displacement Coefficient Method (DCM) stipulated in the ASCE 41-06 standard is becoming the preferred method for seismic rehabilitation of buildings in many high-seismic-hazard countries. Applications of the method for non-building constructions such as bridges are beyond the scope of this standard. Thus its application to this kind of structure should be approached with care. Target displacement has reasonable accuracy for buildings with strong columns and weak beams, where there is the development of plastic hinges. Due to high stiffness and strength of the deck relative to the piers in most bridges, this mechanism does not occur, and it is necessary to evaluate the accuracy of DCM for such structures. In this research, an attempt is made to evaluate the credibility of DCM in the ASCE/SEI 41-06 standard for estimating Target drifts in concrete regular bridges under strong ground motions. To apply the extension of the method to bridge structures, the definition of new correction factor CB, which should be multiplied to previous coefficients, is required. This novel coefficient can improve the accuracy of the mentioned method in accessing seismic displacement demands. The coefficient is presented for soil types A to D based on NEHRP soil classification. The validity of the modified DCM is examined for several bridges with use of nonlinear dynamic analysis. Good correlation is found between both procedures.

Pushover analysis is a simplified nonlinear analysis technique that can be used to estimate the dynamic demands imposed on a structure under earthquake excitations. One of the first steps taken in this approximate solution is to assess the maximum roof displacement, known as Target displacement, using the base shear versus roof displacement diagram. That could be done by the so-called dynamic pushover analysis, i.e. a dynamic time history analysis of an equivalent single degree of freedom model of the original system, as well as other available approximate static methods. In this paper, a number of load patterns, including a new approach, are considered to construct the related pushover curves. In a so-called dynamic pushover analysis, the bi-linear and tri-linear approximations of these pushover curves were used to assess the Target displacements by performing dynamic nonlinear time history analyses. The results obtained for five different special moment resisting steel frames, using five earthquake records were compared with those resulted from the time history analysis of the original system. It is shown that the dynamic pushover analysis approach, specially, with the tri-linear approximation of the pushover curves, proves to have a better accuracy in assessing the Target displacements. On the other hand, when nonlinear static procedure seems adequate, no specific preference is observed in using more complicated static procedures (proposed by codes) compared to the simple first mode Target displacement assessment.

A main challenge for performance-based seismic engineering is to develop simple, practical and precise methods for assessing existing structures to satisfy considerable performance objectives. Pushover analysis is a simplified nonlinear analysis technique that can be implemented for estimating the dynamic demands imposed on a structure under earthquake excitations. In this method, structure is subjected to specified load pattern to reach a Target displacement. The present study provides a Target displacement for estimating the seismic demand of eccentrically braced frames (EBFs). A parametric study is conducted on a group of 30 EBFs under a set of 15 accelerograms. The results of nonlinear dynamic analyses of EBFs have been post-processed by nonlinear regression analysis and a relation is proposed for Target displacement. In order to verify the capability of the proposed procedure, three EBFs are assessed by the present method in which the results show that the proposed method is capable of reproducing the peak dynamic responses with relatively good accuracy. Additionally, the comparison of obtained results with those of other conventional Target displacement methods such as N2 method, and displacement coefficient method confirms the efficiency of the suggested one.

In this study, a performance-based optimal design of moment frames is presented based on Target roof displacement criteria. Four performance Levels defined by four roof Target displacements are considered and moment frame has subjected to constant gravity loads and incrementally lateral loads until meet the end roof displacement. In each performance Target displacement, hinge rotations, inter-story drifts and internal forces have controlled in accordance with provisions. Because axial force has decreasing influence on plastic moment capacity, magnitude of column axial forces is needed before pushover analysis for modeling column hinges. To solve this problem, an approximate pushover analysis without considering axial forces for column hinges performed to calculate column forces in the final Target displacement. Then final pushover analysis executed by considering influence of calculated axial forces in plastic hinges. This pushover analysis and defined constraints only guarantee ductility criteria for the structure until now. To ensure that structure has enough strength, before pushover analysis it has checked for enough strength by gravity load combination and allowable vertical deflection of beams under service loads. To avoid other undesirable mechanisms like soft and hard story or weak column-strong beam, other equations considered as Target function and constraint respectively. The proposed pushover analysis has modeled with joining two springs and an elastic element so that moment-rotation parameters introduced as a material to the springs based on FEMA 356 tables. For all models and analysis, Open Sees finite element software utilized in such a way that all text codes write and run in Matlab without opening Open Sees directly. When completed all analysis and calculated all constraints and Target functions; cost function assigns a grade to the suggested structure using weight and penalties for violated constraints and this cycle continues for other structures. Two meta-heuristics, gray wolf optimization (GWO) and particle swarm optimization (PSO) are utilized for optimization. Proposed analyse is illustrated for a three story four bay and a nine story five bay building frame work examples.

Considering appropriate lateral load pattern and determining Target displacement for bridges in nonlinear static pushover (NSP) analysis have been important issues for researchers. There are two conventional load patterns in the standard codes of practices which are called: 1- Mode shape proportional load pattern, 2-Mass proportional load pattern.Capacity Spectrum Method (CSM) is one of the approaches applied in determining Target displacement of structures usually using the first mode proportional load pattern. In conventional (CSM) method for determining the spectrum capacity curve during NSP analysis, the base shear of the multi degrees of freedom system versus displacement of the control point is drawn using the first mode proportional load pattern, and then is converted to spectral displacement and spectral acceleration format.Converting base shears and control point displacements into spectral accelerations and displacements is based on the assumption that the dynamic behavior is dominated with only one of the natural vibrational mode shapes which is assumed to be constant and not changing during the (NSP) analysis. Assessing this assumption for horizontally curved bridges shows that the lateral load patterns are effected with combination of modes and are not proportional to one especial mode shape. In this context, mass proportional load pattern is usually used to consider the effects of some special pre-specified mode shapes in (NSP) analysis.In this research, the (CSM) method is further developed and a method is proposed for determining Target displacements using the mass proportional load pattern.In the proposed method, the capacity spectrum is drawn using mass proportional load pattern based on the displacement vector in the linear range instead of some specified mode shapes. Therefore, the developed proposed method is not dependent on some pre-specified modes of vibration and the effects of all modes of vibration are considered simultaneously. The efficiency of the proposed method is proved by determining Target displacements of control points on a horizontally curved bridge using the proposed method and then comparing the results with the results of incremental dynamic analysis (IDA).

In recent years, nonlinear static analysis (pushover) has been rapidly developed. Simplicity, speed and ease of interpretation of results are some advantages of this method, rather than the nonlinear dynamic analysis procedure, as the most accurate method for seismic analysis. Target displacement or performance point is a fundamental component of each nonlinear static analysis, where displacements and stresses of structures are evaluated. The N2 method is a well-known procedure for determination of the performance point, by which, Target displacement is determined through intersecting the capacity curve and corresponding inelastic response spectrum, using a trial and error method. In this procedure, determination of the inelastic response spectrum is an important problem.To achieve an easy and quick analysis in the seismic design of structures, using the concept of a spectrum is common. A response spectrum is a simple plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of SDOF systems with various natural frequencies that are forced into motion by the same base vibration. This concept fairly estimates the characteristics of ground motion and maximum amounts of displacement, velocity and acceleration due to an earthquake. Since, in severe ground motions, structures experience deformations beyond the elastic range, the inelastic spectrum is utilized to account for the inelastic behavior. The shape and magnitude of inelastic response spectra are dependent on the period and damping characteristics of the structure, the hysteresis behavior of used material and some seismic parameters, such as soil condition, earthquake magnitude and epicenter distance.In this paper, with regard to existing equations for determination of the inelastic response spectrum, a combinatory approximate method, based on soil condition and the ductility ratio period of the structure, is developed, by which the inelastic response spectrum is estimated using the elastic design response spectrum. Using this inelastic response spectrum, the Target displacement of regular systems is estimated with admirable accuracy.

The recent trend in structural earthquake engineering practice is to use performance-based seismic evaluation methods for the estimation of inelastic demands in structures. Nonlinear static analysis, commonly referred to as pushover analysis, is becoming a popular simplified tool for seismic performance evaluation of existing and new structures. The pushover analysis of a structure is a static nonlinear analysis under permanent vertical load vectors and gradually increasing lateral loads until reaching the predetermined Target displacement at roof level. Target displacement serves as an estimate of the global displacement of the structure expected to experience in a design earthquake.The accurate estimation of Target displacement associated with specific performance objective affect the accuracy of seismic demand predictions of pushover analysis. Recently, the researchers have proposed various enhanced methods that aim to capture the true seismic-induced Target displacements. Most of the reported research on development of improved Nonlinear Static Procedures (NSPs) is based on the response of analytical models subjected to Far-Fault (FF) earthquake records and less have been investigated for Near-Fault (NF) ground motions. NF motions differ from FF ones in that they often contain strong coherent dynamic long period pulses and/or permanent ground displacements. Out of the two kinds of NF ground motions, ground motions with velocity pulses caused by NF directivity effects have received a great deal of attention because of their potential to cause severe damage to structures. Capacity Spectrum Method (CSM) and displacement Coefficient Method (DCM) are the two methods presented in FEMA-440 (2005) and ASCE/SEI 41-13 (2013) as standard methods of estimating the Target displacement. DCM is considered in this paper as the basis of the presented method. In DCM, the Target displacement, which corresponds to the displacement at roof level of a building, shall be calculated by applying appropriate modification factors to the elastic spectral displacement of SDOF system. In this method, C0 is modification factor to relate spectral displacement of an equivalent SDOF system to the roof displacement of the building, C1 is the modification factor to relate the expected maximum displacements of an inelastic SDOF oscillator, and C2 is the modification factor to represent the effect of pinched hysteretic shape, stiffness degradation, and strength deterioration on the maximum displacement response. It should be noted that the coefficients of this equation have been derived from FF motions in FEMA-440 (2005). Therefore, applying these coefficients to estimate the Target displacement for NF ground motion may not yield accurate results. Due to this, CN, need to be used to modify the C1 coefficient when a SDOF system is subjected to NF ground motion. This modification factor was previously presented by Esfahanian and Aghakouchak (2015). This paper investigates inelastic seismic demands of the normal component of near-fault pulse-like ground motions.20 near-fault and 20 far-fault ground motions and the responses of 10-, 15-, and 20-story multi degrees of freedom (MDOF) systems constitute the dataset.These systems are all steel moment-resisting frames, designed according to allowable stress design method. The buildings’ lateral load-resisting system is steel special moment-resisting frame. All buildings are 15 m in width.The bays are 5 m on center with three bays. Story heights of all buildings are 3.2 m. The seismic masses of all level floors for each structure are assumed to be equal and consist of dead load plus 20% of live load. Dead and live loads are equal to 650 and 200 kg/m2 on the floor area that loading width of the frames is assumed to be 5 m. Design is performed based on the weak beam-strong column. In analysis and design, P-D (second order) effects are included. Nonlinear static and dynamic analyses were performed by the OpenSees (2013) software to simulate the performance of structural systems subjected to earthquakes. Both geometrical nonlinearity and material inelasticity were taken into account in the models.The material inelasticity was explicitly considered by employing a fiber modeling approach. Beams and columns have been modeled as finite elements with distributed inelasticity in a specified length of the member ends, using force-beam-column elements. For all of the NL-THAs, the damping matrix was defined using Rayleigh damping with a damping ratio of 5% for the first and third modes of vibration. In this paper, wavelet analysis method, presented by Baker (2007, 2008) is used for selecting pulse-like NF ground motions. NL-THA is utilized as the benchmark for comparison with nonlinear static analysis results. A new method for estimating Target displacements are presented, using response spectrum analysis method and appropriate modification factors. As the proposed method considers the MDOF effects, C0 coefficient is not used in this method and only C1, C2, and CN are applied in this method. The Target displacements resulting from the proposed procedure are then compared to those from the NL-THA and displacement coefficient method of ASCE 41-13, as well as to those predicted from Modal Pushover Analysis (MPA) methods. MPA is an enhanced NSP presented by Chopra, which utilizes the concept of modal combinations through several pushover analyses using invariant load patterns based on elastic mode shapes where the total response is determined with combination of each mode at the end (Chopra and Goel, 2001, 2002).It should be noted that, various methods applied to nonlinear models developed using generally accepted methods provide either overestimation or underestimation of the Target roof displacement when compared to the value derived from NL-THA of recorded motions. It is shown that these procedures may lead to significantly different estimates of the Target displacement, particularly for high-rise buildings responding in the nonlinear range. The results of the proposed procedure demonstrate acceptable values for Target displacement, especially for near-fault earthquake records in comparison to the approximate and exact ones.

A comprehensive closed-form approach is presented to approximately evaluate the probability distribution of displacement of SDOF and MDOF systems subjected to stationary and non-stationary Gaussian excitations. The probability distribution of displacement of a SDOF system is investigated on the basis of statistical relations, and a closed-form method is presented to approximately detect the structural response without any need to perform exact dynamic analysis. Buildings with BW hysteretic behavior can easily be modeled with the aid of the proposed approach. The approximate procedure can significantly facilitate the utilization of non-stationary models in engineering practice, because it avoids computational difficulties. The method is based on the approximation of a non-stationary process by an equivalent stationary process. In this study, six systems with initial periods of 0.4, 0.6, 0.8, 1, 1.2 and 1.4 sec. are considered for the validation of the presented relations. With the aid of the determined linearization coefficients of the system, the Target displacement and IDA curves are also determined. The previous investigations into development and evaluation of the coefb03cient method to compute the Target displacement used computer models of the buildings; an exhaustive list of references is available in the FEMA-440 report. The “exact” value of the Target roof displacement was taken as the peak roof displacement computed by nonlinear response history analysis of the computer model subjected to selected earthquake motion at its base. But, generally, determining the probability distribution of structural demands and the response of structural systems at different confidence levels, based on nonlinear dynamic analysis, can be very time consuming. With regard to this need, developing a simple computational approach that replaces exact methods and the time consuming dynamic analysis of structures is the aim of this research. The computed Target displacements for six systems are compared with the Target displacement under 300 non-stationary records and from nonlinear static procedure in FEMA-440. In comparison to the exact dynamic analysis procedure, the proposed approach provides an acceptable probabilistic result with less computational time and cost.

Background: In Genu-valgum tibiofemoral angle increases above its normal value of 6°. This disorder causes difficulty in walking and sport activities in short-.term. But in long-term, because of increased force on lateral compartment of the knee, osteoarthritic changes of the lateral side of the knee and ligamentous laxity of medial side of knee could happen. In the past, osteotomies have been done on lateral side of distal femur for correction of Genuvalgum. We are suggesting a medial approach, posterior to vastus medialis with close-wedge osteotomy from medial side as an alternative approach for correction of genovalgum. Method: A Clinical trial study of 20 lower limbs operated between 1988 to 2002. Results: 20 lower limbs were operated with this technique. The mean age was 23.2, 14 patients were female and 2 male. 10 limbs were left and the other 10 were right side. Mean valgus angle was 14.75° preoperatively and 3° postoperatively the mean follow-up period was 628 days (Minimum 50 and maximum 1111 days). At follow-up, the range of knee motion in all limbs was normal. There was no infection postoperatively, quadriceps force was 5/5 in 18 and 4/5 in two limbs. Functional improvement was observed in 15 cases and all 16 patients had full satisfaction from the appearance of the limbs.