Seismic evaluation method and seismic evaluation system for structure assembly

Abstract

To provide an earthquake resistance evaluation method and an earthquake resistance evaluation system of a structure assembly capable of performing earthquake resistance evaluation of a structure in consideration of frictional force from a support part without performing nonlinear analysis.SOLUTION: A seismic evaluation method for a structure assembly 100 according to the present disclosure is a seismic evaluation method for the structure assembly 100 that includes a structure 10 and a support portion 20 supporting the structure 10 and in which a frictional force acts on the structure 10 from the support portion 20, the method including preparing a calculation model of the structure 10 and the support portion 20, calculating an equivalent damping constant ζ eq when it is assumed that absorbed energy due to structural damping of the structure 10 is equal to damping energy due to the frictional force acting on the structure 10, and calculating a response to a vibration input using the equivalent damping constant ζ eq.SELECTED DRAWING: Figure 1A

Description

[Technical Field]

[0001] The present disclosure relates to a method and system for seismic evaluation of a structural assembly. [Background technology]

[0002] In low seismic class piping in nuclear power plants and the like, structures such as piping are often supported by simple supports such as U-bolts (for example, Patent Document 1). In addition, in the seismic design of low seismic class piping, a fixed pitch design method is used, but with the recent trend toward improved safety evaluations, there are cases where seismic resistance based on response analysis similar to that of high seismic class piping is required. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-156338 Summary of the Invention [Problem to be solved by the invention]

[0004] Response analysis has traditionally been performed under the condition that the translational displacement of structures such as pipes is fixed in two directions, but the pipe axis direction is not fixed. As a result, response analysis has sometimes resulted in large displacement in the pipe axis direction, making it impossible to ensure the structural integrity of structures such as pipes. To address this, measures such as adding or strengthening supports are sometimes taken, but in actual structures, pipes are subjected to frictional forces in the pipe axis direction from supports due to friction and minute vibration collisions, so the displacement in the pipe axis direction may not be as large as the results obtained from response analysis. As a result, measures such as adding or strengthening supports have sometimes been taken excessively.

[0005] Therefore, a response analysis that takes into account factors such as friction between pipes and other structures and their supports is required, but in order to handle hysteretic resistance, a nonlinear response analysis is necessary. However, nonlinear response analysis cannot be considered a general-purpose analytical method, and there is still room for improvement in this regard.

[0006] The present disclosure addresses the above-mentioned problems, and its objective is to provide a method and system for seismic evaluation of a structural assembly that can perform seismic evaluation of a structure taking into account frictional forces from supporting parts without performing nonlinear analysis. [Means for solving the problem]

[0007] In order to solve the above-mentioned problems, the present disclosure provides a method for seismic evaluation of a structural assembly, comprising: [1] A method for seismic evaluation of a structure assembly, comprising: a structure; and a support portion that supports the structure; and a frictional force acting on the structure from the support portion, the method comprising: providing a computational model of the structure and the support; calculating an equivalent damping constant when it is assumed that the absorbed energy due to structural damping of the structure is equal to the damping energy due to the friction force acting on the structure; calculating a response to a vibration input using the equivalent damping constant; The present invention is characterized by comprising:

[0008] Further, the seismic evaluation method for a structural assembly according to the present disclosure includes: [2] In the configuration of [1] above, it is preferable that the equivalent damping constant is calculated based on the maximum response displacement of the structure obtained from the energy spectrum at the time of vibration.

[0009] Further, the seismic evaluation method for a structural assembly according to the present disclosure includes: [3] In the configuration of [1] above, it is preferable that the equivalent damping constant is calculated based on the maximum response displacement of the structure obtained from a response analysis that takes into account only structural damping.

[0010] Further, the seismic evaluation method for a structural assembly according to the present disclosure includes: [4] In the configuration described in any one of [1] to [3] above, it is preferable that the structure is a pipe, the support part is a fixed member surrounding the pipe from the radial outside, and the response is an axial response of the pipe.

[0011] In order to solve the above-mentioned problems, the seismic evaluation system for a structural assembly according to the present disclosure includes: [5] A seismic evaluation system for a structural assembly, comprising: a structure; and a support portion that supports the structure, wherein a frictional force acts on the structure from the support portion, a model storage unit having a calculation model of the structure and the support; a damping constant calculation unit that calculates an equivalent damping constant when it is assumed that the absorbed energy due to structural damping of the structure is equal to the damping energy due to the friction force acting on the structure; a response calculation unit that calculates a response to a vibration input using the equivalent damping constant; The present invention is characterized by comprising: [Effects of the Invention]

[0012] According to the present disclosure, it is possible to provide a seismic evaluation method and a seismic evaluation system for a structural assembly that can perform seismic evaluation of a structure taking into account frictional forces from supporting parts without performing nonlinear analysis. [Brief explanation of the drawings]

[0013] [Figure 1A] 1 is a front view showing an example of a structure and a support part that are the subject of evaluation by the seismic evaluation method for a structure assembly according to the first and second embodiments of the present disclosure. FIG. [Figure 1B]1 is a perspective view showing an example of a structure and a support portion that are the subject of evaluation by the seismic evaluation method for a structure assembly according to the first and second embodiments of the present disclosure. FIG. [Figure 2] 1 is a block diagram showing the configuration of a seismic resistance evaluation system according to first and second embodiments of the present disclosure. [Figure 3] 1 is a flowchart showing the procedure for carrying out a seismic resistance evaluation method according to a first embodiment of the present disclosure. [Figure 4] FIG. 2 is a diagram showing the relationship between the period and the energy spectrum in the seismic resistance evaluation method according to the first embodiment of the present disclosure. [Figure 5] FIG. 2 is a diagram showing the relationship between the period and the equivalent damping constant in the seismic resistance evaluation method according to the first embodiment of the present disclosure. [Figure 6] 10 is a diagram showing the relationship between the relative displacement and friction force between a structure and a support, which is an evaluation target by the seismic evaluation method for a structure assembly according to the first and second embodiments of the present disclosure. FIG. [Figure 7] FIG. 2 is a diagram showing a comparison result of acceleration response spectra obtained using different analysis methods in the seismic resistance evaluation method according to the first embodiment of the present disclosure. [Figure 8] 10 is a flowchart showing the procedure for carrying out a seismic resistance evaluation method according to a second embodiment of the present disclosure. [Figure 9] FIG. 10 is a diagram showing the relationship between the period and the maximum response displacement in the seismic resistance evaluation method according to the second embodiment of the present disclosure. [Figure 10] FIG. 10 is a diagram showing the relationship between the period and the equivalent damping constant in the seismic resistance evaluation method according to the second embodiment of the present disclosure. [Figure 11] FIG. 10 is a diagram showing a comparison result of acceleration response spectra obtained using different analysis methods in the seismic resistance evaluation method according to the second embodiment of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0014] The present disclosure will be described in more detail below with reference to the drawings.

[0015] 1A and 1B are diagrams showing an example of a structure assembly 100 that is an object to be evaluated by the seismic evaluation method for a structure assembly 100 according to the first embodiment of the present disclosure, the structure 10 having a structure 10 and a support part 20. In this embodiment, the structure 10 is a cylindrical pipe that is used in a nuclear power plant or the like and is required to have seismic performance, and the support part 20 is a U-shaped pipe support that surrounds a portion of the structure 10 at an axial position from the radial outside.

[0016] As shown in Figures 1A and 1B, the support part 20 is an annular member having an approximately upside-down U-shape, and has an enclosing part 21 that surrounds the upper part of the structure 10 from the radially outside, a base plate 23 that is a flat member against which the lower end of the structure 10 abuts, and a fastening screw 25 for fastening the lower end of the enclosing part 21, which has a male threaded part, to the base plate 23.

[0017] 1A is defined as the X-axis direction, the up-down direction as the Y-axis direction, and the direction perpendicular to the paper surface as the Z-axis direction (see FIG. 1B). Furthermore, the radially outward direction refers to the direction away from the Z-axis along a straight line passing through the Z-axis of the structure assembly 100 in FIGS. 1A and 1B and perpendicular to the Z-axis, and the radially inward direction refers to the direction toward the Z-axis along that straight line. The structure 10 is fixed in the radial direction (X-axis direction and Y-axis direction) by the support parts 20, and a friction force in the Z-axis direction acts between the structure 10 and the support parts 20 in the Z-axis direction.

[0018] 2 is a block diagram showing the configuration of a seismic evaluation system 200 for a structure assembly 100 according to the first embodiment. The seismic evaluation system 200 includes a model storage unit 221 having calculation models of the structure 10 and the support parts 20, a damping constant calculation unit 211 that calculates an equivalent damping constant equivalent to the damping due to frictional force acting from the support parts 20 to the structure 10, and a response calculation unit 213 that calculates a response to a vibration input using the equivalent damping constant.

[0019] In this embodiment, the damping constant calculation unit 211 and the response calculation unit 213 may be functional units included in the control unit 210 provided in the seismic evaluation system 200, for example. The functions of the damping constant calculation unit 211 and the response calculation unit 213 in the control unit 210 can be realized as software processing by being executed by a CPU (Central Processing Unit) or a DSP (Digital Signal Processor) provided in the control unit 210. However, the present invention is not limited to this embodiment, and each process may be configured to be realized as hardware processing by, for example, an ASIC (Application Specific Integrated Circuit), a PLD (Programmable Logic Device), an FPGA (Field Programmable Gate Array), or the like.

[0020] In this embodiment, the calculation model of the structure 10 and the support part 20 is, for example, a finite element model, density, boundary conditions, etc. of the structure 10 and the support part 20. When performing a response analysis of a single mass point, the calculation model of the structure 10 and the support part 20 may be their mass information, etc.

[0021] In this embodiment, the model storage unit 221, which stores the calculation models of the structure 10 and the support unit 20, can be allocated, for example, in the memory unit 220. The memory unit 220 stores the programs executed by the control unit 210, the acquired calculation models of the structure 10 and the support unit 20, and the equivalent damping constants and response results calculated by the control unit 210. The memory unit 220 includes a readable storage medium, and the storage medium may be a rewritable and programmable ROM such as an EPROM, an EEPROM, or a flash memory, or another tangible storage medium such as a magnetic disk storage medium or an optical disk storage medium capable of storing information, or any combination thereof. The storage unit 220 may be provided integrally with the control unit 210 or may be provided in a computer in which the control unit 210 is provided. The storage unit 220 may also be a storage medium in an external storage device connectable to the computer in which the control unit 210 is provided, or may be a storage device provided in a remote location connected to the computer via a network via the communication unit 230.

[0022] The control unit 210 can communicate with an external device via the communication unit 230 to send and receive data. The communication unit 230 communicates with the external device by a communication means including wired communication such as USB (Universal Serious Bus) or Ethernet (registered trademark), or wireless communication such as Bluetooth (registered trademark) or WiFi (registered trademark). However, the communication means are not limited to the exemplified communication means, and various other communication means can be used.

[0023] The display unit 240 can display the acceleration response spectrum calculated by the response calculation unit 213, and can also display a graphical user interface (GUI) for controlling the seismic evaluation system 200. The display unit 240 is, for example, a liquid crystal display or an organic EL display equipped with an input function. The display unit 240 may be provided within the seismic evaluation system 200, or may be an external display connectable to the seismic evaluation system 200.

[0024] The seismic evaluation system 200 may further include an input unit 250 for controlling the seismic evaluation system 200 and inputting evaluation parameters.

[0025] The seismic resistance evaluation system 200 can be configured using, for example, a personal computer (PC).

[0026] Next, the procedure for carrying out the seismic evaluation method for the structural assembly 100 using the seismic evaluation system 200 of this embodiment will be described in detail with reference to FIG. 3 and other figures.

[0027] First, the control unit 210 acquires a calculation model of the structure 10 and the support unit 20 via the input unit 250 or the communication unit 230, and stores the calculation model in the model storage unit 221 of the memory unit 220 (step S101 in FIG. 3). The calculation model of the structure 10 and the support unit 20 is acquired and stored by, for example, the evaluator reading a file from the input unit 250 or inputting numerical values.

[0028] Next, the control unit 210 calculates the velocity response spectrum S from the time-axis waveform of the acceleration data of the seismic wave. v (In this embodiment, 10% attenuation is assumed) is calculated (step S102 in FIG. 3). The seismic wave acceleration data used is, for example, data from El Centro (NS), Hachinohe (EW), Kobe (NS), etc. (NS and EW in parentheses indicate the north-south and east-west directions, respectively).

[0029] Next, the control unit 210 calculates the velocity response spectrum S v From the equation, the number of seismic wave repetitions f, the attenuation constant h, and the effective duration e Energy spectrum V taking into account t0 etc. E0 The energy spectrum V E0 According to Reference 1, the calculation is performed using the following formulas (1) and (2). (Reference 1) Hiroshi Akiyama and Haruyuki Kitamura, “Correspondence between Energy Spectrum and Velocity Response Spectrum,” Journal of Structural Engineering, Architectural Institute of Japan, Vol. 608, pp. 37-43.

[0030]

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[0031] The energy spectrum V used for the evaluation of this disclosure E According to Reference 2, the energy spectrum V obtained by, for example, Equations (1) and (2) is E0 is used as a bilinear envelope as shown by the dashed line in Fig. 4, and the natural period T is the limit period T G In the region up to T G In the above region, a constant value (this constant value is the maximum value V of the energy spectrum) EM ) is taken. Figure 4 shows the energy spectrum V calculated from the acceleration data of the seismic wave at Kobe (NS). E0 This is an example using (Reference 2) Hiroshi Akiyama, Earthquake-Resistant Design of Buildings Based on Energy Balance, Gijutsudo Publishing, 2017.

[0032] The energy spectrum V shown by the dashed line in Figure 4 E can be expressed by the following formula (3). The control unit 210 calculates the energy spectrum V E0 From the bilinear envelope curve shown by the dashed line in Figure 4, the energy spectrum V is calculated again using equation (3). E is calculated (step S103 in FIG. 3).

[0033]

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[0034] Furthermore, based on the method for estimating the maximum response by balancing the energy during vibration proposed in Reference 3, the energy balance equation during vibration when considering frictional force as a nonlinear characteristic is shown in the following equation (4). (Reference 3) Takeshi Fukasawa and Satoshi Fujita, “Study on seismic response prediction of base-isolated structures combining elasto-plastic elements and sliding elements based on energy balance,” Transactions of the Japan Society of Mechanical Engineers, Vol. 85, No. 876, 2019.

[0035]

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[0036] In addition, when the natural period T, maximum response displacement X, damping constant ζ, equivalent repetition number n, friction coefficient μ, and gravitational acceleration g are used, W r ,W d and W b can be expressed as the following equations (5), (6), and (7). Note that, with reference to Reference 4, μ can be set to 0.2, with reference to Reference 5, ζ can be set to 0.5%, and with reference to Reference 3, n can be set to 2. (Reference 4) Ryo Kawamura, Shigeki Okamura, Satoshi Fujita, Takeshi Fukasawa, Hideo Machida, Hiroshi Ogawa, Manabu Arakawa, Ryoko Tamaki, “Study on response evaluation methods for low seismic class piping supported by U-bolts (static element test of frictional resistance force due to the weight of the pipe),” 2022 Annual Meeting of the Japan Society of Mechanical Engineers. (Reference 5) Nuclear Standards Committee of the Japan Electric Association, Seismic Design Technical Regulations for Nuclear Power Plants JEAC4601-2015 Electrical Technical Regulations for Nuclear Power Plants.

[0037]

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[0038] By substituting equations (5) to (7) into equation (4), we obtain the following equation (8).

[0039]

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[0040] By rearranging equation (8) with respect to X, we can obtain the following equation (9).

[0041]

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[0042] By solving equation (9) for X, the maximum response displacement X shown in equation (10) can be obtained.

[0043]

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[0044] The control unit 210 calculates the maximum response displacement X by calculating the formula (10) (step S104 in FIG. 3).

[0045] Here, by referring to the method proposed in Reference 6 to estimate the equivalent damping constant from the acceleration response spectrum of the friction system, we newly assume that "the damping energy due to friction force is equal to the absorbed energy due to structural damping," and calculate the equivalent damping constant ζ as shown in Equation (11). eq The equivalent damping constant ζ eqBy using this method, it is now possible to perform analyses that take frictional forces into account using a linear analysis code, as explained below. (Reference 6) Tetsuya Watanabe and Kohei Suzuki, “Estimation of Equivalent Damping Ratio of Piping Systems Using Friction System Response Spectrum,” Transactions of the Japan Society of Mechanical Engineers, Vol. 66, No. 642 (2000-2), Paper No. 99-1069

[0046]

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[0047] The damping energy due to frictional force is the hysteretic damping energy W b The energy absorbed by the structural damping is the energy absorbed by the structural damping of the piping system mentioned above, W d Therefore, the above formula (11) is expressed as W in formulas (6) and (7). d =W b It can be derived by:

[0048] Furthermore, by substituting equations (3) and (10) into equation (11), the equivalent damping constant ζ eq can be expressed as the following formula (12): The damping constant calculation unit 211 of the control unit 210 calculates the equivalent damping constant ζ for each period T based on formula (12). eq (Step S105 in FIG. 3). The control unit 210 calculates the calculated equivalent damping constant ζ eq The energy spectrum V of the seismic wave at Kobe (NS) shown in FIG. E0 The equivalent damping constant ζ calculated using e This is an example.

[0049]

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[0050] As shown in FIG. 5, in this embodiment, the equivalent damping constant ζe The equivalent damping constant ζ is truncated at 50%, including the structural damping of the piping system of 0.5%. e takes a constant value when the natural period is less than the limit period, and increases with the natural period up to 50%, which is the truncated damping constant, in the range beyond that.

[0051] Next, the response calculation unit 213 of the control unit 210 calculates the equivalent damping constant ζ eq Using the above formula, it is possible to calculate the acceleration response spectrum when a frictional force from the support part 20 acts on the structure 10 (step S106 in FIG. 3). In this embodiment, it is assumed that a hysteretic frictional force acts as shown in FIG. 6, for example, and the equation of motion in the axial direction of the structure 10 (the Z-axis direction in FIGS. 1A and 1B) can essentially be expressed by the following formulas (13) and (14).

[0052]

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[0053] In this embodiment, in order to avoid nonlinear analysis including a sign function, the equivalent damping constant ζ expressed by the following formula (15) is used instead of formulas (13) and (14). eq The acceleration response spectrum etc. is calculated using the equation of motion including

[0054]

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[0055] When calculating the acceleration response spectrum using Equation (15), the control unit 210 performs eigenvalue analysis and calculates the equivalent damping constant ζ eqA spectral modal analysis is performed using the above method to calculate the response acceleration for each mode. The obtained response accelerations are combined using a method such as the SRSS (Square Root of Sum of Squares) method to calculate the acceleration response spectrum of the structure 10 such as a pipe.

[0056] Although not shown in FIG. 3, the acceleration response spectrum of the structure 10 may be calculated using a correction formula expressed by the following formula (16) with reference to Reference 7. (Reference 7) Kazuhiko Kawashima and Osamu Aizawa, "Correction Method of Earthquake Response Spectrum for Damping Constants," Transactions of the Japan Society of Civil Engineers, Vol. 1984, No. 344, pp. 351-355, 1984.

[0057]

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[0058] Figure 7 shows a comparison of acceleration response spectra obtained using different analysis methods. The input seismic wave data was from Kobe (NS) with a maximum input velocity of 100 kine.

[0059] According to Figure 7, the results of calculating the acceleration response spectrum etc. using the equation of motion in Equation (15) (thick solid line) are in excellent agreement with the results of calculating the acceleration response spectrum etc. using the correction equation in Equation (16) (thick dashed line). Therefore, when the acceleration response spectrum considering a damping constant of 5% has already been calculated, it is possible to use the correction equation to calculate the friction force as the equivalent damping constant ζ eq The acceleration response spectrum that takes this into account can be calculated with a relatively light calculation load.

[0060] In addition, the friction force is expressed as the equivalent damping constant ζ eq The acceleration response spectrum taking into account frictional forces is reduced to about half the maximum acceleration, particularly in the period between 0.1 sec. and 1.0 sec., compared to the acceleration response spectrum obtained using a linear model that does not take frictional forces into account. Therefore, compared to conventional countermeasures that use analysis results that do not take frictional forces acting between the structure 10 and the support 20 into account, excessive countermeasures such as adding or strengthening the support 20 can be effectively prevented.

[0061] In addition, the friction force is expressed as the equivalent damping constant ζ eq The acceleration response spectrum considering the friction force as a nonlinear sign function (Equations (13) and (14)) is slightly larger in the period between 0.1 sec. and 1.0 sec. Therefore, the friction force is considered as a nonlinear sign function (Equations (13) and (14)). eq By taking measures such as adding or strengthening the support parts 20 in accordance with the acceleration response spectrum that takes this into consideration, it is possible to make it less likely that problems will occur due to insufficient addition or strengthening of the support parts 20.

[0062] As described above, this embodiment is a method for evaluating the seismic resistance of a structural assembly 100 having a structure 10 and a support portion 20 that supports the structure 10, and in which a frictional force acts on the structure 10 from the support portion 20, and includes the steps of preparing a calculation model of the structure 10 and the support portion 20, and calculating an equivalent damping constant ζ when it is assumed that the absorbed energy due to structural damping of the structure 10 is equal to the damping energy due to the frictional force acting on the structure 10. eq and the equivalent damping constant ζ eq and calculating the response to vibration input using the above-mentioned method. By adopting such a configuration, it is possible to perform seismic evaluation of the structure 10 on which frictional force acts from the support parts 20 without performing nonlinear analysis, and therefore it is possible to take measures such as appropriate addition or reinforcement of the support parts 20 using general-purpose analysis means.

[0063] In this embodiment, the equivalent damping constant ζ eqis calculated based on the maximum response displacement of the structure 10 obtained from the energy spectrum at the time of vibration. By adopting such a configuration, the equivalent damping constant ζ eq can be calculated and response analysis can be performed.

[0064] In this embodiment, the structure 10 is a pipe, the support 20 is a fixed member that surrounds the pipe from the outside in the radial direction, and the response is configured to be the response in the axial direction of the pipe. By adopting such a configuration, it is possible to evaluate the displacement, acceleration, etc. in the axial direction of the pipe where frictional force acts without performing nonlinear analysis, so that it is possible to perform seismic evaluation in the axial direction of piping in nuclear power plants, etc. using general-purpose analysis means.

[0065] Furthermore, this embodiment is a seismic evaluation system 200 for a structural assembly 100, which has a structure 10 and a support part 20 that supports the structure 10, and in which a frictional force acts on the structure 10 from the support part 20, and includes a model storage part 221 that has a calculation model of the structure 10 and the support part 20, and an equivalent damping constant ζ when it is assumed that the absorbed energy due to structural damping of the structure 10 is equal to the damping energy due to the frictional force acting on the structure 10. eq a damping constant calculation unit 211 that calculates an equivalent damping constant ζ eq and a response calculation unit 213 that calculates the response to vibration input using the above-mentioned equation. By adopting such a configuration, it is possible to perform seismic evaluation of the structure 10 on which frictional force acts from the support parts 20 without performing nonlinear analysis, and therefore it is possible to take measures such as appropriate addition or reinforcement of the support parts 20 using general-purpose analysis means.

[0066] Next, a method for evaluating the seismic resistance of the structure assembly 100 according to the second embodiment of the present disclosure will be described in detail with reference to FIGS. 8 to 11 and the like.

[0067] In addition, the method for evaluating the seismic resistance of the structure assembly 100 according to this embodiment has a function of reducing the equivalent damping constant ζ eqThe method for calculating the maximum response displacement X for calculating σ is different, but the method is similar to the seismic evaluation method for the structure assembly 100 according to the first embodiment. Therefore, the differences from the first embodiment will be mainly explained here. The configuration of the seismic evaluation system 200 also has the configuration shown in Fig. 2, except for some differences in the processing by the control unit 210, as will be described later.

[0068] The procedure for carrying out the seismic evaluation method for the structure assembly 100 according to this embodiment using the seismic evaluation system 200 will be described in detail with reference to FIG. 8 and other figures.

[0069] As in the first embodiment, the control unit 210 acquires a calculation model of the structure 10 and the support unit 20 via the input unit 250 or the communication unit 230, and stores the calculation model in the model storage unit 221 of the memory unit 220 (step S201 in Figure 8).

[0070] Next, the control unit 210 performs a single mass response analysis considering only the structural damping of the piping system, and calculates the maximum response displacement X at each natural period from the equation of motion expressed by the following formula (17) (step S202 in FIG. 8).

[0071]

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[0072] FIG. 9 shows the relationship between the period T and the displacement when "Kobe (NS)" is used as the acceleration data of the seismic wave, calculated in step S202.

[0073] Next, as in the first embodiment, the damping constant calculation unit 211 of the control unit 210 calculates the equivalent damping constant ζ by the above-mentioned formula (11) by assuming that "the damping energy due to frictional force is equal to the absorbed energy due to structural damping." eq (Step S203 in FIG. 8). The control unit 210 calculates the calculated equivalent damping constant ζ eq may be stored in the storage unit 220, displayed on the display unit 240, or transmitted to an external device via the communication unit 230. Fig. 10 shows the equivalent damping constant ζ calculated from the displacement (maximum response displacement X) at each natural period when Kobe (NS) shown in Fig. 9 is used as the input seismic wave. e This is an example.

[0074] As shown in FIG. 10, in this embodiment, the equivalent damping constant ζ e The equivalent damping constant ζ is truncated at 50%, including the structural damping of the piping system of 0.5%. e tends to be smaller when the natural period is in the range of 0.1 to 1 second, and tends to be larger when the natural period is in the range of 1 to 10 seconds than when the natural period is in the range of 0.01 to 0.1 seconds.

[0075] Next, the response calculation unit 213 of the control unit 210 calculates the equivalent damping constant ζ eq is used to calculate the acceleration response spectrum etc. when a frictional force from the support part 20 acts on the structure 10 (step S204 in FIG. 8).

[0076] In this embodiment, similarly to the first embodiment, in order to avoid nonlinear analysis including a sign function, the equivalent damping constant ζ expressed by the formula (15) is used instead of the formulas (13) and (14). eq The acceleration response spectrum etc. is calculated using the equation of motion including

[0077] Moreover, similarly to the first embodiment, the acceleration response spectrum of the structure 10 is calculated using the correction formula expressed by Equation (16).

[0078] Figure 11 shows a comparison of acceleration response spectra obtained using different analysis methods. The input seismic wave data is from Kobe (NS) with a maximum input velocity of 100 kine.

[0079] According to Figure 11, the results of calculating the acceleration response spectrum etc. using the equation of motion in Equation (15) (thick solid line) are in excellent agreement with the results of calculating the acceleration response spectrum etc. using the correction equation in Equation (16) (thick dashed line). Therefore, when the acceleration response spectrum considering a damping constant of 5% has already been calculated, it is possible to use the correction equation to calculate the friction force as the equivalent damping constant ζ eq The acceleration response spectrum that takes this into account can be calculated with a relatively light calculation load.

[0080] In addition, the friction force is expressed as the equivalent damping constant ζ eq In the acceleration response spectrum obtained without considering frictional forces, the maximum acceleration is reduced to about two-thirds, particularly in the period between 0.1 sec and 1.0 sec. Compared to the acceleration response spectrum obtained without considering frictional forces, the acceleration response spectrum obtained with considering frictional forces is reduced to about two-thirds, particularly in the period between 0.1 sec and 1.0 sec. Therefore, compared to the results of conventional linear analysis that do not consider frictional forces acting between the structure 10 and the support 20, excessive measures such as adding or strengthening the support 20 can be effectively prevented.

[0081] In addition, the friction force is expressed as the equivalent damping constant ζ eq The acceleration response spectrum considering the friction force as a nonlinear sign function (Equations (13) and (14)) is slightly larger in the period between 0.1 sec. and 1.0 sec. Therefore, the friction force is considered as a nonlinear sign function (Equations (13) and (14)). eq By taking measures such as adding or strengthening the support parts 20 in accordance with the acceleration response spectrum that takes this into consideration, it is possible to make it less likely that problems will occur due to insufficient addition or strengthening of the support parts 20.

[0082] As described above, in this embodiment, the equivalent damping constant ζ eqis calculated based on the maximum response displacement of the structure 10 obtained from a response analysis that takes into account only structural damping. By adopting such a configuration, the equivalent damping constant ζ eq can be calculated to perform a response analysis that takes frictional forces into account.

[0083] Although the present disclosure has been described based on the drawings and examples, it should be noted that those skilled in the art can easily make various modifications or alterations based on the present disclosure. Therefore, it should be noted that these modifications and alterations are included in the scope of the present invention. For example, the functions included in each component can be rearranged so as not to cause logical inconsistencies, and multiple components can be combined or divided into one.

[0084] For example, in this embodiment, the structure 10 is assumed to be a pipe, and the support part 20 is assumed to be a U-shaped fixing member shown in Figures 1A and 1B, but this is not limited to this form and can also be applied to structures 10 of other shapes and supporting parts 20 that fix them.

[0085] In addition, in this embodiment, the response calculation unit 213 is configured to calculate the acceleration response spectrum for the vibration input, but is not limited to this, and may be configured to calculate other responses such as velocity or displacement. [Explanation of symbols]

[0086] 10 Structures 20 Support part 21 Encirclement 23 Base Plate 25 Fastening screw 100 Structure assembly 200 Earthquake Resistance Evaluation System 210 Control Unit 211 Attenuation constant calculation section 213 Response Calculation Unit 220 Storage section 221 Model Storage Unit 230 Communications Department 240 Display section 250 Input section

Claims

1. A method for seismic evaluation of a structure assembly, comprising: a structure; and a support portion that supports the structure; and a frictional force acting on the structure from the support portion, the method comprising: providing a computational model of the structure and the support; calculating an equivalent damping constant when it is assumed that the absorbed energy due to structural damping of the structure is equal to the damping energy due to the friction force acting on the structure; calculating a response to a vibration input using the equivalent damping constant; A method for seismic evaluation of a structural assembly, comprising:

2. 2. The method for evaluating the seismic resistance of a structural assembly according to claim 1, wherein the equivalent damping constant is calculated based on a maximum response displacement of the structure obtained from an energy spectrum during vibration.

3. 2. The method for seismic evaluation of a structural assembly according to claim 1, wherein the equivalent damping constant is calculated based on a maximum response displacement of the structure obtained from a response analysis that takes into account only structural damping.

4. 3. The seismic evaluation method for a structural assembly according to claim 1, wherein the structure is a pipe, the support portion is a fixed member surrounding the pipe from the radial outside, and the response is an axial response of the pipe.

5. A seismic evaluation system for a structural assembly, comprising: a structure; and a support portion that supports the structure, wherein a frictional force acts on the structure from the support portion, a model storage unit having a calculation model of the structure and the support; a damping constant calculation unit that calculates an equivalent damping constant when it is assumed that the absorbed energy due to structural damping of the structure is equal to the damping energy due to the friction force acting on the structure; a response calculation unit that calculates a response to a vibration input using the equivalent damping constant; A system for seismic evaluation of a structural assembly, comprising:

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