Calculation method for use in seismic design of structures and seismic design support system using the same

Abstract

To provide a calculation method for seismic design that enhances the seismic damping capabilities of structures, eliminating the need to rely on the individual designer's experience and skill. [Solution] (1) The spatiotemporal shape and frequency of the natural vibration of a structure are calculated using the natural vibration vector based on measurement data related to natural vibration obtained by ambient microtremor measurement, and (2) The spatiotemporal shape and frequency of the natural motion of the structural model used for seismic design of the structure are calculated using the natural motion vector, based on analysis data regarding the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of the structure. (3) A step of relating the index value obtained by the measurement in (1) and the index value obtained by the analysis in (2) on the same dimension, A calculation method for use in seismic design of structures, which has the following characteristics.

Description

[Technical Field]

[0001] This invention relates to a calculation method for use in seismic design of structures and a seismic design support system using the same. [Background technology]

[0002] Our country is one of the most earthquake-prone nations, and various proposals regarding earthquake countermeasures have been put forward over the years. Specifically, these include seismic isolation technology, seismic damping technology, and earthquake-resistant technology. These technologies, respectively, refer to technologies that prevent earthquake tremors from being directly transmitted to the structure, technologies that absorb tremors in advance to reduce the shaking transmitted to the structure, and technologies that allow the structure to withstand shaking without being destroyed.

[0003] Furthermore, seismic damping technology exists. This technology aims to restore a structure by controlling the shaking caused by an earthquake within its own motion and deformation, thereby avoiding damage. Prior art related to seismic damping technology includes, for example, a method for diagnosing and evaluating structures based on ambient micro-vibrations of structures (Patent Document 1), an explanation of structural diagnosis using natural vibrations obtained from ambient micro-vibration measurements (Non-Patent Document 1), and a seismic reinforcement method using the SRF method (Non-Patent Document 1).

[0004] In addition, computer software is available on the market that models structures and calculates indices related to the r-th eigenmode from eigenvalue analysis of the modeled structures. Building designers can use this available computer software to calculate indices related to the r-th eigenmode from eigenvalue analysis of the modeled structures. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2022-121674 [Non-patent literature]

[0006] [Non-Patent Document 1] "Seismic Recovery" by Shunichi Igarashi, Structural Quality Assurance Institute Co., Ltd., 2022. [Overview of the Initiative] [Problems that the invention aims to solve]

[0007] (1) Regarding seismic isolation technology, seismic control technology, earthquake-resistant technology, etc. Regarding the above-mentioned seismic isolation, vibration control, and earthquake-resistant technologies, the following points can be made: All of these methods evaluate the shaking, response, and performance of structures during earthquakes based on non-existent forces, such as inertial forces or inertial resistance. For major earthquakes, performance evaluations are conducted on the premise that structural materials become inelastic and are damaged without recovering. Therefore, even if it is claimed that the structure does not directly transmit earthquake tremors, absorbs tremors in advance to reduce the shaking transmitted to the structure, or that the structure will not be destroyed even if it shakes, the actual outcome remains unclear. From a calculation standpoint, there is a fundamental problem in that cracks will inevitably form, damage will occur, and the structure will cease to function. While it is essential for urban administrators, users, and owners to avoid structures becoming non-functional due to earthquakes, current technologies such as seismic isolation, vibration control, and earthquake-resistant technologies, although nominally appearing to address this issue, actually have problems in that they fail to do so. Actual earthquake cases include, for example, apartment buildings that were designed and constructed according to current standards and had undergone seismic reinforcement but still developed cracks and became unusable, cases where seismic isolation and damping devices broke down, and cases where the upper floors experienced severe shaking.

[0008] Regarding the handling of numerical values ​​related to structural analysis in relation to the design methods, diagnostic methods, etc., specified in the current seismic standards and seismic diagnosis standards for buildings (hereinafter referred to as "current standards"), the following points can also be made.

[0009] Under current standards, seismic activity is represented by an external force called seismic force, which acts on each part of a structure in proportion to its mass. In static structural calculations, seismic forces correspond to inertial resistance, while in dynamic calculations, seismic forces correspond to inertial forces. In actual practice, the two are often confused; a fictional force that does not actually exist is often perceived as a real force. The calculation results are considered to several decimal places, and judgments differ greatly depending on whether or not they exceed a certain threshold.

[0010] Furthermore, under the current standards, two types of models are applied to the target structure: a simple model for calculating seismic forces and a complex model used for structural calculations such as stress calculations, ultimate horizontal load capacity calculations, and time history response analysis. This creates a dual structure where consistency between the two models is not ensured. In addition, the static structural calculation has a contradictory, self-contradictory structure in that it calculates inelastic stresses using inertial resistance that balances the stresses calculated by the elastic model as input. The coordinate system is a non-inertial frame of reference with its origin at the point that generates the acceleration time history used to calculate seismic forces; however, under current standards, it is considered an inertial frame of reference. Furthermore, under current standards, it is generally assumed that structures move and deform in only one direction.

[0011] Furthermore, the current standards for earthquake-resistant structural calculations have a major problem: they represent earthquake action using inertial resistance in static calculations and inertial force in dynamic calculations—forces that do not actually exist—yet they are both referred to as "earthquake forces" and confused, and the calculations are presented as if they were using actual forces.

[0012] Furthermore, the inertial resistance, which is a statically calculated seismic force, is calculated from the response acceleration, which cannot be known until the design is completed and the structural specifications are determined. Furthermore, the inertial force, which is the seismic force in dynamic calculations, is calculated from the acceleration at the origin of the non-inertial frame that describes the motion, and this is considered to be a broad region called the open bedrock surface. In these respects, it can be argued that the current structural calculation standards are self-contradictory and contain unrealistic elements.

[0013] (2) Computer software On the other hand, if structural calculations are left to individual discretion, problems such as the earthquake-resistant construction fraud scandal that occurred in the past could arise. This is because there is room for the computer software used in calculations to be modified in order to derive favorable values. To prevent the deriving of favorable values, there are also limitations on the index values ​​that can be used in design and handled by computer software.

[0014] In conventional seismic design, there is virtually only one type of index value used in the design. This value is determined based on the elastic analysis of a simple model and is calculated using computer software according to the method described in the standards, using coefficients that represent the structural characteristics described in the standards. Consequently, it was virtually impossible for individual designers to set the index values ​​they would use in their designs.

[0015] Under the current standards, calculations are performed using methods far more advanced than rudimentary elastic analysis. Therefore, it is a fact that, in terms of calculating indices related to the r-th order eigenmode from eigenvalue analysis of structures using rudimentary models, and in terms of calculating from microtremor diagnosis using ambient microtremor measurements, publicly known technologies are not yet up to par with the calculations required by the current standards. Actual seismic structural calculations under current standards inherently contain the aforementioned problems, resulting in discrepancies between the structural models used until now and the seismic calculations under current standards. The question remains as to how to address these discrepancies. In order to specifically resolve this discrepancy, the reality is that we have no choice but to rely on the individual experience and skills of each designer in terms of structural design.

[0016] Furthermore, as mentioned above, known computer software for performing eigenvalue analysis of modeled structures is based on elastic analysis of simple models and uses coefficients representing structural characteristics specified in seismic design standards. For cases that conform to the methods described in the seismic design standards, it can achieve a certain level of success in eigenvalue analysis of structures.

[0017] However, publicly available computer software restricts free modification to prevent the output of arbitrary results. If publicly available computer software is used to calculate an index under these conditions, it will output a certain calculation result even if, for example, the input settings for the index used in the calculation are not appropriate. Therefore, it has the weakness of returning a meaningless calculation result even if the input settings are ultimately meaningless. From this perspective, the only problems that can be solved by the existence of publicly available computer software are limited to eigenvalue analysis of structures modeled using the simple modeling methods described above. Publicly available computer software is merely a tool for problem-solving, and the existence of such software does not mean that the problems inherent in current standards can be resolved spontaneously.

[0018] (3) Regarding seismic damping Ground vibrations and the resulting vibrations of structures are called vibrations. Structures designed and constructed to support their own weight and maintain their function have the property of absorbing ground vibrations caused by earthquakes and maintaining their shape and position. If this is within their inherent limits, the structure will recover. This is called seismic damping. Furthermore, when ground movement becomes extremely large, objects as a whole will tilt, shift, or sometimes even jump relative to the ground to avoid excessive deformation. These properties of structures are known as seismic damping properties, and they are directly related to maintaining the functionality of the structure.

[0019] Regarding seismic damping, while there are known examples of calculating certain indicators from microtremor diagnosis using ambient microtremor measurements, there are still aspects that remain unclear as to how the indicator values ​​calculated from eigenvalue analysis of modeled structures, related to the r-th order eigenmode, are specifically linked to the indicator values ​​obtained from measuring the performance of the structure.

[0020] (4) Challenges in comprehensively resolving the above issues If structural diagnosis and design of conventional structures are judged individually based on response values ​​from individual response analyses or numerical results from single indicator calculations, it is difficult to move beyond the current level of technology that relies on the individual experience and skills of each designer. Furthermore, while conventional seismic isolation, vibration control, and earthquake-resistant technologies, as explained earlier, can prevent the collapse of structures, they may still lead to the need to discontinue the use of structures due to cracks or other damage.

[0021] The objective of this invention is to provide a calculation method for use in seismic design to improve the seismic damping properties of structures, which eliminates the need to bridge the gap between measurement results and actual designs based on the individual designer's experience and skill. The objective is to provide a calculation method for use in seismic design of structures that can be applied to evaluating and improving the performance of structures, aiming to assess the actual performance of structures during earthquakes without using non-existent forces such as inertial forces or inertial resistance, and to ensure that structural materials do not become inelastic, structures recover, and structural damage is reduced. [Means for solving the problem]

[0022] As a result of diligent research by the inventors, it has been discovered that the spatiotemporal shape and frequency of natural vibrations, which are manifestations of the seismic damping properties of a structure, can be treated using natural vibration vectors. Furthermore, we discovered that by using natural motion vectors to handle the spatiotemporal shape and frequency of natural vibrations, which are manifestations of a structure's seismic damping properties, it becomes possible to quantify and improve seismic damping properties due to inertia, elasticity, and gravity. As a result of utilizing these insights, (1) The spatiotemporal shape and frequency of the natural vibration of a structure are calculated using the natural vibration vector based on measurement data related to natural vibration obtained by ambient microtremor measurement, and (2) The spatiotemporal shape and frequency of the natural motion of the structural model used for seismic design of the structure are calculated using the natural motion vector, based on analysis data regarding the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of the structure. (3) A step of relating the index value obtained by the measurement in (1) and the index value obtained by the analysis in (2) on the same dimension, We found that a calculation method having such properties, for use in seismic design of structures, is suitable for the purpose of the present invention, and thus completed the present invention.

[0023] In other words, the present invention is [1] (1) The spatiotemporal shape and frequency of the natural vibration of a structure are calculated using the natural vibration vector based on measurement data related to natural vibration obtained by ambient microtremor measurement, and (2) The spatiotemporal shape and frequency of the natural motion of the structural model used for seismic design of the structure are calculated using the natural motion vector, based on analysis data regarding the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of the structure. (3) A step of relating the index value obtained by the measurement in (1) and the index value obtained by the analysis in (2) on the same dimension, It has, The present invention provides a calculation method for use in seismic design of structures, characterized in that the natural ground motion vectors in (1) and (2) above include a natural ground motion shape vector, a natural ground motion number vector, and a natural ground motion period vector.

[0024] Furthermore, one aspect of this invention is, [2] RMS is the mean square root of the time history over the duration, Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. Surface measurement of constant microtremor is performed at each center point of a plane formed by at least three measurement points. This is a measurement, The center point of the surface measurement in continuous micro-tremor measurement is the centroid of at least three measurement points. Each of the measurement points in the point measurement of the continuous micro-motion measurement or the center point of the surface measurement of the continuous micro-motion measurement is In the case of a multi-layered structure with two or more layers, the upward direction from the part of the structure that is in contact with the ground. Each measurement axis corresponds to a point on each layer of a multi-layered structure through which a measurement axis runs vertically. (4) The natural vibration vector obtained by the measurement in (1) above includes the natural vibration shape vector, The natural vibration shape vector is, A vector representing the natural vibration shape, wherein the absolute value of its components is the RMS ratio of at least one time history selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point, with respect to the reference time history. (5) The natural vibration vector obtained by the measurement in (1) above includes the natural vibration number vector, The natural frequency vector is, A vector representing the frequency of natural vibration, the vector whose components are at least one central frequency selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. (6) The natural vibration vector obtained by the measurement in (1) above includes the natural vibration period vector, The natural vibration period vector is, A vector representing the period of natural vibration, the vector whose components are at least one central period selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. (7) The natural vibration vector obtained by the analysis in (2) above includes the natural vibration shape vector, The natural vibration shape vector is, A vector representing the natural vibration shape, wherein the absolute value of its components is the RMS ratio of at least one time history selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point, with respect to the reference time history. (8) The natural vibration vector obtained by the analysis in (2) above includes the natural vibration period vector, The natural vibration period vector is, A vector representing the period of natural vibration, the vector whose components are at least one central period selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. (9) The natural motion vector obtained by the analysis in (2) above includes the natural motion number vector, The natural frequency vector is, A vector representing the frequency of the natural vibration, the components of which are at least one central frequency selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. This provides a calculation method for use in seismic design of the structures described in [1] above.

[0025] Furthermore, one aspect of this invention is, [3](10) The natural period of the translational motion of the measurement point obtained by point measurement of constant microtremor measurement is The steps involve calculating the three directional components in a Cartesian coordinate system corresponding to the velocity component of the point measurement of the natural frequency vector, and the three directional components in a Cartesian coordinate system corresponding to the displacement component of the point measurement of the natural frequency vector, The natural period of the translational motion of the center point, as measured by surface measurement using continuous micro-motion measurement, The steps involve calculating the three directional components in the Cartesian coordinate system corresponding to the velocity component of the surface measurement of the natural frequency vector, and the three directional components in the Cartesian coordinate system corresponding to the displacement component of the surface measurement of the natural frequency vector, The natural period of rotational motion of the center point, measured by surface measurement using continuous micro-motion measurement, The steps involve calculating the three directional components in the Cartesian coordinate system corresponding to the rotation angle component of the surface measurement of the natural frequency vector, and the three directional components in the Cartesian coordinate system corresponding to the angular acceleration component of the surface measurement of the natural frequency vector, including, This provides a calculation method for use in seismic design of the structures described in [1] or [2] above. .

[0026] Furthermore, one aspect of this invention is, [4](11) The step of calculating the kinetic energy composition ratio in point measurements as the ratio of the total kinetic energy of the point-dominated portion at each measurement point in the constant microtremor measurement to the three directional components in the Cartesian coordinate system, (12) The kinetic energy composition ratio in surface measurement is calculated as the ratio of the total kinetic energy of the center point-dominated portion at each center point obtained from surface measurement of constant micro-motion measurement, by separating it into the translational motion component from the relationship between the translational motion component and the rotational motion component, and then calculating the three directional components in the orthogonal coordinate system. The kinetic energy composition ratio in surface measurement is calculated as the ratio of the kinetic energy composition ratio calculated for the three directional components of the orthogonal coordinate system for each measurement point to the kinetic energy composition ratio calculated for the three directional components of the orthogonal coordinate system for each center point obtained by surface measurement of constant micro-tremor measurement. This is done by separating the rotational motion component from the relationship between the translational motion component and the rotational motion component, and then calculating it for the three directional components of the orthogonal coordinate system. (13) A step in which the spatiotemporal shape of the natural motion of a structural model used for seismic design of a structure is calculated based on data relating to the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of a structure, The kinetic energy composition ratio of the dominant part corresponding to each measurement point is calculated for each measurement point using the components of the r-order eigenmode vector, which corresponds to the three-directional components of the orthogonal coordinate system of the displacement of the contact point of the structural model corresponding to each measurement point, and for the three-directional components of the orthogonal coordinate system of the contact point of the structural model corresponding to each measurement point. The steps include: calculating the translational motion component of the kinetic energy composition ratio of the dominant portion corresponding to each center point obtained by surface measurement for the three directional components of the Cartesian coordinate system corresponding to each center point of measurement; The rotational motion component of the kinetic energy composition ratio of the dominant portion corresponding to each center point measured on the surface is calculated for the three directional components of the Cartesian coordinate system corresponding to each center point measured. including, This provides a calculation method for use in seismic design of any of the structures described in [1] to [3] above.

[0027] Furthermore, one aspect of this invention is, [5](14) The rate of change of kinetic energy in point measurement is calculated for the three directional components of the Cartesian coordinate system as the ratio of the kinetic energy composition ratio of the measurement point to the kinetic energy composition ratio of the reference point obtained by each point measurement of the constant microtremor measurement, in the calculation step, (15) The translational component of the rate of change of kinetic energy in surface measurement is calculated for the three directional components of the Cartesian coordinate system as the ratio of the kinetic energy composition ratio of the translational component in surface measurement of the center point-dominated portion at the center point for each surface measurement of the reference surface for each surface measurement of the normal microtremor measurement, to the ratio of the kinetic energy composition ratio of the translational component in surface measurement of the center point-dominated portion at the center point for each surface measurement of the normal microtremor measurement, The rotational component of the rate of change of kinetic energy in surface measurement is calculated for the three directional components of the Cartesian coordinate system as the ratio of the kinetic energy composition ratio of the rotational component in surface measurement of the center point in the center point-dominated portion of surface measurement by constant micro-motion measurement to the kinetic energy composition ratio of the rotational component in surface measurement of the center point-dominated portion of surface measurement by constant micro-motion measurement for each surface measurement, and (16) A step in which the spatiotemporal shape and frequency of the natural motion of a structural model used for seismic design of a structure are calculated based on analysis data relating to the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of a structure, The step involves calculating the rate of change of kinetic energy of the dominant portion corresponding to each measurement point, as the ratio of the kinetic energy composition ratio of the dominant portion corresponding to each measurement point to the kinetic energy composition ratio of the dominant portion corresponding to the reference point, for the three directional components of the Cartesian coordinate system of the measurement point. The process involves calculating the translational component of the rate of change of kinetic energy of the dominant portion corresponding to each center point, as measured by surface measurement, as the ratio of the translational component of the kinetic energy composition ratio of the dominant portion corresponding to each center point, as measured by surface measurement, to the translational component of the kinetic energy composition ratio of the dominant portion corresponding to the reference point, for the three directional components of the Cartesian coordinate system of the center point. The step of calculating, for each center point by surface measurement, the ratio of the rotational motion component of the change rate of the kinetic energy of the governing part corresponding to the center point to the rotational motion component of the kinetic energy composition ratio of the governing part corresponding to the reference point by surface measurement, for the three direction components of the orthogonal coordinate system of the center point, and including A calculation method for use in the seismic design of the structure according to any one of the above [1] to [4] is provided.

[0028] Also, one aspect of the present invention is [6] The k component is one of the three direction components of the orthogonal coordinate system where k = x, y, z, The center point P is the center point of three measurement points A(x a ,y a ,0), B(x b ,y b ,0) and C(x c ,y c ,0) on the measurement surface, The coordinate values x a ,y a ,x b ,y b ,x c , and y c of each measurement point are related to a coordinate system parallel to the inertial system that describes at least one selected from the group consisting of velocity, acceleration, jerk, rotational angular velocity, rotational angular acceleration, and rotational angular jerk, with the center point P as the origin, The displacement p k (t) and the rotation angle θ k (t) of the center point P are calculated from the k components a a ,y a ,0), B(x b ,y b ,0) and C(x c ,y c ,0) of the three measurement points on the measurement surface, for the respective displacement time histories of the k components a k (t), b k (t) and c k (t), The velocity p ’ k(t) and the rotational angular velocity θ ’k(t) is the three measurement points A(x) on the measurement surface. a ,y a ,0),B(x b ,y b ,0) and C(x c ,y c The k-component a of the respective velocity time history of ,0) ’ k(t),b ’ k(t) and ck ’ The step calculated from (t), Acceleration p at the center point P ’’ k(t) and rotational angular acceleration θ ’’ k(t) is the three measurement points A(x) on the measurement surface. a ,y a ,0),B(x b ,y b ,0) and C(x c ,y c The k-component a of the respective velocity time history of ,0) ’’ k(t),b ’’ k(t) and ck ’’ The step calculated from (t), jerk p of the center point P ’’’ k(t) and rotational angular jerk θ ’’’ k(t) is the three measurement points A(x) on the measurement surface. a ,y a ,0),B(x b ,y b ,0) and C(x c ,y c The k-component a of the respective jerk time history of ,0) ’’’ k(t),b ’’’ k(t) and ck ’’’ The step calculated from (t), A group consisting of each of the steps is selected, and includes at least one step, The single '' symbol in each step represents the first time derivative, the '' symbol represents the second time derivative, and the '''' symbol represents the third time derivative. This provides a calculation method for use in seismic design of any of the structures described in [1] to [5] above.

[0029] Furthermore, one aspect of this invention is, [7] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The coordinates in the inertial frame of the equilibrium positions of both measurement points A and B are given by A(x a ,y a ,z a ), B(x b ,y b ,z b ) and Displacement time history is a k (t),b k (t) and The process includes a step in which the strain between two measurement points A and B is calculated as the ratio of the length of deformation to the original length of the two measurement points A and B before deformation, The length of the aforementioned deformation is, The coordinates of the two measurement points A and B are A(x a ,y a ,z a ) and B(x b ,y b ,z b ) Furthermore Displacement time history a k (t) and b k (t) Calculated using, This provides a calculation method for use in seismic design of any of the structures described in [1] to [6] above.

[0030] Furthermore, one aspect of this invention is, [8] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The continuous micro-vibration measurement is performed at each individual measurement point. Each measurement point is assigned a number where i=1 is the lowest point on each measurement axis, and each measurement axis is assigned a number where j=1 is the axis with a reference point, and is identified by a pair of natural numbers ij. The continuous micro-vibration measurement of each plane is performed at the center point of a plane formed by at least three measurement points. The center point is P ij So, the three points A are used to calculate the motion of the central point. ij B ij , Cij It is represented as, When a measurement point or center point is hypothetically defined within the ground directly below the lowest point of each measurement axis, this is set to i=0. RMS is the root mean square of a time history x(t) at a duration t0.

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[0031] Furthermore, one aspect of this invention is, [9] The transmission rate is the RMS ratio of the time history x(t) with respect to the reference time history y(t).

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[0032] Also, one aspect of the present invention is

[10] The k components are the three-direction components of the orthogonal coordinate system where k = x, y, z, The point measurement of the microtremor measurement is the measurement for each measurement point, The measurement points are identified by a pair of natural numbers ij, where the numbering of the lowest point for each measurement axis is i = 1, and the numbering of the axis having the reference point for the measurement axis is j = 1, The surface measurement of the microtremor measurement is the measurement for each center point of the plane formed by at least three measurement points, The center point is P ij where the three points for calculating the movement of the center point are A ij 、B ij 、C ij It is expressed as When a measurement point or a center point is assumed in the ground directly below the lowest point of each measurement axis, this is set to i = 0, The absolute value of the α ijk component of the eigenvibration shape vector in the point measurement is the transmission rate of the k component such as the displacement of the ij-th measurement point

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[0033] the k component, where k = x, y, z, is the three-direction component of the orthogonal coordinate system, the measurement point of the r-th natural mode vector corresponding to the measurement point by point measurement of the constant micro-vibration measurement is the contact point of the structural model corresponding to the ij-th measurement point, the center point P of the plane formed by at least three measurement points A ij , B ij , C ij by surface measurement of the constant micro-vibration measurement corresponds to the center point P ij of the r-th natural mode vector, and the center point P ij is the contact point of the structural model corresponding to the center point P ij , the number with the lowest point of each measurement axis of the structural model set as i = 1 is assigned a number with the axis having a reference point as j = 1 on the measurement axis of the structural model, and is identified by a pair of natural numbers ij. When a measurement point or a center point is assumed in the ground directly below the lowest point of each measurement axis, this is set as i = 0. The (r) on the right shoulder of the following formulas indicates that it is calculated from the r-th natural mode. The spatio-temporal shape and vibration frequency of the natural vibration of the structural model used for the seismic design of the structure are obtained from the r-th natural mode obtained by eigenvalue analysis of the structural model used for the seismic design of the structure, and are values corresponding to the absolute values of the components of the natural vibration shape vector

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[10] above.

[0034] Furthermore, one aspect of this invention is,

[12] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. Each measurement point is assigned a number where i=1 is the lowest point on each measurement axis, and each measurement axis is assigned a number where j=1 is the axis with a reference point, and is identified by a pair of natural numbers ij. Surface measurement in continuous micro-vibration measurement is a measurement at the center point of a plane created by at least three measurement points. The center point is P ij So, the three points A are used to calculate the motion of the central point. ij B ij , C ij It is represented as, When a measurement point or center point is hypothetically defined within the ground directly below the lowest point of each measurement axis, this is set to i=0. T tijk However, this is the natural period of the k component of the translational motion at the first measurement point ij. T tPijk However, the P ij This is the natural period of the k-component of the translational motion of the central point. The first measurement point ij, or the center point P. ij The natural period of translational motion in is

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[11] above.

[0035] Furthermore, one aspect of this invention is,

[13] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. Each measurement point is assigned a number where i=1 is the lowest point on each measurement axis, and each measurement axis is assigned a number where j=1 is the axis with a reference point, and is identified by a pair of natural numbers ij. Surface measurement in continuous micro-vibration measurement is a measurement at the center point of a plane created by at least three measurement points. The center point is P ij So, the three points A are used to calculate the motion of the central point. ij B ij , C ij It is represented as, When a measurement point or center point is hypothetically defined within the ground directly below the lowest point of each measurement axis, this is set to i=0. In point measurement, the part governed by the ij-th measurement is the part of the structure that is considered to move together with the ij-th measurement point in point measurement. The proportion of each kinetic component in the total kinetic energy of the part dominated by the ij-th in point measurements is called the kinetic energy composition ratio, and is calculated using the following formula:

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[12] above.

[0036] Furthermore, one aspect of this invention is,

[14] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The measurement point of the r-th order eigenmode vector corresponding to the measurement point obtained by point measurement in continuous microtremor measurement is the junction of the structural model corresponding to the ij-th measurement point. At least three measurement points A by surface measurement using continuous micro-vibration measurement. ij B ij , C ij The center point P of the plane created by ij Center point P of the r-th eigenmode vector corresponding to this vector ij However, the center point P ij It is the point of contact of the corresponding structural model, Each measurement axis of the structural model is assigned a number with i=1 at its lowest point, and the measurement axes of the structural model are assigned numbers with j=1 for axes having a reference point, and are identified by pairs of natural numbers ij. When a measurement point or center point is hypothetically defined within the ground directly below the lowest point of each measurement axis, this is set to i=0. The (r) in the superscript of each of the following equations is calculated from the r-th eigenmode, The spatiotemporal shape and frequency of the natural vibration of a structural model used in seismic isolation design for structures. From the r-th order eigenmodes obtained by eigenvalue analysis of the structural model used for seismic isolation design of structures, the kinetic energy composition ratio of the ij-dominant portion and the Pil-dominant portion is calculated. The kinetic energy composition ratio of the ij-dominated portion in point measurements is,

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[13] above.

[0037] Furthermore, one aspect of this invention is,

[15] In the case where there are multiple layers in a structure that include parts that move together in a generally horizontal direction, and measurement points are provided on these layers along the vertical measurement axis, In point measurements of continuous microtremor measurement, the jth measurement axis of the relative displacement of the i+1 layer with respect to the i-th layer. The value at is the inter-layer displacement of the ijth layer, In surface measurements using continuous micro-motion measurement, the relative displacement and relative rotation angle of each layer on the Pj measurement axis are measured by P ij Interstory displacement and P ij This is the interlayer rotation angle, i is i=0, ..., n, In the virtual layer and virtual measurement point (i=0), the relative displacement and relative rotation angle are set to zero, and the interlayer displacement of the 0th layer is calculated. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Interlayer displacement of the ijth layer, and the Pth layer ij Interstory displacement is,

number

number

number

number

number

number

[14] above.

[0038] Furthermore, one aspect of this invention is,

[16] The value corresponding to the inter-story displacement transmission coefficient of the ijth order of the structure is obtained from the point measurement or the junction value corresponding to the surface measurement of the rth order eigenmode obtained by eigenvalue analysis of the structural model.

number

number

[15] above.

[0039] Furthermore, one aspect of this invention is,

[17] In the case where there are multiple layers in a structure that include parts that move together as a whole in a generally horizontal direction, and measurement points are provided on these layers along the vertical measurement axis, In point measurements of constant microtremor measurement, the value of the relative displacement of the i+1th layer with respect to the i-th layer at the j-th measurement axis is the inter-layer displacement of the ij-th layer. The inter-story stiffness of the ijth inter-story is calculated from the ratio of the inter-story displacement of the ijth inter-story to the inter-story stress of the ijth inter-story. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The inter-story stiffness of the structure, and its value converted to a natural period, i.e., the translational motion k-direction component of the inter-story vibration period of the structure,

number

number

number

[16] above.

[0040] Furthermore, one aspect of this invention is,

[18] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. From the junction values ​​corresponding to point measurements or surface measurements of the r-th order eigenmode obtained by eigenvalue analysis of the structural model, the values ​​corresponding to the k-direction component of the translational motion of the inter-story stiffness of the ij-th story and the inter-story vibration period are obtained.

number

number

number

[17] above.

[0041] Furthermore, one aspect of this invention is,

[19] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. Each measurement point is assigned a number where i=1 is the lowest point on each measurement axis, and each measurement axis is assigned a number where j=1 is the axis with a reference point, and is identified by a pair of natural numbers ij. Surface measurement in continuous micro-vibration measurement is a measurement at the center point of a plane created by at least three measurement points. The center point is P ijSo, the three points used to calculate the motion of the center point are A ij B ij , C ij It is represented as, If a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this point is set to i=0. The support portion is a measurement point located above a measurement surface, or a portion of the measurement surface that is located above a measurement surface on the same measurement axis. Support portion ij and P of the structure ij Displacement (α=d), velocity (α=v), and acceleration (α=a) of the support part, and the P ij Rotation angle (β=θ) of the support part, angular velocity (β=θ ’ ) and angular acceleration (β=θ ’’ The k-direction component of the response magnification of ) is

number

number

number

number

[18] above.

[0042] Furthermore, one aspect of this invention is,

[20] The k component is the three components of the Cartesian coordinate system k=x,y,z, The component e corresponding to the k-direction displacement of the r-th eigenmode vector at the ij-th measurement point obtained by eigenvalue analysis of the structural model dijk (r) Using this, the value corresponding to the response magnification of the ij-th support portion is

number

number

number

number

[19] above.

[0043] Furthermore, one aspect of this invention is,

[21] The magnitude of the elastic response that occurs in each part of the structure due to the assumed seismic motion is calculated by multiplying the average value of the displacement strong motion RMS that is estimated to occur at a reference point or reference plane due to the assumed seismic motion by the transmissibility obtained by ambient microtremor measurement or eigenvalue analysis. Assuming that the period of the elastic response is equal to the natural vibration period, The k component is the three components of the Cartesian coordinate system k=x,y,z. The estimated values ​​of the elastic displacement, velocity, and acceleration of the strong earthquake at measurement point ij, as well as the period, are:

number

number

number

number

[20] above.

[0044] Furthermore, one aspect of this invention is,

[22] The magnitude of the inelastic response that occurs in each part of the structure due to the assumed seismic motion is calculated from the average value of the strong motion RMS of the displacement at a reference point estimated to occur due to the assumed seismic motion, the duration of the strong motion, and the transmissibility. The magnitude of the inelastic response occurring in each part of the structure due to the assumed seismic motion is calculated from values ​​including the average value of the strong motion RMS of the reference plane displacement estimated to occur due to the assumed seismic motion, the duration of the strong motion, and the transmissibility. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The cumulative inelastic displacement occurring in the k direction between layers ij is

number

number

number

number

[21] above.

[0045] Furthermore, one aspect of this invention is,

[23] The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The component e of the r-th order eigenmode vector obtained by eigenvalue analysis of the structural model dijk (r) and natural period T r A step of calculating the magnitude of the elastic and inelastic responses caused by the assumed seismic motion using the following: The strong motion RMS of elastic displacement, velocity, and acceleration occurring at the r-th eigenmode vector, as well as the period, are calculated from the r-th eigenmode vector.

number

number

number

number

number

number

number

[22] above.

[0046] Furthermore, one aspect of this invention is,

[24] To calculate using a computer, This provides a calculation method for use in seismic design of any of the structures described in [1] to

[23] above.

[0047] Furthermore, the present invention is

[25] To calculate using a computer, A seismic design support system that uses a calculation method for use in seismic design of any of the structures described in [1] to

[23] above, (1) A means for calculating an index value for a structure based on measurement data related to natural vibrations obtained by ambient microtremor measurement, using the spatiotemporal shape and frequency of the natural vibration of the structure, and a means for storing the index value obtained by measurement. (2) A means for calculating an analytical index value for a structure based on data relating to the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of a structure, using the spatiotemporal shape and frequency of the natural motion of the structural model used for seismic design of a structure, and a means for saving the analytical index value. Equipped with, (3) A means for comparing index values ​​obtained by measuring the structure with index values ​​obtained by analyzing the structural model, This invention provides a seismic design support system that includes [specific features / features].

[0048] Furthermore, one aspect of this invention is,

[26] (4) Means for classifying structures and structural models into similar groups, (5) A means for determining a recommended range for the index value obtained by measurement for each similar group of classified structures, (6) A means for determining a recommended range for the index value obtained by analysis for each similar group of classified structural models, (7) A means for comparing the recommended range for the index value determined by at least one of (5) and (6) above with the index value obtained by at least one of (1) and (2) above, The present invention provides the seismic design support system described in

[25] above, which has the following features.

[0049] Furthermore, one aspect of this invention is,

[27] The seismic design support system described in

[25] or

[26] above is provided, wherein the index for determining the index value includes at least one selected from the group consisting of natural vibration displacement shape vector, natural vibration acceleration shape vector, natural vibration rotation angle shape vector, natural vibration angular acceleration shape vector, rotational motion natural period vector, translational motion natural period vector, r-th order natural period, interstory vibration period, acceleration distribution coefficient, angular acceleration distribution coefficient, base stress coefficient, base moment coefficient, rate of change of kinetic energy, degree of damage, and risk index.

[0050] Furthermore, one aspect of this invention is,

[28] (8) Means for proposing reinforcement for the structure under evaluation, It has, The indicators used to determine the index value include the degree of damage, The present invention provides a seismic design support system according to any one of the above

[25] to

[27] , which has a means for determining the location of reinforcement for a structure under evaluation based on a comparison of an index value of the degree of damage with a recommended range of the index value of the degree of damage.

[0051] Furthermore, one aspect of this invention is,

[29] A means by which the recommended range for the index value obtained by the measurement in (5) above is determined by artificial intelligence, The recommended range for the index value obtained by the analysis in (6) above is determined by artificial intelligence, The recommended range and index values ​​in (7) above are compared by artificial intelligence, The present invention provides a seismic design support system according to any one of the above

[25] to

[28] , which has the following characteristics.

[0052] Furthermore, one aspect of this invention is,

[30] The present invention provides the seismic design support system described in

[29] above, which has means for determining the locations of seismic reinforcement required for the structure to be evaluated using artificial intelligence.

[0053] Furthermore, one aspect of this invention is,

[31] A means for registering the estimation items and unit prices for each estimation item necessary for seismic reinforcement of the structure to be evaluated, A means for calculating the estimated cost of seismic reinforcement for a structure under evaluation in multiple stages, depending on the timing and scope of the seismic reinforcement to be implemented, The present invention provides a seismic design support system described in any of the above

[25] to

[30] , which has the following characteristics:

[0054] Furthermore, the present invention is

[32] A step of comparing the index values ​​obtained by eigenvalue analysis using the structural model of the structure to be evaluated before seismic reinforcement of the structure to be evaluated with the recommended range proposed by the seismic design support system, The process involves comparing the index values ​​obtained from ambient microtremor measurements of the structure under evaluation before seismic reinforcement with the recommended range proposed by the seismic design support system. The process involves comparing the index values ​​obtained from ambient microtremor measurements of the structure under evaluation after seismic reinforcement with the recommended range proposed by the seismic design support system. The present invention provides a seismic design method using a seismic design support system described in any of the above

[25] to

[31] , including the above.

[0055] Furthermore, the present invention is

[33] A step of calculating index values ​​by analysis using a structural model of the structure to be evaluated, before seismic reinforcement of the structure to be evaluated. and A step to calculate index values ​​by measuring the ambient microtremors of the structure under evaluation before seismic reinforcement of the structure under evaluation. This includes at least one of the following steps: The steps include identifying structures similar to the structure being evaluated that have been damaged by earthquakes in the past, The index values ​​obtained from at least one of the analysis and measurement of the structure under evaluation, The index values ​​obtained from at least one of the analysis and / or measurement of a structure similar to the structure being evaluated, Based on the comparison, the damage status of the structure to be evaluated is predicted based on the damage status of structures similar to the structure to be evaluated that have been damaged by earthquakes in the past. This invention provides a method for predicting earthquake damage to a structure under evaluation, using a seismic design support system described in any of the above

[25] to

[31] , including the above.

[0056] Furthermore, one aspect of this invention is,

[34] A step of calculating index values ​​by analysis using a structural model of the structure to be evaluated, before seismic reinforcement of the structure to be evaluated. and A step to calculate index values ​​by measuring the ambient microtremors of the structure under evaluation before seismic reinforcement of the structure under evaluation. This includes at least one of the following steps: The process includes a step of calculating an index value by measuring the ambient microtremor of the structure to be evaluated after seismic reinforcement of the structure to be evaluated, The steps include identifying structures similar to the structure under evaluation that have undergone seismic reinforcement before being damaged by an earthquake in the past, and that have been damaged by an earthquake in the past, The index values ​​obtained from at least one of the analysis and / or measurement of the structure under evaluation before seismic reinforcement, The index values ​​obtained from measurements after seismic reinforcement of the structure under evaluation, The index values ​​obtained from at least one of the analysis and / or measurement of a structure similar to the structure being evaluated, From the contrast, A step of predicting the damage status of the structure under evaluation based on the damage status of structures similar to the structure under evaluation, which have undergone seismic reinforcement before being damaged by earthquakes in the past, and which have been damaged by earthquakes in the past. This invention provides a method for predicting damage caused by earthquakes after seismic reinforcement of a target structure, using a seismic design support system described in any of the above

[25] to

[31] , including the above. [Effects of the Invention]

[0057] The calculation method for seismic design of structures according to the present invention opens the way to performing calculations for seismic design of structures from multiple perspectives using various index values ​​obtained through analysis and measurement. Conventionally, the structural characteristics of a structure under design have been determined based on elastic analysis of a simple model, and its structural performance has been evaluated and designed using index values ​​calculated using coefficients according to the method described in the standards. However, with the present invention, it is possible to express structural characteristics and structural performance using various index values ​​obtained from actual measurements and detailed structural model analysis, thereby improving the seismic resistance of structures without relying on the skills and abilities of individual designers.

[0058] Furthermore, the seismic design support system, which applies the calculation method for seismic design of structures according to the present invention, allows for the determination of the design validity of improving the seismic damping properties of a structure under evaluation by comparing it with similar structures. This eliminates subjective judgments based on the individual designer's experience and skill, thereby improving the accuracy of seismic design more objectively.

[0059] Furthermore, by using a seismic design support system that applies the calculation method for seismic design of structures according to the present invention, seismic design of structures can be performed quickly and accurately. [Brief explanation of the drawing]

[0060] [Figure 1] Figure 1 is a schematic conceptual diagram illustrating the performance evaluation of a structure (Explanation Figure 1.3.1). [Figure 2] Figure 2 is a schematic diagram illustrating the recognition structure of objects and events in the database used for seismic isolation design (seismic isolation design DB) (Explanation Figure 1.4.1). [Figure 3] Figure 3 is a seismic isolation design flowchart illustrating one form of the present invention (Figure 1.4.2). [Figure 4] Figure 4 is a schematic diagram illustrating the relationship between the arrangement of the measurement axis, measurement point, center point, and measurement surface, and the governing area (Explanation Figure 2.3.1). [Figure 5] Figure 5 is a schematic diagram illustrating the small displacement AA' caused by rotation of vector PA at a small rotation angle |θ| with γ as the axis of rotation (Explanation Figure 3.1.1). [Figure 6] Figure 6 is a schematic diagram illustrating the relationship between physical quantities related to structures, ground, and their vibrations, and the indicators used in seismic design obtained by measuring and calculating these quantities (Explanation Figure 3.3.1). [Figure 7] Figure 7 is a schematic conceptual diagram illustrating the dominant parts in point measurement and surface measurement (Explanation Figure 3.5.1). [Figure 8] Figure 8 is a schematic diagram illustrating the relationship between the layers, measurement points, center point, dominant portion, and supporting portion of the structure (Explanation Figure 4.1.1). [Figure 9] Figure 9 is a schematic diagram illustrating the relationship between the components of interstory displacement and interstory rotation angle (Explanation Figure 4.1.2). [Figure 10] Figure 10 is a table summarizing the average RMS values ​​of the three components of earthquake and displacement, as well as the duration of the strong motion (Table 4.4.1). [Figure 11] Figure 11 is a graph showing the relationship between the average RMS displacement σEd calculated from seismic motion observation records and the measured seismic intensity (Explanation Figure 4.4.1). [Figure 12] Figure 12 is a graph showing the relationship between the average duration of strong displacement motion s0 calculated from seismic motion observation records and the measured seismic intensity (Explanation Figure 4.4.2). [Figure 13] Figure 13 is a graph showing the relationship between the average displacement strong motion duration s0 calculated from seismic motion observation records and the magnitude (Explanation Figure 4.4.2). [Figure 14] Figure 14 is a schematic diagram illustrating the relationship between the current standards for seismic action, structural models, and coordinate systems (Explanation Figure 4.5.1). [Figure 15] Figure 15 is a schematic diagram illustrating the relationship between actual seismic activity and inertial and non-inertial frames of reference (Explanation Figure 4.5.2). [Figure 16] Figure 16 is a table (Explanation Table 6.2.1-1) that explains the timing, indicators, and judgment criteria for performance evaluation up to the completion of seismic reinforcement design. [Figure 17] Figure 17 is a table explaining the timing, indicators, and criteria for performance evaluation up to the completion of seismic reinforcement design (Table 6.2.1-2). [Figure 18] Figure 18 is a schematic diagram illustrating the relationship between the overall structural model of a 6-story reinforced concrete apartment building and the measurement axes (Explanation Figure 6.2.1). [Figure 19] Figure 19 is a schematic diagram illustrating the structural framework of a six-story reinforced concrete (RC) apartment building along the Y1 axis. [Figure 20] Figure 20 shows schematic enlargements, each of which is a division of the frame diagram in Figure 19, enlarged sequentially from left to right. [Figure 21]Figure 21 shows schematic enlargements, each of which is a division of the frame diagram in Figure 19, enlarged sequentially from left to right. [Figure 22] Figure 22 shows schematic enlargements of the frame diagram in Figure 19, each divided into three sections and enlarged sequentially from left to right. [Figure 23] Figure 23 is a schematic diagram illustrating the floor plan of a six-story reinforced concrete apartment building along the Y1 street. [Figure 24] Figure 24 shows schematic enlargements, each of which is a three-part diagram of the layout in Figure 23, enlarged sequentially from left to right. [Figure 25] Figure 25 shows schematic enlargements, each of which is a three-part division of the layout diagram in Figure 23, enlarged sequentially from left to right. [Figure 26] Figure 26 shows schematic enlargements, each of which is a three-part diagram of the layout in Figure 23, enlarged sequentially from left to right. [Figure 27] Figure 27 is a table summarizing the natural periods, stimulation coefficients, and effective mass ratios of the 1st to 10th orders (Table 6.2.2). [Figure 28] Figure 28 is a graph plotting the values ​​of the natural vibration displacement shape vectors measured at points, with the x-component of the displacement on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 29] Figure 29 is a graph plotting the values ​​of the natural vibration displacement shape vectors measured at points, with the y-component of the displacement on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 30] Figure 30 is a graph plotting the values ​​of the natural vibration displacement shape vectors measured at points, with the z component of the displacement on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 31] Figure 31 is a graph plotting the values ​​of the natural vibration displacement shape vectors measured on the surface, with the x-component of the displacement along the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 32]Figure 32 is a graph plotting the values ​​of the natural vibration displacement shape vectors measured on the surface, with the y-component of the P1-axis displacement in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 33] Figure 33 is a graph plotting the values ​​of the natural vibration displacement shape vectors measured on the surface, with the z component of the displacement along the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 34] Figure 34 is a graph plotting the values ​​of the natural vibration rotation angle shape vector obtained from surface measurements, with the x-component of the rotation angle of the P1 axis in Figure 18 on the horizontal axis (radians / cm) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 35] Figure 35 is a graph plotting the values ​​of the natural vibration rotation angle shape vector obtained from surface measurements, with the y-component of the rotation angle of the P1 axis in Figure 18 on the horizontal axis (radians / cm) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 36] Figure 36 is a graph plotting the values ​​of the natural vibration rotation angle shape vector obtained from surface measurements, with the z component of the rotation angle of the P1 axis in Figure 18 on the horizontal axis (radians / cm) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 37] Figure 37 is a graph plotting the values ​​of the natural vibration acceleration shape vectors measured at points, with the x-component (1 / s²) of the acceleration on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 38] Figure 38 is a graph plotting the values ​​of the natural vibration acceleration shape vectors measured at points, with the y-component (1 / s²) of the acceleration on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 39] Figure 39 is a graph plotting the values ​​of the natural vibration acceleration shape vectors measured at points, with the z component (1 / s²) of the acceleration on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 40]Figure 40 is a graph plotting the values ​​of the natural vibration acceleration shape vectors measured on the surface, with the x-component of the acceleration along the P1 axis in Figure 18 on the horizontal axis (1 / s²) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 41] Figure 41 is a graph plotting the values ​​of the natural vibration acceleration shape vectors measured on the surface, with the y-component of the acceleration along the P1 axis in Figure 18 on the horizontal axis (1 / s²) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 42] Figure 42 is a graph plotting the values ​​of the natural vibration acceleration shape vectors measured on the surface, with the z component of the acceleration along the P1 axis in Figure 18 on the horizontal axis (1 / s²) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 43] Figure 43 is a graph plotting the values ​​of the natural vibration angular acceleration shape vectors measured on the surface, with the x-component of the angular acceleration of the P1 axis in Figure 18 on the horizontal axis (radians / (s²cm)) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 44] Figure 44 is a graph plotting the values ​​of the natural vibration angular acceleration shape vectors measured on the surface, with the y-component of the angular acceleration of the P1 axis in Figure 18 on the horizontal axis (radians / (s2cm)) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 45] Figure 45 is a graph plotting the values ​​of the natural vibration angular acceleration shape vector from surface measurements, with the z component of the angular acceleration on the P1 axis in Figure 18 on the horizontal axis (radians / (s²cm)) and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 46] Figure 46 is a graph plotting the values ​​of the translational motion natural period vectors measured at points, with the x-component of the r-th order natural period on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 47] Figure 47 is a graph plotting the values ​​of the translational motion natural period vectors measured at points, with the y component of the r-th order natural period on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 48]Figure 48 is a graph plotting the values ​​of the translational motion natural period vectors measured at points, with the z component of the r-th order natural period on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 49] Figure 49 is a graph plotting the values ​​of the translational motion natural period vectors measured on the surface, with the x-component of the r-th order natural period of the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 50] Figure 50 is a graph plotting the values ​​of the translational motion natural period vectors measured on the surface, with the y component of the r-th order natural period of the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 51] Figure 51 is a graph plotting the values ​​of the translational motion natural period vectors measured on the surface, with the z component of the r-th order natural period of the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 52] Figure 52 is a graph plotting the values ​​of the rotational motion natural period vectors measured on the surface, with the x-component of the r-th order natural period of the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 53] Figure 53 is a graph plotting the values ​​of the rotational motion natural period vectors measured on the surface, with the y component of the r-th order natural period of the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 54] Figure 54 is a graph plotting the values ​​of the rotational motion natural period vectors measured on the surface, with the z component of the r-th order natural period of the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 55] Figure 55 is a graph plotting the values ​​of the rate of change of kinetic energy measured at a single point, with the x-component of the rate of change of kinetic energy on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 56]Figure 56 is a graph plotting the kinetic energy change rate values ​​measured at points, with the y-component of the kinetic energy change rate on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 57] Figure 57 is a graph plotting the kinetic energy change rate values ​​measured at points, with the z component of the kinetic energy change rate on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 58] Figure 58 is a graph plotting the values ​​of the rate of change of kinetic energy measured across surfaces, with the x-component of the rate of change of kinetic energy on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 59] Figure 59 is a graph plotting the kinetic energy change rate values ​​measured across surfaces, with the y-component of the kinetic energy change rate on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 60] Figure 60 is a graph plotting the kinetic energy change rate values ​​measured across surfaces, with the z component of the kinetic energy change rate on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 61] Figure 61 is a graph plotting the values ​​of the rotational kinetic energy change rate measured on a surface, with the x-component of the rotational kinetic energy change rate on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 62] Figure 62 is a graph plotting the values ​​of the rotational kinetic energy change rate measured on a surface, with the y component of the rotational kinetic energy change rate on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 63] Figure 63 is a graph plotting the values ​​of the rotational kinetic energy change rate measured on a surface, with the z component of the rotational kinetic energy change rate on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 64]Figure 64 is a graph plotting the inter-story seismic period vector values ​​measured at points, with the x-component (s) of the inter-story seismic period on the X1Y1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 65] Figure 65 is a graph plotting the inter-story seismic period vector values ​​measured at points, with the y-component (s) of the inter-story seismic period on the X1Y1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 66] Figure 66 is a graph plotting the inter-story seismic period vector values ​​measured at points, with the z component (s) of the inter-story seismic period on the X1Y1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 67] Figure 67 is a graph plotting the inter-story vibration period vector values ​​measured on the surface, with the x-component (s) of the inter-story vibration period on the P1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 68] Figure 68 is a graph plotting the inter-story vibration period vector values ​​measured on the surface, with the y-component (s) of the inter-story vibration period on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 69] Figure 69 is a graph plotting the inter-story vibration period vector values ​​obtained from surface measurements, with the z component (s) of the inter-story vibration period on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 70] Figure 70 is a graph plotting the inter-story vibration period (rotation) values ​​measured on the surface, with the x-component (s) of the inter-story vibration period (rotation) on the P1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 71] Figure 71 is a graph plotting the inter-story vibration period (rotation) values ​​measured on the surface, with the y-component (s) of the inter-story vibration period (rotation) on the P1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 72]Figure 72 is a graph plotting the inter-story vibration period (rotation) values ​​measured on the surface, with the z component (s) of the inter-story vibration period (rotation) on the P1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 73] Figure 73 is a graph plotting the values ​​of the acceleration distribution coefficient measured at a single point, with the x-component (s) of the acceleration distribution coefficient on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 74] Figure 74 is a graph plotting the values ​​of the acceleration distribution coefficient measured at a single point, with the y-component (s) of the acceleration distribution coefficient on the X1Y1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 75] Figure 75 is a graph plotting the values ​​of the acceleration distribution coefficient measured at a single point, with the z component (s) of the acceleration distribution coefficient on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 76] Figure 76 is a graph plotting the acceleration distribution coefficient values ​​measured on the surface, with the x-component (s) of the acceleration distribution coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 77] Figure 77 is a graph plotting the values ​​of the acceleration distribution coefficient measured on a surface, with the y component (s) of the acceleration distribution coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 78] Figure 78 is a graph plotting the values ​​of the acceleration distribution coefficient measured on the surface, with the z component (s) of the acceleration distribution coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 79] Figure 79 is a graph plotting the values ​​of the angular acceleration distribution coefficient measured on the surface, with the x-component (s) of the angular acceleration distribution coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 80]Figure 80 is a graph plotting the values ​​of the angular acceleration distribution coefficient measured on the surface, with the y component (s) of the angular acceleration distribution coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 81] Figure 81 is a graph plotting the values ​​of the angular acceleration distribution coefficient measured on the surface, with the z component (s) of the angular acceleration distribution coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 82] Figure 82 is a graph plotting the values ​​of the base stress coefficient measured at points, with the x-component (s) of the base stress coefficient on the X1Y1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 83] Figure 83 is a graph plotting the values ​​of the base stress coefficient measured at points, with the y-component (s) of the base stress coefficient on the X1Y1 axis in Figure 18 as the horizontal axis, and each floor of the 6-story reinforced concrete apartment building in Figure 18 as the vertical axis. [Figure 84] Figure 84 is a graph plotting the base stress coefficient values ​​measured at points, with the z component (s) of the base stress coefficient on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 85] Figure 85 is a graph plotting the values ​​of the base stress coefficient measured on the surface, with the x-component (s) of the base stress coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 86] Figure 86 is a graph plotting the values ​​of the base stress coefficient measured on the surface, with the y-component (s) of the base stress coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 87] Figure 87 is a graph plotting the base stress coefficient values ​​measured on the surface, with the z component (s) of the base stress coefficient on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 88]Figure 88 is a graph plotting the damage values ​​measured at individual points, with the x-component (s) of the damage level on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 89] Figure 89 is a graph plotting the damage values ​​measured at individual points, with the y-component (s) of the damage level on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 90] Figure 90 is a graph plotting the damage values ​​measured at individual points, with the z-component (s) of the damage level on the X1Y1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 91] Figure 91 is a graph plotting the damage values ​​measured by surface measurement, with the x-component (s) of the damage degree on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 92] Figure 92 is a graph plotting the damage values ​​measured from surface measurements, with the y-component (s) of the damage degree on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 93] Figure 93 is a graph plotting the damage values ​​measured from surface measurements, with the z-component (s) of the damage degree on the P1 axis in Figure 18 on the horizontal axis and each floor of the 6-story reinforced concrete apartment building in Figure 18 on the vertical axis. [Figure 94] Figure 94 is a table showing the values ​​and percentage changes in the degree of damage before and after reinforcement. [Figure 95] Figure 95 is a table illustrating the input values, the determination method, and the performance evaluation metrics used (Table 6.3.1). [Figure 96] Figure 96 is a schematic diagram illustrating repeated testing of a three-dimensional partial frame (Explanation Figure 6.3.1). [Figure 97] Figure 97 is a table summarizing the explanations of terms used in this specification. [Figure 98] Figure 98 is a table summarizing the explanations of terms used in this specification. [Figure 99] Figure 99 is a table summarizing the explanations of terms used in this specification. [Figure 100] Figure 100 is a table summarizing the explanations of terms used in this specification. [Figure 101] Figure 101 is a table summarizing the explanations of terms used in this specification. [Figure 102] Figure 102 is a table summarizing the explanations of terms used in this specification. [Figure 103] Figure 103 is a table summarizing the explanations of terms used in this specification. [Figure 104] Figure 104 is a table summarizing the explanations of terms used in this specification. [Figure 105] Figure 105 is a table summarizing the explanations of terms used in this specification. [Figure 106] Figure 106 is a flowchart illustrating the calculation method used for seismic isolation design of a structure according to Embodiment 2. [Figure 107] Figure 107 is a schematic diagram illustrating the overall configuration of the seismic isolation design support system of Embodiment 4. [Figure 108] Figure 108 is an example table that summarizes the data of existing structures for each identification ID of an existing structure. [Figure 109] Figure 109 is a schematic diagram illustrating the overview of the storage device 202 installed in the seismic isolation design support system 100 of Embodiment 4. [Figure 110] Figure 110 is a flowchart illustrating the operation of the calculation process of a seismic isolation design support system using a calculation method for seismic isolation design of structures, according to Embodiment 4. [Figure 111] Figure 111 is a flowchart illustrating the operation of the calculation process of a seismic isolation design support system using a calculation method for seismic isolation design of structures, according to Embodiment 4. [Figure 112] Figure 112 is a flowchart illustrating the operation of the seismic design support system 100 according to Embodiment 4 when processing a group of index values ​​for a structure to be evaluated. [Figure 113]Figure 113 is a flowchart illustrating the operation of the seismic design support system 100 according to Embodiment 4 when processing a group of index values ​​for a structure to be evaluated. [Figure 114] Figure 114 is a schematic diagram illustrating the hardware configuration of the seismic isolation design support system 100, in which an artificial intelligence processing unit is incorporated into the auxiliary storage unit 206 within the server 106. [Figure 115] Figure 115 is a flowchart illustrating the steps performed according to Embodiment 6. [Figure 116] Figure 116 is a flowchart illustrating a method for predicting earthquake damage to a structure under evaluation using the seismic design support system 100. [Figure 117] Figure 117 is a flowchart illustrating the operation of the seismic design support system 400, which includes a function to estimate the cost. [Figure 118] Figure 118 is a flowchart illustrating the operation of the seismic design support system 400, which includes a function to estimate the cost. [Modes for carrying out the invention]

[0061] [[Chapter 1: Basic Principles of Seismic Design Guidelines]] [1.1 Purpose] Seismic isolation design aims to ensure that the target structure and the city to which it belongs maintain their functionality during a major earthquake.

[0062] In modern times, many people live in cities. Modern cities are composed of a wide variety of structures, including buildings and infrastructure facilities constructed using concrete, steel, wood, etc., and they serve various functions as places of life and production for those who live and work there, and as places of service for visitors. Furthermore, some cities also serve as the base or center of businesses, local governments, or the nation. It is extremely important for our lives that cities do not lose their functions, but rather maintain and recover them when they are hit by a major earthquake. Seismic isolation design aims to ensure that the target structures and the cities they comprise maintain their functions in the event of a major earthquake.

[0063] [1.2 Target] This guideline applies to all aspects of urban life, including living, production, transportation, and transport, regardless of whether they are existing or newly constructed, made of materials or large. This includes structures that contribute to the above, as well as structures that connect cities and cities and form lifelines.

[0064] The maintenance of a city's functions depends on all the structures that make up the city. In both the design of new structures and the design of renovated existing structures, it is necessary to evaluate how they will affect the city's ability to maintain its functions. Therefore, seismic design, in order to achieve the aforementioned objective, targets all structures that make up the city, regardless of whether they are existing or new, made of different materials, or large or small. This includes buildings, railway viaducts, towers and other structures composed of beams and columns, massive structures such as dams, and even ancillary structures such as block walls and ceilings.

[0065] [1.3 Basic concept] Seismic design is based on the following concepts regarding the properties of structures and earthquakes, and performance evaluation.

[0066] (1) Earthquakes and structures exist with uncertainty, irregularity, and non-stationarity on a large spatiotemporal scale. Therefore, understanding these properties, and evaluating and judging their performance, must be done consistently over the long term using numerous indicators and case studies.

[0067] (2) An earthquake is a phenomenon in which waves transmitted through the ground cause motion and deformation in various parts of a structure. If the vibration of the structure is within the limits inherent to the structure and the surrounding ground, the structure will recover. This property is called seismic damping. This is due to elasticity, inertia, and gravity, and is a property that is directly related to maintaining function, and can be improved by reinforcement.

[0068] (3) During a major earthquake, structures may cease to function, be destroyed, or collapse. Therefore, it is necessary to create fail-safe mechanisms to protect human lives even if structures are destroyed or collapse during a major earthquake, and to prevent catastrophic damage from spreading to the surrounding area.

[0069] [1.3 Explanation of Basic Concepts]

[0070] (1) Earthquakes are phenomena that occur when rock masses tens to hundreds of kilometers thick rupture at depths of tens of kilometers, and their direct effects alone can extend to an area of ​​1,000 square kilometers. The recurrence period of major earthquakes is thought to be hundreds, thousands, or even centuries. They are phenomena that occur in a time and space far beyond human comprehension.

[0071] It is impossible to predict when or how an earthquake will occur. Man-made attacks are also almost impossible to predict. It is impossible to fully understand the shape, dimensions, and materials of structures and surrounding ground. The vibrations caused by earthquakes in the ground and structures are irregular. Structures change over time between completion and the occurrence of an earthquake. Regarding major earthquakes, it is impossible to calculate or predict the effects of earthquakes on structures or the responses of structures. Even if such calculations were made, they cannot be verified in reality. Therefore, even if a structural model of the entire structure is used to calculate the response to a major earthquake and a design is created to ensure earthquake resistance by incorporating walls, bracing, and seismic isolation / damping devices, it is uncertain whether it will not collapse and will be safe in the event of an actual major earthquake.

[0072] Figure 1 is a schematic conceptual diagram illustrating the performance evaluation of a structure (Explanation Figure 1.3.1).

[0073] Thus, earthquakes and structures exhibit uncertainty, irregularity, and non-stationary nature on large spatiotemporal scales. Therefore, the properties of structures in relation to earthquakes cannot be easily evaluated with a few indicators. It is necessary to use a large number of indicators and numerous case studies, and to conduct the evaluation consistently over a long period. As conceptually shown in Figure 1 (Explanation Figure 1.3.1), the performance evaluation of structures needs to be conducted consistently throughout the entire service life of the target structure, including design, construction, maintenance, renovation, repair, and when it encounters an earthquake. This allows the results of analyzing a vast number of past design and construction cases, as well as cases of damage and no damage, to directly benefit individual designs, rationalize design decisions, and become essential for mitigating damage.

[0074] (2) An earthquake is a phenomenon in which the impact of fracture caused by the movement of the Earth's crust propagates through the bedrock and ground to reach the ground surrounding a structure, causing movement and deformation in various parts of the structure. The mechanical effect of an earthquake on a structure, that is, the seismic action, is a wave caused by the displacement of the ground. Buildings and the like are structures made up of layers of slabs and beams, and in this type of structure, the wave propagates sequentially from the lowest layer (the first layer) to the upper layers, and is reflected and transmitted repeatedly in each layer.

[0075] The structures that make up modern cities are designed and constructed to support their own weight and transmit it to the ground, and to prevent excessive deformation or collapse from external forces such as wind, or from the loads of equipment, people, and objects. Many of these structures have already had their various performance characteristics confirmed in practice over a long history. Their own weight is constantly acting on them, and loads such as strong winds are experienced several times during their service life, so even new structures that have been completed for some time have almost certainly undergone practical testing regarding their ability to withstand their own weight. The same applies to small and medium-sized earthquakes in Japan.

[0076] Structures designed and constructed to support their own weight and maintain their function have the property of containing the deformation and movement (vibration) of the ground caused by earthquakes within their own motion and deformation, thus maintaining their shape and position. If this is within their inherent limits, the structure will recover. This is called seismic containment. The actual motion and deformation of the ground and structures can be seen in real-world footage from security cameras, dashcams, etc., and in personal accounts. Full-scale shaking table experiments are not conducted on the ground, but on steel plates, and the steel plates are moved against structures that are usually firmly fixed. However, these experiments represent the actual motion and deformation under these conditions. When these videos are taken, it can be seen that when the motion and deformation are small, not only structures but also objects on the ground contain the movement of the ground or floor beneath them within their own deformation and motion. This is seismic containment. When the movement of the ground becomes extremely large, objects as a whole tilt, shift, or sometimes even jump relative to the ground to avoid excessive deformation. This is also included in the concept of seismic containment.

[0077] Earthquake settling is a phenomenon observed in all structures and is a manifestation of the fundamental properties and functions inherent in objects on Earth. Earthquake settling is a phenomenon caused by elasticity, which tries to maintain its original shape, inertia, which tries to continue its original motion, and gravity, which constantly acts on objects on Earth.

[0078] Damage and failure occur when a part of a structure cannot return to its original state. In other words, the deformation of that part exceeds the elastic limit, or to put it another way, the deformation deviates from elastic deformation. Therefore, if the deformation is symmetrical rather than irregular, the likelihood of damage decreases even when subjected to the same ground movement. Also, even with the same deformation, if the elastic limit is not reached, that is, if the structure is made of a material with a high elastic limit, no damage will occur. Seismic damping is a property that directly relates to the ability of a structure to maintain its function. Since seismic damping is a property brought about by elasticity and inertia, it can be measured and calculated by vibration measurement and elastic eigenvalue analysis. Furthermore, it can be improved by reinforcement.

[0079] (3) Since major earthquakes are unpredictable, the risk of damage will always remain, no matter how much seismic damping is improved. Therefore, it is necessary to have a mechanism that can support the weight of the structure even if a large deformation occurs in part or all of the structure. Furthermore, in a major earthquake, deformations and accelerations not anticipated in the design occur, and it is unavoidable that structures will be destroyed and collapse. Just as seat belts and airbags in automobiles, it is necessary to create fail-safe mechanisms in structures to protect human lives even if actual destruction or collapse occurs. Even if seismic damping is improved and fail-safe mechanisms are installed, the risk of structures being forced to cease functioning or collapsing will never be zero. Measures are needed to avoid a catastrophic situation in which urban functions are greatly impaired due to ripple effects such as loss of life, fires, traffic disruptions, crowd crushes, and economic chaos. The above is the basic concept of seismic damping design.

[0080] [1.4 Method] The following methods are used in seismic isolation design. (1) Through document research, on-site surveys, and microtremor measurements, information related to structures, earthquakes, and ground conditions will be acquired and compiled into a database that can be understood and used by designers, stakeholders, etc., to serve as the basis for various decisions at each stage of design, construction, and maintenance. (2) Reinforcement is carried out to improve seismic damping by using highly elastic materials and a foundation type that allows sliding and uplift. (3) Anticipate direct and cascading damage in the event of a structure becoming non-functional or collapsing, and take measures to protect human lives and avoid catastrophic cascading damage. This includes reviewing the construction plan for the structure.

[0081] [1.4 Explanation of the Method]

[0082] (1) In order to understand the properties related to earthquakes and structures, and to rationally perform performance evaluations and judgments, it is first necessary to accurately recognize these properties. Figure 2 is a schematic diagram illustrating the recognition structure of objects and events in the database used for seismic isolation design (seismic isolation design DB) (Explanation Figure 1.4.1). Figure 2 (Explanation Figure 1.4.1) illustrates the recognition structure of objects and events in the database used for seismic isolation design (seismic isolation design DB). The structures depicted at the top include not only existing structures but also those to be constructed. The structure consists of five layers, with increasing levels of abstraction at deeper levels, and each layer containing information with clear meaning tailored to its specific situation and purpose.

[0083] The information in the first layer, which is the surface layer, is a direct conversion of the object or event into words, sentences, images, and numerical values. This includes information about the structural model, such as the mass matrix M, the stiffness matrix K, and the coordinate values ​​(x) of the point of contact l. l , y l , z l ) Set, acceleration time history p of measurement point ij obtained by micro-motion measurement aijk , the acceleration time history q of the observation point obtained from strong motion observation ak This includes supplementary information regarding the target structure, surrounding ground conditions, earthquakes, and seismic motion, such as the location conditions of the structure, various design conditions such as structure, scale, and specifications, year of completion, history of extensions and renovations, repair history, damage / no damage record, and past seismic damping evaluation index values, photographs, drawings, and survey forms of reinforcement examples.

[0084] The first layer of information gathering and processing regarding actual objects and phenomena is primarily performed by humans. Of these, the creation of an overall structural model is only performed in the case of new construction. This is done by experts using commercially available structural analysis programs and is close to an activity performed as a routine part of structural design work. However, in seismic design, it is common to ignore the weight and stiffness of the foundation and the lower half of the first floor and use a model in which the point of contact representing them is a fixed point. In seismic damping design, degrees of freedom and mass are assigned to the point of contact representing the foundation, natural modes are calculated, and seismic damping performance is evaluated using this point of contact as a reference point (see Chapters 2 and 3). For realistic measurement and analysis of deformation, it is necessary to consider the three directions (up, down, left, right, front, and back) and rotation in each direction as functions of space and time, i.e., 4 dimensions and 6 degrees of freedom. The specifications of the members can be within the elastic range, but it is necessary to define the ground spring that represents the support conditions of the ground. Numerical processing 1 is eigenvalue analysis, and the r-th natural frequency ω r and intrinsic mode e (r)This becomes the second layer.

[0085] Microtremor measurements can be performed using commercially available accelerometers. It is necessary to set up numerous measurement points (identified by ij) that represent the structure and measure them simultaneously. Generally, the displacement time history is obtained by performing a Fourier transform on the acceleration time history to convert it to the frequency domain, applying low-pass and high-pass filters, and then performing a process equivalent to integration in the frequency domain. This can be done. In the disclosure of this invention, applying this low-pass / high-pass filter is referred to as filtering. Specific methods are described in Chapter 2. Measured acceleration time history p aijk Filtering and calculus are applied to obtain the jerk, velocity, and displacement time history p. αijk We obtain the following. However, the subscripts α=a, α=v, etc., represent acceleration, velocity, etc., and k=x, etc., represent direction.

[0086] Strong motion observations are conducted nationwide by various organizations, and the data is publicly available, so this can be used. This data can also be filtered to obtain the acceleration time history p ak The following is obtained. Numerical processing 2 and 3 on the acceleration time history are filtering and calculus. The questionnaires are formatted (data cleansing) into a format that can be entered into the database and used as DB data. Information processing from the second layer onward is performed by a computer under human direction and supervision. All information from the third layer onward is stored in a computer dedicated to the seismic design database (seismic design DB).

[0087] Time history, stiffness matrices, etc., are large amounts of numerical data, while supplementary information is in the form of text and image data. The information processing work in the third and fourth layers involves synthesizing and abstracting these to transform them into a meaningful form that allows designers to understand the target structure, ground, and seismic motion, and to use this as a basis for making various decisions. Of these, the calculation of natural vibration vectors and strong motion parameters in the third layer also serves as input values ​​for each index in the fourth layer. In the fourth layer, various index values ​​are calculated using these. The data processing in the third layer regarding supplementary information also includes preprocessing for the fourth layer. In the fourth layer, this is linked to seismic convergence indices 1 and 2. As a result, supplementary information regarding natural vibration and strong motion is organized and stored as related data in the third layer, and supplementary information regarding seismic convergence indices 1 and 2 is organized and stored in the fourth layer. The conversion method and meaning of numerical values ​​obtained from microtremor measurements and structural models are described in Chapters 3 and 4. As a result, a set of numbers A is defined as seismic convergence index 1 and seismic convergence index 2, with meaning assigned to the magnitude and distribution, respectively. αijkm , C Y1ijkm , and A (r) ijkm , C (r) Y1ijkm Numerous such results can be obtained. The method for calculating strong motion parameters from the strong motion time history and the meaning of each parameter can be processed according to the known method described in Reference 1.

[0088] The deepest, fifth layer contains information with the highest level of abstraction, where the meaning is clear according to each situation and purpose. Specifically, regarding various judgments using each indicator value at each stage of the structure's lifecycle, it includes recommended ranges where, if the evaluation indicator values ​​fall within a certain range, construction defects are expected to be absent and no damage will be anticipated, along with reinforcement content (reinforcement proposals) and data explaining these. This range takes into account design and construction examples of similar structures and damage / no-damage records.

[0089] Of course, designers and others can directly access the information in the fourth layer to find various recommended ranges and create reinforcement plans, but by using artificial intelligence (AI) for this classification, extraction, and analysis work, it is possible to make seismic isolation design more objective and rational by making full use of large amounts of data. Furthermore, by using generative AI to learn the above information, the process of proposing seismic isolation and reinforcement designs (reinforcement proposals) that have a low probability of causing damage and a high probability of causing no damage can also be automated, which can be used to optimize the design. In addition, providing information on microtremor measurements to diagnosticians, receiving the microtremor measurement results, processing them to calculate seismic isolation evaluation index values ​​and providing them to diagnosticians, displaying recommended ranges for index values ​​based on various conditions of the target structure, and storing this in the seismic isolation design DB can all be done by a computer system via the internet (microtremor diagnostic system).

[0090] By integrating the above seismic isolation design database, recommended range / reinforcement proposal artificial intelligence (AI), and microtremor diagnosis system, we have constructed a system that can automate data processing, analysis, and the creation of justifications for decisions at each stage of the design process as a seismic isolation design support system. This is described in detail in the embodiments described in Chapter 6 and subsequent chapters.

[0091] Figure 3 is a seismic isolation design flowchart illustrating one form of the present invention (Figure 1.4.2). Figure 3 (Explanation Figure 1.4.2) shows the flow of seismic isolation design as an example to explain the overall picture. In design, first, design conditions are determined based on the construction plan and various conditions, and structural specifications are assumed accordingly. Based on this, if necessary, an overall structural model is created, and the structural specifications are determined to satisfy conditions other than earthquakes, such as supporting the self-weight (long-term load) and not having the function impaired by wind, rain, snow, etc. This is called design based on conditions other than earthquakes. For this, current design guidelines and standards for the target structure and commercially available design software that incorporates them can be used.

[0092] Next, an overall structural model is created for use in eigenvalue analysis. This is an elastic model designed to calculate natural vibration shapes close to reality and to lead to seismic isolation reinforcement design. It models even so-called non-functional walls, which are often overlooked in seismic design standards, as faithfully as possible. The model also includes the first layer, including the foundation, and the surrounding ground. Eigenvalue analysis is performed on this structural model to calculate seismic isolation performance evaluation index values. From the natural deformation shape (r-th order natural mode), the r-th order natural period, the limit value of inelastic deformation of each part of the structure, and the average value of the strong-motion RMS of displacement and the strong-motion duration, which are strong-motion parameters of the assumed large earthquake, seismic isolation performance index value 1 and risk index value, indicated by (r) in the upper right corner of the first to fourth layers in Figure 1.4.1, can be obtained using the calculation formulas described in Chapters 3 and 4. This is referred to as performance evaluation index value A.

[0093] However, since it is impossible to create a structural model that perfectly reproduces the natural vibrations of a structure on the ground, each of the following steps must be carried out while considering the differences from reality. In a major earthquake, the deformation and movement of the ground around the foundation are expected to be greater than that of the structure, so it is not possible to ignore this mass and stiffness in the design. However, it is difficult to realistically reflect this in the structural model. In the end, the designer will model it in the most implementable way they deem best, and proceed with the design while comparing this vibration mode with the actual vibration shape obtained from microtremor measurements. Furthermore, ground conditions are not limited to those directly beneath the foundation, but also include surrounding spatiotemporal conditions such as underground topography and past land use.

[0094] The judgment A made based on performance evaluation index value A includes two aspects. The first is the validity of the overall structural model. If each index value is generally within the recommended range A calculated from index values ​​obtained from eigenvalue analysis and microtremor diagnosis of similar structures, the overall structural model can be judged as valid. If it is not, the overall structural model is reviewed, and eigenvalue analysis, performance evaluation index value calculation A and judgment A are repeated. The second is the necessity of seismic damping reinforcement. If each index value is generally within the recommended range A obtained from the seismic damping design DB, and there are no irregular parts, it is judged that reinforcement is not necessary. However, if high-elasticity material reinforcement has not been performed, the risk index value and damage level of performance evaluation index value A usually exceed the recommended range, and it is judged that reinforcement is necessary.

[0095] If reinforcement is deemed necessary, seismic damping reinforcement design will be carried out to improve seismic damping performance, while considering the seismic damping performance evaluation index A and risk index values ​​obtained from eigenvalue analysis. The installation location and specifications of high-elasticity reinforcement materials will be determined with the aim of seismic adjustment to correct the natural vibration shape and high elasticity to increase the elastic deformation limit. Reinforcement will be carried out without distinguishing between so-called shear walls and non-shear walls, avoiding localized and irregular deformation, dispersing cracks, and improving elastic deformation. Next, considering the current state of the surrounding ground and the target structure, as well as the movement and deformation during a major earthquake, seismic damping performance will be ensured so that during a major earthquake, the structure moves as a whole, avoiding excessive deformation, and returning to roughly its original position. This is called seismic damping design of the foundation.

[0096] Seismic reinforcement design preferably includes the installation of a fail-safe mechanism. Damage is elastic deformation. Since the deformation is a deviation from the original shape, any deformation that causes damage will be localized. Therefore, instead of analyzing the entire structural model, the location and specifications of fail-safe mechanisms can be determined by dividing the structure into localized spaces, applying excessive deformation to those spaces, and evaluating the risk of collapse, falling, etc. Reinforcing columns with highly elastic materials to prevent collapse even if a large deformation occurs in a part of the structure is called axial strength reinforcement, while reinforcing finishes, equipment, etc., with highly elastic materials to prevent collapse and falling / overturning is called collapse prevention reinforcement and falling / overturning prevention reinforcement. In calculating the risk index value, which is a performance evaluation index for these reinforcements, the seismic action on the target part can be expressed using inertial force.

[0097] The determination of the reinforcement locations and specifications is made by comparing the [index value] and [risk index value] for seismic damping evaluation, calculated by taking into account the reinforcement effect and referring to past reinforcement examples, with the recommended range for each [index value] for seismic damping evaluation. The presentation of these reinforcement examples, or the proposal of reinforcement for the target structure, and the calculation of the recommended range are performed by extracting a group of structures with similar conditions to the target structure from past design and construction examples in the seismic damping design database, and analyzing the range of [index values] in that group, as well as the relationship between damage / no damage records and the index values. AI can be used for this. The system that stores the above data, presents examples, and makes proposals is called the design decision support AI. Seismic damping reinforcement design is completed by calculating the performance evaluation index value B after the reinforcement design and confirming that it falls roughly within the recommended range B (decision B). With reinforcement, the elastic limit value B and the service limit value B are improved from the elastic limit value A and service limit value A before reinforcement.

[0098] Judgment C involves evaluating the impact of a situation where the designed structure is forced to cease functioning or collapses. If the impact is significant and countermeasures are difficult, the decision is made to revise the construction plan itself. As a result of the above, once the seismic reinforcement design is completed, design documents are prepared, and construction of the main structure and installation of equipment are carried out. At this point, the first (I=1) microtremor measurement is performed, and judgment 1 regarding the quality of the construction of the main structure is made based on the results. Performance evaluation index value 1 is calculated from the microtremor measurement, and if it generally falls within the recommended range 1 calculated considering the performance evaluation index value 1 obtained by eigenvalue analysis, and there are no irregularities, the main structure is judged to be correctly constructed (pass), and high-elasticity material reinforcement work (SRF method) is carried out prior to the finishing work. After this, a second microtremor measurement is performed to confirm the reinforcement effect. Performance evaluation index value 2 is calculated from the microtremor measurement results, and if it is confirmed to be generally within the recommended range 2, it is judged that the seismic reinforcement effect is present, and the construction is completed.

[0099] Of the processes described above, the calculation and evaluation of index values ​​used for performance evaluation through microtremor measurement is called microtremor diagnosis. If the microtremor diagnosis after the construction of the building structure and equipment yields results that raise concerns about construction defects in the building structure, a detailed investigation will be conducted, and corrective design and work on the building structure will be carried out as necessary. AI can also be used to identify these concerns and propose corrective designs. Furthermore, if it is determined that the improvement in seismic damping performance due to reinforcement is insufficient (or not), a redesign of the seismic damping reinforcement will be carried out, additional reinforcement work will be implemented, and microtremor measurement and evaluation will be repeated before and after reinforcement. After completion, microtremor diagnosis will be conducted again periodically, and index values ​​I (I=3,4,...) will be calculated and reflected in the maintenance plan. Index values ​​A, B, I (I=1,2,3...), repair records, and damage / no damage records at each point in time from design to maintenance will be stored in the seismic damping design DB along with supplementary information and will be used as valuable data for seismic damping design in the seismic damping design support system.

[0100] (2) Since seismic damping is a property of elasticity, seismic damping can be improved by installing materials with a large elastic limit deformation, i.e., highly elastic materials, on the surfaces of structural members, equipment, finishes, etc., thereby improving the elastic deformation limit and shaping the natural vibration pattern. Highly elastic materials in the form of belts or sheets woven from polyester fibers, etc., exhibit restorative force mainly against tensile strain and do not resist other deformations. This flexibility can be used to create a fail-safe mechanism to prevent partial collapse of an object or to prevent detachment like a seat belt. For example, it is possible to reinforce finishes, equipment, etc., to prevent collapse and falling or toppling, and to reinforce against falling and toppling. Furthermore, reinforcing columns in a closed type with highly elastic materials has the dual effect of improving seismic damping and providing a fail-safe.

[0101] Understanding ground deformation, like structural deformation, requires a spatiotemporal treatment of six degrees of freedom. Considering the irregularity and uncertainty of earthquakes, predicting ground movement during an earthquake is nearly impossible. Therefore, it is crucial to ensure seismic damping by designing the structure, specifications, and materials of the parts of the structure that contact the ground and those connected to it, thereby creating a foundation that allows for sliding and uplift, preventing ground movement from forcing deformation beyond the elastic deformation limit. This method has been widely used in everything from traditional wooden structures to pre-war reinforced concrete buildings like Tokyo Station, and there is much research and literature on it. In addition to these foundation types, high-elasticity materials can be used to ensure restorative force against excessive uplift and movement.

[0102] (3) Even if seismic damping design enhances seismic damping capabilities and fail-safe mechanisms are installed, the risk of a structure becoming non-functional or collapsing cannot be eliminated entirely. In the event of such a situation, measures must be taken to address the ripple effects, namely, harm to surrounding human lives and impairment of urban functions. This involves first anticipating the nature, scale, and scope of direct and ripple effects that would occur if the target structure were to become non-functional or collapse, and then taking measures to prevent each individual damage event. Examples include providing open spaces such as parks around the structure and securing evacuation routes. If the impact of non-functionality or collapse is significant, or if these measures are difficult to implement due to surrounding land use issues, the construction plan itself will need to be reviewed.

[0103] Seismic isolation design is a method that focuses on the fundamental properties of structures, ground, and earthquakes / earthquake motion, using measuring instruments and computers to recognize and evaluate them, and using highly elastic materials to improve the seismic isolation properties of structures and reduce risks. Based on the premise that earthquake action is not an imaginary external force but the movement and deformation of structures due to ground displacement, design decisions are not made using a small number of judgment indicators and fixed standard values, but rather by calculating a wide variety of indicator values ​​through measurement and analysis at each stage of the design, and confirming that these generally fall within the recommended range obtained from a database consisting of supplementary information such as damage and no-damage records during earthquakes in past design and construction cases.

[0104] On the other hand, recognizing that major earthquakes are uncertain and far exceed human scale, the method involves detailed measurements up to the elastic limit and calculations of performance evaluation index values ​​in 4 dimensions and 6 degrees of freedom. However, it does not perform detailed calculations or predictions for the vibrations of the ground and structures after they exceed the elastic limit during a major earthquake. In the face of natural disasters on a scale beyond human comprehension, complacency on the part of humans who believe that certain measures are sufficient to prevent the disaster can actually lead to an increase in damage. From the perspective of preventing the expansion of damage resulting from such lax judgment, even if the numerical values ​​obtained through calculations are based on measurements and a large number of real-world examples, they are not intended to dictate the design, but rather to assist the designer's judgment and judgment based on past data in the face of natural disasters on a scale beyond human comprehension, and actual fail-safe mechanisms are intended to deal with destruction and collapse that may actually occur.

[0105] Seismic isolation design is based on the fundamental concepts of using elasticity, the uncertainty and irregularity of earthquakes and structures, and the possibility of malfunction or collapse during major earthquakes. Its design philosophy is similar to that of traditional wooden structures, which were designed and constructed by utilizing the elastic properties of wood with little reliance on calculations, and pre-war reinforced concrete (RC), steel-reinforced concrete (SRC), and steel-frame structures, which were built using a large safety factor within the elastic limit, limiting height, and incorporating parks and other features.

[0106] As shown in this section, Chapters 3 and 4, the calculation of index values ​​for seismic isolation design involves eigenvalue calculation of the structural analysis model, filtering of time history data obtained from microtremor measurements, calculus, RMS calculation, This involves arithmetic operations using these values ​​along with the dimensions and mass of the structure, and is a common numerical processing method. The resulting index values ​​each have meaning and evaluate the structure, surrounding ground, and seismic motion from various perspectives. Therefore, the index values ​​obtained in seismic isolation design, along with supplementary information such as the design conditions, environmental conditions, and damage / no-damage records of the target structure, can be compiled into a large database, and recommended ranges can be identified and used as the basis for judgment using general data analysis tools. Furthermore, artificial intelligence technology makes it possible to build a system that supports design by proposing recommended ranges of index values ​​and presenting specific reinforcement design plans toward achieving no damage. The structural difference between current seismic standards and seismic isolation design is that it incorporates a mechanism that connects the design of individual structures to the rationalization of the design of subsequent structures.

[0107] The seismic isolation design method is rooted in the long-standing experience of the Japanese people in relation to nature, and focuses on seismic isolation, an essential property related to the motion and deformation of objects: elasticity and inertia. It utilizes mechanics, elasticity theory, continuum mechanics, disordered vibration theory, 21st-century data processing using computers and networks, and communication technologies between people, people and machines, and machines and machines. It can be applied to various structures, from traditional wooden buildings to skyscrapers, as well as infrastructure facilities such as railway viaducts, highway bridges, and dams. It has the potential to become a core technology for building safe and comfortable cities and countries through the cooperation of people and machines.

[0108] Chapter 2: Vibration Measurement

[0109] [2.1 Purpose] In seismic isolation design, vibration measurement aims to quantify the seismic isolation properties of a structure.

[0110] The seismic damping properties of a structure are determined by its elasticity, inertia, and gravity, and are manifested in the vibrations of the structure. Vibration measurement in seismic damping design aims to quantify the seismic damping properties of a structure.

[0111] [2.2 Equipment Used] The following equipment is used for measuring the vibration of structures in seismic isolation design. (a) Measuring device (b) Laptop for data retrieval and analysis (c) Computers for computation and databases (d) Other equipment

[0112] In seismic design, vibration measurement of structures is fundamentally based on simultaneously installing numerous lightweight, compact accelerometers inside and around the structure. The following equipment can be used for this purpose.

[0113] (a) The measuring device is installed on the structure and the surrounding ground to measure the vibration of the structure. Measurement is made easier by using a device that integrates a three-component accelerometer, amplifier, battery, memory device, and communication device. For example, the DATAMARKJU410 manufactured by Hakusan Kogyo Co., Ltd. can be used. This is a measuring device that incorporates a servo-type accelerometer (JA40GA04 manufactured by Japan Aviation Electronics Co., Ltd.) and has a 24-bit AD conversion function.

[0114] (b) The data retrieval and analysis laptop is a personal computer (PC) equipped with software that retrieves acceleration data from the measuring device and displays the results of filtering, index values, etc. It is connected to the measuring device and the computer that performs calculations via Wi-Fi. Configure the VPN.

[0115] (c) The computer for calculation processing and database operations calculates, analyzes, and returns index values ​​from time history data transmitted from the laptop for data retrieval and analysis. It also has a database function to store the index values ​​and perform various analyses.

[0116] (d) Other equipment includes external power supplies and cables attached to the measuring device, signs indicating that measurements are being taken, etc.

[0117] [2.3 Measurement Method] In seismic design, vibration measurements of structures are performed using the following methods.

[0118] (1) Numerous measurement points shall be established from near the point of contact with the ground to the upper boundary, so as to represent the entire structure. If the structure has a part (layer) that moves as a whole, roughly horizontally, the measurement points shall be established on this part as a general rule. If the layer is supported by vertical members such as columns, the measurement points shall be established in the vicinity of these members. The part that is considered to move as a whole with the measurement points or measurement surface shall be called the dominant part.

[0119] (2) A measurement that represents the motion around a single measurement point is called a point measurement, and a measurement that uses the motion of the center point of a plane formed by three measurement points is called a surface measurement. In principle, the measurement point for point measurements, or the center point for surface measurements, should be placed on a vertical axis extending upward from the part of the structure that is in contact with the ground. This axis is called the measurement axis. Among the measurement points or center points, a point that represents the natural vibration shape in a standardized manner should be set up close to the ground and close to the center of the foundation. This is called the reference point.

[0120] (3) The measuring device shall be installed near the measurement point. If the total number of measurement points exceeds the number of measuring devices, the measurement shall be carried out in multiple steps, but the measuring device shall be installed at the reference point each time.

[0121] (4) Each measurement point is assigned a number with i=1 for the lowest point on each measurement axis, and each measurement axis is assigned a number with j=1 for the axis containing the reference point, and identified by a set of natural numbers ij. In surface measurements, the center point is P ij So, the three points A are used to calculate the motion of the central point. ij B ij , C ij This is expressed as follows. Note that if a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this point is set to i=0.

[0122] (5) In eigenvalue analysis, the junctions corresponding to the measurement points of vibration measurement are selected from the junctions of the structural model and used as the measurement points for eigenvalue analysis.

[0123] [2.3 Explanation of Measurement Method]

[0124] Figure 4 is a schematic diagram illustrating the relationship between the arrangement of the measurement axis, measurement point, center point, and measurement surface, and the governing area (Explanation Figure 2.3.1). Figure 4 (Explanation Figure 2.3.1) conceptually shows the arrangement of measurement points. Structures include massive structures such as dams, and structures with floors composed of beams, columns, and slabs, such as buildings.

[0125] (1) Numerous measurement points shall be established within the structure, from near the point of contact with the ground to the upper boundary, to represent the entire structure. If the structure has parts (layers) that move as a whole in a generally horizontal manner, such as floors, the measurement points shall be established on these layers as a general rule. The measurement devices shall be installed near the measurement points. Furthermore, if the layers are supported by vertical members such as columns, the measurement points shall be established in the vicinity of these members. The part represented by the measurement point or measurement surface, that is, the part that is considered to be moving in conjunction with the measurement point or measurement surface, is called the dominant part.

[0126] (2) There are two methods for calculating index values ​​from data obtained by measuring devices: one method (point measurement) in which the acceleration measured at a measurement point is considered representative of the surrounding motion, and another method (plane measurement) in which the motion of the center point of a plane formed by at least three measurement points is calculated using the method described in Chapter 3, Section 3.1, and the motion of each plane is considered representative. In principle, the measurement points for point measurement, or the center point for plane measurement, should be placed on a vertical axis extending upward from the part of the structure that is in contact with the ground. This axis is called the measurement axis. If a layer is supported by vertical members such as columns, the measurement axis should be located in the vicinity of these members. A point is established near the ground and close to the center of the foundation as a measurement point or center point, where the natural vibration shape is standardized and represented. This point is called the reference point. The measurement surface on which the reference point is located is called the reference surface.

[0127] (3) The measuring device shall be installed near the measurement point. If the total number of measurement points exceeds the number of measuring devices, the measurement shall be carried out in multiple steps, but by installing the measuring device at the reference point each time, the natural vibration shape of the entire structure shall be standardized through multiple measurements.

[0128] (4) The measurement axes are numbered with j=1 for the axis with the reference point, and the measurement points are numbered with i=1 for the lowest point of each measurement axis. Measurement points are identified by a set of natural numbers ij. The center point of surface measurement is denoted by the letter P. ij The identifier is set to A. Three measurement points are used to calculate the motion of the center point. ij B ij , C ijThis is expressed as follows. In vibration measurement, the measuring device is placed near the measurement point. Furthermore, in order to calculate the stiffness between the ground and the structure, if a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this is set to i=0, and the 0th,j measurement point, It is called the center point.

[0129] (5) The total number of contact points in the structural model used for eigenvalue analysis will be greater than the total number of measurement points for vibration measurement. From among the contact points, contact points corresponding to the measurement points for vibration measurement will be selected and used as measurement points when calculating index values ​​from the eigenvalue analysis results. Note that the fixed end of the ground spring of the structural model is the 0th, j measurement point. This corresponds to a measurement point.

[0130] [2.4 Calculation method] In seismic design, index values ​​are calculated from vibration measurement data using the following method.

[0131] (1) The measurement time for a single measurement shall be in the range of 10 to 20 times the length of 50 to 100 times the expected natural vibration period, preferably 14 to 16 times plus 1 minute. The sampling time step shall be 1 / 20 or less of the natural vibration period.

[0132] (2) Each measurement data is treated as one acceleration time history for each measurement point and each directional component, and the jump, velocity, and displacement time histories are calculated by differential and integral calculus of these histories. However, the initial values ​​of velocity and displacement are set to values ​​where the time average value over the measurement period is zero.

[0133] (3) The above-mentioned acceleration time history and time history of velocity, etc. are divided into 10 to 20 parts, preferably 14 to 16 parts, and 8 to 12 parts are selected that contain a small proportion of vibrations other than natural vibrations.

[0134] (4) Calculate an evaluation index for each selected part, and use the average value as the evaluation index value.

[0135] [2.4 Explanation of Calculation Method] Typically, the total number of measurement points to be installed on the target structure exceeds the number of measurement devices, so the measurement is divided into multiple sessions, with simultaneous measurements performed for each session. The index value is calculated by dividing the time history obtained from a single simultaneous measurement into parts and using the RMS (square root of the mean square) of each part; therefore, it is necessary for each part to have multiple repetitions. Furthermore, a large number of repetitions is desirable to mitigate the influence of non-stationary parts.

[0136] However, increasing the measurement time would be counterproductive to a rapid diagnosis. For example, for structures with a natural vibration period of around 1 second, the standard measurement time is 31 minutes, which is 30 minutes plus 1 minute, allowing for 15 calculation units (parts) of 2 minutes each. This is because, assuming the natural vibration period of the structure is in the range of 0.1 to 3 seconds, more than 40 repetitions appear in one part, and for a steady-state Gaussian process, this length of measurement results in a peak factor (RMS ratio to maximum value) that is generally greater than 3. A sampling time step of, for example, 1 / 20th or less of the natural vibration period allows for smooth capture of the vibration waveform. Typically, it is set to 1 / 200th of a second.

[0137] The differential and integral calculations of the measured acceleration time history are performed prior to part division. Here, the k-direction refers to the x, y, and z directions in the three-dimensional coordinate system relative to the inertial frame that describes acceleration, etc., for each measurement axis. The velocity time history in the k-direction obtained by integrating the acceleration time history in the k-direction.

[0138]

number

[0139] Initial value v k (0) is unknown, but since constant tremors are steady elastic vibrations, the average value will be approximately zero over a sufficiently large measurement time t0.

[0140]

number

[0141] Therefore, it is thought that...

[0142]

number

[0143] The same applies to displacement. The time history of acceleration, velocity, etc., described above is divided into, for example, 15 parts. Parts in which non-steady vibrations are considered to be dominant are excluded, and, for example, 10 parts are selected. For each selected part, the diagnostic index shown in Chapters 3 and 4 is calculated. The average of the index values ​​calculated for each part is used as the evaluation index value.

[0144] [[Chapter 3: Calculation of Indices Related to the Natural Vibration of Structures]] This chapter describes a method for calculating indices related to the spatiotemporal shape of a structure's natural vibration from the acceleration time history of ambient tremors at measurement points installed on the structure, the jump, velocity, and displacement time histories obtained by differential and integral calculus of this history, or the natural modes and natural frequencies obtained from eigenvalue analysis of the structural model.

[0145] [3.1 Motion of the measurement surface] In surface measurement, assuming that the measurement surface does not deform, the displacement p of its center point P is measured. k (t), and rotation angle θ k (t) is measured at three measurement points A(x) on the measurement surface. a ,y a ,0), B(x b ,y b ,0),C(x c ,y c k-component a of the displacement time history of ,0) k (t),b k (t),c k Calculate from (t). Here, k = x, y, z, and the coordinate value x of each measurement point. aThese relate to a coordinate system with its center point P as the origin, where each axis is parallel to an inertial frame describing acceleration, etc.

[0146] (1) The x, y, and z components of the displacement of the center point are:

[0147]

number

[0148]

number

[0149]

number

[0150] It can be calculated as follows. Furthermore, the x, y, and z components of the rotation angle of the center point are:

[0151]

number

[0152]

number

[0153]

number

[0154] It can be calculated as follows. Velocity p of the center point ’ k(t), acceleration p ’’ k(t), jerk p ’’’ k(t) and rotational angular velocity θ ’ k(t), rotational angular acceleration θ ’’ k(t), rotational angle jump θ ’’’k(t) is, in the above equation, a k (t),b k (t),c k (t) is the velocity a ’ k(t),b ’ k(t),c ’ k(t), acceleration a ’’ k(t),b ’’ k(t),c ’’ k(t), jerk a ’’’ k(t),b ’’’ k(t),c ’’’ This can be calculated by substituting k(t). Here, the apostrophe (') represents the time derivative, and the subscript k (k=x,y,z) represents the k-component.

[0155] [3.1 Explanation of motion on the measurement surface]

[0156] Figure 5 shows the small displacement AA due to rotation of vector PA with a small rotation angle |θ| around γ as the axis of rotation. ’ This is a schematic diagram to explain the concept (Figure 3.1.1). The constant micro-movements of the structure are expected to result in minute rotation angles and displacements. Figure 5 (Explanation Figure 3.1.1) shows the minute displacement AA that occurs when an arbitrary point A is rotated by a small rotation angle |θ| around a rotation axis γ with a certain direction, centered on point P on the axis, as if advancing a right-hand screw. ’ It depicts that.

[0157] This is vector AA. ’ Let =△PA be written as the cross product of the vector PA pointing from point P to point A and the vector PR = θ, which is parallel to the axis of rotation and has magnitude |θ|,

[0158]

number

[0159] It can be expressed as follows. However, by the definition of the cross product (vector product), triangle PA is perpendicular to both vectors, and from PR=θ, the direction and magnitude of the right-hand screw relative to PA is the length of the foot of the perpendicular AH drawn from point A to the line passing through PR (axis of rotation),

[0160]

number

[0161] Therefore, the vector PR=θ represents the magnitude and direction of the rotation, along with its own magnitude and direction, and is called a rotation vector. In Figure 3.1.1, let P be the center point of the surface measurement, and let A be a measurement point on this surface. Furthermore, if we express the positions of both points and their respective vectors with respect to a coordinate system with a fixed point O in the space shown in the figure as the origin, i.e., an inertial frame O, then the position vector of point A with respect to the inertial frame is:

[0162]

number

[0163] It can be written as follows: The small displacement of measurement point A with respect to the inertial frame is expressed as a small change in the position vector OA,

[0164]

number

[0165] This can be written as follows. Assuming that the measurement surface does not deform, that is, the length of line segment PA does not change, the triangle PA in the second term is produced by the rotation of the center point. This is expressed as a rotation vector in equation (Solution 3.1.1). Substituting this into the above equation (Solution 3.1.4),

[0166]

number

[0167] Therefore, PA can be considered to be the position vector of measurement point A with respect to a coordinate system parallel to an inertial frame of reference with the center point P as the origin and each axis describing acceleration, etc. The components with respect to that inertial frame of reference, that is, the coordinate values ​​of point A with respect to coordinate system P, arranged vertically.

[0168]

number

[0169] Substituting this into equation (Solution 3.1.5), and following the notation in the text, expressing the other vectors in component form and expanding the cross product,

[0170]

number

[0171] This is the result. Write this for measurement points B and C as well, and solve the simultaneous equations to get p k (t) and θ k The solutions for (t) are given by equations (3.1.1) to (3.1.6) in the main text. However, z a =z b =zc=0 The vector θ is defined using the unit vector ik (k=x,y,z) of the inertial frame.

[0172]

number

[0173] This can be expressed as follows. This shows that a rotation represented by the vector θ is a superposition of rotations represented by each term in the above equation, that is, rotations of magnitude θk around the k axis. The distributive property also holds for the cross product,

[0174]

number

[0175] Thus, as described above, small rotations can be decomposed into components related to the inertial frame O. If the components of vector θ are not infinitesimal, for example, if we consider a Cartesian coordinate system with point P as the origin and each axis parallel to the inertial frame, with θx=π / 2, θy=0, and θz=π / 2, and apply a rotation represented by vector θ to it, the result will differ depending on the order in which the rotations of each term in the above equation, i.e., the rotations around each coordinate axis, are performed. Assuming that the measurement surface does not deform and the displacement of each point is infinitesimal, the change in vector PA on the measurement surface is solely due to the infinitesimal rotation of the measurement surface as shown in (Solution 3.1.1) below. Therefore, the time derivative of equation (Solution 3.1.5)

[0176]

number

[0177] The magnitude of the second term that appears is

[0178]

number

[0179] This becomes a second-order infinitesimal quantity and is considered to be almost zero. Therefore,

[0180]

number

[0181] This is the result. However, ( ) ’ Δt represents the first derivative with respect to time, and Δt represents an infinitesimal time interval. The same applies to measurement points B and C. From these, we can determine the a of formulas (3.1.1) to (3.1.6) in the main text. k (t),b k (t),c k (t) is the velocity a ’ k(t),b ’ k(t),c ’ Replace k(t) with the rotational angular velocity θ. ’ It can be seen that the formula for calculating k(t) is obtained. Differentiating equation (Solution 3.1.5) further gives the rotational angular acceleration θ’’ A similar formula can be obtained for k(t).

[0182] [3.2 Calculation of strain between measurement points] The strain between the two measurement points A and B is,

[0183]

number

[0184] It can be calculated as follows: However, the coordinates of the equilibrium positions of both points in the inertial frame are A(x a ,y a ,z a ), B(x b ,y b ,z b )year, The time history of the k-component displacement (k=x,y,z) is a k (t),b k Let (t) be the case.

[0185] [3.2 Explanation of the calculation of strain between measurement points]

[0186] When investigating whether a measurement surface is unlikely to deform, or when deformation is a concern, the strain between measurement points on the measurement surface can be calculated. Furthermore, in the design of large-span roofs and other structures, it may be necessary to calculate strain between support points. Measurement point A(x a ,y a ,z a ), B(x b ,y b ,z b The distance between them is,

[0187]

number

[0188] It can be calculated from the coordinates and displacements. However, since the order of magnitude of the micro-displacement is extremely small compared to the coordinate values, the squared term of the micro-displacement can be ignored in the above equation.

[0189]

number

[0190] Furthermore, since we assume that the average value of the time history of micro-motion displacement is zero, the average distance between point A and point B is

[0191]

number

[0192] This can be calculated. Therefore, the strain between points A and B can be calculated using formula (3.2.1) in the main text. Note that if points A and B, as assumed in Section 3.1, are on a roughly horizontal measurement surface that does not deform, lAB(t) = lAB0, and z a =z b Since = 0, we equate equation (Solution 3.2.2) and (Solution 3.2.3),

[0193]

number

[0194] Therefore, the second and fifth sides of the formula (3.1.6) in Section 3.1 are

[0195]

number

[0196] However, this is a necessary and sufficient condition for (Solution 3.2.4), namely, that the length of line segment AB remains unchanged. However, y a -y b ≠0, x a -xb≠0. By replacing point A and point B with point B, point C, or point C and point A above, equation (3.1.6) in Section 3.1 becomes line segment AB, BC, CA It can be shown that the length of the plane remains unchanged, that is, the plane does not deform and measurement points A, B, and C lie on this plane.

[0197] [3.3 Natural vibration shape vector, natural vibration number vector, and natural vibration period vector minute] The spatiotemporal shape of a structure's natural vibration can be represented by a natural vibration shape vector and a natural vibration number vector relating to displacement, velocity, acceleration, rotation angle, angular velocity, angular acceleration, etc. The absolute value of each component of the natural vibration shape vector is obtained by normalizing the RMS of the time history of displacement, velocity, etc. at the measurement point or center point with the average value of the RMS of the three components of the reference point displacement, and each component of the natural vibration number vector is obtained by normalizing the RMS of the differential time history with its own RMS.

[0198] The natural vibration shape vector and natural vibration number vector are column vectors representing the components related to the displacement, velocity, etc., at each measurement point and the center point, respectively, arranged in a single column. The portion related to displacement is called the natural vibration displacement shape vector or displacement natural vibration number vector. The same applies to velocity, etc. The ratio of each component of the natural vibration velocity shape vector and the natural vibration displacement shape vector is equal to the ratio of each component of the displacement natural vibration number vector. The same applies to velocity, etc.

[0199] (1) RMS, transmittance, and center frequency are defined as follows: RMS: The RMS (root mean square) of a time history x(t) at duration t0 is:

[0200]

number

[0201] It is defined as follows and denoted by the symbol σx. The dimension of RMS is equal to the dimension of the time history x(t). Also, the k-component time history y of the displacement at the first measurement point ij is defined. ijk (t), or the P ij k-component time history y of the displacement of the center point Pijk(t), and its differential time history RMS is σα ijk That is to say,

[0202]

number

[0203] This is expressed as follows: where the first subscript α of σ is the displacement (α=d), velocity (α=v), and acceleration (α=a). Also, the P ij k-component time history θ of the rotation angle of the center point Pijk (t) and its differential time history RMSσβijk are given by the rotation angle (β=θ) and angular velocity (β=θ). ’ ), angular acceleration (β=θ ’’ ) as,

[0204]

number

[0205] This is how it is written. However, the apostrophe ('') represents the time derivative.

[0206] Transmission rate: The RMS ratio of the time history y(t) to the reference time history x(t).

[0207]

number

[0208] This is called the transmission rate of y with respect to x. Note that when the reference time history is clear, the subscript / x is omitted, and it is simply written as |hy|.

[0209] Central frequency: Differential time history y(t) ’ The ratio of (t)'s RMS to its own RMS.

[0210]

number

[0211] This is called the central frequency. This is the transmission rate hy of the differential time history relative to itself. ’ / y .

[0212] (2) The α of the natural vibration shape vector in point measurement ijk The absolute value of the component is the transmission coefficient of the k component, such as the displacement at the first measurement point ij.

[0213]

number

[0214] However, the reference time history x d11 (t) is the average of the RMS values ​​of the three components of the displacement of the reference point.

[0215]

number

[0216] This is the time history. In surface measurement,

[0217]

number

[0218]

number

[0219] Therefore, the α of each natural vibration shape vector is ijk The dimensions of the components and the βijk components are obtained by dividing the dimensions of α and β by the dimension of displacement [length]. That is, for displacement (α=d), it is [dimensionless], and for velocity (α=v), it is [time]. -1 ], in terms of acceleration (α=a), [time -2 ], with rotation angle (β=θ), [length -1 ], angular velocity (β=θ’ ) then, [length -1 time -1 ], angular acceleration (β ’’ =θ) then [length -1 time -2 ] The components of the natural frequency vector ω are the central frequency of the natural vibration shape vector.

[0220]

number

[0221]

number

[0222] This is the ratio of the components of the eigenform vector of the differential time history, where α = a ’ This is the jerk, β = β ’’’ This is the angular jerk. Each component of the natural period vector T is derived from the components of the natural frequency vector,

[0223]

number

[0224] It can be calculated as follows. Note that in performance evaluation, the period representation will be used. Therefore, the dimension of the natural frequency vector is [time -1 The dimension of the natural vibration period vector is [time].

[0225] (3) From the r-th order eigenmode obtained by eigenvalue analysis of the structural model, the value corresponding to the absolute value of the component of the natural vibration shape vector

[0226]

number

[0227] This can be calculated. However, e (r) dijk This is a component of the r-th order eigenmode vector, which corresponds to the k-component of the displacement of the junction of the structural model corresponding to the ij-th measurement point. Also, ω r This is the r-th natural frequency. The (r) in the upper right corner indicates that it was calculated from the r-th natural mode. The reference amplitude is the average of the three absolute values ​​of the displacement components at reference point 11 (i=1, j=1) or P11 (i=1, j=1):

[0228]

number

[0229] That is the case. center point P ij The value corresponding to the absolute value of the components of the natural vibration shape vector is obtained from three measurement points A set on the measurement surface. ij B ij , C ij The center point P calculated from the components and coordinate values ​​of the r-th order eigenmode shape vector at the junction of the corresponding structural model. ij In the mode shape,

[0230]

number

[0231] It can be calculated as follows. However,

[0232]

number

[0233]

number

[0234]

number

[0235] Therefore, the value corresponding to the absolute value of the components related to the rotation angle, etc., is

[0236]

number

[0237] It can be calculated as follows: where k=x,y,z,

[0238]

number

[0239]

number

[0240]

number

[0241] It is. Also, the subscript P ij , A ij B ij , C ij , is the center point P in surface measurement. ij And the three measurement points A in response to this ij B ij , C ij This indicates that it is a point of contact in the corresponding structural model. For example, x Aij , y Aij , z aij , e dAijx (r) These are, respectively, measurement point A ij These are the x, y, and z coordinate values ​​and the x component of the r-th eigenmode vector. The values ​​corresponding to the components of the natural frequency vector and the natural period vector are:

[0242]

number

[0243] This is the result. Also, ω r This represents the r-th natural frequency. The (r) in the upper right corner indicates that it was calculated from the r-th natural mode.

[0244] [3.3 Explanation of the components of the natural vibration shape vector, natural vibration number vector, and natural vibration period vector] Figure 6 is a schematic diagram illustrating the relationship between physical quantities related to structures, ground, and their vibrations, and the indicators used in seismic design obtained by measuring and calculating these quantities (Explanation Figure 3.3.1). Figure 6 (Explanation Figure 3.3.1) shows the physical quantities related to structures, the ground, and their vibrations, as well as the indices used in seismic design obtained by measuring and calculating these quantities.

[0245] Structures and the ground are solids, and seismic motion is a wave that propagates through them. The resultant force of the acceleration and acting forces on a part of a solid is related by the equation of motion and can be obtained by multiplying and dividing by the mass. Of these, stress is generally related to displacement, velocity, acceleration, etc. by constitutive laws, but if elasticity is assumed, there is a linear relationship between displacement and force and can be obtained by multiplying and dividing by the stiffness. Acceleration, velocity, and displacement at a given time are generally related by calculus with respect to time, but in elastic vibration, the amplitudes of each are obtained by multiplying and dividing by the frequency.

[0246] Acceleration and displacement can be related via force, using mass and stiffness, by moving clockwise around the vertices of the tetrahedron in the figure, but they can also be related via velocity, using two frequencies, by moving counterclockwise. Integrating these and directly relating acceleration and displacement are the eigenvalues ​​of the simultaneous equations of motion using stiffness and mass. Velocity and force can be related via displacement, using frequency 2 and stiffness, or via acceleration, using frequency 1 and mass, but integrating these and directly relating velocity and force is the energy of elastic vibration, which is the sum of kinetic energy and strain energy. When analyzing a solid as a whole without considering its deformation, a method is used in which it is treated as a set of point masses whose positions do not change, i.e., a rigid body, and six degrees of freedom are given to its center point: three translational components and three rotational components. In this case, the same relationships as above hold between rotation angle, angular velocity, angular acceleration, and moment.

[0247] When acceleration and other parameters are measured at a specific location within a solid at a specific time, a time history can be obtained for each of the three spatial directions. This is a plot of the values ​​of acceleration and other parameters as amplitudes over the duration, relative to the time axis. For steady-state time histories, such as ambient tremors, a steady-state Gaussian process is used as a mathematical model. For time histories exhibiting strong unstationarity, such as seismic motion, methods have been developed to represent them as a part of an equivalent steady-state time history.

[0248] The RMS, central frequency, bandwidth index, etc., calculated from the time history are related to properties such as the threshold exceedance probability, maximum value, zero-crossing period, and frequency configuration of the time history, according to the model described above. Methods have been developed to analyze the mechanical properties of a solid by treating it as a set of finite points of contact, and software that performs eigenvalue analysis to calculate the r-th order eigenvector and natural frequency from the equations of motion is widely used. The above is explained in prior art reference 1.

[0249] This chapter demonstrates that the components of the natural vibration shape vector and natural vibration period vector can be calculated from the time history obtained from ambient microtremor measurements and the RMS of their calculus time history. Furthermore, it shows that the components corresponding to each component of the natural vibration shape vector can be calculated from the r-th eigenvector and frequency obtained from eigenvalue analysis of the structural model. Chapter 4 describes a method for calculating the elastic response by adding the mass distribution to obtain response magnification and distribution coefficients, and further adding the elastic limit value to obtain the base stress coefficient, etc., representing the seismic motion in strong-motion RMS with magnitude and seismic intensity as the background, and then adding the strong-motion duration to calculate the cumulative inelastic response and the damage level, which is an index that comprehensively represents the seismic convergence performance normalized by the usage limit value, and it is shown that the corresponding values ​​for each can be calculated from the r-th eigenvector and frequency. Calculation examples are in Chapter 6.

[0250] (1) The RMS (root mean square) of equation (3.3.1a) is the estimate of the only parameter when a steady time history with a mean of zero is modeled as a steady Gaussian process of duration t0. Furthermore, the transmission coefficient in equation (3.3.2) is a normalized version of this, and various properties are expressed by these. A representative index among these is the central frequency in equation (3.3.3), which is the expected value of the zero-crossing frequency of the time history y(t)²). As shown in the next section, the transmission coefficient is the absolute value of each component of the natural vibration shape vector, so the absolute value is indicated in the notation.

[0251] (2) Solids possess elasticity and inertia, and their elastic vibrations are represented by a superposition of natural vibrations. The steady portion of ambient tremors is also an elastic vibration, a superposition of multiple natural vibrations, but superimposed in a specific ratio, and is thought to have a unique spatiotemporal shape and frequency. This is called natural vibration. The displacement, velocity, and acceleration at each measurement point, and the rotation angle, angular velocity, and angular acceleration at the center point, each have different shapes and frequencies, but these are combined and called the natural vibration shape vector and natural vibration frequency vector. The magnitude of each component is obtained by normalizing the RMS of the time history, which is obtained by differential and integral calculus of the acceleration time history obtained from continuous microtremor measurements, using the method shown in equation (3.3.4) and subsequent equations in the main text. The above is derived as follows.

[0252] Solids, including structures and surrounding ground, are collections of countless points (masses) that possess only mass and exert forces on each other. By considering it as a combination, its motion and deformation can be analyzed. Furthermore, by providing a finite number of contact points, the solid can be analyzed. Analysis methods that divide the problem into a finite number of parts have also been put into practical use.

[0253] While a solid can be considered as a collection of point masses, resulting in an infinitely large number of degrees of freedom, analytical methods have been developed to describe it with a finite number of degrees of freedom, and these methods are widely used in research and design practice. Specifically, n points of contact are established on the surface or inside of a structure, and each point of contact is given 3 degrees of freedom with 3 translational components, or 6 degrees of freedom by adding 3 rotational components to these, and these are arranged vertically to define a vector x with l elements. For example, if a structure has s axes and multiple points of contact are placed on each axis, and there are r points of contact on the s-th axis, and each point of contact is given 6 degrees of freedom, then:

[0254]

number

[0255] This is the result. However, following the notation of the text, each junction is denoted with two subscripts ij representing the axis and height order, and a third subscript k representing the component. Also, y represents displacement and θ represents rotation angle. Furthermore, for each physical quantity shown in Solution Figure 3.3.1, by setting a rule to interpolate the values ​​of each mass point within the structure with the values ​​of the junction, we can obtain l equations of motion relating to the degrees of freedom assigned to the junctions.

[0256] The elastic stress f within a structure is expressed as a linear combination of the displacements at each contact point. That is, the resultant force of the forces acting at the contact point is l × Assuming that f can be expressed as f = Kx using a stiffness matrix K of l, the equation of motion for the contact displacement is:

[0257]

number

[0258] This is the result. However, x ’’ is the acceleration, which is the second time derivative of the displacement vector x with l elements, and M is the l × l mass matrix. Note that, unless specifically emphasized, suffixes such as "vector" and "matrix" will be omitted below. Also, arrows, bold text, etc., will not be used for symbols. Subscripts will be used to indicate components of vectors, etc.

[0259] In the equation of motion (solution 3.3.2), there is an elastic contact force f = Kx generated by a certain displacement x, and a contact force g = λM that is proportional to the mass and displacement. x However, if λ is a constant, then they are equal. If a displacement x exists, then the equation

[0260]

number

[0261] However, it has non-zero roots. The necessary and sufficient condition for this is det(K-λM)=0, which is an l-degree equation and has l roots, including repeated roots. The r-th root λr, arranged in ascending order, is called the r-th eigenvalue. Substituting this into equation (Solution 3.3.3),

[0262]

number

[0263] Thus, l displacements x(r) can be calculated. Multiplying x(r) by a scalar also satisfies the above equation. Therefore, the parameters of x(r) can be normalized, for example, by determining that the value at the reference junction is a certain specified value. (r)These are represented by the r-th order natural vibration shapes (r-th order modes). That is, with ηr as a scalar,

[0264]

number

[0265] The following relationship holds. Substituting this into equation (Solution 3.3.2),

[0266]

number

[0267] This is the result. (r) Since each component is calculated from the components M and K, if we assume that the components M and K are independent of time, then we can assume that the component itself is independent of time and is not zero. Therefore,

[0268]

number

[0269] This gives us a second-order homogeneous ordinary differential equation in ηr. The general solution to this equation is, with Ar and φr as integration constants,

[0270]

number

[0271] If you leave it as is,

[0272]

number

[0273] However, when λr < 0, a steady-state oscillation solution cannot be obtained, so when λr > 0 The equation (Solution 3.3.2) is linear, so the displacement vector that satisfies it is:

[0274]

number

[0275] As shown above, it can be expressed as a superposition of the product of the general solution and the eigenmodes.

[0276] The above modeling can also be applied to structures on ground experiencing ambient tremors. Each measurement point or center point on the structure is identified with the aforementioned junction, and the column vector y(t), obtained by vertically arranging the components of the ambient tremor at these points, is considered one of the realized values ​​of the displacement vector x(t). Furthermore, if ambient tremors are considered to be elastic free vibrations occurring in the structure as a result of forced displacement in response to vibrations in the surrounding ground at the junctions where the structure is bound to the ground, then they can be expressed as a superposition of natural vibrations using equations (Solution 3.3.9) and (Solution 3.3.10). That is, ambient tremor displacement is,

[0277]

number

[0278] This is the result. Here, y(t) has a steady portion, which is assumed to be a sinusoidal oscillation of approximately a single mode, and this is called the natural vibration. That is, εd(t) is the transient oscillation included in the constant micro-displacement, and over a sufficiently long measurement time t0,

[0279]

number

[0280] Assuming this is the case, the constant micro-displacement is,

[0281]

number

[0282] Let us assume that this can be written as follows: where hd is the shape vector of the natural vibration displacement, and Ad, ωd, and φd are the amplitude, frequency, and initial phase of the sinusoidal vibration corresponding to it.

[0283]

number

[0284] σe is the mean square root (RMS) of the time history e(t) with respect to the duration t0, and is denoted as σe. In general, the square of the RMS of two time histories x1(t) and x2(t) is:

[0285]

number

[0286] It can be written as follows. However, σx1 etc. means the RMS of x1(t) etc. Also, the second term on the right side

[0287]

number

[0288] This is the correlation coefficient function of the time histories x1(t) and x2(t), where -1 ≤ ρx1x2 ≤ 1. Therefore,

[0289]

number

[0290] The following relationship is obtained. However, equality is held when ρx1x2 = ±1. Using this relationship in equation (Solution 3.3.13) and referring to equation (Solution 3.3.12), for a sufficiently long measurement time t0,

[0291]

number

[0292] This is the result. However, Ad>0 was assumed.

[0293]

number

[0294] For a sufficiently long duration, the frequency ω d and initial phase φ d Regardless of this, it becomes approximately equal to 1 / √2. Also, the constant micro-motion velocity y ’ As for (t), by differentiating equation (Solution 3.3.13), we can assume that it can be expressed as a sinusoidal oscillation of approximately a single mode, similar to the displacement.

[0295]

number

[0296] The following relationship is obtained, and by applying the relationship in equation (Solution 3.3.17), Assuming RMS[εv(t)]≈0, with respect to the natural ground velocity,

[0297]

number

[0298] This is the result. Furthermore, regarding acceleration, we differentiate (Solution 3.3.19) and make the same assumption as for displacement and velocity.

[0299]

number

[0300] The following relationship is obtained, and by applying the relationship in equation (Solution 3.3.17),

[0301]

number

[0302] This is the result. The natural vibration shape vector h defined in this text is a standardized column vector formed by combining the absolute values ​​of each of the above natural vibration shape vectors ha, hv, hd, and the rotation angle, etc., into a single column vector. Below, its components are expressed according to the notation in this text as follows: α or β representing displacement, etc., or rotation angle, etc., the letters P, A, B, C representing the center point of surface measurement or measurement point, i=1,... representing the upper limit placement of measurement point or center point, j=1,... representing the axis, and four or five subscripts α representing the k-axis component (k=x,y,z). ijk , αP ijk Alternatively, βP ijk Add h αijk h βPijk This is how it will be expressed.

[0303] Now, let the reference time history be the displacement α=d at the reference point i=1, j=1, and its RMS is,

[0304]

number

[0305] Let's assume that this is the case. From the component representation of the above equations (Solution 3.3.23) and (Solution 3.3.18),

[0306]

number

[0307] This is the result. However, the last equality sign is,

[0308]

number

[0309] This is the case. The same applies when the center point is used as the reference point. From this relationship and the component representation of equation (Solution 3.3.18),

[0310]

number

[0311] Thus, we obtain the second equation of the main text (3.3.4). The third equation is obtained by expressing the components of equation (Solution 3.3.20),

[0312]

number

[0313] Therefore, the fourth equation is obtained by expressing the components of equation (Solution 3.3.22),

[0314]

number

[0315] This is the case. The same applies when the center point is used as the reference point.

[0316] The rotation angle and its differential time history are defined in equations (3.1.4) to (3.1.6) of Section 3.1. For rotational angular velocity and rotational angular acceleration, the natural vibration shape vector in equation (3.3.6) can be defined based on the average RMS value of the three displacement components at the above reference point. However, it should be noted that these have dimensions that are the reciprocal of length. On the other hand, from the component representation of equations (Solution 3.3.18) and (Solution 3.3.20), the RMS ratio of velocity and displacement of the k component at the ij-point can be determined.

[0317]

number

[0318] This roughly corresponds to the ijk component ωdijk of the frequency (hereinafter referred to as the natural displacement frequency) vector of the k-axis component of the natural vibration displacement at the ij-th junction, and the relationship of equation (3.3.7) 1 in the main text is obtained. Similarly, from the component representation of equations (Solution 3.3.20) and (Solution 3.3.22), with respect to the velocity natural frequency,

[0319]

number

[0320] Furthermore, from the relationship obtained by differentiating equation (Solution 3.3.21) and equation (Solution 3.3.22), a relationship concerning acceleration can be obtained. However, y ’’’ (t) is the time derivative of acceleration and is a quantity called the jerk. The calculation of each component of the vibration number vector relating to the rotation angle, etc., from equation (3.3.7) 3 onwards is the same. It is important to note that these also have dimensions of the reciprocal of time, corresponding to the order of differentiation. Note that equation (3.3.7) 1 in this text is

[0321]

number

[0322] Thus, each component of the displacement in the natural frequency vector is the ratio of the components of the natural velocity shape vector and the natural displacement shape vector at the same measurement point. The same applies to acceleration, etc.

[0323] The shape vector of a single r-th order natural vibration mode e obtained from equations (Solution 3.3.4) to (Solution 3.3.6) (r) For the amplitude ηr related to this, the acceleration and velocity frequencies obtained by differentiating it are all ω r Equivalent to, all spatial shapes are e (r)And they are all equal. However, since ambient tremors and their steady-state portion, the natural vibration, are superpositions of multiple natural vibrations, as shown in equation (Solution 3.3.13), they are not equal. However, as described above, the shape vectors of acceleration, velocity, and displacement representing the spatial shape of the natural vibration, and the frequency vector representing the temporal shape can be defined as the RMS ratios between acceleration, velocity, and displacement at the same point of contact, or the RMS ratio with respect to a reference point. These are indices that quantitatively represent the shape and frequency of the natural vibration, which is the steady-state portion of ambient tremors, i.e., the spatiotemporal shape in three dimensions, and by integrating displacement, velocity, acceleration, etc., a single shape vector h αijk and frequency vector ωα ijk It can be expressed as follows. From the relationship in equation (Solution 3.3.17),

[0324]

number

[0325] And, with a being a constant,

[0326]

number

[0327] Therefore, the upper or lower limit of the transmission coefficient related to the time history, calculated by linear calculation from the displacement at a certain point, such as relative displacement and relative acceleration, can be calculated from each component of the natural vibration shape vector and frequency vector using the above relationship, and is therefore considered to be approximately constant. The central frequency of the time history y(t) defined in equation (3.3.3) is the expected value of the zero-crossing frequency, assuming that the time history y(t) is a steady Gaussian process. In the definition of the natural vibration shape vector and frequency vector, it was assumed that the constant micro-displacement y(t) has a steady portion, which can be represented by a sinusoidal vibration of approximately a single mode, and this means that it has the same zero-crossing frequency. The natural vibration period vector in equation (3.3.9) is the natural frequency vector converted into a period. This periodic representation will be used for performance evaluation.

[0328] (3) From the r-th order natural mode vector and r-th order natural frequency of the structural model, the natural vibration shape vector can be calculated as follows. From equation (Solution 3.3.10), if the structural model is generating an r-th order natural vibration, then the displacement vector and RMS are:

[0329]

number

[0330] It can be written as follows. Differentiating this with respect to time, the velocity vector and RMS are:

[0331]

number

[0332] Furthermore, the acceleration vector and RMS are,

[0333]

number

[0334] This is the result. By expressing the above relationship in terms of components and substituting it into equation (3.3.4) and subsequent equations, we obtain equation (3.3.10). For example, from equations (Solution 3.3.29) and (Solution 3.3.31),

[0335]

number

[0336] Thus, we obtain the third equation of the main text (3.3.10). The time history of the displacement and rotation angle of the center point in surface measurement is calculated using the formula in Section 3.1, by setting three points on the measurement surface. It is calculated from the time history and coordinate values ​​of the three translational components. Therefore, the natural vibration shape vector of the center point can also be calculated using the r-th order eigenmode vectors of the junctions of the structural model corresponding to these three points.

[0337] For example, the center point P of the natural vibration shape vector. ij The RMS of the time history of the x component of the displacement is obtained by writing each time history in equation (3.1.1) in Section 3.1 in the form of (Solution 3.3.29) and taking the RMS.

[0338]

number

[0339] This is the result. However, x Aijx (t), x Bijx (t), x Cijx (t), y Aij , y Bij , y Cij , e dAijx (r) , e dBijx (r) , e dCijx (r) , e θPijx (r) These are, respectively, measurement point A ij B ij , C ij The x-component time history of the displacement, the y-coordinate value, the x-component of the r-th eigenmode vector, and the center point P. ij This is the z-component of the rotation angle. This is shown in the denominator of equation (Solution 3.3.32) as RMS[x 11 (r) Dividing by (t), we obtain the result of setting k=x in the first equation of the main text (3.3.11). The same applies to the same equation with k=y, k=z, the second equation and subsequent equations, and the main text equations (3.3.12) and subsequent equations.

[0340] For the r-th eigenmode, the RMS ratio of the differential time history with respect to itself is given by equations (Solution 3.3.29) to (Solution 3.3.31), and this is given by ω rTherefore, equation (3.3.18) is obtained. The natural vibration period vector in the second equation is obtained by converting the natural vibration number vector in the first equation into a period. This period representation will be used in performance evaluation.

[0341] [3.4 Natural period] The first measurement point ij, or the center point P. ij The natural period of translational motion in is:

[0342]

number

[0343] It can be calculated from the vijk, vPijk, dijk, and dPijk components of the natural frequency vector. Center point P ij The natural period of rotational motion in is

[0344]

number

[0345] As such, the θ of the natural vibration vector of angular velocity and rotation angle ’ P ijk Components, and θP ijk It can be calculated from the ingredients.

[0346] If the vibration of a structure is a single natural vibration, i.e., an r-th order mode corresponding to the eigenvalue r, then, as shown in equations (Solution 3.3.9) and (Solution 3.3.10) of Section 3.3, the acceleration, velocity, and displacement components at all measurement points will vibrate at the same frequency r. However, the natural vibration of a structure on the ground is a steady-state vibration, but it can be considered to be a superposition of multiple natural vibrations. Therefore, even at the same measurement point, the frequencies of acceleration, velocity, and displacement will differ. This is represented by the natural frequency vectors and natural period vectors in equations (3.3.7) to (3.3.9) and (3.3.19) of the main text of Section 3.3.

[0347] From the relationship shown in Figure 3.3.1 in Section 3.3, the eigenvalues ​​of elastic vibration relate to acceleration and displacement. From the perspective that it is such that, the measurement point ij, or the center point P ij Assuming that the acceleration and displacement amplitude of the translational motion in the k-direction are related, i.e., the RMS, then the eigenvalues

[0348]

number

[0349] This is defined as the ijk-formation of the natural vibration number vectors of velocity and displacement calculated in Section 3.3. It can be calculated from minutes. In other words, regarding the measurement point ij,

[0350]

number

[0351] This is the period.

[0352]

number

[0353] The result obtained by this conversion is the natural period of the first equation of formula (3.4.1) in the main text. Center point P ij no k-kata Similarly, for translational and rotational motion in the direction, equations (3.4.1) 2 and (3.4.2) in the main text are obtained. In the r-th order eigenmode obtained by eigenvalue analysis of the structural model, the r-th order eigenperiod is T (r) =2π / ω r This matches the value from the previous section.

[0354] [3.5 Composition ratio and rate of change of kinetic energy] (1) The proportion of each kinetic component in the total kinetic energy of the part dominated by the ij-th in point measurement is called the kinetic energy composition ratio and is calculated as follows.

[0355]

number

[0356] However, p ’ ijk (t) is the velocity time history at the measurement point ij. Also, the rate of change of kinetic energy is

[0357]

number

[0358] It is defined as follows.

[0359] (2) The proportion of each kinetic component in the total kinetic energy of the Pil-dominated portion in surface measurements is called the kinetic energy composition ratio and is calculated as follows: The translational kinetic component is

[0360]

number

[0361] Furthermore, the rotational motion component is,

[0362]

number

[0363] However, p ’ Pilk (t), θ ’ Pilk (t) is the velocity time history and angular velocity time history of the center point Pil, and κ Pilk This is the radius of rotation about the k-axis with respect to the portion governed by the center point Pil. Also, the translational component of the rate of change of kinetic energy is:

[0364]

number

[0365] As such, the rotational motion component is,

[0366]

number

[0367] We will calculate it as follows.

[0368] (3) From the r-th eigenmode obtained by eigenvalue analysis of the structural model, the kinetic energy composition ratio of the ij-dominated part and the Pil-dominated part can be calculated. The kinetic energy composition ratio of the ij-dominated portion in point measurements is:

[0369]

number

[0370] It can be calculated as follows. The translational motion component of the kinetic energy composition ratio of the Pil-dominated portion in surface measurements is:

[0371]

number

[0372] It can be calculated as follows. Also, the rotational motion component is,

[0373]

number

[0374] It can be calculated as follows. The rate of change of kinetic energy in point measurements

[0375]

number

[0376] The translational component of the rate of change of kinetic energy in surface measurements is

[0377]

number

[0378] As such, the rotational motion component is,

[0379]

number

[0380] It can be calculated as follows, where e (r) dijk This is a component of the r-th eigenmode vector, which corresponds to the k-component of the displacement of the junction of the structural model corresponding to the ij-th measurement point.

[0381] Also, e (r) dPilk , and e (r) θPilk These were calculated using formulas (3.3.12) to (3.3.14) and (3.3.16) to (3.3.18) in the main text of Section 3.3. Note that i=1, j=1 represents the reference point, and i=1, l=m represents the reference plane.

[0382] [3.5 Explanation of Kinetic Energy Composition Ratio and Rate of Change] (1) and (2) The governing part is the part of the structure that is considered to move in conjunction with the measurement point or measurement surface. In point measurement, the governing part of the measurement point is considered to be a point mass, and in surface measurement, the governing part of the measurement surface is considered to be a rigid body.

[0383] To describe the motion of a rigid body, it is necessary to use a total of six variables: three variables describing the position of a representative point and three variables indicating the orientation of the rigid body. This is referred to as the rigid body having six degrees of freedom. For example, if a representative point and a line segment passing through this point are fixed on the rigid body, the motion can be represented by three position coordinates of the representative point, two angles indicating the direction of the line segment, and one angle representing the rotation of the rigid body around this line segment as an axis. In seismic design, in surface measurement, the center point is used as the representative point, and the motion of the portion governed by the measurement surface, viewed as a rigid body, is described using three variables indicating the position of this point relative to the inertial frame and three variables indicating the rotation angles of this point around each coordinate axis of the inertial frame. These are the formulas in Section 3.3. According to (3.1.1) to (3.1.6), it is calculated from the translational motion of three measurement points placed on the measurement surface.

[0384] Figure 7 is a schematic conceptual diagram illustrating the dominant parts in point measurement and surface measurement (Explanation Figure 3.5.1). Figure 7 (Explanation Figure 3.5.1) conceptually shows the dominant parts in point measurement and surface measurement. In point measurement, the mass m of the part of the structure that is considered to move together with the measurement point ij is shown. ij Assign the mass to the position of the first measurement point ij. In surface measurements, the part of the structure that is considered to move together with the plane formed by the three points used to calculate the motion of the center point Pil is assigned the center point Pil as its center of gravity and mass m Pil The lengths of the three sides are L Pilx , L Pily , L Pilz Assume that this is a rectangular prism, where each side is roughly parallel to the coordinate axes of the inertial frame. The radius of rotation of this rectangular prism about an axis of rotation parallel to the k-axis of the inertial frame, with respect to its center point Pil, is:

[0385]

number

[0386] This is the case where k = x, y, z, and m and o are the two directions other than k. The first measurement point ij or center point P ijThe translational kinetic energy of the k component of the dominant part is equal to the mass m of this part. ij , m Pij and speed time history p ’ ijk (t), p ’ Pijk Using (t),

[0387]

number

[0388] It can be defined as follows. Furthermore, the rotational kinetic energy of the k component of the dominant portion of the first ij measurement surface is given by treating this portion as a rigid body and the center point P ij Radius of rotation κ around the k-axis centered at Pijk and rotational angular velocity time history θ ’ Pijk Using (t),

[0389]

number

[0390] It can be written as follows. Therefore, the total kinetic energy for point measurement and surface measurement is,

[0391]

number

[0392] Yes. Each index in the text is the RMS ratio of these values. Here, the subscript t represents translational motion, and r represents rotational motion.

[0393] (3) Express the components of the equations in Section 3.3 (Solution 3.3.29) to (Solution 3.3.31), and the p of the definition of the equation (3.5.1) in the main text. ’ ijk Substituting this into (t), in point measurement,

[0394]

number

[0395] Thus, we obtain equation (3.5.7) in the main text. In surface measurement, similar to equation 3.3 (solution 3.3.33), the center point P ij The displacement y and z components at are calculated using equations (3.1.1) to (3.1.6) in Section 3.1, and the velocity is determined in the same way as in equation (Solution 3.3.30). Substituting the three components into the definition equations (3.5.3) to (3.5.4) in the main text, equations (3.5.8) to (3.5.9) are obtained. Equations (3.5.10) to (3.5.12) can be calculated from these. However, e dPijk (r) and e θPijk (r) These were calculated using formulas (3.3.12) to (3.3.14) and (3.3.16) to (3.3.18) in the main text of Section 3.3.

[0396] [[Chapter 4: Calculation of Indicators Related to Structural Deformation, Stiffness, Elastic Limit, and Risk]] The first half of this chapter describes how to calculate indices related to the deformation, stiffness, and elastic limit of a structure-ground system from the shape and dimensions of the structure, mass distribution, elastic limit deformation, and the acceleration time history of measurement points installed on the structure, the displacement time history obtained by integrating these, or the natural modes and natural frequencies obtained from eigenvalue analysis of the structural model. The second half of this chapter describes the calculation methods for the elastic and inelastic responses to assumed seismic motion, the calculation methods for risk indicators, and their relationship to coefficients in current standards.

[0397] [4.1 Interlayer deformation and transfer coefficient] In a structure with multiple parts (layers) that move together in a generally horizontal direction, and where measurement points are set along the vertical measurement axis, in point measurements, the value of the relative displacement of the i+1th layer with respect to the i-th layer at the j-th measurement axis is called the ij-th inter-layer displacement. Similarly, in surface measurements, the relative displacement and relative rotation angle of each layer on the Pj measurement axis are called the P ij Interstory displacement, P ijThis is called the inter-story rotation angle. Note that, assuming i=0, ...n, the displacement etc. is set to zero for the virtual layer and virtual measurement point (i=0), and the displacement etc. between the 0th layer (floor) is calculated.

[0398] (1) Inter-story displacement of the ijth layer, or the Pth layer ij Interstory displacement is,

[0399]

number

[0400] These can be calculated as follows: The deformation angle and the stretch ratio can be calculated from these.

[0401]

number

[0402] The shear deformation angle of the first ij (k=x,y), and the first ij, the first P ij The ratio of extension (k=z) and To refer to. Part P ij The interlayer rotation angle is,

[0403]

number

[0404] It can be calculated as follows: ij Curvature (k=x,y), and the Pth ij Torsion ratio (k=z)

[0405]

number

[0406] It can be calculated that p ijk (t) is the k-direction component of the displacement obtained from the measurement at measurement point ij (k=x,y,z), p Pijk (t), θPijk (t) is the center point P calculated in Chapter 3, Section 3.1, equations (3.1.1) to (3.1.6). ij Let the displacement and rotation angle be the components in the k-direction. Also, H 0ijk Or H 0Pijk are the ij and P ij This is the height in the k-axis direction between floors (structural floor height in the k-axis direction of the ij-th floor: i=1~n).

[0407] (2) The inter-story displacement transmission coefficient of the structure is measured at a point,

[0408]

number

[0409] It can be calculated as follows. Furthermore, the transmission coefficient of the interlayer displacement and rotation angle of the Pij-th layer is, in surface measurement,

[0410]

number

[0411] It can be calculated as follows. However, let i=0, ...n, where i=1 and j=1 represent the reference point. Also, p 0jk Let (t) = 0. Note that if the center point is used as the reference point, change the subscript d11 to dP11 in the above three equations.

[0412] (3) The value corresponding to the inter-story displacement transmission coefficient of the ijth-order structure is obtained from the point measurements of the r-th order eigenmode obtained by eigenvalue analysis of the structural model, or from the junction values ​​corresponding to surface measurements.

[0413]

number

[0414] It can be calculated as follows. Also, the P ij The interlayer rotational angle transfer coefficient is,

[0415]

number

[0416] It can be calculated as follows, where e dPijk (r) , and e θPijk (r) These were calculated using formulas (3.3.12) to (3.3.14) and (3.3.16) to (3.3.18) in the main text of Section 3.3. Also, let i=0, ...n, where i=1 and j=1 represent the reference point. e dP0jk (r) =0, e θP0jk (r) Set = 0. Note that if the center point is used as the reference point, change the subscript from d11 to dP11 in the above three equations.

[0417] [4.1 Explanation of Interlayer Deformation and Transduction Coefficient] Generally, if we consider an object as a continuum composed of countless point masses, its deformation can be expressed as the ratio (displacement gradient) of the change in displacement (difference) of each point mass to the change in its position coordinate. An object generates internal stress in response to its deformation, which is expressed as the forces acting between each point mass. The resultant force of the stress acting on a point mass from surrounding point masses and other external forces is equal to the product of the point mass's acceleration and mass. If the stress is elastic, a linear relationship exists between deformation and stress, represented by the elastic modulus. By measuring the deformation, acceleration, mass, and external forces of each part of a structure, we can determine the stress acting on each part and thus its stiffness (elastic modulus).

[0418] Typically, structures have sections that are thought to move roughly horizontally as a whole. These sections are called layers, and multiple measurement points are placed on them. The measured accelerations are used to represent the deformation and stress of the structure. Layers are important parts of a structure, such as areas where people are active, equipment operates, vehicles travel, or things are stored. Layers are generally composed of girders, beams, and slabs, and are supported by vertical members such as columns. Layers are often connected vertically.

[0419] Figure 8 is a schematic diagram illustrating the relationship between the layers, measurement points, center point, dominant portion, and supporting portion of the structure (Explanation Figure 4.1.1). Figure 8 (Explanation Figure 4.1.1) conceptually illustrates structures and layers. Imagine structures such as buildings, railway viaducts, and dams in the areas enclosed by solid lines, and layers such as floors in the vertically aligned rectangles. Multiple measurement axes are provided for each structure, and they are distinguished by assigning numbers j=1, 2, .... Measurement axes for surface measurements are distinguished by adding the letter P before the number. At measurement points on a given measurement axis, the relative positions are represented by assigning numbers i=1, 2, .... from the lowest layer upwards. In addition, a virtual measurement point, center point, and layer can be provided directly below the foundation to represent support by the ground. This is represented as i=0, and the displacement is considered to be zero. Floor height is not considered between layers 0. Measurement points are placed on each layer within the structure, and deformation is measured on a layer-by-layer basis, axis by axis. The value of the relative displacement of the i+1th layer directly above the i-th layer on the j-th measurement axis is called the ij-th inter-layer displacement, and the relative rotation angle on the Pj-th measurement axis is called the P ij This is called the interlayer rotation angle.

[0420] In point measurement, where one measurement point is placed on each measurement axis of each layer, the measurement point of the i-th layer on measurement axis j is called the ij-th measurement point. The space between the i-th layers on measurement axis j is called the ij-th layer space, and this supporting portion is called the ij-th support portion. In surface measurement, the center point is P, and the three points used to calculate this motion are represented by the letters A, B, and C. ij The center point is the center point on the measurement axis j of the i-th layer. The dominant part is the part that is thought to move in the same way as the measurement point or the center point. For example, the dominant part of the i-th layer refers to the part of the structure that is thought to move in the same way as the measurement point of the i-th layer.

[0421] (1) The motion and deformation components of the structure are measured at point ij in the i-th layer, j-axis, and at the center point P in the surface measurement. ij Each component of the relative displacement, and the center point P ijThe formulas used to calculate the relative rotation angle components and the height between the first ij-th floor (floor height of the ij-th floor) are given by equations (4.1.1) to (4.1.4) in the main text. Figure 4.1.2(a) shows the relative displacement component e in the xz plane, which is one of the components of relative displacement and relative deformation angle shown in equation (4.1.1) and equation (4.1.3) in the main text. Pijx (t), e Pijz (t), and relative rotation angle component e rPijy Figure (t) is shown. Figure (b) shows the relative displacement component e in the xy plane. Pijx (t), e Pijy (t), and relative rotation angle component e rPijz (t) is shown in the diagram. As shown in equations (4.1.2) and (4.1.4), the inter-story drift angle and the like can be obtained by dividing these by the structural floor height.

[0422] Figure 9 is a schematic diagram illustrating the relationship between the components of interstory displacement and interstory rotation angle (Explanation Figure 4.1.2).

[0423] (2) In accordance with the definition in Section 3.3 of Chapter 3, equation (3.3.2), the transmission coefficients of interstory displacement and interstory rotation angle can be calculated using equations (4.1.5) to (4.1.6) in the main text.

[0424] (3) The denominator of the transmission coefficient for interlayer displacement and rotation angle defined in equations (4.1.5) to (4.1.6) in the main text is the RMS of the quantity obtained by calculations relating to the measurement location for the displacement and rotation angle, and the numerator is the RMS of the displacement at a certain location. Therefore, by substituting the time history in equations (4.1.5) to (4.1.6) in the main text with the corresponding component of the r-th order eigenmode vector obtained by eigenvalue analysis of the structural model, taking the absolute value and ignoring the RMS, a corresponding value can be calculated. This is because the vibration time history x(r)(t) of the r-th order eigenmode is a function of the measurement location that does not depend on time, and the eigenmode vector e (r) As can be seen from the fact that it can be expressed as a product of and ηr(t), which is a function of time only, and from the definition of RMS in the main text of Section 3.3 (3.3.1a), it can be specifically verified as follows.

[0425] The transmission coefficient of the inter-story displacement of the ijth-order structure is the component e of the eigenmode vector corresponding to the point of contact of the r-th order eigenmode obtained by eigenvalue analysis of the structural model. (r) dijk This can be calculated using the first equation of formula (4.1.7) in the main text. This can be verified by substituting the component representation of the formula explained in Section 3.3 (Solution 3.3.29) into formula (4.1.5) in the main text.

[0426] P of the structure ij The value corresponding to the transmission coefficient of interstory displacement can be calculated using equation (4.1.7), second equation in the main text. This can be verified by substituting equations (3.3.1) to (3.3.3) from Section 3.3 into equation (4.1.6), first equation in the main text, and then substituting the component representation of the explanatory equation (solution 3.3.29) from Section 3.3 into each time history in this equation. ij The transmission coefficient of the interlayer rotation angle is calculated from the contact point value corresponding to the surface measurement, using the component e of the eigenmode vector calculated using equations (3.3.16) to (3.3.18) in Section 3.3. θPijk (r) This can be calculated using formula (4.1.8) in the main text. This can be verified by substituting formulas (3.3.4) to (3.3.6) from Section 3.3 into the second equation of formula (4.1.6) in the main text, and substituting the component representation of the formula in the explanatory section 3.3 (solution 3.3.29), where d→θ, into each time history.

[0427] [4.2 Interstory Stiffness and Interstory Vibration Period] (1) The inter-story stiffness of the structure and its value converted to a natural period, that is, the translational motion component in the k direction of the inter-story vibration period of the inter-story structure,

[0428]

number

[0429] It can be calculated as follows: However, the k-direction component of the natural vibration acceleration shape vector of the first ij measurement point is h aijk , the interlayer displacement transmission coefficient is h eijk , the dominant mass is m ij Let it be so. Furthermore, m 0jLet i=0. i=0 represents the ground stiffness and its natural period equivalent. Part P ij The k-direction component of the translational motion of the interstory stiffness and interstory vibration period is:

[0430]

number

[0431] The stiffness of rotational motion around the k-axis and the inter-story vibration period are:

[0432]

number

[0433] Assuming that is the case, the P ij The component hθ in the k-direction of the natural vibration angular acceleration vector of the dominant portion. ’’ P ijk and interlayer rotation angle transmission coefficient h erPijk , and P ij Moment of inertia I of the dominant part around the k-axis Pijk It can be calculated from this.

[0434] (2) From the r-th order eigenmode obtained by eigenvalue analysis of the structural model, the values ​​corresponding to the k-direction component of the translational motion of the ij-th interstory stiffness and interstory vibration period are:

[0435]

number

[0436] It can be calculated as follows, where e (r) dijk This is a component of the r-th order eigenmode vector that corresponds to the k-direction component of the displacement of the junction of the structural model corresponding to the ij-th measurement point. Also, ω r r is the r-th natural frequency, T r This is the r-th order natural period. Part P ij The k-direction component of interlayer stiffness is,

[0437]

number

[0438] It can be calculated as follows: the P ij The values ​​corresponding to the inter-story stiffness and inter-story vibration period for rotational motion between layers around the k-axis are:

[0439]

number

[0440] However, e dPijk (r) , and e θPijk (r) These were calculated using formulas (3.3.12) to (3.3.14) and (3.3.16) to (3.3.18) in the main text of Section 3.3. i=1 and j=1 represent the reference point. Note that ω r r is the r-th natural frequency, T r is the r-th order natural period. i=0 is the stiffness of the ground spring converted to its natural period.

[0441] [4.2 Explanation of Interstory Stiffness and Interstory Vibration Period] (1) The part governed by the ijth shown in Figure 4.1.1 in the previous section and Figure 3.5.1 in Section 3.5, or the Pth ij The dominant part has a mass of m ij Or m Pij Therefore, gravity m ij g or m Pij A force g is acting on the material. Additionally, stresses from adjacent sections or external forces are thought to be acting on the sides, but in the following calculations, these will be considered small compared to the inter-story stresses and will be ignored. Stress, acceleration, etc., are functions of time, but the notation (t) for each variable will be omitted below. Also, the P ij We will discuss the dominant parts, but the same applies to the translational motion of the ijth dominant part.

[0442] Q TPijk M TPijk is the P ij On the upper surface of the controlling part, QBPijk M BPijk If these are the force and moment acting on the lower surface, then the P ij The resultant force acting on the controlled part is,

[0443]

number

[0444] It can be written as follows: The sum of moments is

[0445]

number

[0446] Therefore, assuming that the part dominated by the first Plj moves in almost the same way as the measurement surface of the first Plj, we consider it to be a rigid body, and the equation of motion for translational motion is:

[0447]

number

[0448] Therefore, regarding rotational motion,

[0449]

number

[0450] This is the result. However, the right side

[0451]

number

[0452] This is the moment of inertia of the Plj portion about the k-axis. Also,

[0453]

number

[0454] is the radius of rotation in the k-direction with respect to the center of mass of the Plj-dominated part. Here, the dominating part is assumed to be a rectangular parallelepiped with sides approximately parallel to each coordinate axis of the inertial frame. Also, LPljk is the length of the side in the k-direction. Note that k = x, y, z, and the subscripts m and o represent the two directions other than k. .

[0455] Substitute equation (Solution 4.2.3) into equation (Solution 4.2.1) and obtain each equation for l=i+1,...n+1 Adding both sides together, we get the P ij The stress on the upper surface of the dominant portion is,

[0456]

number

[0457] As, the P ij This is the sum of the products of the acceleration and mass of each dominant part that constitutes the support. However, according to the law of action and reaction, the stresses on the lower and upper surfaces of the intermediate dominant part cancel each other out. Also, the term m of gravitational acceleration is used. Pij g k In the horizontal direction k=x,y, it is zero, and in the vertical direction k=z, it is the vertical component p of the observed acceleration. ’’ pijz It is ignored as it is included in [the equation]. For rotational motion as well, if we substitute equation (Solution 4.2.4) into equation (Solution 4.2.2) and add both sides of each equation for l=i,...n+1, then the P ij The moment on the upper surface of the dominant part is,

[0458]

number

[0459] As, the P ij It is the sum of the products of the rotational angular acceleration and moment of inertia of each dominant part that constitutes the support structure. Taking the RMS of both sides of equation (Solution 4.2.7),

[0460]

number

[0461] As described above, the P ij The stress acting on the dominant part is related to the acceleration transfer coefficient via mass. The same applies to the moment. Stiffness is the ratio of inter-layer stress to inter-layer displacement, and is considered to be a constant value if elastic,

[0462]

number

[0463] This can be written as follows. However, the inequality in the above equations (Solution 4.2.11) and (Solution 4.2.9) uses the equation from Section 3.3 (Solution 3.3.16). The same applies to rotational stiffness. From the above, the first equation of (4.2.2) is obtained. The first equation of the main text (4.2.1) is thus, P ij →This is obtained as ij. The second equation converts these stiffnesses into natural periods. That is, assuming that the supporting part moves as a single unit, the eigenvalues ​​of this part are

[0464]

number

[0465] It can be calculated as follows. The natural period is, by definition,

[0466]

number

[0467] It can be calculated as follows. The same applies to rotational motion. (2) Equations (4.2.4) to (4.2.6) are obtained by replacing the transmission rates of equations (4.2.1) to (4.2.3) in the main text with the r-th order eigenmode vectors of the eigenvalue analysis, using equations (4.1.7) and (4.1.8) in Section 4.1 and equations (3.3.10) to (3.3.18) in Section 3.3.

[0468] Furthermore, the relationship in equation 1 of the main text (4.2.1) can also be derived from the characteristics of the stiffness matrix and mass matrix of the stacked model. A stacked model is the simplest structural model of a structure, consisting of point masses and springs connected in series, with each point mass having only one degree of freedom. It is commonly called a "skewer of dumplings." Consider a skewer of dumplings model in which the point masses measured at the points in solution 3.5.1 are numbered from 1 to n+1, the measurement axis numbers are omitted, and each is designated as the j-th junction. If the junction displacement vector is a column vector obtained by arranging the displacements of the j-th junctions vertically from the n+1th junction to the 1st junction in order, then the stiffness matrix is:

[0469]

number

[0470] This results in a symmetric matrix with a narrow bandwidth. However, the force acting between the j-th tangency and the (j-1)-th tangency is not considered. Let the elastic modulus be kj. The 0th tangency is a fixed point. If the mass of the jth tangency is mj, then the tangency mass matrix is:

[0471]

number

[0472] This results in a diagonal matrix. From the explanatory formula in Section 3.3 (Solution 3.3.4), the above skewer model is given by The r-th eigenmode vector is e (r) , the eigenvalue is λr=ω r 2 given that,

[0473]

number

[0474] Therefore, between the first elements of the column vector obtained by expanding both sides, i.e., the elements corresponding to the (n+1)th point of tangency: ,

[0475]

number

[0476] There is such a relationship. Between the components corresponding to the j-th junction,

[0477]

number

[0478] Therefore, between the components corresponding to the first contact point,

[0479]

number

[0480] This is the result. (Solution 4.2.17) Adding the left side from j=i+1 to j=n+1,

[0481]

number

[0482] This is the result. If we equate this with the sum of the right-hand side of (Solution 4.2.17) from j=i+1 to j=n+1, then

[0483]

number

[0484] This is the result. The ki+1 on the left side is the elastic modulus between point mass j+1 and point mass j, and therefore corresponds to the interlayer stiffness of the ij-th layer shown in Solution Figure 4.1.1. Note that the above equation includes all eigenmode vectors e (r) and natural frequency ω r It is valid.

[0485] The second equation in the main text, corresponding to equations (4.2.1) and (4.2.2), is derived from the first equation and the sum of the mass and moment of inertia of the supporting part.

[0486]

number

[0487] It can be calculated as follows: Here, T r is the r-th natural period. Equation (Solution 4.2.21) shows that the average mass load of the natural deformation shape of the ij-th support part, i.e., the average displacement, is equal to the inter-story displacement of the ij-th layer. Therefore, we show that the average natural period of this part is equal to the natural period of the r-th mode. The same applies to the rotation angle. However, in the r-th mode, all parts have a period T. r Since it is moving, the above equation T r No different natural periods appear. Such formulas are only meaningful when we simplify the motion of the supporting parts.

[0488] [4.3 Response magnification, distributed coefficient, base stress coefficient, and base moment coefficient] The stress and deformation distribution and elastic limit of a structure and ground system can be expressed using response ratio, distribution coefficient, base stress coefficient, and base moment coefficient.

[0489] (1) The ij-th support portion of the structure, and P ij Displacement (α=d), velocity (α=v), acceleration (α=a) of the support part, and P ij Rotation angle of supporting part (β=θ), rotational angular velocity (β=θ ’ ), rotational angular acceleration (β=θ ’’ The k-direction component of the response magnification of ) is

[0490]

number

[0491] It can be calculated as follows: However, h αijk h αPijk and h βPijk This is Chapter 3, Section 3. The natural vibration shape vector, m, defined in Section 3. ij The dominant mass of the ijth layer is m Pij , and I Pijk is the P ij These are the dominant mass of the layer and its moment of inertia around the k-axis.

[0492] The response magnification is set to the first j support part, or the P 1j The value normalized by the response magnification of the support part is called the distribution coefficient.

[0493]

number

[0494] It can be calculated as follows: where i=0, ...n, and i=0 represents the boundary between the ground and the structure.

[0495] (2) Interlayer deformation of the ijth layer, or the Pth layer ij The first j interlayer, or the P interlayer, when the interlayer deformation reaches the elastic limit. 1j The inter-story stress coefficient is called the ijth inter-story base stress coefficient, or the Pth inter-story base stress coefficient. ij This is called the inter-story base stress coefficient.

[0496]

number

[0497] It can be calculated as follows. However, the inter-story displacement of the ijth or the Pth ij The k-direction component of the interstory displacement transmission coefficient and the elastic limit value is h eijk , e Yijk , or hePijk , e YPijk Let G be the magnitude of the acceleration due to gravity. Part P ij The P2 when the interlayer rotation angle reaches the elastic limit. 1j The moment coefficient between layers is the P ij This is called the interlayer base moment coefficient.

[0498]

number

[0499] It can be calculated as follows, however, the P ij The transmission coefficient of the interlayer rotation angle and the elastic limit value are h erPijk , e rYPijk Let's assume that i=0, ...n, where i=0 represents the boundary between the ground and the structure.

[0500] (3) The component e corresponding to the k-direction displacement of the r-th eigenmode vector obtained by eigenvalue analysis of the structural model is the r-th measurement point ij. dijk (r) Using this, the value corresponding to the response magnification of the ij-th support portion is

[0501]

number

[0502] Part P ij Component e corresponding to the k-direction displacement of the center point dijk (r) Therefore, the P ij The value corresponding to the response magnification of the support part is

[0503]

number

[0504] It can be calculated as follows. Note that if the center point is used as the reference point, change the subscript from d11 to dP11 in the above 9 equations. The supporting part of the ij, or the Pij The value corresponding to the distribution coefficient of the support portion is

[0505]

number

[0506] It can be calculated as follows. Furthermore, between layers ij, or between layers P ij Interlayer base stress coefficient, and P ij The value corresponding to the base moment coefficient between layers is,

[0507]

number

[0508] It can be calculated as follows: where α=d, α=v, and α=a represent displacement, velocity, and acceleration. Also, β=θ, β=ω, β=ω ’ represents the angle of rotation, angular velocity, and angular acceleration. (r) d11 This refers to the reference points i=1, j=1, or P11 as defined in the formula (3.3.10a) in Section 3.3. This is the average value of the RMS of the three components of the displacement, e (r) dijk , and e (r) θijk This is a component of the r-th order eigenmode vector that corresponds to the k-direction component of the displacement of the junction of the structural model corresponding to the ij-th measurement point. Also, e dPijk (r) , and e θPijk (r) This was calculated using formulas (3.3.12) to (3.3.14) and (3.3.16) to (3.3.18) in the main text of Section 3.3. Note that i=0,...n, where i=0 represents the boundary between the ground and the structure. Note that ω r This is the r-th natural frequency. Let G be the magnitude of the acceleration due to gravity.

[0509] (1) The acceleration response ratio is an indicator that shows how much acceleration a part of a structure generates in response to ground vibration. Formula (4.3.1) in this text is the acceleration transmission coefficient h for the lj-dominant part that constitutes the ij-support part. aljk This is the average mass value.

[0510]

number

[0511] This can be transformed as follows. The numerator on the left side of the inequality gives the upper limit of the RMS of the time history of the mass load mean acceleration of the ij-th support part. However, the inequality uses the relationship in Section 3.3 (Solution 3.3.17). Therefore, the acceleration response magnification B of the ij-th support part aijkm The denominator on the right side is σ d11 Multiplying by this gives the upper limit of the RMS of the average mass load of the acceleration generated at the ij-th support point when the structure experiences natural vibration. However, the ij-th support point is the part supported by the ij-th floor (j-axis of the i-th floor), the top floor is the n-th floor, and the topmost floor is i=n+1. Velocity response magnification B vijkm Displacement response magnification B dijkm This is obtained by replacing the acceleration in the above terms with velocity and displacement. Also, the P in surface measurement ij Regarding the response magnification of the support part, by replacing the acceleration time history in the above equation with the rotational angular acceleration time history of the center point calculated using the formula in Section 3.1, the second and third equations of equation (4.3.1) in the main text can be obtained. The distribution coefficient in formula (4.3.2) is the part where the first floor supports the response magnification (the first j-support part, or the P- 1j This is standardized by the response magnification of the support portion.

[0512] (2) The value obtained by dividing the inter-story stress by the weight of the supporting part is called the stress coefficient. The k-component of the k-component of the inter-story stress of the ij-th inter-story stress obtained by dividing the maximum value of the time history by the weight of the supporting part is the k-component of the inter-story stress of the ij-th inter-story stress.

[0513]

number

[0514] and the k component of the first j interlayer stress coefficient

[0515]

number

[0516] The ratio to is given by the explanatory formula in Section 4.2 (Solution 4.2.7), P ij →As ij,

[0517]

number

[0518] Therefore, it can be roughly expressed using acceleration distribution coefficients. The k component of the inter-story displacement of the ijth layer is equal to the elastic limit displacement e Yijk The value of the k-component of the stress between the first ij-th layers when it reaches this point is given by the stiffness,

[0519]

number

[0520] This can be expressed as follows. From the above relationship, the first j inter-story stress coefficient when the k component of the ij-th inter-story displacement reaches the yield value, that is, the value obtained by dividing the k component of the first j inter-story stress by the supporting weight, is

[0521]

number

[0522] Thus, the expression for the base stress coefficient in equation (4.3.3) 1 is obtained. The same applies to equation (4.3.3) 2 and the base moment coefficient in equation (4.3.4) in surface measurements. However, the moment coefficient is obtained by dividing the inter-story moment by the sum of the moments of inertia of the supporting parts. That is,

[0523]

number

[0524] This is the result.

[0525] (3) Using the relationship between equations (3.3.10) and (3.3.11) in Chapter 3, Section 3.3, the transmission coefficient of acceleration, etc., in equation (4.3.1) of the main text is obtained as shown below, using the interlayer displacement of the r-th order eigenmode vector obtained by eigenvalue analysis of the structural model, or the P ij Equations (4.3.5) to (4.3.6) in the main text express the components of the eigenmode vector corresponding to the k-direction displacement between layers. However, the commas in the subscripts are for clarity and do not represent partial derivatives. For example, the value corresponding to the acceleration response magnification is:

[0526]

number

[0527] It can be calculated as follows. Velocity, displacement, rotational angular acceleration, etc. are calculated similarly. Furthermore, from the above formula and formula (4.3.2) in the main text, the value corresponding to the acceleration distribution coefficient is

[0528]

number

[0529] This yields the first equation of the main text (4.3.7). The same applies to velocity, displacement, rotation angle, etc. Using the relationship between equations (3.3.10) and (3.3.11) in Section 3.3 of Chapter 3 and the relationship between equations (4.1.7) to (4.1.8) in Section 4.1, equation (4.3.8) is obtained. The value corresponding to the inter-story base stress coefficient of the ijth in the first equation is:

[0530]

number

[0531] This is the case. The same applies to the base moment coefficient in the second equation. Note that the inter-story displacement of the ijth or the Pth in the above is ij k-direction component e of the elastic limit value of interstory displacement YPijk , e Yijk Regarding the interior of the structure, the yield deformation angle R YPijk and structural floor height H 0Pijk It can be expressed as follows.

[0532]

number

[0533] Note that the P ij The yield value of the interlayer rotation angle in the k-direction of the layer is given by i=1, ...n.

[0534]

number

[0535]

number

[0536] You can also calculate it this way. Note that for a typical RC building, R YPijx =R YPijy = 1 / 150~1 / 250, R Yiz A heat value of approximately 1 / 500 is typical. Also, Mi.() indicates the minimum value. Note that for i=0 (the interface with the ground),

[0537]

number

[0538]

number

[0539] This is a possible approach. However,

[0540]

number

[0541] This is the k-direction displacement of the reference point or reference plane when the ground yields, and it varies depending on the conditions of the ground and foundation. Referencing the results of plate load tests, pile horizontal resistance tests, etc., for example, e YP0jk It is also possible to consider a value of approximately 2.5 cm (k=x,y,z).

[0542] [4.4 Elastic response, cumulative inelastic displacement, elastic limit ratio, and degree of damage to assumed seismic motion] (1) The magnitude of the elastic response that occurs in each part of the structure due to the assumed seismic motion can be calculated by multiplying the average value of the strong-motion RMS of the displacement estimated to occur at the reference point or reference plane due to the assumed seismic motion by the transmissibility obtained from ambient microtremor measurements or eigenvalue analysis. Furthermore, the period of the elastic response can be estimated to be equal to the natural motion period. The estimated values ​​of the strong-motion RMS and period of the elastic displacement, velocity, and acceleration occurring at the measurement point ij are:

[0543]

number

[0544] That is the case. Part P ij The estimated values ​​of the elastic rotation angle, angular velocity, and angular acceleration of a strong earthquake at the center point, along with the period, are:

[0545]

number

[0546] That is the case. The estimated RMS value of the elastic inter-story displacement occurring between the i-j layers during a strong earthquake is:

[0547]

number

[0548] That is the case. Part P ij The estimated RMS values ​​for the elastic inter-story displacement and rotation angle occurring between stories during a strong earthquake are:

[0549]

number

[0550] This is the case where i=0, ...n, and i=0 represents the interface between the ground and the structure. Furthermore, the average value of the strong motion RMS of the three components of the reference point displacement estimated to be caused by the assumed seismic motion is σ Ed Let's assume that h αijk h αPijk and h βPijk This is defined in Chapter 3, Section 3.3. Each component of the natural vibration shape vector is, i.e., the transmissibility. Also, T αijk These are the components of the natural frequency vector. Note that h eijk h ePijk h erPijk The inter-layer displacement transmission coefficient of the ijth layer and the Pth layer are shown. ij Interstory displacement transmission coefficient, and P ij This is the interlayer rotation angle transmission coefficient. Note that displacement (α=d), velocity (α=v), acceleration (α=a), rotation angle (β=θ), and angular velocity (β=θ) are used. ’ ), angular acceleration (β=θ ’’ )

[0551] (2) The magnitude of the inelastic response that occurs in each part of the structure due to the assumed seismic motion can be calculated from the average value of the strong motion RMS of the displacement at the reference point or reference plane estimated to be affected by the assumed seismic motion, the duration of the strong motion, and the transmission coefficient. The cumulative inelastic displacement occurring in the k-direction between layers ij is:

[0552]

number

[0553] This can be calculated as follows. Furthermore, this can be used as the elastic limit magnification.

[0554]

number

[0555] And the degree of damage

[0556]

number

[0557] It can be standardized as follows. However, let i=0, ...n, where i=0 is the ground and This represents the interface of a structure. Furthermore, the average value of the three components of the strong motion RMS of the reference point displacement caused by the earthquake is σ Ed Let s0 be the duration of the strong earthquake. Also, let T be the central period of the k component of the velocity at the i+1,j measurement point. vi+1,jk , the bandwidth index is α vi+1,jk The k component of the acceleration response magnification of the ij-th support portion is B aijk , speed response magnification B vijk The interlayer displacement transmission coefficient in the k-direction between the first ij layers is h eijk , the elastic limit displacement is e Yijk The limit value of the elastic limit magnification is μ csijk Let's assume that the bandwidth index of the k-component of velocity is:

[0558]

number

[0559] That is the case. Part P ij The cumulative inelastic displacement occurring in the k-direction between layers is expressed in the above equations as follows: ij → P ijIt can be calculated as follows.

[0560] (3) Components e of the r-th order eigenmode vector obtained by eigenvalue analysis of the structural model dijk (r) and natural period T r Using this method, the magnitudes of the elastic and inelastic responses caused by the assumed seismic motion can be calculated. The strong-earth RMS and period of the elastic displacement, velocity, and acceleration occurring at the r-th eigenmode vector at the ij-th measurement point are calculated from the r-th eigenmode vector.

[0561]

number

[0562] That is the case. The P-th eigenmode vector calculated from the r-th eigenmode vector ij The elastic displacement, velocity, and acceleration of a strong earthquake at the center point, along with its RMS and period, are as follows:

[0563]

number

[0564] However, T (r) αijk These are the natural vibration periods. The strong-motion RMS of the elastic inter-story displacement occurring between the r-th eigenmode vectors is:

[0565]

number

[0566] That is the case. The P-th eigenmode vector calculated from the r-th eigenmode vector ij The RMS of strong ground motion, which is the elastic inter-story displacement and rotation angle between layers,

[0567]

number

[0568] That is the case. The cumulative inelastic displacement in the k-direction between the ij-th layers, which corresponds to the k-component of the r-th eigenmode vector, is:

[0569]

number

[0570] However, |h (r) αijk |, |h (r) αPijk |, |h (r) βPijk |, |h (r) eijk |, |h (r) ePijk | represents the interlayer between the rth eigenmode vectors, or the Pth eigenmode vector, respectively. ij The transmission coefficient of inter-story displacement in the k-direction and the inter-story displacement transmission coefficient are B (r) dijk This is the displacement response magnification. These calculation methods are described in Chapter 3, Section 3.3. , and are listed in Chapter 4, Section 4.3. r It is an r-th order eigentype. The P-th eigenmode vector calculated from the r-th eigenmode vector ij Cumulative inelastic displacement u occurring in the k-direction between layers (r) sPij As mentioned above, ij→P ij It can be calculated as follows. Furthermore, the elastic limit magnification calculated from the r-th eigenmode vector is

[0571]

number

[0572] And the degree of damage

[0573]

number

[0574] This can be standardized as follows: where i=0, ...n, i=0 represents the interface between the ground and the structure.

[0575] (1) Seismic motion is a phenomenon in which the effects of displacement and rupture at the epicenter become waves that reach the surrounding ground of a structure, causing the surrounding ground and the structure to vibrate. The magnitude, shape, and period of seismic motion are influenced not only by the properties of the surrounding ground and the structure, but also by the characteristics of the displacement at the epicenter and the properties of the bedrock and ground present between the epicenter and the structure. Furthermore, in the case of a large earthquake, both the surrounding ground and the structure vibrate accompanied by rupture, making it nearly impossible to accurately calculate the response of a structure to seismic motion. This section describes a method for calculating the magnitude of the elastic response to assumed seismic motion, assuming that the structure and the surrounding ground undergo elastic vibration until the amplitude of the seismic motion exceeds the elastic limit, using the natural vibration obtained from ambient microtremor measurements or the shape and period of the natural vibration obtained from eigenvalue analysis.

[0576] Normal tremors are steady-state vibrations. By modeling them using a steady-state Gaussian process, many of their properties can be expressed using RMS. On the other hand, earthquake motion exhibits strong unsteadiness. As a means of utilizing research results on steady-state Gaussian processes to analyze the properties of earthquake motion, a method has been proposed to model earthquake motion as a finite-duration portion of a steady-state Gaussian process. This duration is called the strong-motion duration, and the RMS calculated using it is called the strong-motion RMS. A detailed explanation of the above concepts, as well as the strong-motion duration s0 and the three-component strong-motion RMS of displacement calculated from observed earthquake motion records of recent major earthquakes, are published in Non-Patent Document 1.

[0577] Figure 10 is a table summarizing the average RMS values ​​of the three components of earthquake and displacement, as well as the duration of the strong motion (Table 4.4.1). Figure 11 is a graph showing the relationship between the average RMS displacement σEd calculated from seismic motion observation records and the measured seismic intensity (Explanation Figure 4.4.1). Figure 12 is a graph showing the relationship between the average duration of strong displacement motion s0 calculated from seismic motion observation records and the measured seismic intensity (Explanation Figure 4.4.2). Figure 13 is a graph showing the relationship between the average displacement strong motion duration s0 calculated from seismic motion observation records and the magnitude (Explanation Figure 4.4.2).

[0578] The average value of the three-component strong motion RMS was calculated from the acceleration time history obtained by applying the filter used by the Japan Meteorological Agency when calculating seismic intensity to the acceleration time history published in Non-Patent Document 1, and this was summarized in Figure 10 (Explanation Table 4.4.1) along with magnitude vibrations, etc.

[0579] The seismic motion numbers 1-3 shown in Figure 10 (Explanation Table 4.4.1) represent the seismic motions that formed the basis of the new seismic standards. The seismic intensity ranges from 5-weak to 5-strong, and the displacement RMS for strong motions is approximately 3-6 cm. Seismic motion number 4 represents the accelerated seismic motion at Tohoku University immediately before the establishment of the new seismic standards, where the building's response was also measured simultaneously and used to verify the validity of various coefficients. Seismic motion number 5 attracted attention as a seismic motion that significantly exceeded the implicit assumptions of the new seismic standards. The situation at the time is explained in detail from page iv onwards in Part 1. Seismic motion number 6 is a record from the Kobe Marine Meteorological Observatory during the Great Hanshin-Awaji Earthquake, and is a record from near the seismic intensity 7 zone.

[0580] Note that the seismic motion observed at Takatori Station (earthquake motion number 7) lacks a vertical component, so the measured seismic intensity and the average RMS value of strong displacement are calculated from the two horizontal components. For large earthquakes with a seismic intensity of 7 observed this century, average RMS values ​​of displacement exceeding 70 cm have also been calculated. However, for those in which large strong displacement RMS values ​​were calculated, it is possible that this is due to the influence of residual tilt near the measuring instrument, permanent displacement, etc.1). Figure 11 (Explanation Figure 4.4.1) plots the average RMS value of strong displacement for the 19 records in Explanation Table 4.4.1 against the measured seismic intensity. A positive correlation is observed, and it increases exponentially with respect to the measured seismic intensity. Also, Figure 12 (Explanation Figure 4.4.2) plots the average duration of strong displacement against the measured seismic intensity. A positive correlation is observed, but the variability increases with increasing measured seismic intensity. Figure 13 (Explanation Figure 4.4.3) plots the average duration of strong displacement for the three components against the magnitude (Japan Meteorological Agency). A positive correlation is observed, but the variability increases with increasing magnitude. Furthermore, among the records of earthquakes with a seismic intensity of 6+, the record from Kuratake with seismic motion number 11 shows that the horizontal two components are significantly larger than the vertical components, suggesting the possibility of residual tilt and thus it can be considered an outlier.

[0581] [Table 1] (Table 4.4.2)

[0582] [Table 2] (Table 4.4.3)

[0583] Table 1 (Explanation Table 4.4.2) shows the approximate average RMS displacement for strong motion relative to the measured seismic intensity, and Table 2 (Explanation Table 4.4.3) shows the approximate average duration of strong motion relative to the magnitude.

[0584] The magnitude of the elastic response generated in each part of a structure due to the assumed seismic motion can be calculated by multiplying the average RMS displacement of the strong-motion earthquake, which is estimated to occur at the reference point or reference plane due to the assumed seismic motion, by the natural motion vector obtained from ambient microtremor measurements or eigenvalue analysis, according to equations (4.4.1) to (4.4.4) in the main text. These values ​​can be determined by referring to Tables 1 (Explanation Table 4.4.1) to 3 (Explanation Table 4.4.3) and Figures 11 (Explanation Figure 4.4.1) to 13 (Explanation Figure 4.4.3). However, it is necessary to note that the displacement on the ground and the displacement at the reference point of the structure are not equal, and that the variability increases as these values ​​increase, both with respect to the instrumental seismic intensity and the magnitude.

[0585] (2) The inelastic deformation of a structure due to seismic motion is the amount of deformation that occurs in the part that exceeds the elastic limit. This depends on the spatiotemporal shape of the structure's natural deformation and the elastic limit deformation. Furthermore, it is also influenced by the nature of the seismic motion that serves as the input. Formula (4.4.5) in this text derives the relationship between the above parameters and the inelastic deformation using a simple model.

[0586] The expected value of the cumulative sliding displacement of a point mass placed on a rough plane due to irregular vibration of the plane is given by parameters related to the steady-state process and the sliding limit acceleration A of the point mass, assuming that the plane vibration is a portion of a steady-state Gaussian process with duration s0. c Analytical solution represented by

[0587]

number

[0588] This has been obtained 2). However, σ a , σ v s0 is the rms of the acceleration time history and velocity time history of the rough plane vibration, and the duration, respectively, and the central period of the velocity time history is t v , the bandwidth index is α v That is what they say.

[0589] The formula in this section considers the support portion of the structure at the ij-th level as a point mass, and the space between the ij-th levels as the boundary between a rough plane and the point mass. By substituting the index for natural vibration into the above model, the cumulative sliding displacement in the k-direction is calculated and this is used as an index for inelastic deformation. In this case, since the vibration of this plane is the vibration of a point mass when no sliding occurs, it is assumed that the natural vibration of the support portion at the ij-th level is amplified. The sliding limit acceleration between the ij-th levels is a cik s0 is the duration of the strong motion in the acceleration time history of the first support part ij, and rms is σ ai+1~n+1,jk , the strong motion rms of the velocity time history obtained by integrating this is σ vi+1~n+1,jk , the central period is t vi+1~n+1,jk , the bandwidth index is α vi+1~n+1,jk Therefore, the expected value of the cumulative slip displacement generated in the k-direction between the ij-th layers due to vibration can be found by applying the above index values ​​to equation (Solution 4.4.1):

[0590]

number

[0591] This is the result. From equation 4.3 (solution 4.3.1), the average acceleration of the mass load occurring at the ij-th support part The upper limit of the strong motion rms in time history is,

[0592]

number

[0593] Therefore, acceleration response magnification b aijk and the average value of the displacement of the reference point during strong earthquakes σ ed It is expressed as follows. By replacing the acceleration time history in the above equation with the velocity time history, the upper limit of the strong earthquake rms of the mass-weighted average velocity of the ij-th support part is:

[0594]

number

[0595] Therefore, the limiting acceleration in the k-direction between the ij-th layers is calculated by dividing the shear force at yield by the mass of the supporting part, and from equation 4.3 (solution 4.3.5),

[0596]

number

[0597] It can be expressed as follows. Also, the central period t of the ij-th support portion. vi+1~n+1,jk and bandwidth α i+1~n+1,jk For this part, we use the one in the k direction of the (i+1)th, j-th layer as a representative. Substituting the above relationship into equation (Solution 4.4.2), we obtain equation (4.4.5) in the main text. This formula (4.4.6) is,

[0598]

number

[0599] It can be transformed into this. However,

[0600]

number

[0601] Here, the elastic response elastic limit modulus is,

[0602]

number

[0603] Let's leave it at that. However,

[0604]

number

[0605] This is the average displacement rms σ of the reference point. edis the elastic interlayer displacement between the i-th and j-th layers. Above is the description. From the above, Equation (Solution 4.4.6) is

[0606] [Number] (Solution 4.4.10)

[0607] becomes as follows. However, the first factor

[0608] [Number] (Solution 4.4.11)

[0609] is the number of repetitions of the vibration of the i-th layer due to the assumed ground motion. Also, the second factor

[0610] [Number] (Solution 4.4.12)

[0611] is the normalized value of the displacement strong motion rms average value σ of the reference point which is the input ed by the interlayer elastic limit displacement e yijk . The third factor

[0612] [Number] (Solution 4.4.13)

[0613] can be interpreted as the response magnification factor regarding the elastic limit magnification factor. The fourth factor hexp(-1 / 2h 2 ) is a function of the response elastic limit ratio h defined by Equation (Solution 4.4.8). When 0 < h < 0.3, it is almost zero due to the influence of the exp term. When 0.3 < h, it increases linearly in response to the increase of h. e ijk is the strong motion RMS of the elastic response interlayer displacement calculated ignoring the elastic limit, and e YijkIf it is less than 30%, almost no inelastic displacement will occur. If the peak factor is 3.0, the maximum value of the above calculation is 3.0e ijk If h is below the elastic limit, almost no inelastic displacement occurs. However, as h increases, inelastic displacement will occur in proportion to h.

[0614] The fifth factor is f(α vijk ) is the bandwidth index α of the velocity in the k-direction of the i-th layer. vijk It is a function of α. vijk By definition, 0 < α vijk <1. α vijk =0 represents white noise, where f(0) = π / 2 = 1.57, and it increases slightly monotonically, α vijk At =0.537, it reaches a maximum value of f(0.537)=1.862, and thereafter decreases monotonically, forming a single sine wave α vijk When = 1, f(1) = 1.0. Therefore, if the bandwidth index is 0.537 or greater, the larger the bandwidth index (the smaller the bandwidth: closer to a simple sine wave), the smaller the elastic limit magnification.

[0615] Also, the elastic limit interstory displacement e Yijk A larger value indicates a higher natural vibration velocity center period T. vijk The longer the value, the speed response magnification B. vijk It can be seen that the smaller the value, the smaller the elastic limit magnification. The model in this section shows that structures with such properties are less susceptible to damage. On the input seismic motion side, it can be derived that the ability to inflict damage increases in proportion to the input displacement and the duration of the strong motion. Part P ij Cumulative inelastic displacement u occurring in the k-direction between layers sPij As mentioned above, ij→P ij It can be calculated as follows.

[0616]

number

[0617] It is experimentally known that vertical structural members such as columns generally recover from repeated deformation beyond their elastic limit, maintaining usability between the i-j floors, as long as the cumulative damage is minor. The damage degree in formula (4.4.7) is an index that quantifies this performance. An example of the usability limit value of the elastic limit multiplier for reinforced concrete structures is the value in Table 4.4.4 obtained from large-scale shaking table experiments using an eccentric piloti building model.

[0618] [Table 3] (Table 4.4.4)

[0619] (3) The component e corresponding to the k-direction displacement between the ij layers of the r-th order eigenmode vector obtained by eigenvalue analysis of the structural model dijk (r) The coefficients in the main text (4.4.5) can be expressed using this. Of these, the interstory displacement transmission coefficient is given by equation (4.1.7) in the main text of Section 4.1. The ratio of the response magnification is given by formula (4.3.5) in Section 4.3,

[0620]

number

[0621] Therefore, it becomes the displacement response magnification. Also, the bandwidth index of the velocity is

[0622]

number

[0623] Therefore,

[0624]

number

[0625] Therefore, we obtain formula (4.4.13) from the above. Part Pij Cumulative inelastic displacement u occurring in the k-direction between layers sPij In the main text (4.4.13), ij → P ij It can be calculated as follows.

[0626]

number

[0627] This is the result. However, Tr is the r-th order natural period.

[0628] [4.5 Relationship with coefficients etc. under current standards] Some of the coefficients in the current standards can be compared with the indices defined in this chapter. However, when making such comparisons, it is necessary to confirm the mechanical models and calculation conditions from which the coefficients were obtained, taking into account that the current standards' provision of representing seismic action on structures as external forces requires many assumptions and has an extremely limited scope of application.

[0629] (1) The first inter-story vibration period in Section 4.2 is the design primary natural period.

[0630]

number

[0631] This can be compared with the natural period of the ij measurement point and obtained from the eigenvalue analysis in Chapter 3, Section 3.4. The r-th natural period is also, indirectly, the first natural period for design.

[0632]

number

[0633] Related to The acceleration distribution coefficient in Section 4.3 is a coefficient that represents the vertical distribution of the seismic story shear force coefficient.

[0634]

number

[0635] It can be compared to this. The acceleration response magnification in Section 4.3 is the acceleration response magnification implied in the current standard seismic force regulations.

[0636]

number

[0637] This can be compared to the above. However, in the four equations above, k = x or y. Also, R t is the vibration characteristic coefficient. Note that r is the order of the eigenmode.

[0638] (2) The base stress coefficient in Section 4.3 corresponds to the base shear coefficient, which is equivalent to the ultimate horizontal load-bearing capacity.

[0639]

number

[0640] And, the cumulative strength index C of the seismic diagnosis T , shape index S D , and the product of the time-series index T

[0641]

number

[0642] It can be compared to this. Furthermore, there is a value F that corresponds to the toughness index. km Through this, structural seismic index for microtremor diagnosis

[0643]

number

[0644] By defining this, it can be compared with the structural seismic index used in seismic diagnosis. Superstructure rating for wooden houses in microtremor diagnosis

[0645]

number

[0646] By defining this, it can be compared with the structural seismic index used in seismic diagnosis. However, in the above four equations, k = x, y. Note that r is the order of the eigenmode.

[0647] [4.5 Explanation of the relationship with coefficients, etc. under current standards]

[0648] There are significant differences between the seismic isolation design method and the design and diagnostic methods outlined in the current seismic standards and seismic diagnostic standards for buildings (hereinafter referred to as "current standards") in terms of how seismic action is represented in structural analysis, the coordinate system, modeling, and how the resulting numerical values ​​are handled. The main differences are as follows:

[0649] (1) Under current standards, seismic activity is represented by an external force called seismic force, which acts on each part of a structure in proportion to its mass. In static structural calculations, seismic force corresponds to inertial resistance, while in dynamic calculations, seismic force corresponds to inertial force. The two are often confused and are considered to be real forces, even though they are fictitious forces that do not actually exist. Calculation results are scrutinized to several decimal places, and judgments differ greatly depending on whether or not they exceed the standard value. The seismic isolation design method is based on the understanding that while earthquake action is the displacement of the ground around a structure, it is difficult to quantify this displacement because the ground exists in three-dimensional space with a semi-infinite extent. Seismic isolation and safety are evaluated using a number of numerical values, and design decisions are not made solely based on the magnitude of these values.

[0650] (2) Under the current standards, two types of models are applied to the target structure: a simple model for calculating seismic forces and a complex model used for structural calculations such as stress calculations, ultimate horizontal load capacity calculations, and time history response analysis. This results in a dual structure where consistency between the two models is not ensured. In addition, the static structural calculation has a contradictory self-contradictory structure in which inelastic stresses are calculated using inertial resistance that balances the stresses calculated by the elastic model as input. The coordinate system is a non-inertial frame of reference with the point that generates the acceleration time history used to calculate seismic forces as the origin, but it is considered to be an inertial frame of reference. Normally, structures are treated as moving and deforming in only one direction. Seismic design methods treat structures as continuums existing in three-dimensional space and describe their motion and deformation through the displacement of a finite number of points of contact. The coordinate system is one that moves with the Earth's surface, with its origin in the space near the structure and the surrounding ground, and is essentially an inertial frame of reference.

[0651] Figure 14 is a schematic diagram illustrating the relationship between the current standards for seismic action, structural models, and coordinate systems (Explanation Figure 4.5.1). Figure 14 (Explanation Figure 4.5.1) schematically depicts the seismic action, structural model, and coordinate system under current standards. The dashed line represents the structure before the earthquake. Seismic action is represented by an external force called seismic force. In static calculations, it is calculated by multiplying the supported weight by a coefficient calculated from the height of the structure, material, type of ground directly beneath the foundation, weight distribution, etc. In dynamic calculations, the seismic force is specified to be calculated by multiplying the mass of each part by a specified acceleration time history (ground acceleration). These are applied as loads to each part of the structural model shown in the figure, and the stresses between each story and The deformation is calculated, and the structural specifications are determined so that it falls within the design limits. Typically, each layer is only given degrees of freedom for translational displacement in the x-direction as shown in the diagram.

[0652] Figure 15 is a schematic diagram illustrating the relationship between actual seismic activity and inertial and non-inertial frames of reference (Explanation Figure 4.5.2). Figure 15 (Explanation Figure 4.5.2) schematically depicts what happens when a structure modeled as shown in Figure 14 (Explanation Figure 4.5.1) is subjected to a real earthquake. This is the moment when the earthquake accelerates the ground surface from the position of the dashed line on the left to the position of the solid line on the right. In reality, the ground surface moves not only horizontally but also vertically and rotates, but for simplicity, only the case of horizontal movement is depicted. Acceleration occurs in each layer, deformation occurs between layers, and corresponding stress is generated. However, external forces like the seismic force in Figure 14 (Explanation Figure 4.5.1) do not occur. It is impossible to apply an external force proportional to the mass of each part of the structure other than gravity. In the previous diagram, the ground surface is not moving at all. In a real earthquake like the one depicted in Diagram 4.5.2, it is impossible for buildings to deform if the ground surface is not moving at all. This unreality indicates that seismic forces do not actually exist. So, what exactly are seismic forces?

[0653] The seismic force used in the static calculations of the current seismic standards (new seismic standards) is the total seismic force (X) acting on the part supported by the part of the building at that height, according to the height of the building. i The calculation is performed by taking the sum of the dead load and the live load (Σw) and the seismic story shear force coefficient at the said height.

[0654]

number

[0655] It is stipulated that the calculation is performed by multiplying by . That is,

[0656]

number

[0657] This is the case. C is defined in equation (Solution 4.5.1). iThe first factor Z is the regional coefficient, and a value of 0.7 to 1.0 is specified depending on the region. The fourth factor C0 is the standard shear force coefficient, which is set to 0.2 or higher, and is specified to be 1.0 or higher in the calculation of the ultimate horizontal load-bearing capacity. The second factor is the vibration characteristic coefficient.

[0658]

number

[0659]

number

[0660]

number

[0661] It is called and, using the numerical value Tc representing the characteristics of the ground as a parameter, is given by the above equations (Solution 4.5.3a) to (Solution 4.5.3c) as a single-valued function of the first natural period T for the design of the building. Third factor A i This is called the distribution of the seismic story shear force coefficient in the height direction of a building, and it is calculated from the above T and the weight distribution of the building α. i As a function of,

[0662]

number

[0663] A formula for calculating this is provided. However, α i This is called the standardized weight, and it is calculated by dividing the sum of the dead load and live load of the part supported by the height portion used to calculate seismic forces by the sum of the dead load and live load of the above-ground portion of the building, resulting in α1=1, or A1=1.

[0664] In the commentary by experts involved in the establishment of the new seismic standards, the above seismic force is described as inertial force and can be expressed as mass × acceleration. This acceleration changes depending on how the building shakes. The explanation is given as if the fact that earthquakes generate seismic force in buildings is a natural law and can be calculated from the height of the building, etc. This is a common understanding among almost all experts and is taught in classrooms as well. However, inertial force is merely a force that appears to act on surrounding objects when the phenomenon of surrounding objects appearing to move from a moving observation point is expressed mathematically. In English, it is called a fictitious force and is nothing more than an imaginary force. If the observation point does not rotate, it is equal to the acceleration of the observation point multiplied by the mass of the surrounding objects and given a negative sign. For example, if the observation point is point G on the ground surface in Figure 14 (Explanation Figure 4.5.1) and Figure 15 (Explanation Figure 4.5.2), then its acceleration a G When the motion is observed from this point, that is, when the motion is described in a coordinate system G with this point as the origin, in addition to the forces actually acting on each part of the building,

[0665]

number

[0666] This is a hypothetical force that causes motion as if a force were acting upon it. If we let f be the resultant force of the forces actually acting on a part of a building, then the equation of motion is:

[0667]

number

[0668] This is the result. Figure 14 (Explanation Diagram 4.5.1) shows the motion shown in Figure 15 (Explanation Diagram 4.5.2) as viewed from a coordinate system G fixed to the ground surface (described in coordinate system G). The inertial force appears to be the driving force causing the structure to vibrate in this figure. However, this force does not appear when viewing the structure and ground from an inertial frame O drawn in the upper right of Figure 15 (Explanation Diagram 4.5.2) (described in coordinate system O). However, if the observation point G moves with rotation relative to the inertial frame, the motion appears to be affected by inertial forces (rotational inertial force) due to rotational angular velocity, angular acceleration, and the distance of the object from the observation point, in addition to the above forces. These are called the Coriolis force, centrifugal force, and Euler force, but none of them are actually acting forces.

[0669] On the other hand, the seismic force defined in equation (Solution 4.5.1) and subsequent equations is obtained by multiplying a coefficient by a gravitational force, that is, (mass × gravitational acceleration), which is the sum of the dead load and the live load. In this respect, it is similar to an inertial force, but if it were an inertial force, the coefficient to be multiplied would be the acceleration a measured in the inertial frame of the observation point. G This does not change depending on the primary natural period of the object, nor does it change depending on the individual parts. Therefore, the vibration characteristic coefficient R in the seismic force calculation formula... t The distribution coefficient of the story shear force coefficient in the height direction must be i=1. In other words, these coefficients become unnecessary.

[0670] According to the expert's commentary mentioned above, "The standard shear force coefficient C0=1.0 for major earthquakes was determined by assuming a ground acceleration of 0.33G~0.4G and a seismic response ratio of 2.5~3 for short-period buildings. The vibration characteristic coefficient R t The shape was determined based on the shape of the acceleration response spectrum of the measured seismic motion, taking into account the acceleration response magnification even when the natural period is zero. i This represents a constant 1 that represents the uniform distribution of seismic intensity and (1-α) that represents the inverse triangular distribution of seismic intensity. i ), and further subject to white noise shear The distribution √α representing the whipping phenomenon in the upper atmosphere, which is obtained as the response of the rod. iIt is a combination of these according to the period. That is, the response acceleration of the supporting part of the first floor is determined using the acceleration response spectrum (the acceleration obtained by calculating the response of a one-degree-of-freedom system to the assumed seismic motion and plotting it against its natural period), and R t It is stated that C0 represents this, and Ai was determined to distribute it to each floor based on the acceleration distribution of the elastic shear rod, etc. From this explanation and equation (Solution 4.5.1) and subsequent equations, it can be concluded that the seismic force used in the static calculation of the new seismic standards is not an inertial force, but rather the inertial resistance of the part supported by the part at that height to the seismic motion assumed by the new seismic standards, that is, the product of the response acceleration and mass of that part to the assumed seismic motion, multiplied by regional coefficients, etc. inertia resistance

[0671]

number

[0672] This refers to the equation of motion of an object.

[0673]

number

[0674] Static equilibrium type

[0675]

number

[0676] A hypothetical force f used when considering this scenario. I This is the case where m is the mass of the object, a is its acceleration, and f is the resultant force of the forces actually acting on it. According to equation (Solution 4.5.1) and subsequent equations, the total seismic force acting on the part supported by the first floor is:

[0677]

number

[0678] Therefore, this is the inertial resistance f in equation (Solution 4.5.6). I If we equate this to m = Σm and ignore the negative sign,

[0679]

number

[0680] Therefore, the vibration characteristic coefficient R t The product of the standard shear force coefficient C0 and the regional coefficient Z is the response acceleration of the part supported by the first floor divided by the acceleration due to gravity G, which is consistent with the explanation gi...

Claims

1. (1) The spatiotemporal shape and frequency of the natural vibration of a structure are calculated using the natural vibration vector based on measurement data related to natural vibration obtained by ambient microtremor measurement, and (2) The spatiotemporal shape and frequency of the natural motion of the structural model used for seismic design of the structure are calculated using the natural motion vector, based on the analysis data regarding the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of the structure. (3) A step of relating the index value obtained by the measurement in (1) and the index value obtained by the analysis in (2) on the same dimension, It has, A calculation method for use in seismic design of a structure, characterized in that the natural ground motion vectors in (1) and (2) above include a natural ground motion shape vector, a natural ground motion number vector, and a natural ground motion period vector.

2. RMS is the mean square root of the time history over its duration. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. Surface measurement of constant microtremor is performed at each center point of a plane formed by at least three measurement points. This is a measurement, The center point of the surface measurement in continuous micro-tremor measurement is the centroid of at least three measurement points. Each of the measurement points in the point measurement of the continuous micro-motion measurement or the center point of the surface measurement of the continuous micro-motion measurement is In the case of a multi-layered structure with two or more layers, the upward direction from the part of the structure that is in contact with the ground. Each measurement axis corresponds to a point on each layer of a multi-layered structure through which a measurement axis runs vertically. (4) The natural vibration vector obtained by the measurement in (1) above includes the natural vibration shape vector, The natural vibration shape vector is, A vector representing the natural vibration shape, wherein the absolute value of its components is the RMS ratio of at least one time history selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point, with respect to the reference time history. (5) The natural vibration vector obtained by the measurement in (1) above includes the natural vibration number vector, The natural frequency vector is, A vector representing the frequency of natural vibration, the vector whose components are at least one central frequency selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. (6) The natural vibration vector obtained by the measurement in (1) above includes the natural vibration period vector, The natural vibration period vector is, A vector representing the period of natural vibration, the vector whose components are at least one central period selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. (7) The natural vibration vector obtained by the analysis in (2) above includes the natural vibration shape vector, The natural vibration shape vector is, A vector representing the natural vibration shape, wherein the absolute value of its components is the RMS ratio of at least one time history selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point, with respect to the reference time history. (8) The natural vibration vector obtained by the analysis in (2) above includes the natural vibration period vector, The natural vibration period vector is, A vector representing the period of natural vibration, the vector whose components are at least one central period selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. (9) The natural motion vector obtained by the analysis in (2) above includes the natural motion number vector, The natural frequency vector is, A vector representing the frequency of the natural vibration, the components of which are at least one central frequency selected from the group consisting of the displacement, velocity, and acceleration of each measurement point and each center point, as well as the rotation angle, angular velocity, and angular acceleration of each center point. A calculation method for use in seismic design of the structure described in claim 1.

3. (10) The natural period of the translational motion of the measurement point obtained by point measurement of constant microtremor measurement is The steps involve calculating the three directional components in a Cartesian coordinate system corresponding to the velocity component of the point measurement of the natural frequency vector, and the three directional components in a Cartesian coordinate system corresponding to the displacement component of the point measurement of the natural frequency vector, The natural period of the translational motion of the center point, measured by surface measurement using continuous micro-motion measurement, The steps involve calculating the three directional components in the Cartesian coordinate system corresponding to the velocity component of the surface measurement of the natural frequency vector, and the three directional components in the Cartesian coordinate system corresponding to the displacement component of the surface measurement of the natural frequency vector, The natural period of rotational motion of the center point, measured by surface measurement using continuous micro-motion measurement, The steps involve calculating the three directional components in the Cartesian coordinate system corresponding to the rotation angle component of the surface measurement of the natural frequency vector, and the three directional components in the Cartesian coordinate system corresponding to the angular acceleration component of the surface measurement of the natural frequency vector, including, A calculation method for use in seismic design of the structure described in claim 2.

4. (11) The kinetic energy composition ratio in point measurements is calculated for the three directional components of the Cartesian coordinate system as the ratio of the total kinetic energy of the point-dominated portion at each measurement point in the point measurements of the constant microtremor measurement, (12) The kinetic energy composition ratio in surface measurement is calculated as the ratio of the total kinetic energy of the center point-dominated portion at each center point obtained from surface measurement of constant micro-motion measurement, by separating it into the translational motion component from the relationship between the translational motion component and the rotational motion component, and calculating it for the three directional components in the Cartesian coordinate system. The kinetic energy composition ratio in surface measurement is calculated as the ratio of the kinetic energy composition ratio calculated for the three directional components of the Cartesian coordinate system of the measurement point to the kinetic energy composition ratio calculated for the three directional components of the Cartesian coordinate system of the center point obtained by surface measurement of constant micro-motion measurement. This is done by separating the rotational motion component from the relationship between the translational motion component and the rotational motion component, and then calculating it for the three directional components of the Cartesian coordinate system. (13) A step in which the spatiotemporal shape of the natural motion of a structural model used for seismic isolation design of a structure is calculated based on data relating to the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic isolation design of a structure, The kinetic energy composition ratio of the dominant portion corresponding to the measurement point is calculated for the three directional components of the Cartesian coordinate system of the contact point of the structural model corresponding to the measurement point, using the components of the r-order eigenmode vector corresponding to the three directional components of the Cartesian coordinate system of the displacement of the contact point of the structural model corresponding to the measurement point. The first step involves calculating the translational motion component of the kinetic energy composition ratio of the dominant portion corresponding to the center point measured by surface measurement, for the three directional components of the Cartesian coordinate system corresponding to each center point measured. The rotational motion component of the kinetic energy composition ratio of the dominant portion corresponding to the center point measured by surface measurement is calculated for the three directional components of the Cartesian coordinate system corresponding to each center point measured. including, A calculation method for use in seismic design of the structure described in claim 3.

5. (14) The rate of change of kinetic energy in point measurement is calculated for the three directional components of the Cartesian coordinate system as the ratio of the kinetic energy composition ratio of the measurement point to the kinetic energy composition ratio of the reference point obtained by each point measurement of the constant microtremor measurement, in the calculation step, (15) The translational component of the rate of change of kinetic energy in surface measurement is calculated for the three directional components of the Cartesian coordinate system as the ratio of the kinetic energy composition ratio of the translational component in surface measurement of the center point dominated portion at the center point in surface measurement by constant micro-tremor measurement to the kinetic energy composition ratio of the translational component in surface measurement of the center point dominated portion at the reference surface for each surface measurement of constant micro-tremor measurement, The rotational component of the rate of change of kinetic energy in surface measurement is calculated for the three directional components of the Cartesian coordinate system as the ratio of the kinetic energy composition ratio of the rotational component in surface measurement of the center point in the center point-dominated portion of surface measurement by constant micro-motion measurement to the kinetic energy composition ratio of the rotational component in surface measurement of the center point-dominated portion of surface measurement by constant micro-motion measurement for each surface measurement, and (16) A step in which the spatiotemporal shape and frequency of the natural motion of a structural model used for seismic design of a structure are calculated based on analysis data relating to the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of a structure, The step involves calculating the rate of change of kinetic energy of the dominant portion corresponding to each measurement point, as the ratio of the kinetic energy composition ratio of the dominant portion corresponding to each measurement point to the kinetic energy composition ratio of the dominant portion corresponding to the reference point, for the three directional components of the Cartesian coordinate system of the measurement point. The process involves calculating the translational component of the rate of change of kinetic energy of the dominant portion corresponding to the center point, as measured by surface measurement, for the three directional components of the Cartesian coordinate system of the center point, as the ratio of the translational component of the kinetic energy composition ratio of the dominant portion corresponding to each reference point, as measured by surface measurement, to the translational component of the kinetic energy composition ratio of the dominant portion corresponding to each center point, as measured by surface measurement. The first step involves calculating the rotational component of the rate of change of kinetic energy of the dominant portion corresponding to each center point, as measured by surface measurement, as the ratio of the rotational component of the kinetic energy composition ratio of the dominant portion corresponding to each center point, as measured by surface measurement, to the rotational component of the kinetic energy composition ratio of the dominant portion corresponding to each reference point, as measured by surface measurement, for the three directional components of the Cartesian coordinate system of the center point. including, A calculation method for use in seismic design of the structure described in claim 4.

6. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The center point P is the three measurement points A(x) on the measurement surface. ａ , y ａ ,0), B(x ｂ , y ｂ ,0) Call C(x ｃ , y ｃ It is the center point of , 0) The coordinate values x of each measurement point ａ , y ａ , x ｂ , y ｂ , x ｃ , and y ｃ each relate to a coordinate system parallel to an inertial system with the center point P as the origin and each axis describing at least one selected from the group consisting of velocity, acceleration, jerk, angular velocity of rotation, angular acceleration of rotation, and angular jerk of rotation. Displacement p of the center point P ｋ (t) and rotation angle θ ｋ (t) is the three measurement points A(x) on the measurement surface. ａ , y ａ ,0), B(x ｂ , y ｂ ,0) and C(x ｃ , y ｃ k component a of the respective displacement time history of , 0) ｋ (t), b ｋ (t) and c ｋ The step calculated from (t), Velocity p of the center point P ’ k(t) and rotational angular velocity θ ’ k(t) is the three measurement points A(x) on the measurement surface. ａ , y ａ ,0), B(x ｂ , y ｂ ,0) and C(x ｃ , y ｃ The k-component a of the respective velocity time history of , 0) ’ k(t), b ’ k(t) and ck ’ The step calculated from (t), Acceleration p at the center point P ’’ k(t) and rotational angular acceleration θ ’’ k(t) is the three measurement points A(x) on the measurement surface. ａ , y ａ ,0), B(x ｂ , y ｂ ,0) and C(x ｃ , y ｃ The k-component a of the respective velocity time history of , 0) ’’ k(t), b ’’ k(t) and ck ’’ The step calculated from (t), jerk p of the center point P ’’’ k(t) and rotational angle jerk θ ’’’ k(t) is the three measurement points A(x) on the measurement surface. ａ , y ａ ,0), B(x ｂ , y ｂ ,0) and C(x ｃ , y ｃ The k-component a of the respective jerk time history of , 0) ’’’ k(t), b ’’’ k(t) and ck ’’’ The step calculated from (t), A group consisting of each of the steps is selected, and includes at least one step, The single '' symbol in each step represents the first time derivative, the '' symbol represents the second time derivative, and the '''' symbol represents the third time derivative. This invention provides a calculation method for use in seismic design of the structure described in claim 5.

7. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The coordinates in the inertial frame of the equilibrium positions of both measurement points A and B are given by A(x ａ , y ａ , z ａ ), B(x ｂ , y ｂ , z ｂ ) and Displacement time history is a ｋ (t), b ｋ (t) and The process includes a step in which the strain between two measurement points A and B is calculated as the ratio of the length of deformation to the original length of the two measurement points A and B before deformation, The length of the aforementioned deformation is, The coordinates of the two measurement points A and B are A(x ａ , y ａ , z ａ ) and B(x ｂ , y ｂ , z ｂ ) Furthermore Displacement time history a ｋ (t) and b ｋ (t) Calculated using, A calculation method for use in seismic design of the structure described in claim 6.

8. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The continuous micro-vibration measurement is performed at each individual measurement point. The measurement points are identified by a set of natural numbers i and j, with the lowest point of each measurement axis assigned a number i=1, and the axis with the reference point assigned a number j=1. The continuous micro-vibration measurement of each surface is performed at the center point of a plane formed by at least three measurement points. The center point is P ｉｊ So, the three points A are used to calculate the motion of the central point. ｉｊ , B ｉｊ , C ｉｊ It is represented as, When a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this is set to i = 0. RMS is the duration t of the time history x(t). ０ RMS (Root Mean Square) in [Number 28] (3.3.1a) It is represented as, The k-component time history of the displacement at the ij measurement point is y ｉｊｋ (t) is expressed as Part P ｉｊ The k-component time history of the displacement of the center point is y Ｐｉｊｋ (t) is expressed as The RMS of the k-component of the displacement at the i-j measurement point and the Pi-j center point, and its differential time history k-component, [Number 29] (3.3.1b) It is represented as, The first subscript α of σ is either displacement (α = d), velocity (α = v), or acceleration (α = a). Part P ｉｊ k-component time history θ of the rotation angle of the center point Ｐｉｊｋ (t), and the RMSσ of its differential time history βｉｊｋ but, [Number 30] (3.3.1c) It is represented as, The first subscript β of σ is the rotation angle (β = θ) and the angular velocity (β = θ). ’ ) or angular acceleration (β = θ ’’ ) is one of the following, The symbols "'" above represent the first derivative in time, and "''" represent the second derivative in time. A calculation method for use in seismic design of the structure described in claim 7.

9. The transmission rate is the RMS ratio of the time history y(t) to the reference time history x(t). [Number 31] （３.３.２） It is represented as, The central frequency is the derivative of the time history y(t) ’ The ratio of (t)'s RMS to its own RMS [Number 32] （３.３.３） Represented by, A calculation method for use in seismic design of the structure described in claim 8.

10. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. The measurement points are identified by a set of natural numbers i and j, with the lowest point of each measurement axis assigned a number i=1, and the axis with the reference point assigned a number j=1. Surface measurement in continuous micro-vibration measurement is a measurement at the center point of a plane created by at least three measurement points. The center point is P ｉｊ and three points for calculating the movement of the center point are A ｉｊ , B ｉｊ , C ｉｊ which are represented by, When a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this is set to i = 0. The α of the natural vibration shape vector in point measurement ｉｊｋ The absolute value of the component is the transmission rate of the k component, such as the displacement at the i-j measurement point. [Number 33] （３.３.４） However, the reference time history x ｄ１１ (t) is the average of the RMS values ​​of the three directional components of the displacement of the reference point. [Number 34] (3.3.4a) It is represented as a time history, The αP of the natural vibration shape vector in surface measurement ｉｊｋ The absolute value of the component is the transmission rate of the k component, such as the displacement at the i-j measurement point. [Number 35] （３.３.５） [Number 36] （３.３.６） However, the reference time history x ｄ１１ (t) is the average of the RMS values ​​of the three directional components of the displacement of the reference point. [Number 34] (3.3.4a) It is represented as a time history, The α of each natural vibration shape vector ｉｊｋ The component α is one of displacement (α=d), velocity (α=v), or acceleration (α=a). The β of the βijk component of each natural vibration shape vector is either the rotation angle (β = θ), the angular velocity (β = θ ’ ), or the angular acceleration (β = θ ’’ ), and The symbols "'" above represent the first derivative in time, and "''" represent the second derivative in time. The components of the natural frequency vector ω are equal to the central frequency of the natural vibration shape vector. [Number 37] （３.３.７） [Number 38] （３.３.８） It is expressed as the ratio of the components of the eigenform vector of the differential time history, d is displacement, v is velocity, a is acceleration, a ’ θ is the jerk, θ is the rotation angle, θ ’ θ is the angular velocity. ’’ θ is angular acceleration. ’’’ This is the angular jerk, Each component of the natural period vector T is derived from the components of the natural frequency vector, [Number 39] （３.３.９） It can be calculated as follows: A calculation method for use in seismic design of the structure described in claim 9.

11. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The measurement point of the r-th order eigenmode vector corresponding to the measurement point obtained by point measurement in continuous microtremor measurement is the junction of the structural model corresponding to the i-th measurement point. At least three measurement points A by surface measurement using continuous micro-vibration measurement. ｉｊ , B ｉｊ , C ｉｊ The center point P of the plane created by ｉｊ Center point P of the r-th eigenmode vector corresponding to this vector ｉｊ However, the center point P ｉｊ It is the point of contact of the corresponding structural model, Each measurement axis of the structural model is assigned a number with i=1 at its lowest point, and the measurement axes of the structural model are assigned numbers with j=1 at the axis containing the reference point, and are identified by pairs of natural numbers i and j. When a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this is set to i = 0. The (r) in the superscript of each of the following equations is calculated from the r-th eigenmode, The spatiotemporal shape and frequency of the natural motion of a structural model used in seismic design for a structure are obtained from the r-th order natural mode, which is derived from the eigenvalue analysis of the structural model used in seismic design for a structure, and the value corresponds to the absolute value of the component of the natural motion shape vector. [Number 40] （３.３.１０） However, it was calculated, e ｄｉｊｋ （ｒ） However, this is a component of the r-th order eigenmode vector that corresponds to the k-component of the displacement of the junction of the structural model corresponding to the i-j measurement point. ω ｒ However, this is the r-th natural frequency, The reference amplitude is the average of the three absolute values ​​of the displacement at the reference point 11 (i=1, j=1) or the center point P11. [Number 41] (3.3.10a) It is represented as, Center point P ｉｊ The value corresponding to the absolute value of the components of the natural vibration shape vector is obtained at three measurement points A set on the measurement surface. ｉｊ , B ｉｊ , C ｉｊ The center point P calculated from the components and coordinate values ​​of the r-th order eigenmode vector at the junction of the corresponding structural model. ｉｊ In the mode shape, [Number 42] （３.３.１１） however [Number 43] （３.３.１２） [Number 44] （３.３.１３） [Number 45] （３.３.１４） It is calculated as follows: The values ​​corresponding to the absolute values ​​of the components related to rotation angle, rotational angular velocity, and rotational angular acceleration are [Number 46] （３.３.１５） however [Number 47] （３.３.１６） [Number 48] （３.３.１７） [Number 49] （３.３.１８） It is calculated as follows: Subscript P ｉｊ A ｉｊ , B ｉｊ , C ｉｊ However, the center point P in surface measurement ｉｊ And the three measurement points A in response to this ｉｊ , B ｉｊ , C ｉｊ It is the point of contact of the corresponding structural model, x Ａｉｊ , y Ａｉｊ and z ａｉｊ , and also, e ｄＡｉｊｘ （ｒ） , e ｄＡｉｊｙ （ｒ） and e ｄＡｉｊｚ （ｒ） These are, respectively, measurement point A ｉｊ These are the x, y, z coordinate values ​​and the x, y, z components of the r-th eigenmode vector. Measurement point B ｉｊ The x, y, z coordinate values ​​and the x, y, z components of the r-th eigenmode vector, as well as the measurement point C ｉｊ For the x, y, z coordinate values ​​and the x, y, z components of the r-th eigenmode vector, respectively, at measurement point A ｉｊ This is similar to the case of the x, y, z coordinate values ​​and the x, y, z components of the r-th eigenmode vector. The values ​​corresponding to the components of the natural frequency vector and the natural period vector are [Number 50] （３.３.１９） And so, ω ｒ However, the r-th natural frequency is A calculation method for use in seismic design of the structure described in claim 10.

12. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. The measurement points are identified by a set of natural numbers i and j, with the lowest point of each measurement axis assigned a number i=1, and the axis with the reference point assigned a number j=1. Surface measurement in continuous micro-vibration measurement is a measurement at the center point of a plane created by at least three measurement points. The center point is P ｉｊ So, the three points A are used to calculate the motion of the central point. ｉｊ , B ｉｊ , C ｉｊ It is represented as, When a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this is set to i = 0. T ｔｉｊｋ However, this is the natural period of the k component of the translational motion at the i-j measurement point. T ｔＰｉｊｋ However, the P ｉｊ This is the natural period of the k-component of the translational motion of the central point. The ij measurement point, or center point P ｉｊ The natural period of translational motion in is [Number 90] （３.４.１） It can be calculated from the vijk, vPijk, dijk, and dPijk components of the natural frequency vector. T ｒＰｉｊｋ However, the P ｉｊ This is the natural period of the k-component of the rotational motion of the central point. Center point P ｉｊ The natural period of rotational motion in is [Number 91] （３.４.２） As such, the θ of the natural vibration vector of angular velocity and rotation angle ’ It is calculated from the Pijk component and the θPijk component, θ ’ θ is the angular velocity, and θ is the angle of rotation. A calculation method for use in seismic design of the structure described in claim 10.

13. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. The measurement points are numbered so that the lowest point on each measurement axis is i=1, and each measurement axis has a reference point. Assign a number to j=1, and identify it as a set of natural numbers i and j. Surface measurement in continuous micro-vibration measurement is a measurement at the center point of a plane created by at least three measurement points. The center point is P ｉｊ So, the three points A are used to calculate the motion of the central point. ｉｊ , B ｉｊ , C ｉｊ It is represented as, When a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this is set to i = 0. In point measurement, the i-th dominant portion is the part of the structure that is considered to move together with the i-th measurement point. The proportion of each kinetic component in the total kinetic energy of the i-th dominant portion in point measurement is called the kinetic energy composition ratio and is calculated by the following formula: [Number 95] （３.５.１） Here, p ’ ｉｊｋ (t) is the velocity time history of the ij measurement point. Furthermore, the rate of change of kinetic energy is [Number 96] （３.５.２） And, The reference point ij is reference point 11 (i=1, j=1), Next, let i be the reference axis and l be the reference plane. In surface measurement, the Pil-dominated portion is the part of the structure that includes the plane formed by the three points used to calculate the motion of the central point Pil, and is considered to move in conjunction with this plane. The proportion of each kinetic component to the total kinetic energy of the Pil-dominated portion in surface measurement is called the kinetic energy composition ratio and is calculated as follows. Note that l indicates the face number of the Pil-dominated portion. The translational kinetic component of the kinetic energy composition ratio is [Number 97] （３.５.３） And, The rotational component of the kinetic energy composition ratio is [Number 98] （３.５.４） And, p ’ Ｐｉｌｋ (t) and θ ’ Ｐｉｌｋ (t) is the velocity time history and angular velocity time history of the center point Pil, respectively, and K Ｐｉｌｋ This is the radius of rotation about the k-axis with respect to the portion governed by the center point Pil, The translational motion component of the rate of change of kinetic energy is [Number 99] （３.５.５） And, The rotational component of the rate of change of kinetic energy is [Number 100] （３.５.６） It is calculated as follows: i = 1 and l = m represent the reference plane. A calculation method for use in seismic design of the structure described in claim 10.

14. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The measurement point of the r-th order eigenmode vector corresponding to the measurement point obtained by point measurement in continuous microtremor measurement is the junction of the structural model corresponding to the i-th measurement point. At least three measurement points A by surface measurement using continuous micro-vibration measurement. ｉｊ , B ｉｊ , C ｉｊ The center point P of the plane created by ｉｊ Center point P of the r-th eigenmode vector corresponding to this vector ｉｊ However, the center point P ｉｊ It is the point of contact of the corresponding structural model, Each measurement axis of the structural model is assigned a number with i=1 at its lowest point, and the measurement axes of the structural model are assigned numbers with j=1 at the axis containing the reference point, and are identified by pairs of natural numbers i and j. When a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this is set to i = 0. The (r) in the superscript of each of the following equations is calculated from the r-th eigenmode, The spatiotemporal shape and frequency of the natural vibration of the structural model used for seismic isolation design of a structure are calculated from the r-th order eigenmode obtained by eigenvalue analysis of the structural model used for seismic isolation design of a structure, and the kinetic energy composition ratio of the i-th order dominant portion and the Pil-th order dominant portion are calculated. The kinetic energy composition ratio of the i-th dominant portion in point measurements is, [Number 101] （３.５.７） It is calculated as follows: In surface measurements, the translational motion component of the kinetic energy composition ratio of the Pil-dominated portion is, [Number 102] （３.５.８） It is calculated as follows: In surface measurement, the rotational motion component of the kinetic energy composition ratio of the Pil-dominated portion is [Number 103] （３.５.９） It is calculated as follows: The rate of change of kinetic energy in point measurement is [Number 104] （３.５.１０） It is calculated as follows: The translational motion component of the rate of change of kinetic energy in surface measurements is [Number 105] （３.５.１１） It is calculated as follows: The rotational component of the rate of change of kinetic energy in surface measurement is [Number 106] （３.５.１２） It is calculated as follows: Here, we （ｒ） ｄｉｊｋ This is a component of the r-th order eigenmode vector, which corresponds to the k-component of the displacement of the junction of the structural model corresponding to the i-j measurement point. e （ｒ） ｄＰｉｌｋ , and e （ｒ） θＰｉｌｋ This is calculated using formulas (3.3.12) to (3.3.14), and formulas (3.3.16) to (3.3.18). Note that i=1, j=1 represents the reference point, and i=1, l=m represents the reference plane. A calculation method for use in seismic design of the structure described in claim 10.

15. In a structure, there are multiple layers that include parts that move as a whole in a generally horizontal direction, and on these layers, measurement points are provided along the vertical measurement axis. In point measurements of continuous microtremor measurement, the jth measurement axis of the relative displacement of the i+1th layer with respect to the ith layer. The value at this point is the inter-i-j interlayer displacement. In surface measurement using continuous micro-motion measurement, the relative displacement and relative rotation angle of each layer on the Pj measurement axis are measured by P ｉｊ Interstory displacement and P ｉｊ This is the interlayer rotation angle, i is i = 0, ..., n, In the virtual layer and virtual measurement point (i=0), the relative displacement and relative rotation angle are set to zero, and the interlayer displacement of the 0th layer is calculated. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The i-th interlayer displacement and the P ｉｊ Interstory displacement is, [Number 112] （４.１.１） It is calculated as follows: The deformation angle and scaling ratio, calculated by formula 4.1.1, are, respectively: [Number 113] （４.１.２） ij and P ｉｊ Shear deformation angle (k = x, y), and the ij and P elements. ｉｊ The expansion coefficient is (k = z), Part P ｉｊ The interlayer rotation angle is, [Number 114] （４.１.３） It is calculated as follows: Part P ｉｊ Curvature (k = x, y) and the P ｉｊ The torsional ratio (k=z) is, [Number 115] （４.１.４） It is calculated as follows: p ｉｊｋ (t) is the k-direction component of the displacement obtained from the measurement at measurement point ij (k = x, y, z), p Ｐｉｊｋ (t) and θ Ｐｉｊｋ (t) is the center point P ｉｊ These are the k-direction components of the displacement and rotation angle. H ０ｉｊｋ and H ０Ｐｉｊｋ These are ij and the P, respectively. ｉｊ This is the height in the k-axis direction between floors (structural floor height in the k-axis direction of the ijth floor: i = 1 to n), The inter-story displacement transmission coefficient of the structure is measured at point measurements in ambient microtremor measurements. [Number 116] （４.１.５） It is calculated as follows: P of the structure ｉｊ The transmission coefficient of interlayer displacement and rotation angle is, in surface measurements of ambient micro-motion measurement, [Number 117] （４.１.６） It is calculated as follows: i is i=0, ..., n, i=1, j=1 represents the reference point, p ０ｊｋ (t) = 0 year, When the center point is used as the reference point, the subscripts in formulas (4.1.5) and (4.1.6) are changed from d11 to dP11, respectively, and the calculations are performed. A calculation method for use in seismic design of the structure described in claim 10.

16. The value corresponding to the inter-i-j inter-story displacement transmission coefficient of the structure is obtained from the point measurement or the junction value corresponding to the surface measurement of the r-th order eigenmode obtained by eigenvalue analysis of the structural model. [Number 118] （４.１.７） It is calculated as follows: Part P ｉｊ Interlayer rotational angle transfer coefficient is [Number 119] （４.１.８） It is calculated as follows: e ｄＰｉｊｋ （ｒ） and e θＰｉｊｋ （ｒ） However, it is calculated using formulas (3.3.12) to (3.3.14) and formulas (3.3.16) to (3.3.18). i is i=0, ..., n, i=1, j=1 represents the reference point, e ｄＰ０ｊｋ （ｒ） = 0 and e θＰ０ｊｋ （ｒ） Let = 0, When the center point is used as the reference point, the subscripts in formulas (4.1.7) and (4.1.8) are changed from d11 to dP11, respectively, and the calculations are performed. A calculation method for use in seismic design of the structure described in claim 10.

17. In a structure, there are multiple layers that include parts that move as a whole in a generally horizontal direction, and on these layers, measurement points are provided along the vertical measurement axis. In point measurements of continuous microtremor measurement, the value of the relative displacement of the (i+1)th layer with respect to the i-th layer at the j-th measurement axis is the inter-i-j layer displacement. The ijth interlayer stiffness is calculated using the ratio of the ijth interlayer displacement to the ijth interlayer stress. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The inter-story stiffness of the structure, and its value converted to a natural period, i.e., the translational motion k-direction component of the inter-story vibration period, [Number 120] （４.２.１） These are calculated as follows: The k-direction component of the natural vibration acceleration shape vector at measurement point ij is h ａｉｊｋ , the interlayer displacement transfer coefficient is h ｅｉｊｋ , the dominant mass is m ｉｊ And, m ０ｊ = 0, and i = 0 is the ground stiffness and natural period equivalent value. Part P ｉｊ The k-direction component of the translational motion of the interstory stiffness and interstory vibration period is, [Number 121] （４.２.２） And, The stiffness of rotational motion around the k-axis and the inter-story vibration period are, [Number 122] （４.２.３） And, Part P ｉｊ The component h in the k-direction of the natural vibration angular acceleration vector of the dominant portion θ’’Ｐｉｊｋ Interlayer rotation angle transmission coefficient h ｅｒＰｉｊｋ , and the P ｉｊ Moment of inertia I of the dominant part around the k-axis Ｐｉｊｋ These are calculated from the following: A calculation method for use in seismic design of the structure described in claim 10.

18. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. From the junction values ​​corresponding to point measurements or surface measurements of the r-th order eigenmode obtained by eigenvalue analysis of the structural model, the values ​​corresponding to the k-direction component of the translational motion of the i-th interstory stiffness and interstory vibration period are obtained. [Number 123] （４.２.４） It is calculated as follows: e （ｒ） ｄｉｊｋ However, this is a component of the r-th order eigenmode vector that corresponds to the k-direction component of the displacement of the junction of the structural model corresponding to the i-j measurement point, and ω ｒ However, the r-th natural frequency, T ｒ The r-th order natural period is, Part P ｉｊ The k-direction component of the interlayer stiffness is, [Number 124] （４.２.５） It is calculated as follows: Part P ｉｊ The values ​​corresponding to the inter-story stiffness and inter-story vibration period of rotational motion between layers around the k-axis are, [Number 125] （４.２.６） It is calculated as follows: e ｄＰｉｊｋ （ｒ） and e θＰｉｊｋ （ｒ） However, it is calculated using formulas (3.3.12) to (3.3.14), and (3.3.16) to (3.3.18), i=1, j=1 is the reference point, ω ｒ The r-th natural frequency is T ｒ The r-th order natural period is given by i=0, where i=0 is the value obtained by converting the stiffness of the ground spring to its natural period. A calculation method for use in seismic design of the structure described in claim 10.

19. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. Point measurement in continuous micro-motion measurement is a measurement performed at each individual measurement point. The measurement points are identified by a set of natural numbers i and j, with the lowest point of each measurement axis assigned a number i=1, and the axis with the reference point assigned a number j=1. Surface measurement in continuous micro-vibration measurement is a measurement at the center point of a plane created by at least three measurement points. The center point is P ｉｊ So, the three points used to calculate the motion of the center point are A ｉｊ , B ｉｊ , C ｉｊ It is represented as, If a measurement point or center point is hypothesized within the ground directly below the lowest point of each measurement axis, this point is set to i = 0. The support portion is located on the same measurement axis, at a measurement point, at a measurement point located above the measurement surface, or This is the dominant part in terms of measurement, The i-j support portion and P of the structure ｉｊ Displacement of the support part (α=d), velocity (α=v), and acceleration (α=a), and the P ｉｊ Rotation angle (β = θ) and angular velocity (β = θ) of the supporting part ’ ) and angular acceleration (β = θ ’’ The k-direction component of the response magnification of ) is [Number 147] （４.３.１） It is calculated as follows: The symbols "'" above represent the first derivative in time, and "''" represent the second derivative in time. h αｉｊｋ , h αＰｉｊｋ and h βＰｉｊｋ However, these are the natural vibration shape vectors calculated by formulas (3.3.4) to (3.3.6), I understand ｉｊ However, the dominant mass of the ij layer, m Ｐｉｊ and I Ｐｉｊｋ However, each is the P ｉｊ The dominant mass of the layer and its moment of inertia around the k-axis, The response magnification is set to the first j support part or the P １ｊ The distribution coefficient is normalized by the response magnification of the support part. The distribution coefficient is, [Number 148] （４.３.２） It is calculated as follows: i is i = 0, ..., n, where i = 0 represents the boundary between the ground and the structure. The inter-j stress coefficient at which the i-j inter-story deformation reaches the elastic limit is defined as the i-j inter-story base stress coefficient. Part P ｉｊ The P2 when interlayer deformation reaches the elastic limit. １ｊ The interlayer stress coefficient is the P ｉｊ As the interlayer base stress coefficient, The ij interlayer base stress coefficient and the P ｉｊ The interlayer base stress coefficients are, [Number 149] （４.３.３） It is calculated as follows: The k-direction component of the transmissibility of the i-th interlayer displacement and the elastic limit value of the i-th interlayer displacement are, respectively, h ｅｉｊｋ and e Ｙｉｊｋ And, Part P ｉｊ Interstory displacement transmission coefficient and P ｉｊ The k-direction component of the elastic limit value of interstory displacement is, respectively, h ｅＰｉｊｋ , e ＹＰｉｊｋ And, The magnitude of the acceleration due to gravity is G, Part P ｉｊ When the interlayer rotation angle reaches the elastic limit, the P １ｊ The moment coefficient between layers is, P ｉｊ This is the interlayer base moment coefficient, Part P １ｊ The moment coefficient between layers is, [Number 150] （４.３.４） It is calculated as follows: Part P ｉｊ The transmission coefficient and elastic limit of the interlayer rotation angle are, respectively, h ｅｒＰｉｊｋ and e ｒＹＰｉｊｋ And, i is i = 0, ..., n, where i = 0 represents the boundary between the ground and the structure. A calculation method for use in seismic design of the structure described in claim 10.

20. The k component is the three components of the Cartesian coordinate system k = x, y, z. The component e corresponding to the k-direction displacement of the ij measurement point of the r-th eigenmode vector obtained by eigenvalue analysis of the structural model ｄｉｊｋ （ｒ） Using this, the value corresponding to the response magnification of the i-th support portion is [Number 151] （４.３.５） It is calculated as follows: Part P ｉｊ Component e corresponding to the k-direction displacement of the center point ｄｉｊｋ （ｒ） Therefore, the P ｉｊ The value corresponding to the response magnification of the support part is [Number 152] （４.３.６） It is calculated as follows: When the center point is used as the reference point, the subscripts in formulas (4.3.5) and (4.3.6) are changed from d11 to dP11, respectively, and the calculation is performed. Support part ij and P ｉｊ The value corresponding to the distribution coefficient of the support portion is [Number 153] （４.３.７） It is calculated as follows: Base stress coefficient between ij layers, P ｉｊ The base stress coefficient between layers, and the P factor. ｉｊ The values ​​corresponding to the base moment coefficients between layers are, [Number 158] （４.３.８） It is calculated as follows: α = d, α = v, and α = a represent displacement, velocity, and acceleration, respectively. β=θ, β=ω, β=ω ’ However, it represents the angle of rotation, angular velocity, and angular acceleration. e （ｒ） ｄ１１ However, it is the average value of the RMS of the three components of the displacement of the reference point i=1, j=1, or P11, as shown by formula (3.3.10a). e （ｒ） ｄｉｊｋ , and e （ｒ） θｉｊｋ However, this is a component of the r-th order eigenmode vector that corresponds to the k-direction component of the displacement of the junction of the structural model corresponding to the i-j measurement point, e ｄＰｉｊｋ （ｒ） and e θＰｉｊｋ （ｒ） However, it is calculated using formulas (3.3.12) to (3.3.14), and (3.3.16) to (3.3.18), i is i = 0, ..., n, where i = 0 represents the boundary between the ground and the structure, ω ｒ However, the natural frequency is r, and the magnitude of the acceleration due to gravity is G. A calculation method for use in seismic design of the structure described in claim 10.

21. The magnitude of the elastic response occurring in each part of the structure due to the assumed seismic motion is calculated by multiplying the average value of the displacement strong motion RMS estimated to occur at a reference point or reference plane due to the assumed seismic motion by the transmissibility obtained from ambient microtremor measurement or eigenvalue analysis. Assuming that the period of the elastic response is equal to the natural vibration period, The k component is the three components of the Cartesian coordinate system k = x, y, z. The estimated values ​​of the elastic displacement, velocity, and acceleration of the strong earthquake at measurement point ij, as well as the period, are: [Number 171] （４.４.１） It is calculated as follows: Part P ｉｊ The estimated values ​​of the elastic rotation angle, angular velocity, and angular acceleration of a strong earthquake at the center point, as well as the period, are [Number 172] （４.４.２） It is calculated as follows: The estimated RMS value of the elastic interstory displacement occurring between the ij layers during a strong earthquake is, [Number 173] （４.４.３） It is calculated as follows: Part P ｉｊ The estimated RMS values ​​of the elastic inter-story displacement and rotation angle occurring between stories during a strong earthquake are, [Number 174] （４.４.４） It is calculated as follows: i is i=0, ..., n, where i=0 represents the boundary between the ground and the structure, and σ is the average value of the three components of the strong-motion RMS of the reference point displacement estimated to occur due to the assumed seismic motion. Ｅｄ toshi, h αｉｊｋ , h αＰｉｊｋ and h βＰｉｊｋ However, each component of the natural vibration shape vector calculated by formulas (3.3.4) to (3.3.6), i.e., the transmissibility, is T. αｉｊｋ , TαP ｉｊｋ and TβP ｉｊｋ These are the components of the natural frequency vector, and h ｅｉｊｋ , h ｅＰｉｊｋ and h ｅｒＰｉｊｋ These are the i-th interlayer displacement transfer coefficient and the P-th interlayer displacement transfer coefficient, respectively. ｉｊ Interstory displacement transmission coefficient and P ｉｊ Interlayer rotational angular transmission rate, displacement (α = d), velocity (α = v), acceleration (α = a), rotation angle (β = θ), angular velocity (β = θ ’ ), angular acceleration (β=θ ’’ ) where the symbol "'" represents the first time derivative and the symbol "''" represents the second time derivative. A calculation method for use in seismic design of the structure described in claim 10.

22. The magnitude of the inelastic response generated in each part of the structure due to the assumed seismic motion is calculated from values ​​including the average value of the strong motion RMS of the displacement at a reference point estimated to be generated by the assumed seismic motion, the duration of the strong motion, and the transmissibility. The magnitude of the inelastic response occurring in each part of the structure due to the assumed seismic motion is calculated from values ​​including the average value of the strong motion RMS of the reference plane displacement estimated to occur due to the assumed seismic motion, the duration of the strong motion, and the transmissibility. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The cumulative inelastic displacement occurring in the k-direction between the i-j layers is, [Number 175] （４.４.５） It is calculated as follows: The cumulative inelastic displacement occurring in the k-direction between the ij layers is equal to the elastic limit magnification. [Number 176] （４.４.６） It was standardized as such, The cumulative inelastic displacement occurring in the k-direction between the ij layers is the degree of damage. [Number 177] （４.４.７） It was standardized as such, i is i = 0, ..., n, where i = 0 represents the boundary between the ground and the structure. The average value of the three components of the strong motion RMS of the reference point displacement caused by seismic motion is σ Ｅｄ , The duration of the strong earthquake was s ０ And, The central period of the k component of the velocity at the (i+1)th,j measurement point is T ｖｉ+１,ｊｋ The bandwidth index is α ｖｉ+１,ｊｋ The k component of the acceleration response magnification of the i-j support part is B ａｉｊｋ , the speed response magnification is B ｖｉｊｋ The interlayer displacement transmission coefficient in the k-direction between the ij layers is h ｅｉｊｋ , the elastic limit displacement is e Ｙｉｊｋ The limit value of the elastic limit magnification is μ ｃｓｉｊｋ And, The bandwidth index of the k component of velocity is [Number 178] （４.４.８） And, Part P ｉｊ The cumulative inelastic displacement, elastic limit magnification, and damage occurring in the k-direction between layers are given by the above formulas (4.4.5) to (4.4.7) as follows: ij → P ｉｊ It can be calculated similarly as follows: A calculation method for use in seismic design of the structure described in claim 10.

23. The k component is the three directional components of the Cartesian coordinate system, k = x, y, z. The component e of the r-th order eigenmode vector obtained by eigenvalue analysis of the structural model ｄｉｊｋ （ｒ） and natural period T ｒ A step of calculating the magnitude of the elastic and inelastic responses caused by the assumed seismic motion using the following: The strong-earthquake RMS of elastic displacement, velocity, and acceleration occurring at the i-th measurement point, calculated from the r-th eigenmode vector, and the period are as follows: [Number 179] （４.４.９） And, The P-th calculated from the r-th eigenmode vector ｉｊ The elastic displacement, velocity, and acceleration of strong earthquakes at the center point, as well as the period, [Number 180] （４.４.１０） And, T （ｒ） αｉｊｋ and T(r)βP ｉｊｋ However, this is the natural vibration period, The strong-motion RMS of the elastic inter-story displacement occurring between the i-th layers, calculated from the r-th eigenmode vector, [Number 181] （４.４.１１） And, The P-th calculated from the r-th eigenmode vector ｉｊ The strong-earth RMS of elastic inter-story displacement and rotation angle occurring between layers is [Number 182] （４.４.１２） And, The cumulative inelastic displacement in the k-direction between the i-th layers, which corresponds to the k-component of the i-th layer displacement calculated from the r-th eigenmode vector, [Number 183] （４.４.１３） And, |h （ｒ） αｉｊｋ |, and |h （ｒ） ｅｉｊｋ | represents the absolute values ​​of the k-components of the displacement, velocity, and acceleration at the ijth measurement point of the natural vibration shape vector calculated from the r-th eigenmode vector, and the transmission coefficient of the ijth interlayer displacement k-component calculated from the r-th eigenmode vector. |h （ｒ） αＰｉｊｋ |, |h （ｒ） βＰｉｊｋ |, and |h （ｒ） ｅＰｉｊｋ | are the P of the natural vibration shape vectors, respectively. ｉｊ Displacement of the center point, absolute value of the k-component of velocity and acceleration, and the P-th of the natural vibration shape vector. ｉｊ The absolute values ​​of the k-components of the rotation angle, angular velocity, and angular acceleration at the center point, as well as the transmission coefficient of the k-component of the i-th interlayer displacement calculated from the r-th order eigenmode, B （ｒ） ｄｉｊｋ However, this is the displacement response magnification, T ｒ However, it has an r-th order natural period, The P-th calculated from the r-th eigenmode vector ｉｊ Cumulative inelastic displacement u occurring in the k-direction between layers （ｒ） ｓＰｉｊ However, in formula (4.4.13), ij → P ｉｊ It can be calculated similarly as follows: The elastic limit magnification calculated from the r-th order eigenmode vector is normalized by normalizing the cumulative inelastic displacement in the k-direction between the i-th layers, which corresponds to the k-component of the i-th layer displacement calculated from the r-th order eigenmode vector. [Number 184] （４.４.１４） And, The degree of damage calculated from the r-th order eigenmode vector is normalized by normalizing the cumulative inelastic displacement in the k-direction between the i-th layers, which corresponds to the k-component of the i-th layer displacement calculated from the r-th order eigenmode vector. [Number 185] （４.４.１５） And, i is i = 0, ..., n, where i = 0 represents the interface between the ground and the structure. A calculation method for use in seismic design of the structure described in claim 10.

24. To perform calculations using a computer, A calculation method for use in seismic design of a structure according to any one of claims 1 to 23.

25. To perform calculations using a computer, A seismic design support system that uses a calculation method for use in seismic design of a structure according to any one of claims 1 to 23, (1) A means for calculating an index value for a structure based on measurement data related to natural vibrations obtained by ambient microtremor measurement, using the spatiotemporal shape and frequency of the natural vibrations of the structure, and a means for storing the index value obtained by measurement. (2) A means for calculating an analytical index value for a structure based on data relating to the natural motion of the r-th order natural mode obtained by eigenvalue analysis of the structural model used for seismic design of a structure, using the spatiotemporal shape and frequency of the natural motion of the structural model used for seismic design of a structure, and a means for saving the analytical index value. Equipped with, (3) A means for comparing index values ​​obtained by measuring the structure with index values ​​obtained by analyzing the structural model, A seismic design support system that includes the following features.

26. (4) Means for classifying structures and structural models into similar groups, (5) A means for determining a recommended range for the index value obtained by measurement for each similar group of classified structures, (6) A means for determining a recommended range for the index value obtained by analysis for each similar group of classified structural models, (7) A means for comparing the recommended range for the index value determined by at least one of (5) and (6) above with the index value obtained by at least one of (1) and (2) above, A seismic design support system according to claim 25, comprising:

27. The seismic design support system according to claim 25, wherein the index for determining the index value includes at least one selected from the group consisting of natural vibration displacement shape vector, natural vibration acceleration shape vector, natural vibration rotation angle shape vector, natural vibration angular acceleration shape vector, rotational motion natural period vector, translational motion natural period vector, r-th order natural period, inter-story vibration period, acceleration distribution coefficient, angular acceleration distribution coefficient, base stress coefficient, base moment coefficient, rate of change of kinetic energy, degree of damage, and risk index.

28. (8) Means for proposing reinforcement for the structure to be evaluated, It has, The indicators used to determine the index value include the degree of damage, The seismic design support system according to claim 26, comprising means for determining the location of reinforcement for a structure under evaluation based on a comparison between an index value of the degree of damage and a recommended range of the index value of the degree of damage.

29. The recommended range for the index value obtained by the measurement in (5) above is determined by artificial intelligence, The recommended range for the index value obtained by the analysis in (6) above is determined by artificial intelligence, The recommended range and index values ​​in (7) above are compared by artificial intelligence, A seismic design support system according to claim 26, comprising:

30. The seismic design support system according to claim 29, comprising means for determining the location of seismic reinforcement for a structure to be evaluated using artificial intelligence.

31. A means for registering the estimation items and unit prices for each estimation item necessary for seismic reinforcement of the structure under evaluation, A means for calculating the estimated cost of seismic reinforcement for a structure under evaluation in multiple stages, depending on the timing and scope of the seismic reinforcement to be implemented, A seismic design support system according to claim 28, comprising:

32. The steps include comparing the index values ​​obtained from eigenvalue analysis using the structural model of the structure under evaluation, before seismic reinforcement of the structure under evaluation, with the recommended range proposed by the seismic design support system, The process involves comparing the index values ​​obtained from ambient microtremor measurements of the structure under evaluation before seismic reinforcement with the recommended range proposed by the seismic design support system. The process involves comparing the index values ​​obtained from ambient microtremor measurements of the structure under evaluation after seismic reinforcement with the recommended range proposed by the seismic design support system. A seismic design method using the seismic design support system according to claim 26, including the above.

33. A step to calculate index values ​​by analyzing the structural model of the structure to be evaluated, before seismic reinforcement of the structure to be evaluated. and A step to calculate index values ​​by measuring the ambient microtremors of the structure under evaluation before seismic reinforcement of the structure under evaluation. This includes at least one of the following steps: The steps include identifying structures similar to the structure being evaluated that have been damaged by earthquakes in the past, The index values ​​obtained from at least one of the analysis and measurement of the structure under evaluation, The index values ​​obtained from at least one of the analysis and / or measurement of a structure similar to the structure being evaluated, Based on the comparison, the damage status of the structure to be evaluated is predicted based on the damage status of structures similar to the structure to be evaluated that have been damaged by earthquakes in the past. A method for predicting damage to a structure under evaluation due to an earthquake, using the seismic design support system described in claim 26.

34. A step to calculate index values ​​by analyzing the structural model of the structure to be evaluated, before seismic reinforcement of the structure to be evaluated. and A step to calculate index values ​​by measuring the ambient microtremors of the structure under evaluation before seismic reinforcement of the structure under evaluation. This includes at least one of the following steps: The process includes a step of calculating an index value by measuring the ambient microtremor of the structure to be evaluated after seismic reinforcement of the structure to be evaluated, The steps include identifying structures similar to the structure under evaluation that have undergone seismic reinforcement before being damaged by an earthquake in the past, and that have been damaged by an earthquake in the past, The index values ​​obtained from at least one of the analysis and / or measurement of the structure under evaluation before seismic reinforcement, The index values ​​obtained from measurements after seismic reinforcement of the structure under evaluation, The index values ​​obtained from at least one of the analysis and / or measurement of a structure similar to the structure being evaluated, From the contrast, A step of predicting the damage status of the structure under evaluation based on the damage status of structures similar to the structure under evaluation, which have undergone seismic reinforcement before being damaged by earthquakes in the past, and which have been damaged by earthquakes in the past. A method for predicting damage caused by an earthquake after seismic reinforcement of a structure to be evaluated, using the seismic design support system described in claim 26.

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