Porous concretes have been used as various construction materials. However, the mechanical properties of the porous concretes are lower than that of the ordinary concrete because of its porous structure. The several techniques to improve the mechanical properties have been developed by many researchers for applying the porous concretes as structural members. The static modulus of elasticity is an important factor for such applications of the porous concretes.
 On the other hand, the authors have been proposed the mix design system of the porous concretes, and the estimating methods for compressive strength, flexural strength and flexural toughness of the porous concretes by applying the law of mixture. This paper deals with a method for estimating the static modulus of elasticity of porous concretes based on Hashin-Hansen's equation as the law of mixture for two-phase composite material.
 The porous concretes using cement mortars as a binder are prepared with the water cement ratios of 22.5, 25.0 and 30.0%, and the percentage of target voids of 10, 15, 20, 25, 30%. Porous concrete specimens are subjected to total voids test and the compression test including the static modulus of elasticity.
 The test results show that the correlation between the compressive strength, the static modulus of elasticity and the total voids of the porous concretes are recognized. Regardless of the water-cement ratio, the static modulus of elasticity of the porous concrete is decreased with an increase in the total voids. The estimated values of the static modulus of elasticity of the porous concrete calculated by the Hashin-Hansen's equation is considerably higher than the experimental values because the equation is not include the factor of the total voids introducing the reduction of the static modulus of elasticity.
 Therefore, the percentage of the total voids is an important factor to estimate the static modulus of elasticity of the porous concretes by applying the law of mixture. Namely, the porous concrete is the three-phase composite material consisted of the phases of matrix, aggregate and voids. To establish the correction coefficient of the voids, the experimental values of the static modulus of elasticity of the porous concretes are divided by the values calculated from the Hashin-Hansen's equation as the static modulus of elasticity of the voids-less porous concrete. The correction coefficient of the voids can be estimated by the function of the total voids. The equation multiplying Hashin-Hansen's equation by the correction coefficient of the voids is proposed to estimating the static modulus of elasticity of the porous concretes.
 The applicability of the proposed equation in this paper will be discussed in more detail because the equation is obtained by using the estimated value for the static modulus of elasticity of the coarse aggregate.

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 Strength correction values of concrete in structure (_mS_n) are necessary for inspections of compressive strength of concrete in structure using standard-cured specimens. _mS_n are determined by production of mock-up specimens for structural members. In the case of high strength concrete, the interior of concrete in structure gets very hot in the early stage. In the case of high strength concrete with a design strength below 60MPa, the influence of temperature conditions on _mS_n for each binder type has been clarified. Therefore, _mS_n for inspections may be set based on the result of experiment in the season (summer or winter) which _mS_n is expected to be largest. On the other hand, in the case of high strength concrete with a design strength over 60MPa, the influence of temperature conditions on _mS_n has not been clarified. Therefore, experiments in several seasons are necessary for setting _mS_n for inspections. For the purpose of resolution of such a problem, in this study, the tendency of the influence of temperature conditions on _mS_n for high strength concrete with a design strength over 60MPa was investigated.
 31 experiments were conducted with ready-mixed concrete plants. In all experiments, the binder for high strength concrete containing silica fume was used. Crushed stones and sands (andesite, hard sandstone, limestone) and natural sands were used as aggregates. Range of water-binder ratio of concrete was 0.14-0.38. Core specimens were collected from mock-up columns with a cross section of 950 × 950 mm or 1000 × 1000 mm. At the age of 56 days, tests for compressive strength with standard-cured specimens and core specimens were conducted to determine the differences between them (₅₆S₅₆).
 In this study, the influence of temperature conditions on _mS_n was evaluated based on the ratio of ₅₆S₅₆ to compressive strength of standard-cured specimen (Sxy). In the case of using andesite crushed stones, Sxy of winter tended to be larger than Sxy of summer. On the other hand, in the case of using the other crushed stones (hard sandstone or limestone), the differences between Sxy of summer and Sxy of winter were small comparatively. In addition, in the case of using limestone crushed sands, Sxy tended to be large. However, rough tendency of the influence of temperature conditions on _mS_n can consider to be evaluated based on coarse aggregate types, because the influence of fine aggregate type on the relative relationship between Sxy of summer and Sxy of winter was small.
 Such the influence of temperature conditions on _mS_n was evaluated quantatively by dividing into two factors (reaction of binder, coarse aggregate type). As a result, the same tendency as previous findings for the both elements was obtained. The influence of binder could be evaluated based on binder-water ratio and maximum temperature. The influence of coarse aggregate could be evaluated based on the amount of temperature change.

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 The 2011 off the Pacific coast of Tohoku Earthquake of Mw9.0 produced many strong motion records, owing to dense strong motion observation networks in Japan. About three thousands records are collected and complied. The records provide a unique opportunity to examine site amplifications in strong shaking level. The available site characteristics data for the records, however, are limited. The soil profile data are available at about 100 sites. For the other data, the available site information is geomorphologic classification from the nation-wide digital map, but it is rather crude for the site characterization. To strengthen the site characteristics data, microtremor measurements are conducted at about 500 strong motion sites in the high seismic intensity zone, as shown in Fig. 1. In the measurement, we use the system whose overall response is almost constant with ground velocity up to 2 seconds, as shown in Fig. 2. The H/V spectral ratios of microtremors for different NEHRP site classes (Table 1) are shown in Fig. 3. The following criteria are determined for site classification from the H/V spectral ratio: 1) the site having the H/V spectral ratio with higher amplitudes at periods 0.6 to 1.2 sec. with respect to those at periods 0.1 to 0.3 sec. is the class E (Fig. 4), 2) the site having the H/V spectral ratio constant with periods is the class B (Fig. 5), and 3) the sites having the H/V spectral ratios with larger and smaller amplitudes at periods of 0.3 to 0.8 sec. with respect to those at periods 0.1 to 0.2 sec. are the classes D and C, respectively, and the site having the intermediate amplitude is the class C or D referring the geomorphologic information (Fig. 6). For the sites where the site class is determined from the velocity profile data, the accuracy of the estimated site class is checked. The overall accuracy is 77 % by the proposed method as shown in Table 2, whereas the accuracy of estimations from the geomorphologic information is 51 % as shown in Table 3. By using the criteria for site classification, the target strong motion sites are classified into 30 class B sites, 153 class C sites, 206 class D sites and 77 class E sites, as shown in Fig. 7. Site effects on the strong motion records are preliminarily discussed from the average spectra for site classes B, C, D and E. The average spectrum with standard deviation for each class is shown in Fig. 8. The velocity response spectra tend to be constant with period at class B. The spectral amplitudes become larger at site classes with slower V_S30. At site class E, the amplitudes tend to be larger at around 1 second. As shown in Table 3, the average and standard deviation of the peak horizontal accelerations at class B are 0.45 g and 0.19 g, respectively. The small deviation suggests that the shaking level inputted to the bedrock at the sites may not have large difference. Therefore, the ratio of the average spectrum at class C, D or E with respect to that at class B is considered to be an approximate of site amplification. As shown in Fig. 9, the amplification of site classes C to B is almost one, but those of site classes D and E to B are larger at longer periods and smaller at shorter periods. The amplification is compared with the site amplification derived from weak motion records. The difference in both amplifications indicates effects of nonlinear soil response.

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 In this paper, an improved ESO (Evolutionary Structural Optimization) method for the topology optimization of 3D structures is proposed. In the proposed method, the idea of BESO method^{6, 7)} and the idea of extended ESO method^{8, 9)} are combined. In this method, the design domain is divided in same eight-node brick elements (voxels)¹⁴⁾, and in the optimization process, for solid element, it will be removed if the strain energy is less than the threshold value. This threshold value is obtained from the equation proposed in extended ESO^{8, 9)}. This equation consists of the mean value of sensitivity number and the average deviation of sensitivity number with a control parameter. In the proposed method, the evolutionary volume ratio (reduction ratio) is given as input data, and this control parameter is determined automatically in the program so as to satisfy the given reduction ratio approximately.
 Three numerical examples have been shown in order to demonstrate the effectiveness of the proposed method for 3D structures. It was found from the results that the proposed method had the following advantages.
 (1) The parameters of optimization process are less than BESO, CA-ESO, and SIMP method. There are only two parameters, that is the evolutionary volume ratio (reduction ratio) and the scale parameter r_min in the filter scheme. Therefore, it is not necessary to do the preliminary analysis for setting the parameters. In the three examples shown in this paper, the evolutionary volume ratio λ is all 0.1, and the scale parameter r_min is all 2l_X (l_X : element's length of X direction).
 (2) The number of steps in the optimization process is very small compared with BESO, CA-ESO and SIMP method. The number of steps is 16 in example 1 (refer to Fig. 5), 22 in example 2 (refer to Fig. 9), and 20 in example 3 (refer to Fig. 13). Therefore, the computational efficiency is much better than the other methods.
 (3) Simple designs can be obtained by the proposed method. The topologies and compliance ratios by the proposed method are similar to ones obtained by SIMP and CA-ESO method. Please refer to Fig. 4 and Fig. 6 for example 1, refer to Fig. 8 and Fig. 10 for example 2, and refer to Fig. 12 and Fig. 14 for example 3.
 It can be seen that though the proposed method is one directional method which does not have additional process of elements, the resultant topologies have sufficient performance to give a hint to the architectural design.

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 This paper focuses on the elasto-plastic behavior on static responses and dynamic responses for plane lattice structures, which are considered as a beam type structure. The purpose is to make clear the relationship between seismic responses and static responses such as load displacement relationships, and to estimate allowable seismic levels with the information of static elasto-plastic behaviors. Two portal frames and column or beam models are treated, as shown in Fig. 1. The energy equilibrium is expressed as Eqn. 2 in static elasto-plastic behaviors. The right term E^F is equal to the energy done by load and may be defined as a static absorbed energy of structures. In this paper, each energy is expressed as an equivalent velocity as Eqn. 3. The maximum value of E^F may be an allowable amount of input energy, for instances, by seismic loads. The relationships between each energy and displacements are shown in Fig. 5. The equivalent velocity of E^F is expressed as a dash and dotted line. The response curves are almost equal although the loading shapes are different as shown in Fig. 3. The fact may show that the differences between static uniform load and quasi-static seismic load do not affect the energy responses, and that the estimation with input energy may not be affected by the shape of loading.
 Secondly, the elasto-plastic behavior on dynamic responses is investigated under seismic loads. The relationships between maximum input acceleration and strain energy of each model are shown in Figs. 11, 16 and 21. The curves of 3 parameters are drawn in each figure. The effect of static safety coefficients v is made clear with the curves, to confirm the effect of vertical oscillations is larger than that of horizontal oscillations. In the three figures, the each curve shows the relationship of bi-linear type. In the range after yielding, the maximum input energies at the limit state are compared as shown in Figs. 22 - 24, which show the ratio of dynamic responses against static ones. The static safety coefficient v is smaller, and then the increasing ratio of dynamic responses is larger than static ones.
 In order to estimate allowable maximum input accelerations, the comparisons between elasto-plastic behavior of dynamic responses as Fig. 25 and that of static response as Fig. 26 are shown in Fig. 27. The dynamic elasto-plastic property q represents the decreasing properties of plastic range against elastic range in the relationships between maximum earthquake input acceleration and input strain energy. The static elasto-plastic property j represents the relationship of two slopes in the static elasto-plastic behavior. The dynamic property q is smaller than the static property j under vertical oscillations and is almost equal to each other under horizontal oscillations. The preceding considerations are carried out under additional seismic waves of Table 6 and the additional models¹⁰⁾. The obtained results are shown in Fig. 28. The results show the same tendency at each seismic loads. The dash and dotted line in Fig. 28 could be presented to estimate the allowable maximum earthquake input acceleration.
 The conclusions are follows in the present study.
 (1) The relationships between the static absorbed energy and displacements are not affected by the loading shape. It may be able to estimate the response of structures with an index of potential energy.
 (2) The fact is confirmed that the allowable maximum earthquake input accelerations are affected with the self-weight under vertical oscillations more than horizontal oscillations.
 (3) In comparing the dynamic property q and the static property j, the dash and dotted line in Fig. 28 could be presented to estimate the allowable maximum earthquake acceleration with the static elasto-plastic behaviors for beam type structures.

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 In early days as in the 1940s, a partial cylindrical concrete shell (long shell) was frequently used as a barrel roof structure. Many detailed investigations have been carried out, since the advent of ASCE Manuals of Engineering Practice in 1952.
 As a result, it has been found difficult to realize a strict membrane stress field in the barrel-roof-type shell, because the number of stress unknowns is unfit for the number of available boundary conditions.

 In a previous paper, the present author showed that a shell segment cut out from a circular cylinder with particular shapes and boundaries was able to satisfy the condition of membrane stress field. In this paper, a segment of partial circular cylinder is investigated, which is partitioned into three parts, by a pair of concave curves into the central thick shell zone with both fixed boundaries parallel to the generator, and two outer thin shell zones.
 The left half of the circular shell segment under consideration is taken to be the mirror image of the right half, or vice versa.

 Each of the left and right thin shell zones has shapes and boundaries that satisfy the requirement of a membrane stress state, in a way similar to the case in the previous paper. The central thick shell zone, on the other hand, behaves like an arch in which breadth and depth vary in the circular direction, keeping a constant cross-sectional area.

 It is noted that similarity exists with regard to the differential equations which relate displacement (denoted as V) in the circular direction with the displacements in the normal direction (denoted as W), between each circular cylinder in membrane stress states and the circular arch with a varied cross-section.
 This fact assures continuity of displacements along the concave partition lines.

 Thus, given a method of distributing suitable thickness to each shell zone, the outer thin shell zones in membrane stress states are cantilever-supported by the inner thick shell zone treated as an arch with varying cross-section along the circular direction.

 After solving the outer thin shell zones by a membrane theory presented in the previous paper, and after introducing pertinent parameters to describe the adequate shell-thicknesses with related shell shape, the thick shell zone is analyzed by solving a set of differential equations on the basis of the arch theory led by eliminating the longitudinal distribution in the general shell theory on a circular cylinder (the Flügge's Theory), including these parameters.

 The results of these parametric analyses are herein presented, and it is confirmed that the partial circular cylinder partitioned into a thick shell and two thin shells by a pair of concave curves can be solved as the Membrane Shell-Arch structure theoretically.

 For comparison, a typical example is selected with consideration of the results of above parametric analyses, and is analyzed by the Finite Element Method of Weak Form, equivalent to the Galerkin Method, by minimizing directly the total potential energy of a general circular cylindrical shell in which finite elements are able to express not only membrane deformations, but also bending deformations.
 This comparison with the FEM results indicates the adequacy of the proposed Membrane Shell-Arch Theory.

 From another point of view, the method introduced here serves as a means of determining an economical thickness distribution, in the design of a shell roof to cover a large space.

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 1. Introduction
 This paper aims at improving a strength reduction factor r₃ related to opening height for RC shear walls in the AIJ design standard¹⁾. FEM analyses were conducted to simulate experimental behavior/performance of three shear wall specimens without/with vertical aligned openings. Based on the analytical results, r₃ was verified through investigating shear contributions of the wall components. Moreover, a new strength reduction factor _newr₃ was proposed to improve the accuracy of the original r₃.
 2. Outline of experimental study on RC shear walls with openings²⁾
 The specimens were designed with different opening configurations: Specimen W0 without opening, Specimen W1 with single-aligned openings, and Specimen W2 with double-aligned openings. As a result, it was experimentally verified that the lateral strengths estimated for the specimens with openings based on r₃ overestimated the maximum strengths obtained from the tests. Therefore, FEM analyses of the specimens were performed mainly to clarify why the overestimations were caused.
 3. FEM analyses
 Two-dimensional FEM analyses were conducted for the specimens to simulate the experimental behavior/performance. The analytical results of all specimens, in particular, the shear force vs. drift angle relationships and damage developments, up to R of 0.5 x 10^-2 rad. showed good agreements with the experimental results. Moreover, contributions of the wall components to the overall lateral strengths were investigated and compared with the estimations by r₃. Consequently, the lateral strengths estimated for the specimens with openings overestimated the experimental maximum strengths. It was concluded that the overestimations were caused by overestimations on the flexural resistances of the partial walls divided by the openings.
 4. Proposal for improving the strength reduction factor related to opening height
 A new strength reduction factor _newr₃ was proposed with a flexural strength reduction index α for this type of wall, in particular the wall with a boundary column on the tensile side. The index α considered reduction of an arm length between coupled forces on the wall bottom from an assumption in the original r₃. The estimations for the ultimate strengths of the above specimens using _newr₃ showed good agreements with the experimental results.
 5. Conclusions
 Major findings from the present study are summarized to show the appropriateness of the proposed strength reduction factor _newr₃ for RC shear walls with vertically aligned openings.

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 Square hollow section members, such as square steel tube members and box section members, are commonly used as columns in structural steel buildings. Their performance during earthquakes significantly affects the seismic capacities of buildings. Since local buckling determines the elasto-plastic behavior of the members except for fracture, it is necessary to examine the large deformation behavior governed by local buckling of the members to accurately evaluate the seismic capacities of buildings. However, the effects of initial imperfections owing to the manufacturing process on the elasto-plastic behavior of the members are not well understood. The purpose of this study is to examine the effects of initial imperfections on the large deformation behavior governed by local buckling of the members.
 The initial imperfections of square hollow section members are examined experimentally. The effects of initial imperfections on the large deformation behavior governed by local buckling of the members are understood by axial compression analysis. The ultimate strength and plastic deformation capacity are derived from analysis and test and the validity of the current values of width‐thickness ratio limitations is examined. It is shown that the geometric imperfections of plate elements significantly affect and other initial imperfections owing to the manufacturing process do not much affect the local buckling behavior of the members.
 First, the material and geometric imperfections of square hollow section members with different manufacturing processes, steel grades, and cross-sectional shapes are examined experimentally. The specimens are cold roll-formed square steel tube members, cold press-formed square steel tube members, and built-up box section members. Variation of material property in the sections and residual stress of the material imperfections and initial deflection of the plate elements of the geometric imperfections are examined.
 Then, after understanding the initial imperfections of real members, the effects of material and geometric imperfections on the large deformation behavior of square hollow section members are examined by axial compression analysis of simple loading condition. The effects of the variation of material property in the sections, residual stress, initial deflection of the plate elements, and curvature radius at the corners of the initial imperfections are understood by finite element analysis. The initial deflection of the plate elements significantly affects and the variation of material property in the sections, residual stress, and curvature radius at the corners does not much affect the local buckling behavior of the members. The valid or safe ultimate strength and plastic deformation capacity can be obtained by using the initial deflection corresponding to buckling mode as the only initial imperfection.
 Finally, based on the understanding of the effects of initial imperfections, the ultimate strength and plastic deformation capacity of square hollow section members under axial compression are examined by analysis and test. It is shown that the values of width‐thickness ratio limitations of the Design Standard for Steel Structures and Recommendations for the Plastic Design of Steel Structures are valid.

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 When joining a larger diameter CHS-column to a smaller diameter one in an elevation of a multi-story steel framed building, a taper CHS is requested at the beam-to-column connection as shown in Fig. 1. The structural properties of such a taper CHS are numerically investigated in this study by means of FEM.
 First, the practices of taper SHS are searched, because CHS is not popular at the present time. Six buildings using SHS-columns shown in Table 1 are examined, from which the connection types in Fig. 2, histogram of end-width differences in Fig. 3 and scattering of taper inclination of Fig. 4 are found.
 On the assumption that the tapers of CHS are similar to those of SHS, the connection models are established for FE analysis as shown in Fig. 5, which includes five series designated by AL, AS, B, C, and D. The stress-strain curves in Fig. 6 are employed for the analysis: one is related to cold-formed CHS and the other to heat-treated one. The models are listed in Tables 2, 3, 4 and 5 corresponding to the series. The FE analysis reveals the failure deformations as shown in Fig. 7. It is observed that the cylindrical wall of CHS fails at the joint to compressive flange of the H-beam.
 The local deformation is not always directly detected from the simulation, because the joint displacements include the rotational and shearing displacements for series B and D under non-symmetric bending moments. In such a case, the joint rotation due to the local deformations is calculated by the method shown in Fig. 8. In result, the relationships between joint moment and joint rotation are obtained as demonstrated in Fig. 9, from which the yield, plastic, and maximum bending strengths as well as initial elastic rotational stiffness are determined as summarized in Tables 2 to 5 for each series.
 The stress and strain distributions in the panel of sample B21H in series B subjected to shearing deformation are presented in Fig. 10, the inspecting lines of which are shown in the left figure. It is observed that either of the shearing stress, equivalent stress, and equivalent plastic strain is not so concentrated in the upper part of the panel, while the concentration is remarkable at the local area of the flange-to-CHS joint.
 The rates of joint strengths of heat-treated CHS to cold-formed CHS are shown in Fig. 11, from which it is noticed that the joint strengths are predominantly governed by the yield stress of the CHS, and little by the shape of the stress-strain curve. The rate of joint strengths of smaller-end compression to larger-end compression, i.e., series AS to series AL are given in Fig. 12, from which it is observed that the former is always larger than the latter. The joint strengths and stiffness of series AL and C are compared in Fig. 13, which indicates that the eccentricity has little influence. In the same way, series AL and B, and series AL and D are compared in Figs. 14 and 15, respectively, which indicates that joint strength is little influenced by the direction of a couple of applied moments, but joint stiffness is significantly influenced.
 The evaluation formulae for the joint strength and stiffness developed for uniform CHS can be easily extended to taper CHS shown in Fig. 16 only with a notice that the bending strength is governed by the joint of the compressive flange, which is detailed in appendices 1 and 2. The predicted values are compared with FEM solutions in Fig. 17, and the statistics of the ratios of predictions to FEM solutions are given in Table 6, which demonstrate a satisfactory level of predictabilities.

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 In the 1995 Kobe earthquake, many steel structures suffered damage at beam-to-column connections. In those damaged buildings, fractures of beam flange at beam-end connections were observed. After that, a remarkable number of studies have been conducted to prevent early fracture at beam-end connections and enhance the plastic deformation capacity of steel beams. In these research studies, it was pointed out that low joint efficiency of beam web, which is caused by out-of-plane deformation of skin plate of rectangular hollow section (RHS) column used for moment resisting frames in Japan, decreases the plastic rotation capacity of beam-end connections governed by beam flange. On the other hands, in high-rise buildings of Japan, the on-site full penetration welding of beam flanges has to be achieved after connecting beam web with high-tension bolts (WBFW type connection). The bolted beam-web joint has the same problem due to its poor joint efficiency. Recently, cyclic deformation capacity of the WBFW connections subjected to long-duration ground motion with many small amplitude cycles emerged as a very important issue for structural engineers in Japan. The cyclic deformation capacity of the WBFW type beam-end connections is evaluated using its low cycle fatigue characteristics described by fracture life vs. ductility factor relations, it is difficult to evaluate several test results with various conditions such as steel grade and beam span.
 In this paper, cyclic loading tests focusing on establishing an appropriate evaluation method of cyclic deformation capacity of WBFW type beam-end connections were carried out. Three groups of specimens were tested. Each group of specimens has similar joint efficiency and connection details. The 400MPa conventional strength steel was used for the first group of specimens, and the 490MPa conventional strength steel and the 590MPa high strength steel were used for the second and third one, respectively.
 The test results can be summarized as follows:(1) the beam-end connection made of the 590MPa steel fractured during the 14th loading cycle with constant rotation angle of 1.5θ_p, although that of the 400MPa steel showed sufficient plastic deformation capacity (more than 100 cycles) under the same ductility factor; (2) cyclic deformation capacity of the 590MPa steel was almost the same as that of other steel grades regarding the evaluation of low cycle fatigue characteristics based on the maximum rotation angle θ_max; (3) finally, the conversion method of ductility factor for various steel grades was proposed.

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