Damage indexes consider different aspects of structural response with the objective of producing a quantitative measure of structural damage. In this paper, damage indexes based on deformation, energy, modal parameters and low cycle fatigue behavior are investigated in order to find a correlation between their numerical values. Selected damage indexes are compared by applying them in the NONLINEAR ANALYSIS of various low rise steel frames subjected to a set of seven earthquake accelerograms corresponding to a specific soil condition. Correlations between various indexes have been presented graphically and approximate conversion formulas are also provided.

Records from near-fault earthquakes to close the distance where the wave propagation source is a special property that their behavior makes them different from other records. Mostly near-fault earthquakes have strong pulse velocity (pulsatile wave) with great period accompanied with permanent deformation of earth. Velocity pulse occurs in horizontal component perpendicular to the motion surface of fault which is resultant of directionality effect of fault rupture. The properties of pulse such as velocity record in near-fault earthquakes cause the response spectrum to show non-ordinary behavior in pulse period. Also, due to imposing much energy to structure in during short period by these pulses, most of earthquake energy is absorbed in first made hinges instead of extension of non-linear behavior and plastic hinges in height of structure and the extension of non-linear behavior is not observed. This absorption of energy causes large relative inter-story displacements. Considering today’s using energy dissipation systems is current due to reducing earthquake vibrations of structures, which one of these energy dissipation systems are passive viscoelastic dampers. In these dampers which their energy dissipation mechanism depends on velocity of motion or in other words, on loading frequency and to be active these dampers there is no need to determined level of external excitation and they act in every earthquake. For this purpose, a number of structural models have been modeled in 2D form in “OpenSees” software for different damping ratios due to the added viscoelastic damper, non-linear dynamic ANALYSIS has been done under acceleration of horizontal earthquake and the amount of reduction of displacement response and base shear have been studied.

In this study, the seismic response of tall concrete structures with a special dual frame-wall concrete system is investigated using the endurance TIME method, and the results are compared with NONLINEAR TIME HISTORY ANALYSIS results. For this purpose, first, appropriate analytical models including buildings with concrete framed-wall system and 20, 30, and 40 stories are modeled non-linearly in PERFORM 3D software, and then, main NONLINEAR TIME HISTORY analyses are carried out for seven ground motions (accelerogram) further from the fault based on the FEMA P695 code and the endurance TIME accelerogram of (in) series. The results of the ANALYSIS are compared using indices (shear, relative displacement, and acceleration). The results indicate that the endurance TIME method is accurate in two indices of shear and acceleration, but the accuracy of the relative displacement index of the floor decreases as the number of stories of the structure increases.

This paper presents an efficient numerical ANALYSIS method called the Newton-Cotes-Hermite-Four-Point (NCH-4P) method for the TIME HISTORY ANALYSIS of structural systems with one and multiple degrees of freedom under earthquake effect. The method combines the numerical integration formula of the Newton-Cotes four-point method with the Hermite interpolation formulas to form a new algorithm for solving the vibration equation. The method can handle both linear and NONLINEAR systems, as well as different types of loading, such as external forces and earthquake excitation. The method is developed for the first TIME for the ANALYSIS of linear and NONLINEAR damped and undamped structural systems with one and multiple degrees of freedom. The method shows remarkable performance superiority in terms of accuracy, speed, convergence and simplicity compared to the pseudo-analytical Newmark-beta method and the semi-analytical Duhamel integral method. The method modifies the differential equation of motion to have a suitable form for numerical integration. Unlike the NONLINEAR Newmark-beta method, the method does not require an independent process such as Newton’s iteration to account for NONLINEAR effects; instead, a series of simple repeated calculations leads to the convergence of the response in NONLINEAR behavior. The numerical results demonstrate the efficiency of the method in estimating the response of systems under the famous EL-Centro record.

A fast and efficient numerical scheme is presented for TIME-HISTORY ANALYSIS of single-degree-of-freedom (SDOF) structural systems undergoing seismic excitation (Chopra, 2003). The new method is called Newton-Cotes-4P-θ Method. It uses the most known 4-point Newton-Cotes quadrature in its body to solve the vibration equation. NONLINEAR ANALYSIS is covered as well as linear ANALYSIS. Any arbitrary external loadings of type force or seismic signals are welcome. The significant advantages of the new formulation are its great simplicity, running speed, and appropriate precision level compared with its counterparts such as Duhamel integral and Newmark-β methods. The accuracy level of the Newton-Cotes-4P-θ is close to the semi-analytical method of Duhamel integration and its speed is similar to the Newmark-β algorithm. Notably, against the NONLINEAR Newmark-β method, the new method does not require a standalone procedure to handle NONLINEAR ANALYSIS; instead, it simply triggers iteration of the same computation used in its first processing round. Moreover, the Newmark-β method loses its performance dealing with stiff and near-conservative () systems; however, the Newton-Cotes-4P-θ method does not loos its accuracy and keeps its well-performed ANALYSIS in this case. Numerical results reveal the superiority of the Newton-Cotes- 4P-θ method against its counterparts such as the Duhamel integral, Newmark-β, and Wilson-θ methods (Babaei et al., 2021; Babaei et al., 2022; Babaei et al., 2023).

This study deals with predicting NONLINEAR TIME HISTORY deflection of scallop domes subject to earthquake loading employing neural network technique. Scallop domes have alternate ridged and grooves that radiate from the centre. There are two main types of scallop domes, lattice and continuous, which the latticed type of scallop domes is considered in the present paper.Due to the large number of the structural nodes and elements of scallop domes, NONLINEAR TIME HISTORY ANALYSIS of such structures is TIME consuming. In this study to reduce the computational burden radial basis function (RBF) neural network is utilized. The type of inputs of neural network models seriously affects the computational performance and accuracy of the network.Two types of input vectors: cross-sectional properties and natural periods of the structures can be employed for neural network training. In this paper the most influential natural periods of the structure are determined by adaptive neuro-fuzzy inference system (ANFIS) and then are used as the input vector of the RBF network. Results of illustrative example demonstrate high performance and computational accuracy of RBF network.

In a core-wall structure with buckling restrained braces (BRB) outrigger, locations of the plastic hinges are influenced by the outrigger action. Therefore, the designer should consider the issue and use suitable details in the plastic hinge area. The essential questions that arise here are the plastic hinge location and the design moment demand used for design of this kind of structure. In this paper, responses of the core-wall buildings with BRB outrigger designed by using the traditional response spectrum ANALYSIS (RSA) procedure, are assessed by implementing the NONLINEAR TIME HISTORY ANALYSIS (NLTHA). The result demonstrates that the plasticity can extend over anywhere within the core-walls specially, at the base, and above or below the outrigger levels. Formation of three plastic hinges in the core-wall is recognized suitable for the system.  To control the plasticity extension in the core-wall, it is recommended that a new modal combination method be applied to calculate the moment strength of the three plastic hinges over the height. A capacity design concept is used to design other regions of the core-wall where the plasticity does not extend to. The proposed procedure improves behavior of the system by restricting the plasticity extension to the predefined plastic hinge regions.

Nowadays, the requirements of designing structures based on low weight and high strength in structural engineering science, have increased the possibility of unwanted and destructive vibrations in these systems. Also, using of computer softwares for modeling alone cannot accurately predict the dynamic behavior of structures. For this reason, a fundamental approach to experimental techniques was developed and made progress in the field of modal ANALYSIS. In recent years, modal ANALYSIS has been applied as a tool to determine and enhance the dynamic properties of structures. The vibrational modes obtained from the modal ANALYSIS, are useful for understanding the behavior of the structure correctly. Modal ANALYSIS is also used in modal TIME HISTORY analyzes and quasi-dynamic ANALYSIS of response spectrum. An important point in modal ANALYSIS is that when using modal ANALYSIS there are two types of analytical models named special vector state and Ritz vector state. Finding the best method for modal ANALYSIS of structural responses is very important in modal ANALYSIS, so far no comprehensive studies have been conducted to date. Considering the importance of this issue, in this study the evaluation of the accuracy between the two modes of vectors (Ritz) and (Eigen) in modal ANALYSIS is done. It is concluded that the modal ANALYSIS of Eigen vector is more accurate than Ritz vector and the results of Eigen modal ANALYSIS are closer to reality.

This paper presents delay-dependent stability ANALYSIS for some types of NONLINEAR TIME-delay systems. Motivated by Lyapunov-Krasovskii functionals and the related theorems on stability of TIME-delay systems, we introduce a new procedure for generating such functionals. The main reason for considering Lyapunov-Krasovskii functionals is the less conservatism of this method. The obtained conditions are sufficient and local. Applying the introduced procedure on a typical system with TIME-invariant parameters derives more results and a numerical example presents the capability of the method.

Perhaps the rational choice approach is the most coherent approach to analyzing human behavior. This approach, which is based on the knowledge of the microeconomics in particular and on the economy as a whole, assumes that humans are rational beings and, according to their information portfolio, make a decision that optimizes their utility. Now, in different people, what is in the utility function can be different, but in general, everyone seeks to maximize their desirability. Although this framework was initially restricted to the field of economics and economic behavior, it gradually expanded economists and claimed that they could explain social, political, and even legal phenomena based on this approach. The tool used to do this was naturally a game theory that considered people's attitudes in the social arena to be strategic. The first critique of this approach was posed by psychologists who questioned the assumption of rationality. These psychologists in the decision-making psychology branch, later known as behavioral and behavioral economics, showed that humans face intense biases in their decisions and choices, which could lead to systematic diversion of choices and decisions from choices and optimal decisions.