The authors have carried out the experiments to identify the effects on fluidity, resistance to segregation, strength, Young's modulus, dry shrinkage and durability of high-strength concrete when unit water content was varied in high-strength concrete while unit bulk volume of coarse aggregate was fixed, or the volumetric ratios of cement paste and fine aggregate were varied.
 Three types of cement, ordinary Portland cement, moderate-heat Portland cement and low-heat Portland cement, were used. Limestones were adopted as coarse aggregate. Water-cement ratio was varied with 45, 35 and 25%.
 Analysis were carried out in concern with properties of fresh concrete, properties of concrete hardening, and properties of hardened concrete where unit water content was varied.
 When water-cement ratio was 35%, changes in the properties of high-strength concrete with hard sandstones used as coarse aggregate owing to the increase of unit water content were also examined.
 As a result of the experiments, it was found that increasing of the water content caused no segregation of materials, facilitation of handling, reducing of changes in the retention of slump and slump flow, increasing of flow velocity in L-box tests and increasing of bleeding only slightly. Few effects were observed on the initial properties and on the properties of hardened concrete.
 Based on the above, it is assumed that slightly increased unit water content in the range between 5 to 10 kg/m³ in high-strength concrete with fixed unit bulk volume of coarse aggregate will improve construction performance without great affection of the quality parameters while the deterioration of the parameters has been afraid when unit water content was increased.

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 In Japan, each prefecture selects some scenario earthquakes, and uses them for making a regional disaster prevention plan. They select scenarios which cause the largest loss, but the scenarios' event probabilities are not considered. It is too conservative and uneconomical to plan a regional disaster prevention for a scenario which has a very low event probability.
 “Hazard-consistent scenario earthquake” was proposed as a method of selecting scenario earthquakes based on probability. But this method is not appropriate to be used for planning a regional disaster plan because this method is based on a hazard analysis at only one point. So, for example, this method can't distinguish a case where a seismic intensity of 5 upper is observed in only small area from a case where it is observed in almost all area in a region. “Risk-consistent scenario earthquake” (Ishiskawa & Okumura, 2001) can avoid this problem. But in a previous study, each risk curve of prefectures is calculated based on an assumption that all houses have been built at a prefectural capital.
 In this study, “PEX-consistent scenario earthquakes” is proposed. This is a new method of probabilistic scenario earthquakes based on the relationship between population exposure to seismic intensity (PEX) and its exceedance probability (P-PEX relation). Population distribution is thought to be positively correlated with various social wealth, so PEX represents simply an effect of earthquakes. The Proposal method consists of three steps. First, calculating P-PEX relation and each seismic zones’ contribution for it. Second, determining the seismic zone corresponding to the target risk level. Third, determining a seismic intensity distribution of the background earthquakes corresponding to the level.
 Following results are obtained in this study.
 1) In almost all prefectures, background earthquakes are included in scenario earthquakes corresponding to the specific risk level. But only about 20 prefectures consider background earthquakes in their loss estimations.
 2) In Tokyo, the seismic intensity distribution of intraplate earthquake of Philippine sea plate corresponding to 100 yr. return period is lower than the scenario of Tokyo prefectural government, and the distribution corresponding to the 2500 yr. return period is very much higher than it.

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 Long-period seismic waves are affected by the propagation path, and have a different nature depending on the source location. In addition to the accretionary wedge and sedimentary basins could affect the long-period seismic waves. The characteristics of ground motions on the irregular sedimentary basin structure vary depending on the incident direction of the seismic wave and the type of incident seismic wave. Therefore it is important to focus on the source location, and to consider the path effect together with the effect of the sedimentary basin beneath the site.
 In this study, the 3D finite difference analysis based on the reciprocity theorem is employed to clarify the path effect and the effect of the sedimentary basin beneath the site. In regard to the path effect, the accretionary wedge could decrease the specific periodic band of seismic waves, in contrast to the Niigata sedimentary basin which could amplify the specific periodic band of seismic waves. In addition, the Kanto plain could so much not amplify the waves on the site in Chukyo area. In regard to the effect of the sedimentary basin beneath the site, the analysis confirm that the characteristic of ground motion fluctuates depending on the incident direction of seismic waves. Especially, the results of some observation points show that when the source located in a particular direction, the seismic wave is strongly amplified by the sedimentary basin.
  Specific amplification of seismic waves is examined by the numerical analysis of wave propagation using the simple soil structure models. As a result, it is revealed that the seismic waves are strongly amplified by the step of the layer near the site. Therefore, the ground motion at the site is amplified and the duration time is extended.
 At last, amplifications of seismic wave radiated from sources of various directions are compared at the site on Chukyo sedimentary basin using the seismic ground motion records. The study revealed that the amplification of the seismic wave radiated from eastern sources is larger than other direction at the specific periodic band. The behavior similar to the result of numerical analysis is shown by the study using the seismic ground motion records.
 According to the result that the effect of the wave propagation path and the sedimentary basin beneath the site varies with respect to the source location, the damage of specific long-period building could be large in specific cases of earthquakes. The examination of the ground motion using 3D finite difference analysis based on the reciprocity theorem is beneficial since the above mentioned effects are complicated and different around the earthquakes.

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 A TMD (Tuned Mass Damper) is a passive-type control device that consists of a small mass, a spring and a damper. And it absorbs the oscillation energy of structures as the kinetic energy of its mass and disperses it via its damper. The TMD shows high control performance for harmonic responses. On the other hand, the TMD has limited capacity to suppress transient responses. The reason is that there is some time delay before the TMD becomes fully effective because they are initially at rest.
 Thus, to control the transient response more effectively, we propose TMDs with initial displacement, that is, dampers whose springs are stretched until the release moment.
 In our previous study, we focused on the considerably high modal damping ratio of the second mode compared to the first mode based on the relationship between the TMD damping ratio and the modal damping ratio of a two-degree-of-freedom model. And we proposed the design formulas for the optimal tuning and damping ratios and the initial displacement to attain high control performance under impulse loading. The proposed design formulas are based on the principle that by giving the specific TMD initial displacement under the specific structural initial condition the structural response of the first mode with low modal damping is eliminated while the structural response of the second mode with high modal damping is only oscillated. But the physical meaning of the design formula for TMD initial displacement is not clear because it is an approximate solution based on the perturbation method.
 Then, we formulated the equation for initial conditions to release TMD initial displacement from the theoretical free vibration solution and showed its physical meaning clearly. We studied about TMD initial displacement and structural conditions to release initial displacement using the complex plane, and we showed that the initial structural condition to oscillate only the second mode was limited to a neighborhood of ẋ₀≠0, x₀=0. On the other hand, we proved that, by dividing one TMD into plural TMDs that have different natural frequencies, any initial structural conditions to release TMDs became possible.
 In this paper, firstly, we analytically study the effect of different settings of two TMDs tuning ratios on TMD initial displacements to eliminate the first modal response with the lowest modal damping and structural responses for free vibration using a basic three-degree-of-freedom model. Next, we decompose the initial condition to modal eigenvectors on the complex plane and study the interrelationship between each initial condition of a main mass and two TMDs. Then, we show the reason why different settings of TMDs tuning ratios affect the TMD initial displacements to eliminate the first modal response and the structural responses. Finally, by using the energy indicator “TMD power flow” that shows an additional TMD damping effect proposed by Soong, T.T. and Dargush, G.F., we study the control performance of TMDs with different tuning ratios condition.

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 We report an active seismic response control system by utilizing an energy conversion in damping devices. In this paper, we propose a system based on hydraulic technology which can control large forces and energies easily. The device model, i.e. the dynamic characteristic of this system is constructed, and its energy characteristics are parametricaly analyzed through 5 cases of natural periods, 1s, 2s, 3s, 4s, 5s. The results noted in this study are as followings:
 (1)the Numerical modelling of an oil pressure system based on the balance of pressures and flow rates is constructed, and the system specifications are established through the seismic response analyses where the damping force and the controlling force are restricted.
 (2)The system using a device model by the hydraulic technology shows the similar response reduction effect to an ideal model.
 (3)The energy conversion ratio using the device model in the oil damper is more than 95 %, and that in the actuator is about 90 %.
 (4)The balance of energy input and output between energy conversions and reuses in the hydraulic analyses shows favorable effect for the earthquake causing large responses; on the other hand, that is aggravated in accordance with the increases of the control gains. The case where the energy balance is more than 1.0 is only for the building model of natural period 3s excited by El Centro.
 (5)The energy balance by the hydraulic analysis is remarkably small compared to the ideal model, since the actual rate of the actuator’s work is small compared to the output energy to an actuator.
 (6)By applying the technique switching the active actuation to the passive damping after a principal motion, the energy balance can be formed in the earthquake causing the maximum response and the maximum response value can be restricted equivalent to the active seismic response control, except for the building model of natural period 2s
 We have evaluated the characteristics of the proposed system based on the numerical analyses considering the dynamic characteristics of the realized system based on the hydraulic technology, and indicated feasibility of the energy balance formation.

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 The TMD (Tuned Mass Damper) is an effective structural control device which has been undergoing continuous development since the 1980's. However, in most situations, its mass has been limited to less than 1% of that of the entire building due to restriction such as weight limitations and spatial difficulties. When mass ratio is small, various problems need to be overcome such as tuning sensitivity and transient characteristics. As a result, in the early studies related to mass dampers, and the efforts were focused on how to compensate for low mass ratio by active control technology. Although performance has been improved by hybrid control technology, devices for controlling major earthquakes have not been put into use for a long while because of the problems of energy supply and stroke control.
 However, recent studies have examined the utilization of a part of a structure's weight as a dynamic damper. Because a much larger mass ratio can be provided than a conventional TMD, these types of structures can potentially achieve a superior seismic control. In addition, the response reductions of a main-system and a sub-system can be made compatible. Furthermore, focusing on stroke control, giving parameters of a sub-system shifted from optimum settings would be effective, while maintaining response reduction owing to the system's high robustness.
 This paper proposes a stroke control strategy for seismic control of a structure that includes large-weight sub-systems. It first defines optimum parameter setting of a sub-system that minimizes the response of a main-system using a 2DOF analytical model. In response evaluation, random vibration theory is introduced, and mean response assuming white noise input is discussed. After several examinations of the influence of a sub-system's parameter on the response reduction effect, a relational expression that connects sub-system's parameters and stroke is derived. We also clarify that the expression is applicable in evaluating maximum response against seismic input which is emphasized in actual design by introducing unique design parameters. Then the setting procedure based on the response spectrum is presented. Finally, the accuracy and the validity of the proposed method are discussed through numerical analyses. By applying the proposed strategy, rational parameter settings of a sub-system matched with the design objective stroke can be obtained without performing any time history analyses.

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 It is difficult to estimate the redundant strength remaining in a building on fire, since the fire conditions such as their ranges and locations may be different in each case. A large-scale fire occurred on the New York World Trade Center 7 (WTC-7) after the 9.11 terrorist attacks in 2001. The building continued to burn for 7 hours, and ended in a total collapse. The official report on the collapse investigation of WTC-7, released by the National Institute of Standards and Technology (NIST) in 2005, had suggested that the total collapse was triggered by a severe damage of an important column of the building called the key element. On the other hand, there is also an example of a high-rise building on fire that avoided a total collapse, regardless of its main structure continuously heated by fire for a long time; the Windsor building of Madrid in 2005. From the viewpoint of preventing the fire-induced collapse of buildings, it is necessary to clarify the relationship between various structural parameters of buildings, fire locations, their ranges, and the scale of collapse.
 The purpose of this study is to predict collapse risks of buildings on fire using a key element index (KI). The KI is defined as the ratio of the ultimate yield strengths of the structure with one column eliminated and the initial, undamaged structure. It indicates the contribution of a structural column to the vertical capacity of the structure. We investigated the relationship between the sum of KI values in various cases of fire range and the sum of the height of remains after the collapse. We applied an adaptively shifted integration (ASI) - Gauss code utilizing linear Timoshenko beam elements to investigate the collapse behaviors of a ten-story steel framed building model with various fire patterns. Fracture contact, contact release and re-contact algorithms were implemented in the code. The reduction curves of elastic modulus and yield strength of steel related to elevated temperature, shown by NIST, were adopted to consider the heat effect of fire. Thermal expansion of materials was also considered.
 From the numerical results of the fire-induced collapse analyses, it is found that the scale of collapse highly depends on fire ranges and locations. The risk of total collapse tends to increase when a large range of fire occurs in the lower layer. In addition, the risk increases much higher in those cases when fire occurs at the peripheral area of the building, compared to those cases at the inner area. The sum of heights of remains seems to depend on the sum of KI values, and there is a specific threshold of the sum of KI values that relates to the initiation of a large scale collapse. Therefore, the sum of KI values may be used to predict and take measures to avoid the risk of collapse under various fire conditions.

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 In our previous paper, centrifuge tests of superstructure-pile-liquefied soil systems have been conducted, and dynamic ultimate mechanism of steel piles subjected to the vertical force and horizontal force in the liquefied soil was clarified. It is shown that piles' ultimate strength was estimated using the M-N interaction curves. In the other hand, for real structures, reinforced concrete is filled at a pile head to fix a connection between steel piles and a reinforced concrete footing beam. It is considered that the flexural buckling length of steel piles becomes shortened because pile head filled with concrete acts as the rigid body. In this paper, centrifuge tests of superstructure-pile-liquefied soil systems are conducted to compare the dynamic ultimate mechanism of steel piles reinforced at pile heads with that of non-stiffened ones. Subsequently, piles' ultimate strength is estimated using M-N interaction curves with pile's equivalent buckling slenderness ratio.
 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 this paper, an aluminum cross section member is inserted into the pile head of a specimen to reproduce a real pile reinforced filled with concrete at the pile head. In Case 1, the pile cap is laterally fixed, and then only varying axial force acts on the piles. In Case 2, the pile cap can laterally move, and the vertical and horizontal forces act on the piles. The centrifuge tests were performed under centrifugal acceleration 40 g.
 Figures 7 and 8 show the response time histories of Case 1 specimens and table 5 shows the pile's maximum axial force. It is shown that the bucking strength becomes larger as reinforcement length at the pile head is longer.
 Figures 14 and 15 show the response time histories of Case 2 specimens. For all Case 2 specimens, the bending strain increased immediately after soil liquefied.
 For specimens of Case 1, the dynamic buckling strength of piles is evaluated. Figure 13 shows the relationship between observed pile's dynamic buckling strength subjected to only vertical load and buckling curves for Japanese limit state design of steel structures and Japanese design standard for steel structures. Here, the equivalent slenderness ratio is calculated by the ratio of pile's elastic flexural buckling load to the yield load. For a pile reinforced at the pile head, elastic flexural buckling load developed by the energy method in Section 3.3 is applied. The buckling curve of Japanese recommendations for limit state design of steel structures is lower bound of flexural buckling strength of piles in the liquefied soil. As the results, it is shown that the buckling stress curve with the equivalent slenderness ratio can be applied to estimate flexural buckling stress of pile reinforced at the pile head.
 Next, for piles subjected to lateral and vertical forces, ultimate strength is evaluated using Japanese current design criteria. Figure 19 shows the relationship between ultimate strength of piles on centrifuge tests and the M-N interaction curves for the 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 as shown in Fig. 13, and the bending moment at the maximum bending strain position is divided by the full plastic moment of piles. It is shown that the M-N interaction curves of Japanese recommendations for design of building foundation is lower bound of pile's ultimate strength in the liquefied soil at the maximum bending strain.

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 There are many examples of application of TMD. A high-rise building and a floor slab with large span in architecture field, a cable stayed bridge and a suspension bridge in civil engineering, for example. The response reduction effects in those examples are verified. TMD is fit for the vibration control of spatial structure because it is possible to install TMDs by a single supporting point. Therefore, there are many studies on spatial structure with TMD. The authors have verified the influences of the number and position of installed TMDs, the period and phase characteristics of earthquake motions and input direction of input wave on seismic response reduction effects. However, influence of free vibration characteristics of cylindrical lattice shell roofs on vibration control effects by plural TMDs have never been examined. From these backgrounds, the purpose of this study is investigation of seismic response reduction effects by plural TMDs for cylindrical lattice shell roofs which have different half open angles and ratios of natural period of supporting substructure to that of roof structure.
 First, the selection method of controlled modes which are larger contribution to response displacement subjected to earthquake motion is proposed by response spectrum analysis. Next, the reduction effects of maximum responses and the sum of square of vertical responses of all nodes at all steps of analysis by plural TMDs for cylindrical lattice shell roofs which have different free vibration characteristics are examined. The relationships between the natural period ratios RT of the natural period of equivalent single mass system to that of antisymmetrical 1 wave mode of roof structure and response reduction factors are investigated. Finally, the response estimation by parallel multi-mass system substituted for shell structure with TMDs is attempted.
 From the numerical results, it is concluded as follows.
 1) As plural TMDs are installed in all antinodes of controlled modes with larger contribution to the response displacements which are the locations that the reduction of responses for all nodes of structure is verified in references (18), (19), the responses reduce regardless of free vibration characteristics of cylindrical lattice shell roofs.
 2) The response reduction effects by TMDs are higher as the sum of ratios of maximum vertical response of all controlled modes which are obtained from the response spectrum analysis is larger. On the other hand, the response reduction effects by TMDs are lower when the vertical response is smaller.
 3) When the responses of the mode with natural period which is shorter than natural period of controlled mode occur in the positions for installing TMDs, the responses of the mode with natural period which is shorter than period of controlled mode reduce.
 4) The reduction effects of response acceleration and response displacement are higher in the range of 0.5 < R_T < 1.25. On the other hand, the responses hardly reduce in the range of R_T > 1.25. Therefore, when TMDs are applied to cylindrical lattice shell roofs, it is necessary to consider not only the natural period of roof structure but also the ratio of natural period of supporting substructure to that of roof structure.
 5) When the sum of effective mass ratios of controlled modes is larger, the response reduction factors of cylindrical lattice shell roofs by installing the TMDs can be estimated by the parallel multi-mass systems substituted for shell structure with TMDs.

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 In this study, the authors evaluated the structure performance in large deformation domain of the traditional wooden building from the micro tremor measurement, namely, micro deformation domain. To evaluate structure performance, the static shear loading tests were carried out using new construction and re-construction of mud-walls. Here, the experiment by the re-construction of mud-walls were carried out for the following reasons. Many Japanese traditional wooden building are being maintained by the half dismantling and the partial dismantling for a long time. In consideration of it, the re-construction of mud wall was built by reusing timber. As a result of the experiment, the shear stiffness with the deformation to increase of the mud-wall was quantified. And the authors hypothesized that the result was similar with shear stiffness by the deformation to increase of ”the real-scale timber case study house” with the mud-wall. At first, the equivalent shear stiffness Km was obtained by substituting the natural period given by the micro tremor measurement into the equation (4). Then, Shear stiffness K_1/600 of a story deformation angle 1/600 demands it by multiplying coefficient of correlation β by equivalent shear stiffness Km. The change of structure performance after story deformation angle 1/600 is decided by parameter a, b of the equation of regression based on the experiment. β in this examination uses equivalent shear stiffness ratio β (K_1/600/K_m) measured at the time of the one-way loading test. The one-way loading test was performed for “the real-scale timber case study house” to confirm the validity of method previously described. In addition, it was performed including a free vibration experiment to evaluate dynamic structure performance. The main results obtained from these studies are as follows. From the result of the static shear loading tests, new construction mud-walls and re-construction mud-walls showed equal structure performance. As for the shear stiffness by the increasing transformation of mud-wall, variation becomes small in the large deformation domain. As a result of having performed curve fitting by orthogonal polynomials and least square approximation for the Fourier spectrum, theoretical formula was almost reproducing the measurements. This is indication that natural vibration mode can be estimated by the free vibration test. In addition, although some difference is observed between the free vibration measurements and one-way loading test, the vibration measurements result obtained from the orthogonal polynomials and least square approximation mostly agree with one-way loading test result. If shear stiffness of story deformation angle 1/600 of the target building is provided, the structure performance in the large deformation domain is almost provided. In the present, it has not been quantified about the correlation in micro tremor measurement result of measurement Km and shear stiffness K_1/600. However, it is revealed to change in β=0.4-0.6 neighborhood by the study in the past. This was provided by analyzing 14-19) of the precedent study. Therefore it will be necessary to quantify it by building data in future.

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 A seismic retrofitting method that uses a newly expanded frame has recently gained popularity. For the joints of structures used in seismic retrofitting, post-installed adhesive anchors are generally used. For rigidly connecting such a newly expanded frame to an existing frame, a design of the joint is very crucial because the joints are subjected to shear and tensile forces during an earthquake. However, the behavior of the anchors under combined forces remains unclear. To address this issue, herein, we conducted cyclic shear loading tests on 13 anchor bolt specimens under constant tensile force.
 In Chapter 2, the details of the test plan are explained. The test parameters considered were as follows: the anchor bolt diameter φ of 13 - 19 mm as well as tensile force T and concrete compressive strength σ_B of 10 - 30 N/mm². We used the tensile force ratio r_N (σ_N/σ_y) as an index of the tensile force, and it ranged from 0 to 0.66. σ_N and σ_y are the tensile stress and the yield strength of the anchor bolts.
 In Chapter 3, the test results are described. First, we observed the relations of shear force Q and joint opening δ_N with slip δ_S. The results indicated that the shear force reduces and the joint opening increases as the tensile force increases.
 Second, we investigated the allowable tensile and shear forces under the combined force using Equation (S1) which is used for a structural design⁶⁾.
 (T/T_a)^α + (Q/Q_a)^α = 1                 (S1)
 Where, T is the allowable tensile force, Q is the allowable shear force, T_a is the allowable tensile force when Q = 0 kN, Q_a is the allowable shear force when T = 0 kN and α is a coefficient, usually ranging 1 - 2. According to the test results, the range of α was 0.75 - 1.5.
 In Chapter 4, we use the test results to investigate the work of post-installed anchors. We found that the total work was almost constant even at varying tensile force. In addition, we proposed an estimation formula of the total work, given by the equation (S2).
 W = ∫Qdδ_S + ∫Tdδ_N = (5.1φ - 40)√( δ²_S + δ²_N )                  (S2)
 In Chapter 5, the conclusions were described. Findings obtained in this study were as follows:
 1) The shear force was decreased and the joint opening increased as the tensile force increased.
 2) For the relation between T/T_a and Q/Q_a, the test results were reasonably estimated by choosing a in the range 0.75 to 1.5.
 3) W_S was dominant in the case of r_N=0.33, but W_N was higher than W_S in the case of r_N=0.56 - 0.66.
 4) The total work was proportional to the absolute value of the displacement vector and was not significantly influenced by the concrete compressive strength in this tests.
 5) A formula for estimating the energy absorption of post-installed anchors under a combined force was proposed.
 Improvements to the proposed model in future studies will focus on considering bond stress–slip behavior of adhesives.

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 The low cost and stable performance of steel dampers are frequently employed to reduce displacement and acceleration responses in an earthquake. Dampers cannot dissipate elastic energy but may increase a structure's absolute acceleration. To overcome these problems, the dampers can be designed for early yielding, so they may be damaged by a small earthquake.
 The authors have proposed Z-type and anti-Z-type NC braced frames that reduce elastic acceleration response by elastic energy accumulation due to incremental deformation. Residual deformation after an earthquake can be reduced by release of NC brace residual tension, so this system is superior to reuse performance. Qualitative performance of these frames is obtained from shaking table tests and numerical analyses, but quantitative estimation of the seismic response values is not clarified and differences among the seismic performances of these braced frames is not investigated.
 Seismic response estimation based on energy balance is often applied in the seismic design field. The concept of the method was proposed by Housner, and its usefulness for seismic response prediction was verified by Akiyama. The energy balance method is an efficient tool for evaluating accumulated plastic deformation and a structure's maximum deformation in an earthquake.
 In this paper, numerical analyses of these NC braced frames as well as an X-type brace are carried out to examine their seismic responses. A seismic response prediction method based on the energy balance principle is formulated and the method's accuracy is evaluated from numerical results. Conclusions are summarized as follows.
 1) Z-type, anti-Z-type and X-type NC braced frames can reduce elastic acceleration response by elastic strain energy accumulation. From numerical results, Z-type and anti-Z-type frames can reduce by up to 40% maximum acceleration, and X-type frames can reduce by up to 22.8%.
 2) Maximum responses of all braced frames under elastic vibrations have the following tendencies. Maximum acceleration is reduced in the order, X-type with initial tension, normal X-type and Z-type, and anti-Z-type. Maximum story-drift deformation of X-type is the same irrespective of initial tension. Maximum story-drift deformation and residual story-drift deformation of both Z-type and anti-Z-type frames are equivalent.
 3) Maximum responses of each braced frame under elasto-plastic vibrations have the following tendencies. Both X-type and anti-Z-type frames show bi-linear cyclic curves around the origin and Z-type around δ_c^* calculated by Eq.(1), and maximum acceleration and maximum deformation from the center of a cyclic curve. Maximum story-drift deformation and residual story-drift deformation of both Z-type and anti-Z-type frames are equivalent.
 4) A seismic response prediction method based on the energy balance principle is formulated, and the maximum acceleration and maximum story-drift deformation of NC braced frames under elastic vibrations and residual story-drift deformation of Z-type and anti-Z-type frames can be predicted. All predictions of seismic responses are in good agreement with the corresponding numerical result. Reduction ratio of maximum acceleration by elastic strain energy accumulation can be calculated by the prediction method without numerical analyses.
 5) Damage to the NC braced frames can be evaluated safely by the prediction method. The residual story-drift deformation of both Z-type and anti-Z-type frames under elasto-plastic vibrations can be accurately predicted.

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 In recent years, buildings in Japan have been required to have high earthquake resistance that can be used continuously after the large-scale earthquakes occurred. In order to achieve this, the damage control design that allows to prevent the damage of main structure by absorbing the seismic energy in damping devices is effective. In addition, it is important to judge appropriately the damage state of the damping devices after the earthquake occurs.
 The Miner's rule has been widely used as the damage evaluation for the random waveform, including the plastic region. On the other hand, the damage evaluation method using the quantity of total energy absorption is considered to be a simple method in comparison with the Miner's rule. Therefore, the authors proposed the average amplitude method as one of the energy evaluation method that can evaluate equivalent to Miner's rule. In this method, the random waveform is replaced by a constant average amplitude waveform so that the total energy absorption becomes equal. However, it was confirmed that there was some difference compared with the damage degree calculated by the Miner's rule.
 In this paper, it aims to clarify the influence on the damage degree by the input order of the magnitude of strain amplitude and the difference in the calculation method of the average strain amplitude. The buckling restrained brace (BRB) to be evaluated is composed of a cross-shaped axial member using a low yield strength steel and restraint member of the welded box-section.
 First, the basic model specimens which exclude the influence of the buckling restraining capacity by shortening the length of the plasticized region of the axial member and by increasing plate thickness of the restraint member is prepared. Then, the multistage amplitude loading tests in which the input order is switched and the dynamic loading tests by the response waveform in which only time axis is reversed are carried out.
 Next, using the real-size specimens, the continuous two-stage amplitude loading tests in which large and small strain amplitude are alternately repeated and the dynamic loading tests in which the input order of magnitude of strain amplitude is exchanged are conducted.
 Furthermore, it is evaluated that the influence on the strain behavior of the BRB by the input order of large and small amplitudes using FEM analysis.
 The main results in this paper are summarized as follows:
 1) The ratio of the damage degree obtained by the energy evaluation method (average amplitude method using logarithmic average strain amplitude) to the damage degree obtained by Miner's law is decreased by about 15% more when receiving the large amplitude first.
 2) The order of the input amplitude including both the increase and the decrease like a seismic wave has little influence on the above damage degree ratio.
 3) The damage degree by the average amplitude method using the cumulative average strain amplitude is calculated to be smaller than the damage degree calculated using the logarithmic mean strain amplitude.
 4) As a result of FEM analysis, it is considered that the local strain concentration by small amplitude input and the residual deformation by large amplitude input influence the change of the restoring force characteristic after that.

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 In Japan, fire tests are not required to evaluate fire performance of curtain walls and instead of fire tests, it is required to use the materials specified in the technical advice of curtain walls. Required fire performance of spandrel area and vision area are different because of another performance of curtain walls. Therefore fire performance of vision area and spandrel area are considered separately but even if parts of curtain walls have fire resistant performance, the performance of whole curtain wall is not confirmed.
 The purpose of this study was to clarify behavior of the mullions of typical stick system aluminum curtain walls exposed to standard fire.
 There are no standard testing methods to evaluate fire resistance performance of curtain walls in Japan, so five types of heating test methods are considered in this study to heat areas of curtain walls with different fire resistance performance. The experiment parameters are heating surface, the size of test specimens and the shape of mullion sections.

 Heating types are shown below
 1. Test specimen of vision area and spandrel area is heated from inside for 20 minutes.
 2. Test specimen of vision area and spandrel area is heated from outside for 20 minutes.
 3. Test specimen of spandrel area is heated from inside for 1 hour.
 4. Test specimen of spandrel area is heated from outside for 1 hour
 5. Test specimen of spandrel area is heated from inside and outside for 1 hour

 Findings are as follows.
 1) Fire insulation material of mullions that protects mullions from heating from inside prevents radiation cooling from unexposed side of mullion in case of heating from outside. Therefore, temperature of mullions with insulation materials will be higher than mullions without insulation materials. When determining the thickness of insulation material of mullions, both heating from inside and heating from outside should be considered.
 2) Deformation of mullions is determined by difference of thermal expansion between inside and outside and compression force with difference of Young's modulus in the section of mullions. Function of connection part called joint sleeve is effected by deformation of mullions. Deformations of mullions is determined by distance between supporting points of mullions, sectional shape of mullions, the temperature difference in section of mullion, temperature of mullions and restrain condition of mullion end.
 3) When test specimen of only spandrel area heated from inside, there are no thermal transmission from mullions of vision area with no insulation materials and temperature of mullions are lower than whole curtain walls are heated from inside. When fire resistant performance of spandrel area is evaluated, thermal influence from vision area should be considered.

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 The membrane architectural structures are constituted by flexible members which do not resist bending such as film materials and cable materials, and their mechanical stability greatly depends on the shape of the initial surface. In order to design a membrane structure having mechanical stability which does not cause wrinkles or slackness, it is common to adopt an isotonic surface as the initial design surface of the membrane structure.
 Some previous studies proposed methods of obtaining a surface with minimal surface area under appropriate subsidiary conditions by utilizing the fact that the isotonic surface is the same as the minimal surface. However, in any of these studies, since the surface is approximated by triangular elements and the sum of the triangular elements area is minimized, the error from the true minimal surface greatly depends on the division method of triangular elements. If the triangulation is made finer, a minimal surface with higher precision can be obtained, but the computational cost increases and the obtained minimal surface becomes a collection of enormous nodal information. The amount of data becomes enormous and it is difficult to smoothly convert or deliver the obtained solution as 3D graphic data in the situation of using CAD/CAE. In contrast, if we use a parametric surface, it is possible to explicitly calculate the surface area in parametric expression. Also, the minimal surface is known as a surface in which the mean curvature is equal to 0 at any point on the surface. By measuring the mean curvature, it is possible to quantitatively evaluate the error from the true minimal surface.
 In this research, to create the minimal surface which can explicitly express numerical functions with a small data volume, we solve the three optimization problems as follows:
 1. Minimization of the sum of areas of triangular elements of triangulated surfaces (Previous method).
 2. Minimizing total surface area of the parametric surface (Proposed method).
 3. Minimizing the square of mean curvature of the parametric surface (Proposed method).
 The results obtained in this study are summarized as follows:
 · Method 1 requires high computational cost in order to get a solution with sufficient accuracy.
 · In the case of methods 2 and 3, if the weights of the parametric surface are set as design variables in addition to the vertical control point coordinates, the objective function becomes highly nonlinear. As a result, the computational cost becomes high and the obtained solution has a greater chance of being a non excellent local optimal solution. So the design variables should be the vertical control point coordinates only.
 · If the vertical control point coordinates are defined as the design variables, methods 2 and 3 can drastically decrease the computational cost as compared with method 1.
 · Methods 2 and 3 are suitable for CAD/CAE use because of their low quantity of the shape information.
 It is confirmed that methods 2 and 3 are very effective methods for finding minimal surface.

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