• Earthquakes and Structures
• /
• v.13 no.3
• /
• pp.231-239
• /
• 2017

Fundamental period is one of the most critical parameters affecting the seismic design of buildings. In this paper, a very simple approach is presented for estimating the fundamental period of multiple-degree-of-freedom (MDOF) structures. The basic idea behind this approach is to replace the complicated MDOF system with an equivalent single-degree-of-freedom (SDOF) system. To realize this equivalence, a procedure for replacing a two-degree-of-freedom (2-DOF) system with an SDOF system, known as a two-to-single (TTS) procedure, is developed first; then, using the TTS procedure successively, an MDOF system is replaced with an equivalent SDOF system. The proposed approach is expressed in terms of mass, stiffness, and number of stories, without mode shape or any other parameters; thus, it is a very simple method. The accuracy of the proposed method is investigated by estimating the fundamental periods of many MDOF models; it is found that the results obtained by the proposed method agree very well with those obtained by eigenvalue analysis.

• Earthquakes and Structures
• /
• v.18 no.2
• /
• pp.263-273
• /
• 2020

The use of energy concepts in seismic analysis and design of structures requires the understanding of the input energy response of multi-degree-of-freedom (MDOF) systems subjected to strong ground motions. For design purposes and non-time consuming analysis, however, it would be beneficial to associate the input energy response of MDOF systems with those of single-degree-of-freedom (SDOF) systems. In this paper, the theoretical formulation of energy input to MDOF systems is developed on the basis that only a particular portion of the total mass distributed among floor levels is effective in the nth-mode response. The input energy response histories of several reinforced concrete frames subjected to a set of eleven horizontal acceleration histories selected from actual recorded events and scaled in time domain are obtained. The contribution of the fundamental mode to the total input energy response of MDOF frames is demonstrated both graphically and numerically. The input energy of the fundamental mode is found to be a good indicator of the total energy input to two-dimensional regular MDOF structures. The numerical results computed by the proposed formulation are verified with relative input energy time histories directly computed from linear time history analysis. Finally, the elastic input energies are compared with those computed from time history analysis of nonlinear MDOF systems.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1998.10a
• /
• pp.473-480
• /
• 1998

The substructuring pseudodynamic test is a hybrid testing method consisting of a numerical simulation of the earthquake response of an analytical model and a loading test of a specimen. The substructuring pseudodynamic testing technique has been applied to various seismic experiments since it has advantages over the shaking table test to study dynamic behaviors of relatively large scale structures. However, experimental errors are inevitable in substructuring pseudodynamic testing. Some of these errors can be monitored during the test, but, due to limitations in control system, they cannot be eliminated. For example, one cannot control exactly the displacements that are actually imposed on the structures at each time step. This paper focuses on a technique to minimize the cumulative effect of such control errors for MDOF system. For this purpose, the modified posterior adjustment of the time increment from a target value $\Delta$t$_{n}$ to an adjusted value is performed to minimize the effect of the control errors for MDOF system.for MDOF system.

• Computational Structural Engineering
• /
• v.8 no.3
• /
• pp.103-111
• /
• 1995

Evaluating nonlinear response of a MDOF system under dynamic stochastic loads such as seismic excitation usually requires excessive computational efforts. To alleviate this computational difficulty, an approximation is developed in which the MDOF inelastic system is replaced by a simple nonlinear equivalent system(ENS).Me ENS retains the most important properties of the original system such as dynamic characteristics of the first two modes and the global yielding behavior of the MDOF system. The system response is described by the maximum global(building) and local(interstory) drifts. The equivalency is achieved by two response scaling factors, a global response scaling factor R/sub G/, and a local response scaling factor R/sub L/, applied to the responses of the ENS to match those of the original MDOF system. These response scaling factors are obtained as functions of ductility and mass participation factors of the first two modes of structures by extensive regression analyses based on results of responses of the MDOF system and the ENS to actual ground accelerations recorded in past earthquakes. To develop the ENS with two response scaling factors, Special Moment Resisting Steel Frames are considered. Then, these response scaling factors are applied to the response of ENS to obtain the nonlinear response of MDOF system.

• Journal of Industrial Technology
• /
• v.25 no.A
• /
• pp.23-30
• /
• 2005

The capacity spectrum method(CSM) can be used for the evaluation of inelastic maximum response of structures and has been recently used in the seismic design using the incorporation of pushover analysis and response spectrum method. To efficiently evaluate seismic performance of multi-degree-of freedom(MDOF) bridge structures, it is important that the equivalent response of MDOF bridge structures should be calculated. To calculate the equivalent response of MDOF system, equivalent responses are obtained by using Song method, Fajfar method and Calvi method. Also, those responses are applied to CSM method and seismic performance of bridge according to the ESDOF method are compared and evaluated straightforwardly.

• Structural Engineering and Mechanics
• /
• v.61 no.1
• /
• pp.105-116
• /
• 2017

In this paper, the optimal extended homotopy analysis method (OEHAM) is introduced to deal with the damped Duffing resonator driven by a van der Pol oscillator, which can be described as a complex Multi-Degree-of-Freedom (MDOF) nonlinear coupling system. Ecumenically, the exact solutions of the MDOF nonlinear coupling systems are difficult to be obtained, thus the development of analytical approximation becomes an effective and meaningful approach to analyze these systems. Compared with traditional perturbation methods, HAM is more valid and available, and has been widely used for nonlinear problems in recent years. Hence, the method will be chosen to study the system in this article. In order to acquire more suitable solutions, we put forward HAM to the OEHAM. For the sake of verifying the accuracy of the above method, a series of comparisons are introduced between the results received by the OEHAM and the numerical integration method. The results in this article demonstrate that the OEHAM is an effective and robust technique for MDOF nonlinear coupling systems. Besides, the presented methods can also be broadly used for various strongly nonlinear MDOF dynamical systems.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.19 no.3
• /
• pp.85-92
• /
• 2015

Response spectra of a building are made with a SDOF system taking into account a first mode shape, even though higher modes may affect on the dynamic responses of a high-rise building. A soft soil layer under a building also affects on the responses of a building. In this study, seismic responses of a MDOF system were investigated to examine the effects of higher modes on the response of a tall building by comparing them with those of a SDOF system including the kinematic interaction effect. Study was performed using a pseudo 3D finite element program with seven bedrock earthquake records downloaded from the PEER database. Effects of higher modes on the seismic responses of a tall building were investigated for base shear force and base moment of a MDOF system including story shear forces and story moments. Study results show that higher modes of a MDOF system contribute to a reduction of base shear force up to 1/4-1/5 of KBC and base moment. The effect of higher modes is more significant on the base shear force than on the base moment. Maximum story shear force and moment occurred at the top part of a building rather than at a base in the cases of tall buildings differently from short buildings, and higher modes of a tall building affected on the base forces making them almost constant at the base. A soft soil layer also affects some on the base shear force of a high-rise building independently on the soft soil type, but a soft soil effect is prominent on the base moment.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.8 no.6 s.40
• /
• pp.13-22
• /
• 2004

Ductiluty factor has played an important role in seismic design as it is key component of response modification factor(R). In this stuty, ductility factors() are calculated by multiplying ductility factor for SDOF systems() and MDOF modification factors(). Ductility factors() for SDOF systems are computed from nonlinear dynamic analysis undergoing different level of displacement ductiluty demands and period when subjected to a large number of recorded earthquake ground motions. The MDOF modification factors() are proposed to account for the MDOF systems, based on previous studies. A total of 108 prototype steel frames are designed to investigate the ductility factors considering the number of stories(4, 8 and 16-stories), framing system(Perimeter Frames, PF and Distributed Frames, DF), failure mechanism(Strong-Column Weak-Beam, SCWB and Weak-Column Strong-Beam, WCSB), soil profiles(SA, SC and SE in UBC 1997) and seismic zone factors(Z=0.075, 0.2 and 0.4 in UBC 1997). It is shown that the number of stories, failure mechanisms (SCWB, WCSB), and soil profiles have great influence on the ductility factors, however, the structural system(Perimeter frames, Distributed frames), and seismic zones have no influence on the ductility factors.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2005.03a
• /
• pp.316-323
• /
• 2005

The capacity spectrum method (CSM) can be used for the evaluation of inelastic maximum response of structures and has been recently used in the seismic design using the incorporation of pushover analysis and response spectrum method. To efficiently evaluate seismic performance of multi-degree-of freedom (MDOF) bridge structures, it is important that the equivalent response of MDOF bridge structures be calculated. In this study to calculate the equivalent response of MDOF system, equivalent responses are obtained by the using Song method, N2 method and Calvi method. Also, these are applied the CSM method and seismic performance of bridge according to the ESDOF method are compared and evaluated.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1995.10a
• /
• pp.818-821
• /
• 1995

A MDOF vibration analysis of the rotor is performed using combined modeling of transfer matrix method and finite element method(FETM). The method combines the advantages of both matrix. Each rotor is modelled using transfer matrix method and treated one element or several ones. The finite element method is applied in composing a system matrix and finding roots. The method used in this is more efficient than conventional finite element method in saving calculation time and provides good results in complex MDOF rotor model.