Progressive collapse studies generally assess the performance of the structure under gravity and blast loads, while earthquakes may also lead to the progressive collapse of a damaged structure. In this study, the progressive collapse response of concentrically braced dual systems with steel moment-resisting frames was assessed under seismic loads through pushover analysis using triangular and uniform lateral load patterns. Two different bracing types (X and inverted V braces) were considered, and their performances were compared under different lateral load patterns using the Nonlinear Static alternate path method recommended in the Unified Facilities Criteria (UFC) guideline. Eventually, the seismic progressive collapse resistance of models was compared to their progressive collapse response under gravity loads. These studies showed that models under the seismic progressive collapse loads satisfied UFC acceptance criteria and limited rehabilitation objective. The structures had better performance under seismic progressive collapse than models under gravity loads because of more resistance, ductility, suitable load redistribution, and more structural elements that participated in load redistribution. Furthermore, despite studies on progressive collapse under gravity loads, the dual system with X braces showed better progressive collapse performance (more resistance, residual reserve strength ratio and ductility) under seismic loads than the model with inverted V braces.

In recent years some multi-mode pushover procedures taking into account higher mode effects, have been proposed. The responses of considered modes are combined by the quadratic combination rules, while using the elastic modal combination rules in the inelastic phases is not valid. Here, an optimum weighted mode combination method for Nonlinear Static analysis is presented. Genetic algorithm is used for optimization of the modal weight. The proposed procedure is applied for a sample building. The results show that the resulted response from the proposed method has minimal error in comparison with the response of the Nonlinear time history analysis.

Nonlinear Static procedure (NSP) is a common technique to predict seismic demands on various building structures by subjecting a monotonically increasing horizontal loading (pushover) to the structure. Therefore, the pushover analysis is an important part of each NSP. Accordingly, the current paper aims at investigating the efficiency of various algorithms of lateral load patterns applied to the structure in NSPs. In recent years, fundamental advances have been made in the NSPs to enhance the response of NSPs toward Nonlinear time history analysis (NTHA). Among the NSPs, the philosophy of "adaptive procedures" has been focused by many researchers. In the case of utilizing adaptive procedures, the use of incremental force vector considering the effects of higher modes of vibration and stiffness deteriorations is possible and seems that it can lead to a good prediction of seismic response of structures. In this study, a new adaptive procedure called energy-based adaptive pushover analysis (EAPA) is implemented based on the work done by modal forces in each level of the structure during the analysis and is examined for steel moment resisting frames (SMRFs). EAPA is inspired by force-based adaptive pushover (FAP) and story shear-based adaptive pushover (SSAP). FAP has applied modal forces directly into load patterns; SSAP, on the other hand, has implemented the energy method in system`s capacity curve for measuring the equivalent movement. EAPA has enforced the concept of energy directly in load pattern; so that by using the modal forces-movements an energy-based adaptive algorithm is obtained. Hence, the effects of higher modes, deterioration in stiffness and strength, and characteristics of a specific site are incorporated and reflected in applied forces on the structure. Results obtained from the method proposed a desirable accordance with the extracted results from NTHA over the height of the structure.

This investigation presents material Nonlinear analysis of a cantilever bar element made of functionally graded material with porosity properties. The material properties of bar element are considered as changing though axial direction based on the Power-Law distribution and uniform porosity distribution. The stress-strain relation of the material is considered as a Nonlinear property according to a Power-Law function. The cantilever bar element is subjected to a point load at the free end. In order to obtain more realistic solution for the Nonlinear problem and axially material distribution, Nonlinear finite element method is used. In the obtaining of finite element equations, the virtual work principle is used and, after linearization step, the tangent stiffness matrix and residual vector are obtained. In the Nonlinear solution process, the incremental force method is implemented and, each load step, the Nonlinear equations are solved by using the Newton-Raphson iteration method. In the numerical results, effects of material Nonlinearity parameters, porosity coefficients, material distribution parameter and aspect ratios on Nonlinear Static deflections of the bar are presented and discussed. The obtained results show that the material Nonlinear behaviour of the bar element is considerably affected with porosity and material graduation.

Various equivalent Nonlinear Static analysis procedures have recently been introduced for seismic assessment of tall buildings. Here, iterative linear equivalent method is proposed for seismic analysis of concrete dams. Regarding important differences between the behavior of concrete dams and high-rise buildings, basic concepts and main steps of this analysis technique are developed to make it applicable for this kind of structures. In comparison with well-known push-over analysis, independency of the results from the lateral load pattern is one of the main advantages of this method. Other important achievements contain: estimating structure's damping and considering the interaction between water, structure and foundation. The proposed method is implemented and verified for Pine Flat dam which shows acceptable results.

This paper presents a force (flexibility) based formulation for Nonlinear Static analysis of reinforced concrete plane frames. Nonlinear behavior of concrete and steel fibers based on a simple one-dimensional constitutive law is considered. Navier- Bernoulli theory is accepted in different sections and the effect of bond-slip is, thus, neglected. The section flexibility and stiffness matrices are extracted by direct integration of tangential modulus of materials all over the sections. Flexibility, stiffness and residual force vector of elements are estimated, using principle of virtual work and based on a force (flexibility) formulation. An iterative algorithm used to satisfy the proposed convergence criterion. Presented samples show accuracy and efficiency of the proposed method in contrast to other existing numerical and experimental results.    

Microelectromechanical systems (MEMS) are used in many elds of industry like automotive، aerospace and medical instruments. Among the various ways to operate the MEMS devices، the electroStatic actuator is the common mechanism، due to simplicity and fast response. Previous experiments have shown that the mechanical behavior of devices، which their sizes are in order of micron and submicron، are dependent to size dependency. They also have illustrated that by decreasing the dimension of structures، the size dependent e ect is highlighted. In this case، the classical theories are not capable to predict the size dependent e ects and mechanical behavior of the microstructures properly. Therefore، nonclassical theories such as modied couple stress and strain gradient theories have been introduced. It was shown that the modied couple stress theory can accurately predict the size dependent behavior of microstructures. There are some in uences observed in the MEMS، that they have notable e ects on the mechanical behavior of microswitches، such as fringing elds and large de-ection. When the air gap is larger than the electrode's width of microswitches، the impacts of fringing elds and geometric Nonlinearity signicantly a ect the mechanical behavior of the system. Therefore، neglecting the abovementioned e ects leads to errors in the instability prediction of microswitches. Most of microswitches consist of a microcantilever with a proof mass and a xed substrate which there is an air gap between them. By applying voltage to the system، the microcantilever starts to de ect into the xed substrate. In this paper، pull-in instability and de ection of MEMS switches are investigated based on the size dependent model. The Nonlinear model is introduced by considering modied couple stress theory and fringing eld e ects as well as geometric Nonlinearity. Utilizing the minimum total potential energy principle، the Static equation of motion is derived in framework of the nonclassical theory. The e ects of various parameters on Static pull-in instability are studied and errors of considering the linear model or classical theories is calculated. The results show that the presented model is capable to predict the displacement and pull-in instability of the microswitches.

Having very simplicity, Nonlinear Static procedures (NSPs) are the most popular tools for estimation of structural capacity. These approaches construct a graphic display of the overall structural response via a pushover curve. The overall response of the system provides a direct simulation of the building as single degree of freedom (SDOF) system that simplifies the design and evaluation of the structure. In this research, the first step in any Nonlinear Static analysis or in other words perform a pushover analysis has been studied. Applied lateral load to the structural model not only affects the overall responses of the structure through structural capacity curve, but also directly affects the local responses of the structure. In order to evaluate these lateral loads, steel buckling restrained braced frame structures are examined by advanced modal pushovers. Next, the results of these pushover analyses will be compared with Nonlinear time history analysis as the most accurate method. Finally, the most efficient method in this particular structure is introduced. The analysis conducted in these structures shows that the lateral load pattern based on story shears offers a good prediction of the maximum response of the concentrically buckling restrained braced frame buildings.

Structural engineers have always sought to design structures that can predict their performance during earthquakes. By using the performance-based design method, the structures can be examined to observe the behavior they show when dealing with the expected earthquake. Nowadays, optimization is very important in the design of structures. Because the amount of cost to implement a structure that is economical from the point of view affects the importance of this issue. In this study, the weight optimization of convergent bracing frames has been measured based on the performance-based design method. Because one of the most common methods of analysis to evaluate the seismic performance is the non-linear Static analysis method, this method has been used as the basis of analysis. In this study, the objective function is considered based on the weight of the structure. The optimization problem considers the acceptance criteria for force-controlled and deformation-controlled members at desired performance levels, as well as geometric constraints. To make the optimal design possible based on the defined problem, optimizing the weight of three- and six-story concentrically braced 2D steel frames have been investigated using EVPS and EWOA algorithms. The results of the optimization show that it is possible to optimize the weight of the concentrically braced frame based on the performance-based method and using the algorithm.