These days, there are a lot of high-rise buildings and it is important for these buildings to be reinforced against earthquakes. As a device to reduce the response of the building, active braces are used. In this paper, their optimal placement method to reduce building's response by limited number of them is researched.
 Firstly, to search optimal placement to set active braces, response comparisons of four setting patterns, which are named Upper, Lower, Middle and Uniform, are carried using sine waves. These sine waves have the same periods with natural periods of the building. It shows that control forces become large at layers which story drifts are large. Thus, the values of the feedback gain matrix on Linear Quadratic Regulator (LQR) method are compared. It appears that the feedback gain matrix has large gains where they are related to displacement. In addition, equation of control force shows each layer's story drift has a great influence on deciding control forces.
 Secondary, setting methods named MSD and NOD are proposed and their effectiveness is verified. MSD places active braces around the layers which will have large story drift and NOD places them around nodal points. In this paper, two earthquakes which have large power on building's 1st or 2nd natural period are used. It is confirmed that Lower pattern is effective for the 1st mode earthquake, but against the 2nd mode earthquake, Upper pattern is more effective. So these setting patterns can't work effectively for all earthquakes. About MSD and NOD pattern, though their effectiveness aren't the best, but they can reduce responses against several frequencies. This means that they can work more effectively for several types of earthquakes.
 Thirdly, to research the safer setting method, the robustness is compared when one active brace breaks down at upper, lower or middle layer. In this paper, three setting patterns, MSD, NOD and Uniform, are used to compare. On almost all of the layers, responses of Uniform became larger than MSD and NOD when the break down happened. From the comparison of MSD and NOD, when the break down happened at lower and middle layer, responses of each layer don't show large difference. But the case when the break down happened at upper layer, responses of NOD pattern became larger than that of MSD pattern. It means MSD pattern has more active braces at effective layers than NOD.
 In this paper, effectiveness comparison on four simple patterns shows that control forces become large at the layers which have large story drift. To research their relationship, the feedback gain matrix is researched. Control forces are decided from the displacements and velocities of each layer and displacements have larger influence. From this relation, two setting patterns, named MSD and NOD, are proposed and comparison of their effectiveness and robustness were carried. Results shows that MSD and NOD can reduce responses on some modes, thus they will work more effectively for many type of earthquakes. In addition, MSD has better effectiveness than NOD when break down happens.
 In future studies, advanced setting pattern which has some active braces for each selected layer will be researched. In addition, optimal control design which considers many types of earthquakes including imitation wave and time lag between earthquake input and control force are needed to research.

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 This paper presented an accurate response reduction factor for non-stationary elastic response which was modified from the past reduction factor in Ref. 6). In the modification, the influence of the asymmetry of the response of the absorbed energy by the damping factor of one cycle just before the maximum response was taken into account, and the influence of the damping factor on the building period was also taken into account.
 Furthermore, the paper proposed the simplified formula for response reduction factor.
 Finally, the compatibility was examined for both the modified formula and the simplified formula using the response analytical results by actual earthquake motions and earthquake motions in notification.
 The major findings obtained in this paper were as follows.
 1) The correction coefficient of the equivalent damping factor for evaluating the response reduction factor in non-stationary response is (y1/y1-)^2. Here, y1 is the peak value before the maximum response, and y1- is the average of y1 and the opposite peak value before the maximum response. The average value of (y1/y1-)^2 is approximately 0.7.
 2) It is proved that the new modified factor β0' of the absorbed energy by damping factor which taken the influence the asymmetry of the response into account is less influenced by the period of the buildings than the modified factor β0 of absorbed energy by damping factor proposed in Ref. 6).
 3) The modified formula for response reduction factor in non-stationary elastic response isexpressed as Fh = [ {β0'/γ0^2·4πh0 + (1-1/γ0^2)} / {β0'/γ0^2·4πh+(1-1/γ0^2)} ] · ζ. Here, γ0 is the projected ratio at the maximum response, and h0(=10%) and h are damping factors.
 4) The modified formula for response reduction factor using β0'/γ0^2 and 1/γ0 for each building period shows better compatibility with the response analytical results using actual earthquake motions and earthquake motions in notification than the past approximate formula of response reduction factor of Ref. 6) does.
 5) The simplified response reduction factor can be expressed as Fh = [ {10h0+2.7(1-1/γ0^2)} / {10h+2.7(1-1/γ0^2)} ] · ζ in which β0'/γ0^2 is set to be 0.3 considering safety side. The simplified formula shows excellent correlation with the results of the response analysis than the past approximation formula dose. When 1/γ0 is set to 0.4, it is close to Akiyama Formula, and when it is set to 0.6, it is close to Kasai formula, and when it is set to 0.8, it is close to Kenken formula.

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 The nonlinear viscoelastic damper has a characteristic that the equivalent stiffness fluctuates due to displacement, so that the hysteresis loop changes depending on the amplitude. Therefore, it is necessary to establish the analytical model that reflecting its characteristics.
 As for the method of installing the damper, a stud type is often used from the demand on the building plan. It has been clarified from previous studies that the interlayer deformation and the damper displacement differ due to various factors in the stud type vibration control system. The purpose of this studies are to evaluate the damping characteristics of the nonlinear viscoelastic damper, and to study the dynamic behavior of the frame installed with this damper as stud type. In addition, it is to study the damping addition effect and efficient arrangement method of the damper in the model simulating a real building.
 In Chapter 2, based on the dynamic vibration test results of the steel frame installed stud type vibration control system with the nonlinear viscoelastic damper, it was studied about such as the evaluation of the damping characteristics, dynamic behavior, the comparison with the analytical model, and the effective damper deformation ratio and the loss displacement. As a result, the nonlinear viscoelastic damper can be performed precisely numerical analysis by using three elements model in which elasto-plastic elements, elastic elements, and viscous elements are arranged in parallel. By using the model of frame structure shown in Chapter 3, it is possible to evaluate the stud type vibration control system with this damper. In addition, the effective damper deformation ratio of the stud type vibration control system with this damper increases logarithmically as the interlayer deformation increases. This phenomenon is due to the nonlinear characteristics of the damper.
 In Chapter 4, based on the parametric studies using the frame analysis model, it was studied about the effective damper deformation ratio due to difference in arrangement method and the damping addition effect of the damper. Analysis models are the three-layer of plane frame model and the eight-layer of three-dimensional frame model. From the comparison of the single layer arrangement and the continuous layer arrangement in the plane frame analysis, in the case of the continuous layer arrangement, the loss displacement of the damper increases due to increase of the rotational deformation of the beam. In other words the effective damper deformation ratio decreases in the continuous layered arrangement. The effective arrangement method of the stud type vibration control system is to make the distributional arrangement rather than the continuous layer arrangement, and install it on a rigid beam rather than install it on a soft beam. Therefore, the energy absorption effect improves due to increase in the effective damper deformation ratio. In addition, the effective damper deformation ratio is affected by the elasto-plastic behavior of the column side end portion of the beam. According to the column side end portion becomes plastic, the rate of the bending moment of the stud side end portion becomes larger than that of the column side end portion, and the loss displacement due to the rotational deformation of the beam increases. Therefore, in order to increase the effective deformation ratio, it is important to suppress the ratio of the bending moment of the stud side end portion of beam.

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 A lead rubber bearing (LRB), one of the major seismic isolation system components, essentially has some weaknesses such as excessive tensile stress at some basemat-edge isolators and degradation of a lead plug damping performance by temperature rising due to responses during large and long deration earthquakes. Recently, a concern with those weaknesses has been growing because of a social recognition that such large and long deration earthquakes may really occur.
 Based on such conditions, in this study, multi-cyclic loading tests of LRB specimens and their analysis studies are performed. Parameters of the multi-cyclic loading tests are a loading velocity (very slow to realistic seismic response speed), a loading strain range (up to elastic limit of rubber), and a loading degree of freedom (single horizontal loading and multiple horizontal & vertical loading), to evaluate the LRB behaviors under several conditions along its thermal conditions. During the tests, displacements, reaction forces and temperatures are observed to comprehensively grasp the LRB behavior.
 Those behaviors are well simulated by a newly developed response analysis program where interactions of mechanical and thermal behavior of the LRB can be evaluated.
 Findings by the tests and analytical simulations are as follows.
 1) By the test, thermal conditions during the test loadings are observed by seven thermocouples in the LRB specimen including the center of the lead plug that had not yet been observed. The observed data show validity (some conservatism is allowed) of evaluation formula by previous studies.
 2) The maximum temperature of the lead plug reached to near 300 degrees Celsius that is close to the melting point of lead, and there still remains approximately 4N/mm2 of yield stress of lead, that is considered to be zero in previous evaluation formula. Therefore, there is still room for eliminating the conservatism of the previous evaluation formula so that more reasonable design of the LRB can be expected.
 3) The newly developed response analysis program (that considers interactions of mechanical and thermal behavior of the LRB) can well simulate the LRB behavior. To have a precise analysis result, proper settings of thermal boundary conditions are essential; that settings are one of the accomplishments of the study.
 4) By checking the LRB performance after the loading tests, it is confirmed that the mechanical characteristics of the LRB are almost recovered when the lead plug temperature is enough cooled even that was once heated up to 300 degrees Celsius or much cumulative deformation (over 50m) is experienced including the multiple horizontal & vertical loading cases. Thus, the robustness of LRB after severe loading experiences is confirmed.

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 In Japan, to prevent the collapse of and power loss in lighthouses due to natural disasters such as earthquakes and typhoons and to ensure safe maritime traffic movement in disaster areas even after a disaster strikes, disaster-related measures including the reinforcement of lighthouses against earthquakes are implemented (Reference 5)). In the Building Standard Law, the design seismic force is calculated using the fundamental natural period of the structure. Therefore, it is important to accurately estimate the fundamental natural period in the seismic design of the structure.
 The purpose of this paper is to propose an equation that can be used to accurately estimate the fundamental natural period of lighthouses. Regression analysis was used to determine the fundamental natural period estimation equation.
 First, to clarify the accuracy of the estimated fundamental natural period from the existing equations, a comparison between the measured fundamental natural period from vibration tests and the value estimated using existing equations is presented. Vibration tests were conducted on four brick lighthouses, seven stone lighthouses, and fourteen reinforced concrete lighthouses (Tables 1 and 2).
 Equations (1) and (2) are the existing equations. Equation (1) is given by the Building Standard Law, while equation (2) is based on the results of vibration tests conducted on eight lighthouses (Reference 8)). The fundamental natural period of chimneys is estimated using equation (3); chimneys are similar to lighthouses. However, chimneys do not have a heavy object at the top. The periods estimated using equation (1) were longer than those obtained from measurements (Fig. 4 (a)). The periods estimated using equation (2) were almost the same as those obtained from measurements (Fig. 4 (b)). The periods estimated using equation (3) were shorter than the periods obtained from measurements (Fig. 4 (c)). However, the corrected measured periods derived using equations (4) and (5) by considering the weight at the top were found to be relatively consistent with the estimated periods using equation (3) (Fig. 4 (d)).
 Next, the relationship between the structural specifications and the fundamental natural period was examined. There are eight structural specifications (Fig. 5 and Equation (6)). The structural specifications that correlate with the fundamental natural period are obtained from the correlation matrix (Tables 3 and 5), and these are correlated to each other. To avoid problems due to multicollinearity in regression analysis, only the height of the structure (H) was used as an explanatory variable. The reason is that H has the strongest correlation with the fundamental natural period (the correlation coefficient was the largest). From the regression analysis, the following equations were obtained as the fundamental natural period estimation equations of lighthouses.
 Brick lighthouse : T = 0.019H + 0.007
 Stone lighthouse : T = 0.014H + 0.015
 Reinforced concrete lighthouse : T = 0.013H
 Among the reinforced concrete lighthouses, the Ujina lighthouse was excluded from the regression analysis. This is because the fundamental natural period of the Ujina lighthouse are outside the 95% prediction interval of equation (13) (Fig. 8 (c)). It appears that the fundamental natural period is increased because of damage to the foundation or structure, and because of the dynamic soil-structure interactions.

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 In recent large earthquakes in Japan, a large number of wooden houses collapsed due to strong ground motions. In order to reduce the damage of buildings and loss of human life, it is important to enhance the seismic performance of wooden houses. To clarify the vibration properties of wooden houses such as a natural period and a damping ratio under a severe earthquake ground motion is an essential point to estimate and upgrade its seismic performance; however, it is generally difficult since the wooden house shows strong non-linearity on its vibration during strong ground motion due to the mechanical property at the connection of wooden members.
 In this paper, the vibration properties of wooden houses are identified using subspace model identification method. The methods used in this paper are the PI-MOESP scheme and the PO-MOESP scheme proposed by Verhaegen. These two methods have different algorithms in terms of the assumption of the additive noise to the system. The PI-MOESP scheme is valid when the system has colored measurement noise, and the PO-MOESP scheme is valid when the system has white process and white measurement noise.
 First, using the numerical model of a two-story unsymmetric-plan wooden house, we compared the characteristics of the PI-MOESP scheme and the PO-MOESP scheme. The numerical results show that the PI-MOESP scheme needs a large value of the line of block Hankel matrix to obtain a true identified value, and the PO-MOESP scheme can estimate the true value when the additive colored noise contains broadband frequency and has low amplitude compared with input-output data. It is also shown that the identified values for the data of non-linear vibration converge with increasing number of the line of block Hankel matrix.
 Then, we identified the vibration properties of the full-scale two story wooden house, which was used as the test structure for the three-dimensional shake table test conducted in 2007, by the PI- and the PO-MOESP schemes. The identification results for the data obtained by white noise shaking shows that the damping ratio of the torsional mode is about 15%, which is approximately three times larger than that of the translational mode. From the identification results for the data obtained by earthquake shaking, it is shown that when the maximum story drift angle is about 1/50 rad, the natural period becomes about three times compared with the value under low-lever vibration and the damping ratio becomes about 20%.

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The purpose of this study is to estimate the response and damage of existing super high-rise buildings in Osaka against strong pulse-like ground motions. In part1, a method of modeling super high-rise non-isolated buildings and a study of response properties for Ricker wavelet are described. It is confirmed that super high-rise buildings modeled by using 1st natural period described in published structural design documents might help grasping tendency and scale of regional damage. Also, aspects of damage might change completely different by the ratio of 1st natural period and pulse period of input wave T₁/T_p and pulse displacement D_p.

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 Formerly, the calculation formulas of the primary natural frequency of the both (A) all edges simply supported and (B) all edges clamped on the rectangular slabs have only been proposed. So Kojima(2012) had derived the calculation formulas of the primary natural frequency on the generalized support conditions of the rectangular flat slabs. The subjects of studies for support conditions on the rectangular flat slabs are (A) all edges simply supported, (B) all edges clamped, (C) two opposite edges simply supported and the other two edges clamped, (D) one edges simply supported and three edges clamped, (E) three edges simply supported and one edge clamped, (F) two adjacent edges simply supported and the other edges clamped, (G) all edges semi-clamped by Kojima(2012) between (A) all edges simply supported and (B) all edges clamped. Since the primary natural frequency of the ordinary flat slabs is intermediate between the simple support and the fix along edges, Kojima(2012) had defined restraints along edges of the flat slabs which are set to 1 by simple support along edges of the flat slabs and set to about 2 by fix along edges. Through the definition of the new restraints along edges, Kojima(2012) had estimated the primary natural frequency of the ordinary flat slabs is intermediate between all edges simply supported and clamped on the rectangular flat slabs, which are the numerical value is 1.5 times of all edges simply supported slabs. Kojima(2013a) had proposed the calculation formulas of the effective mass coefficient that the concentrated load affected the rectangular flat slabs. As the support conditions, Kojima(2013a) had calculated (A) all edges simply supported, (B) all edges clamped, (F) two adjacent edges simply supported and the other edges clamped and (G) all edges semi-clamped by Kojima(2012). Through a series of these processes, Kojima(2013b) had derived the calculation formulas of the maximum deflections from the concentrated load on the rectangular flat slabs. Timoshenko(1959) proposed the accurate solutions of the deflection on the rectangular flat slabs through both the all edges simply supported and clamped with the both the concentrated load and the uniformly distributed load. Kojima(2106) has proposed the following calculation formulas of the effective mass coefficients and the maximal deflection amount with the uniform load on the rectangular flat slabs. The support conditions on the rectangular flat slabs are the support conditions of (A) to (G).
 It's said to a support conditions on flat slabs of real buildings is the (G) all edges semi-clamped by Kojima(2012) between (A) all edges simply supported and (B) all edges clamped. The calculation formulas of the maximum deflection with the uniform load under the support conditions of (A) to (F) was the solutions of the Fourier polynomial proposed by Timoshenko (1959).
 This paper is the following calculation formulas of the maxim deflection with the uniform load on the rectangular flat slabs. The subjects of studies for support conditions on the rectangular flat slabs are (A) to (F) and (G) all edges semi-clamped by Kojima(2012). The support conditions on the flat slabs of the real buildings have been said to be (G) all edges semi-clamped between (A) all edges supported and (B) all edges clamped. The author has proposed the solutions incorporating the effective mass coefficient and the polynomial solutions of the function on the slenderness ratio λ by using the deflection amount at the center of the rectangular flat slabs with uniformed load under the various support conditions by Timoshenko(1959) and FEM analysis.

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 Recently, it has been reported that severe disasters cause serious, such as The 1995 Southern Hyogo Prefecture Earthquake and The 2011 off the Pacific coast of Tohoku Earthquake, damage to a lot of building structures. Based on these experiences, there are many discussions about RESILIENCE, REPAIRABILITY and RECOVERY for damaged building structures.
 When building structures are designed considering these design concepts, it is necessary to prepare effective repair methods for structural damage which generated by seismic loads, and to establish methods to set objectives of the structural performance of repaired frames.
 A lot of past research reported the methods related to seismic retrofitting and reinforcement before suffering from great earthquake disaster, and technical manuals has been published. However, although a technical guideline and design procedure to repair damaged building structures has been published, few studies has reported on investigating the relationship and the recovery of the structural performance after repair. Furthermore, planning method for repairing strategies to actualize objectives of the structural performance after repair has not been reported. When repairing strategies for damaged building structures are planned, it is necessary to verify the influence of repaired members on whole system of the repaired building structure. Although the technical guideline provides repair methods for damaged structural members and general evaluation of the performance recovery of repaired members, No methods to set the objective of the structural performance of the whole system after repair has not been established, and also no effective methods to estimate ultimate behavior and likely collapse modes of repaired building structures subjected to seismic loads are provided
 This research focuses on the ultimate limit state of steel frames subjected to seismic loads, and try to investigate ultimate behavior and likely collapse modes of repaired frames. This study models a limit state function of repaired frames that have experienced severe earthquake, and try to investigate likely collapse modes of repaired frames based on first order reliability method. This limit state function is formulated using probability distribution of strength and load effect considering the influence of the repair.
 In order to investigate structural performance parameters which affect ultimate state and collapse modes of repaired frames, simple analytical studies using the formulated limit state function and first order reliability method are conducted. From the result of analytical study, the influences of beam column strength ratio, strength increasing ratio by repair and load distribution are described.
 Based on previous experimental studies which have investigated the recovery of structural performance of steel members repaired by actual repair methods, analytical model of multi-story steel moment resisting frame are constructed. And in order to verify the validity of proposed estimation method, analytical studies using this frame model are conducted. From the results of analytical studies, it is confirmed that the proposed method can evaluate likely collapse modes of repaired steel frame.

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It is known that the topology optimization (TopOpt) problem of frame structures by selecting cross-sections from a given list can be formulated as a mixed-integer second-order cone programming problem (MISOCP). Previous studies have demonstrated the effectiveness of TopOpt by MISOCP for the simple stiffness maximization problem of medium-sized structural frames. However, if we consider real-world design and construction of real-world building structures, it is insufficient to optimize only the mechanical performance. Development of a topology optimization method that can take non-mechanical performance into account is required. In this paper, we present a new approach to TopOpt by MISOCP in which upper bounds for the member lengths and the number of nodes are considered.

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 The appearance of a concrete shell structure has developed the construction of free curved shell structures as many attractive architectures. However, in design of such continuum shell structures, it is difficult to find an optimal structure analytically. Because, in the optimal analysis, shape, thickness and topology of shell structure become design variables simultaneously. Therefore, in this paper, a simple method to find an optimal shell structure is proposed. In this method, a rectangular fixed design domain with given boundary conditions and body forces is modeled by voxel mesh, and strain energies of elements (voxels) are obtained by voxel finite element method. Next, elements with small strain energy are gradually removed by the Improved ESO (IESO) method. Finally, we can obtain a shell structure that shape, thickness and topology are optimized. In this paper, several numerical examples will be shown in order to verify the effectiveness of the proposed method.
 In the IESO method, the fixed design domain is divided in same eight-node rectangular elements (voxels), and in the optimization process, for solid element, it will be removed if the sensitivity number is less than the threshold value. This threshold value is obtained from the equation proposed in the extended ESO method²⁾. This equation consists of the mean value of sensitivity number and the average deviation of sensitivity number with a control parameter. In the proposed method, the evolutionary volume ratio (reduction ratio) is given as an input data, and this control parameter is determined automatically in the program to satisfy the given reduction ratio approximately.
 In section 4, several numerical examples are shown to demonstrate the effectiveness of the proposed method. A basic numerical example shows that IESO can obtain a natural and simple topology. In addition, we analyze the case of giving vertical body force (gravity), analyze the case of giving the vertical gravity and vertical physical strength of 0.2 times the vertical weight in the vertical direction, and conduct the morphological creation corresponding to the seismic force. In next numerical examples, a cylindrical shell is created due to the setting of supported areas as parallel lines, and a spherical shell is created due to the setting of supported area as a circle. Therefore, various optimal shell structures can be generated by the IESO method. Moreover, it is shown that the complicated structure is created in application example. From these examples, it is concluded that the IESO method is a method that can be used to create a shell structure.

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 Eccentric arrangement of shear walls leads to torsional vibration, which is one of the reasons for collapses or severe damages of huge number of wooden houses in the past earthquakes. Therefore eccentricity ratio R_e is defined in Japanese Building Standard Law to confirm the adequacy of shear walls' arrangement. Although R_e is calculated in each story and in each direction, it does not consider interaction between different stories. For example, even though a story does not have any eccentricity, torsional response can be excited by another story with eccentricity. Such a phenomenon is not simulated by R_e.
 Most of Japanese wooden houses are two-story, and some of them have setback. In addition, the lower story typically has larger eccentricity and the upper story has less eccentricity. The torsional interaction as stated above is likely to affect the displacement mode of wooden houses.
 In this paper, prediction method of displacement mode for two-story wooden structure with eccentricity is proposed, and the applicability is discussed. When a single-story structure is considered, dynamic displacement mode including torsional response is approximated by our previous method⁷⁾ instead of solving eigen value equation. Therefore displacement mode in each story without interaction is firstly evaluated, and the interaction effect is added to it. The key idea is based on "Force-Dependent Ritz Vector" which gives simple formulae of practical use.
 The structure is assumed to be linearly elastic and to have uni-axial eccentricity and infinitely-rigid floor diaphragm. Uni-directional earthquake input is considered. The followings are findings of this paper.
 1) Prediction method of torsional displacement mode considering interaction between upper and lower stories was proposed, and the accuracy was confirmed by comparison with numerical analyses.
 2) While torsion in lower story is not so affected by upper story, the one in upper story is clearly affected by lower story.
 3) A story with eccentricity apparently has less lateral story stiffness compared to the one without eccentricity, resulting in large story drift.
 4) If a deference of eccentricity ratios in upper and lower stories exceeds 0.15, an interaction of torsion between upper and lower stories should be considered. If not, it is negligible.
 In this research, two-story wooden house was focused on as a representative of multi-story building having different length of eccentricities in each story. However, a base isolated building whose superstructure has eccentricity has the same problem, and the proposed method can be applied to such structures.
 Since this research considers linearly elastic structures with uni-axial eccentricity, issues like non-linearity and bi-axial eccentricity will be investigated in the future research.

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 It is thought that the previous equation for the flexural ultimate strength of shear walls has enough accuracy. But, it was found that the calculation results by the previous equation became often bigger or smaller than experiment results. So, the characteristics of the previous equation were investigated using the previous experiment results, and the flexural resistance mechanism of shear walls was investigated by FEM analysis. As a result, it was found that the flexural ultimate strength of shear walls was affected by shear force. Therefore, the proposed method for the flexural ultimate strength of shear walls taking account of shear resistance mechanism was developed.

 By investigating the characteristics of the previous equation, the following knowledge was obtained.
 1. For I shaped shear walls, the accuracy of calculated results changes according to the size of strength ratio (shear strength / flexural strength) , shear span ratio and section area ratio (area of side column / whole area).
 2. For rectangular shear walls, the accuracy of calculated results changes according to the size of whole components.
 3. The previous equation for the flexural ultimate strength of shear walls has several problems, but the accuracy of calculated results is almost good.

 By FEM analysis which parameter is loading type, one is horizontal force loading, another is only flexural moment loading, the following knowledge was obtained.
 1. The flexural strength is influenced by shear force.
 2. A difference of strength between horizontal force loading type and flexural moment loading type is variable according to the size of several components of shear walls.

 Assumptions of the proposed method are the following.
 1. The flexural strength decreases by the compressive strut of concrete in wall plate.
 2. The flexural strength increases by the horizontal resistance mechanism of side columns.
 3. The distribution shape of compressive stress at wall plate leg portion when horizontal force reaches the flexural strength is triangular.

 It was confirmed that calculation results by the proposed method corresponded well with experiment results.

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 The upper flanges of H-shaped beams are often restrained by the floor slab or purlin members. When beams undergo lateral buckling, the stiffening effect of a restraint on the upper flange is significant. When the upper flange is compressed by such a long-term load, lateral buckling rarely occurs. Although lateral buckling may occur, if the lower flange is compressed by seismic or wind loads, the constraint on the upper flange works effectively, which increases the elastic lateral buckling strength. However, the elastic–plastic behavior of H-shaped beams is not completely understood as only a few experimental studies exist that consider the effects of continuously restraining the upper flange of H-shaped beams. In a common experiment, experiment that simulated an H-shaped beam by continuously restraining the upper flange was conducted by constructing a floor slab for the beam. This arrangement may be considered as almost practical; however, the behavior of the H-shaped beam itself is unclear because the influences of the floor slab and the stud bolt cannot be completely removed. In this study, the influences of the floor slab and the stud bolt are removed, and the consecutive restriction jigs of the upper flange are suggested. The large-deformation behavior of the H-shaped beam via a loading experiment is confirmed.
 As a result, the following conclusions are reached: (1) The continuous, complete restraint on the upper flange significantly increases the maximum strength and plastic deformation capacity of the beam with respect to lateral buckling. The buckling wave are observed close to the fixed end. Although the web tends to be deformed on the side close to the upper flange, the amount of lateral displacement of the lower flange is suppressed. (2) The continuous, complete restraint on the upper flange slightly increases the maximum strength and plastic deformation capacity of the beam in the local buckling of the web. Moreover, the lateral displacement of the lower flange and the deformation of the web do not change considerably. And continuous complete restraint of the upper flange does not affect the maximum buckling strength, plastic deformation capacity and degradation gradient for the beam in the local buckling of the flange. (3) When the upper flange is continuously constrained, the provision of the stiffener may possibly achieve the same effect as restraint lateral buckling. In addition, since the continuous restraint itself of the upper flange itself increases the plastic deformation magnification, it is possible to make the lateral stiffening interval longer than the reference. However, as in the case of unconstrained, deterioration is caused by repeated loading, so care must be taken. (4) The collapse mode of the H-shaped section beam that is continuously restrained by the upper flange can be divided with W_F=1.4λ_b as a boundary, and the maximum yield strength and plastic deformation capacity can be evaluated according to the collapse mode using this division. (5) The maximum yield strength of the H-shaped cross-section beam that is continuously restrained by the upper flange can be evaluated by the same method as in the case where there is no restraint on the upper flange by the aforementioned collapse type classification. Plastic deformation capacity can be evaluated by using the plasticity limit value as a reference for both the local buckling collapse type and the lateral buckling collapse type.

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 In Japan, steel moment frames, which consist of H-shaped beams and square tube columns with through diaphragms, are often used for low and medium rise steel building structures. Joint panel usually has the same cross section as the column just below it. In case of these steel frames, it is very probable that joint panels will yeild earlier than columns or beams under strong ground motion.
 A lot of numerical studies have been conducted to examine the influence of in-plane elasto-plastic behavior of joint panels on seismic response of plane frames under uni-directional ground motion. However there are few researches to focus on seismic response of 3D frame under bi-directional ground motion.
 On the other hand, axial force, bi-direction shear force and bi-axial bending moment will act on the joint panel under bi-directional ground motion. Although shear force has a dominant influence on the elasto-plastic behavior of joint panel, the influence of bending moment is not negligible for the joint panel with large aspect ratio or under bi-direction loading. However, an analytical model, which is considering the elasto-plastic behavior of joint panel under bi-direction shear force and bi-axial bending moment, has not been proposed yet.
 This paper proposes a new analytical model for squqre steel tube joint panel with through diaphragm. Chapter 2 describes the basic concept of the analytical model for joint panel, which consists of 3 multi-spring components are placed in series as shown in fig. 1. Those multi-spring components, which are built by introducing the degree of freedom of shear force to each spring, can consider the the elasto-plastic behavior under correlation between axial force, bi-direction shear force and bi-axial bending moment. As the bending moments at the end of joint panel is larger than the one in the middle, the multi-spring components at the ends consider axial deformation, shear deformation and flexural deformation, while the multi-spring component in the middle consider axial deformation and shear deformation. And the total length of 3 multi-spring components must equal to the panel length.
 Chapter 3 describes the numerical method to build the analytical model for joint panel by multi-spring components and the stiffness equation of the model. Chapter 4 describes the restoring force characteristics of springs under axial and shear force. Chapter 5 proposes the method to calculate the length of multi-spring components at the ends, in order to ensure that the plastic flexual deformation of multi-spring components at the ends equal to the plastic flexual deformation of joint panel ends. And chapter 6 describes the method to install the analytical model for joint panel into the 3D frame anaysis program proposed by Ref. [17].
 In chapter 7, analytical results of single joint panel, as shown in fig. 11, and cruciform frame, as shown in fig. 16, under bi-direction loading by the proposed analytical model are compared with results of finite element method and experimental results from previous researches. From the comparison, analysis by the proposed model and the finite element method analysis or experimental results correspond well. Also the analysis result shows that, the proposed model is possible to express difference of the plasticity state of springs in multi-spring component varies depending on the input direction and the aspect ratio of the joint panel.

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