Structural evaluation method, structural evaluation program, and structural evaluation device

Abstract

To accurately evaluate a multi-degree-of-freedom system structure that receives different input vibrations or a single input vibration from a plurality of support points.SOLUTION: A structure evaluation method performs structure evaluation of a multi-degree-of-freedom system structure that receives different input vibrations or a single input vibration from a plurality of supporting points. The method comprises a response value calculation step and a combined response calculation step. In the response value calculation step, a plurality of response values including at least one of (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom system structure in a frequency range below a cutoff frequency, and (ii) a higher-order response corresponding to the vibration mode of the multi-degree-of-freedom system structure in the frequency range above the cutoff frequency, or a displacement response between the plurality of support points is calculated. In the combined response calculation step, a combined response of the plurality of response values is calculated using a correlation coefficient indicating the correlation between time history responses proportional to each of the plurality of response values.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present disclosure relates to a structural evaluation method, a structural evaluation program, and a structural evaluation device for a multi-degree-of-freedom structure that is supported at multiple support points and receives multiple input vibrations or a single input vibration. [Background technology]

[0002] For example, structures such as piping systems used in plant facilities are required to have an earthquake-resistant design that provides appropriate durability against input vibrations such as earthquake motions. For structural evaluation of such structures, spectral modal analysis and time history modal analysis are known as analytical methods that utilize modal analysis. These analytical methods calculate the vibration response to input vibration as a composite response of each vibration mode, and then evaluate the structure by comparing the displacement (deformation) and member forces of the structure obtained based on the composite response with allowable ranges. For example, Patent Document 1 discloses an example of structural evaluation using spectral modal analysis, one of the two analytical methods mentioned above. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Application Laid-Open No. 2003-132107 Summary of the Invention [Problem to be solved by the invention]

[0004] In the modal analysis method described in Patent Document 1, the frequency range above a predetermined cutoff frequency (e.g., 33 Hz) is considered to be a range where there is no response amplification in the floor response curve, and the frequency range below the cutoff frequency is the target of analysis. Higher-order responses in such frequency ranges above the cutoff frequency can be calculated by multiplying the total mass of vibration modes not considered in the floor response spectrum analysis (modes with frequencies higher than the cutoff frequency) by the acceleration of the building floor, as in the missing mass method. Furthermore, when a piping system is supported by multiple support points on different floor surfaces and relative displacement occurs between the floor surfaces, the building displacement response resulting from such relative displacement must also be considered in the structural analysis.

[0005] When considering the higher-order responses and building displacement responses mentioned above in addition to the modal response obtained by modal analysis, structural evaluation is performed by combining these responses, but the type of synthesis method used can affect the conservatism of the evaluation results. For example, when the square root sum of squares (SRSS) method is used as the synthesis method, results that are not conservative may be obtained depending on the conditions of the structure, making it difficult to adopt this method uniformly for a variety of structures. Furthermore, when the absolute sum of squares (ABS) method is used as the synthesis method, evaluation results tend to be conservative, which may lead to increased costs due to over-design.

[0006] At least one embodiment of the present disclosure has been made in consideration of the above-mentioned circumstances, and aims to provide a structural evaluation method, a structural evaluation program, and a structural evaluation device that can accurately evaluate a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from multiple support points. [Means for solving the problem]

[0007] In order to solve the above problems, a structure evaluation method according to some embodiments of the present disclosure includes: A structural evaluation method for a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from a plurality of support points, comprising: a response value calculation step for calculating a plurality of response values ​​including at least one of (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range below a cutoff frequency, and (ii) a higher-order response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range equal to or higher than the cutoff frequency, or a displacement response between the plurality of support points; a composite response calculation step of calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; Equipped with.

[0008] In order to solve the above problems, the structural evaluation program according to some embodiments of the present disclosure includes: A structural evaluation program for a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from multiple support points, using a computer, a response value calculation step for calculating a plurality of response values ​​including at least one of (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range below a cutoff frequency, and (ii) a higher-order response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range equal to or higher than the cutoff frequency, or a displacement response between the plurality of support points; a composite response calculation step of calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; is possible.

[0009] In order to solve the above problems, a structural evaluation device according to some embodiments of the present disclosure includes: A structural evaluation device for a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from multiple support points, a response value calculation unit for calculating a plurality of response values ​​including at least one of (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range less than a cutoff frequency, and (ii) a higher-order response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range equal to or greater than the cutoff frequency, or a displacement response between the plurality of support points; a composite response calculation unit for calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; Equipped with. [Effects of the Invention]

[0010] According to at least one embodiment of the present disclosure, a structural evaluation method, a structural evaluation program, and a structural evaluation device can be provided that can accurately evaluate a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from multiple support points. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a schematic diagram illustrating an example of a structure to be subjected to structural evaluation. [Figure 2] FIG. 1 is an overall configuration diagram of a structural evaluation system. [Figure 3] FIG. 3 is a block diagram functionally showing the internal configuration of the main server of FIG. 2. [Figure 4] 4 is a flowchart illustrating a structure evaluation method implemented by the main server of FIG. 3. [Figure 5] The modal response, higher-order response, and building displacement response to be synthesized in step S500 are displayed together in list form. [Figure 6] FIG. 4 is a block diagram functionally showing the internal configuration of a modal response calculation unit in FIG. 3. [Figure 7] 4 is a flowchart showing a method for calculating a modal response performed by a modal response calculation unit in FIG. 3. [Figure 8] FIG. 2 is a block diagram showing the functional configuration of a main server related to calculation of a floor response spectrum. [Figure 9] 1 is a flowchart showing the steps of a method for calculating a floor response spectrum. [Figure 10A] 10 is an example of a time history response acceleration obtained in step S114 of FIG. 9. [Figure 10B]10B is an example of a floor response spectrum obtained from the time history response acceleration of FIG. 10A. [Figure 11] 4 is a block diagram functionally showing the internal configuration of a high-order response calculation unit in FIG. 3. FIG. [Figure 12] 4 is a flowchart showing a method for calculating a higher-order response performed by a higher-order response calculation unit in FIG. 3. [Figure 13] FIG. 4 is a block diagram functionally showing the internal configuration of a building displacement response calculation unit in FIG. 3. [Figure 14] 4 is a flowchart showing a method for calculating a building displacement response performed by a building displacement response calculation unit in FIG. 3. [Figure 15] FIG. 10 is a block diagram showing the functional configuration of a main server related to calculation of a correlation coefficient. [Figure 16] 1 is a flowchart showing a method for calculating a correlation coefficient for each step. DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. However, unless otherwise specified, the configurations and the like described in the embodiment are merely illustrative examples and are not intended to limit the scope of the present invention.

[0013] <Structural evaluation target> First, with reference to Figure 1, a structure 1 (multi-degree-of-freedom structure) to be subjected to structural evaluation will be described. Figure 1 is a schematic diagram showing an example of the structure 1 to be subjected to structural evaluation. The structure 1 is supported at a plurality of support points corresponding to a plurality of floors k and l of buildings 4a and 4b (hereinafter, buildings 4a and 4b will be collectively referred to as 4) erected on the ground 2. In the example of Figure 1, two buildings 4a and 4b are erected on the ground 2, with building 4a having a three-story structure and building 4b having a two-story structure. The structure 1 is supported on floors k and l of building 4a and building 4b, respectively.

[0014] In the following explanation, floors k and l are each treated as corresponding to one support point, but multiple support points may be provided for each floor. In this case, by treating each support point as equivalent to floors k and l in Figure 1, the structural evaluation described below can be similarly applied. Furthermore, the number of buildings 4 erected on the ground 2 and the number of floors in each building 4 may be arbitrary.

[0015] The building 4 is a structure that constitutes a nuclear power plant, such as a nuclear power plant, and the structure 1 is a piping system used in the nuclear power plant, but these are merely examples.

[0016] <Structural evaluation system> Next, a description will be given of a structural evaluation system 100 for performing a structural evaluation of the above-mentioned structure 1. FIG.

[0017] 2, the structural evaluation system 100 comprises a main server 300, a data server 400, and a user terminal 500, which are connected to each other via a communication network 200. The communication network 200 is a network that can transmit and receive various data between the components of the structural evaluation system 100, and may be wired or wireless.

[0018] The main server 300 is a server that performs the main information processing in the structural evaluation system 100, and functions as a structural evaluation device according to at least one embodiment of the present disclosure. The main server 300 has a hardware configuration including, for example, an electronic processing device such as a computer, and is configured to be able to implement a structural evaluation method according to at least one embodiment of the present disclosure by installing a structural evaluation program according to at least one embodiment of the present disclosure. The main server 300 can access the data server 400 via the communication network 200, and performs structural evaluation using information stored in the data server 400. The structural evaluation results of the main server 300 are output to a user terminal 500 via the communication network 200. It is possible.

[0019] The structural evaluation program may be recorded in, for example, a predetermined storage medium. In this case, the main server 300 is configured by reading the storage medium and installing the structural evaluation program. Such a storage medium on which the structural evaluation program is recorded is also included in one embodiment of the present disclosure.

[0020] The data server 400 is a server that stores various data related to the operation of the structural evaluation system 100, and includes at least one database corresponding to the type of data stored. In Fig. 2, the data server 400 includes an analytical model database 410, a floor response spectrum database 420, a floor surface time history acceleration database 422, a floor surface time history displacement database 424, and a correlation coefficient database 430 (details of each database will be described later).

[0021] The data server 400 may be configured to be able to appropriately store the results of calculations performed by the main server 300 by accessing it via the communication network 200. The data server 400 may also be configured to allow various pieces of information to be stored in the data server 400 to be input via an input interface (not shown).

[0022] The user terminal 500 is a terminal that can be used by a user who is the recipient of the structural evaluation results. The user terminal 500 is configured to be able to receive the structural evaluation results output from the main server 300 via the communication network 200, and any device can be used.

[0023] <Structural evaluation equipment> Next, details of the main server 300 that functions as a structural evaluation device according to an embodiment of the present disclosure will be described. Fig. 3 is a block diagram functionally showing the internal configuration of the main server 300 of Fig. 2. Note that each functional block shown in Fig. 3 is merely an example defined to correspond to each step of a structural evaluation method described below, and some functional blocks may be integrated or further divided into multiple functional blocks.

[0024] The main server 300 includes a modal response calculation unit 302, a higher-order response calculation unit 304, a building displacement response calculation unit 306, a correlation coefficient acquisition unit 308, a response synthesis unit 310, and an output unit 312. The modal response calculation unit 302 calculates the modal response q R ik The higher-order response calculation unit 304 is configured to calculate the higher-order response q R (n+1)k The building displacement response calculation unit 306 is configured to calculate the building displacement response q R (n+2)k The correlation coefficient acquisition unit 308 is configured to calculate the correlation coefficient ρ ikjl The response synthesis unit 310 is configured to acquire the correlation coefficient ρ ikjl Using the modal response q R ik , higher-order responses q R (n+1)k , and building displacement response q R (n+2)k Response synthesis by synthesizing q The output unit 312 is a component for calculating response R. q This is the configuration for outputting R.

[0025] The main server 300 having the above configuration is configured to be able to carry out the following structural evaluation method: Figure 4 is a flowchart showing the structural evaluation method carried out by the main server 300 of Figure 3 .

[0026] First, the modal response calculation unit 302 calculates the modal response q R ik (Step S100). q R ik is a response corresponding to each vibration mode of the structure 1 in the frequency range below the cutoff frequency (for example, 33 Hz). q R ik A specific calculation method will be described later.

[0027] Next, the high-order response calculation unit 304 calculates the high-order response q R (n+1)k (Step S200).q R (n+1)k is a response corresponding to the vibration mode of the structure 1 in the frequency range above the cutoff frequency (for example, 33 Hz). q R (n+1)k A specific method for calculating the high-order response in step S200 will be described later. q R (n+1)k The calculation of the higher order response q R (n+1)k is the modal response q R ik If it is sufficiently small with respect to

[0028] Next, the building displacement response calculation unit 306 calculates the building displacement response q R (n+2)k As described above with reference to FIG. 1, the structure 1 is supported on a plurality of floors k and l via a plurality of support points, and the building displacement response q R (n+2)k is the static response corresponding to the displacement between these multiple support points. q R (n+2)k A specific calculation method for the building displacement response in step S300 will be described later. q R (n+2)k The calculation of the building displacement response q R (n+2)k is the modal response q R ik If it is sufficiently small with respect to

[0029] In steps S100 to S300, the modal response q R ik , higher-order responses q R (n+1)k , and building displacement response q R (n+2)k are calculated in turn, but the calculation of each of these responses may be performed in a different order or simultaneously.

[0030] Next, the correlation coefficient acquisition unit 308 calculates the correlation coefficient ρ ikjl(Step S400). The correlation coefficient database 430 stores the correlation coefficient ρ used when synthesizing the response values ​​obtained in steps S100 to S300. ikjl are stored in advance, but the correlation coefficient ρ ikjl may be calculated in advance by the main server 300. ikjl A specific calculation method will be described later.

[0031] Next, the response synthesis unit 310 calculates the correlation coefficient ρ ikjl Using the modal response q R ik and higher-order responses q R (n+1)k or building displacement response q R (n+2)k Response synthesis by synthesizing at least one of the q R is calculated (step S500). Here, FIG. 5 shows the modal response to be synthesized in step S500. q R ik , higher-order responses q R (n+1)k , and building displacement response q R (n+2)k are displayed in a list format.

[0032] In Figure 5, the total number of inputs that Structure 1 receives from each support point is m, and the modal order up to the cutoff frequency in the response spectrum analysis of Structure 1 is n. In Structure 1, dynamic responses occur for each mode in response to each input, resulting in a total of m × n modal responses. q R ik It is possible that the reference vibration will cause responses in multiple directions on the building floor, and the number of these directions is m d Then (m d is an integer less than or equal to 3), the total number of inputs m is the total number of building floors m d In addition, there are m high-order responses for each input. q R (n+1)k Furthermore, since there is a building displacement for each input, a total of m building displacement responses are calculated as static responses due to these building displacements. q R (n+2)k is shown.

[0033] In Figure 5, the modal response, which is the dynamic response to m inputs, q R ik n higher-order responses q R (n+1)k There is one static response, and one building analysis response. q R (n+2)k Since there is one matrix, the matrix is ​​(n+2) × m. In this matrix, the maximum value of the response in the i-th row and k-th column is R ik Let R ik includes all modal, higher-order, and static responses, where 1 ≤ i ≤ n + 2 and 1 ≤ k ≤ m.

[0034] In another embodiment, the response synthesis unit 310 calculates the correlation coefficient ρ ikjl Using the modal response q R ik and higher-order responses q R (n+1)k Response synthesis by synthesizing q Calculate R. In this case, response synthesis q R is calculated using the following formula: TIFF0007737846000001.tif10170In this case, the correlation coefficient ρ ikjl The multiple response values ​​synthesized by q R ik In addition to the above, the higher-order response, which is the dynamic response in the frequency range above the cutoff frequency, q R (n+1)k Thus, the modal response q R ik as well as higher-order responses q R (n+1)k Synthetic response taking into account q By calculating R, higher-order responses can be calculated, for example, when structure 1 is rigidly supported. q R (n+1)k Even when the influence of noise is large, excellent analysis accuracy can be obtained.

[0035] In another embodiment, the response synthesis unit 310 calculates the correlation coefficient ρikjl Using the modal response q R ik and building displacement response q R (n+2)k Response synthesis by synthesizing q Calculate R. In this case, response synthesis q R is calculated using the following formula: TIFF0007737846000002.tif10170In this case, the correlation coefficient ρ ikjl The multiple response values ​​synthesized by q R ik In addition to the static response, the displacement response q R (n+2)k Thus, the modal response q R ik as well as the displacement response q R (n+2)k Synthetic response taking into account q By calculating R, the displacement response can be calculated, for example, when relative displacement occurs between multiple support points supporting structure 1. q R (n+2)k Even when the influence of noise is large, excellent analysis accuracy can be obtained.

[0036] In another embodiment, the response synthesis unit 310 may ikjl Using the modal response q R ik , higher-order responses q R (n+1)k , and building displacement response q R (n+2)k Response synthesis by synthesizing q Calculate R. In this case, response synthesis q R is calculated using the following formula: TIFF0007737846000003.tif10170In this case, the correlation coefficient ρ ikjl The multiple response values ​​synthesized by q R ik In addition to the above, the higher-order response, which is the dynamic response in the frequency range above the cutoff frequency, q R(n+1)k , and the displacement response, which is the static response q R (n+2)k Thus, the modal response q R ik as well as higher-order responses q R (n+1)k and static response q R (n+2)k Synthetic response taking into account q By calculating R, better analytical accuracy can be obtained.

[0037] Next, the output unit 312 outputs the response synthesis calculated in step S500. q R is output as the structural analysis result (step S600). The output format in step S600 may be any format.

[0038] (Calculation method of modal response) Next, the modal response calculated by the modal response calculation unit 302 q R ik 6 is a block diagram showing the internal configuration of the modal response calculation unit 302 in FIG. 3, and FIG. 7 is a block diagram showing the modal response calculation performed by the modal response calculation unit 302 in FIG. q R ik 10 is a flowchart showing a method for calculating

[0039] 6, the modal response calculation unit 302 includes a structural model acquisition unit 320, an eigenvalue analysis unit 322, a floor response spectrum acquisition unit 324, and a response calculation unit 326. The structural model acquisition unit 320 acquires a structural model corresponding to the structure 1 from the analysis model database 410. The eigenvalue analysis unit 322 performs eigenvalue analysis of the structure 1 based on the structural model acquired by the structural model acquisition unit 320. The floor response spectrum acquisition unit 324 acquires a floor response spectrum from the floor response spectrum database 420. The response calculation unit 326 uses the floor response spectrum acquired by the floor response spectrum acquisition unit 324 to find a response value corresponding to each vibration mode of the structure 1 for each input to a support point.

[0040] 7, first, the structural model acquisition unit 320 acquires the structural model 412 corresponding to the structure 1 (step S101). Specifically, the structural model acquisition unit 320 accesses the analytical model database 410, and searches for and acquires the structural model corresponding to the structure 1 to be structurally evaluated from the analytical models stored in advance in the analytical model database 410.

[0041] Next, the eigenvalue analysis unit 322 performs eigenvalue analysis on the structural model 412 acquired in step S101 (step S102). In step S102, for example, by analyzing the structural model 412, natural frequencies and eigenvectors for identifying each vibration mode of the structure 1 are obtained.

[0042] A specific example will be described below using the structure 1 in Fig. 1. The equation of motion of the structure 1 supported by a plurality of support points (floor surfaces k, l) is generally expressed by equation (4). In TIFF0007737846000004.tif10170 structure 1, the constrained direction of a node supported by the floor is called the constrained node degree of freedom, and the direction of a free node not supported by the floor is called the unconstrained node degree of freedom. The upper part of equation (4) represents the equation of motion for the unconstrained node degree of freedom, and the lower part represents the equation of motion for the constrained node degree of freedom. where M P is the mass matrix of the unconstrained nodal degrees of freedom of structure 1, C P is the damping matrix of the unconstrained nodal degrees of freedom of structure 1, K P is the stiffness matrix of the unconstrained nodal degrees of freedom of structure 1, C B is the damping matrix of the constrained node degrees of freedom of structure 1, K B is the stiffness matrix of the constrained node degrees of freedom of structure 1, C PB or C BP is the coupling damping matrix between unconstrained and constrained nodal degrees of freedom of structure 1, K PB or K BP is the coupling stiffness matrix between the unconstrained node degrees of freedom and the constrained node degrees of freedom of structure 1, F Bis the reaction vector of the constrained nodal degree of freedom of structure 1, X is the response vector of the unconstrained nodal degree of freedom of structure 1, and Z is the displacement vector of the constrained nodal degree of freedom of structure 1.

[0043] The response of structure 1 in equation (4) can be expressed as the dynamic response {X D} and static response {X S} is expressed as the sum of TIFF0007737846000005.tif6170StaticResponse{X S} is calculated using equation (6) based on static balance. TIFF0007737846000006.tif6170By substituting equation (6) into the upper equation of equation (4) and ignoring the damping term of the restrained node degree of freedom of structure 1, equation (7) is obtained. TIFF0007737846000007.tif6170Equation (7) obtained in this way is the basic equation for calculating the dynamic response of structure 1 supported by multiple support points.

[0044] where the dynamic response {X D} can be expressed as equation (8) using the modal matrix [Φ] and modal response vector {q}. TIFF0007737846000008.tif6170By substituting equation (8) into equation (7), the equation of motion of equation (7) is expressed in the modal coordinate system by equation (9). TIFF0007737846000009.tif6170Where, ξ i is the modal damping constant, ω i is the modal angular frequency.

[0045] In equation (9), the coefficients on the right side represent the stimulus coefficients in the vibration response of a multi-input system. The stimulus coefficient β of the i-th vibration mode due to input vibration of floor surface k is ik teeth TIFF0007737846000010.tif5170, and the equation of motion for the ith vibration mode due to input vibration of floor surface k is expressed as follows: TIFF0007737846000011.tif6170Equation (11) is the basic equation for calculating the dynamic response of structure 1 that receives multiple inputs from multiple support points expressed in a modal coordinate system. ik is the modified stimulus factor.

[0046] Next, the floor response spectrum acquisition unit 306 acquires the floor response spectra corresponding to each of the floor surfaces k and l from the floor response spectrum database 420 (step S103). The floor response spectrum database 420 stores in advance the floor response spectra associated with the floor surfaces k and l, but these floor response spectra may be calculated in advance by the main server 300.

[0047] Here, the specific contents of the floor response spectrum will be explained based on the procedure for calculating the floor response spectrum by the main server 300. Fig. 8 is a block diagram showing the functional configuration of the main server 300 related to the calculation of the floor response spectrum, and Fig. 9 is a flowchart showing each step of the method for calculating the floor response spectrum. 8 and 9 show the configuration and method for calculating the floor response spectrum for floor surface k, but the same applies to floor surface l.

[0048] As shown in Figure 8, the main server 300 for calculating the floor response spectrum is configured to include a reference vibration acquisition unit 330, a building model acquisition unit 332, a floor surface time history acceleration calculation unit 334, a single-degree-of-freedom system oscillator model acquisition unit 336, and a floor response spectrum calculation unit 338. Each functional block shown in FIG. 8 is an example defined to correspond to each step of the floor response spectrum calculation method described below, and multiple functional blocks may be integrated, or may be further divided into multiple functional blocks.

[0049] 9, first, the normal vibration acquisition unit 330 acquires the normal vibration (step S110). The normal vibration is a vibration corresponding to an input vibration to the ground 2 (see FIG. 1), and is a time-history wave whose vibration amplitude varies over time and includes multiple frequency components. Such a normal vibration is, for example, a time-history wave that simulates earthquake motion.

[0050] Next, the building model acquisition unit 332 acquires a building model 414 corresponding to the building 4 from the analysis model database 410 (step S111). In this embodiment, as shown in FIG. 1, building models 414 corresponding to two buildings 4a and 4b erected on the ground 2 are acquired.

[0051] Next, the floor acceleration time history calculation unit 334 inputs the reference vibration acquired in step S110 into the building model 414 acquired in step S111, thereby calculating the floor acceleration time history A k (t) is calculated (step S112). As a result, the acceleration behavior of the floor surface k when the reference vibration is input to the building model 4 is calculated as the floor surface time history acceleration A k (t) is obtained. The floor time history acceleration A calculated in step S112 k (t) is stored in the floor surface time history acceleration database 422 so as to be readable as needed.

[0052] Next, the single-degree-of-freedom oscillator model acquisition unit 336 acquires a single-degree-of-freedom oscillator model from the analysis model database 410 (step S113). The single-degree-of-freedom oscillator model is, for example, a single-degree-of-freedom oscillator model having an arbitrary natural frequency corresponding to the characteristics of the structural evaluation target, and is stored in advance in the analysis model database 410. For example, when performing structural evaluation against earthquake motion, multiple single-degree-of-freedom oscillator models are acquired, each having a natural frequency included in the band of 1 to several tens of Hz, which is the main component included in the earthquake motion.

[0053] Next, the floor response spectrum calculation unit 338 calculates the floor time history acceleration A corresponding to each floor k calculated in step S112. k(t) into a single-degree-of-freedom oscillator model having various natural frequencies included in the predetermined band obtained in step S113, a plurality of time history response accelerations RA corresponding to the natural frequencies of each single-degree-of-freedom oscillator model are obtained. k (t) is calculated (step S114). k At each of (t), the maximum acceleration RA k max (the acceleration with the largest absolute value) is identified (step S115). k max is plotted against the natural frequency f to create a floor response spectrum for the floor surface k (step S116).

[0054] FIG. 10A shows the time history response acceleration RA obtained in step S114 of FIG. k (t) is an example of the time history response acceleration RA k Fig. 10A shows an example of the floor response spectrum obtained from the time history response acceleration RA corresponding to various natural frequencies f. k Of (t), the time history response acceleration RA corresponding to the natural frequency f1 k 1(t) and the time history response acceleration RA corresponding to the natural frequency f2 k 2(t) and are shown as representative examples. Time history response acceleration RA k At 1(t), the maximum acceleration RA k 1max is specified, and the time history response acceleration RA k At 2(t), the maximum acceleration RA k The maximum acceleration RA 2max is determined. k max is plotted against the corresponding natural frequency f to obtain the floor response spectrum shown in Figure 10B.

[0055] Such a floor response spectrum is calculated for each of the floor surfaces k and l (step S117: YES), and is stored in the floor response spectrum database in association with each of the floor surfaces k and l (step S118).

[0056] 7, the response calculation unit 326 in FIG. 6 calculates a response value corresponding to each vibration mode of the structure 1 for each input to the support point using the floor response spectrum acquired by the floor response spectrum acquisition unit 324 in step S103 (step S104). That is, for each vibration mode corresponding to the natural frequency identified by the eigenvalue analysis in step S102, the response value to the excitation from each floor surface k, l on which the structure 1 is supported is calculated as a modal response q R ik are calculated as follows:

[0057] (Higher order response q R (n+1)k (Calculation method) Next, the higher-order response calculation unit 304 calculates the higher-order response q R (n+1)k 11 is a block diagram showing the internal configuration of the high-order response calculation unit 304 in FIG. 3, and FIG. 12 is a block diagram showing the calculation of the high-order response performed by the high-order response calculation unit 304 in FIG. q R (n+1)k 10 is a flowchart showing a method for calculating

[0058] As shown in FIG. 11 , the high-order response calculation unit 304 includes a structural model acquisition unit 340, an eigenvalue analysis unit 341, a normal vibration acquisition unit 342, a building model acquisition unit 343, a floor time history acceleration calculation unit 344, and a response calculation unit 345. The structural model calculation unit 340, like the structural model acquisition unit 320 (see FIG. 6 ), acquires a structural model corresponding to the structure 1 from the analysis model database 410. The eigenvalue analysis unit 341, like the eigenvalue analysis unit 322 (see FIG. 6 ), performs eigenvalue analysis of the structure 1 based on the structural model acquired by the structural model acquisition unit 340. The normal vibration acquisition unit 342, like the normal vibration acquisition unit 330 (see FIG. 8 ), acquires a normal vibration. The building model acquisition unit 343, like the building model acquisition unit 332 (see FIG. 8 ), acquires a building model 414. The floor surface time history acceleration calculation unit 344 calculates the floor surface time history acceleration A k The response calculation unit 345 calculates m high-order responses (t) corresponding to each input.q R (n+1)k Calculate.

[0059] 12, first, the structural model acquisition unit 340 acquires the structural model 412 corresponding to the structure 1 (step S201). Specifically, the structural model acquisition unit 340 accesses the analytical model database 410, and searches for and acquires the structural model corresponding to the structure 1 to be structurally evaluated from the analytical models stored in advance in the analytical model database 410.

[0060] Next, the eigenvalue analysis unit 341 performs eigenvalue analysis on the structural model 412 acquired in step S201 (step S202). In step S202, for example, by analyzing the structural model 412, natural frequencies and eigenvectors for identifying each vibration mode of the structure 1 are obtained.

[0061] Meanwhile, the normal vibration acquisition unit 342 acquires the normal vibration (step S203). The normal vibration is a vibration corresponding to an input vibration to the ground 2 (see FIG. 1), and is a time history wave whose vibration amplitude varies over time and includes multiple frequency components. Such a normal vibration is, for example, a time history wave that simulates earthquake motion.

[0062] Next, the building model acquisition unit 343 acquires a building model 414 corresponding to the building 4 from the analysis model database 410 (step S204). In this embodiment, as shown in FIG. 1, building models 414 corresponding to two buildings 4a and 4b erected on the ground 2 are acquired.

[0063] Next, the floor acceleration time history calculation unit 344 inputs the reference vibration acquired in step S203 into the building model 414 acquired in step S204, thereby calculating the floor acceleration time history A k (t) is calculated (step S205). As a result, the acceleration behavior of the floor surface k when the reference vibration is input to the building model 4 is calculated as the floor surface time history acceleration A k (t) is obtained.

[0064] In FIG. 12, steps S203 to S205 are described as being performed after steps S201 to S202, but steps S203 to S205 may be performed before steps S201 to S202, or steps S201 to S202 and steps S203 to S205 may be performed simultaneously (in parallel).

[0065] Next, the response calculation unit 345 calculates the maximum response (displacement of all nodes, member forces, etc.) of the equipment and piping system on the floor surface k as a high-order response q R (n+1)k (Step S206). q R (n+1)k The calculation of can be performed by, for example, missing mass analysis.

[0066] In this way, the high-order response calculation unit 304 calculates the floor time history acceleration A obtained by inputting the reference vibration into the building model 414, which is a structural model corresponding to the structure 1. k (t) based on higher-order responses q R (n+1)k can be suitably calculated.

[0067] (Building displacement response q R (n+2)k (Calculation method) Next, the building displacement response calculation unit 306 calculates the building displacement response. q R (n+2)k 13 is a block diagram functionally showing the internal configuration of the building displacement response calculation unit 306 in FIG. 3, and FIG. 14 is a block diagram functionally showing the internal configuration of the building displacement response calculation unit 306 in FIG. 3. q R (n+2)k 10 is a flowchart showing a method for calculating

[0068] As shown in FIG. 13 , the building displacement response calculation unit 306 includes a normal vibration acquisition unit 350, a building model acquisition unit 351, a floor time history displacement calculation unit 352, a response calculation unit 353, and a structural model acquisition unit 354. The normal vibration acquisition unit 350 acquires the normal vibration, similar to the above-mentioned normal vibration acquisition units 330 (see FIG. 8) and 342 (see FIG. 11). The building model acquisition unit 351 acquires the building model 414, similar to the above-mentioned building model acquisition units 332 (see FIG. 8) and 343 (see FIG. 11). The floor time history displacement calculation unit 352 calculates the floor time history displacement D based on the normal vibration acquired by the normal vibration acquisition unit 350 and the building model acquired by the building model acquisition unit 351. k The response calculation unit 353 calculates a total of m building displacement responses corresponding to each input. q R (n+2)k Calculate.

[0069] As shown in Fig. 14, first, the normal vibration acquisition unit 350 acquires the normal vibration (step S301). The normal vibration is a vibration corresponding to an input vibration to the ground 2 (see Fig. 1), and is a time history wave whose vibration amplitude varies over time and includes multiple frequency components. Such a normal vibration is, for example, a time history wave that simulates earthquake motion.

[0070] Next, the building model acquisition unit 351 acquires a building model 414 corresponding to the building 4 from the analysis model database 410 (step S302). In this embodiment, as shown in FIG. 1, building models 414 corresponding to two buildings 4a and 4b erected on the ground 2 are acquired.

[0071] Next, the floor time history displacement calculation unit 352 inputs the reference vibration acquired in step S301 into the building model 414 acquired in step S302, thereby calculating the floor time history displacement D k (t) is calculated (step S303). As a result, the displacement behavior of the floor surface k when the reference vibration is input to the building model 4 is calculated as the floor surface time history displacement D k (t) is obtained. The floor time history displacement D calculated in step S303 k(t) is stored in the floor surface time history displacement database 424 so as to be readable as needed.

[0072] Next, the structural model acquisition unit 354 acquires a structural model (step S304), and the response calculation unit 353 inputs the floor time history displacement Dk(t) calculated in step S303 into the structural model acquired in step S304 to calculate the maximum response (displacement of all nodes, member forces, etc.) of the equipment and piping system on floor k by building displacement input analysis as the building displacement response q R (n+2)k (step S305).

[0073] In this way, the building displacement response calculation unit 306 calculates the floor time history displacement D obtained by inputting the reference vibration into the building model 414, which is a structural model corresponding to the structure 1. k Building displacement response based on (t) q R (n+2)k can be suitably calculated.

[0074] (correlation coefficient ρ ikjl (Calculation method) Next, the correlation coefficient ρ ikjl The main server 300 calculates the correlation coefficient ρ ikjl 15 is a block diagram showing the functional configuration of the main server 300 for calculating the correlation coefficient, and FIG. ikjl 1 is a flowchart showing a method for calculating the value of

[0075] As shown in Fig. 15 , the main server 300 includes a normal vibration acquisition unit 360, a building model acquisition unit 361, a floor acceleration time history calculation unit 362, a floor displacement time history calculation unit 363, an eigenvalue analysis unit 364, a single-degree-of-freedom oscillator model acquisition unit 365, a dynamic response calculation unit 366, and a correlation coefficient calculation unit 367. The normal vibration acquisition unit 360 acquires a normal vibration, similar to the normal vibration acquisition units 330 (see Fig. 8), 342 (see Fig. 11), and 350 (see Fig. 13) described above. The building model acquisition unit 361 acquires a building model 414, similar to the building model acquisition units 332 (see Fig. 8), 343 (see Fig. 11), and 351 (see Fig. 13) described above. The floor acceleration time history calculation unit 362 calculates the floor acceleration time history A k The floor surface time history displacement calculation unit 363 calculates the floor surface time history displacement D k (t). The eigenvalue analysis unit 364 performs eigenvalue analysis of the structure 1 based on the structural model acquired by the structural model acquisition unit 340, similar to the above-mentioned eigenvalue analysis units 322 (see FIG. 6) and 341 (see FIG. 11). The single-degree-of-freedom oscillator model acquisition unit 365 acquires a single-degree-of-freedom oscillator model from the analysis model database 410, similar to the above-mentioned single-degree-of-freedom oscillator model acquisition unit 336 (see FIG. 8). The dynamic response calculation unit 366 calculates a dynamic response based on the analysis result of the eigenvalue analysis unit 364, the single-degree-of-freedom oscillator model acquired by the single-degree-of-freedom oscillator model acquisition unit 365, and the floor time history acceleration calculated by the floor time history acceleration calculation unit 362. The correlation coefficient calculation unit 367 calculates a correlation coefficient based on the floor time history acceleration A calculated by the floor time history acceleration calculation unit 362. k (t), the floor time history displacement D calculated by the floor time history displacement calculation unit 363 k (t) and the dynamic response calculated by the dynamic response calculation unit 366, the correlation coefficient ρ ikjl Calculate the following. Note that each functional block shown in FIG. 15 is an example defined to correspond to each step of the correlation coefficient calculation method described below, and each functional block may be integrated or further subdivided.

[0076] As shown in Fig. 16, first, the normal vibration acquisition unit 360 acquires the normal vibration (step S401). The normal vibration is a vibration corresponding to an input vibration to the ground 2 (see Fig. 1), and is a time history wave in which the vibration amplitude varies over time and includes multiple frequency components. Such a normal vibration is, for example, a time history wave that simulates earthquake motion.

[0077] Next, the building model acquisition unit 361 acquires a building model 414 corresponding to the building 4 from the analysis model database 410 (step S402). In this embodiment, as shown in FIG. 1, building models 414 corresponding to two buildings 4a and 4b erected on the ground 2 are acquired.

[0078] Next, the floor time history acceleration calculation unit 362 and the floor time history displacement calculation unit 363 input the reference vibration acquired in step S401 to the building model 414 acquired in step S402, thereby calculating the floor time history acceleration A k (t) and floor time history displacement D k (t) are calculated (steps S403 and S404). As a result, the acceleration behavior of the floor k when the reference vibration is input to the building model 414 is calculated as the floor time history acceleration A k (t) and floor time history displacement D k (t) is obtained.

[0079] Next, the eigenvalue analysis unit 364 performs eigenvalue analysis on the structural model to obtain an eigenvalue analysis result (step S405). In step S405, for example, by analyzing the structural model, natural frequencies and eigenvectors for identifying each vibration mode of the structure 1 are obtained. Then, the single-degree-of-freedom oscillator model acquisition unit 365 acquires a single-degree-of-freedom oscillator model from the analysis model database 410 (step S406), and the dynamic response calculation unit 366 calculates a dynamic response for each vibration mode floor based on the analysis result of the eigenvalue analysis unit 364, the single-degree-of-freedom oscillator model acquired by the single-degree-of-freedom oscillator model acquisition unit 365, and the floor time history acceleration calculated by the floor time history acceleration calculation unit 362 (step S407).

[0080] Next, the correlation coefficient calculation unit 367 calculates the correlation coefficient ρ ikjl is calculated (step S408). The time history response of the modal response is proportional to the time history response calculated by the dynamic response calculation unit 366, the time history response of the higher-order response is proportional to the floor time history acceleration calculated by the floor time history acceleration calculation unit 362 because there is no amplification of the response, and the time history response of the building displacement response is proportional to the floor time history displacement calculated by the floor time history displacement calculation unit 363 because it is a static response. Therefore, the time history response (proportional to the modal response) corresponding to the i-th vibration mode and the input vibration of floor surface k is expressed as X ik (t) (where 1≦i≦n), and the floor time history acceleration (proportional to the higher order response) at floor surface k is X (n+1)k (t), the floor time history displacement (proportional to the building displacement response) at floor k is X (n+2)k (t), then for 1≦i≦n+2, X ik (t) and X jl Correlation coefficient ρ of (t) ikjl is calculated using the following formula: TIFF0007737846000012.tif12170

[0081] Such a correlation coefficient ρ ikjl The calculation of the correlation coefficient ρ is repeated for all responses consisting of a total of (n+2) dynamic responses, higher-order responses, and building displacement responses due to a total of m inputs (total accelerations and displacements of all floors) (step S409: YES), and then the correlation coefficient ρ ikjl are stored in the correlation coefficient database 430 in association with each vibration mode and floor surfaces k and l (step S410).

[0082] As described above, according to the above embodiment, when a single or multiple input vibrations are input to the structure 1, the modal response corresponding to the vibration mode in the frequency range below the cutoff frequency is calculated. q R ik In addition, higher-order responses q R (n+1)k or displacement response q R (n+2)kThese response values ​​are synthesized using a correlation coefficient, and structural analysis is performed based on the synthesized response. The multiple response values ​​synthesized using the correlation coefficient include modal response, which is a dynamic response in a frequency range below the cutoff frequency. q R ik In addition to the above, the higher-order response, which is the dynamic response in the frequency range above the cutoff frequency, q R (n+1)k , or a displacement response which is a static response q R (n+2)k In this way, the modal response q R ik as well as higher-order responses q R (n+1)k and displacement response q R (n+2)k By calculating the composite response taking these into consideration, excellent analytical accuracy can be achieved. In addition, by calculating the correlation coefficient used when combining these response values ​​as the correlation between multiple time history responses proportional to each response value, it is possible to effectively prevent over- or under-evaluation compared to synthesis using the conventional SRSS method or ABS method.

[0083] In addition, within the scope of the present disclosure, the components in the above-described embodiments may be replaced with well-known components as appropriate, and the above-described embodiments may be combined as appropriate.

[0084] The contents described in each of the above embodiments can be understood, for example, as follows.

[0085] (1) A structure evaluation method according to an embodiment of the present disclosure includes: A structural evaluation method for a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from a plurality of support points, comprising: a response value calculation step for calculating a plurality of response values ​​including at least one of (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range below a cutoff frequency, and (ii) a higher-order response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range equal to or higher than the cutoff frequency, or a displacement response between the plurality of support points; a composite response calculation step of calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; Equipped with.

[0086] According to the above aspect (1), when a single or multiple input vibrations are input to a multi-degree-of-freedom structure, at least one of a higher-order response or a displacement response is calculated as a response value in addition to a modal response corresponding to a vibration mode in a frequency range below the cutoff frequency. These response values ​​are combined using a correlation coefficient, and structural analysis is performed based on the combined response. The multiple response values ​​combined using the correlation coefficient include at least one of a higher-order response, which is a dynamic response in a frequency range above the cutoff frequency, and a displacement response, which is a static response, in addition to a modal response, which is a dynamic response in a frequency range below the cutoff frequency. By calculating a combined response that takes into account not only the modal response but also the higher-order response and the displacement response, excellent analysis accuracy can be achieved. Furthermore, by calculating the correlation coefficient used to combine these response values ​​as a correlation between multiple time history responses proportional to each response value, over- or underestimation can be effectively prevented compared to synthesis using the conventional SRSS method or ABS method.

[0087] (2) In another embodiment, in the above embodiment (1), In the response value calculation step, the modal response and the higher-order response are calculated as the plurality of response values.

[0088] According to the above aspect (2), the multiple response values ​​synthesized by the correlation coefficient include not only the modal response, which is a dynamic response in a frequency range below the cutoff frequency, but also the higher-order response, which is a dynamic response in a frequency range above the cutoff frequency. By calculating the synthesized response taking into account not only the modal response but also the higher-order response, it is possible to obtain excellent analysis accuracy even when the influence of the higher-order response is large, for example, when a multi-degree-of-freedom structure is rigidly supported.

[0089] (3) In another embodiment, in the above embodiment (1), In the response value calculation step, the modal response and the displacement response are calculated as the plurality of response values.

[0090] According to the above aspect (3), the multiple response values ​​synthesized by the correlation coefficient include not only the modal response, which is a dynamic response in the frequency range below the cutoff frequency, but also the displacement response, which is a static response. By calculating the synthesized response in this way, taking into account not only the modal response but also the displacement response, it is possible to obtain excellent analysis accuracy even when the influence of the displacement response is large, for example, when relative displacement occurs between multiple support points supporting a multi-degree-of-freedom structure.

[0091] (4) In another embodiment, in the above embodiment (1), In the response value calculation step, the modal response, the higher-order response, and the displacement response are calculated as the plurality of response values.

[0092] According to the above aspect (4), the multiple response values ​​synthesized by the correlation coefficient include not only the modal response, which is a dynamic response in the frequency range below the cutoff frequency, but also the higher-order response, which is a dynamic response in the frequency range equal to or higher than the cutoff frequency, and the displacement response, which is a static response. By calculating the synthesized response in this way, taking into account not only the modal response but also the higher-order response and the static response, it is possible to obtain higher analysis accuracy.

[0093] (5) In another embodiment, in any one of the above (1) to (4), The higher-order response is calculated based on a plurality of time history accelerations corresponding to the plurality of support points, which are obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

[0094] According to the above aspect (5), it is possible to appropriately calculate a higher-order response, which is a dynamic response in a frequency range above the cutoff frequency, based on the time history acceleration obtained by inputting a reference vibration including a frequency range above the cutoff frequency into a structural model of a multi-degree-of-freedom structure.

[0095] (6) In another embodiment, in any one of the above (1) to (5), The displacement response is calculated based on a plurality of time history displacements corresponding to the plurality of support points, which are obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

[0096] According to the above aspect (6), it is possible to appropriately calculate the displacement response, which is a static response, based on the time history displacement obtained by inputting the reference vibration into the structural model of the multi-degree-of-freedom structure.

[0097] (7) In another embodiment, in any one of the above (1) to (6), The correlation coefficients for the modal response and the higher-order response are calculated using, as the time history response, a time history acceleration obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

[0098] According to the above aspect (7), among the correlation coefficients for synthesizing each response value, the correlation coefficients for modal responses and higher-order responses can be calculated based on the time history acceleration obtained by inputting the reference vibration into the structural model of the multi-degree-of-freedom structure, since these are dynamic responses.

[0099] (8) In another embodiment, in any one of the above (1) to (7), The correlation coefficient for the displacement response is calculated using, as the time history response, a time history displacement obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

[0100] According to the above aspect (8), the correlation coefficient for the displacement response among the correlation coefficients for synthesizing each response value can be calculated based on the time history displacement obtained by inputting the reference vibration into the structural model of the multi-degree-of-freedom structure, since the displacement response is a static response.

[0101] (9) A structure evaluation program according to one embodiment includes: A structural evaluation program for a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from multiple support points, using a computer, a response value calculation step for calculating a plurality of response values ​​including at least one of (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range below a cutoff frequency, and (ii) a higher-order response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range equal to or higher than the cutoff frequency, or a displacement response between the plurality of support points; a composite response calculation step of calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; is possible.

[0102] According to the above aspect (9), when a single or multiple input vibrations are input to a multi-degree-of-freedom structure, at least one of a higher-order response or a displacement response is calculated in addition to a modal response corresponding to a vibration mode in a frequency range below the cutoff frequency. These response values ​​are combined using a correlation coefficient, and structural analysis is performed based on the combined response. The multiple response values ​​combined using the correlation coefficient include at least one of a higher-order response, which is a dynamic response in a frequency range above the cutoff frequency, and a displacement response, which is a static response, in addition to a modal response, which is a dynamic response in a frequency range below the cutoff frequency. By calculating a combined response that takes into account not only the modal response but also the higher-order response and the displacement response, excellent analysis accuracy can be achieved. Furthermore, by calculating the correlation coefficient used to combine these response values ​​as a correlation between multiple time history responses proportional to each response value, over- or underestimation can be effectively prevented compared to synthesis using the conventional SRSS method or ABS method.

[0103] (10) A structure evaluation device according to one aspect includes: A structural evaluation device for a multi-degree-of-freedom structure that receives different input vibrations or a single input vibration from multiple support points, a response value calculation unit for calculating a plurality of response values ​​including at least one of (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range less than a cutoff frequency, and (ii) a higher-order response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range equal to or greater than the cutoff frequency, or a displacement response between the plurality of support points; a composite response calculation unit for calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; Equipped with.

[0104] According to the above aspect (10), when a single or multiple input vibrations are input to a multi-degree-of-freedom structure, at least one of a higher-order response or a displacement response is calculated as a response value in addition to a modal response corresponding to a vibration mode in a frequency range below the cutoff frequency. These response values ​​are combined using a correlation coefficient, and structural analysis is performed based on the combined response. The multiple response values ​​combined using the correlation coefficient include at least one of a higher-order response, which is a dynamic response in a frequency range above the cutoff frequency, and a displacement response, which is a static response, in addition to a modal response, which is a dynamic response in a frequency range below the cutoff frequency. By calculating a combined response that takes into account not only the modal response but also the higher-order response and the displacement response, excellent analysis accuracy can be achieved. Furthermore, by calculating the correlation coefficient used to combine these response values ​​as a correlation between multiple time history responses proportional to each response value, over- or underestimation can be effectively prevented compared to synthesis using the conventional SRSS method or ABS method. [Explanation of symbols]

[0105] 1 structure 2 ground 4 Building 100 Structural Evaluation System 200 Communication Network 300 Main Server 302 Modal response calculation section 304 Higher-order response calculation unit 306 Building displacement response calculation section 308 Correlation coefficient acquisition unit 310 Response Synthesis Unit 312 Output section 400 Data Server 410 Analysis Model Database 420 Floor Response Spectrum Database 422 Floor Acceleration Time History Database 424 Floor Time History Displacement Database 430 Correlation Coefficient Database 500 user terminals

Claims

1. A structural evaluation method for a multi-degree-of-freedom structure supported at a plurality of support points corresponding to a plurality of floor surfaces of a plurality of buildings erected on the ground, comprising: a response value calculation step for calculating, using a computer, a plurality of response values ​​including (i) modal responses corresponding to vibration modes of the multi-degree-of-freedom structure in a frequency range less than a cutoff frequency, and (ii) displacement responses between the plurality of support points; a composite response calculation step of calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between time history responses proportional to the plurality of response values, using the computer; Equipped with the correlation coefficient related to the modal response is calculated using, as the time history response, a time history acceleration obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure; A structural evaluation method in which the correlation coefficient for the displacement response is calculated using, as the time history response, a time history displacement obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

2. the plurality of response values ​​calculated in the response value calculation step further include, using the computer, a higher-order response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency region equal to or higher than the cutoff frequency, 2. The structural evaluation method according to claim 1, wherein the correlation coefficient for the higher-order response is calculated using a time history acceleration obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure as the time history response.

3. 3. The structural evaluation method according to claim 2, wherein the higher-order response is calculated based on a plurality of time history accelerations corresponding to the plurality of support points obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

4. 4. A structural evaluation method according to claim 1, wherein the displacement response is calculated based on a plurality of time history displacements corresponding to the plurality of support points obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

5. A structural evaluation program for a multi-degree-of-freedom structure supported at a plurality of support points corresponding to a plurality of floor surfaces of a plurality of buildings erected on the ground, the program being carried out by a computer. a response value calculation step for calculating a plurality of response values ​​including (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency region less than a cutoff frequency, and (ii) a displacement response between the plurality of support points; a composite response calculation step of calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; is executable, the correlation coefficient related to the modal response is calculated using, as the time history response, a time history acceleration obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure; A structural evaluation program in which the correlation coefficient for the displacement response is calculated using a time history displacement obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure as the time history response.

6. A structural evaluation device for a multi-degree-of-freedom structure supported at a plurality of support points corresponding to a plurality of floor surfaces of a plurality of buildings erected on the ground, comprising: a response value calculation unit for calculating a plurality of response values ​​including (i) a modal response corresponding to a vibration mode of the multi-degree-of-freedom structure in a frequency range less than a cutoff frequency, and (ii) a displacement response between the plurality of support points; a composite response calculation unit for calculating a composite response of the plurality of response values ​​using a correlation coefficient indicating a correlation between a plurality of time history responses that are proportional to the plurality of response values, respectively; Equipped with the correlation coefficient related to the modal response is calculated using, as the time history response, a time history acceleration obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure; A structural evaluation device in which the correlation coefficient related to the displacement response is calculated using, as the time history response, a time history displacement obtained by inputting a reference vibration into a structural model of the multi-degree-of-freedom structure.

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