Water content and temperature of concrete have an influence on various properties of concrete. For example, water content and temperature of concrete in the hardening process have an influence on the strength development. The change of water content after the hardening participates in the durability of concrete. Furthermore, water content and temperature are different by the position in the concrete when it is scaled the full-size concrete member. Therefore, the prediction of water content and temperature in the concrete member is important.

In this study, water content and temperature in the concrete member were numerically predicted using the mathematical model for cement hydration and microstructure formation. The mathematical model for cement hydration and microstructure formation has been proposed in the previous study. The model dealt with the diffusion of water into cement particles and the diffusion of cement components out of cement particles. The model made it possible to express not only the progress of cement hydration but the progress of formation of the hydrated cement microstructure.

The simulation model for water diffusion in full-size concrete member was proposed. This model made it possible to express the water consumption by cement hydration, water diffusion in concrete member, and water evaporation from the surface of concrete after removing forms. Water content at each position in concrete member could be calculated by the model.

The simulation model for heat conduction during heat generation caused by cement hydration was proposed in the previous study. The previous model was improved in this study, by introducing the effect of radiation heat and evaporation heat of water on the surface of concrete. Temperature at each position in concrete member could be calculated by the improved model. Furthermore, the heat conduction model was connected with the water diffusion model.

The predicted water contents were compared with the measured water contents of wall and column specimens. As a result, it was confirmed that the predicted water contents agreed with the measured water contents. In the N28.3 and N48.4 concrete column specimens, the water content after removing forms was the smallest on the corner of the column and largest at the center. The difference in the water content of the center and corner was especially noticeable in the N48.4 concrete. In the N48.4 concrete wall specimen, the water content after removing forms is nearly constant at 100 mm or deeper from the surface. This suggests that at deeper than 100 mm from the surface, the water content is not affected by water dissipation to the outside of concrete but mainly by the cement hydration in the concrete interior.

The predicted concrete temperatures were compared with the measured concrete temperatures of column specimens. As a result, it was confirmed that the predicted temperatures agreed with the measured temperatures. Especially, the tendency that the drop in temperature caused by water evaporation from the surface of concrete after removing forms could be predicted accurately.

With the improvement of earthquake resistance and large scale of buildings, the number of cases where it is difficult to fill the form work with conventional slump-managed concrete is increasing. In addition, slump flows 45 cm, 50 cm, 55 cm, and 60 cm have been added due to the JIS (Japanese industrial standard) revision made in March 2019. In the future, it is estimated that the use of slump flow managed concrete will increase. Furthermore, in recent years, new admixtures have been actively developed, and it is necessary to correctly grasp the flow characteristics of concrete using these admixtures from a rheological point of view. It is the cement paste in concrete that is most affected by the flow properties of the admixture. Therefore, it is useful to be able to grasp the flow characteristics of cement paste.

We have already examined the relationship between the rheology constants obtained from the rheology test and the flow characteristics obtained from the paste flow test, and we proposed a rheology constant estimation method. In this study, we reexamined the rheological constant estimation method based on the correlation analysis findings using the visco-plastic finite element method (FEM).

First, flow analysis was performed by FEM using any combination of rheological constant and paste density (yield stress: 10 patterns, plastic viscosity: 7 patterns, paste density: 3 patterns, total 210 patterns) as input values. Next, based on the analysis results, the relationship between the paste flow characteristics (flow value, each flow arrival time, flow stop time) and the rheology constant and paste density was examined by correlation analysis.

As a result, it was found that the yield stress can be estimated by the flow value, and the plastic viscosity can be estimated by the multiple regression equation of the paste density and the 150 mm flow arrival time.

Furthermore, we proposed a new rheological constant estimation equation using the actual test results of the cement paste for the relationship obtained from the correlation analysis. After that, the rheology constant was estimated from the actual paste flow test results using the rheology constant estimation equation. Finally, a paste flow simulation was performed using the MPS method, which can consider the influence of the flow cone, and it was compared and examined: the actual paste flow test results and MPS analysis results.

As a result, the actual paste flow test results could be reproduced by MPS analysis, and the validity of the rheological constant equation was confirmed.

To investigate the applicability of VAR-X model to estimating moisture condition of concrete exposed to ordinary natural environment, concrete internal humidity data reported previously were analyzed with weather data from Japan Meteorological Agency. The first 90 days were used for parameter estimation and the second 60 days were used to validate the model and predicted values. The results are summarized below.

(1) Within the scope of this study, VAR-X model was applicable to the humidity data in the non-rainfall environment. VAR-X model was also able to predict the internal humidity for 60 days based on the estimated parameters and weather data (temperature and humidity), and the RMSE ranged from 0.87 to 2.04%.

(2) It was judged that the VAR-X model was not appropriate to be applied to the humidity data of rainfall environment. The main reason for this is that the impact of rainfall was underestimated by assuming constant coefficients in the model.

(3) The mechanisms of humidity fluctuation in concrete are discussed, which include the absorption and release of water and the temperature dependence of concrete water content. Based on the mechanism, difference between rainfall and non-rainfall environment was pointed out and the conditions under which the VAR-X model can be applied are discussed.

(4) Methods of utilization and improvement of VAR-X model were discussed for cases where the moisture transfer characteristics of concrete changed and where the data increased or decreased in high humidity region. The advantages of time series analysis, including VAR-X model, were also pointed out in comparison with conventional physical models.

VAR-X model can predict humidity fluctuations in concrete using weather data when certain conditions are met. In

the future study, the model will be modified and its application to the durability evaluation of various materials will be investigated.

There is concern about the occurrence of long-period ground motions in Japan. In particular, if the seismic isolation building is subjected to a long-period ground motion, the seismic isolation device is likely to affect the horizontal performance by the resonance and long repeated deformation. As evaluation methods, two analysis methods have been proposed. They are “detailed method” and “simplified method”. “Detailed method” is an evaluation method that considers the repetitive dependence by changing the horizontal performance of the seismic isolation device at each step of time history response analysis. “Simplified method” is calculated by time history response analysis in two steps. First, time history response analysis is calculated using the model parameters of the seismic isolation devices. Next, the cumulative absorbed energy amount per unit volume of the seismic isolation device is calculated, and the reduction rate of the model parameters is calculated. Finally, the repeated deformation dependence of the seismic isolation device is taken into consideration by performing time history response analysis calculation using that parameter.

It is very important in structural design to examine the validity of the above analysis method. In this study, we use a real-time on-line test that can reflect the complicated nonlinear characteristics of seismic isolation devices in time history response analysis. The proposed test method is a test method that replaces the shaking table tests.

This paper verifies the analysis method considering the repetitive dependency of the laminated rubber bearings by real-time on-line tests. The validity of the response analysis method is discussed by comparing the results of the proposed test method with time history response analysis results by “simplified method” and “detailed method”. In order to carry out the above purpose of this research, tests are conducted using three types of laminated rubber bearings. The findings obtained in this paper are shown below.

・In order to verify the accuracy of the proposed test method, we conducted a test using natural rubber bearing

(NRB). As a result, it was confirmed that time history response analysis had high reproducibility. Therefore, the effectiveness of the proposed test method was shown.

・The seismic response characteristics of the lead rubber bearing (LRB) has a good correspondence with time history response analysis results because the bilinear restoring force characteristics depend on it. The seismic response characteristics of high-damping rubber bearing (HDR) show complex response due to its very high nonlinearity. The excitation of the mode’s eigen-periodic components confirmed the response characteristics different from the numerical analysis results.

・The differences between the response analysis methods and the real-time on-line test became clear. In addition, the horizontal performance that decrease due to the repeated deformation dependence are compared.

In recent years, regarding buildings that serve as bases for disaster relief work and as living spaces, the social desire is for continued use of and less repair work for such buildings after earthquakes. To meet that kind of wish, post-quake building damage must be kept to the slightest minimum. With the aim of continues use of buildings after earthquakes, this report deals with medium and low-rise steel structure buildings, giving consideration to practical guidelines for base shear coefficients in order to minimize building damage to the slightest possible after foreshocks, main shocks and aftershocks.

The first priority was to theoretically speculate based on energy balance to derive a calculation formula for cumulative plastic deformation ratio corresponding to level of damage, the speed conversion value equivalent to total energy input and the natural period parameterized base shear coefficient (α₁). Also, the application of this calculation formula to foreshocks, main shocks and aftershocks was made possible by introducing a cumulative energy spectrum. The derivation processes for the above are explained in Chapters 2 and 3.

Next, from analysis results of α₁ applied to seismic waves widely used in actual design, consideration was given to base shear coefficients that meet the current seismic code together with guidelines for base shear coefficients that would make it possible for continued use of buildings after earthquakes. By setting base shear coefficient guidelines in which a building’s D_s value is 0.4 or more with the 1^st natural period at less than 1s, or where the D_s value is 0.25 or more with a natural period of 1s to 2s, the degree of damage is less than moderate even for earthquakes that very rarely occur, which fulfills the required performance in the seismic code. If a design is oriented to continuous use of the building after foreshocks, main shocks and aftershocks, then the pragmatic assessment would be to aim for a natural period of 1s or more and a base shear coefficient of 0.45 or greater as the D_s value. These analytical considerations are explained in Chapter 4.

Finally, Chapter 5 explores the observation waves for the Pacific Coast of Tohoku Earthquake (2011) and Kumamoto Earthquake (2016), considering base shear coefficients that will make continued use of buildings possible after earthquakes. Regarding a building with first natural period of less than 1s, a short period region (greatly exceeding the energy input of an earthquake that very rarely occurs [a wave arrival count of 2]) existed in the energy input of observation waves of accumulated foreshocks, main shocks and aftershocks. Thus, this research confirmed that a natural period of 1s or more and a D_s value of 0.45 or more as the base shear coefficient will, generally speaking, minimize damage to less than slight for the abovementioned accumulated observations waves.

Uniform inter-story drift angle in seismic response of buildings is effective in improving structural performance. Because it is expected to prevent pancake collapse due to concentration of deformation, and to decrease the maximum inter-story drift angle by efficient absorption of damping energy in each story.

In this paper, inter-story drift angle is controlled by stiffness calculated using the closed-form representation of a primary mode, and the method is applied with the results of time history analyses. Then the primary mode shapes are obtained from the results of time history analyses on 120 model cases, and the values of maximum inter-story drift angle are investigated.

The conclusions are obtained as follows.

1) It is possible to realize the uniform inter-story drift angle even in responses that envelop the maximum response values for multiple earthquake responses, by adjusting and updating the stiffness obtained from primary mode shape.

2) Primary mode shapes for uniform inter-story drift angle are shown with number of building stories and dimensionless height as parameters.

3) An equation for estimating the uniform inter-story drift angle is shown with building representative height, natural period, and damping constant as parameters.

4) From the results of 2) and 3), a simple method determining the building stiffness that realizes uniform inter-story drift angle is shown.

The presented method does not require repeated calculations. Therefore, this method is useful at the initial design stage.

In addition, the method of adjusting the stiffness to achieve uniform inter-story drift angle, which is shown in 1) above (see Chapter 5), has the advantage that an accurate solution can be obtained in a few convergence calculations for arbitrary seismic motion without much computational load. The direct use of this method is also useful. Furthermore, it is possible to specify an arbitrary deformation distribution with this method.

　A vibration control system using building connection is one of the most popular methods in passive structural control of building structures. Most of the previous researches on this subject deal with buildings connected by steel dampers or oil dampers. There is a limited number of papers which deal with buildings connected by inertial mass dampers (IMD). It is well known that IMD has some advantageous properties, i.e. an input reduction effect, a lengthening effect of natural period and a tuning damping effect. While IMD between two buildings does not have the input reduction property, the response of a building with longer natural period can be reduced more effectively than the building connecting by steel dampers or oil dampers due to the lengthening property of natural period and the tuning damping effect. However, many previous researches are based on the frequency-domain formulation using a two-mass connection model and the effects of higher modes and connection height are not always taken into consideration. In addition, there is no research focusing on the energy characteristics of buildings connected by IMD. We propose a substructure tuned-mass-damper (TMD) connection damping system in this paper. In this system, the substructure vibration is synchronized with the main structure by connecting with IMD. It may be difficult to reduce the response transfer function from the height of the so-called fixed point by connecting with oil dampers. On the contrary, it may be possible to reduce the height of the fixed point by connecting with IMD.

　The purpose of this paper is to clarify the damping effect and the optimal properties of IMD between two buildings. The optimal quantity of IMD is obtained by using the fixed-point theory and the energy analysis for a two-mass connection model and an MDOF connection model. Its validity is verified by time history analysis. IMD between two buildings does not absorb energy, but it transfers energy from the building with longer natural period to the building with shorter natural period. It is shown that too much quantity of IMD makes two buildings getting rigid and an effect of oil dampers parallel to IMD is getting worse. We dealt with multiple analysis models with different connection heights. The numerical analysis showed that the optimal quantity of IMD in the buildings connected at higher levels is larger than that in the buildings connected at lower levels. The optimal quantity of IMD that minimizes the input energy into the main structure is made clear by using the energy-based method for a double impulse (a representative of a pulse-like earthquake ground motion) and a multi-impulse (a representative of long-duration and long-period earthquake ground motion). The maximum response under pulse-like motions cannot be reduced by connecting with IMD. However, the effect of reducing the vibration amplitude after the maximum response is remarkable. In addition, the reduction rate of the maximum response to long-duration and long-period ground motions is large. The energy analysis method can consider the effects of higher modes and the vibration after the maximum response. The optimal quantity of IMD derived by using the energy analysis is shown to be the most effective for the reduction of response especially when connecting at lower levels. It is concluded finally that the method using the energy transfer function is effective for the buildings connected by IMD.

Seismic damages have been observed on concrete piles after recent large earthquakes. Most, pile damages have been found in such a visible change in superstructures as tilting. If no change is observed in a superstructure, it is difficult to know the damage status of piles without excavation survey. Since the survey takes time and cost, it is desirable to judge whether the survey is necessary and/or to specify which piles are to be surveyed in advance. Under this background, detecting methods of the pile damage based on seismic records of the superstructure have been studied. However, they have not been verified through actually damaged piles, and mutual influence between seismic response of the superstructure and damage to the piles has not been clarified.

To investigate damage mechanism of the piles, a series of shaking table tests were conducted in this study using “E-Defense” facility. A 3 × 2 reinforced concrete (RC) pile group was installed in a model ground consisting of two soil layers of dry and slightly wet sand with different relative densities. The pile group and the model ground were excited by the E-Defense shaking table. The employed input motions were multiple simulated seismic motions, observed seismic records and sine waves with different acceleration amplitude. The pile damage was evaluated from rebar strain measurements with strain gauges, while seismic behavior of the superstructure was measured by accelerometers and laser displacement transducers.

Inertial force of the superstructure acted on the pile heads as lateral loads, and bending deformation was generated along the pile shafts. Furthermore, rocking motion of the superstructure caused axial load variation in the piles. As a result, multiple cracks and rebar yielding were generated along the pile shafts. Focusing on the axial load variation, the examination yielded the following damage characteristics of the piles.

1. Near the heads of the edge piles, strain due to axial load variation was generated simultaneously with that due to bending in the same direction on the side facing the structure’s center. Along the deeper parts of the edge piles, the same tendency occurs on the side facing the free-field. As a result, these sides become susceptible to damages such as rebar yielding and concrete crushing. Therefore, it is considered efficient to focus on these sides when investigating the pile damage after an earthquake.

2. The shaft rigidity becomes smaller in the pull-out piles than that in the push-in piles due to damages such as concrete cracking and rebar yielding. The rotational center of the rocking motion then moves horizontally from the bottom center of the structure toward the push-in piles. As a result, the pile cap is temporarily uplifted in conjunction with the rocking motion and responds vertically at twice the frequency of the horizontal response of the superstructure. By observing this phenomenon during an earthquake, it may be possible to detect the pile damage.

It is possible to accurately predict the large deformation behavior of the circular film by representing the ETFE film as an elasto-plastic model and solving the equilibrium equation between the internal pressure and the film tension assuming that the film surface is spherical. The circular air cushion receiving applied pressure can limit the unknown values of the displacement to two vertical displacements at the center of the upper and lower membrane, assuming that the curved surface shape is a sphere. It is possible to express in a simple form the equilibrium condition formula strictly based on Boyle-Charles’ law considering the pressure, volume, amount of air, temperature parameters, wrinkle and elastoplasticity of the air cushion. The validity of these is verified by comparison with the pressure experiment of circular air cushion.

When a positive applied pressure of the same magnitude as the initial internal pressure acts on the constant pressure type air cushion, the membrane tension becomes zero and the stiffness is lost. Since the internal pressure of the closed type air cushion changes in the direction of canceling the applied pressure w, the displacement and stress change of the closed type with respect to the same additional pressure is smaller than that of the constant pressure type. When the initial rise ratio h₁/L ≥ 0.1, wrinkle does not occur until the absolute value of the applied pressure reaches about twice the initial internal pressure p₁. When one of the upper and lower membranes wrinkles due to the applied pressure, the wrinkled membrane is in an unstable state that causes rigid body displacement, but the stiffness of the air contained in the air cushion (pneumatic stiffness) is maintained. Therefore, the decrease in stiffness of the entire air cushion is slight and maintains a stable state. When the film yield by the applied pressure, the stiffness of the air cushion is reduced, but it retains sufficient load bearing capacity. The smaller the initial rise ratio h₁/L and the higher the initial internal pressure p₁, the more difficult it is for the closed type air cushion to wrinkle when a positive pressure is applied to the upper membrane side. However, when the initial rise ratio h₁/L is small, the initial tension σ₁ becomes high, and the inferior membrane tends to yield.

For closed type air cushion that receives negative pressure on the upper membrane side, the upper membrane is less likely to yield when the initial rise ratio h₁/L is large and the initial internal pressure p₁ is small. The geometric stiffness effect due to the initial internal pressure p₁ is smaller than the effect of curvature, and an excessive p₁ often leads to an increase in stress σ_i and is disadvantageous. While the atmospheric pressure P_e and temperature T_i change slowly over time, the amount of air n_i inside the air cushion may change significantly in a short time due to the movement of air through the air duct.

The behavior of the air-moving type air cushion changes depending on the magnitude of resistance to the movement of air. When the resistance is large, it shows characteristics close to the closed type, and when the resistance is small, it shows characteristics close to the constant pressure type.

Panel sheathed shear walls are widely used in Japanese wooden buildings as structural elements to resist seismic forces. Thus far, many experimental and theoretical studies have been conducted. In particular, the theoretical equation proposed by Murakami et al. has been adopted as one of guidelines for the structural calculation of these shear walls in Japan. As one of the testing methods for single nailed joints in Japan, a testing method was adopted to perform a the full-scale cyclic in-plane shear test of a panel sheathed shear wall and to calculate the results in reverse using the Murakami’s equation (hereafter, referred to as “the racking test”). Additionally, another testing method was proposed wherein compressive monotonic force was applied from above on a small rocket-shaped specimen composed of timber, nailed with panels on both sides (hereinafter, referred to as “rocket-type test”). However, there are few studies that compare the results of the two tests, and the correspondence between the results of the two tests is necessary for structural design of the sheathed wall based on the results of the rocket-type test. Racking tests were conducted with parameters, such as the species of frame, nail, nail space, and thickness of the panel(medium density fiberboard), and then rocket-type tests were conducted with materials cut from the specimens of the racking test. In comparison of the results of both tests, the initial stiffness value obtained in the rocket-type test was approximately twice that obtained in the racking test. Previously, the difference between cyclic and monotonic tests was usually suggested to be the cause for this difference in initial stiffness. However, one previous study suggested that this may not be the only cause. We pointed out three new causes. The first is the anisotropy of the performance of the nailed joint due to the fiber direction. The Murakami equation assumes that the performance of the nailed joint does not differ in the grain direction. However, additional rocket-type tests demonstrated that the stiffness perpendicular to the grain was approximately a half of that in the parallel to the grain. The second is the asymmetric deformation caused by the rotation of the wall body and the concomitant prior yielding of some joints. The Murakami equation assumes that the deformations of the nailed joints were point-symmetrical; however, the experimental results showed that the deformation of the nailed joints to the one side of the column loaded compressively and the sill was large. The elasto-plastic frame analysis revealed that this asymmetric deformation becomes more pronounced as the rotation of the wall body increases, and that the apparent stiffness is reduced by the prior yielding of those nailed joints. The third is the variation in the performance of the nailed joints. Using the same analytical model, a Monte Carlo simulation was performed considering the variation in the performance of the nailed joints. As a result, it was found that the higher the variability of the performance of the nailed joints, the lower the apparent stiffness. We modified Murakami’s equation to take these factors into account, and the results of the racking test were reevaluated. Consequently, the results of both tests were somewhat close to each other and the possibility that the results of rocket-type test could be applied to the design of the sheathed wall was presented.

We aim to apply the natural frequencies obtained from ambient vibration measurements to the following three points for traditional wooden buildings: simple seismic diagnoses, rapid assessment of the degree of damage, and verification of the analytical models of buildings. However, there are some problems in achieving each of them as follows:

1) A simple seismic diagnosis is to estimate the maximum response of a building to a postulated earthquake ground motion from the amplitude dependency of the natural frequency using the response spectrum method. If the amplitude dependency of natural frequency can be estimated using the natural frequency obtained from ambient vibration measurement, the maximum response of the building can be easily predicted. However, we had not obtained the amplitude dependency of natural frequency from the extremely minute deformation region related to the ambient vibration to the large deformation region related to the collapse, which is necessary for this purpose.

2) In the rapid assessment of the degree of damage, we focus on the fact that the natural frequency of a building, which is obtained by ambient vibration measurement, decreases after an earthquake occurs. The maximum deformation angle during an earthquake can be estimated from the rate of decrease in the natural frequency of the building, which is obtained from ambient vibration measurement. However, there were insufficient data on the rate of decrease.

3) The validity of the analytical model is verified by comparing the fundamental natural frequency that corresponds to the initial stiffness of the solid analytical model, which is usually prepared in detailed seismic diagnosis, with that obtained from ambient vibration measurement. In general, the natural frequencies of models are lower than those obtained from ambient vibration measurement, but the quantitative relationship has not been fully understood.

Based on the above background, in this study, we gained quantitative data that is essential for realizing the above purposes on five kinds of test specimens with different building components. The test specimens consisted of a common planar framework and various building components, such as dry mud wall panels and plasterboards. Two wooden frames were made for each type of test specimen, and these were connected by orthogonal beams so that they could stand on their own.

Three relationships were quantitatively clarified by combining ambient vibration measurements, vibration tests, and static loading tests: the amplitude dependency of the equivalent natural frequency, the maximum deformation angle dependency of the natural frequency in ambient vibration, and the relationship between the natural frequency that corresponds to the initial stiffness of analytical model and the natural frequency obtained from ambient vibration measurement. These results are essential to realizing the application methods: simple seismic diagnosis, rapid assessment of the degree of damage, and validation of the analytical model of the building, respectively. In addition, we proposed models based on previous studies for each relationship, which is useful to realize each of the application methods.

Exposed column-base had double flag type restoring force characteristics, and it strength, rotational rigidity & hysteresis were affected by the column axial force. That characteristics understand obtain from partial frame experiment. Moreover, the influence of its characteristics on steel structure seismic response examined by time history analysis of steel structure with rotational spring, that rotational spring had double flag type restoring force characteristics.

However, partial frame experiment was no agreement boundary condition of column-base in structure on ground motion, and rotational spring was no agreement influence of axial force. Therefore, seismic response & working stress of exposed column-base with steel structure included many uncertainty about building structural design.

The author discussed exposed column-base behavior and structure response on ground motion, that uses seismic response analysis results obtain from low-rise steel structure with model that can reproduce the column-base behavior.

In this paper, elucidate and estimate for exposed column-base mechanism and effective working stress, frame response. The following conclusions were drawn.

1. Exposed column-base around plastic deformation are affected by variable axial force caused shear force gap of beams of layer direction. As a results, yield element changes around of column-base in column-base strength ratio range from 0.8 to 1.2.

2.Exposed column-base around plastic deformation are unaffected by up-down acceleration of earthquake. On the other hand, gravity acceleration are very important consideration in its understand.

3. Exposed column-base had semi-rigid connect behavi　, if its strength over the column full-plastic strength.

4. A change in rotational rigidity change in variable axial force were few effect to frame response.

5. Shear force of anchor-bolts and shear-key occurs external column and internal column. And its values approximately equal yield shear strength of single anchor-bolt.

6. Maximum of base plate rotation evaluated method shown, obtain from maximum story drift angle and mechanics model of column with rotational spring.

In Steel Framed Housing (SFH), built-up compression members composed with light gauges are used for vertical frame of the shear wall, and the built-up compression member is composed by two light gauges and interconnected by self-drilling screws. When a destructive earthquake attacks the SFH, the ultimate strength of the shear wall is determined by the peeling off the structural plywood. After the peeling off the structural plywood, there is a possibility that flexural buckling occurs at the built-up compression member. The occurrence of the flexural buckling leads to the loss of vertical bearing sharply. Therefore, it is necessary to confirm the safety for the flexural buckling around the weak-axis.

The main purpose of this study is to analyze the flexural buckling behavior of light gauge built-up compression members jointed by self-drilling screws based on the energy method. A non-conventional mechanical model that simulates the flexural buckling behavior of the built-up member was proposed, and the contradictions of Bleich's model was described. A simple design formula that directly reflects the built-up member's parameters was derived based on the proposed model. Furthermore, the required stiffening rigidity and the required number of self-drilling screws are proposed to ensure flexural buckling as a unit member.

From this research, the following are found.

1) A rotational spring's effect having a spring rigidity ratio γ_ir to rotation in the longitudinal-direction on the compression member was examined. As γ_ir increases, the flexural buckling strength increases from Euler's buckling strength, and the flexural buckling strength reaches a convergent value at about γ_ir = 10³. The flexural buckling strength and flexural buckling mode at this convergent value are equal to the sway buckling with a buckling length of L/n and fixed support at one fixed end at the other end and free support for horizontal movement.

2) The batten plate's restraining effect on the built-up member is obtained by the batten plate's rotation, including the local deformation of the plate around the batten plate, the shear deformation, and the axial deformation of the batten plate. These were replaced with rotational springs, shear springs, and shaft springs, respectively. Shear springs can be replaced with apparent rotational springs, and the apparent rotational rigidity is exceptionally high compared to rotational spring rigidity.

3) A non-conventional mechanical model of the flexural buckling mode C in which the flexural buckling occurs around the centroid axis of the chord due to rotation and shear deformation of the batten plates is proposed. From the numerical analyses based on the energy method, design formulae for the flexural buckling strength and the effective length factor are proposed. Furthermore, a design method based on the effective slenderness ratio is proposed.

4) The required number of panels and the required number of self-drilling screws for the light gauge built-up compression member ensure flexural buckling as one member. The total number of required self-drilling screws can be calculated from Eq. 39. Based on this required number of panels, the required number of self-drilling screws can be calculated as n_b(n+1). Besides, in the range of the built-up compression members used as the vertical frame material of SFH, the built-up compression members can be designed as a unit member by using DNH4819 as the batten plate and setting the number of panels to 2.

In steel roof gymnasiums with RC substructures, out-of-plane response of cantilevered RC walls are predominant during seismic responses, which triggers sequential damages of structural or non-structural components. Detailed regulations have been not included in the current Japanese building code yet even though Gymnasium is used as a shelter in disaster. In this paper, a design procedure for out-of-plane response control of a cantilevered RC wall connected by roller supports to metal spatial roof was proposed. While many researchers proposed response evaluation methods for cantilevered RC walls, those methods are too complicated to be implemented in the actual design process. Therefore, the proposed design procedure is carefully formulated based on Japanese structural engineer’s practice. The design equation is derived from both equivalent linear approach simulating damping effect and continuum mechanics where a cantilevered RC wall is modeled as single beam or single plate. In Section 2, the detailed design procedure (the scope, the design criteria, the seismic load and the actual design process) is carefully explained for engineers. In Section 3, the derivation process from the response evaluation to the design equations is explained. Both single beam and single plate are modeled as secant bending stiffness of RC members yielding. In Section 4, the response evaluation values are compared with the numerical simulation results of the actual damage gymnasia. In Section 5, the response evaluation values are compared with a shake table testing of 1/2.5-scaled model of school gymnasium. In summary, the following results were obtained:

1) Both of single beam model and single plate model are more accurate than simplest formulas of cantilevered beam against non-linear response history analysis results of the actual damaged gymnasia. The single beam model is suitable for a cantilevered RC wall where span is long and the bending stiffness of beam is negligible. The single plate model is suitable for a cantilevered RC wall where span is short and the bending stiffness of beam is not negligible. Threshold value is 0.409 of the coefficient q determined by both width-to-height ratio L/h_c and bending stiffness ratio D_y /D_x .

2) The static stress analysis results of numerical frame model composed of only the cantilevered RC wall was corresponding to the non-linear response history analysis results of the damaged gymnasia with no friction dampers.

3) The response evaluation results of the single beam model was corresponding with error 10mm to 15mm to the shake table testing results.

4) The response evaluation results of the simplest static formula of a cantilevered beam were too conservative compared with the others, and may produce uneconomical design.

A moment-resisting frame used for the seismic force-resisting system will resist the lateral forces by the columns' flexural manner. Flexural deformation of the column will cause a bending moment; the column in this system will be subjected to axial force with bending moment (i.e., combined loading condition). In the ultimate limit state design, the column's structural safety should also be confirmed under this condition.

In this paper, the column testing under compressive axial force with bending moment was conducted based on this background. A shallow H-shaped section was selected as a specimen; the bending moment was applied around the major axis. Therefore, local buckling, out-of-plane instability caused by lateral-torsional deformation, or in-plane instability due to Pδ effects will determine the column's ultimate limit state. Monotonic and cyclic loading patterns were used in the testing to understand structural behaviors; a direct comparison between the difference of loading sequences was also made. The strength, plastic deformation performance, and ultimate limit state were evaluated from the test results.

From the testing, following results were found.

1) Under monotonic loading, two ultimate limit states were observed. One was the strength degradation due to the out-of-plane deformation that was caused by the lateral-torsional deformation. The other was the strength degradation due to the Pδ effect caused by in-plane deformation with compressive axial force. The ultimate limit state determined by in-plane behavior was observed in the specimen where the axial force was relatively high, and the member was relatively stocky. Under cyclic loading, all specimens' ultimate limit state was out-of-plane deformation due to lateral-torsional deformation, and the strength degraded. In this testing, the ultimate limit state dominated by local buckling around the loading point was not observed.

2) Some of the specimens conducted in the testing did not fulfill the AIJ recommendation requirements. However, the column's strength (i.e., full plastic moment and maximum bending moment obtained from the testing) achieved the theoretical full plastic moment considering the existing axial force.

3) The plastic deformation performances stipulated in the AIJ recommendation were achieved when the column fulfilled the ultimate limit state's design requirements.

4) The design index weighted by the sensitivity of lateral-torsional buckling was used to evaluate plastic deformation performances. The weighted design index showed a high correlation with the column's plastic deformation performances; quantitative formulas that can evaluate on the safe side were proposed. Moreover, the plastic deformation performances under cyclic loading were shown with the relationships between ductility that can be defined from the monotonic loading.

The columns' design index weighted by the sensitivity of lateral-torsional buckling was used to evaluate plastic deformation performances. However, the lateral-torsional buckling's sensitivity was evaluated by the lateral slenderness ratio without considering the axial force in the column, and the cross-section used in the regression analysis is limited. These issues will be studied in future research.

1. Introduction

The objective of this study is to examine the relations between the simple superposed strength and generalized superposed strength of CFT cross sections subjected to axial load and flexural moment, regarding the allowable stress design. AIJ CFT Recommendations specify the simple superposed strength for calculating the allowable strength of CFT sections, whereas reference 4) it is supposed to use the generalized superposed strength. About the allowable strength, the differences between two superposed strengths are not clarified, and the calculation method of generalized superposed strength has not been shown explicitly.

2. Analytical work

In addition to the simple superposed strength, the equations to calculate the generalized superposed strength is presented. The equations to evaluate the generalized superposed strength for the square and circular CFT sections are Eqs. (29) ~ (33) and (34) ~ (38), respectively. It is shown that the differences between two superposed strengths appear in low axial load level, that is the limiting axial loads are obtained by Eqs. (21) and (26) for square and circular section, respectively.

3. Results and discussions

The comparison between two superposed strengths was carried out taking the width (diameter) -to-thickness ratio and strengths of materials as the analytical parameters. Moment-axial load relations for the allowable strength are shown in Figs. 5 and 6. The differences between the generalized superposed strength and simple superposed strength are shown in Figs. 7 and 9, and the maximum differences are shown in Figs. 8 and 10. It is observed that the difference becomes large when the width (diameter) -to thickness ratio and the allowable stress of concrete is large and the allowable stress of steel is small. The maximum differences can be estimated by the Eqs. (39) and (40).

4. Conclusions

The conclusions derived from this study are as follows:

1) The equations to evaluate the generalized superposed strength for the square and circular CFT sections are presented as the Eqs. (29) ~(33) and (34) ~ (38), respectively.

2) The differences between two superposed strengths appear in low axial load level. The limiting axial loads are obtained by Eq. (21) and (26)for square and circular section, respectively.

3) The maximum differences are estimated by the Eqs. (39) and (40).