Simplified method for evaluating the seismic margin of power transmission towers

Abstract

Provided is a method for evaluating the seismic margin of a simple and efficient transmission tower. 【Solution means】Based on various data of all the towers G belonging to the tower group G in the computer database 1 lim , m-n , lim , p , p , T ,the static elastic response deformation φ at the top of the tower G caused by the seismic load Q acting on the panel i stacked in the height direction of the tower G m-n is calculated, where the seismic load Q is replaced by the equivalent bending rigidity E·I m-n and the equivalent shear rigidity G·A i of each panel i to form an equivalent cantilever beam model of the tower G i ,and the deformation φ at the top when the web members of the panel i buckle under the seismic load Q si ,the deformation φ at the top when the main column material reaches the compressive endurance limit m-n are calculated from predetermined approximate formulas respectively. The values of the top deformations φ e ,φ i are substituted into a predetermined formula to calculate the elastoplastic response deformation φ y occurring at the top of the tower G,and the ratio φ lim / φ e is calculated as the seismic index value DCR y of the tower G. The above procedure is executed for all the towers.​​​​​​​​​​​​​​

Description

[Technical Field]

[0001] This invention relates to a method for easily evaluating the margin of safety for seismic resistance of power transmission towers. [Background technology]

[0002] Traditionally, tower-like structures such as steel towers, lacking exterior finishes and being relatively lightweight, have often been dominated by wind loads, and seismic load considerations have frequently been omitted. However, in recent years, with the increasing magnitude of earthquakes, it has become necessary to increase the assumed input earthquake motion and to clarify seismic performance to understand the seismic margin for structures, including existing steel towers.

[0003] Among existing tower-like structures, transmission towers are particularly numerous, with approximately 250,000 currently existing nationwide. As mentioned above, seismic load considerations have been omitted, so there is an urgent need to address insufficient resistance to increased assumed seismic motion, or to prepare for the replacement of towers that will exceed their service life in the near future.

[0004] However, since it is practically impossible to immediately reinforce or rebuild this vast number of transmission towers, it is necessary to prioritize each response by some means, and the means for doing so should be simple and efficient based on a rational standard.

[0005] In the structural design of transmission towers, the ratio of member stress σ to allowable stress f for each constituent member, σ / f, is used to determine if all members are within the elastic range. Therefore, in seismic diagnosis, it is common practice to check the margin of safety in the stress ratio σ / f of each member against the assumed seismic load. However, as mentioned above, this method of individually calculating the stress of a vast number of transmission towers and taking countermeasures based on a binary judgment—that it is dangerous if there are members with insufficient margin, and safe if there are none—does not allow for prioritization based on the difference in deformable reserve capacity from response deformation after structural yielding to the safe limit deformation, i.e., seismic margin, making practical responses difficult. Therefore, a more rational method for evaluating the seismic margin of transmission towers has been desired.

[0006] One simple method for evaluating the seismic margin of structures similar to transmission towers is, for example, Patent Document 1, which discloses a simple seismic evaluation method for outdoor steel structures of substations. The seismic evaluation method described in Patent Document 1 is characterized by utilizing the engineering phenomenon that, once the voltage class is determined, the height and span of outdoor steel structures of substations become almost the same, and the member sizes also become almost the same. Therefore, if the voltage class is the same, the characteristics of a representative steel structure of the same class can be approximately applied to any steel structure being evaluated that belongs to the same class.

[0007] The aforementioned evaluation method is divided into a preparation phase and an evaluation implementation phase. As a preliminary step, we obtain a regression equation for the relationship between the beam attachment height H and the first natural period T1 of a representative steel structure (hereinafter referred to as Relationship 1) from the eigenvalue analysis of detailed models (three-dimensional elastic models) of several typical representative steel structures belonging to that voltage class.

[0008] A time history response analysis using multiple assumed seismic waves was performed on the detailed model described above to obtain the primary natural period T1 and the maximum acceleration response value A corresponding to that primary natural period T1. x1 The relationship (hereinafter referred to as Relationship 2) is determined as the acceleration response spectrum.

[0009] The ratio of the stress σ of a specific member obtained from the time history response analysis to the short-term allowable stress f of that member, σ / f, is calculated, and the maximum acceleration response value A corresponding to the first natural period T1 is obtained. x1 The relationship between this and the aforementioned short-term allowable stress ratio σ / f (hereinafter referred to as Relationship 3) is determined as a regression equation.

[0010] During the evaluation phase, for any outdoor steel structure (I) whose seismic resistance is to be evaluated, the primary natural period t1 is calculated using the relationships 1 to 3 described above, and the maximum acceleration response value a is calculated. x1 We estimate the short-term allowable stress ratio σ / f for specific members of the outdoor steel structure I.

[0011] If the calculated short-term allowable stress ratio σ / f of the specified member exceeds 1.0, outdoor steel structure A is determined to be an outdoor steel structure requiring reinforcement study, and the priority of reinforcement studies is determined based on the relative magnitude of the short-term allowable stress ratio σ / f of other outdoor steel structures that require reinforcement study.

[0012] As described above, Patent Document 1 states that by using a simplified method that includes omitting time history response analysis for the outdoor steel structure A under consideration, it becomes possible to prioritize outdoor steel structures requiring reinforcement in a short time, resulting in significantly greater efficiency and cost reduction compared to conventional methods.

[0013] However, in the evaluation method of Patent Document 1, the stress ratio of a specific member is estimated from various relationships obtained based on the results of elastic model analysis. If the specific member is, for example, a main column, then when comparing towers where the stress ratio of the main column exceeds 1.0, the stress state of the web members of each tower is unknown. Therefore, the difference in the deformable margin from response deformation after structural yielding to the safety limit deformation, i.e., the difference in seismic margin, cannot be determined from the magnitude of the stress ratio of the main column. [Prior art documents] [Patent Documents]

[0014] [Patent Document 1] Patent No. 6542012 [Overview of the Initiative] [Problems that the invention aims to solve]

[0015] This invention provides a simple and efficient method for evaluating, based on a common and rational scale, how much margin of safety remains for the vast number of power transmission towers currently existing in Japan before they collapse under assumed seismic loads. [Means for solving the problem]

[0016] The first means of the present invention for solving the above problems is a method for evaluating the seismic margin of a steel tower, which is executed by a computer according to the procedure described below. (Step 1) Various data lists of the steel towers to be examined sorted by group under certain conditions, and data of the design acceleration response spectrum according to the ground type are stored in advance in the storage device of the computer as Database 1. By the input device of the computer, the first steel tower group G to be examined m is selected by inputting the group number m.

[0017] Database 1 A) Various data lists of the steel towers to be examined sorted by group · Group number m (1 to M), steel tower number n (1 to N) · Voltage scale, steel tower type, construction site (ground condition) · Height H, base opening B, panel dimensions (height, width) · Member size (main column material, web member) · Fixed load W i (Self-weight of panel, weight of cross span wire) · Cross span wire support type (suspension type, strain type), horizontal angle B) List of the design acceleration response spectrum · Acceleration response spectrum (ground type: type 1, type 2, type 3)

[0018] (Step 2) The group number m input in Step 1 is compared with the various data lists of the steel towers to be examined sorted by group in the Database 1, and all the steel towers G m belonging to the steel tower group G m-n (n = 1 to N) are obtained, and also the data of the design acceleration response spectrum according to the ground type stored in advance are obtained.

[0019] (Step 3) The natural periods T0 of all the steel towers G m-n (n = 1 to N) obtained in Step 2, and those steel towers G m-nThe design acceleration response spectrum is matched with the ground conditions of the construction site. The natural period T0 can be approximated by preparing an approximate formula in advance, for example, based on numerical values ​​(detailed solution) obtained by performing an eigenvalue analysis on a three-dimensional frame model of a similar tower group beforehand. However, for simplicity, an existing first-order natural period estimation formula (T0 (seconds) = H / 100, H: tower height in m) can also be used.

[0020] (Step 4) By matching with the design acceleration response spectrum, the tower G m-n The natural period T0 of (n=1~N) is the upper limit period T of the constant acceleration region of the design acceleration response spectrum. c Super(T0>T c ) If so, it falls outside the scope of the assumption of using the constant energy law, and is therefore excluded as it will be considered separately, and the upper period T c (T0≦T) c If so, proceed to step 5.

[0021] (Step 5) Tower G identified as the subject of consideration in Step 4 m-n Based on the various data obtained in step 2, the transmission tower G m-n The seismic load Q acts on each panel i, which is stacked in the vertical direction and consists of main columns of a certain height, bracing members (web members), and horizontal members. i However, it is calculated by the computer's arithmetic unit based on a predetermined calculation formula (a) for calculating the equivalent static seismic load. Here, the symbol i is the panel number counted from the top of the tower.

[0022] Formula (i) Transmission Tower G m-n Calculation of equivalent static seismic load Q (i=1~l) Q i =R t ·C h ·A i ·W i ···(stomach) Q i : Layer shear force of the i-th panel from the top R t : Response characteristic coefficient (suspension type, tension type) C h: Correction coefficient related to damping A i : Story shear force distribution coefficient (track direction, orthogonal direction) W i : Total weight of panels above the center of the i-panel

[0023] (Step 6) Tower G identified as the subject of consideration in Step 4 m-n Based on the various data obtained in step 2, the transmission tower G m-n The equivalent bending stiffness E·I of the aforementioned panel i i and equivalent shear stiffness G·A si However, this is calculated by the arithmetic unit of the aforementioned computer.

[0024] (Procedure 7) The aforementioned tower G m-n This is the equivalent bending stiffness E·I calculated in step 6. i and equivalent shear stiffness G·A si Considering the panels i having the same configuration as a cantilever beam formed by continuously stacking them, the tower G calculated in step 5 m-n Seismic load Q i When it acts, the transmission tower G is generated. m-n Static elastic response deformation φ at the apex e However, this is calculated by the arithmetic unit of the aforementioned computer. The static elastic response deformation φ e For simplicity, the calculation method can be, for example, the virtual work method. Here, the ratio of the horizontal displacement at the top to the tower height is defined as the top deformation. The same applies hereafter.

[0025] (Step 8) As described above, tower G is considered to be a single cantilever beam. m-n All panels i are subjected to seismic load Q i When the force acts on the tower G, it is estimated that the bracing material of one of the panels i will buckle. m-n Top deformation φ y However, transmission tower G m-n It is calculated by the computer's arithmetic unit using a predetermined approximation formula (b) that is applied to similar groups of transmission towers.

[0026] Approximation formula (b) Tower G during buckling of bracing members m-n Top deformation φ y Calculation φ y = y1 + y2 · (H / B)

[0027] (Procedure 9) Here, the coefficients used in the predetermined approximation formula (b) are the pre-determined and organized transmission tower G that are stored in the computer's memory as database 2. m-n The search is performed using a list of coefficients for similar tower clusters.

[0028] Database 2 (Group-based) List of coefficients related to tower top deformation (Based on static incremental analysis results considering buckling of the bracing material) ·When buckling the belly material (φ y ): y1, y2 ·When the main column buckles (φ lim ): l1, l2

[0029] (Step 10) Tower G is treated as a single equivalent cantilever beam. m-n All panels i are subjected to seismic load Q i The force acting on the tower G is estimated to have reached the compressive limit strength at which one of the main support members will buckle. m-n Top deformation φ lim However, transmission tower G m-n It is calculated by the computer's arithmetic unit using a predetermined approximation formula (c) that is applied to a group of transmission towers similar to the one in question.

[0030] Approximation formula (c) Tower G during buckling of main column member m-n Top deformation φ lim Calculation φ lim = l1 + l2 · (H / B)

[0031] (Procedure 11) Here, the coefficients used in the predetermined approximation formula (c) are the pre-determined and organized pylon G that are stored in the computer's memory as database 2. m-n The search is performed using a list of coefficients for similar tower clusters.

[0032] (Step 12) Tower G calculated in Steps 7-11 m-n Each of the deformations φ at the top e , φy The value is substituted into a predetermined formula (II) with these as variables, and when the seismic load Q i acts, the plastic response deformation φ m-n occurring at the top of the tower G p is obtained.

[0033] Formula (II) For the tower G m-n Calculation of the plastic response deformation φ p at the top φ p =〔(α - 1)·φ y +√{(1 - α)·φ y 2 +α·φ e 2}〕 / α However, α is the rigidity reduction rate with respect to the initial rigidity after the web buckling

[0034] (Step 13) Then, taking the top deformation φ m-n of the tower G lim as the safety limit deformation, the ratio φ p of the plastic response deformation φ p to this, φ lim / φ m-n is calculated by the arithmetic unit of the computer as the seismic resistance index value DCR T of the tower G

[0035] (Step 14) For all the towers belonging to the tower group G m , if the seismic resistance index value DCR T has not been calculated (n < N), set n = n + 1 and return to Step 5, and Steps 5 to 13 are repeated for the next tower G m-n . Otherwise (n = N), proceed to the next Step 15. For the towers excluded from consideration in Step 4, Steps 5 to 13 are skipped.

[0036] (Step 15) Proceed to the next tower group G m , and for each tower belonging to this, Steps 1 to 14 for calculating the seismic resistance index value DCR T are repeated until n = N, and this repetition is performed for all the tower groups G mIf not completed for (m < M), set m = m + 1, return to step 1, and repeat steps 1 to 14 for each tower belonging to the next tower group G m Otherwise (m = M), assuming that the calculation of the seismic index value DCR for all towers is completed, all calculation results are output by the output device of the computer (step 16). T A method for simple evaluation of the seismic margin of a transmission tower, characterized by including the above steps. A method for simple evaluation of the seismic margin of a transmission tower, characterized by including the above steps.

[0037] Further, the second means of the present invention is, in the first means of the present invention, the equivalent bending rigidity E·I i and the equivalent shear rigidity G·A si For the tower G for which the above are calculated m-n A method for simple evaluation of the seismic margin of a transmission tower, characterized by including a procedure for identifying whether the shear resistance of the panel i is determined by either the compression buckling or the joint tensile fracture of the web members constituting the panel i.

[0038] Also, in the method for simple evaluation of the seismic margin of a transmission tower, the database 2 relates to the various coefficients used in the predetermined approximate formulas (b) and (c). A plurality of three-dimensional analysis models of a group of towers similar to the tower to be considered are created, and the web members of those models are used as elasto-plastic truss elements. The coefficients of the approximate formulas obtained by regression from the results of performing a static load increment analysis of the tower structure with web member buckling are approximate formulas that approximate the relationships between the ratio of the height H / span B and the top deformation φ y when any web member of the tower structure buckles, and the relationship between the top deformation φ lim when the main column member of the tower structure reaches the compressive limit bearing capacity, and are organized and listed. A method for simple evaluation of the seismic margin of a transmission tower, characterized by this.

[0039] Note that in the evaluation method according to the present invention, since the replacement and reinforcement of the web members are relatively easy, it targets the case where the buckling of the web members precedes that of the main column members of the tower. For such existing towers, it utilizes the following characteristics confirmed by the present inventor up to the present time.

[0040] (a) Even if the actual steel tower is replaced with a simple single - span beam model that can be calculated manually, the static elastic behavior has no practically problematic difference compared to the case of the three - dimensional analysis model. (b) In similar steel tower series, the top deformations (φ y , φ lim ) with respect to the input seismic load can be regarded as having a linear relationship with the ratio of height H / span B. (c) For transmission steel towers, even if the web members buckle earlier than the main column members, the reduction in the rigidity of the entire steel tower is small, and stable hysteretic characteristics can be expected. (d) In the non - linear relationship between the input seismic load and the top deformation of a steel tower with web member buckling, when the fundamental natural period of the steel tower is generally considered to be included in the constant - acceleration region of the acceleration response spectrum (see Fig. 3(c)), the generally known energy conservation law can be used to estimate the elastic - plastic response deformation at the top.

Advantages of the Invention

[0041] Since the present invention is a simple method for evaluating the seismic margin of a transmission steel tower using a computer according to the above - mentioned procedure, it has the following effects.

[0042] 1) For a transmission steel tower in which the buckling of the web members precedes that of the main column members with respect to seismic loads, no matter which position (panel) the web members buckle, the reduction in the rigidity of the entire steel tower is small, and stable hysteretic characteristics can be expected. Therefore, a seismic performance curve for estimating the seismic margin of the steel tower can be determined in a simple manner as the relationship between the input seismic load and the deformation represented at the top of the steel tower. Thus, in the practical process of evaluating the seismic margin of a steel tower, three - dimensional analysis of the structure and time - history response analysis are not required.

[0043] 2) The static elastic response deformation (φ e ) at the top of the steel tower, the elastic - plastic response deformation (φ y ) after web member buckling, and the time - dependent deformation (φ limSince the seismic margin of the transmission tower is calculated from these three values, unlike conventional seismic diagnoses which make a binary judgment of whether it is dangerous if there are members with insufficient margin or safe if there are none, based on the stress ratio calculation of individual members, it is possible to relatively grasp the difference in the deformable reserve capacity from the response deformation after yielding of the bracing members to the safe limit deformation, i.e., the difference in seismic margin, based on a rational scale.

[0044] 3) This invention enables efficient relative evaluation of seismic margins based on a common rational scale, and can greatly contribute to reducing time, effort, and costs when examining the approximately 250,000 power transmission towers currently existing throughout Japan. [Brief explanation of the drawing]

[0045] [Figure 1(a)] This is an example of a flowchart for a simplified seismic safety margin evaluation method for transmission towers according to the present invention. [Figure 1(b)] Figure 1(a) shows an example with added procedures for identifying towers where bracing material fracture occurs first. [Figure 2] Examples of the shapes of power transmission towers considered in this invention (two series each for heights H=30m and 40m) are shown. [Figure 3] This is a schematic diagram of the relationship between the base shear Q and the top displacement δ1 of a transmission tower, where (a) is the seismic performance curve of the transmission tower according to the present invention, (b) is a conceptual diagram explaining the constant energy law, and (c) is an explanatory diagram of the constant acceleration region of the acceleration response spectrum. [Figure 4] This diagram illustrates a method for replacing a transmission tower with a simplified structural model. (a) is an image of an equivalent cantilever beam formed by stacking panels, and (b) is a diagram showing the bending moment distribution resulting from the horizontal force acting on each panel. [Figure 5] This is an explanatory diagram illustrating the configuration of one panel of a transmission tower, where (a) is a plan view and (b) is an elevation view. [Figure 6]Figures 4 and 5 show calculation examples in which the accuracy of the horizontal displacement (horizontal axis) of each panel obtained by the virtual work method for the equivalent cantilever beam was compared with the horizontal displacement (vertical axis) of each panel obtained by the elastic analysis of the stereoscopic analysis model. (a) is a graph in the direction of the overhead line, and (b) is a graph in the direction perpendicular to the line. [Figure 7] This diagram outlines the three-dimensional analysis models used for elastoplastic analysis of several similar tower series. (a) shows the overall structure, (b) shows the hysteresis rule for static incremental analysis of the web members modeled with elastoplastic truss elements, and (c) shows the hysteresis rule for time history response analysis. However, all materials except the web members are assumed to be elastic. [Figure 8] Figure 7 shows the results of an incremental static load analysis using the 3D analysis model (types (1) and (3) of the transmission towers in Figure 2), illustrating the relationship between the input seismic load (base shear coefficient CB) and the top deformation φ up to the point when the main column member reaches its compressive limit (safety limit). (a) is the case in the direction of the overhead line, and (b) is the case perpendicular to the line. Note that in the figure, the top deformation φ (=δ1 / H) is denoted as φ1. The same applies to Figures 9-11. [Figure 9] Figure 8 schematically represents the relationship between the input seismic load (base shear coefficient CB) and the top deformation φ using a bilinear curve. The second gradient after buckling (yielding) of the web members indicates that the rate of stiffness reduction compared to the first gradient is α (=k2 / k1). [Figure 10] The graph in Figure 7 shows the elastoplastic analysis results of the 3D analysis model (corresponding to the tower in Figure 2), organizing the deformation φ at the top of the tower by the ratio of height H to base spread B. (a) shows the deformation φy when the web members buckle, and (b) shows the deformation φlim when the main column members reach their compressive limit strength. [Figure 11] This graph shows the correspondence between the results of the static load incremental analysis (horizontal axis) and the results of the time history response analysis (vertical axis) using the 3D analysis model in Figure 7 (corresponding to the tower in Figure 2) for the deformation φlim of the main column member at its compressive limit strength. (a) shows the case in the direction of the overhead line, and (b) shows the case perpendicular to the line. [Figure 12]This graph compares the results of the simplified seismic resistance index DCRT (invention) with the corresponding time history response analysis results, with (a) showing the case in the direction of the overhead line and (b) showing the case perpendicular to the line (see Tables 1 and 2). [Modes for carrying out the invention]

[0046] Embodiments of the present invention will be described with reference to Figures 1 to 11. Figure 1 is an example of a flowchart for a simplified seismic margin evaluation method for a transmission tower according to the present invention. The target transmission tower is, for example, as shown in Figure 2, a transmission tower with four main columns, each of which is composed of a double Warren truss and has crossarms to which overhead wires are attached near the top. The web members are angle members, and the main columns are angle members or steel pipes.

[0047] The basic concept of the seismic safety margin evaluation method of the present invention is to use a seismic performance curve that represents the nonlinear relationship between the input seismic load (base shear) Q and the displacement δ at the top of the transmission tower, as shown in Figure 3(a), and the elastic limit (branch buckling) point δ. y and the safety limit (main column buckling) point δ lim The elastoplastic response displacement δ at the top of the tower, corresponding to the assumed seismic load level, is defined using the constant energy law, as shown in Figure 3(b). p Determine the safety limit displacement δ lim This estimates how much leeway there is until the deadline.

[0048] An embodiment of the first means of the present invention will be described below with reference to the flowchart in Figure 1. (Procedure 1) Various data lists of the towers under consideration, organized into groups under certain conditions, and data of design acceleration response spectra according to the type of ground are stored in the computer's storage device as database 1 in advance, and the first tower group G to be considered is entered into the computer's input device. m The group number 'm' is entered for selection purposes.

[0049] (Step 2) The group number m entered in Step 1 is compared with the various data lists of the towers under consideration, which are organized by group in the database 1, and the corresponding tower group G m All transmission towers G belonging to this group m-n Various data related to (n=1~N) are acquired, and similarly, data on the design acceleration response spectrum corresponding to the ground type, which is stored in advance, is also acquired.

[0050] It is desirable that the transmission towers under consideration be organized into groups of similar towers. For example, as shown in Figures 2(1) to (4), these could be similar tower types with almost the same mounting configuration of the crossarms and height H, but with different base spreads B.

[0051] (Step 3) All of the aforementioned transmission towers G obtained in Step 2 m-n The natural period T0 (n=1~N) and the corresponding transmission tower G m-n The system is then compared with the design acceleration response spectrum, which is set according to the ground conditions of the construction site (subroutine A).

[0052] Regarding the natural period T0, it is possible to prepare an approximate formula in advance based on numerical values ​​(detailed analysis) obtained by performing eigenvalue analysis on the three-dimensional structural model of each tower. However, considering that it will be used for screening purposes to evaluate the seismic margin of the towers, a simpler method may be used, which is the commonly used conventional first-order natural period estimation formula (T0 (seconds) = H / 100, H: tower height in m).

[0053] (Step 4) By matching with the design acceleration response spectrum, the tower G m-n The natural period T0 of (n=1~N) is the upper limit period T of the constant acceleration region (see Figure 3(c)) of the design acceleration response spectrum. c Super(T0>T c ) If so, it falls outside the scope of the assumption of using the constant energy law, and is therefore excluded as it will be considered separately, and the upper period T c (T0≦T) c If so, proceed to step 5.

[0054] (Step 5) Tower G identified as the subject of consideration in Step 4 m-n Based on the various data obtained in step 2, the transmission tower G m-n The seismic load Q acts on each panel i, which is stacked in the vertical direction and consists of main columns of a certain height, bracing members (web members), and horizontal members. i Equation (a) in Figure 1(5) is calculated by the arithmetic unit of the computer. Here, the symbol i is the panel number counted from the top of the tower.

[0055] The seismic load used here is, for example, the seismic load Q acting on each panel i, as described in the Electrical Cooperative Research Association's "Seismic Design of Transmission Towers and its Challenges" (Vol. 73, No. 3, March 2018). i This may be set. Note that there are two types of transmission towers: suspension type, where the overhead wires are simply suspended from the crossarms, and tension type, where tension is normally applied to the overhead wires. Furthermore, it should be noted that the input load values ​​differ depending on whether the overhead wires are extended in the direction of the line or perpendicular to it.

[0056] (Step 6) Tower G identified as the subject of consideration in Step 4 m-n Based on the various data obtained in step 2, the transmission tower G m-n The equivalent bending stiffness E·I of the aforementioned panel i i and equivalent shear stiffness G·A si However, this is calculated by the arithmetic unit of the aforementioned computer.

[0057] When a predetermined seismic load acts on a transmission tower, it is necessary to determine the seismic energy absorbed by the tower. For simplicity, as shown in Figure 4, the transmission tower is replaced with a non-uniform, equivalent cantilever beam model in which numerous panels, consisting of main columns of a certain height and bracing members and horizontal members, are stacked to have cross-sections of each stiffness calculated in step 6.

[0058] The configuration of one panel of the transmission tower, as shown in the plan view of Figure 5(a), consists of main column members (two on the compression side and two on the tension side) and bracing members (cross braces) installed on the structural planes of each of the two main column members on the compression side and the two main column members on the tension side, which act as cross-sectional elements that resist bending, and the equivalent bending stiffness E·I of panel i i That will be decided.

[0059] Furthermore, as shown in the panel elevation view in Figure 5(b), the horizontal shear resistance elements of the panel are the cross sections of pairs of intersecting bracing members, and the equivalent shear stiffness G·A is derived from their inclination angle. si This will be decided.

[0060] (Procedure 7) The aforementioned tower G m-n This is the equivalent bending stiffness E·I calculated in step 6. i and equivalent shear stiffness G·A si Considering the panels i having the same configuration as a cantilever beam formed by continuously stacking them, the tower G calculated in step 5 m-n Seismic load Q i When it acts, the transmission tower G is generated. m-n Static elastic response deformation φ at the apex e However, this is calculated by the arithmetic unit of the aforementioned computer.

[0061] Static elastic deformation φ e Any method can be used for the calculation, but for example, as mentioned above, it is convenient to replace the actual transmission tower with a simplified cantilever beam model and use the virtual work method, and the accuracy is not so different from the detailed values ​​obtained from a 3D analysis that models all members that it poses a practical problem.

[0062] (Step 8) As described above, tower G is considered to be a single cantilever beam. m-n All panels i are subjected to seismic load Q i When the force acts on the tower G, it is estimated that the bracing material of one of the panels i will buckle. m-n Top deformation φ y However, transmission tower G m-n It is calculated by the computer's arithmetic unit using a predetermined approximation formula (b) (formula b in Figure 1(8)) that is applied to similar groups of transmission towers.

[0063] (Procedure 9) Here, the coefficients used in the predetermined approximation formula (b) are the pre-determined and organized transmission tower G that are stored in the computer's memory as database 2. m-n The search is performed using a list of coefficients for similar tower clusters.

[0064] When it is estimated that the bracing material of the aforementioned panel i will buckle, the tower G m-n Top deformation φ y Regarding the calculation, in similar series of transmission towers, as shown in Figure 10(a), the top deformation φ in response to the input seismic load is y This utilizes the results of a preliminary study, which concluded that there is a linear relationship between the height H and the root spread B.

[0065] (Step 10) Also, tower G, which is considered to be a single equivalent cantilever beam m-n All panels i are subjected to seismic load Q i When the force acts on the tower, it is estimated that one of the main support members will reach its compressive strength limit. m-n Top deformation φ lim However, transmission tower G m-n It is calculated by the computer's arithmetic unit using a predetermined approximation formula (c) (formula c in Figure 1(10)) that is applied to a group of towers similar to the one shown.

[0066] (Procedure 11) Here, the coefficients used in the predetermined approximation formula (c) are the pre-determined and organized pylon G that are stored in the computer's memory as database 2. m-n The search is performed using a list of coefficients for similar tower clusters.

[0067] The tower G when the aforementioned main column is estimated to have reached its compressive limit strength. m-n Top deformation φ lim Regarding the calculation, in similar series of transmission towers, as shown in Figure 10(b), the top deformation φ in response to the input seismic load is lim This utilizes the results of a preliminary study, which concluded that there is a linear relationship between the height H and the root spread B.

[0068] The database 2 used in this invention relates to the coefficients used in the approximation formulas (b) and (c), and was created as follows.

[0069] Multiple 3D analysis models of towers similar to the tower under consideration were created, and the web members of these models were used as elastoplastic truss elements. A regression equation was derived regressively from the results of static load incremental analysis of the tower structure with web member buckling, and the ratio of height H / root spread B and the top deformation φ when any web member of the tower structure buckles. y The relationship with, and the top deformation φ when the main column members of the aforementioned steel tower frame reach their compressive limit strength. lim This is a list that organizes and presents the relationship between the terms and the coefficients obtained when approximating the results for each term with a linear equation.

[0070] Incidentally, Figure 11 compares the results of the static load incremental analysis of the aforementioned tower frame with web member buckling with the results of the time history response analysis using the same frame model. The figure shows the top deformation φ when the main column reaches its compressive limit strength. lim This comparison examines the two approaches for each series, and it shows that they demonstrate a good response.

[0071] (Step 12) Tower G calculated in Steps 7-11 m-n Each of the deformations φ at the top e , φ y The value of is substituted into the predetermined equation (ii) (equation ii in Figure 1(12)), and the seismic load Q i When it acts, pylon G m-n Elastoplastic response deformation φ occurring at the apex p This is required.

[0072] Here, Figure 8 shows the results of an example of static load incremental analysis using the 3D analysis model in Figure 7 (types (1) and (3) of the transmission towers in Figure 2), but the point at which the main column member reaches its compressive limit strength (safety limit φ) lim Input seismic load up to (base shear coefficient C) BIn the relationship with the top deformation φ, after the web member initial buckling, although the horizontal rigidity of the tower is slight, it decreases. Therefore, the rigidity reduction rate α (= k2 / k1) after the web member buckling (yield) defined as shown in Fig. 9 is considered in the above formula (Two).

[0073] The predetermined formula (Two) is derived from the energy conservation law assuming that the elastic input energy at the time of the static elastic response deformation φ of the tower top calculated in Step 7 is equal to the elasto-plastic absorption energy after the web member buckling in the non-linear relationship between the input seismic load and the top deformation of the tower with web member buckling (see Fig. 3(b)). e (See Fig. 3(b)).

[0074] (Step 13) Then, the ratio φ of the top deformation φ of the tower G defined as the safety limit deformation m-n to the elasto-plastic response deformation φ lim is calculated by the arithmetic unit of the computer as the seismic resistance index value DCR p of the tower G p / φ lim (see the formula Ho in Fig. 1(13)). m-n The smaller the value of the ratio φ T / φ p is, the greater the deformation margin until the web member buckles and no strength reduction occurs until reaching the safety limit deformation (the time deformation of the compressive limit strength of the main column member), that is, the higher the seismic margin. If this value exceeds 1.0, it means that the main column member buckles and yields first. In that case, it is necessary to consider countermeasures separately.

[0075]

[0076] (Step 14) If the calculation of the seismic resistance index value DCR lim has not been completed for all the towers belonging to the tower group G (when n < N), set n = n + 1 and return to Step 5, and Steps 5 to 13 are repeated for the next tower G m . Otherwise (when n = N), proceed to the next Step 15. The towers excluded from consideration in Step 4 skip Steps 5 to 13. T m-n

[0077] ​​(Step 15) Proceed to the next tower group G m and, for each tower belonging to this group, repeat Procedures 1 to 14 for calculating the seismic index value DCR T until n = N. If this repetition is not completed for all tower groups G m (m < M), set m = m + 1, return to Procedure 1, and repeat Procedures 1 to 14 for each tower belonging to the next tower group G m Otherwise (m = M), assuming that the calculation of the seismic index value DCR for all towers has been completed, the total calculation results are output by the output device of the computer (Step 16). T

[0078] Next, as an example of the second means of the present invention, a flowchart is shown in Fig. 1(b). The second means of the present invention is in Procedure 6 of the first means (Fig. 1(a)) of the present invention, and the equivalent bending rigidity E·I i and the equivalent shear rigidity G·A si are calculated for the tower G m-n to identify whether the shear strength of the panel i of the tower is determined by the shear strength Q iN determined by the buckling strength of the web members constituting the panel i or the shear strength Q iT determined by the joint (tensile fracture) strength. To do this, the procedure (6-1) of the subroutine B shown in Fig. 1(b) is incorporated.

[0079] The reason for incorporating the subroutine B is that in the simplified seismic margin evaluation method according to the present invention, it is premised that the tower yields due to the buckling of the web members first, and it is necessary to avoid the fracture at the joint of the web members having a cross-sectional defect due to the bolt holes from occurring first.

[0080] However, even for a tower including a panel in which fracture at the joint of the web members occurs first, since the reinforcement of the joint is relatively easy, it is considered that the fracture is avoided by the reinforcement, and the calculation after Procedure 7 proceeds.

[0081] ​Furthermore, in subroutine B, towers identified as being prone to fracture at the bracing joints are classified, listed, and saved as towers requiring reinforcement at the bracing joints. This data can then be used to prioritize reinforcement efforts at the bracing joints. The above is a description of an embodiment of the simplified seismic margin evaluation method according to the present invention.

[0082] The simplified seismic resistance index value DCR according to the present invention T To confirm the validity of the (evaluation value), for each of the 12 transmission towers (see Figure 2), site seismic waves were assumed for each tower, and elastoplastic time history response analysis was performed using the three-dimensional analysis model shown in Figure 7 to obtain the seismic resistance index value DCR. T Tables 1 and 2 show the results of the comparison with (analyzed values). Table 1 shows the values ​​in the direction of the overhead line, and Table 2 shows the values ​​in the direction perpendicular to it, with input acceleration level (a m ) The seismic margin of each transmission tower according to the index value DCR T ) and the priority of countermeasures are summarized.

[0083] [Table 1]

[0084] [Table 2]

[0085] Furthermore, Figure 12 shows the simplified seismic resistance index value DCR according to the present invention, based on the results in Tables 1 and 2. T This graph compares and organizes the results (evaluation values) on the horizontal axis and the results of the time history response analysis (analysis values) on the vertical axis. The results according to the present invention evaluate the nonlinear time history response analysis results, which take into account damage to the bracing material, to the over-side by approximately 40%, i.e., the seismic margin to the safe side.

[0086] Furthermore, while the "priority order for countermeasures" of the two parties does not necessarily coincide, it is perfectly practical to use it as a screening indicator for prioritization. In addition, for transmission towers with an evaluation value exceeding 1.0, there is a possibility that the yielding of the main column members will occur first, so it is desirable to confirm the seismic margin through a separate detailed examination.

[0087] While this invention provides a simplified method for evaluating seismic margins for the vast number of existing power transmission towers, it goes without saying that it can also be applied to tower-like truss structures such as communication towers. [Industrial applicability]

[0088] According to this invention, given the current situation where there is an urgent need to address insufficient strength to withstand the increased assumed seismic input motions that have become required in recent years for the approximately 250,000 power transmission towers currently existing in Japan, or to prepare for the replacement of towers that will exceed their service life in the near future, it is possible to easily and efficiently evaluate the margin of safety before collapse due to assumed seismic loads based on a common rational scale, thereby making a significant contribution to seismic countermeasures for power transmission towers.

Claims

1. A method for evaluating the seismic margin of power transmission towers, which is performed using a computer in the following procedure, (Procedure 1) Various data lists of the towers under consideration, organized into groups under certain conditions, and data of design acceleration response spectra according to the type of ground are stored in the computer's storage device as database 1 in advance, and the first tower group G to be considered is entered into the computer's input device. ｍ The group number 'm' is entered for selection purposes. Database 1 A) List of various data for the transmission towers under consideration by group Group number m (1 to M), tower number n (1 to N) - Voltage scale, tower type, construction site (ground conditions) • Height H, root spread B, panel dimensions (height, width) • Member sizes (main columns, bracing) Fixed load W ｉ (Panel weight, overhead wire weight) ・Cable wire support type (suspended type, tension type), horizontal angle B) List of acceleration response spectra for design - Acceleration response spectrum (Ground type: Type 1, Type 2, Type 3) (Step 2) The group number m entered in Step 1 is compared with the various data lists of the towers under consideration, which are organized by group in the database 1, and the tower group G ｍ All transmission towers G belonging to ｍ-ｎ Various data related to (n=1 to N) are acquired, and similarly, data on the design acceleration response spectrum corresponding to the ground type, which is stored in advance, is also acquired. (Step 3) All of the aforementioned transmission towers G obtained in Step 2 ｍ-ｎ Natural period T (n=1 to N) 0 And those transmission towers G ｍ-ｎ The system is then compared with the design acceleration response spectrum, which is set according to the ground conditions at the construction site. (Step 4) By comparing with the design acceleration response spectrum, the natural period T of the tower G m-n (n = 1 to N) 0 is greater than the upper limit period T of the acceleration constant region of the design acceleration response spectrum c (T 0 > T c ), then it is excluded as an object not subject to the premise of using the energy conservation law and is separately considered, and if it is below the upper limit period T c (T 0 ≤ T c ), proceed to the next Step 5. (Step 5) Tower G identified as the subject of consideration in Step 4 ｍ-ｎ Based on the various data obtained in step 2, the transmission tower G ｍ-ｎ The seismic load Q acts on each panel i, which is stacked in the vertical direction and consists of main columns of a certain height, bracing members (web members), and horizontal members. ｉ However, it is calculated by the computer's arithmetic unit based on a predetermined calculation formula (a) for calculating the equivalent static seismic load. Here, the symbol i is the panel number counted from the top of the tower. Formula (i) Transmission Tower G ｍ－ｎ Calculation of equivalent static seismic load Q (i = 1 to l) Q ｉ = R ｔ ・C ｈ A ｉ ・W ｉ ···(stomach) Q ｉ : Layer shear force of the i-th panel from the top R ｔ : Response characteristic coefficient (suspension type, tension type) C ｈ : Correction coefficient related to damping A ｉ : Story shear force distribution coefficient (track direction, orthogonal direction) W ｉ : Total weight of panels above the center of the i-panel (Step 6) Tower G identified as the subject of consideration in Step 4 ｍ-ｎ Based on the various data obtained in step 2, the transmission tower G ｍ-ｎ The equivalent bending stiffness E・I of the aforementioned panel i ｉ and equivalent shear stiffness G・A ｓｉ However, this is calculated by the arithmetic unit of the aforementioned computer. (Procedure 7) The aforementioned transmission tower G ｍ-ｎ The equivalent bending stiffness E・I calculated in step 6 ｉ and equivalent shear stiffness G・A ｓｉ Considering the panels i having the same configuration as a cantilever beam formed by continuously stacking them, the tower G calculated in step 5 ｍ-ｎ Seismic load Q ｉ When this acts, the resulting transmission tower G ｍ-ｎ Static elastic response deformation φ at the apex ｅ However, this is calculated by the arithmetic unit of the aforementioned computer. Here, the ratio of the horizontal displacement at the top to the height of the tower is defined as the top deformation. The same applies hereafter. (Step 8) The transmission tower G, which was considered as a single cantilever beam as described above ｍ-ｎ All panels i are subjected to seismic load Q ｉ When the force acts on the tower G, it is estimated that the bracing material of one of the panels i will buckle. ｍ-ｎ Top deformation φ ｙ However, transmission tower G ｍ-ｎ It is calculated by the computer's arithmetic unit using a predetermined approximation formula (b) that is applied to similar groups of transmission towers. Approximation formula (b) Tower G during buckling of bracing members ｍ－ｎ Top deformation φ ｙ Calculation φ ｙ =y １ +y ２ ・(H / B) (Procedure 9) Here, the coefficients used in the predetermined approximation formula (b) are the pre-determined and organized transmission tower G stored in the computer's memory as database 2. ｍ-ｎ The search is performed using a list of coefficients for similar tower clusters. Database 2 List of coefficients related to deformation at the top of transmission towers (by group) (Based on static incremental analysis results considering buckling of the bracing material) • When the belly material is bent (φ) ｙ ): y １ y ２ • When the main column buckles (φ) ｌｉｍ ):l １ l ２ (Step 10) Tower G is treated as a single equivalent cantilever beam. ｍ-ｎ All panels i are subjected to seismic load Q ｉ The power of the transmission tower G is estimated to have reached the compressive limit strength at which one of the main support members will buckle. ｍ-ｎ Top deformation φ lim However, transmission tower G ｍ-ｎ It is calculated by the computer's arithmetic unit using a predetermined approximation formula (c) that is applied to similar groups of transmission towers. Approximation formula (c) Tower G during buckling of main column member ｍ－ｎ Top deformation φ ｌｉｍ Calculation f ｌｉｍ =l １ +l ２ ・(H / B) (Procedure 11) Here, the coefficients used in the predetermined approximation formula (c) are the pre-determined and organized transmission tower G that are stored in the computer's memory as database 2. ｍ-ｎ The search is performed using a list of coefficients for similar tower clusters. (Step 12) The tower G calculated in Steps 7-11 ｍ-ｎ Each of the deformations φ at the top ｅ , φ ｙ The values ​​of these are substituted into the predetermined equation (ii) with these variables, and the seismic load Q ｉ When it acts, the transmission tower G ｍ-ｎ Elastoplastic response deformation φ occurring at the apex ｐ This is required. Formula (2) Transmission Tower G ｍ－ｎ Apex-plastic response deformation φ ｐ Calculation f ｐ =〔(a-1)・φ ｙ +√{(1-a)・φ ｙ ２ +a・f ｅ ２ }〕 / a However, α is the rate of decrease in stiffness relative to the initial stiffness after buckling of the bracing members. (Step 13) Then, Tower G ｍ-ｎ Top deformation φ lim The elastoplastic response deformation φ is defined as the safety limit deformation. ｐ Ratio φ ｐ / φ lim However, transmission tower G ｍ-ｎ Seismic resistance index value DCR Ｔ This is calculated by the arithmetic unit of the aforementioned computer. (Step 14) For all the towers belonging to tower group G ｍ if the seismic index value DCR Ｔ has not been calculated (n < N), set n = n + 1, return to Step 5, and repeat Steps 5 to 13 for the next tower G ｍ-ｎ Otherwise (n = N), proceed to the next Step 15. (Step 15) Proceed to the next tower group G ｍ and for each tower belonging to this group, repeat Procedures 1 to 14 for calculating the seismic index value DCR Ｔ until n = N. If this repetition is not completed for all tower groups G ｍ (m < M), set m = m + 1, return to Step 1, and repeat Procedures 1 to 14 for each tower belonging to the next tower group G ｍ Otherwise (m = M), assuming that the calculation of the seismic index value DCR Ｔ for all towers has been completed, the total calculation results are output by the output device of the computer (Step 16). A simplified method for evaluating the seismic margin of a power transmission tower, characterized by including the above steps.

2. In the simplified seismic margin evaluation method for power transmission towers according to claim 1, equivalent bending stiffness E・I ｉ and equivalent shear stiffness G・A ｓｉ The aforementioned transmission tower G was calculated ｍ-ｎ A simplified method for evaluating the seismic margin of a power transmission tower, characterized in that it incorporates a procedure for identifying whether the shear strength of the panel i is determined by compression buckling or tensile fracture of the joints of the bracing members constituting the panel i.

3. In the simplified seismic margin evaluation method for power transmission towers according to claim 1 or 2, the database 2 relates to the coefficients used in the predetermined approximation formulas (b) and (c), and is an approximation formula regressively derived from the results of performing a static load incremental analysis of a tower frame with buckling of the web members, using multiple three-dimensional analysis models of tower groups similar to the tower under consideration, with the web members of these three-dimensional analysis models as elastoplastic truss elements, and is the ratio of height H / base spread B and the top deformation φ when any of the web members of the tower frame buckles. ｙ The relationship with, and the top deformation φ when the main column members of the aforementioned steel tower frame reach their compressive limit strength. lim A simplified method for evaluating the seismic margin of power transmission towers, characterized in that the relationship with and the coefficients of the approximation formulas that approximate the results for each are organized and listed.

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