We constructed the full-scale specimens with the surface coating method of the lithium nitrite-containing polymer modified cement mortar. The test specimens were exposed to the Okinawa coastal area for 27 years; we evaluated carbonation suppression effect and salt damage suppression effect. Furthermore, using the diffusion equation proposed by the authors, the osmotic diffusivity of nitrite ion, lithium ion, and chloride ion was verified by the measured values in the 27th year, and the following findings were obtained.

　(1) The surface coating method suppressed the progress of carbonation of the concrete for 27 years.

　(2) The surface coating method suppressed the penetration of airborne salt into the concrete for 27 years.

　(3) The surface coating method for the lithium nitrite-containing polymer modified cement mortar had a high balance with respect to the initial value of nitrite ion, and the added nitrite ion was retained for 27 years.

　(4) Nitrite ion amount to chloride ion content of around reinforcing bars after 27 years, it was confirmed to be sufficient nitrite ion amount which exhibits corrosion inhibition of reinforcing bars.

　(5) In the surface coating method for lithium nitrite-containing polymer cement, the amount of soluble lithium ions was 66% of the total amount of lithium ions. In addition, the balance of total lithium ions showed a high value of 97%.

　(6) As a result of the diffusion simulation of nitrite ion, the outflow of nitrite ion to the outside is small and the diffusion in the mortar is slow, so it stayed in the mortar for a long time and could continuously supply the nitrite ion to the inside of the concrete.

　(7) As a result of the simulation of total lithium ions, the lithium ions are less eluted from the lithium nitrite-containing mortar to the outside and diffused slowly in the mortar, so that the lithium ions can be retained for a long period of time. However, the diffusion coefficient of the concrete inside of the lithium-ion is a 1/19 of nitrite ion, became the penetration difficult result.

　(8) As a result of the diffusion simulation of chloride ions, the diffusion coefficient of the lithium nitrite-containing polymer cement modified mortar and the paste was small, and the salt permeation inhibitory effect was confirmed.

　(9) The proposed diffusion equation verified that the lithium nitrite-containing polymer modified cement mortar and paste could be evaluated for the penetration and diffusion of nitrite, lithium and chloride ions in the evaluation of the measured values in the 27th year.

　(10) A 100-year simulation was performed for column 1 using the coefficients obtained by the diffusion equation. As a result, the molar ratio of the nitrite ion to the soluble chloride ion was 1.19 to 1.39 in the near of the reinforcing bar (20 to 50 mm), which was the molar ratio having the effect of suppressing the corrosion of the reinforcing bar. The molar ratio of the nitrite ion to the total chloride ion near the reinforcing bar (20 to 50 mm) was 0.63 to 0.74, which exceeds 0.6, which is said to have a corrosion suppressing effect, in the simulation 75 years later.

　In several previous studies tilt motions of big earthquakes were estimated using some acceleration records. The ground deformation is sometimes generated after the strong shaking accompanied with the liquefaction. Therefore, in this study tilt deformation both during and after the strong shaking using DC offsets of 27 strong motion records of big earthquakes and weak motions of the other earthquakes observed at the same K-NET and KiK-net stations. During most of the 27 strong motions, the possibility of the liquefaction, the increase of the excess pore water pressure or the negative dilatancy was pointed out or extremely large ground motions were observed.

　The tilt angle is proportional to DC offsets of acceleration records of horizontal components and the tilt direction in horizontal plane is arctangent of the ratio of DC offsets of two horizontal components if DC offsets are caused by only the ground tilt. Since DC offsets are also caused by the accelerometer characteristic, the DC offsets for 27 strong motion records of big earthquakes are defined as the difference between DC offsets in last 5 s and those in the first 5 s of observed records. For the other records the DC offsets are defined as the difference between DC offsets in the first 5 s and those in the first 5 s of the strong motion records of the big earthquakes at the same stations. The tilt estimated from DC offsets at HKD086 (Chokubetsu) where liquefaction occurred during the 2003 Tokachi-oki earthquake is the largest (36 cm/s²). The tilt and its direction estimated from DC offsets in this study agree well with the deformation observed by the site investigation by NIED after the main shock. Although remarkable spiky acceleration records suggesting the effects of cyclic mobility were observed at NIG018 (Kashiwazaki) during the 2007 Niigata-ken Chuetsu-oki earthquake, it was confirmed by the site investigation by NIED that the accelerometer kept in a horizontal position after the earthquake. The tilt estimated from DC offsets there is confirmed to be zero. DC offsets at MYG013 (Sendai), IBR014 (Tsuchiura) and CHB024 (Inage) during the 2011 Tohoku earthquake and NIG019 (Ojiya) during the 2004 Niigata-ken Chuetsu earthquake were larger than 5 cm/s² and changed within one day after the main shocks. The acceleration records at the four stations have slight spiky pulses. Since the liquefaction or the increase of the excess pore water pressure were pointed out for these records by previous studies, the tilt was thought to be generated by these effects. On the other hand, DC offset at CHB008 (Urayasu) where it was pointed out that liquefaction did not occur during the 2011 Tohoku earthquake is less than 5 cm/s² and does not change after the main shock. DC offset at TTRH02 (Hino) during the 2000 Tottori-ken Seibu earthquake is the second largest (13 cm/s²) but does not change after the main shock. DC offsets at IBUH01 (Oiwake) and HKD128 (Hayakita) during the 2018 Hokkaido eastern Iburi earthquake are about 5 cm/s² and do not change after the main shock. These results are consistent with the interpretation of generation of negative dilatancy of unsaturated soil at these three stations during the main shocks. This study suggests that DC offsets of strong motion records would be useful to one of indices to identify the ground tilt.

　One of the ways to mitigate earthquake damage due to suspended ceiling collapse is to improve earthquake-resistant performance of the ceilings. In E-Defense, shake table tests were conducted for a structural frame assuming a school gymnasium with seismic ceilings designed in accordance with the technical standards. The experimental results showed that the specimen had enough earthquake-resistance performance for the assumed seismic excitations. However, in this experiment, it had not been clarified how several seismic countermeasures applied to the ceilings work under seismic excitation. In other words, although the seismic performance had been verified, it was not clear how the countermeasures work to prevent the ceilings from damage. Therefore, it is necessary to evaluate function and effectiveness of the countermeasures in detail.

　In this study, we conducted seismic response analyses of gymnasiums with different earthquake-resistance countermeasures to investigate effectiveness of three types of countermeasures, that is, seismic braces, clearance and reinforced joint metals. The finite element method incorporating the Adaptively Shifted Integration (ASI)-Gauss technique were used to simulate suspended ceiling collapse. In the previous paper, it had been confirmed that the proposed simulation method can accurately reproduce behavior and collapse of non-resistant suspended ceilings.

　Here, firstly, we validated the numerical model of earthquake-resistant ceilings through reproduction simulation for the shake table test of the specimen with earthquake-resistant ceilings introducing all three countermeasures. As a result, detachment of joint metals and collapse of ceilings were not observed at all as in the experiment. Also, response acceleration and displacement were in good agreement with the experimental results.

　Secondly, we investigated the effectiveness of each countermeasure. In the case with only seismic braces, ceilings collapsed in larger area than without any countermeasures. That was because response acceleration increased as the braces stiffen the structure. According to the result in the case only with clearance, ceilings collapsed in a similar way as the non-resistant ceilings, though the ceiling collapse near the walls due to collisions between the ceilings and the walls was observed only in this case. In the case only with the reinforced joint metals, only slight damage occurred near the ceiling top, and a proposed detachment risk index of clips significantly reduced in the whole area. Also, it was confirmed that the case installing both seismic braces and reinforced joint metals had almost the same seismic performance as the case with all three countermeasures.

　Hysteretic dampers have been widely used as effective passive dampers installed at interstories since they are inexpensive compared with other types of passive dampers. It is well known that added stiffness of hysteretic dampers increases floor acceleration responses. However, they are effective for pulse-like ground motions with sudden input and short duration.

　Problems of optimal design of viscous dampers have been tackled by many researchers. However, the research on the optimal design of hysteretic dampers is quite limited. Optimization of hysteretic dampers in time-domain seems difficult because drastic stiffness change resulting from the insert and remove of hysteretic dampers changes the natural period of structures irregularly and uncontinuously, and diverse restoring-force characteristics of hysteretic dampers make the structural responses complicated. Some researchers applied equivalent linearization techniques or complex-stiffness formulations to the expression of hysteretic characteristics of hysteretic dampers. However, these approaches tend to overestimate or underestimate the energy dissipating performances of hysteretic dampers. For these reasons, sensitivity-based design approaches with above-mentioned response simulation procedures seem to be difficult for its implementation. Therefore, an approach dealing with elastic-plastic responses directly in time-domain and avoiding the unstable response sensitivity evaluation is strongly desired to provide designs with high reliability.

　Compared with the above-mentioned sensitivity-based approaches, the optimization methods using metaheuristics are expected to be effective for the smart treatment of problems of optimal hysteretic damper design. However, it is also true that these methods require much computational effort.

　The purpose of this paper is to propose a new optimal design method of hysteretic dampers using a hybrid method of the real-coded genetic algorithm (GA) and local search. In the application of the crossover procedure in the real-coded GA, the sum of damper damping coefficients is kept constant. This constraint enables an efficient search of the solution. In addition, in the real-coded GA, design variable vectors are directly treated to create new individuals and the binary expression is not required.

　It should also be remarked that elastic-plastic MDOF structures are treated in this paper. In most researches on optimal design of dampers, elastic structures are treated because the main objective of the introduction of passive dampers is to reduce the earthquake response of main structures to the elastic range. However, an optimal damper designed under a specified-level ground motion may not be necessarily effective for larger-level ground motions inducing elastic-plastic responses unintentionally in main structures. For this reason, elastic-plastic structures are treated in the application of the optimization procedure in this paper.

　We have developed the new hybrid structure of CLT infill and steel frame for middle-rise and high-rise buildings. This structural system can achieve the high structural potential of the CLT panel by holding around the CLT panel with steel frame. Steel frame can support sustained load of a high-rise building without CLT panels and can build long-span beams reasonably. Compression stress of CLT seismic panel can be transmitted to the upper and bottom steel beams through high strength mortal layer, and the steel beams can secure high shear strength as boundary beams. Shear of the CLT panel is transmitted by drift pined joints with insert-steel gusset plate. And tension stress balanced with compression stress of CLT is supported by steel tie bar.

　To clarify the performance of this structural system, we have conducted the structural experiment series with seven test frames in 1/2 scale. The result of the structural experiment series provided the following findings.

　Firstly, all of the CLT specimens reached compressive or shear failure, and performed to their full structural potential. Because of that, it has been found that it is possible to perform structural design that takes advantage of full CLT performance. The structural performance has increased up to max. 3.48 times for the horizontal stiffness and up to max. 2.67 times for the horizontal bearing capacity, by inserting CLT panels into the streel frames.

　All CLT panel showed slip type restoring force characteristic. In case of shear failure, the decreases in shear force were caused at story deformation angle greater than 1/71 radian. In case of compression failure, the decreases of shear force were gradual, and their deformation performances were excellent.

　It has been found by the experiment series that these failure modes of CLT depend on aspect ratio (H/L) of CLT, and in case of low H/L, shear failure tends to occur. The shear strength and elastic shear modulus of test frame CLTs in shear failure could be reduced to about 70% of the material shear test.

　When the story deformations of the CLTs are separated into the deformation components of shear deformation, slip displacement of the joints, and rotational deformation of the CLTs, the rotational deformations of the CLTs are the largest. And the rotational deformation ratio of story deformation tends to increase by H/L of CLT

　Based on the above findings, a subsequent paper will show the detail study on compressive stress transfer in the upper and bottom surfaces of CLT with analytical studies, and propose structural design and stress analysis method of the structural system.

1. Introduction

　It is well known that panel zones at beam-column joints of steel moment-resisting frames may yield under strong ground motion as well as beams and columns. It has been mentioned that the effect of shear force is dominant in the elasto-plastic behavior of panel zones, but as the panel aspect ratio, that is ratio between height and diameter of panel, increases, the effect of bending moment cannot be ignored. The main objective of this paper is to clarify the effect of aspect ratio on elasto-plastic behavior, e.g, elastic stiffness, full plastic strength and plastic deformation capacity, of panel zones with circular hollow sections.

2. Cyclic loading test of single panel specimen

　To reveal elasto-plastic behavior of circular hollow section panel zones, cyclic loading test of single panel zones with a large aspect ratio were conducted. The ultimate state of the panel zones was either shear buckling, local buckling due to bending moment, or ductile crack at the surface of panel flange. The elastic stiffnesses of single panel zones agree well with the results by Eq. (3), which considers both shear deformations and flexural deformations.

3. Finite element analysis for reproducing test results

　To examine in detail the test results in Chapter 2 and validate the finite element analysis (FEA) described in Chapter 4, reproduction FEA was performed. The analysis results correspond well with the test results and the validity of the FEA model is confirmed. The analysis results show that the presence of the backing bar affects initiation of ductile crack at the surface of panel flange observed during the cyclic loading test.

4. Parametric study by finite element analysis

　FEA was conducted on a wider range of parameters than experiments to confirm the influence of parameters, including aspect ratio, on the full plastic strength and plastic deformation capacity due to buckling of single circular cross-section panel zones. The analysis results show that the effect of the diameter-to-thickness ratio on the full plastic strength is quite small, while the full plastic strength decreases as the aspect ratio rises. Moreover, it is found that the yielding part of the entire panel zone varies with the aspect ratio and axial force ratio when the panel reaches the full plastic strength. In addition, the analysis results show that in the case those panel zones reaches the ultimate state by local buckling due to bending moment, the plastic deformation capacity tends to decrease as the aspect ratio rises, while in the case of shear buckling, the plastic deformation capacity is minimized around the aspect ratio of 1.4.

5. Investigation of calculating method of the full-plastic strength of circular hollow section panel zones

　The validity of the previous calculation method^{2), 9), 10)} of full-plastic strength of circular hollow section panel zones with large aspect ratio was examined based on the results of FEA. The calculation results in Ref.9) agreed well with FEA results as shown in Fig.17.

6. Conclusions

　This paper investigates the effect of aspect ratio on elastic stiffness, full plastic strength and plastic deformation capacity of panel zones with circular hollow sections. As a result, it is confirmed that the influence of the aspect ratio appears for all of the above properties.

　The purpose of this research is to drive the evaluation formula of coupled local buckling strength of wide flange shapes under uniform bending, which is a closed-form expression. The Local buckling of I-shaped members has been investigated by many researchers. Furthermore, its maximum strength, deformation capacity, and buckling deflection are clarified by experimental testings. At the same time, the evaluation formulae were proposed theoretically. However, most formulae were not able to explain the local buckling behavior of wide flange shapes because the local buckling behavior of the wide flange shape is complicated. To solve this problem, Prof. Ikarashi proposed a displacement function using a Fourier series to drive an evaluation formula based on the energy method. By using the Fourier series, the buckling deflection can be described even if combined stresses act on wide flange shapes. In this paper, the evaluation formula is proposed based on the energy method, as well as Prof. Ikarashi did. The difference between this research and Prof. Ikarashi's research is the displacement function. In this paper, the exponentiation of the trigonometric function is used as a particular displacement function of the buckling deflection. Only two terms of the trigonometric function can describe the buckling deflection of wide flange shapes under uniform bending because the function is fast-converging compared to the Fourier function. Additionally, the function can describe elastic web-flange interaction amongst the elements comprising the cross-section. As a result, the proposed closed-form evaluation formula of wide flange shapes is proposed. To verify the reliability and the effectiveness of the proposed formula, modal analysis based on the finite element method (FEM) is conducted. The accuracy of the evaluation was shown by comparing it to FEM results.

　From this research, the following are found.

1)　The buckling deflection of wide flange shapes under uniform bending can be described with a linear combination of two terms, the exponentiation of the trigonometric function expressing the deflection of the simple supported web and the exponentiation of the trigonometric function expressing the deflection of the clumped supported web. And the trigonometric functions are totally different from the shapes under compreession.

2)　The web buckling coefficient and the flange buckling coefficient ratio have a linear relationship with the coordinate axis of the width-to-thickness ratio of the web and flange plate element. This linear relationship changes according to the section aspect ratio. The local buckling properties of the wide flange shapes were classified into four types by using the buckling coefficient as the fixed support on the four sides subjected to uniform bending and the buckling coefficient as the simple support on the four sides as boundaries. Even under compression, it can be classified into four types, however, the range is different from under uniform bending.

3)　Because the proposed buckling displacement function of the web has fast convergence and can be described with two exponentiation of the trigonometric functions, the evaluation formula of wide flange shapes under uniform bending can be derived as a closed-form expression. The average value of the finite element elastic eigenvalue analysis results against the elastic local buckling strength obtained from the proposed formula is 0.9878 , the standard deviation is 0.009095, and the maximum error is 4.891 %.

　It cannot be overstated that the accurate prediction of the temperature rise of a structural member is of primary importance in the analytical study of the fire resistance of structural components. The configuration factor of each surface needs to be determined for the calculation of the radiant heat transfer of a member with complex geometry, where the radiation received from the fire flame is different in each part. The configuration factors for a web or flange surface can be easily calculated using the formulae found in design guidelines for the fire resistance of steel structures. However, the formulae are not applicable to an inner surface of the opening of the perforated steel beam, since the relationship with the radiating surface is different from that of ordinary web surfaces. As far as the authors know, any formulae for calculating the configuration factor of the inner surface is not found in the exiting literature. If one uses the configuration factor for web instead, it may lead to a decrease in accuracy of temperature estimation of perforated steel beams during fire.

　A method for accurately calculating the configuration factor of an inner surface of opening of protected steel cellular beams is proposed in this paper. In deriving the equations, the radiant area from the fire flame to be received by each part of the inner surface of the circular hole when it is shielded only by the protected beam itself was accurately estimated. Then the situation where a part of the radiant area was shielded by an object including such as a web stiffener, an orthogonal beam connection, a column–beam panel zone, a compartment wall, or a furnace wall was also considered. The effectiveness of the proposed equations is verified by comparing steel temperatures of finite element heat transfer analysis using the proposed configuration factors with the results of loaded heating tests of perforated steel beams, and with the results of analysis in which the configuration factors of the inner face are set to the same value as that of steel web. The findings of this paper are as follows:

　●　Formulae for accurately calculating the configuration factor of an inner surface of the protected steel cellular beam is presented, considering the shielding provided by the beam itself. In addition, the formulae that consider shielding by such as web stiffeners, orthogonal beam connection, compartment walls, furnace walls, etc. are also derived.

　●　Numerical examples show that the configuration factor of the inner surface is the smallest at the top (or bottom) of the hole and the largest at both ends of the hole when only the shielding of the beam itself is considered.

　●　The configuration factor of the inner surface is considerably smaller than that of the web surface, and it is appropriate to use the factor calculated by the formula presented in this paper for accurate heat transfer analyses.

　●　Finite element heat transfer analyses using the configuration factors calculated by the proposed equation reproduced the steel temperature distribution of protected steel cellular beams, which was measured in loaded heating tests. The accuracy of the estimated steel temperatures was better in the analysis using proposed configuration factors than the analysis that used configuration factor of web for inner surface of the opening.