A response spectrum S(T) of a seismic wave record is empirically expressed as a function of earthquake magnitude M and hypocentral distance X to calculate an averaged S(T) from observed strong ground-motion records. The following formula is commonly used to calculate the averaged S(T): log S(T)=a(T)M-b(T)logX+c(T) where a(T), b(T), and c(T) are regression coefficients at a period of T sec. Their physical meanings are investigated on the basis of the theory of earthquake fault-model. a(T), b(T), and c(T) can be expressed as simple functions of some physical parameters, in the case that the term in relation to X is written as (b(T)X+logX), instead of b(T)logX. The values of these functions, which are calculated theoretically, are consistent with those of repression coefficients obtained from the observed data in the period range from 0.1 to 1.0 sec.

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It is important to clarify the relation between Fourier (amplitude, phase) spectra and the corresponding time function, in order to generate simulated earthquake ground motion based on those spectra expressed in frequency domain. In this paper, the meaning of the Fourier phase of a corresponding time function is investigated based on an analytical expression in time domain of a band-pass filter with linear phase. The analytical expression f_e(t). showed as eq. (8), is a closed form time function with 5 parameters A,t_<gr>, ω_0,ω_c, φ_0. Because the meanings of the parameters are respectively clear, the expression is useful to comprehensive understanding of a role of Fourier phase in the corresponding time function. Especially effect of φ_0 on the maximum, minimum, and their occurrence time of f_e(t) is investigated. η_<e,max>(φ_0), η_<e,min>(φ_0), τ<max>(φ_0), τ<min>(φ_0), respectively, normalized maximum, minimum, and their occurrence time of f_e(t), are plotted versus'φ_0 in Figs.6〜9. Figs.10〜17 are results in cases of 1st and 2nd time differentials of f_e(t). From these figures, the following remarks can be made, that maximum, minimum, and their occurrence time of f_e(t) are deterministically prescribed, and that maximum, minimum of f_e(t) change sinusoidally on φ_0 and their occurrence time does linearly. The same remarks can be made on the time differentials. These mean that φ_0 is a significant parameter in simulating a time function based on Fourier spectra. f_e(t) described by eq. (8) can be approximate causal function. So it is possible to generate a simulated earthquake ground motion wave f(t) by superposing f_e(t). A method of generating f(t) by probablistic superposition of band-pass filters with linear phase, is presented. The sample functions of f(t) generated by the method are showed.

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Seismic design for multistory shear-type buildings with eccentricity is proposed based on examples of nonlinear earthquake response analysis for multistory structures subjected to earthquake ground motions in the x and y directions. It is concluded that the damage concentration in a particular story of multistory buildings with eccentricity is nearly equal to that of multistory buildings without eccentricity, if they have the same value of strength ratio evaluated by the method introduced in this paper. It is also confirmed that the effect of stiffness in each frame of stories is relatively small for the prediction of the damage concentrated story in multistory shear-type buildings with eccentricity.

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From a statistical point of view, glastic and inelastic responses of multi-degree-of-freedom systems are studied on the basis of the numerical results by the simulation and modal spectral analysis. The first and second order statistics on energy, maximum deformation, cumulative plastic deformation and peak factor in glastic ald plastic response are presented to be compared with those of single degree-of-freedom systems and also, simplified methods of evaluating the energy response are discussed.

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in this paper, a finite element displacement method is applied to the analysis problem of shear stress distributions in beam sections which has been usually calculated by the semi-inverse method or the shear flow theory in the field of material mechanics. It is also confirmd that the effective shear coefficients can be easily obtained byusing this finite element solution. The calculation procedure in case of thin-walled beam sections are explained through several numerical examples which show a good convergence to the exact solution.

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In this paper various types of panel moment (_pM) and panel shear deformation (γ) relations are experimentally obtained by monotonic loading tests of T or X type subassemblages which are composed of various types of H-shaped beams and columns made of comparatively thin steel plates. After eight test results are selected and compared with FEM numerical results, following conclusions are obtained. 1) An increase of panel moment carrying capacity after general yielding of beam-to-column connection panels mainly depends upon increase of panel moment carrying capacity due to strain hardening of panel itself and ultimate moment carrying capacity of column flanges, beam flanges and horizontal stiffeners at four corner points of the panel. In addition as the shear forces acting in these flanges and stiffeners near the intersection point range from 0.15 to 0.25 times the yielding shear forces Q_<fy>, an increase of panel moment carrying capacity is expected in proportion to the length of rigid zone near the intersection point between beam and column flanges. 2) More than 80% of total displacement at loading point of subassemblages whose a is equal to or less than 0.4 is attributed to deformation of beam-to-column connectioon panel. 3) Subassemblages of weak panel type (a<0.4) have enough plastic deformation capacity (γ/γ>40) of beam-to-column connection panels. 4)These plastic behaviors mentioned above of weak panel type subassemblages whose members belong to FA or FB rank are almost the same.

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In the solution of the semi-infinite elastic medium for a point load excitation of the soil surface, an infinite integral appears. In order to evaluate the resoonse, the value of this infinite integral must be obtained. The method to transform this infinite integral to a finite integral has been already reported in the case of no internal damping of the soil. In this paper, a same kind of method is introduced to transform the infinite integral to finite integral considering internal damping of the soil. In this method, an adequate complex function corresponding to the integrand is adopted and an identical equation which involves the infinite integral is obtained based on Cauchy's theorem. Using this identical equation, the infinite integral in the original solution can be teplaced by the finite integral. This method is very useful by the following reasons. 1) If the numerical integral procedure is applied directly to the infinite integral, it is impossible to execute it to infinite range. It must be stopped at a suitable range. In this case, a cut off error is produced. But when the numerical integral procedure is applied after transforming the infinite integral to finite integral, this cut off error is not produces. 2) There is the Rayleigh oole near or on the contour of the infinite integral. Near the pole, the integrand falls into ill condition for a numerical integration and special procedure is required especially in the case of small or zero internal damping of soil. But this pole does not exist near the contour of the transformed finite integral and there is no difficulty in the numerical integral process. 3)The range of numerical integral is very short. It is only from 0 to 1.

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According to the ordinary linear potential flow theory, natural frequencies of the containing liquid and linear responses of the storage except those on the neighborhood of the resonance frequencies can be obtained with relatively good accuracy. There is however possibility that the containing liquid is enforced to oscillate with the frequencies in the neighborhood of the resonance points resulting in large amplitude liquid motion, as frequently mentioned in the recent disaster reports. Under these circumstances, the effect of nonlinearity due to finite free surface elevation comes to be necessary to be taken into account for the correct analysis of the behavior of the containing liquid as well as the responses of the storage. In this paper, a numerical method for solving the nonlinear sloshing problem of the inner liquids of cylindrical rigid storage is presented. The variational principle is adopted to formulate the governing nonlinear equation interms of the unknown velocity potential and response free surface elevation by means of the Taylor series expansion of the unknown variables about the undisturbed free surface. In order to obtain the oscillative characteristics over a wide range of sloshing frequencies the stationary oscillative analysis based on a harmonic balance technique is presented. From the results of the numerical calculations, possibilities of existence of some nonlinear resonance responses in the neighborhood of the first resonance frequency are shown as well as the bi-harmonic responses of the spatial mode with the circumferential wave number n=0 or 2.

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To obtain a reinforced concrete wall having large shear ductility, author propose to collapse the panel locally. Two experimental and an analytical programs were undertaken to grasp the inelastic cyclic behavior of walls with faults causing to collapse the panel locally. At first, cyclic lateral loading test of shear walls was carried out. Four one-story, one-third scale reinforced concrete shear walls were constructed. Reference shear wall, HN-1 was estimated to fail in shear before yielding. Specimen HP-1, 2 and 3 had faults (circular holes) along the boundary columns and beams. Each specimen was tested under static, reversed cvclic lateral load and boundary columns were burdened vertical load constantly. In the walls, HP-1, 2 and 3, the loss of load capacity resulted from the shear sliding at the faults was observed by 30% of maximum load capacity until the displacement about 0.02 radian, respectively. For compressive loading test of faults, eighteen blocks of the panel were constructed. Considering the stiffness of boundary elements, specimens were classified into two imagined parts of a wall-panel, that is (1)corner of a panel with the boundary column and beam, (2)wall panel with the boundary beam. Each specimen behaved a same manner with that of faults along the boundary elements in the walls, respectively. An analytical study on the shear wall with faults based on simple assumptions was carried out. The load-deflection diagram obtained by the analysis showes a good agreement with the experimental results.

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In this study, stresses of wall with round opening are analyzed for the case of vertical loads acting on the straight boundary of a semi-infinite plane. For this solution, Bariansky and Ohkawa have given to apply Jeffery's approach which gave the general solution of the plane oroblem using bipolar coordinates, to the problem of the distortion introduced in the so-called plane Boussinesq field by the presence of a circular hole. But, the method is solved with the great complexity of expression by decomposing the Boussinesq stress function into Fourier series. Therefore, in this paper, a new stress function χ_0 is assumed in terms of bipolar coordinates, and the distribution of vertical loading along the straight upper edge is directly expanded to Fourier series. In treating the stress function in the coordinates, the distributions of arbitrary loads along the straight boundary are easily expressed to Fourier series. The solution of the case acting a concentrated vertical load at the center on the straight boundary agrees with that of Boussinesq problem. For the each case under (1) a concentrated load, (2) concentrated loads acting at two points placed distance γ apart, and (3) uniform loading on the distance at the center of the straight boundary, the stress distributions of the analytical and the experimental results are shown in Figs.7, 9 and 11, respectively. The distributions of the case (1) are analogous to the case (3). The maximum tensile stress produces on the top of a circular hole. In Fig. 13, the tensile stress of the case (1) is about 2.5 times of (3) in the type λ=0.80 and so the case is notable. On the other hands, the case (2) is effective for diminishing the tensile stress, as increasing values ofλ. The analytical and the expimental results accord with each other.

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