The main objective of this study is to estimate seismic demands of MDOF frames, using SDOF system demands and to presents a procedure to evaluate maximum story drift and ductility demands of MDOF Steel Moment Resisting Frames. Some modifications have been studied, in order to evaluate MDOF system demands, including higher modes. These modification factors are computed as the ratios between MDOF and the first mode SDOF seismic demands for each record, making them independent from the intensity and duration of ground motion. This permits the statistical averaging of modification factors computed for ground motions of different intensities and duration. The results of this study show that the distribution of story drift and dynamic ductility demand over the height of the frames (specially high-rise ones), have an irregular trend. The reason is attributed to higher modes and MDOF effects, which is intensified with increasing the structure height and fundamental period. It was also concluded that the amplification of deformation demands (story drift and ductility respresented by adH.M and aµH.M modification factors), are mostly increasing with fundamental period and level of ductility (µSDOF).

In this paper, the effects of higher modes on seismic response of multi degree of freedom (MDOF) steel moment-resisting frames (SMRF) are investigated. Modification factors to the response of first mode SDOF system are presented in order to estimate seismic MDOF system demands. The study is based on spectral analysis and linear and nonlinear dynamic time history analysis of 4, 10, 15, 20 and 25 storey SMRFs under Elcentro, Tabas, Naghan and Manjil earthquake loading. A modification factor αeldisp is defined in order to estimate roof elastic displacement demands of an MDOF frame from first mode elastic displacement spectra. Base shear modification factor αvH M (to compute MDOF strength reduction factors), maximum story drift demand modification factor αdH M , and maximum story dynamic ductility demand modification factor αµH M are defined and presented for SDOF system responses in order to estimate the main MDOF system nonlinear seismic responses, including higher mode effects.

In recent years, various studies have been performed on the nonlinear responses of steel moment resisting frames under the near-fault earthquakes. Due to the event of near-fault earthquake, a significant amount of energy is exerted upon the structure, in a very short time. For this reason, the nonlinear distribution of demands differ with respect to those of the far-fault earthquakes. Investigating previous damages due to near-fault earthquakes indicated that significant inter-story drift demands are formed within the structure, which endanger its safety and stability. Near-field earthquakes containing forward directivity effects, due to the pulse in the velocity record, cause significant demands on the steel frames with respect to the ordinary earthquakes. Therefore, investigating the steel frames behavior as well as the higher modes effects under near-fault earthquakes is essential. For this purpose, five intermediate (ductility) steel moment resisting frames with 4, 7, 10, 15 and 20 stories under 20 far and near-fault accelerogram have been investigated. Finally, by examining the elastic responses of the single degree of freedom structure (SDOF) under considered accelerograms, the coefficients for transforming response of the SDOF structure to that of the MDOF structure are presented. The results of this research show that higher modes effects under the far-fault earthquakes are greater in comparison to those of the near-fault earthquakes. Besides, for about 30%-50% of the height of upper stories of the structures, the drift angle resulting from the near-fault earthquakes with the forward directivity effect is greater than that of far-fault earthquakes. RESEARCH METHOD Validation of analytical models is one of the most important steps of a study. In numerical studies, especially when a considerable database should be prepared for the extraction of the empirical expressions, lack of certainty concerning the validity of that created model could lead to inaccurate results. To avoid this issue in this article, all models are validated. In order to investigate the higher modes effects, 4, 7, 10, 15 and 20 stories 5-span 2D frames selected. Each model has 4 m story height and 5 m span length. The frames are intermediate (ductility) moment resisting frames. The structures being investigated in this research are designed completely based on the ANSI/AISC 341-05 and ASCE/SEI7-05 codes for gravity and seismic loads. Both the equivalent static lateral force and the modal response spectrum analysis were used for the models. ST37-type steel is used in design of the structures with the yield stress of 2400 KgCm2 and the ultimate stress of 3600 KgCm2 and the Poisson's ratio is 0. 30. The lateral drift values in all the structures are compared with the allowable value in the ASCE/SEI7-05 code. All elements have been chosen as compact sections (limiting local buckling) assuming enough lateral supports. Extended Abstracts سال پنجم، شماره دوم، تابستان 9317 15 km from the fault. All chosen accelerograms in this research have the moment magnitude greater than 6. 5 and the soil properties are of the Class D soil type based on the Fema 356 classification guidelines and are taken from the PEER website. The elastic response spectrum created by Seismosignal software. Besides, all acceleration time history has been normalized to their peak ground acceleration (PGA) before being scaled. All used accelerograms in this research are scaled according to the method presented in the Iranian Seismic Code (Standard 2800) and used in the NTHA method. Nonlinear time history analysis is also conducted by OpenSEES. CONCLUSION  The higher modes effects under far-fault earthquakes are greater than those of the near-fault earthquakes with the forward directivity effect.  By an increase in the structure height (period), the difference in seismic demands values of structures under the far and near-fault earthquakes decreases.  Investigating the drift angle over the height of various structures shows that for about 30%-50% of the height of structure, at the upper stories, the response obtained from the near-fault earthquakes with forward directivity effect is greater than the response obtained from the far-fault earthquakes. The buildings’ lateral load-resisting system is steel special moment-resisting frame. All buildings are 15 m in width.

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.

In this paper, prediction of maximum response of a structure subjected to the impulsive loads, using of simple analytic relations developed for linear SDOF systems is presented. Duration of underwater explosion pulse in comparison with the natural period of studied structure in this paper is enough short to consider it as an impulsive load and hence, maximum response of the structure can be estimated without dynamic analysis. After modeling of concrete wall of cylindrical water tank used as an 'explosion test chamber' in SAP2000 and explosion loading and analyzing of it in both static and dynamic methods, Results obtained from both SDOF and MDOF methods compared with each other and hence, the accuracy of the analytical relations based on the SDOF method in the estimation of maximum dynamic response of the structure was investigated. Considering that the response of the structure is mainly function of the impulse of the explosion in the structural and loading conditions studied in this paper, using an explosion loading function evaluating the impulse more precisely such as linear triangular pulse extracted from the field tests data results in more accurate response of a structure.

The purpose of paper is qualitative and quantitative study of the relationship between the energy demand of multi-degree-of-freedom systems, MDOF, and equivalent-single-degree-of-freedom systems to calculate the total energy demand of the MDOF system using the ESDOF energy demand. For this purpose, multi-story special steel moment frames designed and analyzed under 10 near-fault earthquake with forward-directivity effects. Moreover, the process done for the ESDOF system considering specified values of R (degree of nonlinearity). Accordingly, linear and nonlinear total dissipated energy (TDE), hysteretic energy (HE), and damping energy (DE) ratios were introduced to estimate the relationship of the ESDOF and MDOF energy. Results shows that ratio of nonlinear to linear TDE and HE/TDE is affected by period and R in ESDOF system. However, as the period and R increase, the ratio converges to one. The same result was observed between the nonlinear TDE of the MDOF system and the linear TDE of the ESDOF system. In other words, ESDOF linear TDE can be used instead of MDOF for long periods. In addition, the nonlinear TDE of the MDOF system to the nonlinear TDE of the ESDOF system ratio is affected by higher modes and period, by increasing the period the ratio is generally greater than one for the constant R. Also the effect of higher modes on the ratio of total story dissipated energy to total structure dissipated energy was significant for low R values. With increasing R, the structure tends to damp all the dissipated energy in the first mode.

The influence of the strength reduction factor due to nonlinear behavior (Rμ, ) on the lateral strength of Single-Degree-Of-Freedom (SDOF) structures causes to limit the displacement ductility demand to the predetermined maximum tolerable ductility. In addition, Rμ,is used for determining the behavior factor in Multi-Degree-Of-Freedom (MDOF) structures. Following this, in this paper, Rμ,and the inelastic displacement ratio (CR) for equivalent SDOF systems under strike-parallel (NF-SP) and strike-normal (NF-SN) components of near-field ground motion, and also far-field (FF) ground motion were assessed. Furthermore, CR obtained by this study was compared with C1 proposed by FEMA440. The deflection amplification factor-to-behavior factor ratio (Cd/Ru) for different ductility levels was computed. After evaluating nonlinear effects of SDOF structures based on Rμ,factors, these factors for MDOF structure were modified considering higher mode effects, and a simplified practical expression was proposed to estimate the base shear modification factor. The results indicated that Rμ, , corresponds to near and far-field ground motions can be different. In addition, CR does not depend on type of earthquake, and it converges to 1 by increasing the period of vibration. In addition, modification factor can be increased with period and ductility demand.