In nonlinear static (PUSHOVER) methods of ANALYSIS as an alternative to time history ANALYSIS, the capacity curve of the structure is established with respect to the roof displacement. Disproportionate increases in the roof displacement and even outright reversals of the higher modes can distort the capacity curve of the equivalent single degree of freedom system in these kinds of method, including MPA. To overcome this problem, recently, “Energy-Based” the MODAL PUSHOVER ANALYSIS (Energy-Based MPA) method has been introduced. In this method, the absorbed energy and/or the external work in the PUSHOVER ANALYSIS is considered. Accordingly, the assessment of the Energy-Based MPA method is important in the seismic ANALYSIS of asymmetrical and tall buildings. In this paper, the seismic demands of concrete structures with irregularity in elevation are determined, using Energy-Based MPA. For assessment of the presented technique, the results are compared with those from the Non-Linear Time History ANALYSIS (NL-THA). Seven examples including a 2-D simulation of a 12-story building are modeled, using the Opensees Code. For each case, different types of irregularity, such as mass, geometry and variations due to the difference in elevation are considered. Story-drifts and floor-displacements are used as the main parameters for assessment of the results. Based on a study of the structural performance of the models, it has been made clear that different types of the above-mentioned irregularity in elevation do not have any significant effect on the Energy-Based MPA method. Consequently, this method can be considered as an accurate alternative technique for NL-THA, to fairly estimate the seismic demands of structures.

Incremental Dynamic ANALYSIS (IDA) procedure is now considered as a robust tool for estimating the seismic sidesway collapse capacity of structures. However, the procedure is time-consuming and requires numerous nonlinear response-history analyses. This paper proposes a simplified MODAL PUSHOVER ANALYSIS (MPA) procedure for IDA of RC moment-resisting frames. The proposed method uses the dynamic response of an equivalent single-degree-of-freedom system, characterized by a bilinear relationship between the lateral force and roof-displacement. This relationship is determined by the ‘ first-mode’ PUSHOVER ANALYSIS of the structure. Four regular RC moment-resisting frames designed based on the current US building codes are selected and subjected to the proposed method. The ANALYSIS results obtained from the original MPA-based IDA method, Static Push-Over to Incremental Dynamic ANALYSIS (SPO2IDA) and the method proposed by Shafei et al are also presented for comparison. The performance of the proposed method is then evaluated through comparisons with the results obtained from IDAs. The results show that the proposed method can efficiently estimate the dynamic capacity of the example buildings for different seismic intensities. Nonetheless like to MPAbased IDA and SPO2IDA methods less accurate results are obtained by the proposed procedure for 16% and 84% IDA fractiles in most case studies.

The procedure of estimating the RC moment-resisting frames under blast loading using a multi-mode adaptive PUSHOVER (MADP) ANALYSIS is investigated in the current study. The main advantage of the proposed procedure is the combination of the multi-mode and adaptive PUSHOVER ANALYSIS approaches, which has not been done in the past for blast loadings. To investigate the efficiency of the proposed approach, several RC moment-resisting frames (RC-MRFs) of the 4-, 8-, and 20- storey are considered in the study. For a better comparison, the conventional MODAL PUSHOVER ANALYSIS (MPA), nonlinear response history ANALYSIS (NRHA), and the proposed approach are considered in the simulations. To this end, various influential parameters including the lateral force, floor displacement, storey drift, storey drift ratio, etc. are considered. For all models, the first three mode shapes were considered in the ANALYSIS procedure, while for the case of 20 storey RC-MRF, the torsional effect is included as well. The results indicated that the proposed MADP procedure has adequate accuracy and efficiency to estimate the blast loading demand on RC-MRFs.

The nonlinear static PUSHOVER ANALYSIS technique is mostly used in the performance-based design of structures and it is favored over nonlinear response history ANALYSIS. However, the PUSHOVER ANALYSIS with FEMA load distributions losses its accuracy in estimating seismic responses of long period structures when higher mode effects are important. Some procedures have been offered to consider this effect. FEMA and MODAL PUSHOVER ANALYSIS (MPA) are addressed in the current study and compared with inelastic response history ANALYSIS. These procedures are applied to medium high-rise (10 and 15 storey) and high-rise (20 and 30 storey) frames; efficiency and limitations of them are elaborated. MPA procedure present significant advantage over FEMA load distributions in predicting storey drifts, but the both are thoroughly unsuccessful to predict hinge plastic rotations with acceptable accuracy. It is demonstrated that the seismic demands determined with MPA procedure will be unsatisfactory in nonlinear systems subjected to individual ground motions which inelastic SDF systems related to significant modes of the buildings respond beyond the elastic limit. Therefore, it’s inevitable to avoid evaluating seismic demands of the buildings based on individual ground motion with MPA procedure.

The traditional PUSHOVER ANALYSIS procedure does not represent adequately, the effects of varying dynamic characteristics caused by structural yielding and the contributions of higher modes to the structural responses. The recently developed MODAL PUSHOVER ANALYSIS (MPA) procedure significantly improves the traditional PUSHOVER ANALYSIS by including the effects of a sufficient number of modes in the ANALYSIS.The present study evaluates the accuracy of the MODAL PUSHOVER ANALYSIS in estimating the seismic demands of vertically irregular planar moment-resisting frames in comparison with the exact results from nonlinear time-history ANALYSIS (NLTHA). In this research, seven irregular 12- story frames representing three types of height-wise irregularities: mass irregularity, vertical geometric irregularity (i.e., setback) and difference in floor levels, and also one regular 12-story frame as a reference are analyzed due to an ensemble of seven ground acceleration records. The earthquake records are chosen such that a wide range of frequency contents, as well as the effects of both near and far fault distances, be taken into account in the ANALYSIS. Findings from this investigation indicate that in most of the irregular models considered, the method of MPA can reasonably estimate the values of critical parameters such as peak floor displacement and storydrift ratios. Furthermore, it is observed that the inclusion of the first two modes improves the accuracy of predictions relative to using only the fundamental mode in the ANALYSIS. Such degree of improvement in accuracy is not reached by including the third mode effects in the MPA procedure.

Nonlinear time history ANALYSIS (NL-THA) is the most accurate method to estimate the seismic demand of structures and predict their failure. To that end, extensive efforts have been made to develop fast and convenient methods to carry out nonlinear static analyses. In recent years, PUSHOVER methods have been widely used as a suitable tool to evalute the seismic performance of structures. Also, various advanced PUSHOVER procedures have been proposed to take into account the effect of higher modes and the change in the dynamic properties of structures in the nonlinear phase. Therefore, different PUSHOVER procedures have been further developed for this purpose. The nonlinear static ANALYSIS has been widely employed to evaluate the nonlinear behavior of structures. The PUSHOVER ANALYSIS was first expanded in a number of studies to investigate buildings. Not many studies have been conducted on the seismic demand of latticed space structures. In the present work, therefore, an optimization procedure has been employed to refine the performance of the PUSHOVER ANALYSIS in estimating the seismic response of double-layer barrel vault roofs with vertical double-layer walls. In the method proposed herein, the coefficients of the MODAL load combinations of the studied structures have been optimized using the simplex algorithm to find the optimum load pattern. Fifteen models with various rise-to-span and height-to-span ratios were considered to assess the accuracy of the proposed method in predicting the seismic demand of these structures. The models were analyzed using the OpenSees software. In order to model the buckling behavior of the members, each member was divided into two nonlinear beam-column elements with an initial imperfection of 0. 1% at its mid-node. The models were designed with the dead, snow, temperature, and earthquake loads having been considered. All of the mentioned loads, with the exception of snow load, were applied to the structures as concentrated nodal loads. The snow load, by contrast, was applied to the structures in two symmetric and asymmetric patterns in accordance with the sixth volume of the Iranian national code of buildings. For earthquake loads, the 4 edition of the Iranian code of practice for seismic resistant design of buildings was used. It should be noted that the seismic mass of the roof of each model was calculated by considering the entirety of the dead load in addition to 40% of the snow load. In the design process of each model, the dead, snow, temperature, and earthquake load combinations were formulated based on the AISCASD89 standard. The sections of the members of the structures were chosen from hollow tubular sections, with their slenderness ratios limited to 100. Afterwards, PUSHOVER analyses were performed using the optimized load pattern. The obtained results were compared to those of the incremental dynamic analyses (IDA) and two other well-known PUSHOVER methods, namely the MPA and the conventional first-mode PUSHOVER ANALYSIS. The results revealed that the proposed PUSHOVER method can provide a good estimation of the base shear and intial stiffness of the structures when compared to dynamic analyses. In addition, an increase in the rise-to-span ratio of the roof causes an improvement in the accuracy of the proposed PUSHOVER method. Also, in comparison with the MPA and conventional PUSHOVER procedures, the responses produced by the proposed method are closer to those generated by dynamic analyses. In addition, a comparison of the obtained drift patterns reveals that the results of both the PUSHOVER and incremental dynamic analyses along the longitudinal direction of the wall are quite close to each other. Another advantage of the proposed PUSHOVER method is that it also produces acceptable results on the nodes on the roof of the space structure. Also, along the transverse direction, the proposed method yields better results.

In this paper, a new nonlinear static (PUSHOVER) ANALYSIS method is presented to evaluate the displacement-based demands of steel moment resisting frames (MRFs) at the collapse prevention performance level. In this method, the MODAL PUSHOVER responses are integrated using MODAL combination coefficients, which are calculated from optimization procedures. Two metaheuristic algorithms, including particle swarm optimization and colliding bodies optimization, are utilized in for this purpose. In the proposed procedure, the collapse prevention performance level is obtained by a new suggested criterion, which is based on the onset of severe local damages at the structure. This criterion corresponds to occur backward shape in the story capacity curves. The MODAL combination coefficients are obtained from incremental dynamic ANALYSIS (IDA) results of 5, 9, and 11 story steel moment resisting frames. The optimized MODAL PUSHOVER (OMPA) method is applied to two 9 and 12 story steel MRF buildings. The results show that the proposed method is easy to implement and is accurate enough to evaluate the displacement-based responses at the CP performance level.

Nonlinear static methods are simplified procedures in which the problem of evaluating the maximum expected response of a MDOF system for a specified level of earthquake motion is replaced by response evaluation of its equivalent SDOF system. The common features of these procedures are the use of PUSHOVER ANALYSIS to characterize the structural system. In PUSHOVER ANALYSIS both the force distribution and the target displacement are based on the assumptions that the response is controlled by the fundamental mode and that the mode shape remains unchanged after the structure yields. Therefore, the invariant force distributions does not account for the change of load patterns caused by the plastic hinge formation and changes in the stiffness of different structural elements. That could have some effects in the outcome of the method depending on different structural parameters. This paper introduces an adaptive PUSHOVER ANALYSIS method to improve the accuracy of the currently used PUSHOVER ANALYSIS in predicting the seismic-induced dynamic demands of the structures. Comparison of the common PUSHOVER analyses, adaptive PUSHOVER analyses and time-history analyses performed for a number of multiple-bay, short and high-rise steel structures, demonstrates the efficiency of the proposed method.

PUSHOVER is a non-linear static process, where a lateral load defined by a different load pattern than before, which represents the inertial forces in a particular earthquake, is defined as increasing uniformly until it reaches the target displacement or destruction. In this ANALYSIS, the overall force intensity has changed, but the load pattern remains the same until the end of the ANALYSIS, so the results of the PUSHOVER ANALYSIS are highly sensitive to the applied load pattern. In the traditional PUSHOVER ANALYSIS, uniform distribution, the response is only considered under the influence of the first mode assuming that it does not change, if the constant force distribution cannot be used in the distribution of internal forces due to the yielding of the structure and the changes related to the vibration characteristics, including the increase the participation of higher modes in the response of the structure gives a correct estimate. Therefore, in order to develop and include the effect of higher modes, three new load pattern examples are proposed in the ANALYSIS of concrete bridge with continuous straight deck and piers of different height. The pattern of uniformly distributed lateral loads based on the FEMA-273 regulation, the upper band method, the MODAL spectral composition, and the second method of MODAL composition of the patterns used here. Based on the results of this research, in short bridges, the MODAL combination method, and in long bridges, the spectral MODAL combination method have created the closest estimation of the response parameters among other methods.