maintained in the 1960s, but the maintenance of the wooden part remained incomplete. In 1987, a thorough study of the structural behaviour of the wooden structure was completed. Instructions were proposed for repairing the structure according to this investigation. This paper demonstrates the maintenance procedure of the whole building and, in particular, the study of the wooden structure, and it presents instructions for maintenance of the wooden structure.
Civil-Comp Proceedings (17593433)83
In this paper we present a numerical method suitable for solution of steady state wave problems in which the material properties vary periodically throughout the domain. Discrete Green's functions, in finite element sense, are selected as the representatives of the problems. The Green's functions are evaluated on unbounded domains and this involves satisfaction of radiation conditions in the solutions. The formulation, given in this paper, is the extension of the one recently proposed by the authors for domains with homogenous materials. Here, the principles of Floquet theory for solution of partial differential equations, with periodic coefficients, are used. First, the fundamental exponential-like wave bases are obtained through the dispersion relations and then the radiation conditions are satisfied by selecting the wave bases. For selecting the wave bases, a quadrant of the main unbounded domain together with a set of appropriate boundary conditions is considered. For satisfaction of the boundary conditions a discrete transformation technique, proposed by the authors, is used. Application of the method is shown on a sample problem and the results are compared with those obtained form exact solution of a rather similar problem with homogenized material. The comparison shows the validity of the solution method. © 2006 Civil-Comp Press.
International Journal for Numerical Methods in Engineering (00295981)67(11)pp. 1491-1530
In this paper we present a new approach for finite element solution of time-harmonic wave problems on unbounded domains. As representatives of the wave problems, discrete Green's functions are evaluated in finite element sense. The finite element mesh is considered to be of repeatable pattern (cell) constructed in rectangular co-ordinates. The system of FE equations is therefore reduced to a set of well-known dispersion equations by using a spectral solution approach. The spectral wave bases are constructed directly from the FE dispersion equations. Radiation condition is satisfied by selecting the wave bases so that the wave information is transmitted in appropriate directions at the cell level. Dirichlet/Neumann boundary conditions are defined at the edges of a quadrant of the main domain while using the axes of symmetry of the problem. A new discrete transformation method, recently proposed by the authors, is used to satisfy the boundary conditions. Comprehensive studies are made for showing the validity, accuracy and convergence of the solutions. The results of the benchmark problems indicate that the proposed method can be used to evaluate discrete Green's functions whose analytical forms are not available. Copyright © 2006 John Wiley & Sons, Ltd.
During construction of one of the Sahand cooling towers due to slip forming performance some imperfections were raised mostly between elevation of +30 and +40 meter. It was evaluated that some points of the shell should be repaired. In constructing the cooling tower from elevation +40 to +60 meter these imperfections were removed and the cooling tower was constructed with no problem until the elevation +130 meter. In this paper reasons of generation of geometric imperfections in Sahand cooling tower are clearly shown and possible ways for preventing them are discussed. Applied repairing method for Sahand cooling tower is explained in detail. Geometrical imperfections of the constructed cooling tower are measured using photogrammetric techniques. The detailed three dimensional models for both perfect and imperfect cooling towers are made using finite element method. Different analyses for different loading of such structures are done and the results are compared. For the cooling tower with imperfections the wind load is applied in 12 directions around the circumference of it so that the effects of imperfections can be seen well. Critical buckling load factors are obtained for both models by linear and nonlinear analysis. The results of analysis of imperfect cooling tower shell are used for checking the design of it. Results show that the maximum values for circumferential and vertical stresses are appeared between level +30 to +40. The increase of circumferential stress is usually more than increase of vertical stresses. This high increase appears locally in some parts of cooling tower shell. The difference of displacements in cooling tower shell in two models is negligible. The critical buckling safety factor of the imperfect model is greater than the perfect one. There is not a large difference between the values of this factor for different wind load directions. © 2006 by School of Engineering and Technology, Asian Institute of Technology.
Journal of Structural Engineering (07339445)132(11)pp. 1801-1805
The wooden columnar structure of the historical building of Ali Qapu in Isfahan is a notable sample of Iranian traditional construction of 350 years ago. In this study, the structural system and load carrying elements of the structure have been identified. Structural analysis due to applied loads has been performed and structural strength of its members has been examined according to related codes. Based on obtained results, suggestions for reinforcement of the structure have been made. In this paper, the results from study on the wooden columnar structure of the Ali Qapu building are presented. © 2006 ASCE.
Composites Science and Technology (02663538)67(6)pp. 1073-1080
An exact thermoelasticity solution for a two-dimensional thick composite consisting of homogeneous and functionally graded layers is presented. The thermomechanical properties of functionally graded layers are assumed to vary exponentially through the thickness while the Poisson's ratio is taken to be constant. The heat transfer problem is solved under steady state condition accounting for the heat convection. Utilizing the stress function the governing equation reduces to a fourth order inhomogeneous partial differential equation which is solved exactly using Fourier series method. A comparative study is done between two sandwich structures with homogeneous and functionally graded coatings, respectively. The results reveal that stress concentration effects are eliminated and interfacial shear stress is reduced when a functionally graded coating is used. © 2006 Elsevier Ltd. All rights reserved.
Coastal Engineering (03783839)54(11)pp. 835-855
For the study of the cross-shore wave-induced hydrodynamics in the swash zone, a numerical model is developed based on the one-dimensional non-linear shallow water (NSW) equations for prediction of hydrodynamic parameters in the swash zone. In order to evaluate the accuracy of the outputs of the numerical model, the model's predictions in terms of water surface elevations and cross-shore velocities, are compared to field data from full-scale experiments conducted on three sites with different beach slope; mild and steep, several bed particle sizes and under various incident wave conditions. The quantitative and qualitative comparison of the results of the numerical model and the full-scale data reveals that the model can generally predict many aspects of the flow in the surf and swash zone on both types of beach. The accuracy is adequate for application in a sediment transport study. Considering the time-history and probability distribution of water surface elevation, the model is generally more accurate on steep beaches than on the mild beach. The model can adequately simulate the dominant frequency across the beach and saturation of higher frequencies on both mild and steep beaches for various incident wave energy characteristics. With regard to the horizontal (cross-shore) velocity, the sawtooth shape of time-history and negative acceleration of water are well predicted by the model for both mild and steep beaches. Due to the uncertainties in maximum and minimum values of velocity data, clear judgement about the accuracy of the numerical model in this matter was not possible. However, the comparison of the minimum velocities (offshore direction) revealed that the application of friction factors below the range which is suggested by literature best match the data. © 2007 Elsevier B.V. All rights reserved.
International Journal of Design and Nature (17443679)1(2)pp. 186-196
The climatic characteristics in different regions of Iran have created architectural design problems. It is advantageous to look at various architectural solutions to such problems. In the hot-dry climate of the indigenous settlements of Iran, particularly interesting design solutions are found. Most solutions, such as high thermal capacity construction materials, compact structure of cities, narrow winding passageways, thick walls, courtyards, internal vegetation, arched roofed chambers, highly elevated wind towers and big water reservoirs, are in conformity with nature and environment. The role of architectural elements is to make use of natural forces such as light, heat, wind and water in design. In this paper, the effects of climatic factors on urban and architectural forms in the hot-dry regions of Iran, climatic design problems and architectural solutions are explained.
A rational function is proposed as a failure criterion for isotropic, dry and intact rocks to be used in both tensile and compressive regions. The criterion is capable of predicting the triaxial behavior of rock under low confinements satisfying the exact values of uniaxial tensile and compressive strengths. The capability of the rational criterion is assessed by applying brittle-ductile transition and downward concavity boundary conditions into the criterion introducing ë and ã parameters. The sensitivity of the criterion response is analyzed by varying under variation of ë and ã parameters. It has been shown that the Hoek's rule of thumb for brittleductile transition could be used for all types of rocks in low confinements and the proper boundary between low and high confinements is obtained. It was also experimental that the acceptable envelope could be obtained for low confinements using a dataset including only two triaxial tests together with uniaxial tensile and compressive strengths. Also, the parameters and concavity of the criterion have been discussed. © ISRM International Symposium - 5th Asian Rock Mechanics Symposium 2008, ARMS 2008. All rights reserved.
Dams are constructed to control the surface runoff. One of the important points involved in grouting operation and cut off curtain design is the geological and hydrogeological investigation of the site and evaluation of its groutability. The commonly method used for determination of permeability coefficient is water pressure test (WPT). The test includes measurement of water pressure (P) and discharge (Q) pumped in the drilled boreholes and its graphical representation as (P-Q) diagrams which can be interpreted to give rock mass hydromechanical behaviour. Based on the test designation, in Ostur dam site, 400 water pressure tests were conducted and analyzed. Results of these tests are used to determine the type of hydrogeomechanical behaviour. In the other hand, the test grouting was also conducted in continuation of the (WPT) operation and the results have shown that the bedrock of this dam is impermeable, with very low groutability potential. However, the shallow part of rock mass is partly affected due to weathering. The type of flow in these parts is identified as turbulent. From the other side, the rock mass is also intersected in deep parts by hydrothermal veins. The flow type in these parts is different from the shallow parts. © ISRM International Symposium - 5th Asian Rock Mechanics Symposium 2008, ARMS 2008. All rights reserved.
In this paper, framework of a decision support system (DSS) for sustainable water resources management in basin-scale is presented. In development of this DSS, focus is on connecting hydrologic, environmental, and economic analysis tools and decision support methods by combining the DPSIR (Driving force, Pressure, State, Impact and Response) approach with multi-criteria analysis methods. The proposed framework can help in involving decision makers and stakeholders in the decision making process using a conceptual framework and procedure. Specific challenges of economic, technical, and political uncertainties in water resources management in developing countries have been discussed in the paper and are also considered in the development of the DSS framework. Different modules of the DSS including the "Database Management", "Model-Base Management", and "Multi-Criteria Analysis Module" have been also presented and their relations with the DPSIR approach are discussed in details. ELECTRE III method has been used in the Multi-Criteria Analysis Module and results of a case study are also presented in the paper. © 2008 ASCE.
Water Resources Management (09204741)22(12)pp. 1835-1857
This paper presents a constrained formulation of the ant colony optimization algorithm (ACOA) for the optimization of large scale reservoir operation problems. ACO algorithms enjoy a unique feature namely incremental solution building capability. In ACO algorithms, each ant is required to make a decision at some points of the search space called decision points. If the constraints of the problem are of explicit type, then ants may be forced to satisfy the constraints when making decisions. This could be done via the provision of a tabu list for each ant at each decision point of the problem. This is very useful when attempting large scale optimization problem as it would lead to a considerable reduction of the search space size. Two different formulations namely partially constrained and fully constrained version of the proposed method are outlined here using Max-Min Ant System for the solution of reservoir operation problems. Two cases of simple and hydropower reservoir operation problems are considered with the storage volumes taken as the decision variables of the problems. In the partially constrained version of the algorithm, knowing the value of the storage volume at an arbitrary decision point, the continuity equation is used to provide a tabu list for the feasible options at the next decision point. The tabu list is designed such that commonly used box constraints for the release and storage volumes are simultaneously satisfied. In the second and fully constrained algorithm, the box constraints of storage volumes at each period are modified prior to the main calculation such that ants will not have any chance of making infeasible decision in the search process. The proposed methods are used to optimally solve the problem of simple and hydropower operation of "Dez" reservoir in Iran and the results are presented and compared with the conventional unconstrained ACO algorithm. The results indicate the ability of the proposed methods to optimally solve large scale reservoir operation problems where the conventional heuristic methods fail to even find a feasible solution. © Springer Science+Business Media B.V. 2008.
Journal of Asian Architecture and Building Engineering (13472852)7(2)pp. 239-245
Today the cultural heritage of humankind is endangered not only by natural catastrophes and the exploitation of resources but also by economic and social problems and institutional weaknesses. Western and Central Asian countries contain a major part of the cultural heritage on the earth, but due to different problems common in developing countries, cultural heritage in such countries suffers from natural and non-natural risks. A lack of public awareness of various types of risks itself worsens the conditions in such countries. It is necessary to clarify the situation within the region regarding different categories of risk, and then considering how to devise measures for heritage sites that are truly endangered at present, as well as how to prepare for risk anticipated in the future. This paper discusses and categorises the risks to cultural heritage in Western and Central Asia.
The Gardaneh Rokh tunnel is being excavated with the length of 1300m it axis striking of N28. The height of tunnel section is 8.6m and its width is 13m. To characteristics of the discontinuities were recorded from 5 outcrops as survey stations. A series of laboratory tests was conducted on the intact rock samples selected from cores taken from two boreholes to get the physical and geomechanical properties. The rock mass along the tunnel enroute was divided into 5 structural zones and were then classified based on the Q and RMR systems. The required support systems were also determined according to the systems. Regarding tunnel stability analysis, the tunnel inlet section as the weakest zone of rock mass located in km 6+300 (structural zone 5) is numerically modelled and analyzed using PLAXIS software with and without support system. The excavation and support installation process was modelled in 3 phases. The results of the numerical modelling show that the crown and sidewalls instabilities are mainly reduced by installation of partial shotcrete support in crown and sidewalls. However, the support installation even in lower sidewalls may not substantially reduce the displacements in invert.
The application of higher order continuum theories, with size effect considerations, have recently been spread in the micro and nano-scale studies. One famous version of these theories is the couple stress theory. This paper utilizes this theory to study the anti-plane problem of an elliptic nano-fiber, embedded in an infinite medium, both made of centrosymmetric isotropic material. In this framework, a characteristic length appears in the formulation, by which examination of the size effect is possible. This work presents an analytical solution for the proposed problem. Copyright © 2008 by ASME.
Scientia Iranica (23453605)16(4 A)pp. 273-285
This paper presents an application of the Max-Min Ant System for optimal operation of reservoirs using three different formulations. Ant colony optimization algorithms are a meta-heuristic approach initially inspired by the observation that ants can find the shortest path between food sources and their nest. The basic algorithm of Ant Colony Optimization is the Ant System. Many other algorithms, such as the Max-Min Ant System, have been introduced to improve the performance of the Ant System. The first step for solving problems using ant algorithms is to define the graph of the problem under consideration. The problem graph is related to the decision variables of problems. In this paper, the problem of optimal operation of reservoirs is formulated using two different sets of decision variable, i.e. storage volumes and releases. It is also shown that the problem can be formulated in two different graph forms when the reservoir storages are taken as the decision variables, while only one graph representation is available when the releases are taken as the decision variables. The advantages and disadvantages of these formulation are discussed when an ant algorithm, such as the Max-Min Ant System, is attempted to solve the underlying problem. The proposed formulations are then used to solve the problem of water supply and the hydropower operation of the "Dez" reservoir. The results are then compared with each other and those of other methods such as the Ant Colony System, Genetic Algorithms, Honey Bee Mating Optimization and the results obtained by Lingo software. The results indicate the ability of the proposed formulation and, in particular, the third formulation to optimally solve reservoir operation problems. © Sharif University of Technology, August 2009.
Composite Structures (02638223)90(1)pp. 92-99
A finite strip method is presented to predict local, distortional, and lateral buckling of composite fiber reinforced plastic (FRP) structural plates. Each plate may be subjected to a combination of longitudinal compression, longitudinal in-plane bending, or shear stress. A sinusoidal function is assumed in the longitudinal direction for a buckling mode of whatever type and a polynomial function is used in the transversal direction. The critical stress and critical moment of I-shape and box and channel sections under bending and uniform loading are obtained by solving an eigenvalue problem. Using this solution technique, a simple expression is developed for prediction of I-shape section beams' buckling stresses in three design curves. The critical stresses for different Ex / Ey values are calculated using the design curves. © 2009 Elsevier Ltd. All rights reserved.
Finite Elements in Analysis and Design (0168874X)45(10)pp. 710-720
An efficient algorithm is presented for the formation of null basis of triangular plane stress and plane strain finite element models, corresponding to highly sparse flexibility matrices. This is achieved by applying a modified ant colony system (ACS). An integer linear programming formulation is also presented to evaluate the quality of the results obtained by the proposed ant colony system algorithm. The efficiency of the present algorithm is illustrated through some examples. © 2009 Elsevier B.V. All rights reserved.
International Journal of Solids and Structures (00207683)46(16)pp. 2978-2987
It is well-known that classical continuum theory has certain deficiencies in predicting material's behavior at the micro- and nanoscales, where the size effect is not negligible. Higher order continuum theories introduce new material constants into the formulation, making the interpretation of the size effect possible. One famous version of these theories is the couple stress theory, invoked to study the anti-plane problems of the elliptic inhomogeneities and inclusions in the present work. The formulation in elliptic coordinates leads to an exact series solution involving Mathieu functions. Subsequently, the elastic fields of a single inhomogeneity in conjunction with the Mori-Tanaka theory is employed to estimate the overall anti-plane shear moduli of composites with uni-directional elliptic cylindrical fibers. The dependence of the anti-plane elastic moduli on several important physical parameters such as size, aspect ratio and rigidity of the fiber, the characteristic length of the constituents, and the orientation of the reinforcements is analyzed. Based on the available data in the literature, certain nano-composite models have been proposed and their overall behavior estimated using the present theory. © 2009 Elsevier Ltd. All rights reserved.
Journal of Applied Sciences (discontinued) (18125654)9(10)pp. 1817-1832
Endurance Time (ET) method has been introduced as a lime-history based dynamic analysis procedure. In this method, structures are subjected to a gradually intensifying acceleration function. Performance of the structures is assessed based on the length of the time interval that they can satisfy required performance objectives. In this study, some fundamental concepts of ET method are explained and the potentials and limitations of this procedure in nonlinear seismic analysis of SDOF structures are investigated. A numerical optimization procedure for generating ET acceleration functions that are compatible with ground motions are explained. Results of ET analysis for inelastic SDOF systems are compared with ground motions analysis results for different strength ratios, ductilities and damping ratios. The accuracy of ET method in predicting the response of SDOF systems with stiffness degradation and strength deterioration is also investigated application of ET method in performance based earthquake engineering is described by an example of a single degree of freedom system. The results show that the approximations of ET method are in good agreement with the exact response history results of the similar ground motions for different nonlinear systems. It is shown that ET acceleration functions optimized in linear range considering long periods can be used in nonlinear analysis with reasonable accuracy. © 2009 Asian Network for Scientific Information.
