岡野 創

This paper describes evaluation of torsional response by equivalent linearization method considering higher mode response. In the authors' study, the equivalent linearization method (after named NoLMM) considering higher mode response for multi-story symmetric buildings was proposed. In this study, NoLMM method is extended for torsional response and adapted to single-story unsymmetric buildings. The NoLMM analysis results agree with that of time domain dynamic analysis. It is important to consider not only higher mode responses but also modes interaction in the analysis of unsymmetric buildings. Accuracy of analysis results is improved by considering failure process.

This paper describes the equivalent linearization method considering strength reduction of brittle elements. The following facts are found by numerical investigation employed time-domain response analyses. The maximum response of the weak story where strength of brittle element is lost is well approximated by the model whose brittle element in weak story is removed in advance. While the maximum responses of the stories where strength of brittle elements are not lost, arise typically before strength of brittle element of weak story has been lost. In the evaluation by equivalent linearization method, both responses, which correspond above-mentioned two states, are evaluated, and greater responses of two states are adopted as final results. Numerical validations are conducted not only for single-story collapse model but also multi-story collapse model. The results of proposed method well agree with time-domain analyses in both cases.

This paper describes the equivalent linearization method considering higher mode effect. In non-linear response, one modal response affects the characteristics of other modes. In order to incorporate mode interaction, a multi-modal analysis method extended to the non-linear region based on the equivalent linearization concept is proposed. The validity of the proposed method is examined through analyses using story shear models that form story collapse mechanisms, because the effects of higher modes are remarkable in the models. The verification results show that the precision of evaluation is markedly improved by the proposed method, in problems where higher mode effects are remarkable. In the latter part of the paper, some problems with the existing capacity spectrum method in the equivalent linear analysis considering higher mode effect are discussed.

The answers are summarized as follows: 1. In estimating maximum deformation, the total energy input is one of the approximate methods based on energy balance. 2. The authors did not use the concept of instantaneous energy input. In estimating maximum deformation, the instantaneous energy input cannot avoid to be assumed value. 3. In reducing one-degree freedom system, damage distribution is presupposed, but it does not become practical limitation of applicability of equivalent linearization method, because the mechanism confirmation is indispensable in seismic design of building structure. 4. It is considered that the design criteria should not be the value, which has advantage in estimating the response by energy balance, but the value, which describe the limit states of building structure appropriately. From the practical standpoint, the authors consider that the maximum deformation is most appropriate value, which define the limit states of building structure.

The closed form equations for equivalent linearization method are presented. In velocity response spectrum constant region, the response ductility is the function of yielding strength, yielding deformation angle and height of structure. But in acceleration response spectrum constant region, yielding deformation angle and height of structure is irrelevant to response ductility. And in deformation response spectrum constant region, yielding strength is irrelevant to response ductility. It is shown that these characteristics are essential by the discussion based on energy balance of stationary random vibration. The evaluation method for probability of failure during design lifetime, which is examined by deformation capacity is also presented. The closed form equations, for equivalent linearization method are utilized in above equation. The influence of variation of deformation capacity is considered in correction coefficient.

The reliability of the shear failure tend to be evaluated regarding the shear force developed at the yielding mechanism as the load, although the seismic reliability of structure is evaluated to the seismic load. The reliability of the shear failure must be evaluated to the seismic load, because it is impossible to compare each other between the reliability indices to the different loads. In this paper, the approximate equation for the probability of shear failure of reinforced concrete building to the seismic load during the reference period is presented. The probability of shear failure is evaluated in explicit form utilizing Cornell's method. By the dynamic magnification effect, the response shear force of column increases over the force developed at the overall yield mechanism. In order to take that effect into account, the increment of shear force over the existing shear force at the mechanism is assumed to be proportional to the peak ground acceleration. The exceeding probability of the peak ground acceleration is approximated by Frechet distribution.

The ultimate limit state is checked by the load carrying capacity in the current AIJ limit state design code. But the reliability of ultimate limit state should be checked by deformation criterion, because the ductile RC building structures does not collapse when the lateral load exceeds the lateral force resisting capacity, but collapse when the response deformation exceed the deformation capacity. The exceeding probability of response deformation is not equal to that of peak ground acceleration, because the response deformation in nonlinear region is not proportional to the intensity of input earthquake motion. The exceeding probability of response deformation is derived, utilizing the explicit relationship between the reference deformation of equivalent SDOF and the velocity response spectrum. The approximate probability of failure which takes account of variability of deformation capacity is evaluated explicitly utilizing the method proposed by Cornell.

The stochastic estimation method for the nonlinear earthquake response of the indeterminate ground is presented based on the first-order-intervening variable method. The first-order-intervening variable method is applicable to the stochastic estimation of the variation of the nonlinear earthquake response of the indeterminate ground, because the parameters of the intervening variables can be determined by the sample values of multiple points without the direct differentiation by the random variables. The accuracy of the presented method is verified by the onedimensional ground model. The necessary number of the sample values for the presented method is proportional to the number of random variables, so that its calculation efficiency is better than Monte-Carlo method.

The nonlinear random response of soil-column subjected to non-white excitation is dealt with. The formulation is based on the stochastic linearization method developed by Atalik and Utku, and the nonlinear hysteretic characteristic of soil is approximated by Wen's model. And its parameter is determined to simulate Ohsaki-Hara model in the prescribed strain range. The numerical method to deal with the arbitrary non-white excitation is also presented. In this method, the autocorrelation of input motion is used as the input of the derivative equation, and the external load term of covariance derivative matrix equation is given by the numerical solution of the vector derivative equation. This method is especially effective when it is difficult to find the linear filter equivalent to the target spectrum. The solutions are compared and well agree with the results of Monte-Carlo simulation.