An activity index test of mineral admixture for concrete is the test of estimates the substitution performance of the mineral admixture to cement. This test is prescribed by JIS A 6201 (Fly ash for use in concrete), JIS A 6206(Ground granulated blast-furnace slag for use in concrete) and JIS A 6207 (Silica fume for use in concrete).

 Mortar with water binder ratio of 50% prescribed in JIS A 6201 isn't suitable to estimate the activity index of the silica fume. This is because silica fume is used by ultra-high strength concrete with low water binder ratio. The water binder ratio of the mortar used for a test after JIS A 6207(2011) was changed to 30% from this reason. About 10 years had passed from this change, but a problem related to a revised point wasn't reported. However, a problem about the repeatability of the activity index test results was pointed out by an experiment related to establishment of JIS A 6209(Volcanic glass powder for use in concrete). Then, repeatability of activity index test results of micro-powder for ultra-high strength concrete based on mortar was investigated. This investigation led to the following conclusions.

 1) It is possible to obtain a compressive strength test result of the standard mortar with repeatability by a present test method when used material is same.

 2) In the range of a mortar flow of this test (200mm-260mm), it is possible to obtain a compressive strength test result of the standard mortar with repeatability. As a result, the repeatability of a result of the activity index test can also be secured.

 3) To change the kind of chemical admixture has a high possibility which influences the repeatability of a result of the activity index test.

 4) Extension of mixing time contributed to increase compressive strength of standard mortar and test mortar. However, a problem of 3) could not be solved by extending mixing time of mortar.

 The polyurethane waterproofing membrane is used to form a waterproofing layer by applying a liquid material to the waterproofing base of a construction site. Particularly, because the construction surface is vertical, the thickness of the polyurethane membrane tends to be uneven, and good construction skills are required. However, relevant studies are scarce, and sufficient knowledge has not been acquired to date. Therefore, this study investigated the actual conditions affecting the membrane thickness of in the vertical part of an actual building and the appropriate tools and viscosity to ensure an appropriate membrane thickness.

 In the examination, two experiments were conducted, which confirmed the effect of the construction work and reinforcing fabrics in practical applications, and the effect of application tools and viscosity on the membrane thickness.

 In the first experiment, the thickness distribution of the vertical part was compared by observing the work carried out by a skilled worker and an unskilled worker using a concrete wall. It was found that the construction of the vertical part consisted of the work for distributing the waterproof material and finishing work, and that the application tools were properly used. Additionally, it was clarified that, by uniformly applying the waterproof material to the reinforcing fabrics, the dispersion of the membrane thickness was effectively reduced, regardless of the construction skill level.

 In the second experiment, the effect of the application tools and viscosity on the membrane thickness during the distribution work was investigated. It was found that the amount of coating per application tended to decrease with the viscosity, regardless of the application tools. Next a T-shaped frame using plywood backing was manufactured, and the effects of the application tools, viscosity (dilution ratio 0%–5%), and reinforcing fabrics on the membrane thickness was investigated. The dispersion of the membrane thickness increased as the viscosity decreased, but a difference was hardly observed in the average value of membrane thickness. Additionally, when the rubber spatula was used, the working time tended to be longer compared with the roller.

 The following results were drawn from this study.

 (1) The reinforcing fabrics of the vertical part held the uncured waterproof material, and effectively ensured the membrane thickness, regardless of the construction skill level.

 (2) In the distribution work, when the viscosity decreased, it became difficult to distribute the waterproof material throughout the construction surface, and the dispersion of the membrane thickness tended to increase. This tendency was particularly remarkable in the rubber spatula case.

 (3) When the viscosity of the waterproof material decreased, the work time tended to be longer, because the amount of coating in the distribution work decreased. Therefore, to ensure an appropriate membrane thickness, the waterproof material should not be diluted.

 (4) In practical situations, it is important to consider a balance amongst the application tools, viscosity, and working time.

 We have proposed a stochastic Green’s function method with rupture directivity effects inside subfaults (hereafter we call SGF_RD) and its verification by simulations of observed strong ground motions has been presented. SGF_RD has advantages in that decreasing of rupture directivity effects with frequency due to heterogeneous rupture and underground structure is controllable and various kinds of rupture patterns are available.

 In conventional stochastic Green’s function methods (SGF), each subfault is represented by a point source. Source spectra of subfaults are assumed to be the omega squared model and rupture directivity effects inside subfaults are not considered. On the condition that Green’s function and rigidity in a source layer are uniform in a subfault and slip time function is delta function, we accounted tr which is S-wave travel time between rupture front and a station in a source spectrum of each subfault. We defined correction function as the ratio of a source spectrum with tr to a source spectrum without tr. In order to avoid artificial fluctuations due to rectangle shape of subfaults in source spectra, we introduced the spatial randomness for tr and slip. The correction functions are complex spectra. By the convolution of a correction function with a source spectrum of each subfault, the rupture directivity effects inside subfaults have been incorporated.

 In order to verify SGF_RD, we simulated the strong ground motions recorded at TTRH02 and SMNH01 stations during the 2000 Tottori-Ken Seibu earthquake (Mj7.3) by SGF and SGF_RD. The 1D velocity structures with decreasing S-wave velocities due to soil nonlinearity were constructed at the stations. Ground motions at depths corresponding to the seismic bedrock were estimated based on the records on ground surface using the 1D velocity structures and compared to synthetic ground motions by SGF and SGF_RD. We decreased rupture directivity effects from 2Hz and diminished at 4Hz with the constraint that the correction function was 1. In a low frequency range, the correction functions were almost 1. The correction functions were less/more than 1 in a frequency range of 1Hz or higher. The correction functions were getting larger as rupture directions in subfaults were from backward to forward. Improvement of reproducibility of the ground motion was not recognized at SMNH01 where the rupture directivity effects seemed to be small. On the other hand, the peak around 2-3 Hz of the observed record was successfully reproduced by SGF_RD at TTRH02. The rupture direction in the asperity was forward direction and the correction functions strongly effected on the synthetic ground motion. Improvement for reproducibility at TTRH02 meant its effectiveness of SGF_RD.

 The simulations of other large earthquakes are necessary to verify SGF_RD for the future work.

 In Japan, seismic design using components that absorb seismic energy has been approved. In fact, this design method has been applied to simple structures such as offices and distribution warehouses with dampers on all stories. We have proposed a design method for a structure of power plant facilities in which dampers are installed only in the lower story. In order to efficiently design such structures, it is important to understand their seismic response performance. Although many studies have been carried out on a structure with dampers installed on all stories, few studies have examined the seismic response characteristics of a frame with dampers installed on some stories of a structure. However, a recent trend is to retrofit some stories of high-rise buildings that will be hit by a major earthquake in order to improve their earthquake resistance while reducing the economic burden. From the viewpoint of improving the earthquake resistance of buildings, this trend is expected to spread to medium-to-low-rise buildings, and it is significant to understand their response characteristics.

 This paper focused on medium-to-low-rise buildings with hysteretic dampers from the first story to the middle story. Based on the energy balance due to the earthquake, an equation was derived to give the yield story-shearing force of the damper, which minimizes the maximum story-shearing force of the story where the damper is installed. The yield story story-shearing force of the damper can be approximately calculated from the story-shearing force coefficient distribution of the main frame, the mass distribution of each story, and the yield story-shearing force of the damper of the first story. The derivation process was described in Chapters 3 and 4, and the prerequisites were described in Chapter 2.

 Next, the effect of the number of stories in which dampers are installed on the seismic response characteristics of the building was discussed. It was found that when the maximum story-shearing force of the story in which the damper is installed is minimal, the maximum story-shearing force of the main frame of the first story is approximately equal to the yielding story-shearing force of the damper. It was also shown that dampers installed on more than 60% of the stories of a building can be expected to absorb roughly the same amount of energy as if they were installed on all stories. On the other hand, when the dampers are concentrated in the lower stories of the building, it was suggested that the elastic vibration energy of the story without the dampers increases. These were mentioned in Chapter 5.

 Finally, in Chapter 6, a time history response analysis was performed using a multi degrees of freedom model that assumes a real building. A comparison of the results of the analysis with the theoretical values based on the equation showed that in most of the analysis cases, the results of the analysis tended to be generally similar to the theoretical values regardless of the difference in seismic motion, although there was some difference between the results of the analysis and the theoretical values when the n_eq was less than 2 and the interlaminar displacement of the damper differed greatly on both positive and negative sides.

 1. Introduction The plate bending problem of flat plate is the basis of not only static analysis but also analyses of three dimensional wall structures. Development of elements having high accuracy with few elements is one essential of the finite element method. A triangular flat plate bending element is indispensable to analyze plates with curved shape boundaries. But shape function is not determined in a simple way, because of using area coordinates. The generalized coordinates of each node of the bending plane plate element are three degrees of freedom, displacement, and rotations in two directions. A triangular three-node element has a total of nine degrees of freedom. The BCIZ element defines the shape function using area coordinate in three order terms. The element is nonconforming and gives static solution with weak constraint. Conforming elements between neighboring elements are developed and show they have strong constraints for models of small element mesh.

 In order to develop a high-performance triangular plate bending element, it is necessary to find a basis function that can control the rotation of the boundary side between adjacent elements. First, the basis functions corresponding to the six degrees of freedom essential for the plate bending element and a particular basis function that can be selected as appropriate are clearly analyzed. Although the latter have three degrees of freedom, there are three boundaries, and if we select a basis function that affects the rotation of one boundary, it is necessary to arrange the basis functions with the same effect on the remaining boundaries. After all, there is only one degree of freedom available to improve the performance of the triangular plate bending element. The purpose of this paper is to add high-order polynomials to this basis function to develop high-performance elements.

 2. Area Coordinate and Basis Functions

 3. Particular Basis Function and its Control

 4. Numerical analyses and verification

 In order to examine the performance of the triangular element developed here, four benchmark tests are carried out using six element meshes. Considering biaxial symmetry condition, 1/4 of the analysis model is set as numerical analyses. Element mesh in two directions 1 × 1, 2 × 2, 3 × 3, 5 × 5, 7 × 7, and 9 × 9 are used. (The numerical integration formula used here is inappropriate, and correction based on analysis obtained by applying high precision formula would be reported in the next journal.)

 5. Conclusion For a triangular plate bending element with nine degrees of freedom, six basis functions corresponding to rigid body motions and constant strains are necessarily determined. Considering the invariance condition of a triangular element, the remaining three degrees of freedom substantially determine one kind of basis function. First, we find this particular basis function and add three kinds of higher-order terms to this function to construct a basis function. Using the element basing on those new basis functions, the typical benchmark test examples of the plane plate were analyzed and compared with the solution of other triangular plane plate elements. It has been demonstrated that new elements give stable and accurate solutions from a region where the element mesh is sparse to a region where the element mesh is dense.

 A new type of buckling-restrained braces with post-tensioned cables (PT-BRB) which provide self-centering force while dissipating seismic energy is proposed. Cyclic tests have been conducted for the developed PT-BRBs, confirming that the proposed numerical model explained in Fig. 2. accurately captures the experimental data. The obtained hystereses are mainly dependent on post-yield stiffness (α) and energy dissipation (β) ratios. Based on the assumed design parameters, PT-BRB can have a hysteretic shape from bilinear (β=2.0) to flag-shaped (β≦1.0) hystereses. Although many numerical studies present in literature about conventional BRBs having fuller hysteresis curves, there are few studies on PT-BRBs which show the effect of α and β values on minimizing residual deformations. Furthermore, quite limited work has been published for the application of any kind of BRBs in structures other than framed buildings. Therefore, this study focuses on the required α and β values to minimize residual deformations in some selected special structures.

 Section 2 presents the outline of the PT-BRB numerical model used in this paper. Effects of α and β on the response are numerically investigated in Sections 3~5 when PT-BRBs are used in various types of steel structures (frame with pinned connections, truss tower, truss roof gymnasium, truss frame). The results are also compared with the responses when conventional BRBs are used in the same structures.

 The following results can be deduced from this work:

 1) In the 4-story frame model with pinned connections, partially self-centering system with α=0.06~0.08 and β=1.92~1.88 have similar peak story drift ratios (SDR) with conventional BRB. Obtained residual story drifts ratios SDRs are less than 0.1% (1/1000rad). Also in the 10-story model, the residual SDR decrease as α increases and β decreases. However, the peak SDR is higher than when conventional BRBs are used.

 2) In the existing retrofitting layout (7~11 stories) of truss tower, the bilinear model (α=0.08, β=2.0) for 1G~3G waves and partially self- centering model (α=0.086, β=1.94) for 1R~3R waves lead to peak responses similar to conventional BRBs. However, the residual SDRs are less than 0.1% (1/1000rad). The same result can be obtained with bilinear (α=0.08, β=2.0) behavior even in the lower layout (1~3 stories).

 3) For the space frame roof of RC gymnasium building which was damaged in the Kumamoto earthquake (main shock) with a magnitude of M7.3 and occurred on April 16th, 2016, the observed damage could have been reduced by introducing BRBs to members connected to the bearings. However, BRBs already have high post-yield stiffness ratio due to the geometric stiffness of surrounding truss frame, and the axial force due to the roof weight is greater than the cable tension applied to the BRBs. Therefore, PT-BRBs may cause more damage due to increased peak acceleration and decreased energy dissipation.

 4) In a truss frame with 40m span that would represent a warehouse or hangar, partially self-centering model with α=0.10~0.115 and β=1.80~1.74 parameters leads to minimization of the maximum SDR and residual SDR values of less than 0.05% (1/2000rad). In addition, increasing α and decreasing β could be effective in improving the damage concentration on one side braces while reducing the maximum and residual roof vertical displacements.

 Seismic isolation is widely used in seismic areas of the world for their functions of securing both of human life and the property. While simple design methods for simple structures have been proposed by many researchers, these methods are generally limited to specific seismically isolated structural systems. Particularly in Japan, the number of challenging structural systems (e.g. a base isolation with tall buildings, mid-story isolation or roof isolation systems having substructures with dampers) where these methods cannot be applied are recently increasing. In practice, many projects require an iterative approach with time-consuming NLRHA to determine the isolation design. Therefore, this paper presents a design method for highly indeterminate seismically isolated structures utilizing generalized response spectrum analysis, which has been extended to simulate both of an elasto-plastic damper with isolator and a nonlinear oil damper. In section 2, the extension of generalized response spectrum analysis (GRSA) is described in detail. The design method of seismically isolated structures based on GRSA is proposed. In section 3, the fundamental accuracy of GRSA is verified using a series of numerical simulation of single-story isolated structure models. Moreover, the range in application of the parameter formulations of complex stiffness for complex multi shear spring element simulating elastoplastic dampers with isolator is discussed. In section 4, the design example of a tall building with base isolation based on GRSA is demonstrated. In section 5, the design example of a 9-story mid-story isolation building having substructure with dampers based on GRSA is demonstrated. In section 6, the design example of an isolated lattice dome building having substructure with dampers based on GRSA is demonstrated.

 In summary, the following results were obtained:

 1) GRSA is extended for highly indeterminate seismically isolated structures and their accuracy was verified in a series of comparison studies with non-linear response history analyses.

 2) While modified geometrical stiffness method (Mod-GSM) is suitable for seismically isolated structure with shorter initial natural period (T₀ = 0.1 and 0.3, ) average damping method (ADM) is suitable for seismically isolated structure with longer initial natural period (T₀ = 0.7 and 1.0.) The range in application of ADM to keep the evaluation error within 30% is that ductility ratio is lower than 1000 and the nonlinear coefficient NL is lower than 0.6. The range in application of Mod-GSM to keep the evaluation error within 30% is that the nonlinear coefficient NL is lower than 0.7.

 3) A design method of seismically isolated structures based on the contour map of GRSA is proposed and the efficiency is demonstrated using a series of the design examples.

 4) When additional dampers are distributed in supporting substructures below the isolated layer of mid-story isolated structures or seismically isolated roof structures, the horizontal stiffness of the substructure incorporating elasto-plastic damper braces should be more reduced compared with that of the substructure incorporating oil damper braces for reducing the acceleration response of the substructure. However, the response acceleration of the substructure may not be reduced for the above seismically isolated systems having substructure with elasto-plastic damper braces.

 To economically design a building, the beams used may contain holes for placing piping. For steel structures and reinforced concrete structures, methods for evaluating the strength of beams with round holes have been established. However, for timber structures in Japan, a method for evaluating the strengths of beams with round holes has not yet been established.

 Several strength evaluation methods have been proposed for the standards of overseas structural design in Japanese research papers. These methods calculate the beam strengths when a hole is split by a tensile force that is perpendicular to the grain. It is possible to determine the strengths of beams with round holes using the proposed strength evaluation method. However, the proposed strength evaluation method has only been verified for homogeneous timber and it is not clear whether this method can be applied to glulams that are glued and laminated timbers composed of heterogeneous grade materials and mainly used for beams in Japan.

 The purpose of this study is to experimentally verify that the proposed strength evaluation method can be applied to glulams. An additional objective is to verify that the strengths of these glued and laminated timbers can be estimated by finite element analysis (FEA).

 Chapter 1 introduces the proposed strength evaluation method. Chapter 2 introduces the shear bending experiments performed on glulams with round holes. Chapter 3 introduces the element experiments for examining shear and tension strength parallel to the grain, tension strength perpendicular to the grain, and mode I fracture energy. Chapter 4 presents the results of verification that the proposed capacity evaluation method is not applicable to glulams. Chapter 5 proposes a method for estimating the strength of glulams with round holes by FEA and shows the verification results.

 The results of this study are as follows.

 1) It was demonstrated that the strength evaluation method proposed for glulams cannot be applied as it currently exists.

 2) The stress distributions around the round holes were obtained by FEA and the method of estimating the splitting strengths using the mean stresses acting across a potential fracture area shown in Reference 11 was verified. As a result, it was found that the splitting strengths were accurately estimated when the round holes were small or large.

 3) By using Equation (5) for correcting ams and Equation (6) for considering the size effect in the mean stress method, it was shown that the splitting strengths can be accurately estimated even when the round holes are small or large.

 When existing buildings are reinforced against earthquakes, concrete roughened through chipping (herein simply referred to as “roughened concrete”) and post-installed anchors are often used to join reinforcing parts, such as steel braces and vibration control braces, to the structures. Roughened concrete increases the rigidity of the interlocking resistance and bearing resistance, and it can also increase the shear strength.

 The authors have proposed the use of cylindrical shear-keys in place of roughened concrete as a joining technique. This combination of a cylindrical shear-key and a post-installed anchor is expected to reduce the shear displacement at the joint surface and increase the shear strength. However, when these techniques are used in combination, the stress state of the joint is complex, and the mechanical behavior of the cylindrical shear-keys and post-installed anchors are different. Therefore, it is necessary to verify whether the combination can be evaluated using a mechanical model that adds the mechanical model of each technique (herein termed “pre-modified model”). The purpose of this study is to perform shearing tests with a test specimen composed of a cylindrical shear-key and a post-installed anchor used in combination, to estimate the axial stress state at the joint from the test results, and to propose a mechanical model for the combination (herein termed “modified model”) reflecting these effects.

 The test results showed that when a post-installed anchor and a cylindrical shear-key were used in combination, the value of the aperture displacement δ_V exceeded the value of δ_V when a single post-installed anchor was utilized. Therefore, because the axial force T at the anchor bolt increased when used in combination, we observed a tendency for the bending moment M to decrease. From these test results, the shearing force ^C_δQ_a resisted by the post-installed anchor when used in combination was estimated to be approximately 0.7 times the value when a single post-installed anchor was used. Furthermore, as the average compressive stress _aσ₀ at the joint surface added by the vertical component of T had an average value of −0.60 N/mm², this axial stress should be considered in the mechanical model of the cylindrical shear-key when used in combination. The shearing force transmitted by the cylindrical shear-key when used in combination could have increased owing to these reasons. Furthermore, considering that the mechanical behavior of the cylindrical shear-key was exhibited in the gradually increasing load region until the anchor bolt yielded when used in combination, the shear displacement, δ_max1, was 0.63 mm when it reached the shear strength based on the mechanical model of the cylindrical shear-key. The average value of δ_H when the anchor bolt reached its yield, resulted in a value exceeding δ_max1 = 0.2 mm when a single anchor bolt was used.

 In this study, we performed a detailed examination, focusing on the stress state at the joint when a post-installed anchor and a cylindrical shear-key were used in combination. We have shown that the modified model can be used to predict experimental values at higher accuracy, compared with the pre-modified model.

 1. Introduction

 It is important for structural design to comprehend plastic deformation demand of members against large earthquakes. We have proposed a predicton method of plastic deformation demand for members in single-story steel frames with braces. To extend the scope of application of the current proposal, this paper discusses with plastic deformation demand for multi-story steel frames with braces. In the case of multi-story braced frames designed as archieving overall collapse mechanism, damages during vibration concentrate on the story where horizontal strength of braces is small. From this viewpoint, this paper develops the method to predict the demanded plastic deformation of braces and beams in each story.

 2. Substitution to equivalent SDOF system

 In order to substitute multi-story braced frame to equivalent SDOF, following assumptions are adopted; total weight and natural period of SDOF are identical to those of multi-story frame, and story moment-interstory drift angle relationship of the equivalent SDOF is obtained approximately from the overturning moment-effective structure rotation angle relationship of the multi-story frame.

 3. Prediction in equivalent SDOF system

 According to Ref.1), the maximum drift angle, the plastic dissipated energy of the braces and the main frame are predicted based on the balance equation of earthquake input energy and energy dissipated by the equivalent SDOF system.

 4. Prediction of demanded plastic deformation of braces and beam in each story

 Maximum drift angle in each story of multi-story frame is calculated based on the results of static analysis. Using the results, the dissipated energy of brace in each story is obtained by dividing the dissipated energy of the braces of the equivalent SDOF. The maximum plastic rotation angle of the beam is calculated by subtracting the elastic rotation angle of the column and the beam from the maximum interstory drift angle, considering that the damage concentrates on the beam plasticized in early stage. The cumulative plastic rotation angle of the beam in each story is calculated so that the energy dissipated by the main frame element of the equivalent SDOF is equal to the energy dissipated by the beam in the multi-story frame.

 5. Comparison between prediction results and time history analysis results

 Time history response analyses are conducted to confirm validity of the proposed prediction method. The main frame is modeled as a fishbone-shaped model, and the braces are modeled by the method in Ref. 11). The analysis parameters are horizontal strength sharing ratio of brace, height direction distribution of horizontal strength sharing ratio of braces, normalized slenderness ratio of brace, number of story, and input level.

 6. Conclusion

 As a result, it is clarified that the prediction with r_cycle = 0.25 captures most of the analysis results for the maximum drift angle and the maximum plastic rotation angle of the beam, and it envelops the analysis results of about 80% of the cumulative plastic rotation angle of the beam. Further, the upper envelope of the prediction with r_cycle = 0.1 to 0.4 envelops the analysis results of about 60% of the dissipated energy of braces.

 This paper dealt with methods of repair time assessment of a building damaged by an earthquake. The repair time is as important as the repair cost as the economic loss by damage of building in an earthquake, because the repair time is directly related to the economic loss of the owner in the profit building, and indirectly to the occupants and the surrounding society due to the loss of its function.

 Repair costs for buildings are, in principle, given as the sum of repair costs for members of building, but it is even more difficult to evaluate the repair period because it is necessary to consider the repair schedule. In this paper, the repair schedule is expressed as a logical network, and a method for automatically generating a logical network for the building repair schedule is proposed, given the member repair schedule.

 Given a list of preceding activities that need to be performed immediately before each activity, the node number of the logical network can be automatically determined, that means that a logical network has been created. In construction process, specific kind of tasks may be required to carry out simultaneously on the floor. Synchronization of activities is realized by manipulating the preceding activity list according to certain rules.

 A method for evaluation of the shortest repair time under the worker resource constraints considering worker types is also proposed. It is possible to find the shortest construction period by appropriately shifting the workers from the activity which has the longest total float among the simultaneously executing activities whose worker type is same as that of the critical activity, to the critical activity. However, the convergence calculation for the shortest repair time, are not stable in many cases because the critical path changes in the process. In order to avoid this problem, a method consist of two steps is proposed. The first step is a searching stage where candidates of critical path those give a shortest repair time. The second step is convergence stage where each candidate is optimized. The second step is carried out progressively not to change critical path. Among the converged candidates, the candidate which has shortest repair time is adopted as the optimum value.

 The method proposed in this paper can automatically generate a repair schedule for arbitrary damaged state and uniquely determine the repair time. Because the calculation process is automated, it can be incorporated into the Monte Carlo simulation proposed in FEMA P-58.