جستجوی مقالات مرتبط با کلیدواژه « nonlinear behavior » در نشریات گروه « عمران »

Composite members consisting of steel beam and CFT concrete column have been of great interest in the last few decades. Tubular columns are highly desirable in bending frames due to their high bending and twisting resistance and stiffness. Composite columns have considerable capabilities and efficiency due to the simultaneous benefit of the beneficial properties of steel and concrete materials. Also, the presence of concrete core in the CFT column causes the local buckling in the steel wall of these columns to be delayed. Therefore, proposing a suitable connection between the steel beam and the composite column makes it possible to take advantage of the potential benefits of these sections. Concrete in steel columns was initially used as a protective layer against impact and especially fire. This is because steel sections in extreme heat, very vulnerable and exposed to fire quickly lose their mechanical properties, as an example of the destruction of the two famous World Trade Towers 11 (WTC), September in America, which is one of the reasons The main effect of fire was to reduce and lower the mechanical properties of the steel used.

Intake towers form the entrance to the reservoir spillway or diversion system and thus play a key role in the seismic resistance of the whole system. safety and proper functioning of the intake towers in the event of a major earthquake is very important, since the release controlled by the reservoir can help to prevent the failure of the dam after an earthquake by reducing the water pressure. In addition, the current seismic assessment based on linear elastic constitutive model cannot adequately describe the seismic capacity of intake towers. Thus, to investigate the proper functioning of intake towers in the event a earthquake, it is necessary to introduce IDA that takes into fully assess the seismic performance of intake towers based on nonlinear dynamic analysis. In this paper by modeling the intake tower of the Briones dam, intake tower in three conditions of the intake tower, the intake tower-reservoir (outside water) and the tower-reservoir-inside water, under the influence of 12 earthquake records, each of which has a magnitude of seven in the earthquake intensity scale, has been investigated. The displacement at the top of the intake tower, damage of the intake tower body and the maximum tensile stress of the rebar in the intake tower were studied in all the three condition are considered as damage measure (DM), and the results were reported in the form of IDA curves. Then based on the results, the function and different limit-states (key points) of the intake tower structure are determined.

One of the effective parameters in performance-based design methods is the determination of lateral displacement demand. Due to the existence of uncertainties in the parameters of analytical models such as mechanical properties of structures and model simplifications, accurate calculation of structural responses is associated with complexities. The use of training-based prediction methods can be a good alternative to accurate analysis in assessing the seismic behavior of a building structure. In this paper, an efficient training approach for modeling and predicting the response of building structures with nonlinear behavior is studied. To perform the training process, an adaptive scheme of fuzzy inference system with the TSK model combined with Multi-Verse optimization algorithm is used to model the seismic behavior of structures. The proposed training model is implemented by optimizing the parameters of the TSK model using the optimization algorithm based on comparing the previous time steps responses. To implement the adaptive design and increase the accuracy of the prediction, three training cases based on the responses of 2, 5, and 10 previous time steps were used. To train this system, the data collected from the results of nonlinear time history analysis under 100 seismic events with different characteristics have been used. Also, 10 events were used to test the inference system. The performance of the proposed design was evaluated on a shear frame structural model with nonlinear hysteresis behavior. The results show that the inference system of the TSK model by combining the optimization method is an efficient computational method for predicting the response of nonlinear structures. The average MSE for the test group ground motions, using three training modes with 2, 5, and 10 previous time steps, 2.817e-03, 1.228e-03, and 2.953e-04, respectively. By increasing the number of time steps from 2 to 10, the prediction error decreases by 89.52%.

Concrete Filled steel Tubes (CFT) have several advantages when used as columns in buildings. These advantages include efficient structural section benefiting from combined action of concrete and steel , drastic reduction of the need for steel rebars, confinement of concrete by steel tube permitting higher compressive strains, increasing resistance of steel tube against local buckling, eliminating a separate formwork for concrete and reduction of construction time. On the other hand, connection of steel beam to round steel columns including CFT has been a major challenge.The main complexity arises from difficulty of accessing the inside of tubular columns for installing continuity plates to transfer tension or compression between opposing beam flanges. Different methods have been proposed in the past to alleviate this problem. Solutions presented so far include external collar stiffener plates connecting opposing beam flanges, extending only the web of beam through steel tube column, extending beam flanges through column, using steel rebars embedded in concrete core and attached to beam flanges and finally, complete passage of steel beam through steel tube. Cyclic behavior of beam-column connection plays a vital role in seismic response of moment frame structures. Literature survey shows that despite numerous methods proposed for steel beam-CFT column connection, not any organized attempt has been undertaken to explore the cyclic behavior of these connections. In this paper, numerical modeling has been utilized to investigate the cyclic behavior of continuous steel girder and circular CFT connection. Before achieving the main analyzes, the modeling and analysis assumptions and techniques were verified using available pushover experiments on typical connections of similar arrangement. In current study, effect of column diameter, thickness of steel tube and thickness of girder flange and girder web have been considered. Fourteen samples with different values of column to beam moment capacity ratios ranging from 0.78 to 1.95 have been analyzed. Actual dimensions of specimens were selected to be compatible with production of steel tubes and have reasonable lateral load bearing strength. Beam and column dimensions were checked to comply with AISC360 compact section limitations. Two diameters of 405 and 505 mm were specified for columns while beams had a fixed depth of 428 mm. Thickness of St37 grade steel tube ranged between 4.5 to 8.5mm. Beams were considered to be of St52 grade with flanges of 12.5 to 16.5mm thickness and webs between 7 to 11mm thick. Some specimens slightly violated seismic compact section regulations of column and girder. Meanwhile, all specimens showed stable and large load-drift cycles and could tolerate 0.04 story drift ratio as stipulated by AISC code for special moment connections. Specimens which fully complied with code reqirements could undergo 0.05 story drift ratio while still maintaining at least 80 percent of their maximum strength. Analysis results show that in specimens with same columns, increasing girder flange or web thickness is accompanied with increased energy absorption. The fraction of energy absorbed by elastic deformation increased more than the energy dissipated through hysteretic nonlinear deformations. As a result, a reduction in hysteretic damping accompanied the increase in beam flange or web thickness.

To reduce the damage and casualties caused by earthquakes, researchers made efforts to introduce seismic resistant structural systems. One of the new lateral force-resisting systems is the steel circular braced system called “Ogrid”. Previous studies shown the high energy dissipation and ductility of this system. This system has a high capacity to withstand nonlinear deformations after the formation of the first plastic hinge until collapse. In the present study, an attempt has been made to introduce a new type of this brace with different types of brace connection to beam and column and to evaluate its performance. For this purpose, the OGrid is used and different connections of the frame to the circular brace that embrace the connection of the brace to the beam and to the columns, as well as comparing the presence of friction and the absence of friction between the brace and the frame are modeled and the results are reviewed. It is found that by releasing the connection of the circular brace with I-shaped cross section to the column and creating friction between them with a coefficient of 0.5, the bearing capacity increases up to 22% compared to the restrained connection. In this case, before yielding, softening is observed in the proposed model, but after yielding compared to the model with restrained connection, better energy dissipation occurs due to deformations in the circular brace. Meanwhile, bearing capacity increases up to 8% by considering friction between the brace and increases up to 17% by considering friction between the brace and the column comparing with the released connections. On the other hand, the use of H-shaped circular brace with friction connection to the column and/or beam is not recommended due to the reduction of bearing capacity by at least 9% compared to the restrained connection.

Progressive collapse is a nonlinear phenomenon that starts from the damage of a part of the structure and ends with the whole structure and its total damage. Therefore, the study of this phenomenon in high-rise and important structures while securing it will ensure the design process of the structure. Progressive collapse usually occurs in the structure due to the loss of one of the main members of the structure, which is usually the desired column. With the sudden removal of a column in the structure, in the node where the column is removed from the structure, there is a displacement that has a seismic nature. In this research, the effect of using steel haunch bracing with different locations in concrete moment frames is investigated under progressive collapse. The purpose of this evaluation was to determine the vulnerability of concrete structures retrofitted with steel haunch bracing as well as the effect of steel haunch bracing in spans and height of the structure, the place of eliminated element (edge or middle) and the number of the story in which the member was removed in the progressive collapse, is studied. A noteworthy point in different cases of component removal is in the wide changes of stresses and change of node displacement and lack of formation of plastic hinges in the members, which can be explained by the proper distribution and placement of steel haunch bracing in spans and height of the structure in the place of elimination of members in the model, there are more structural elements and this issue strengthens the catenary action of the members to transport and transfer load and also the immediate stabilization of the situation.

Shape Memory Alloys (SMAs) are new material in structural engineering. They can be used as reinforcement for the concrete walls. In this research, a numerical model was first developed based on an experimental test of a tall reinforced concrete wall with steel reinforcement subjected to an earthquake, and the numerical model responses were compared to the experimental model. Then, three other approaches were examined; first, the shape memory alloys were replaced only as vertical bars on the first story; in the second one, Shape memory alloy bars were replaced only on the first and sixth stories; and in the third approach, the whole vertical bars were replaced with shape memory alloy bars. Nonlinear time history analysis and comparison of model responses were performed. In addition, the parametric study of the responses was also done by changing some model characteristics such as axial force and earthquake intensity. In all three approaches with the shape memory alloy bars, the base moment demand value decreased by approximately 15% compared to the model with steel reinforcement. In the moment demand diagram, the amount of moment demand at the mid-height of the structure is relatively increased compared to the base moment demand. This is due to the effect of higher modes on wall behavior. The moment diagram graph is not uniformly decreasing along the height is not like a straight line. In addition, parametric study of the responses is also performed by changing some model characteristics such as axial force and earthquake intensity. With the formation of a plastic hinge at the base of the wall,approximately, the amount of moment demand in this area remains constant and the effect of higher modes increases the moment demand at the mid-height of the structure and may result in the formation of another plastic hinge at the mid-height of the structure.

After poor performance and brittle fracture of moment connections in the 1994 earthquake in Northridge, researchers proposed new connections to improve the behavior of steel moment frames. Generally, these modified connections can be classified into two main categories: reduced beam section (RBS) and other than RBS connections such as bolted flange plate, bolted unstiffened and stiffened extended end-plate moment, and welded unreinforced flange-welded web moment connections. In this study the behavior of special steel moment frames using each of these two types of connections was investigated. For this purpose, several steel moment frames made up of these two types of connections were analyzed using Opensees software through nonlinear static procedure. For modeling, the behavior of connections was modeled using Bilin material. Then, using FEMAP696, the seismic parameters of all moment frames were determined and compared. Results indicated that the moment frames of RBS connections have higher seismic performance than the other moment frames. Furthermore, based on the numerical results, regardless of the connection type, it seems that 3 is not an appropriate value for the over-strength factor. Based on these numerical results, values equal to 4 and 5 can be proposed for the over-strength factor for moment frames of RBS and other than RBS connections respectively.

In order to provide a comprehensive assessment of the structural components, behavior of structures should be traced and predicted far into inelastic region. For this purpose, analytical hysteresis models are needed which are capable of representing all modes of deterioration. In order to utilize these models,a database is required to calibrate models. In this paper relationships are proposed to predict modified Ibarra-Krawinkler model parameters for welded flange plate steel connections. To provide the database, a number of welded flange plate connections are designed based on Iran Steel Code. The designed connections have been modeled and analyzed numerically in a finite element software. Prior to proceed the investigation, finite element numerical model of the connection was created in the ABAQUS computer program in order to predict the micro-mechanical behavior of the welded flange plate steel connection. Using the nonlinear method of analysis, the cyclic behavior of such moment resisting connection was obtained. The numerical results were verified by comparing the results obtained experimentally and specifically for the steel welded flange plate moment connection. Simulation of several numerical models and in comparison with the laboratory results indicate the accuracy of the finite element model. Once the finite element micro behavior was verified, then fifty three different welded flange plate moment connections were designed for different number of steel moment frame with various heights and floor numbers. All the connections are modeled in the ABAQUS computer program and the cyclic behavior of such connections such as the hysteresis behavior are obtained. The hysteresis behavior of the connections were included in the moment frame connections by utilizing the rotation behavior in the connection. The steel frames are modeled in a customized version of OPENSEES computer program. The numerical model consists of nonlinear beam column elements with the rotational spring element at the end in which the rotational behavior of the spring were the hysteresis behavior of the connection obtained from ABAQUS computer program. These springs simulate the hysteretic response a steel component (beam or olumn) subjected to cyclic loading including strength and stiffness deterioration based on the modified Ibarra-Krawinkler deterioration model. Panel zones are modeled in such away that the shear distortions were explicitly included with the possibility of nonlinear behavior during an earthquake. The numerical results show that most numerical specimens predict the plastic hing location to be right after the top flange plate. Using numerical results as a database, the model parameters are calibrated and effective geometrical properties of connections are determined. The most effective parameters are beam depth, beam span to beam depth ratio, beam web depth to web thickness ratio, top plate length to top plate thickness ratio, bottom plate length to bottom thickness ratio, and beam flange width to beam flange thickness ratio. Finally, using nonlinear regression equations, relationships for predicting the model and deterioration parameters are proposed. Also different rotational capacity such as maximum plastic rotation, plastic rotation spectrum and cumulative plastic rotation are predicted. From the regression analysis the pertinent parameters effecting the detioration of the connection are identified.

The aim of this research is to study the parameters of nonlinear dynamic behavior of steel tall buildings having a compound braced-tube resistant skeleton with belted trusses in higher levels. For this purpose, four 30-story study models have been designed in 3D. The first study model has a resistant skeleton without a belted truss. Yet, the remaining three structural models, each have a belted truss in higher levels with layouts of one, two and three stories, respectively. Numerical study results of this research are acquired according to a set of time-history nonlinear analyses on the mentioned study models. The chosen ensemble of three-component ground motions includes six highly powerful near-field records and one far-field record. Assessing study results reveal that applying belted trusses in tall braced-tube skeletons would lead in a remarkable increase in stiffness and a growth in the capability to absorb the earthquake’s kinetic energy. This issue also results in a large decrease in lateral displacement and dynamic drift of the structure and will therefore cause an increase in using the axial capacity of peripheral columns of the structure plan. Thus it becomes possible to introduce the application of resistant structures with belted trusses in structural skeletons of high-rise buildings, especially in areas with high seismicity as a suitable and efficient alternative plan compared to other structural systems.

In this research, the effect of nonlinear behavior of concrete on seismic performance of roller compacted concrete (RCC) is discussed. Nonlinear behavior of material shows the behavior close to reality due to use of all structural capacity and it is considered the most appropriate method for design. So in this paper, by using the appropriate definition of nonlinear behavior of RCC, the Ansys software based of finite element method is used for modeling and analysis considering dam-reservoir-foundation interaction. Consider to behavior of roller concrete dam, two-dimensional model is selected and the dynamic analysis is carried out in time domain applying the Northridge earthquake components for linear and nonlinear cases. For evaluation of the effect of nonlinear behavior on the output results, the maximum hydrodynamic pressure, dam crest displacement, tensile stress in heel and compressive stress in the toe of dam are selected as critical responses. Finally, for accurate evaluation of the effect of nonlinear behavior on output responses, the results has been obtained as time history curves for both linear and nonlinear cases and the difference of responses has been determined.

The Seismic analysis of concrete dams had been considered in an ideal form by means of two dimensional Monoliths in analyse and design procedures and structures had been subjected to ground motions with defining seismic coefficient. Lately, the research focus, however, has been more on linear time history analytics and fracture analysis of concrete dams in 3D space. With the advancement of knowledge in the field of earthquake engineering and the development of more precise methods for estimating the intensity of possible earthquakes, The methods of analyzing and evaluating the seismicity of the structures have been improved and the effects of more parameters can be considered in assessing the risk of each structure. In the present study, the seismic response of a concrete arch-gravity dam under the influence of earthquake stimulation is investigated in a three dimensional finite element analysis. The effects of dam-reservoir-foundation interactions are considered and the nonlinear behavior of the concrete and also the different patterns of the arc radius of the dam are studied. Finally, the contribution of response of each of the sustainability factors to seismic stimulation is evaluated. The Seismic analysis of concrete dams had been considered in an ideal form by means of two dimensional Monoliths in analyse and design procedures and structures had been subjected to ground motions with defining seismic coefficient. Lately, the research focus, however, has been more on linear time history analytics and fracture analysis of concrete dams in 3D space. With the advancement of knowledge in the field of earthquake engineering and the development of more precise methods for estimating the intensity of possible earthquakes, The methods of analyzing and evaluating the seismicity of the structures have been improved and the effects of more parameters can be considered in assessing the risk of each structure. In the present study, the seismic response of a concrete arch-gravity dam under the influence of earthquake stimulation is investigated in a three dimensional finite element analysis. The effects of dam-reservoir-foundation interactions are considered and the nonlinear behavior of the concrete and also the different patterns of the arc radius of the dam are studied. Finally, the contribution of response of each of the sustainability factors to seismic stimulation is evaluated. The Seismic analysis of concrete dams had been considered in an ideal form by means of two dimensional Monoliths in analyse and design procedures and structures had been subjected to ground motions with defining seismic coefficient. Lately, the research focus, however, has been more on linear time history analytics and fracture analysis of concrete dams in 3D space. With the advancement of knowledge in the field of earthquake engineering and the development of more precise methods for estimating the intensity of possible earthquakes, The methods of analyzing and evaluating the seismicity of the structures have been improved and the effects of more parameters can be considered in assessing the risk of each structure. In the present study, the seismic response of a concrete arch-gravity dam under the influence of earthquake stimulation is investigated in a three dimensional finite element analysis. The effects of dam-reservoir-foundation interactions are considered and the nonlinear behavior of the concrete and also the different patterns of the arc radius of the dam are studied. Finally, the contribution of response of each of the sustainability factors to seismic stimulation is evaluated.

In this paper, new algorithm is proposed for fictitious mass of Dynamic Relaxation (DR) method with viscous damping. First, the incremental equations are derived for DR procedure. By using the transformed Gershgörin theory, new boundaries are achieved for fictitious mass. This formulation leads to a new algorithm for viscous DR method. For evaluating the efficiency of the proposed method, some 2D and 3D truss and frame structures are analyzed by elastic linear and geometrically nonlinear behaviors. Results show that the proposed scheme for fictitious mass improves the convergence rate of DR method so that the suggested algorithm presents the structural response with less iteration in comparison with other common DR techniques.

One of the most vital, essential human being requirements is water, which it has become increasingly sensitive owing to population growth, the need to develop agriculture and industry, and restriction in water resources. Considering this, the need to store water and to use its potential for generating hydroelectric power, which it can be achievable by constructing dams, will be necessitated. Concrete dams play a significant role in Infrastructure in each country. One important part of dams exiting in the world are made of gravity dams and earthquake seems to be the major threat for them in earthquake-prone areas. Hence, the dam fracture, with much stored water, might have brought many conspicuous threats about in these zones. Also, any structural damage could lead to some negative economic effects. These facts have increased the scholars’ attention to the mechanical behavior of dams during the decades. The Seismic analysis of gravity concrete dams, usually, had been considered in an ideal form by means of 2D Monolith in mechanism design and an earthquake effect coefficient. Lately, the research focus, however, has been more on linear time history analytics and fracture analysis of concrete dams in 3D. The numerical modelisation of huge structures such as dams is a proper tool for Seismic analysis and performance evaluation. The valley shape is one of the important parameters in the selection of the dam structure. This parameter plays a crucial role in both Seismic stimulation and its results. In this paper, a 3D finite element model of Pine-flat gravity dam, without interruption seams with a non-linear behavior of the dam’s material, is considered. . Loading has two stages: static and dynamic. In this modelisation, static loading includes both the weight of dam body and the load of filled Hydrostatic tanks. After static loading, loading of Seismic dynamic is begun. Owing to the importance of valley shape, the changes/ deformations of valley width and the dam response to every three elements of ground is investigated. The impact of the ratio changes of width in dam height, as well as the importance of the transverse component of ground motion, along the vertical and horizontal, has been explored. Interaction effects of dam-reservoir-foundation is considered in the considered analysis and ultimately, the output of which is compared with two dimensional model results. The aim of this study is comparing two and three dimensional seismic response of concrete gravity dams and also necessity of providing more realistic models for considering the effects of cross stream modes. Also, not only are interaction effects of dam-reservoir-foundation, the nonlinear behavior of concrete, studied different Valley shapes, and the effect of them on non-liner response investigated, but also the Seismic stability of gravity concrete dams under longitudinal, vertical and the chosen transverse record earthquake are separate and simultaneously studied. The effects of dam-reservoir-foundation interaction, nonlinear behavior of mass concrete, also different shapes of valley are studied and their effect on nonlinear response and seismic stability of concrete gravity dams are evaluated under two and three-component earthquake records.

Performance-based earthquake engineering requires accurate estimation of the seismic demand and capacity of structures. In recent years, various kinds of nonlinear static and dynamic analyses have been developed for the seismic evaluation of structures. Nonlinear dynamic time history analysis method is not only very time consuming, but also needs a proper skill and proficiency in order to interpret its results. For the performance evaluation of the structures, the speed and also the precision of conducting different analyses are very significant criteria. This issue has led to the creation of various new methods based on the principles of nonlinear and incremental static and dynamic analysis. One of the methods that has been proposed to tackle this task is incremental dynamic analysis (IDA). This procedure requires non-linear time history analyses (NL-THA) of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover a wide range of structural response; all the way from elastic behaviour to global instability. From the results of such computation, it is possible to determine structural capacities (or ground motion intensities) corresponding to various limit states; immediate occupancy (IO), life safety (LS), or collapse prevention (CP). Another approach to reduce the computational effort required for IDA is to estimate seismic demands for the practical structures by modal pushover analysis (MPA), an approximate procedure, instead of non-linear RHA. Thus, each of the many non-linear RHA required in IDA is replaced by a MPA. In addition, a more recent proposed method logically combines two different techniques, IDA and MPA is employed, presented by modal incremental dynamic analysis (MIDA). Using MIDA procedure, simple approximate curves that present a realistic linear and non-linear seismic behavior of the structure headed for the calculation of the damage measure (DM) due to the applied scaled level of earthquakes can easily be extracted. In this study, the capability, limitation and precision of MPA in comparison with NL-THA and also MIDA in comparison with IDA method are evaluated. For this purpose, two steel building models of 5 and 15-story with special moment resisting frame (MRF) in X direction and simple frame with X-bracing in Y direction has been designed. Furthermore, seven far field earthquake records are used for nonlinear analyses. In the current article, acceleration spectral intensity of the first mode of vibration with 5% damping, i.e. Sa(T1, %5) factor, are used as of intensity measure (IM). The story deflection and story drift are chosen as of the most important DM parameters to estimate the seismic vulnerability of structures in design practice. Comparison of the numerical results reveals that the MPA method has good accuracy in building seismic demands evaluation for 5-story frames (MRFs and braced frames) and 15-story MRF. However, no exact response is obtained for 15-story braced frame, considering the first three vibration modes of the structure. It is also shown that the results from MIDA simple method compares favorably to the IDA method. Thus, MIDA can be served by design engineers for seismic analysis in order to evaluate structural performance due to its relative simplicity and minimal computational effort.

In this article, an unreinforced masonry wall under in-plane load was numerically modeled using the ABAQUS software. In order to model the material of masonry, concrete material in the material library of Abaqus software was used. The concrete damaged plasticity method in the Abaqus software is a model that was meticulously studied in this research. Initially the governing factors influencing the behavior of this model were introduced, and then the cases provided for this purpose were separately investigated. To this end, an unreinforced masonry wall (100 × 990 × 1000 mm) which has been placed under the in-plane load in the lab, and its laboratory results are available was modeled in the Abaqus software and after defining the required specifications, the effect of various parameters such as stress cracking, dilation angle, strain cracking, viscosity, and etc. was investigated. For modeling the wall, macro method, which is one of the modeling methods of masonry materials was used. After calibration of the numerical model with the laboratory results, the effect of all of the available parameters in the concrete damaged plasticity model was investigated, and their effect was shown in the load-displacement diagram as well as the contour stress. A meticulous parametric investigation would give a better understanding of the way of functioning of these parameters in the modeling. In addition, it offers a better understanding for the users to use appropriate parameters in the modeling.

In this research the effects of nonlinear behavior of concrete on seismic performance of double curvature arch dam have been investigated. ANSYS software was used for analysis of the model which is based on finite element method. The Morrow Point double curvature arch dam is selected as the seismic analysis case study model and the interaction effect of dam, reservoir and foundation has been considered in the model. To investigate the seismic behavior of dam the El Centro earthquake components has been applied to the model. Both linear and nonlinear behavior of concrete has been investigated by dynamic analysis separately. Results of the displacement of dam crest and principle stresses have been extracted and compared. The results of the analysis have shown the effects of nonlinearity behavior of the concrete on the responses which means that the nonlinearity behavior of concrete would increase the displacement of dam crest and decrease principle stresses. The results have shown that by applying the nonlinearity behavior of concrete, the maximum structural capacity can be used which leads to increasing the accuracy in the field of linearity and nonlinearity material behavior to offer optimal models.

In spite of extensive studies since 1970 on Soil Structure Interaction (SSI), there is still controversy regarding the seismic performance of the structures rested on soft soil. SSI is known as a phenomenon influencing beneficial and sometimes detrimental effects on the response of structures. The response of soil–structure system depends basically on the size of the structure, its dynamic properties, and the soil profile as well as the applied excitation. Under strong shaking the response of soil–structure system is nonlinear and a combination of different types of nonlinearity as well as sliding, uplift and soil yielding will occur. Although foundation uplift in conjunction with soil yielding may dissipate energy during earthquakes, they may also lead to excessive permanent deformations in the structures.
In such case, soil- structure interaction (SSI) is not only beneficial, but also detrimental to the seismic response of the structures. In order to investigate the beneficial and detrimental effects of SSI on the nonlinear response of building, damage spectra on the basis of Park and Ang damage Index for the SDOF models are provided by considering and neglecting the SSI effects. The bilinear SDOF models are supported by Beam on Nonlinear Winkler Foundation. Two non-dimensional parameters are used to control the modeling. (I) non-dimensional frequency a0 which is a statement of the structure-to-soil stiffness ratio (II) the aspect ratio of the structure h/r. The systems are subjected to three earthquake ground motions recorded on soft soil. For each period, first the yield strength demand of the structure is calculated by iteration in order to reach the specified target ductility in the fixed-base model within 1% of accuracy when subjected to the ground motions. The dissipated hysteretic energy in the structure is also calculated accordingly. Then, the ductility and the hysteretic energy demands are calculated for the soil–structure systems under different values of a0 and h/r subjected to the same ground motion providing the same yield strength for the structure. Consequently, the damage index is calculated for the structure in the fixed-base state as well as for the structure when located on soil. The result showed that for most of structures with long period SSI decrease the damage index. How ever It is observed that in some cases of structure to soil stiffness, SSI increases the damage index before a threshold period which is closely related to the predominant period of the ground motion. It means that the conventional fixed-base model underestimates the damages sustained by buildings having periods less than this threshold period. In particular, the SSI substantially increases the damage index of short-period buildings located on soft soils. It is also observed that increasing the aspect ratio of the structure increases this effect. However, the trend is reversed after the threshold period. it is observed that the increase in the slenderness ratio and ductility ratiob of structures leads to increase in the maximum damage.