In this paper, uncertainty propagation analysis was applied to investigate accuracy of wind response prediction of high raise buildings and influence of uncertainties in each parameter used in wind response analysis. A new parameter which is “related sensitivity coefficient” concerning propagation was defined to consider wind response prediction more analytically and efficiently. The values of uncertainties of each parameter were also investigated on the basis of prior literature. Furthermore, the accuracy of wind response predictions calculated by spectra-modal analysis was revealed from investigation of related sensitivity coefficients and values of uncertainties of each parameter.
 The following conclusions can be drawn from this study.

 1) Regarding the mean and maximum response displacements, the natural frequency and design wind speed had the largest influence exerted by any factor on the wind response predictive value. On the contrary, the relative sensitivity coefficient was low for the damping ratio as well as the resonance wind force spectrum (i.e., resonance component of the wind power spectrum density of the fluctuating wind force).
 2) Regarding the maximum response acceleration, the relative sensitivity coefficient was high for the natural frequency and low for the damping ratio and the resonance wind force spectrum. It had the same characteristics with the mean response displacement. However, the design wind speed with high sensitivity in the maximum response displacement had low sensitivity for the maximum response acceleration.
 3) The damping ratio had the highest uncertainty value for any factor. The resonance wind force spectrum had the next highest uncertainty value. The lowest uncertainty value was the design wind speed.
 4) The uncertainty propagation value to the mean response displacement was larger for the natural frequency than any other factor. That is, the uncertainty of the mean response displacement was affected by the uncertainty of the building's horizontal stiffness and mass.
 5) The uncertainty propagation value to the maximum response displacement was the highest for the natural frequency. That is, the uncertainty of the maximum response displacement was largely dependent on the uncertainty of the natural frequency. The damping ratio and the resonance wind force spectrum had high uncertainty. However, their propagation values were low because their relative sensitivity coefficients were low.
 6) The uncertainty propagation value to the maximum response acceleration was similar for all factors because the relative sensitivity coefficient was low, where the uncertainty of factors was high, and the relative sensitivity coefficient was high, where the uncertainty of factors was low.

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 Site amplification is one of the most important factors in strong ground motion prediction at construction sites. In ground motion calculation methods such as the stochastic Green's function method, seismic motions are first synthesized on an outcrop of engineering bedrock with an S-wave velocity of more than 400 m/s. Ground motions on the ground surface are then evaluated using the substructure method by independently modeling only the shallow part of the subsurface structure, using ground motions on the outcropped engineering bedrock as input motions. This approach sometimes yields inaccurate results because the coupling effect between the shallow and deep parts of the subsurface structure is ignored.
 In the present study, the calculation accuracy of the conventional substructure method is first investigated for various soil layers. A rigorous method that incorporates the coupling effect with the deep subsurface structure is then proposed based on the nonlinear substructure method in terms of velocity convolution integrals.
 As an example, synthesized surface motions calculated by the conventional substructure method and a full rigorous analysis are compared using the S-wave structure of the Osaka Plain, where the S-wave velocity between the seismic bedrock and overlying sediments varies abruptly, for deep soil layers of various thicknesses. Although the onset S-wave parts coincide for both methods, differences in the later phase of the waveforms are observed. These differences occur because the reflected waves from seismic bedrock transmitted from the shallow layer to the deep layer are essentially ignored in the conventional substructure method.
 Next, generalized soil models are used to assess errors in the conventional substructure method by varying three and fixing one of the following four parameters: the S-wave velocity just above the seismic bedrock, the S-wave velocity just above the engineering bedrock, and the thicknesses of the shallow and deep parts of the soil. The error index, FDE, is used to quantify the calculation accuracy of the conventional substructure method. The error becomes large when the thickness of the deep soil is small and the thickness of the shallow soil is large, due to the difference in the travel time of the waves reflected from the boundary of the seismic bedrock. The impedance ratio between the seismic rock and sediments also contributes to the error.
 In order to rigorously incorporate the coupling effect of the deep and shallow soil layers into the conventional substructure method, a frequency-dependent dynamic impedance function is added to the bottom layer, instead of the viscous boundary for the engineering bedrock. First, the dynamic impedance function on an outcrop of engineering bedrock that includes the deep part of the soil is calculated in the frequency domain. The nonlinear behavior of the shallow soil layer requires a seismic response analysis in the time domain. The frequency-dependent dynamic impedance function for the deep soil layer is converted into a time-domain impulse response, which is used in the convolution integral of the velocity in the time-domain analysis.
 The proposed method is applied to the ground motion evaluation using the subsurface structure of the Osaka Plain. The acceleration response time histories and the response spectra obtained by the proposed method coincide well with those obtained through a full rigorous analysis. In the case of the nonlinear analysis, the coupling effect decreases because of the hysteretic damping effects of the shallow soil. However, the results obtained using the proposed method have been verified to approximately coincide with those obtained through the full rigorous analysis, implying that the proposed method provides a rigorous solution that considers the coupling effect with the deep part of the subsurface structure.

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 An irregularly layered subsurface structure (hereafter irregular site) amplifies earthquake motions sometimes more than a stratified media (hereafter flat site) due to, for example, a focusing effect of seismic waves. An exploration of a depth distribution of a structural boundary is too costly at each site in practice. A preliminary examination is desirable to discriminate sites where an amplification factor can be approximately estimated with stratified media from irregular sites. Focusing on spatial variation of horizontal to vertical spectral ratios (hereafter HVSRs) of microtremors, we performed 3 investigations with respect to a relationship between coefficients of variation of HVSRs' peak periods (hereafter CVs) and effects of irregular interfaces of a subsurface structure.
 First, we conducted densely mobile microtremor measurements at 4 sites, which consist of 2 irregular sites and 2 flat sites. The values of CVs on the irregular sites are significantly larger than those on the flat sites, and they can be obviously separated.
 Second, in order to reveal the characteristics of shapes of sediment interfaces affected the values of CVs, we analyzed sensitivity to CVs by numerical simulations for wave propagation with complex media. The basic subsurface structure model was constructed based on results of the drilling method at Nabari site where mobile microtremor measurements were also conducted. CVs of simulated motions with the basic model are almost consistent with the CVs by the observation. We found that slope angles and wave number of irregular boundaries of layers respectively affected amplitudes of CVs and inflection distances making a smaller inclination of CVs.
 Third, we compared CVs with irregularity of subsurface structure, using results of simulated microtremors and subsurface structure models. For a comparison, we converted CVs to a power spectral density (hereafter PSD) via a semivariogram. The PSD estimated from CVs showed a good agreement with the PSD calculated from the subsurface structure model in the wave number range corresponding to interstation distances of the CVs.
 Through the above investigations regarding the difference of CVs of irregular and flat sites, we concluded that CVs can be a proxy to represent an irregularity effect of sediment interfaces.

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 We have proposed the simple modeling method for the lateral resistance of elastic retaining wall portion (retaining wall + backfill soil) using fiber model, and we have showed the collision analysis model using the method. This paper aims to confirm the applicability of the method in case of retaining wall with elasto-plastic property.
 First, we conduct the seismic response collision analysis of a base-isolated structure-soil interaction system using 3D-FEM and estimate the structural behavior and impulse force when it collides uniformly and without twisting into retaining wall. Figure 1 shows 3D-FEM analysis model. Basic specifications and conditions are same as reference No. 11. The thickness of retaining wall is taken as t =300mm, its flexural strength assumes two types of Mu≒145kN·m/m (“flexural strength 1.0 times type”) and Mu≒72.5kN·m/m (“flexural strength 0.5 times type”). Figure 5 shows the time-history response displacement of isolation layer in 3D-FEM collision analysis. The maximum response displacement for both types is the same as approximately 523mm, however their behavior after the maximum displacement is different. Figure 6 shows the time-history response acceleration of superstructure (top floor and 1st floor). With respect to maximum response acceleration (16.5m/s²) at the top floor of elastic retaining wall, flexural strength 1.0 times type is reduced by approximately 12%(14.6m/s²), and flexural strength 0.5 times type is reduced by approximately 23%(13.4m/s²). Meanwhile, with respect to maximum response acceleration (12.4m/s²) at the 1st floor of elastic retaining wall, which values of both types are almost the same. Figure 7 shows the time-history impulse force on lower edge position of girder directly above isolation layer at which maximum impulse force is obtained. Maximum impulse force of both types is reduced approximately 21% against elastic retaining wall.
 Next, we confirm the applicability of the simple modeling method in case of retaining wall with elasto-plastic property. The verification position is three cases; GL±0m, GL-1.2m, and GL-1.5m. Figure 12 and Figure 13 shows the hysteresis loop of retaining wall portion. In case of GL-1.5m, a difference occurs in the maximum response displacement because the simple modeling method may not accurately reproduce strength of retaining wall portion obtained from 3D-FEM analysis. Also, in case of GL±0m and GL-1.2m, a difference between 3D-FEM result analysis and the simple modeling method is large. This reason is considered to be not conformed the condition of maximum range 3t for the backfill soil considered as added mass because the maximum response displacement of elasto-plastic retaining wall is larger than elastic retaining wall. So, we modify the maximum range from 3t to 6t, and we re-estimate the lateral resistance of retaining wall portion. As a result, hysteresis loop shapes are greatly improved, and it shows relatively good agreement to 3D-FEM analysis result.
 Finally, we conduct collision analysis using the simple modeling method, and we compare the structure response with the 3D-FEM analysis results. Figure 18 shows the analysis model using the method. In the case of the collision springs taking into account axial stiffness of the girder directly above isolation layer, the method largely captures trends in restoring force characteristics of entire isolation layer (isolation layer + collision spring) from 3D-FEM analysis. The method estimates maximum response acceleration at 1st floor approximately 14% smaller compared to 3D-FEM analysis result. However, it shows relatively good agreement to 3D-FEM. Meanwhile, in the case of the rigid collision springs, the maximum response values are overestimated. This tendency is the same as case of elastic retaining wall.

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 This paper discusses the relationship between the probability distribution functions (PDFs) of residual deformation and total plastic deformation of a perfectly elastic-plastic single-degree-of-freedom oscillator, from a viewpoint that, if this relationship is known, it is possible to use the residual deformation after an earthquake as an index of the total plastic deformation, that is, the accumulated structural damage.
 In the previous study, the author showed, using the “random walk hypothesis”, that the conditional probability of the residual deformation given the number of plastic excursions, n, and the total plastic deformation, d_t, is almost a normal distribution with an average of zero and a standard deviation of d_t over the square root of n. By calculating the inverse probability, in this paper, the conditional PDF of d_t under the residual deformation, d_r, was formulated. This formula enables one to estimate the structural damage the structure has received during an earthquake, by measuring the residual deformation after the earthquake.
 In order to validate the derived formula for the conditional PDF of d_t given d_r, dynamic response analysis was performed using a large number of pseudo ground motions simulated by the inverse Fourier transform and actual ground motions recorded at two locations in Japan over the period of 10 years.
 To calculate the conditional PDF of d_t given d_r with the formula, it is necessary to obtain the joint PDF of n and d_t. In order to do this, first, the log-normal PDFs for n and d_t were obtained by regression analysis of dynamic response analysis results. The joint PDF of n and d_t can be assumed as a product of each log-normal PDF of n and d_t, if n and d_t are statistically independent. This assumption is used although it is not always justified and therefore this may affect the accuracy of the estimation.
 Once the joint PDF of n and d_t are obtained, it is possible to calculate the conditional PDF of d_t given d_r. This calculated PDF shows reasonable agreement with the histogram obtained from the dynamic response analysis, for both cases of simulated ground motions and actual ground motions, although the accuracy for the actual ground motions is worse than that for the simulated ground motions. It is presumed that this error might come from the rough assumption of statistical independence in the joint PDF of n and d_t for the case of actual ground motions. There may be a possibility to improve the accuracy by obtaining more accurate joint PDF of n and d_t, which is considered as an index of earthquake characteristics.

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 High-rise buildings existing in the Tokyo metropolitan area are responsible for the central function of the society. Therefore it is predicted that the damage of the high-rise building caused by the major earthquake has a serious influence on Great Society. In the 2011 Great East Japan earthquake, even though structural members of buildings were very little damage, damage of sprinkler-heads, fall of ceiling boards on upper floors, movement of furniture on casters such as a photocopy machine, and fall of books occurred. These damages led to the function loss of the building and had an influence on recovery after the earthquake greatly. Considering those aspects, this paper investigates the seismic loss of functionalities in high-rise buildings through large scale shaking table tests on a high-rise building.
 The substructure test method was employed, and a test specimen representing a 30-story steel high-rise building was shaken on the E-Defense shaking table. In the test specimen, a large interior space with 18.9m×9.0m plane size, 3.8m floor height, and 2.4m ceiling height to simulate interior space damages due to interaction among ceiling, partition wall, air-conditioning equipment, sprinkler pipes filled with water, and office furniture. Some equipment and furniture was prepared for prevention of swinging and falling in order to evaluate the effect of prevention. And the test specimen was designed to be able to reproduce the low-rise buildings response to evaluate comprehensive basic data of interior space damage.
 The predominant period of input motions were considered both characteristics of subduction earthquakes and near fault earthquakes. The observed record concerning the 2011 Great East Japan Earthquake from Nishi-Shinjyuku observation site of the MeSO-net were used for the shake table tests while changing the amplitude level of the record. Also the record of the 1995 Hyogo-ken Nanbu Earthquake (JMA-Kobe), which included short period components, was adopted.
 A series of experimental results confirmed effectiveness of the seismic countermeasure for office furniture, suspended air conditioners, and steel bed of ceiling, to reduce the interior space damage. From the test results of high-rise building model, prevention of furniture overturning and moving is a very effective mitigation of the interior space damage, because of seismic response characteristics of high-rise buildings.
 From the test results of low-rise building model, prevention of furniture overturning is also a very effective mitigation of the interior space damage. However, depending on the characteristics of the input ground motion, low-rise building response may become very large, evacuation activity in the room is also required in order to ensure personal safety, for example, books jump out of from the bookshelf which are prepared fall prevention. Two types of system ceiling, the line type and the grid type, were adopted during the low-rise building tests without braces for the light-weight steel bed of ceiling. The test results provide evidence of safety of the ceiling against a middle-size earthquake, and shows the checkpoint for confirmation of safety at the time of a large-size earthquake.
 In order to reduce the seismic loss of functionality of buildings due to interior space damage, design and construction considering the interaction among the non-structural elements, equipment instruments, and furniture is important. This paper shows the basic data and the check points for this consideration.

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 A pile top seismic isolation system is used for constructing base-isolated buildings. In this system, seismic isolators are set on the pile's top directly, and piles are connected with thin foundation girders or a mat slab. In recent years, many logistics centers have been constructed using this system because it enables significant cost reductions in underground construction.
 However, this system does have some problems. For example, the laminated rubber bearing's bottom part easily undergoes bending rotation because the thin foundation girders have low stiffness. This tendency becomes more pronounced in the case of soft ground. If bending rotation occurs, the laminated rubber bearing's horizontal stiffness reduces under the influence of the horizontal component of the axial load, and its inflection point moves downward from the center height of the device (usually, the point does not move). This, in turn, significantly affects the structural characteristics of the pile top seismic isolation building. In addition, it has been noted that the horizontal stiffness and rotational stiffness of the laminated rubber bearing show deformation-dependent nonlinearity.
 In order to evaluate such special behaviors of the pile top seismic isolation building appropriately, it is required to consider the dynamic soil－structure interaction and the nonlinearity of the laminated rubber bearing. In particular, analytical models that can consider the geometric nonlinearity and various nonlinear characteristics caused by the bending rotation of a laminated rubber bearing have been proposed. However, highly specialized knowledge is needed to use these models, and such knowledge is difficult to incorporate into general-purpose design software. Therefore, it's not considered sufficiently their effects in conventional structural design at present.
 This paper describes the seismic behaviors of laminated rubber bearings in pile top seismic isolation buildings through numerical experiments by considering the nonlinearity of the laminated rubber bearing and the dynamic soil－structure interaction.
 The parametric analytical study is performed by the elasto-plastic earthquake response analysis. The analytical model is of the fishbone type, and it represents one span of the logistics center. It consists of a superstructure, seismic isolated layer, thin foundation girders, a pile, soil-pile springs, and free field. The laminated rubber bearing model is based on Miyama's method, and this model is constructed using three matrices: horizontal stiffness matrix, geometric nonlinear matrix, and rotational stiffness matrix.
 The following conclusions are obtained through numerical experiments on the pile top seismic isolation building.
 1. By a quantitative evaluation of the response of the superstructure, the problems of current structural design method is clarified.
 2. The dynamic characteristics of the laminated rubber bearing are quantitatively evaluated depending on the characteristics of the substructure. In addition, it is shown that their values are affected by the influence of the correlation between the horizontal deformation and the rotational angle of the laminated rubber bearing.
 3. It is clarified that the dynamic characteristics of the laminated rubber bearing can be evaluated using a simple indicator called the rotational stiffness ratio.

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 In this study, we identified superstructure stiffness and sway/rocking stiffness using seismic observation data for an eight-story steel-encased reinforced concrete building for which continuous seismic observation had been made since the completion of construction. We analyzed the structural aging and amplitude dependence of superstructure stiffness and sway/rocking stiffness.
 The target building is the Research Center for Disaster Risk Management of the National Institute for Land and Infrastructure Management (completed in March 1998). Accelerometers on the nearby surface ground, the first basement level, the first floor, the second floor, the fifth floor, and the eighth floor are utilized for the identification.
 Following three types of natural frequencies with consideration of the influence of the interaction were determined:
 1) Combined system, including horizontal motion and rotational motion of the foundation: Natural frequency of SRB type; f_SRB
 (Input: Acceleration of the ground surface 20 m away from the building)
 2) Upper deformation + rotational motion: Natural frequency of RB type; f_RB
 (Input: Acceleration of the first basement level)
 3) Fixed-base system of building deformation only: Natural frequency of B type; f_B
 (Input: Acceleration of the first basement level + rotational motion of the foundation)
 These tree-type natural frequencies tend to decrease due to aging and dropped down after the 2011 off the pacific coast of Tohoku earthquake.
 By using these three natural frequencies, sway/rocking stiffness is estimated. The rocking stiffness tends to increase due to aging, and after Tohoku earthquake sway/rocking stiffness decreases. In large-PGA cases, the sway/rocking stiffness tends to be smaller. Minimum identified values are a little larger than values calculated from soil investigation data.
 Superstructure stiffness is identified by using natural frequency and participation function. Superstructure stiffness tends to decrease due to aging and dropped down after the 2011 off the pacific coast of Tohoku earthquake. By comparing the identified superstructure stiffness after the 2011 off the pacific coast of Tohoku earthquake and the stiffness from push-over analysis, structure should be between crack point and yielding point. Decreasing rate of lower story stiffness is a little bit larger than that of upper story stiffness. This tendency is same as the results by visual inspection.

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 Recently it has been demanded to evaluate structural safety and function recovery of buildings shortly after subjected to an earthquake. Seismic response of each floor of a building can be easily measured if sensors are installed on every floor. High performance sensors are generally expensive, so it is difficult to install sensors on every floor of a building, especially of a high rise building. Several methods have been proposed to estimate seismic response of each floor of a building by utilizing sensors installed on a limited number of stories. Most of these methods are techniques based on the modal analysis, and have already attained to a practical application level. The main aim of those methods is to estimate structural health determination and damage-identification at each floor level by using a limited number of high-precision conventional servo-type accelerometers. However, applicability of those methods has not been examined in detail as for nonlinear deformation of the building and as for effects of location and numbers of sensors on simulation response analyses.
 In this paper, we will examine the applicability and effects of our estimation method according to the modal shape calculated on the basic of the design model of building by using experimental data of the large shaking table test of the 1/3 scaled 18-story steel high-rise building executed in December 2013 at E-Defense. Artificial generated earthquake motions were used as input for the large shaking table test, and the amplitude levels of the input motions were repeatedly increased until the model specimen was collapsed. We installed 25 servo-type accelerometers in the model specimen on each floor. Response states of the whole building were evaluated by using a few points of sensors. From the viewpoint of structural health monitoring, we focus on the maximum story drift angle of buildings. We analyzed the results estimated from limited point accelerometers by comparing with observed data form all sensors in addition to other data such as displacement meters.
 In this paper, we can draw our conclusions as follows.
 1) Up to 0.03 radian in the maximum story drift angle, results estimated from 5 points of sensors (1, 4, 10, 15 and RFL) correspond approximately to the observed results in the 18 story steel high-rise building model.
 2) It is important that sensors should be properly installed on the building by considering the mode shape of design model in order to evaluate better seismic response.
 3) It is true that more sensors give better accuracy of evaluating building response. Especially, more sensors are needed if the building shows strong nonlinearities over 0.01 radian.

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 This paper proposes a practical evaluation method of vibration control performance of a tuned mass damper (TMD) mounted on rooftop of buildings without time history analysis. The response quantity of interest has been taken to be the peak seismic response of the buildings with the TMD. In this study, the seismic effectiveness of the linear TMD is assessed in terms of an equivalent damping factor of the overall vibration system. The objective of this paper is to formulate the equivalent damping factor of the building subjected to strong ground motions.
 Firstly, the vibration system consisting of both the multi-story building and the TMD on the seismic response is idealized as an equivalent two degrees of freedom (2-DOF) system. Based on this simplified model, parameters of interest are a mass ratio and a tuning ratio, which govern the seismic effectiveness. The mass ratio is the ratio of the TMD mass to the effective mass of the building. Using these parameters, the equivalent damping factor based on random vibration theory is employed in optimal conditions (perfect-tuning case). The remaining parameters of interest are effective duration and a fundamental period of ground motions. The equivalent damping factor is empirically modified with the help of a solution of the time-dependent mean squared response under non-stationary random disturbances.
 Secondary, the response to base excitation having a single sinusoidal wave, which is degenerated from historical records of ground motion pulses, is investigated. It is confirmed that the maximum response obtained by the SDOF system with the proposed damping factor show good accordance with those calculated by the 2-DOF system in a wide variety of natural periods through time history analysis. The closed form equation of the equivalent damping factor is also verified under population of historical earthquakes. Subsequently, the relationship between the maximum displacement of the building and the TMD is examined. Time history analysis demonstrates that the ratio of the TMD deformation to the building displacement is almost constant over a wide range of periods. The ratios, however, tend to significantly decrease in long period regions. A closed form expression of this ratio derived from random vibration theory is empirically modified to take account of this inherent dynamic characteristic through parametric study.
 Finally, the evaluation method of the maximum response is developed to cover non-tuning cases in the light of design practice. The design damping factor of the TMD is assumed to be larger than its optimal value. The equivalent damping factor and the deformation ratio are theoretically decomposed into its optimal value and correction factors. Using these results, a performance curve diagram is presented. This diagram consists of the response reduction factor of the building and the amplification factor of the TMD in terms of the mass ratio and the damping factor. It is shown that the proposed method to design parameters of the TMD based on the diagram approach is useful in engineering applications.

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 Characteristics of inverse problem analysis techniques on structural system identification based on filtering theory using as iterative calculation algorithm were studied computationally. Three- story frame models shown in Fig. 3 were adopted as the structural system and the projection filter was chosen from among Kalman filter, projection filter parametric projection filter and variable parametric projection filter. The projection filter is the simplest formula among filters mentioned above shown in eq.(8). Thus, characteristics of the projection filter were investigated from viewpoints of engineering quantities which are consisted of sensitivity matrix, filter gain, lateral stiffness, determinant of sensitivity matrix and initial values due to iterative calculations. In this study, iterative calculation procedures due to filter gain given as inverse matrix of sensitivity matrix based on the projection filter are proposed focusing on the difference calculation methods of sensitivity matrix especially. Results obtained from the inverse problem analysis due to system identification of three- story frame models can be summarized as follows.

 (1) System identification analysis in the case of using “local forward difference method” can be performed iterative calculations computationally and stably.
 (2) System identification due to iterative calculations assuming damage to the intermediate story cannot be performed stably.
 (3) Iterative calculations due to inverse problem on structural system identification tend to diverge, even in the case where sensitivity matrix is compatible with the structural or mathematical model and determinant due to sensitivity matrix based on the projection filter alter on each filtering step.
 (4) Iterative calculation can be performed stably by changing the initial value on intermediate story to be given among the sensitivity matrix, even in the case where sensitivity matrix is not compatible with the structural or mathematical model.
 (5) In this study, iterative calculation can be carried out stably, even in the case where the initial value of intermediate story was given as half value of other stories.

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 Steel piles beneath a building structure may buckle when the piles carry the high axial compression forces increased by overturning moment of the superstructure in liquefied soil during a strong earthquake. In our previous papers, centrifuge tests of superstructures with circular tube piles and liquefied soil have been performed to clarify the piles' dynamic buckling behavior subjected to only compressive force. The pile cap is laterally fixed to give piles the axial force due to the weight and the overturning moment of a superstructure. Actually, the pile cap moves because of a superstructure inertia and soil deformation. In this paper, the centrifuge tests, the pile cap is free to move laterally, are conducted. The piles' dynamic collapse mechanism in the liquefied soil is described, and piles' ultimate strength is estimated using M-N interaction curves.
 Figure 1 shows a specimen of centrifuge tests. The specimen is configured by a superstructure represented consisting of a mass and a pair of spring elements, four piles and a saturated sand layer. In Case 1, the pile cap can laterally move, and the vertical and horizontal forces act on the piles head. In Case 2, the pile cap is laterally fixed and only varying axial force due to the weight and the overturning moment of the superstructure act on the piles. The parameters are a natural period of a superstructure, relative density and input waves in addition to an initial axial force ratio of piles, a slenderness ratio, and a material property of the pile as shown in Table 2. The acceleration time history is shown in Fig. 3. The centrifuge tests were performed under centrifugal acceleration 40 g.
 Figures 6-8 show the response time histories of specimens of Case 1. After the soil liquefied the bending strain of the pile increased for all specimens. It is shown that the pile's axial force immediately decreased after the pile had the maximum bending strain.
 For specimens of Case 2, the dynamic buckling strength of piles is evaluated. Figure 12 shows the relationship between observed dynamic buckling strength of piles and buckling curves for design criteria. The lower bound of observed dynamic buckling strength of the piles in the liquefied soil is estimated by the buckling curve of Japanese recommendations for limit state design of steel structures. It is shown that the buckling stress curve with the equivalent slenderness ratio can be applied to estimate dynamic buckling stress of piles. Here, the equivalent slenderness ratio is calculated from the ratio of elastic flexural buckling load of piles in the liquefied soil, which is developed by the energy method in Section 4.1, to the yielding load. Next, for specimens of Case 1, ultimate strength of piles is evaluated using Japanese current design criteria about steel pipe's ultimate strength. Fig. 13 shows the relationship between ultimate strength of piles on centrifuge tests and the M-N interaction curves for design criteria. The axial force of piles is divided by elastic-plastic buckling stress of piles obtained from buckling curve of Japanese recommendations for limit state design of steel structures in Fig. 12, and the bending moment is divided by the full plastic moments of piles.
 It is shown that the results of centrifuge tests and the M-N interaction curves of Japanese recommendations for design of building foundation are almost same at the pile's maximum bending strain, and ultimate bending strength curve (reference (8)) is upper bound to these results.

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 Recently, research and practical application of free-form shells are very active owing to development of computer software tools as well as progress of technology of construction and material. Design problem of free-form shells can be naturally formulated as an optimization problem considering mechanical performances. Parametric surfaces such as Bézier surfaces are effectively used for generating smooth and complex surfaces of continuum and latticed shells. However, to design a practically acceptable design, non-structural performances such as cost of construction should be taken into account. In this study, a shape optimization approach is presented for free-form shells using ruled surface. Latticed shells consisting of ruled surface have high constructability, because members on generating lines require no torsion.
 Boundary shape of the latticed shell is defined using a pair of Bézier curves to reduce the number of variables. The points with the same parameter value of the two curves are connected by a line to model a ruled surface. The locations of control points of Bézier curves are chosen as design variables.
 A latticed shell modeled by ruled surface consisting of two parabolic boundary curves is selected as the initial shape for optimization. Since a simple ruled surface does not have high degree of freedom for shape representation, two ruled surfaces are connected to model a roof with a ridge line. The members of latticed shell is modeled using beam elements, and the four corners are fixed. The vertical self-weight and live loads as well as horizontal loads representing seismic loads are considered in the process of optimization.
 First, we minimize the strain energy under volume constraint to obtain a stiff structure. It is confirmed that the strain energy due to vertical and horizontal loads is drastically reduced through shape optimization. Constructability is maintained, because the stiff beams along the generating lines can be manufactured without torsion.
 Although a stiff structure is obtained through strain energy minimization, the local stress may not be reduced.
 Therefore, we solve the additional optimization problem, which minimizes the material volume under stiffness and stress constraint. The parameter defining the cross-sectional property of each member is considered as design variables of this optimization problem, which is carried out after shape optimization. By solving this problem, the member stresses are reduced through the process of minimizing the material volume, while maintaining the stiffness.

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 Connection of which the beam web is connected to gusset plate of column through high strength bolts is considered as a pin connection in structural design of Japan. In the pin connection, a number of bolts are used to resist axial and/or shear forces due to the external force such a seismic excitation. Moreover, at a pin beam-end connection in braced frame, the connection is required to resist not only axial force but also sufficient rotation. However, design procedures in order to achieve sufficient rotation capacity of the pin connection under compression have not yet been established. In other words, effects of the number of bolts and their arrangement on the rotation capacity is unclear. A purpose of the present study is to evaluate rotation capacity of the pin connection under compression and to establish requirements to achieve a sufficient rotation capacity.
 At first of the present paper, cyclic loading tests of pin connection under compression were carried out to investigate the effects of different connection details on rotation capacity. The test specimen is a full-scale cantilever beam consisting of a beam, a gusset plate, and their bolted connection. The main test parameter is the differences in connection detail, such as beam-web thickness, depth of beam, bolt pitch, diameter of bolt, and the number of bolts. In addition, compressive axial force and the loading protocol (constant or perfectly rigid-plastic slip) are also important parameters to confirm rotation capacity. The pin connection without compressive force has sufficient rotation capacity until reaching 0.08rad rotation although the wider pitch causes bolt fracture. On the other hand, compressive force caused local buckling at the beam web near the connection and reduced rotation capacity of the pin connection down to less than 0.006rad. It indicates that local buckling has very important effect on the rotation capacity of the pin connection under compression. Local buckling might occur at the effective cross section, because force transfer from beam to gusset plate might cause stress concentration around the bolts depend on the bolt arrangement. It is clarified because the rotation capacity limited by local buckling is affected by beam-web thickness, bolt pitch, and the number of bolts. Therefore, in this paper, the effective cross section related with local buckling occurrence is proposed by an assumption of force transfer based on the test results. The axial stress at the effective cross section has negative correlation to rotation capacity of pin connection under compression. It enables to achieve sufficient rotation capacity if the effective stress is less than 155 N/mm². Here, the required rotation capacity is assumed as ±0.03rad rotation at the beam-end connection in braced frame subjected to a strong earthquake excitation.
 Finally, cyclic loading tests of a full-scale braced frame were carried out to verify the applicability of the proposed requirements in the frame. The test specimen is a 2 story-1 bay braced frame with various connection details. The test parameters are beam-web thickness, bolt pitch, and yield strength of the braces. The braced frames with the thick beam-web plate showed the predictable lateral strength based on yielding of brace, and a sufficient plastic deformation of over 0.02rad. On the other hand, because the local buckling occurred at the beam web near the connection before reaching 0.02rad beam rotation, the braced frames with the thin beam-web plate, of which the effective stress is over 155 N/mm², showed a poor seismic performance. Therefore, the proposed requirements for achieving sufficient rotation capacity have been proved to be applicable in the frame.

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This paper presents a numerical study on 3D steel moment frames with square tube columns. The major parameters are column overdesign factor, horizontal load bearing capacity, shape of frames and input direction of ground motion. From the analysis, it is revealed that the relationships between cumulative plastic deformation of columns and column overdesign factor, with the similar horizontal load bearing capacity, are not affected by the shape of frames and input direction of ground motion. The required column overdesign factor to keep the damage of columns below the limit of plastic deformation is proposed under the reliability index of 2.

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 In recent years, high strength steels, whose tensile strength is more than 780 MPa, have been developed in Japan, and are used mainly for columns of high rise building structures. However, it is difficult to secure not only quality but also workability of welding at beam-to-column connections with high strength steel. In Japan, most well used shape of columns is a square hollow section but this type of closed cross section is neccesary to stiffen the section by a diaphragm at the location of the joint with beam flanges to restrain local deformation. In this study, we focus on exterior diaphragm type connection. Because a diaphragm plate is attached only from outside of a column and columns need not to be cut, this type of diaphragm has advantage to overcome the problem about workability of welding of high strength steels. Furthermore, exterior diaphragms are suitable for applying concrete filled steel tubes with high strength steels.
 For improving convenience of construction and transportation efficiency, this study regards a square diaphragm of thick steel plate, whose depth of projection is smaller than a conventional exterior diaphragm. In case of the exterior diaphragm, out-of-plane deformation of steel tube wall occurs. Accordingly, the methods to evaluate elastic stiffness and yield strength of beam-to-column connection are necessary to design the connection. In this study, we focus on tension sides of moment connection where tensile force is transmitted from a beam flange.
 To evaluate elastic stiffness and yield strength theoretically, only the beam flange connection is picked up and a mechanical model composed of two parts, i.e. "exterior diaphragm model" and "column model", is used. The exterior diaphragm model is made of elasto-plastic wire elements having the same mechanical properties as diaphragms, and the column model is made by rigid-body spring model of the column. Then, we consider that elastic stiffness of the beam flange connection occurs under the same deformations of two parts, and presume that elastic stiffness of the connection is equal to the sum of stiffness of two parts. We consider yield strength of the beam flange connection as the sum of resistant forces of two parts at the instant when the diaphragm model yields under bending moment and shear force or axial force while the column model is still under elastic range.
 FEM analysis and loading tests are conducted on beam flange connections, and caluculated values of elastic stiffness and yield strength were compared with results of analysis and tests. Investigated parameters are the thickness and the width of columns, width of beam flanges, and the thickness and depth of the projection of diaphgrams. The beam flange is subjected to only tensile force in one direction, and elastic stiffness and yield strength of beam flange connections were obtained. As a result, it is confirmed that calculated values correspond with results of many analysis and tests well and the validity of the proposed method is confirmed.

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H-shaped beams installed in a braced structure are subjected to compressive and tensile forces from buckling restrained braces. In our previous paper, experiments on H-shaped beams which possess various beam sections under compressive and tensile forces were conducted. However, evaluations for the capacities of H-shaped beams under these two forces have not been scrutinized yet. In this paper, additional experiments and numerical analyses are carried out to reveal the influences of beam sections and magnitudes of axial forces on t he performances. Based on the obtained results, this paper presents evaluation formulae for estimating the maximum strength, plastic deformation capacity, and cumulative plastic deformation capacity. In the end, an empirical formula to predict the Bauschinger e ffect coefficient is proposed to convert the cumulative plastic deformation capacity to the hysteretic energy absorption.

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