We must take measures to mitigate damages from large-scale earthquakes effectively and efficiently. It is important to determine the amount of damage reduction as a numerical target, select effective countermeasures through analysis of the damage factors, and intensively promote them. For estimating building damage in the effort to reduce loss and destruction, a damage index function was used; accordingly, a building was considered as a unit. For vulnerability function, area was a unit. To set disaster reduction targets according to region, a vulnerability function that strongly takes account of regionality and construction year is necessary. In this paper, the proposed methodology is the use of a vulnerability function incorporating regionality and construction year.
 To construct the vulnerability function, an estimating method using past earthquake damage data was used. This method reflects the characteristics of the area where earthquake damage occurred. We constructed the regional damage rate function of wooden houses by considering the results of a regional seismic diagnosis based on the damage index function. With this method, it becomes possible to evaluate the earthquake resistance of buildings in the area by the probability density distribution of the seismic performance index. If there is a distribution of seismic performance indices for each area, it is possible to construct a highly accurate regional damage rate function without damage data from the region.
 The following is shown as a method of constructing the regional damage rate function:
 a) We estimated the new damage index function with diagnostic results obtained from utilizing the 2004 version of the seismic evaluation method for wooden buildings.
 b) For construction year without diagnostic results, we proposed a method to estimate the seismic index distribution from the new damage index function and the damage rate of destructive earthquakes occurring close to the construction year.
 c) If the area's seismic diagnostic results were small, we proposed estimating the seismic index distribution from Bayesian inference with the diagnostic results of Mokutaikyo as the prior distribution and the results in the area as the likelihood function.
 d) From the above results, we estimated the seismic index distribution of wooden houses in Hokkaido. In houses built before 1950, the average of the scores of Hokkaido and Mokutaikyo (nationwide average) was almost the same. In houses built after 1960, the average for Hokkaido was 1.4 to 1.7 times that of Mokutaikyo. The standard deviation in the case of Hokkaido was larger than for Mokutaikyo, and diversity of seismic performance by various building construction methods was found.
 e) From the new damage index function and the regional seismic performance index distribution of wooden houses, the regional damage rate function in Hokkaido was estimated.

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 Since it is well known that the vibration characteristics such as the natural period and the damping ratio of buildings are dependent on the shaking amplitude of the building. In the previous paper, these characteristics of the horizontal 1st mode for the low and middle raised RC and SRC buildings were studied. In this paper, those of the horizontal 1st and 2nd mode for 8 high rised steel buildings are studied.
 The observed seismic data including the 2011 off the Pacific Coast of Tohoku Earthquake (hereafter, 3.11 earthquake) are analyzed using the ARX (Auto-Regressive eXogenous) model. The results are estimated for 2 averaged drift angle levels (the micro amplitude (10^-6) and the middle amplitude (10^-3)) to consider the amplitude dependency. The effects of aging of the buildings are also investigated. From above study, following results are obtained.

 1) In both 1st and 2nd natural periods, comparatively small amplitude dependency is seen and their angles of inclination are almost the same. The variation of 1st and 2nd natural periods between before and after 3.11 earthquake is small, since all buildings studied in this paper were in almost the elastic condition though all observed data.
 2) The 1st damping ratio before and after 3.11 earthquake have a tendency that the ratio increases corresponding to the increase of the amplitude from the micro amplitude level.
 3) The 1st damping ratio during 3.11 earthquake, when the amplitude was large, tends to decrease corresponding to the increase of the amplitude. The value becomes less than 2% when the drift angle is more than 10^-3. It is considered this tendency is not due to the nonlinear condition because all the buildings seemed to be in the elastic condition.
 4) The 2nd damping ratio has almost the same tendency as the 1st, qualitatively. Some differences are seen between them, quantitatively. The accuracy of the 2nd seems to be not high.
 5) The relationship between the experienced maximum drift angle during 3.11 earthquakeand the variation of natural periods is studied for all buildings. The ratio is between from 1.0 and 1.1. However, the amplitude dependency is not seen clearly.
 6) Concerning to the secular change of the 1st and 2nd natural periods, clear tendency cannot be seen while some previous research showed obvious change.

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 1. Introduction
 This paper proposes a design method utilizing Building Mass Damper (BMD) system for the mid-story isolation structure. In general, it is well known that Tuned Mass Damper (TMD) is required a larger auxiliary mass in order to exert damping effect against large-scale earthquake. BMD is a creatively system which can construct a larger auxiliary mass by utilizing the entire upper structure as an auxiliary mass. This paper proposes optimal design conditions of BMD based on complex eigenvalue analysis. Assuming an actual design, optimal design conditions are proposed for three cases of the lower structure, the upper structure, and the lower and the upper structures. Furthermore, it shows the design method of the isolation layer performance which satisfies the target response performance by using the performance based design diagram. In addition, it shows the flowchart of the proposed design method and the definite design example. By using this design method, it is possible to determine the parameters of the mid-story isolation layer which satisfy the target performance without performing the time history response analysis.

 2. Optimal design equations of BMD
 BMD can reduce the response by tuning the upper structure and the lower structure through the isolation layer. BMD can be represented by the 2 degrees-of-freedom (DOF) system by reducing upper and lower structures respectively. For this reason, optimal design equations are derived based on the invariant point theory as relational of the natural period for the 2 DOF system. It shows the design examples applying the optimal design equations and verify the validity of the proposed optimal design equations.

 3. Outline of design method using the performance based design diagram
 The traditional problem on the design of the seismic isolation structure is that it is necessary to repeatedly assume the combination of the base isolation layer parameters until satisfy the target performance and to confirm by time history analysis. In order to solve this problem, I.Hata and S.Ishimaru et al. proposed the seismic design method using the performance based design diagram. This design method can predict the maximum response of the 1 DOF system with the elasto-plastic properties. By using this design method, it is possible to design the isolation layer performance which satisfy the target performance without performing the time history response analysis.

 4. Design method of BMD
 This section shows the flowchart of the proposed design method of BMD by using the performance based design diagram. In addition, it shows the design example of BMD following the proposed design flowchart. It verifies the validity of the proposed design method through the design example with the lower structure as the design target. Using proposed design method, it is possible to optimally design by the same design procedure even when the upper structure and the lower and the upper structures are targeted.

 5. Conclusion
 This paper proposes the design method for BMD applied to mid-story isolation structure. The optimal design equations of BMD based on complex eigenvalue analysis are derived, and it shows that the effectiveness of the proposed design method through the design example. From the above, it shows that the proposed design method can be applied to design of BMD using mid-story isolation structure.

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 Seismic design has been conducted usually by parametric studies. So a lot of simplified design method have been reported in recent years. The proposed method is able to minimize the total number of necessary dampers for a MDOF model to keep the maximum ductility factor under the specified value. Design examples of the optimum story-wise placement of oil dampers are shown for two MDOF building models. Time history response analyses are carried out for buildings installed with the necessary number of dampers subjected to the design earthquake. The results demonstrate the effectiveness of the proposed design method.

 Based on these studies, the following results are obtained.
 1) By means of optimum design based on the fixed-point theory and seismic performance design diagram, the necessary damping for criteria is obvious. We can determine damper placement for MDOF easily and rationally.
 2) If considering elastic-plastic behavior of main frame, we can minimize total number of dampers with placement of seismic control devices that depends on natural period of the building for design. If first mode is dominant, the combination of proportion to story stiffness (arrange1), constant for all stories (arrange2) and proportion to interstory modal shape (arrange3) is rational design. The influence of higher mode is significant, the combination of arrange1 and arrange2 is better.
 3) If considering elastic-plastic behavior of main frame, non-linear dynamic behavior of a certain story without dampers tends to be progressing. Seismic control devices of each floor are desirable.

 The extension of proposed method for seismic control device except oil damper and bending shear model which is assumed super high rise buildings is made will be an issue to be addressed in the future.

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 When seismically isolated buildings are exposed to strong long-period and long-duration ground motions, seismic isolation devices such as Lead Rubber Bearings (LRBs) can be subjected to larger and more cyclic deformations than anticipated in conventional structural design. In an LRB, seismic input energy is absorbed as hysteresis energy of a lead plug and finally transformed into thermal energy. The large and multiple cyclic deformations of the LRB generate a large amount of heat, causing high temperature in the lead plug. The resulting deterioration of damping characteristics, which encompasses complex thermal and mechanical phenomena, may adversely affect a seismically isolated building's response. There are two important requirements when simulating the heat-mechanics interaction behavior of an LRB. The first is to evaluate the temperature rise of the lead plug due to the energy absorption, and the second is to evaluate the change of mechanical properties it causes.
 This paper describes a response analysis method considering the heat-mechanics interaction behavior of an LRB. A heat conduction analysis applying the difference method and the configuration of a simple analytical model are proposed. A relationship between the temperature and the yield stress of the lead plug is also proposed based on a simulation analysis of conventional experimental results. The effects of absorbed energy distribution in the calculation of the temperature rise of the lead plug for the analysis are investigated, as well as the effects on the evaluation of the equivalent temperature of the lead plug. Simulation analysis results using the proposed method are compared to conventional experimental one, the validity of the proposed method regardless of the size of the LRB is verified, and an arrangement of lead plug and loading condition is proposed.
 The proposed analysis method is applied to evaluate the heat-mechanics interaction behavior of the LRB. This method is useful for damage evaluation of seismically isolated buildings using LRBs under multi-cyclic deformation caused by long-period and long-duration ground motions.

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After unexpected disasters such as off the Pacific coast of Tohoku earthquake (2011) and the Kumamoto earthquake (2016), structural health monitoring techniques are strongly desired to evaluate the structural state of a building immediately. In the structural health monitoring system, the system identification (SI) method plays an important role in dealing with a large amount of monitoring data. As far as the SI methods are concerned, there may exist two branches classified into a modal-parameter SI and a physical-parameter SI. The main objective of the modal parameter SI is to identify the modal quantities and damping ratios. On the other hand, in the physical-parameter SI, the story stiffnesses of the objective building are directly identified from the floor response data. In order to assess the structural state of the possibly damaged building, the physical-parameter SI method is more appropriate for the structural health monitoring compared with the modal-parameter SI method. In this paper, from the viewpoint of the development of the structural health monitoring system using the physical-parameter SI method, a new structural damage localization algorithm for frame buildings is proposed based on the additivity on story stiffness deterioration caused by structural member damages. In the additivity on story stiffness deterioration, the sensitivities of story stiffnesses to structural damages of structural members are used to identify the location of damaged structural members. The additivity on the story stiffness deterioration can be proved by the Taylor series expansion of a multi-dimensional function. Based on the additivity on the story stiffness deterioration, the story deterioration of the damaged building with multiple structural members can be estimated by the superposition of the story stiffness variation due to the structural damage in a single member. In Section 3, it is shown that the story stiffnesses of a 1-bay 2-story frame are formulated by using the moment distribution method. Since the stiffness ratio of column and beam members are included explicitly in the formulated story stiffnesses, the sensitivity of the story stiffness to the stiffness of each structural member can be derived explicitly and we can understand that the story stiffness varies even if the structural members are damaged in other stories. Therefore, in the proposed damage localization method based on the additivity assumption, the location of the damaged members can be determined by evaluating the error of estimation of the story stiffness deterioration for various combinations of story stiffness deterioration for a single damaged member. The story stiffnesses of a multi-story frame are evaluated by estimating the relationship between the story shear force and the interstory drift derived by the time-history record of floor accelerations. In order to evaluate the story stiffness reliably, it is desirable to obtain the stationary floor responses. For denoising the observed response data, the singular value decomposition using low-rank approximation is applied to the floor acceleration records. It is confirmed that the relationship between the story shear force and the interstory drift can be derived smoothly by denoising, which is important to evaluate the story stiffness. In numerical examples, both a symmetric 2-bay 5-story frame and a setback 5-story frame subjected to two different excitation scenarios such as the ground motion and the top floor forced excitation are used to investigate the validity of the proposed damage localization method in Section 4. For the practical application to possibly damaged buildings, it is assumed that the damage severities of structural members and the number of damaged members are unknown. These problems are solved by the proposed damage localization method by improving the searching algorithm based on the superposition of story stiffness variation using the additivity assumption.

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 After Parkfield earthquake (1966), San Fernando earthquake (1971), Northridge earthquake (1994) and Hyogoken-Nanbu earthquake (1995), many aspects of near-fault ground motions have been made clear and the effects of near-fault ground motions on structural response have been investigated. The fling-step (parallel to the fault plane) and forward-directivity (perpendicular to the fault plane) inputs have been characterized by two or three sinusoidal wavelets. For such near-fault ground motions, many analyses have been conducted from various viewpoints. However, as far as a forced base input is used, both a free-vibration term and a forced-vibration term arise inevitably and the closed-form expression of the elastic-plastic response may be difficult. In order to overcome this difficulty, the double impulse has been introduced by some of the present authors as a good substitute for the near-fault ground motion and the closed-form expression has been derived for the undamped elastic-plastic response and linearly damped elastic-plastic response of a structure under the critical double impulse. Furthermore, this approach has been extended to other various vibration models, e.g. soil-structure interaction problems, dynamic collapse problems, repeated ground motion problems, overturning rocking problems of rigid blocks.
 The double impulse input is introduced here again as a substitute for the fling-step near-fault ground motion and some closed-form expressions are derived for the elastic-plastic response of a structure with nonlinear viscous damping under the ‘critical double impulse’. It is shown that, since only the free vibration appears under such double impulse, the energy approach enables the derivation of the closed-form expression of a complicated elastic-plastic response with nonlinear viscous damping. It is also shown that the critical timing of the second impulse is the time with the zero restoring force in the case where the input velocity is small. On the other hand, the critical timing of the second impulse is the time with the maximum velocity in the case where the input velocity is large. The quadratic-function or elliptical-function approximation for the damping force-deformation relationship is introduced. The combination of the timings of the structural yielding and the damper relieving is considered in detail and the closed-form expressions are derived for all the combinational cases.
 The validity of the proposed theory using the quadratic-function or elliptical-function approximation and the assumption of the critical impulse timing has been investigated through the comparison with the critical elastic-plastic response under double impulse using the time history response analysis. The validity of the proposed closed-form solution has also been demonstrated through the comparison with the response analysis to the corresponding one-cycle sinusoidal input as a representative of the fling-step near-fault ground motion. It has been demonstrated that the maximum response to the critical double impulse and the response to the corresponding one-cycle sinusoidal input coincide fairly well. This supports the validity of the proposed theory.

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 Static soil springs of a spread foundation is often evaluated by finite element method, Mindlin's solution, Steinbrenner method, Cerruti's solution, and so on. However, both of these methods have disadvantages that calculation cost is high, and it is difficult to make a prospect of calculation results. This kind of difficulty to evaluate static soil springs is considered to be an obstacle for reasonable design of spread foundations.
 In this paper, the authors propose a simple method for evaluating a static soil spring of footings on the surface of elastic half space. The method is to multiply a soil spring of a single footing by a interaction factor. This interaction factor is given by: ξ = 1/(1 + (n − 1)B/Δr) (where, n: the square root of the total number of footings, B: a width of a footing, Δr: the distance between footings).
 The proposed interaction factor derived from 2 assumptions and 1 condition. One assumption is that the interaction factor is the same regardless of whether the loading condition of footings is a constant stress distribution or a constant displacement distribution. The other assumption is that the displacement around a loaded footing decreases in inverse proportion to the distance from the footing. Combining these 2 assumptions, it leads that the interaction factor is expressed as a closed - form function given by: ξ = 1/(1 + eB/Δr) (where, e: the undetermined coefficient). The undetermined coefficient e can be determined by using 1 condition that is led by the equivalence of 2 systems, single footing with a width of nB and n × n contacted footings with each width of B. That is, e = n − 1. From the above, the proposed interaction factor is derived.
 And as a result of comparing the proposed interaction factor and a interaction factor evaluated by using analytical solution (superposition of Mindlin's solution), the following conclusions is obtained.
 1. With square arrangement of footings, the proposed method agrees well with the analytical solution.
 2. With rectangle arrangement of footings, in the case where the long side / short side ratio is about 1.8 or less, the proposed method generally agrees with analytical solution.
 3. If the ground contact pressure distribution of a single footing is already known, approximate load distribution of footings can be calculated by using the proposed interaction factor.

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 Spatial structures are also used as evacuation facilities in the event of a disaster, so social demands for human life protection and function maintenance are high. Therefore, there are many studies on applications of response reduction mechanisms to spatial structures.
 TMD is cited as one of the vibration control methods for spatial structures. There are many examples of applications 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 these examples are verified.
 TMD has the advantage that the damping effect can be obtained by the mass of 1 to 3% of structure. In addition, TMD is fit for the vibration control of spatial structures because it is possible to install TMDs by a single supporting point. Therefore, there are many studies on spatial structures with TMDs. The authors have verified the influences of number and position of installed TMDs, the period and phase characteristics of earthquake motions, input directions of input waves and free vibration characteristics of spatial structures on seismic response reduction effects. However, when TMD is actually applied to structures, construction error of target structures, calculation error of natural periods, manufacturing error of TMDs and the like may also affect the response reduction effects by TMD. In addition, there is no study in which the influence of change of design parameters for TMD installed on spatial structures is investigated systematically. From these backgrounds, the purpose of this study is investigation of the influences of the change of designed values of TMDs on seismic response reduction effects by plural TMDs for cylindrical lattice shell roofs.
 From the numerical results, it is concluded as follows.
 1) The effects of change of mass ratio on response reduction effects are small regardless of half open angle, magnification of out-of-plane stiffness of roof and input wave. The robustness of response reduction effect by TMD with respect to the change in mass ratio is high.
 2) The response reduction effect decreases due to the change in the damping ratio. In addition, the influence of increase and decrease of damping ratio on the response reduction effect varies depending on half open angles, magnification of out-of-plane stiffness of roof and input waves.
 3) As the damping ratio becomes smaller than the optimum value, the stronger asymmetry appears in the shapes of maximum response distributions. Therefore, the nodes in which the maximum vertical responses become larger than those in non-vibration control appear.
 4) The effects of the change of frequency ratio on response reduction effects are large regardless of half open angle, magnification of out-of-plane stiffness of roof and input wave. As the frequency ratio becomes smaller than the optimum value, the response reduction effect decreases in comparison with the frequency ratio becoming larger than that.

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 Some new multi-story buildings constructed in recent years employs single-layer latticed walls as the outer-tube, because of attractive appearance and great in-plane stiffness. In the region at high seismicity as Japan, structural walls are used as earthquake resistant shear walls and subjected to severe cyclic shear deformation during strong earthquakes. Ductility is the most critical factor to be considered as well as strength for such shear walls. The present paper gives a summary on the cyclic tests of steel hexagonally latticed shear plates and discusses on the inelastic strength and buckling characteristics based on the theoretical and FE analysis.
 Four steel hexagonally latticed plates (denoted by H1, H2, H3 and H4) were manufactured. The width and height of the plates were 1484mm and 1284mm, respectively. The thickness was 22mm (H1) and 16mm (others). The number of hexagon was 6 in both width and height. The H1 and H2 plates were composed of regular hexagon. The H3 plate comprised orthotropic slender hexagon and the H4 plates was composed of the irregular hexagon determined by the Voronoi rule. Forced cyclic shear was given to these for plates. The shear strain (denoted by γ) amplitude in each cycle gradually increased from ±1/900 to ±1/25. Two cycles were given in one amplitude.
 Three plates except H3 yielded at the cycle where γ=1/300 but the H3 did at γ=1/450. After yield, the plastic response behavior of the H1 and H2 plates was very stable without out-of-plane buckling until the final cycle. On the other hand, out-of-plane buckling was clear in the tests of the H3 and H4 plates. Buckling caused from the cycle where γ=1/75 in the H3 test and during the final cycle in the H4 test. Moreover, after buckling, break of three lattice members occurred in the H3 test during the first cycle where γ=1/25. Crack was also observed in the H2 and H4 tests. All these breaks and cracks occurred on the vertical members.
 The hysteresis curves were not slip but spindle shape even in the H3 test where severe buckling was observed. Significant strain hardening was observed in all the tests. The following FE analysis shows the appearance of yield hinges in the vertical members from the early stage. This is a characteristic of hexagonally latticed plates when subjected to shear. As shown in the theoretical analysis, the rotation of yield hinge is amplified to almost twice the shear strain even on the regular hexagon. The FE analysis also shows that the bending moment at the yield hinges increases significantly due to strain hardening and the accumulated plastic strain was extreme at the spots where break occurred in the H3 plates.
 An effective framework to estimate the shear strain when out-of-plane buckling initially occurs, has been proposed by Tamai on steel shear panel dampers. In this study, the estimation formula is modified to a function of the generalized slenderness to apply to buckling of latticed plates. The regression coefficient in the formula is re-determined by the test results of latticed plates including the past tests on triangularly latticed plates. The modified formula well estimates the buckling shear strain and that shows the effectiveness of this framework proposed for steel panel dampers.

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 This study deals with the dynamic elasto-plastic analysis considering a member buckling and the fuse type connection composed of of an aluminum hub and a steel bolt. A ductile elongation of the steel bolt due to a tensile stress is expected by avoiding the brittle collapse in our previous paper⁵⁾. The study proposes a fuse type connection by means of yield of the steel bolt due to a tension stress realize the ductile failure collapse mechanism of the wall type spatial structure.
 The seismic response characteristics of spatial structures such as roof and wall types depend on their form and support conditions. Several reviews and guidelines quoting many studies have been published depending on the performance of building structures. Several performance prediction methods have been developed for this purpose, however, the earthquake resistance capacity of spatial structures requires the variation of the form and the support condition. On the other hand, it is very difficult to apply them to wall type spatial structures. For the performance design, several prediction methods such as a pushover analysis and an adaptive capacity spectrum method have been developed for structures such as buildings and bridges.
 The control of the dynamic collapse mechanism is also proposed to improve the earthquake resistant capacity by the fuse type connection using the steel bolt elongation.
 Effect of the member buckling and yield elongation of the steel bolt on the seismic response of the out of the plane is shown in comparison with response of the wall structure subjected to the horizontal earthquake motions. The earthquake evaluation method is also proposed considering the dynamic collapse mechanism. A validity of the proposed method is shown by means of the accuracy between the analysis and the estimation.
 The study deals with the partial cylindrical truss wall with the fuse type joint connection subjected to horizontal earthquake motions. It is confirmed in the dynamic elasto-plastic analysis that the control of the dynamic collapse mechanism such as the steel bolt elongation can avoid a brittle collapse mechanism such as a chain of the member buckling. The behavior due to the member buckling and yield elongation of the steel bolt is shown in the dynamic response of the wall structure subjected to horizontal earthquake motions.
 The evaluation method is also proposed by means of the limit displacement considering a ductility factor of the steel bolt within 4. This means that the response control can be feasible by the damper connection such as the steel bolt elongation due to a tension stress.

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 Multi-story structural walls, which are one of the most important lateral load carrying components in reinforced concrete buildings, often have openings for architectural reasons. Although these openings hamper the formation of diagonal compression strut in wall panels and decrease ultimate shear capacity, the Japanese design standard and guidelines do not consider the effect of location of openings on the assessment of the ultimate shear capacity. The objective of this study is to simulate the effect of staggered openings on shear resisting mechanism of walls and propose analytical methods with line element models.

 Two 2/5-scale reinforced concrete multi-story structural wall specimens, L5 and L6 were tested. Both specimens had one opening on each story and these openings were staggered. The openings of L5 specimen were arranged close to the boundary columns and those of L6 specimens were arranged closer to each other, respectively. Shear failure and tensile yielding of longitudinal bars in the boundary beam resulted in lower ultimate shear capacity than the one calculated by the current design method.

 Nonlinear static analyses were conducted on line element models of the specimens. In these analyses, members around openings were modeled as column elements with a wing wall, wall elements with a boundary column and elements between openings. The restoring force characteristics of axial, shear and flexural springs in these elements were modeled based on the current commentary on structural regulations and other design guidelines. The ultimate shear capacities of column elements and wall elements were increased by from 20% to 40% based on the database of past experiments. The ultimate shear capacities of elements between openings were determined by punching shear capacities of boundary beams with a hanging wall.

 The proposed models simulated the lateral stiffness after cracking, the maximum lateral load and failure mechanisms of L5 specimen in both positive and negative loading directions and L6 specimen only in positive loading direction. However, they overestimated the ultimate shear capacities by approximately 30% and did not simulate shear failure of the wall with a boundary column on the second story in negative loading direction of L6 specimen. The opening of the first story might have caused deterioration of ultimate shear capacity of the wall of the second story. In order to obtain better analytical results, the paper adopted an evaluation method of ultimate shear capacity for wall located above open story proposed by Izumi et al. The modified models agreed well with the experimental results of L6 specimen in negative loading.

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 In this paper, the effect of out-of-plane deformation between attachment and beam flange on Joint yield moment of Web-clamped type beam-to-column connection was investigated. In this study, simple mechanical model implied following joint behavior; 1) In the case that the shape of attachments is determined, out-of-plane deformation increases when the distance between the beam center and the bolt hole center b_f becomes wider or the thickness of beam flange t_f becomes thinner; 2)The joint yield moment degrades when the out-of-plane deformation increases. These behaviors of the simple mechanical model were investigated by finite element analysis.

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 1. Introduction
 Numerous structures are recently required continuous use even after large earthquakes. An efficient technique is to employ elasto-plastic dampers, such as buckling-restrained braces (BRBs), which act as fuses. Although response spectrum analysis (RSA) has a good time efficiency for damper design, relative to non-linear response history analysis (NLRHA), the conventional methods are generally limited to specific structures that are easily translated into simple models. With a suitable RSA method, computational optimization of damped structures will be also important, considering recent trends towards the use of algorithmic modelling, scripting and cloud-based high performance computing servers. Thus, this paper presents a damper design routine for highly indeterminate 3D structures utilizing computational optimization and response spectrum analysis, which has been extended to incorporate non-proportional damping.
 2. Generalized Response Spectrum Analysis and computational work flow
 The proposed routine (GRSA) is presented, and the accuracy is verified in the comparison with THA.
 3. Damper layout or distribution optimization for the lattice tower
 A series of optimizations, including damper layout or distribution, is performed for the lattice tower in order to verify the efficiency of the proposed design routine, and to analyze the efficiency of the existing retrofit design.
 4. Damper distribution optimization for the conventional BRBFs
 A multi objective damper distribution optimization is performed in order to verify whether the well-known performance curve can be found in a detailed BRBFs. Additionally, the optimization results are compared with that of the conventional design method.
 5. Layout optimization for a concentric braced frame skin structure and the practical optimization conditions
 A series of detailed layout optimizations, including BRB replacements of the concentric braces, BRB replacements of the first story columns or the concentric brace removals, is performed in order to investigate both the optimal layout tendencies and the practical optimization conditions.
 6. Conclusions
 In summary, the following results were obtained:
 1) GRSA can be used for direct RSA of 3D structural analysis models including dampers of various types, with buckling-restrained braces used in this study, and the accuracy is verified in a series of comparison studies with NLRHAs. In the study of the systems including 810 degree-of-freedoms, NLRHAs (7,000 steps) take 15 to 30 min., GRSAs take 5~10 s, which indicates GRSA has a good time efficiency compared with NLRHA.
 2) While improved layouts and distributions were identified for certain constraint and target objectives, the existing design for a particular lattice tower was found to be close to the optimal solution for minimizing the buckling utilization. While the layout and distribution trends are usefully indicated by the optimal solutions, the results are dependent on the input waves, suggesting that there may be no versatile optimum solution to every possible scenario.
 3) Even for the multi degree-of-freedoms models, the well-known performance curve related to the response reduction of passively-controlled buildings can be found, utilizing a multi objective distribution optimization method. While the full proportional distribution method of equivalent single degree of freedom is reasonable for low rise structures.
 4) A single objective optimization may be an inadequate optimization condition for the concentric braced frame skin structures. A penalty is suitable for this situation in order to reduce both the story drifts and demand capacity ratios of member buckling. Nevertheless, BRB replacements of columns or concentric brace removals enable simple single objective optimization.

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 In moment frame combined with dampers, the beam-to-column connection is subjected to not only bending moment but axial force in accordance with the damper arrangements. Previous investigation on existing steel passive controlled building structures [Ref. 1] pointed out that the beam axial force reaches up to 30% of its yield strength on entire beam cross section. For such beams, in addition to causing beam instability [Ref. 2], the presence of axial force tends to reduce the magnitude of plastic strength. Furthermore, Not only WF section but also RHS is commonly used for column in Japan. When the beam is connected to RHS column, it is well recognized that the strength of beam-to-column connection is significantly affected by out-of-plane bending strength of column flange (wall) and the lack of design consideration for this effect lead to decrease of plastic deformation capacity[Ref. 3 and 4]. The current recommendation for design of connections in steel structures [Ref. 5] specified the strength evaluation in consideration of this effect. However, the recommendation is only applicable to beam-to-column connection subjected to only bending moment.
 This paper presents strength evaluation of H-beam-to-RHS connection subjected to both bending moment and axial force. In order to derive the strength formulae, the limit analyses based on upper bound theorem were performed. Six collapse mechanisms of beam-to-column connection including the mechanism proposed by [Ref. 6] shown in Fig. 3 and Fig. 4 are considered in this study. All collapse mechanisms consist of axial yielding of beam flange, yielding of beam web along the beam depth and multiple out-of-plane yielding lines on the column flange. The best upper bound can be given by the lowest value of six collapse loads under axial force given. Therefore, the plastic strength of beam-to-column connection is defined by whichever is smaller of the upper bound solution aforementioned and plastic strength of beam.
 The axial force-moment interaction curves (N-M interaction curves) obtained by derived equations shown in Fig. 7, clearly indicated that when strength of beam-to-column connection were governed by collapse load of column flange, the strength of beam-to-column connection was significantly decreased with increase in axial force even if the plastic neutral axis exists within the beam web. Based on this observation, N-M interaction curves for the collapse load were approximated with bi-linear N-M interaction, as shown in Fig. 8. In response, the practical design equations for the yield strength and plastic strength were further developed ensuring a consistency with current design equations.
 In order to examine the validity of proposed design formulae, Finite element analyses were conducted with beam-column subassemblage models under bending moment and/or axial tensile force shown in Fig. 11, In the analysis, axial force ratio of beam, thickness of beam web and thickness of column were varied within the range of practical application. Additionally, the presence of weld access hole placed at beam ends was also examined. As shown in Fig. 15, the prediction by proposed design equations agreed with FEA results within the 8% error for the range of properties examined.

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 In the current fire safety design of steel structures in Japan, joints between steel beam ends and steel girders using friction type high strength bolts (this joint type is referred to as “pin joint”) are designed as pinned, therefore the fire resistance of the steel beams is determined only by the sagging moment resistance at the mid-span. On the other hand, research activities in Europe show that hogging moment resistance at pin joints of steel beams may be somewhat expected at elevated temperature. Moreover, in the case of steel - concrete composite beams, the reinforcing bars fixed in the concrete slab on the steel girders with headed studs work effectively so that the hogging moment resistance at the pin joints may be further improved. Furthermore, the sagging moment resistance at the mid-span is improved by the composite effect with concrete with small temperature rise. Considering these effects, there is a possibility that fire protections of the steel beams can be omitted or reduced.
 This paper presents results of load-bearing fire tests of unprotected fully composite beams pinned with steel girders conducted for the purpose of clarifying the deflection behavior and the fire resistance. 3 specimens were used, and the main test parameters were end boundary conditions (simply supported, pinned with the girders) and joint specifications (number of bolts, fire protection of joints). (Simply supported beam and beam pinned with girders are referred to as “simple-beam” and “pin-joint-beam” respectively.) The load level was a third of the yield moment, and the heating was in accordance with ISO 834 standard curve.
 The main conclusions from the test results were as follows:
 1) The bending stiffness of the pin-joint-beams at ambient temperature was close to that of the simple-beam. On the other hand, the deflection was largely suppressed by the restraining effect against rotation at the pin joint at elevated temperature. This effect was exerted because the rebar worked effectively by tying the steel girder and the concrete slab with the headed stud. As a result, the time to reach ISO limiting deflection of the simple-beam No. 1 was 24 min, whereas that of the pin-joint-beam No. 2 and No. 3 were 61 min and 57.5 min respectively, the fire resistance was greatly improved.
 2) Bending collapse was not observed for the pin-joint-beams. On the other hand, shear buckling of the web and local buckling of the lower flange occurred at the ends of the beam, but it is inferred that the load-bearing capacity was not lost immediately after the shear yield of the web.
 3) No significant damage (such as bolt failure and plate tear-out failure) and no deformation (such as shear deformation of the bolt and bearing deformation of plate) at the pin joints were observed during heating and cooling process. On the other hand, immediately after stopping heating, as the ends of the concrete slab was damaged due to cooling shrinkage of the unprotected steel beam, the deflection sharply increased temporarily.
 4) The full-plastic moment calculated using the strength obtained by the coupon test was able to accurately evaluate the sagging moment resistance for fully composite beam where the temperature of the lower flange reached 800 °C.
 5) The moment resistance of the pin-joint-beam was discussed by using the hogging moment resistance at pin joint considering the rebar inside the slab calculated by the equation (4). As a result, the effect on the total moment resistance was dominated by the sagging moment resistance at the mid-span at ambient temperature, whereas the influence of the hogging moment resistance at pin joint tended to increase at elevated temperature.

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 Fire resistance design for steel structures reccomended by the Architectural Institute of Japan (referred to as the AIJ Reccomendation) is widely used in Japan as a design guideline to ensure the fire resistance performance in practice. The AIJ Reccomendation requires excessive safety factors for use in the verification methods on both fire actions and load bearing capacity of the steel member to consider uncertainty in building fire such as fire loads based on calorific values of combustibles, working loads, and steel strength at elevated temperature. However the validity on the excessive safety factors has not been well investigated. In particular, the quantitative estimation of the fire resistance performance for the steel member considering the uncertainty of the live fire load, which is one of the main uncertainty sources in the fire resistance design, has not been conducted. The main purpose of this study is to propose a theoretical solution on conditional failure probability of the protected steel member under natural fire after flashover (fully-developed compartment fire) by formulating relationships between the dispersion of the live fire load and that of the steel member temperature raised by the fully-developed compartment fire.
 Numerical approach using the Monte Carlo (referred to as MC) simulation combined with a thermal conduction analysis of the protected steel member and a compartment fire zone model analysis is conducted. The influences of the dispersion of the live fire loads on the fire compartment room temperature as well as on the fire duration time are investigated by the compartment fire zone model analysis. The various types of the compartment room size, opening size, protection and steel member thickness, fire temperature rise coefficient are considered in the analysis, in order to simulate the steel member temperature under the various fire actions. Furthermore, the theoretical failure probability model for the steel member under the fully-developed compartment fire considering the uncertainty of the live fire loads, dead and live loads and the steel strength at the elevated temperature is proposed and the applicability is verified by using MC simulation.
 Conclusions of this paper can be summarized as follows:
 1) Based on the numerical results of the parametric compartment fire zone model analyses using MC simulation, it was clarified that coefficient of variations of both maximum temperature of the fire compartment room and fire duration time are independent of floor area of the fire compartment room.
 2) The standard deviation of the maximum temperature of the steel member under the fully-developed compartment fire depends on the values of both average temperature of that and the coefficient of variation of the live fire load. The relationship between the standard deviation of the maximum temperature of the steel member and the coefficient of variation of the live fire load can be estimated by the equation (3).
 3) The theoretically estimated failure probability of the steel member under the fully-developed compartment fire considering the uncertainty of the live fire loads, dead and live loads and the steel strength at the elevated temperature agrees well with analytically estimated failure probability using MC simulation.

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