An aim of this paper is to obtain fundamental information for understanding the varied and complex shape of Fourier amplitude spectrum of the earthquake motion wave. Fourier amplitude spectrum of the earthquake motion wave can be simulated by the superposition of a class of Fourier transforms, because an earthquake motion wave can be regarded as consisting of the successively reached element waves. To achive the object of this paper, a variety of Fourier amplitude spectra were calculated analytically according to idealized patterns of superposition of a class of Fourier transforms (Tables 1〜3). Through the examination of the shape of the calculated Fourier amplitude spectra showed in Figs.1〜3, the following general properties were abstracted. ・Fourier amplitude spectrum of a time function consisting of element waves with time lag, has a fluctuating shape along the frequency band common to the element waves. The degree of fluctuation is related to the randomness of the time lag, and the case of the time lag being random has less fluctuating shape of the Fourier amplitude spectrum than the case of constant time lag. ・The shape of Fourier amplitude spectrum of a time function, which consists of element waves having the mutually identical shape of the amplitude spectrum and common frequency band, is not almost affected by the randomness with respect to weight of the amplitude value.

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In this paper we enforce the estimation of seismic damage from a new view-point of considering temporal and spatial growth of a region. It is quite natural that the risk potential inherent to a region, i.e., the potential loss of an earthquake receiver side, such as seismic resistivity of builbings and their distribution pattern, should be gradually changing in the longer term of several decades. This is due to such facts as the increasing diversity of modern buildings and the expansion of residential areas in some large cities over the surrounding land. Most of the past studies are insufficient in a point that the probable damages in a region were estimated in no much attention to such changeability of risk potential. This paper introduces a case study for long term estimation of the seismic risk in an expanding urban area of Sapporo Region, Japan. First, the seismic intensity distribution in Sapporo Region is estimated for the presumed earthquake which might occur at Ishikari Bay near this region. Then, the probable damage of dwelling houses is estimated for occurrence at any time during the next 50 years considering the time-dependent growth of the urban area. The urbanized Sapporo area has rapidly been growing toward the presumed source region and the projected areas for new suburbia are sited on soft soil deposits of peat and clayey silt etc., which correspond to the high intensity zones for the Ishikari Bay earthquake. Therefore, considering the future growth of urban area, the estimated damage rate of residential buildings would be doubled after 50 years. This tells the definite importance of long term land use planning, especially in urban and vicinity area, in consideration of the time dependency of risk potential in the receiver side as well as seismic activities influencing the region.

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This paper is concerned on the effect of boundary members on the elastic member buckling of parallel chord rigid-jointed trusses and on the required rigidity of boundary members to hold the effective strength of the truss determined by the elastic member buckling. To treat the problem simply and analytically, an approximate method is presented by using a mathematical model where the nodal translation is ignored. The bifurcation buckling from the uniform original shape of pre-buckling state is only treated. Then, the buckling modes are expressed in the form of the linear combination of the homogeneous solutions of difference equation. The types of the solutions are determined from the roots of the characteristic equation in the periodic or decreasing forms depending on the structure and stress state. The main conclusions obtained are as follows. 1) The validity of the presented method is verified by the comparison between the value obtained by this method and that by the exact method for the elastic member buckling bifurcated from the original configuration. 2) Within the presented approximate method, the effect of boundary members on the elastic member buckling of parallel chord rigid-jointed trusses is cleared by the introduction of the concept of critical rigidity of the boundary member. If the rigidity of the boundary member is larger than the value depending on the combination of sectional forces, the elastic member buckling strength in terms of sectional forces of the truss is not smaller than the value of the effective strength. The effective strength is defined as the lowest buckling strength of repetitive modes without macro-deformation, and has the mode of repetition of two structural units. So in this paper, the minimum rate of the rigidity of boundary web members mentioned above to that of non-boundary web members is defined as the critical value. Then, the effect of the boundary member on the elastic member buckling is classified and explained as follows. a) In case the rotational restraint rigidity of boundary joints is not smaller than that of critical value, the value of macroscopical sectional forces at buckling state is not smaller than that of the effective strength. The buckling mode is constituted with repetitive and decreasing type terms of the homogeneous solutions, and is repetitive type in the middle portion of the truss. b) In case the rotational restraint rigidity of boundary joints is smaller than that of critical value, the value of the sectional forces at buckling state is smaller than that of the effective strength. The buckling mode is decreasing from boundary and is constituted with decreasing type terms of the homogeneous solutions. From a view point of material efficiency, it is better for the truss to buckle in repetitive mode all over the whole structure than to buckle in narrow boundary portions at the lower load. In case the boundary portions are stiffened enough, the effective strength for continuum analogy method is applicable to the calculation of the elastic buckling load. In case the strength is determined by elastic buckling at boundary portions, the elastic buckling load can be calculated by the present method.

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Under the circumstances that earthquake occurs once in a while as in our country, it is an important problem for buildings to posses safety against quake, and structures are demanded to have sufficient deformability. For low-rise buildings, factories, storehouses and gymnasiums pairs of braces are the main earthquake-proof elements. However, the damage of these steel structures attaked by earthquakes was centered on the braces, among them round bar and angle ones were broken remarkably. Many studies have been made on the earthquake-proof of braces, and yet most of them are based on the staticloaded tests. As braces are considered to be tensioned shockingly by the furiousness of quakes, it cannot be enough to evaluate the safety of bracing merely with the knowledge oh statically tested and obtained data. Especially, the uprising of yield point and yield ratio involved by increasing stranin rate should influence the brace design condition that the joint-end fracture strength must exceed teh brace-body yield strength. This report includes, therfore, cosidering that serious earthquake hit the-steel braced structures, high-speed and static tensile tests of real scale braces with angle section. The steel material tests in various loading speed are also included to examine whether the strain rate change influence the material characteristics. The test results are summarized as follows. (1) Influenced by the strain rate, changes are seen in the material characteristics. The typical one is the uprising value of the upper yield point. (2) From the material tensile tests under the various strain rates, the strain rate is related to upper yield point and tensile strength, then the relationships are approximated in the simple equations. (3) When loading speed changes from static to dynamic, fracture forms of braces will also chage from yielding alomg full length to earlier fracture accross joint-end bolt holes. This shows that increacing strain rate raises up the yield ratio and lower the deformability of steel equations (4) The author suggest a coefficient of the designed joint ultimate strength Ku for judging the brace joint safty. To satisfy the conditions of brace designing, the value of Ku should be sufficiently larger than 1.0.

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In structural design, structural experts pass many kinds of subjective and fuzzy judgements which are not described obviously in formal calculation notes. The purpose of this paper is to formulate quantitatively such subjective structural judgements by means of the "Analytic Hierarchy Process (AHP)" and the "Fuzzy Confluence Rule". The former was proposed by Saaty, and the latter by the authors. In this paper, the "AHP" is applied to the formulation of damage assessments of R/C columns with flexural yielding type and R/C shear walls with shear failure type. Polynomial of degree 2 or 3 have a good approximation to the damage assessment functions of deformation. The "Fuzzy Confluence Rule" is applied to the formulation of the total damage assessment of R/C buildings composed of damaged columns and damaged shear walls and to the formulation of aseismic capacity assessments of R/C buildings in consideration of the relation of seismic damage and the time elapsed after completion. The approximate functions are expressed by the linear summation of intersection, union, algebraic summation and product functions with mutual inference parameter α, overestimation parameter β and weighting parameter γ. The all approximations of formulas are carried out by using the answers to the questionnaires distributed to practical experts of structural design. The approximated formulas show the mechanism of fuzzy and subjective judgements by structural experts and very useful for composing expert systems which enable us to assess safety and damage of structures and to perform optimum design of structures.

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A general problem of a straight bar of rectangular section subjected to normal and tangential loadings on its top and bottom surface is considered. High order theories of the straight bar, which include the effect of the transverse normal stress and the transeverse shear stress, and keep numbers of unknown functions at three, are developed and examined by several examples.

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Enunciation of the principle of strong columns and weak girders is a recent worldwide trend in earthquake-resistant design of R/C frames. However not much is yet clarified on the sufficiently reliable requirements of column-to-girder relative strength for realizing the target of girder-yielding failure. The effects of multi-dof dynamic loading influence significantly their yielding and hysteretic performance, and are not so simple as to permit a straightforward use of dynamic modification factors toward the peak stress produced at unyielding sections. Actually the latter exhibits markedly erratic nature in the increasing order of story shearing forces, member shearing forces and bending moments. The associated higher-order effects become particularly noticeable at side columns of moment-resisting frames and at coupled shear walls. In the present quantitative study for practical purposes, the peak stress is resolved into the SRSS pair of reference and residual components. The residual component is designed to stand for the dynamic effects, and examined advantageously in two separate steps of its relative distribution and a single absolute factor in acceleration. Contrary to an ordinary understanding, this proves unbounded even after the formation of kinematic sway mechanism. Rather this tends to increase in proportion to ground acceleration, which allows to identify the absolute factor in a form of amplification ratio. Thus the current problem is reduced to the relative distribution and the amplification ratio, both of which are then characterized with relation to the contribution of higher-order oscillation in ideally elastic system or pseudo-elastic system accounting for the partially differing reduction of secant stiffness.

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This paper proposes the shear strength of stud connectors and behaviors of composite beams. The experimental work of the investigation reported herein is consisted of tests of 26 solid Push-out specimens, 24 Deck Push-out specimens and 15 composite beams. From this study, we could find out the following conclusions. 1. The shear strength of stud connectors in solid slab is also concerned with exponent function of cross-sectional areas of stud connectors. 2. The shear strength of stud connectors with Deck is concerned with Deck ribs ratio and stud connector length above ribs. 3. Effective moment of inertia and effective section modulus of partial composite beams are concerned with exponent function α=1/3 of composite degrees.

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The restrained orthotropic square reinforced concrete slabs which has two way is considered to be property of both X direction and Y direction : transverse hollow system reinforced concrete hollow slab and longitudinal hollow system reinforced concrete hollow slab. Therefore, in this report we described on obtainning the load-deflection curve of the square reinforced concrete hollow slabs that happened shearing failure by applicable shearing strength equation of the both ends fixed one way RC hollow slabs to the suggestion equation of the previous report and compared the curve of calculated results with the curve of experimental values, then investigated. The result that the curve calculated values showed a fairly good approximate tendency of the curve experimental values found.

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High triaxial compression tests (the maximum lateral pressures are P=-900 kgf/cm^2) and hydrostatic loading tests (the maximum pressures are P=-2000 kgf/cm^2) are conducted for concrete cylindrical specimens. The dependences of mechanical characteristics (elastic moduli and failure criterion) of concrete on the octahedral stresses and strains are discussed. Then, an incremental model of stress-strain relationship for con-crete under high triaxial compressive stresses using the tangent bulk and shear moduli is proposed. Furthermore, by comparing the calculated results using this model with the experimental ones, it is confirmed that this model is applicable to predict the behavior of concrete under high triaxial compressive stresses.

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Usually, the moment capacity of web at beam end connected to RHS column is negle cted because that web plate dose not penetrate column. But some amount of web moment are coveied to column and it depends on lateral stiffnes of column flange. Still rats hole (so called scallop) of beam web at the joint decreases deformation capacity of beam and becomes the cause of crack or collapse of beam flange. The pourpose of this paper is to point out (1) computational method of plastic moment of beam web and (2) effects of rats hole on the strength and deformation capacity of beam. For the purpose above mentioned, analytical and experimetal study were done and following conclusions were gained. (I) Evaluate equations for plastic moment of beam end were induced based on plastic yield line theory and on 4 cases those are varried the position of plastic neutral axis of beam approximate equations were induced from precise equations. Solutions by approximate equations were compaired with experimental results and showed a good agreement. (II) Experimental results of joint with rats holes and without rats holes were compaired. The results of specimens with rats hole were collapsed at flange under 2〜3 cyclic laoding but on specimen without rats hole, collapse of flange did not occur and strength were about 10 % over those of specimen with rats hole.

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The bending stresses in the web plate of H-beam welded to RHS-column are less than those of prediction by beam theory, because the flange plate of RHS lacks out-of-plane rigidity. In this paper, it is pointed out that the maximum flexural strengths of H-beams welded to RHS-columns are affected by the yield ratio of the beam flange material, Y_f, width-to-thickness ratio of RHS, B/T, and the full plastic moment of the web part to that of the beam neglected the cross section of the scallops, M_<ws>/M_<ps>. Based on the extensive test results, the empirical formula, Eq (10), predicting the maximum flexural strength of H-beam is derived by dimensional analysis and regression analysis. For RHS-column connections with B/T≦25 and Y_f<0.7, the maximum flexural strengths of beams are satisfied the following conditions. For SS41 : M_<max>/M_<ps>>1.30 For SM 50 : M_<max>/M_<ps>>1.20

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The conventional way of the design of a structure having pile foundations subjected to lateral load is the method which piles are divided from the super-structure then it is assumed that the super-structure is supported on the footings and does not subside. And the stress of pile is obtained by Chang's equation based on the assumptions that pile's length is infinite, pile is treated as a beam supported elastically and the behavier of pile and soil under lateral loading is in the range of elasticity. But it is well-known that there is obvious disagreement between the stress and deformation of pile top and those of super-structure which are obtained by the method descrived above. Therefore, with the view that the stress of super-structure and piles must be solved in one, in this paper, stress solution of group piles for structural analysis under the condition subjected to lateral load is derived. The solution starts from the transformation of Chang's equation due to convenience of the theoretical development. And new ideas that the horizontal movement and the rotation of footing are restricted by beams which connect footings each other are introduced into the theory. It is considered that the real condition of pile top embeded in footing is different from the condition that is rigid or freely rotative in Chang's equation. The coefficient which expresses the connective condition between pile top and footing is named "connective ratio at pile top" and is symbolized by "α". The concept of "α" is explained using fig.3 and 4 (fig.4 is called "α-line figure"). The value of α in the lateral loading experiment of a pile embeded in the concreate basement can be obtained with the following method. δ^^・ denotes the rotative component of horizontal displacement at free end of a pile and Q_0 is the lateral load (see fig.6). Q_0〜δ^^・ curve is superposed on the α-line figure, then α can be read. The solutions of group piles considering the rotative angle of footing and the connective ratio α at pile top are derived as (46), (47) and (48) equations. In the stress analysis of the structure supported on pile's foundation, the equation of pile top moment is expressed by the theory of group piles and the equation of bending moment of super-structure is expressed by the slop deflection method. And two equations of moment are suited through the rotative angle of footing, then the stiffness matrix is derived from the coefficients of equations. The rotative angles of footing and the other unknowns can be obtained by solving the stiffness matrix as simultaneous equations. The stress value which are calcurated by substituting the unknowns into (47), (48) equation and the equation of bending moment of super-structure are called "theoretical value". The results of stress analysis using a structural model and varying pile's diameter, structural rigidity, etc., are summarized as follows. (1) Part of stress values of structure obtained by the theoretical method excluding the equation of subsidence at footing is smaller than the theoretical values. (2) Stress of structure which has no piles and whose footing do not subside is called "stress of supported type". Stress of supported type is approximately equl to the theoretical valu at α=0. But α increases, then so dose the theoretical value of structural stress. For example, at α=1.0. the bending moment M_G at the exterior end of beams which connect footing each other, increases by 1.7〜1.9 times stress of supprted type. (3) _TI_E denotes the inertia moment of area of piles in the footing which locates in the corner of the structural frame and _TI_C denotes the others. The ratio of _TI_C to _TI_E (_TI_C/_TI_E) increaes, then so does the moment of pile top M_h in the corner footing. And M_h at _TI_C/_TI_E=3.0 is approximately 1.2 times MF which is the bending moment of

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