JP5395636B2 - Structural analysis method for structures - Google Patents

Description

  The present invention relates to a structure analysis method for a structure for analyzing a collapse phenomenon of the structure when one member constituting the structure is broken.

  In recent years, truss bridge collapse accidents and member fracture accidents have occurred in Japan and overseas. As a result of these accidents, analysis of fracture phenomena of steel truss bridges is regarded as important, and research on the field of bridge maintenance and management is underway. As one of the analysis methods, a redundancy analysis of a bridge is known. Redundancy means the margin of the entire structure after the members constituting the structure are broken (margin to the final state). If this redundancy analysis can accurately determine the redundancy of the bridge and the important members of the structure, it can be used for determining the inspection period and the inspection members.

  For example, in the redundancy analysis disclosed in Non-Patent Document 1, a linear analysis is performed to calculate a cross-sectional force of another member at the time of destruction of the member of interest, and whether or not each member is in an ultimate state using the cross-sectional force Is judged. In the analysis of the cross-sectional force, the upper and lower chord members and diagonal members of the bridge are modeled as beam elements, and the RC floor slab is modeled as a shell element, and analysis is performed by loading a predetermined load. The load to be loaded is multiplied by an impact coefficient (in this case, an impact coefficient of 1.854) in order to take into account the impact due to sudden stress release due to member destruction in addition to the dead load and live load.

Hideki Nagatani and 8 others, “Examination of redundancy analysis for steel truss bridges in Japan”, JSCE A, Vol.65 No.2 p.410-425, May 2009

However, the redundancy analysis according to Non-Patent Document 1 has the following problems.
(1) An impact coefficient (impact coefficient of 1.854) with an unclear basis is used in calculating the impact force generated when a member breaks down. Even if the member breaks, such a cross-sectional force may not actually be generated. In other words, when the behavior after member destruction is in the elastic range, the impact force tends to be overestimated.
(2) Since the analysis method is linear analysis, the behavior when the member is plasticized is unclear. That is, when the load acting on the member increases and reaches the plastic region, the response value is underestimated.

(3) With one member determined to be broken, the entire bridge is evaluated and structurally important members are determined. If one member breaks, redistribution of member forces and member breakage may be broken in a chain, but these cannot be considered.

  The present invention was created in order to solve such problems, and analyzes the collapse phenomenon of a structure in consideration of chained member destruction when a certain member constituting the structure breaks. An object of the present invention is to provide a structure analysis method for a structure.

  In order to solve the above problems, the present invention creates a structural analysis model by modeling a structure composed of a plurality of members with elements that can take into account the nonlinearity of each of the members. Is a structural analysis method for a structure that analyzes the fracture phenomenon of the structure using static electricity, and performs static analysis on the structural analysis model, and the stress acting on each member constituting the structural analysis model A static analysis step for obtaining a structural analysis, a modified model creating step for newly creating a structural analysis model in a state where one of the members of the structural analysis model is deleted, and a structural analysis created in the modified model creating step A free vibration analysis step in which free vibration analysis is performed by applying a stress acting on each member immediately before the member is deleted to the model for use, and a member newly destroyed in the free vibration analysis step When it is determined that there is no newly destroyed member in the destructing member determining step and the destructing member determining step for determining whether or not there is a structural analysis model after performing the free vibration analysis Performing a static analysis and determining whether or not the structural analysis model has collapsed, and until determining that there is no newly destroyed member in the destructive member determination step, The modification model creation step, the free vibration analysis step, and the fracture member determination step are repeated.

According to such a method, in the free vibration analysis step, in the free vibration analysis after deleting one of the members, the stress applied to each member in the structural system immediately before the member is deleted is applied. It is possible to perform a dynamic response analysis using a step load as a stress borne by the member.
In addition, in order to repeat the change model creation step, the free vibration analysis step, and the destruction member determination step until it is determined that there is no newly destroyed member, the structural system that changes according to the chain destruction of the members is considered. Dynamic analysis can be performed. That is, according to the present invention, since the actual collapse process of the structure can be taken into consideration, the destruction phenomenon can be analyzed with high accuracy.

  In the static analysis step, static analysis is performed by applying an additional load obtained by multiplying the reference load by the variable α, and in the collapse determination step, the structural analysis model is determined not to collapse After increasing the variable α, the process proceeds to the static analysis step, and until it is determined that the structural analysis model has collapsed, a modified model creation step, a free vibration analysis step, a fracture member determination step It is preferable to repeat the collapse determination step.

  According to this method, the margin can be quantitatively calculated by setting the variable α when it is determined that the structural analysis model has collapsed as the margin of the structure.

  Further, when there is a member destroyed in the static analysis step, it is preferable to select this member as a member to be deleted first in the change model creation step. According to this method, it is possible to calculate the margin due to the member that was first destroyed.

  Further, it is possible to arbitrarily select one member from the structural analysis model after the analysis in the static analysis step and select this member as a member to be deleted first in the change model creation step. preferable. According to this method, it is possible to calculate a margin due to an arbitrarily selected member.

  Further, before the static analysis step, it further includes a constant loading analysis step of creating an initial state of the structural analysis model by performing a static analysis by always loading, and among each member constituting the structure, It is preferable to select a member to be deleted first in the modified model creation step based on the strain energy obtained in the constant loading analysis step.

  According to this method, the margin resulting from the selected member can be calculated. In addition, for example, by selecting a member having a large strain energy obtained in the always loading analysis step as a member to be deleted first, a member that is highly likely to be destroyed can be efficiently determined.

  ADVANTAGE OF THE INVENTION According to this invention, the collapse phenomenon of a structure can be analyzed after considering the chain member destruction when the certain member which comprises a structure destroys.

It is a functional block diagram which shows the computer for analysis used for the structural analysis method which concerns on this embodiment. (A) is a side view which shows an example of a structure, (b) is a schematic diagram for demonstrating a fiber model, (c) is a schematic diagram for demonstrating a shell model. It is a schematic diagram for demonstrating a shell element. It is a flowchart which shows the procedure of the calculation method of the basic margin which concerns on this embodiment. It is the model conceptual diagram which showed the first half of the calculation method of the basic margin which concerns on this embodiment in steps. It is the model conceptual diagram which showed the latter half of the calculation method of the basic margin which concerns on this embodiment in steps. It is the flowchart which showed the procedure of the first half of the calculation method of the individual margin which concerns on this embodiment. It is the flowchart which showed the procedure of the second half of the calculation method of the individual margin which concerns on this embodiment. It is the model conceptual diagram which showed the first half of the calculation method of the separate margin concerning this embodiment in steps. It is the model conceptual diagram which showed the latter half of the calculation method of the basic margin which concerns on this embodiment in steps. The side view which showed the object bridge used in the Example, and the design condition table | surface are shown. It is the perspective view which modeled the object bridge used in the Example. FIG. 4 is a schematic diagram illustrating a live load loading position in a constant loading analysis according to the first embodiment. It is the graph which showed the maximum strain distribution of each member of the constant load analysis which concerns on Example 1, Comprising: (a) shows diagonal material, (b) shows vertical material, (c) shows lower chord material. FIG. 3 is a side view showing a member fracture position in the ultimate strength analysis according to Example 1. It is the graph which showed the maximum strain distribution of each member in the ultimate strength analysis which concerns on Example 1, Comprising: (a) is a diagonal material, (b) is an upper chord material, (c) shows a lower chord material. In the ultimate strength analysis which concerns on Example 1, it is the graph which showed the distortion | strain history of the destroyed member, (a) shows an upper chord material, (b) shows a lower chord material. In the ultimate strength analysis concerning Example 1, it is a stress contour figure of a floor slab just before collapse. It is the figure which showed the important member candidate in the redundancy analysis which concerns on Example 1. FIG. It is an analysis result of the redundancy analysis which concerns on Example 1, Comprising: (a) shows the maximum strain distribution of each diagonal after deleting an oblique, (b) shows the fracture position of a member. It is an analysis result of the redundancy analysis which concerns on Example 1, Comprising: (a) shows the largest strain distribution of each perpendicular | vertical material after deleting a perpendicular | vertical material, (b) shows the fracture position of a member. It is an analysis result of the redundancy analysis which concerns on Example 1, Comprising: (a) shows the largest strain distribution of the lower chord material after deleting a lower chord material, (b) shows the fracture position of a member. In the redundancy analysis which concerns on Example 1, it is the table | surface which put together the important member candidate and the individual margin. It is a figure for demonstrating the two member analysis which concerns on Example 2, Comprising: (a) is a side view of a bridge, (b) (c) shows the analysis method. 6 is a graph comparing a theoretical solution and an analytical solution of a two-member analysis according to Example 2. It is a figure for demonstrating the simple truss analysis which concerns on Example 3, Comprising: (a) is a side view of a bridge, (b) is the schematic diagram which showed the simple truss, (c) comprises a simple truss. It is the table | surface which put together the cross-sectional shape etc. of the member. FIG. 6 is an axial force diagram in a prior analysis according to Example 3, wherein (a) is a structure before the diagonal breakage, (b) is a structure where no diagonal is present, and (c) is a portion where the diagonal is present. The structure which made the impact load act on both ends of is shown. It is the graph which showed the axial force log | history in the simple truss analysis concerning the 1500kN load of Example 3, Comprising: (a) is an upper chord material, (b) is a vertical material, (c) shows a diagonal material. In the simple truss analysis which concerns on the 1500 kN load of Example 3, it is the schematic diagram which showed the deformation | transformation state when the axial force of a vertical material is the maximum, (a) is this analysis, (b) shows the conventional method. In the simple truss analysis which concerns on the 1500kN load of Example 3, it is the graph which showed the axial force log | history of three places of a vertical material. In the simple truss analysis concerning the 1500 kN load of Example 3, it is the graph which showed the axial force log | history in the subdivision analysis of a perpendicular | vertical material. It is the graph which showed the analysis result which concerns on the 3500kN load of Example 3, Comprising: (a) shows the axial force log | history of a perpendicular | vertical material, (b) shows the stress-strain relationship of a perpendicular | vertical material. In Example 3, it is the table | surface which put together the damage state which acts on each member in the conventional method and this analysis.

  Embodiments of the present invention will be described in detail with reference to the drawings. The structural analysis method for a structure according to this embodiment is for a bridge composed of a plurality of members, and the structural analysis (numerical analysis) is performed by modeling the bridge with elements that can take into account the nonlinearity of the material. Model is created, and the destruction phenomenon is analyzed in consideration of the chain destruction when a certain member breaks. In the present embodiment, a case where a margin of a structure is calculated and an important member among members constituting the structure is determined based on the calculated margin is illustrated.

  In the present embodiment, a steel-structured bridge including a steel truss and a reinforced concrete slab (RC floor slab) is illustrated, but the type of structure and materials used are not limited.

  The structural analysis according to the present embodiment is executed using an analysis computer C shown in FIG. The analysis computer C includes at least a storage unit 1, an arithmetic processing unit 2, an input unit 3, a display unit 4, and a bus line 5 that connects these units to each other.

  The storage means 1 stores various programs and data, and includes a main storage device (for example, DRAM), an auxiliary storage device (for example, a writable nonvolatile semiconductor memory (flash memory), a magnetic disk drive, Optical disc drive etc.). The storage means 1 includes an editor program 11 that is activated when a model for structural analysis is created, a basic model file 12 that stores a basic model, and a constant loading analysis program 13 that is activated when a constant loading analysis is performed. The static analysis program 14 that is activated when the static analysis is performed, the change model file 15 that stores the modified model, the free vibration analysis program 16 that is activated when the free vibration analysis is performed, and the bridge collapsed A collapse determination program 17 that is activated when the determination is performed, a result file 18 that stores the results of each analysis, and the like are stored.

  The arithmetic processing means 2 includes an MPU (microprocessor) that performs arithmetic processing. The arithmetic processing means 2 functions as the structural analysis model creation means 31 when the editor program 11 is read from the storage means 1 and executed, and functions as the constant loading analysis means 32 when the constant loading analysis program 13 is read and executed. When the static analysis program 14 is read and executed, it functions as the static analysis means 33, when the free vibration analysis program 16 is read and executed, it functions as the free vibration analysis means 34, and when the collapse determination program 17 is read and executed, the collapse determination is performed. It functions as the means 35.

  The structural analysis model creation means 31 is used when creating an analysis model of a bridge to be analyzed. Data about the created model is stored in the basic model file 12 and the modified model file 15, respectively. The model (basic model) stored in the basic model file 12 is a model of a bridge without a broken member. The model (change model) stored in the change model file 15 is a model of a bridge in which one or more members are destroyed.

  The constantly loaded analysis means 32 reads data relating to the basic model from the basic model file 12, performs a static analysis by constantly loading using the read model, and obtains an analysis result (for example, acting on the model). The relationship between the loaded load, the stress generated in each element, the amount of displacement, etc.) is written in the result file 18.

  The static analysis means 33 reads out data relating to the basic model from the basic model file 12, performs a static analysis by applying a predetermined load using the read model, and the obtained analysis result is obtained as a result file 18. Write to.

  The free vibration analysis means 34 reads data relating to the changed model from the changed model file 15, performs free vibration analysis using the read model, and writes the obtained analysis result to the result file 18.

  The collapse determination unit 35 reads out data related to the current changed model (the newest changed model) from the changed model file 15, performs static analysis using the read model, and outputs the obtained analysis result to the result file. 18 is written.

  The input means 3 is for inputting data necessary for creation of a model and each analysis described above (for example, member specifications, loading load, load increment amount, boundary conditions, etc.) to the arithmetic processing means 2, It consists of a keyboard and mouse. Data input to the analysis computer C using the input unit 3 is temporarily stored in the storage unit 1 and then output to the arithmetic processing unit 2.

  The display unit 4 displays an input form for assisting data input by the input unit 3, contents of various files (basic model file 12, modified model file 15) stored in the storage unit 1, a chart representing the calculation result, and the like. It consists of a display device.

Here, the structural analysis model used in this embodiment will be described.
In this embodiment, as shown to (a) and (b) of FIG. 2, the upper chord material 61 which comprises steel trusses is provided with a plurality of fiber elements 7 connected in the longitudinal direction (in the member axis direction). 7... (Hereinafter sometimes referred to as a fiber model), and is modeled so that plasticization can be expressed. In addition, although illustration is abbreviate | omitted, the lower chord material 62, the diagonal material 63, and the vertical material 64 which comprise a steel truss are also modeled with a fiber model.

  On the other hand, as shown in FIG. 2 (c), the RC floor slab 65 is an aggregate of shell elements 8, 8,... (Hereinafter sometimes referred to as a shell model) so that plasticization can be expressed. Model.

  The fiber element 7 is a kind of a beam element (one-dimensional element) formed on the basis of “planarity maintaining assumption” and “planarity invariant assumption”, and can take into consideration the nonlinear property of the material. An integration point provided at an appropriate position of the fiber element 7 is given a “stress-strain relationship” and a “sharing area”.

  The shell element 8 is “the plate thickness does not change during deformation”, “the stress perpendicular to the neutral plane is zero, and the in-plane is in a plane stress state”, “at time 0, it is perpendicular to the neutral plane. The normals vary with spacing and remain straight, but need not be perpendicular to the neutral plane (ie, allow out-of-plane shear deformation) ”. It is a kind of dimension element) and can take into account the nonlinearity of the material. An integration point provided at an appropriate position of the shell element 8 is given a “stress-strain relationship” and a “sharing area”. As shown in FIG. 3, the shell element 8 has a laminated structure in this embodiment, and includes a concrete layer 8a and a reinforcing bar layer 8b. The shell element 8 is a floor slab model that takes into account cracks and plasticization of the floor slab by applying the material constitutive law of concrete and reinforcing bars.

Next, a specific procedure of the structural analysis method according to the present embodiment will be described.
In the structure analysis method for a structure according to the present embodiment, after calculating two types of margins of “basic margin” and “individual margin”, an important member is selected based on the basic margin and the individual margin. decide. The “basic margin” means a margin calculated when a member to be destroyed first among members constituting the bridge is selected based on a result of static analysis. The “individual margin” means a margin calculated when a member to be destroyed first is arbitrarily selected from among members constituting the bridge.
First, a method for calculating the basic margin will be described.

<Calculation method of basic margin>
In the basic margin calculation method according to the present embodiment, as shown in FIG. 4, a preparation step, a static analysis step, a change model creation step, a free vibration analysis step, a fracture member determination step, and a collapse determination Steps. In the calculation method of the basic margin, the process excluding the preparation step may be referred to as “final strength analysis”.

  In the preparation step, a basic model is created and the initial state of the bridge is acquired. In the preparation step, first, a structural analysis model (hereinafter also referred to as a basic model) is created on the assumption that the members constituting the bridge are free from fractures and cross-sectional defects (step S1). When creating the basic model, the editor program 11 shown in FIG. 1 is activated. When the editor program 11 is activated, the analysis computer C functions as the structural analysis model creation means 31 and an editor screen or the like is displayed on the display means 4. When data relating to the bridge (member shape, coordinates, element type, number of element divisions, stress-strain function assigned to the element, etc.) is input to the analysis computer C through the input means 3 by the operator's operation, structural analysis The model creation means 31 creates data in a format suitable for elasto-plastic finite analysis. Data relating to the created basic model is stored in the basic model file 12.

  When the basic model is created, a predetermined load is placed on the basic model, and a constant load analysis (step S2) is performed to obtain an initial state of the bridge (step S3). In the constant loading analysis, in order to evaluate the RC floor slab 65 of the bridge, an analysis considering the placement of the RC floor slab is performed to acquire stress, strain, etc. acting on each member.

  When performing the constant load analysis, the constant load analysis program 13 shown in FIG. 1 is activated to cause the analysis computer C to function as the constant load analysis means 32. When the basic model file 12 is designated by the operator's operation after starting the always-on load analysis program, the always-on load analysis means 32 reads the data related to the basic model from the basic model file 12 and always loads the basic model. Static analysis is performed by loading. Specifically, in the constant loading analysis, a floor slab load calculating step, a first always loading step, and a second always loading step are performed.

  In the floor slab load calculating step, the constant load analysis means 32 applies a dead load (D) to the basic model, and a load value generated at the joint (slab anchor or the like) between the RC floor slab 65 and the upper chord material 61. Is written in the result file 18 as the floor slab weight.

  In the first load step, the always-loading analysis means 32 reads the floor slab weight written in the result file 18 and displays the floor slab weight and the dead load of each member constituting the truss in a state where the RC floor slab 65 is not present ( The RC floor slab 65 is loaded on the basic model (with the rigidity and elastic modulus made zero).

  In the second load step, since the basic model is displaced in the vertical direction in the first load step described above, the constant load analysis means 32 returns the coordinates to the original state and sets the displacement to zero. After inputting the plate stiffness, a live load (L) is loaded between the central diameters of the bridge.

  The constant loading analysis means 32 receives data such as stress and strain acting on each member (the upper chord material 61, the lower chord material 62, the diagonal material 63, the vertical material 64, and the RC floor slab 65) obtained by the above-described constant loading analysis. The initial state of this bridge is written in the result file 18 (step S3).

  If the initial state is obtained, a static analysis step is executed. In the static analysis step, a static analysis (step S4) is performed on the basic model by causing the additional load α (D + L) obtained by multiplying the reference load by the variable α to act vertically on the basic model.

  When performing a static analysis, the static analysis program 14 shown in FIG. 1 is started and the analysis computer C functions as the static analysis means 33. When the basic model file 12 is designated by the operator's operation after the static analysis program 14 is activated, the static analysis means 33 reads data related to the basic model from the basic model file 12. Furthermore, when the result file 18 is designated by the operator's operation, the static analysis means 33 reads data relating to the initial state of the bridge. The static analysis means 33 performs elasto-plastic finite displacement analysis based on the basic model and the initial state data, and acquires stress, displacement, and the like acting on each member of the bridge.

Here, FIG. 5A is a schematic conceptual diagram showing the first half of the basic margin calculation method according to the present embodiment step by step. FIG. 5B is a schematic conceptual diagram showing the second half of the basic margin calculation method according to the present embodiment in stages.
A basic model G shown in FIG. 5A schematically shows a part of the bridge shown in FIG. 2 (a). The upper chord members 61a and 61b, the lower chord members 62a and 62b, the diagonal members 63a and 63b, It consists of materials 64a, 64b, 64c and RC floor slab 65. The static analysis step to the fracture member determination step will be described with reference to FIGS. 5A and 5B.

Specifically, the static analysis (step S4) is performed by changing the variable α to the reference load (dead load (D) + live load (L)) with respect to the basic model G, as shown in FIG. The additional load α (D + L) multiplied by is applied. The initial value of the variable α is set to α = 1. The static analysis means 33 executes a static analysis and converts the stress (maximum stress) acting on each member of the basic model G to the stress state F ₁ (σ ₁₁ , σ ₂₁ , σ ₃₁ , σ ₄₁ , σ ₅₁ , σ ₆₁ , [sigma] ₇₁ , [sigma] ₈₁ , [sigma] ₉₁ , [sigma] ₁₀₁ ) and the displacement of each member is acquired, and these data are associated with the value of the variable [alpha] and written to the result file 18.

  If the static analysis (step S4) is performed, the static analysis means 33 determines whether or not the entire bridge has collapsed (step S5). The static analysis means 33 determines that “the entire bridge has collapsed” when the basic model has an unstable structure, and writes the variable α at that time in the result file 18.

  If it is determined in the determination step that “the entire bridge has collapsed” (Yes in step S5), the static analysis means 33 sets the value of the variable α at that time (here, the initial value α = 1) to the “basic” of this bridge. The margin is determined (step S13), and the analysis is terminated.

In the determination step, when it is determined that “the entire bridge does not collapse” (No in step S5), the static analysis means 33 determines whether there is a broken member in the basic model (step S6). In the present embodiment, it is assumed that “there is a broken member” when the maximum strain value of each member exceeds a preset value (member breaking strain value). The member fracture strain value may be set as appropriate, but in the present embodiment, it is set to 3 times the yield strain ε _y (= 3ε _y ) in consideration of allowing the member to be plasticized to some extent.

  In the determination step, when the static analysis means 33 determines that “there is no destroyed member” (No in step S6), the variable α is changed (step S7), and the process proceeds to the static analysis (step S4). Then, until it is determined that “the entire bridge has collapsed” (step S5) or “there is a destroyed member” (step S6), the static analysis (step S4) and the determination step ( Steps S5 and S6) are repeated. The change width of the variable α may be set as appropriate, but in this embodiment, for example, it is set to increase by 0.1.

  The static analysis means 33 associates the gradually increasing variable α with the stress state and displacement of each member of the basic model corresponding to the variable α at that time, and writes them in the result file 18. The process of repeating from the static analysis (step S4) to the change of the variable α (step S7) may be performed by configuring the analysis computer C as such.

  In the determination step, when it is determined that “there is a destroyed member” (Yes in step S6), the static analysis means 33 writes the destroyed member in the result file 18 and causes the display means 4 to display it.

In the present embodiment, for example, as shown in (b) of FIG. 5A, it is assumed that it is determined that the diagonal material 63a has been destroyed when the variable α ₃ (= 1.2). Hereinafter, the destroyed member is also referred to as a “destructive member”. In the result file 18, the stress state F ₃ (σ ₁₃ , σ ₂₃ , σ ₃₃ , σ ₄₃ ,...) Applied to each member of the basic model G immediately before the diagonal member 63 a is destroyed in association with the variable α ₃ . (σ ₅₃ , σ ₆₃ , σ ₇₃ , σ ₈₃ , σ ₉₃ , σ ₁₀₃ ) and displacement are stored.

In the changed model creation step, the operator deletes the destroyed member destroyed in the static analysis step from the basic model and creates a new model (step S8). Specifically, as shown in (c) of FIG. 5A, in the present embodiment, since the diagonal members 63a are determined to have been destroyed, create a change model G ₁ deleting the diagonal member 63a from the basic model G To do.

  When creating a new model, the basic model should be used. In this case, it is only necessary to read out data related to the basic model from the basic model file 12 and delete all the fiber elements 7 representing the members determined to be destroyed. Data on the created new model is stored in the modified model file 15 as a modified model.

  The change model may be created according to an instruction from the operator via the input means, but may be created by the analysis computer C. In this case, the model generation means 31 for structural analysis reads the data related to the basic model from the basic model file 12, deletes all the fiber elements 7 representing the member determined to be destroyed, and the created change A process of writing the model into the change model file 15 is executed.

  In the free vibration analysis step, free vibration analysis is performed using the stress borne by the fracture member as a step load (step S9). When performing free vibration analysis, the free vibration analysis program 16 shown in FIG. 1 may be activated to cause the analysis computer C to function as the free vibration analysis means 34. The free vibration analysis means 34 reads the data related to the changed model from the changed model file 15 and applies the additional load α (D + L), and also acts on the basic model immediately before the fracture member is destroyed. The free vibration analysis is performed by giving the stress state and the amount of variation (the newest stored one). The free vibration analysis means 34 acquires the stress state and displacement acting on each member of the changed model, and writes them in the result file 18 in association with the changed model at this time.

Specifically, as shown in FIG. 5A (d), the free vibration analysis means 34 applies an additional load α ₃ (D + L) to the modified model G ₁ created in the modified model creating step, Stress state F ₃ (σ ₁₃ , σ ₂₃ , σ ₃₃ , σ ₄₃ , σ ₅₃ , σ ₆₃ , σ ₇₃ , σ ₈₃ , σ ₉₃ , σ ₁₀₃ ) acting on the basic model G immediately before the destruction of the destructive member Free vibration analysis is performed by giving displacement and the like.

Then, as shown in (a) of FIG. 5B, the free vibration analysis unit 34, the vibration is applied to each member of the change model G ₁ until convergence stress (maximum stress) stress state F _{4 (sigma 14} , σ ₂₄ , σ ₃₄ , σ ₄₄ , σ ₅₄ , σ ₆₄ , σ ₇₄ , σ ₈₄ , σ ₉₄ , σ ₁₀₄ ) and the displacement of each member and the like, and these data are changed to the change model G ₁ And stored in the result file 18.

  If the free vibration analysis is executed for the changed model, the free vibration analyzing means 34 executes a destructive member determining step for determining whether or not there is a newly destroyed member in the changed model (step S10). The determination as to whether or not the member has been destroyed is the same as the above-described determination step (step S6), and thus description thereof is omitted.

  In the destructive member determination step, when it is determined that there is “a newly destructed member” (Yes in step S10), the creation of the change model (step S8) and the free vibration analysis (step S9) are performed. The process is repeated until it is determined in the determination step (step S10) that “there is no newly destroyed member”.

  If it is determined in the determination step that “there is a newly destroyed member” (Yes in step S10), the newly destroyed member is deleted from the changed model, and a new changed model is created. When a new change model is created, the change model stored in the change model file 15 may be used. In this case, it is only necessary to read out data related to the changed model from the changed model file 15 and delete all the fiber elements 7 expressing the newly destroyed member. Data relating to the newly created change model is stored in the change model file 15.

More specifically, for example, as shown in (a) and (b) of FIG. 5B, diagonal members 63b changes the model G ₁ performs free vibration analysis it is assumed that was destroyed. In the change model creation step after the loop to create a change model G ₂ obtained by deleting the diagonal member 63 b.

  In the free vibration analysis step after the loop, an additional load α (D + L) is applied to the newly created modified model, and the stress state and displacement immediately before the newly destroyed fracture member is deleted are given. Then, free vibration analysis is performed (step S9). Then, the free vibration analyzing unit 34 writes the stress state and displacement acting on each member of the changed model after the free vibration analysis in the result file 18 in association with the changed model.

Specifically, in the free vibration analysis step after the loop, as shown in FIG. 5B (c), the additional load α ₃ (D + L) is applied to the changed model G ₂ and the previous free vibration analysis is performed. The free vibration analysis is performed by giving the stress state F ₄ (σ ₁₄ , σ ₂₄ , σ ₃₄ , σ ₄₄ , σ ₅₄ , σ ₆₄ , σ ₇₄ , σ ₈₄ , σ ₉₄ , σ ₁₀₄ ) and the displacement obtained in the above. .

Then, as shown in (d) of FIG. 5B, the free vibration analysis unit 34, the stress acting on the members of the changed model G ₂ until vibration converges (maximum stress) stress state F _{5 (sigma 15} , σ ₂₅ , σ ₃₅ , σ ₄₅ , σ ₅₅ , σ ₆₅ , σ ₇₅ , σ ₈₅ , σ ₉₅ , σ ₁₀₅ ) and the displacement of each member and the like, and these data are changed to the change model G _2. And stored in the result file 18.

As described above, when the creation of the modified model (step S8) and the free vibration analysis (step S9) are repeated, a new model is created while creating a modified model in which the fractured member determined to have been destroyed is deleted as needed. The stress state acting on the change model immediately before fracture is given to the changed model. This makes it possible to perform dynamic response analysis using the step load as the stress borne by the destroyed member, and to perform analysis that takes into account the structural system that changes in response to chain failure of the member. it can.
In addition, the process which repeats from change model preparation (step S8) to destruction member determination (step S10) should just comprise the computer C for analysis like that.

  In the collapse determination step, static analysis is performed on the current change model (step S11), and it is determined whether or not the entire bridge has collapsed (step S12). When performing the analysis, the collapse determination program 17 of FIG. 1 is started, and the analysis computer C functions as the collapse determination means 35. The collapse determination means 35 is the change model when it is determined from the change model file 15 that “there is no newly destroyed member” in the destruction member determination step (step S10), that is, the change model file 15 is the most. A new changed model is read out, and data relating to the stress state and displacement related to the changed model is read out from the result file 18 and a plastic finite displacement analysis is executed without applying a load.

  When the static analysis (step S11) is performed, the collapse determination unit 35 determines whether or not the entire bridge has collapsed (step S12). The collapse determination means 35 determines that “the entire bridge has collapsed” when the current change model has an unstable structure.

  In the determination step, when it is determined that “the entire bridge does not collapse” (No in step S12), the collapse determination unit 35 changes the variable α (step S7), and proceeds to the static analysis (step S4). In the static analysis after the loop (step S4), the process after the static analysis is performed by increasing the value of the variable α with the current changed model and applying the additional load α (D + L) to the basic model.

In the determination step, when it is determined that “the entire bridge has collapsed” (Yes in step S12), the current variable α (variable α ₃ (= 1.2) in the examples of FIGS. 5A and 5B) is set to “basic margin”. Degree "(step S13) and the process ends.

  In the basic margin calculation method described above, among the members constituting the bridge, the member to be destroyed first is selected based on the result of the static analysis step, and the chain destruction phenomenon caused by the destroyed member. The basic margin can be calculated quantitatively in consideration of the above.

<Individual margin calculation method>
Next, a method for calculating the individual margin according to the present embodiment will be described. In the individual margin calculation method, as shown in FIGS. 6A and 6B, a preparation step, a static analysis step, a change model creation step, a free vibration analysis step, a fracture member determination step, a collapse determination step, , Including. Of the individual margin calculation method, the process excluding the preparation step may be referred to as “redundancy analysis”.

  The individual margin calculation method differs from the basic margin calculation method described above in that the member to be destroyed (deleted) first in the change model creation step is arbitrarily selected. Since the other steps of the individual margin calculation method are substantially the same as the basic margin calculation method, the common parts will be described briefly.

  As shown in FIG. 6A, in the preparation step, a basic model is created (step S21), and a constant loading analysis (step S22) is performed to acquire the initial state of the bridge (step S23). The initial state of the bridge is stored in the result file 18.

  If the initial state is acquired in the preparation step, the static analysis step (step S24) is executed. In the static analysis step, an elasto-plastic finite displacement analysis is performed based on the basic model and the initial state data to acquire the stress state and displacement acting on each member of the bridge, and the obtained data is written to the result file 18. .

Here, FIG. 7A is a schematic conceptual diagram showing in a stepwise manner the first half of the individual margin calculation method according to the present embodiment. FIG. 7B is a schematic conceptual diagram showing the latter half of the method for calculating the individual margin according to the present embodiment in a stepwise manner.
The basic model J shown in FIG. 7A schematically shows a part of the bridge shown in FIG. 2A taken out. The upper chord members 61a and 61b, the lower chord members 62a and 62b, the diagonal members 63a and 63b, It consists of materials 64a, 64b, 64c and RC floor slab 65. The steps from the static analysis step to the destructive member determination step will be described with reference to FIGS. 7A and 7B.

Specifically, in the static analysis (step S24), as shown in (a) of FIG. 7A, a variable α is set to a reference load (dead load (D) + live load (L)) with respect to the basic model J. The additional load α (D + L) multiplied by is applied. The initial value of the variable α is set to α = 1. The static analysis means 33 performs a static analysis and applies stress (maximum stress) acting on each member of the basic model J to the stress state H ₁ (γ ₁₁ , γ ₂₁ , γ ₃₁ , γ ₄₁ , γ ₅₁ , γ ₆₁ , γ ₇₁ , γ ₈₁ , γ ₉₁ , γ ₁₀₁ )) and the displacement of each member is acquired, and these data are associated with the value of the variable α and written to the result file 18.

  In the change model creation step, one member constituting the bridge is arbitrarily selected as an “important member candidate”, and a new model (change model) is created by deleting the member from the basic model (step S25). When creating a change model, the basic model should be used. Data relating to the created change model is stored in the change model file 15.

  In the present embodiment, the member is deleted in the change model creation step. The operator may read out the data related to the basic model from the basic model file 12 and delete all the fiber elements 7 expressing the important member candidates.

Specifically, as shown in FIGS. 7A and 7B, in the modified model creation step, the vertical material 64b is selected as an “important member candidate” and the vertical material 64b is deleted. to create a J _1.

  The method for selecting the important member candidate is not particularly limited. For example, the analysis result of the constant loading analysis (step S22) may be used. Data such as load and strain acting on each member constituting the bridge is written to the result file 18 by the constant loading analysis (step S22). For example, even if a member having a large strain energy value is selected as an important member candidate Good.

  In the free vibration analysis step, an additional load α (D + L) is applied to the modified model created in the modified model creating step, and the free vibration analysis is performed by giving the stress state and displacement immediately before the important member candidate is deleted. This is performed (step S26). That is, in the free vibration analysis, a dynamic response analysis is performed using the stress borne by the important member candidate as a step load. Then, the free vibration analysis means 34 writes the stress state, displacement, and the like acting on each member of the changed model after performing the free vibration analysis in the result file 18 in association with the variable α at that time.

Specifically, in the free vibration analyzing step, as shown in (c) and (d) of FIG. 7A, with respect to change model J _1, together with the action of extra load α (D + L), remove the key member candidates The stress state H ₁ (γ ₁₁ , γ ₂₁ , γ ₃₁ , γ ₄₁ , γ ₅₁ , γ ₆₁ , γ ₇₁ , γ ₈₁ , γ ₉₁ , γ ₁₀₁ ) and the displacement acting on the basic model J immediately before Give free vibration analysis.

Then, as shown in FIG. 7A (d), the free vibration analysis unit 34, the vibration is applied to each member of the change model J ₁ until convergence stress (maximum stress) stress state H _{2 (gamma 12} , Γ ₂₂ , γ ₃₂ , γ ₄₂ , γ ₅₂ , γ ₆₂ , γ ₇₂ , γ ₈₂ , γ ₉₂ , γ ₁₀₂ ) and the displacement of each member, etc. The result file 18 is stored in association with each other.

  If the free vibration analysis is executed for the changed model, the free vibration analyzing means 34 determines whether or not there is a newly destroyed member in the changed model (step S27). The determination of whether or not a member has been destroyed is common to the member destruction determination step of the basic margin calculation method.

  In the member destruction determination step, when it is determined that “there is no newly destroyed member” (No in step S27), the collapse determination step is executed. The collapse determination step is common to the collapse determination step of the basic margin calculation method. In the collapse determination step, the current change model and data relating to the stress state and displacement of the change model are read out, a static analysis is performed without applying a load (step S28), and whether or not the entire bridge has collapsed. Is determined (step S29).

  In the determination step, when it is determined that “the entire bridge has collapsed” (Yes in Step S29), the variable α (variable α = 1 here) at that time is determined as the “individual margin” (Step S30). finish.

  On the other hand, if it is determined in the determination step that “the entire bridge does not collapse” (No in step S29), the variable α is changed (step S31a), and the member deleted in the changed model creation step is restored to the basic model ( After returning to the basic model J), the initial state is read (step S31b). Then, static analysis is performed again using the basic model and the initial state data (step S24). In the present embodiment, static analysis is performed again by increasing the variable α by 0.1.

  That is, in the static analysis after the loop (step S24), the model is returned to the basic model (the state in which there is no destructive member), the variable α is increased, and a load of α (D + L) is applied to the basic model. Perform a statistical analysis. Then, until it is determined that there is a newly destroyed member (Yes in Step S27) in the destructive member determining step (Yes in Step S27), or until it is determined that the entire bridge has collapsed (Yes in Step S29). ), The static analysis (step S24) to the restoration to the initial state (step S31b) is repeated. About this repeating process, the computer C for analysis should just be comprised in that way.

  In the destructive member determination step, when it is determined that “there is a destructed member” (Yes in step S27), the free vibration analyzing unit 34 writes the destructed member in the result file 18 and causes the display unit 4 to display it. . Then, as shown in FIG. 6B, a modified model creation step is executed (step S32).

In the present embodiment, for example, as shown in FIG. 7B, it is assumed that the diagonal material 63b is destroyed when the variable α becomes the variable α ₄ (= 1.3). Hereinafter, the destroyed member is also referred to as a “destructive member”. In the result file 18, the stress state H ₄ (γ ₁₄ , γ ₂₄ , γ ₃₄ , γ ₄₄₎ acting on each member of the changed model J ₁ immediately before the diagonal member 63 b is destroyed in association with the variable α _4. , Γ ₅₄ , γ ₆₄ , γ ₇₄ , γ ₈₄ , γ ₉₄ , γ ₁₀₄ ) and displacement and the like are stored.

In the change model creation step, the destructive member is deleted from the basic model, and a new change model is created (step S32). Specifically, as shown in FIG. 7B (a) and (b), since the present embodiment is determined that the diagonal member 63b is destroyed, the change model J ₂ from changing model J ₁ deleted the diagonal member 63b create.

  In the free vibration analysis step, an additional load α (D + L) is applied to the modified model created in the modified model creating step, and a free vibration analysis is performed by giving the stress state and displacement immediately before deleting the fracture member. This is performed (step S33). That is, the free vibration analysis means 34 performs a dynamic response analysis using the stress borne by the breaking member as a step load. Then, the free vibration analyzing means 34 acquires the stress state and displacement acting on the changed model after the free vibration analysis, and writes it in the result file 18 in association with the changed model at this time.

Specifically, in the free vibration analysis step, as shown in (c) of FIG. 7B, an additional load α ₄ (D + L) is applied to the changed model J ₂ and obtained by the previous free vibration analysis. It performs free vibration analysis gives stress state H ₄ and the displacement or the like.

Then, as shown in (d) of FIG. 7B, free vibration analysis unit 34, the vibration is applied to each member of the change model J ₂ until convergence stress (maximum stress) stress state H _{5 (gamma 15} , γ ₂₅ , γ ₃₅ , γ ₄₅ , γ ₅₅ , γ ₆₅ , γ ₇₅ , γ ₈₅ , γ ₉₅ , γ ₁₀₅ ) and the displacement of each member, etc., and these data are changed to the change model J _2. And stored in the result file 18.

  If the free vibration analysis is performed on the newly created changed model, the free vibration analyzing means 34 executes a destructive member determination step for determining whether or not there is a newly destroyed member in the changed model. (Step S34). The destructive member determination step (step S34) is common to the destructive member determination step (step S10) of the basic margin calculation method.

  Further, in the destructive member determination step (step S34), the loop process when it is determined that “there is a newly destructed member” starts from the change model creation step (step S8) of the basic margin calculation method. This is common with the process of repeating the member determination step (step S10). This makes it possible to perform dynamic response analysis using the step load as the stress borne by the destroyed member, and to perform analysis that takes into account the structural system that changes in response to chain failure of the member. it can.

  When it is determined in the destructive member determination step that “there is no newly destroyed member” (No in step S34), a collapse determination step is executed. The collapse determination step is common to the collapse determination step (step S11, step S12) of the basic margin calculation method.

  When it is determined that the entire bridge does not collapse in the collapse determination step (No in step S36), the variable α is changed (step S31a (see FIG. 6A)), and the member deleted in the change model creation step is restored. After returning to the basic model (basic model J), the initial state is read (step S31b). Then, static analysis is performed again using the basic model and the initial state data (step S24). That is, in the static analysis step after the loop (step S24), the model is returned to the basic model (the model without the fracture member), and the value of the current variable α is increased so that α (D + L) Perform static analysis by applying a load.

When it is determined in the collapse determination step that “the entire bridge has collapsed” (Yes in step S36), the variable α at that time (variable α ₄ (= 1.3) in the example of FIGS. 7A and 7B) is set to “individual”. The margin is determined (step S37), and the analysis is terminated.

  In the method for calculating the individual margin described above, the member to be destroyed (deleted) first among the members constituting the bridge is arbitrarily selected, and quantification is performed while taking into account the chain breaking phenomenon caused by the failure of this member. Thus, the individual margin can be calculated.

<Calculation method of important members>
Next, an important member calculation method will be described. In the individual margin calculation method described above, a plurality of members to be destroyed first (members to be deleted first) are selected as important member candidates, and a plurality of margins attributable to the respective members are calculated. Then, among the values obtained by dividing the calculated individual margins by the basic margin, the member having the smallest decrease rate with respect to the basic margin is determined as an important member (Fracture Critical Member).

  As described above, according to the structure analysis method for a structure according to the present embodiment, in the free vibration analysis step, the stress of the structural system immediately before the member is deleted in the free vibration analysis after one of the members is deleted. Since the state is given to the structural analysis model, it is possible to perform a dynamic response analysis using the stress borne by the broken member as a step load.

  In addition, until it is determined that there is no newly destroyed member, the modified model creation step of creating a new model by deleting the destroyed member and the free vibration analysis step based on this new model are repeated. It is possible to perform a dynamic analysis considering a structural system that changes according to the chain fracture of the. Therefore, since the collapse of the actual structure is taken into consideration, a more accurate collapse phenomenon can be analyzed.

  Further, according to the structure analysis method for a structure according to the present embodiment, the basic margin and the individual margin can be quantitatively calculated. Moreover, an important member can be determined based on the basic margin and the individual margin.

  Next, an example of a structure analysis method for a structure according to the present invention will be described. In the first embodiment, the basic margin and the individual margin are calculated using the basic margin calculation method and the individual margin calculation method described above for the actually constructed bridge, and the results are important. Determine the part.

  The target bridge is an upper road type steel truss bridge as shown in FIG. 8 and was constructed in 1981. This bridge is a bridge type in which the position of the center of gravity of the RC floor slab, which occupies most of the superstructure, is separated upward from the truss girder. The design conditions and the like are as described in the table of FIG.

<Creation of basic model>
When a basic model is created for the target bridge (step S1 in FIG. 4), the result is as shown in FIG. In order to consider damage due to member destruction, each member is modeled by a fiber model that can express plasticization. About element division of a member, one member was made into about 8 division. The joint between the members was set to a rigid joint.

  The RC floor slab was modeled by a laminated type shell element (see FIG. 2C). For the reinforcing bar layer, the plate thickness is determined so as to be equal to the actual cross section of the reinforcing bar, and the reinforcing bar is evaluated. By applying the material constitutive law of concrete and reinforcing bars to each layer, it is a floor slab model that considers cracks and plasticization of the floor slab.

  The slab anchor that joins the upper chord and the floor slab is defined by a non-linear spring. In the present invention, in order to perform free vibration analysis (dynamic analysis), mass is defined at the nodes between the members. In addition, the damping constant of free vibration analysis was calculated by the half power method based on the actual measurement of the target bridge.

<Rules for RC slabs>
In evaluating the strength of the target bridge, it is necessary to accurately calculate the strength of the slab. To that end, cracks and yielding must be taken into account in the concrete. In particular, if cracks are not taken into account, the proof strength of the RC slab will be highly evaluated. Therefore, in this example, in order to set the concrete tensile strength to 3 MPa, the extended Drucker prager was adopted as the material constitutive law for the concrete.

The extended Drucker prager yield function is as shown in Equation (1). In addition, the case where l ₀ = 0 in the equation (1) is a normal Drucker prager yield function.

Here, q is equivalent stress, and l is a first invariant amount of stress. α, l ₀ , and k are calculated from Equation (2), Equation (3), and Equation (4), respectively.

As the physical properties of the concrete, the tensile strength σ _t was 3 MPa, the yield stress σ _c was 21 MPa, and the friction angle β was 30 degrees. In addition, about the material constitutive law of the reinforcement of RC floor slab, it was set as the bilinear model of strain hardening E / 100.

<Always loading analysis>
In order to create an initial state of the analysis model, a static analysis based on a constant loading analysis in consideration of the placement of the RC floor slab was performed according to the steps described above (step S2 in FIG. 4). The live load (L) was applied as a fixed load. As shown in FIG. 10, the loading position was between the center spans, and the P1 load was loaded on the left side from the center.

FIG. 11 is a graph showing the maximum strain distribution of each member in the constant load analysis according to Example 1, wherein (a) is a diagonal material, (b) is a vertical material, and (c) is a lower chord material. Indicates. As shown in (a) to (c) of FIG. 11, each member has a strain value that is about half of the yield strain. It is considered that the relatively large margin is due to the influence of the floor slab rigidity.
For confirmation, a constant load analysis was performed on an analysis model having no floor slab stiffness. As a result, the strain value of the diagonal member was increased by about 1.7 times. Also, in the constant loading analysis, the analysis considering the slab stiffness from the beginning would overestimate the slab stiffness, and it was confirmed that the response value of each member was 30% smaller.

<Final strength analysis: Calculation of basic margin>
The ultimate strength analysis (static analysis step, change model creation step, free vibration analysis step, fracture member determination step, and collapse determination step) was performed according to the flow of FIG. FIG. 12 is a side view showing a member breaking position in the ultimate strength analysis according to the first embodiment. FIG. 13 is a graph showing the maximum strain distribution of each member in the ultimate strength analysis according to Example 1, wherein (a) is an oblique material, (b) is an upper chord material, and (c) is a lower chord material. Indicates.

  As shown in FIG. 12, when the static analysis step was performed, the diagonal member 101 first reached the member fracture strain value and broke (step S6 in FIG. 4). The value of the variable α at this time was α = 2.6.

Thereafter, the upper chord material 102 and the lower chord material 103 were sequentially broken in the order shown in FIG. 12 by repeating the modified model creation step (step S8 in FIG. 4) and the free vibration analysis step (step S9). Thereafter, there were no new members to be destroyed, and in the collapse determination step (step S12 in FIG. 4), it was determined that the bridge had an unstable structure and the entire bridge was collapsed, and the analysis was completed. As a result of this analysis, the basic margin of the target bridge was calculated as “2.6”.
The broken members are all members on the left side (see FIG. 10) where the load acts more greatly.

  Here, as shown in FIG. 13 (a), regarding the destruction of the diagonal member 101, the diagonal member 101 near the pier K1 and the pier K2 has a large strain, and the diagonal member 101 on the pier K1 side slightly breaks the member first. It can be seen that the strain value has been reached. Considering the upper chord material 102 destroyed second and the lower chord material 103 destroyed third, it can be said that damage concentrates near the diagonal material 101 destroyed first, and the entire bridge collapses.

  In the normal loading analysis, the same ultimate strength analysis was performed from the beginning in consideration of the rigidity of the floor slab, but the upper chord material did not break and other members broke. In other words, it has been confirmed that the destruction mode has changed.

FIG. 14 is a graph showing the strain history of a broken member in the ultimate strength analysis according to Example 1, wherein (a) shows the upper chord material and (b) shows the lower chord material.
As shown in (a) of FIG. 14, after the diagonal members 101 is broken, it reached 3Ipushiron _y is the strain value destruction strain New Moon member 102 after 0.031 seconds, it can be seen that destroyed. Further, as shown in (b) of FIG. 14, after the diagonal members 101 is broken, the strain of the lower chord member 103 after 0.038 seconds reaches 3Ipushiron _y is the strain value destruction, it can be seen that destroyed. The target bridge is 0.038 seconds after the diagonal member 101 is destroyed, and the entire bridge becomes unstable and collapses.

  FIG. 15 is a stress contour diagram of a floor slab immediately after collapse in the ultimate strength analysis according to the first embodiment. In FIG. 15, the black portion indicates tensile stress, the gray portion indicates compressive stress, and the white portion indicates that small stress is generated. It can be seen that the RC floor slab at the center of the bridge is in a compressed state, and most of the RC floor slabs near the pier K1 and the pier K2 reach a tensile strength of 3 MPa. Further, it can be seen that only the vicinity of the RC floor slab where the fracture members on the left side are concentrated is in a tensile stress state. In the RC floor slab, it was confirmed that the part of the reinforcing steel where the concrete had reached the tensile strength was not yielding. In addition, it was confirmed that most of the slab anchors were plasticized and partially ruptured (excess allowable displacement).

<Redundancy analysis: Calculation of individual margin>
Next, according to the flow of FIG. 6A and FIG. 6B, redundancy analysis (static analysis step, change model creation step, free vibration analysis step, fracture member determination step, collapse determination step) was performed. In the change model creation step (step S25 in FIG. 6A), the member to be deleted first (important member candidate) may be arbitrarily selected by the operator, but in this embodiment, the result of constant loading analysis was used. That is, based on FIG. 11, members having a large strain and a high yield point were selected one by one from the diagonal materials, the vertical materials, and the lower chord materials as important member candidates. The important member candidates are all members on the left side of the bridge. The positions of the diagonal member 111, the vertical member 112, and the lower chord member 113 selected as important member candidates are shown in FIG.

<Individual margin of diagonal material 111>
FIG. 17 is an analysis result of the redundancy analysis according to the first embodiment, where (a) shows the maximum strain distribution of each diagonal material after the diagonal material is deleted, and (b) shows the fracture position of the member. .
In the modified model creation step (step S25) shown in FIG. 6A, the diagonal material 111 (left side) is deleted to create a modified model, then the variable α is changed (step S31a), and steps S24 to S31b are repeated. However, as shown in FIG. 17B, the left lower chord material 114 was newly broken. The value of the variable α at that time was α = 1.8.

Thereafter, the lower chord material 114 is deleted in the modified model creation step (step S32) shown in FIG. 6B and the automatic vibration analysis step (step S33) is performed, but it is determined that there is no newly broken member (step S34). In addition, it is determined that the entire bridge has collapsed in the collapse determination step (step S36), and the analysis is completed.
As a result, the individual margin when the important member candidate is selected as the diagonal member 111 in the target bridge was determined to be “1.8”.

  When the fracture situation is considered with reference to FIG. 17B, only the lower chord material 114 (left side) near the diagonal member 111 (left side) is damaged, and the fracture member does not expand further, and the entire bridge collapses. I was able to confirm.

<Individual margin of vertical member 112>
FIG. 18 is an analysis result of the redundancy analysis according to the first embodiment, where (a) shows the maximum strain distribution of each vertical material after the vertical material is deleted, and (b) shows the fracture position of the member. Show.
In the modified model creation step (step S25) shown in FIG. 6A, the vertical member 112 (left side) is deleted to create a modified model, and then the variable α is changed (step S31a), and steps S24 to S31b are repeated. However, as shown in FIG. 18B, the left lower chord material 114 was newly broken. The value of the variable α at that time was α = 1.4.

Thereafter, the lower chord material 114 is deleted in the modified model creation step (step S32) shown in FIG. 6B and the automatic vibration analysis step (step S33) is performed, but it is determined that there is no newly broken member (step S34). In addition, it is determined that the entire bridge has collapsed in the collapse determination step (step S36), and the analysis is completed.
As a result, the individual margin when the important member candidate in the target bridge is selected as the vertical member 112 is determined to be “1.4”.

  When the fracture situation is considered with reference to FIG. 18B, only the lower chord material 114 (left side) near the vertical material 112 (left side) is damaged, and the fracture member does not expand further, and the entire bridge collapses. I was able to confirm.

<Individual margin of lower chord material 113>
FIGS. 19A and 19B are analysis results of the redundancy analysis according to the first embodiment, where FIG. 19A shows the maximum strain distribution of the lower chord material after the lower chord material is deleted, and FIG. 19B shows the fracture position of the member. .
In the modified model creation step (step S25) shown in FIG. 6A, after the lower chord material 113 (left side) is deleted to create a modified model, the variable α is changed (step S31a), and steps S24 to S31b are repeated. However, as shown in FIG. 19B, the right lower chord material 115 (right side) was newly broken. The value of the variable α at that time was α = 1.7.

Thereafter, the lower chord material 115 is deleted in the modified model creation step (step S32) shown in FIG. 6B and the automatic vibration analysis step (step S33) is performed, but it is determined that there is no newly broken member (step S34). In addition, it is determined that the entire bridge has collapsed in the collapse determination step (step S36), and the analysis is completed.
As a result, the individual margin when the important member candidate in the target bridge is the lower chord material 113 (left side) is determined to be “1.7”.

  When considering the fracture situation with reference to FIG. 19 (b), only the lower chord material 115 (right side) near the lower chord material 113 (left side) was damaged, and the destruction member did not expand further, and the entire bridge collapsed. I was able to confirm.

  FIG. 20 is a table in which the redundancy analysis results are organized. The “α reduction rate” in the table is a value obtained by dividing the individual margin in each member by the basic margin α = 2.6 obtained by the ultimate strength analysis. From FIG. 20, the vertical member 112 having the smallest individual margin reduction rate is determined as the important member (FCM).

  In Example 2, an analysis using two members (hereinafter also referred to as a two-member analysis) was performed to verify the structure analysis method for a structure according to the present invention. In the two-member analysis, the analytical solution obtained by the two-member analysis and the theoretical solution of the step response analysis in which a load of 750 kN is applied to one member are compared and verified.

<Analysis conditions>
As shown in (a) and (b) of FIG. 21, two members of the target bridge (in this case, diagonal materials) are taken out, one end is constrained in a state where the taken out members 201 and 202 are overlapped, A tensile load of 1500 kN is applied to the free end portion in the member axial direction.

  Next, as shown in FIG. 21C, the member 201 is broken (deleted), and the response characteristics of the remaining members 202 are observed. As an analysis model, one member is one element, and the mass is concentrated at the contact point at the free end. The attenuation was assumed to be 0.1%.

<Analysis method>
In the analysis method, first, a static analysis in which a tensile load of 1500 kN is applied in a state where two members are stacked is performed, and the stress state is stored. This process corresponds to, for example, the static analysis step (step S4) shown in FIG.

  Next, the member 201 is removed. This process corresponds to, for example, a change model creation step (step S8) shown in FIG.

  Next, the stored stress state is read and a dynamic analysis is performed in consideration of the attenuation of 0.1%. This process corresponds to, for example, the free vibration analysis step (step S9) shown in FIG. At the time of starting the dynamic analysis, the stress borne by the member 201 is acting on the member 202.

  In the dynamic analysis in this analysis, the Newmark β method used in the seismic response analysis was adopted. The time integration interval Δt is set to 0.0001 so as to be smaller than Δt (for example, 0.01) used in the seismic response analysis and to sufficiently satisfy the Courant condition of Expression (5).

Here, l _min is the minimum distance between nodes, and c is the velocity of the stress wave (= (E / p) ^1/2 , E: elastic modulus, p: density).
The analysis software used in this analysis uses Sean FEM (manufactured by Seismic Analysis Laboratory Co., Ltd.), and the type of analysis is elasto-plastic finite displacement analysis.

<Comparison verification>
As shown in FIG. 22, a theoretical solution obtained by performing a step response analysis of 750 kN (a burden of one member) from one initial state on one member is compared with an analytical solution obtained by a two-member analysis. As a result, almost equivalent results are obtained. That is, according to the structure analysis method for a structure according to the present invention, it can be said that the impact force when one member breaks can be evaluated.

  In Example 3, the behavior after member destruction is analyzed using a simple truss structure in which a part of the target bridge is extracted, and the structure analysis method for a structure according to the present invention is verified. Note that the analysis using the simple truss structure as in the present embodiment is also referred to as “simple truss analysis”.

<Analysis conditions>
As shown in FIGS. 23A and 23B, a part of the target bridge on the pier K1 is extracted to create a simple truss structure 120. FIG. The simple truss structure 120 includes upper chord members 121 and 122, lower chord members 123 and 124, vertical members 125, 126 and 127, and diagonal members 128 and 129. The vertical members 125 and 127 were formed longer than the actual length so that the lower chord members 123 and 124 were horizontal. The conditions of each member of the simple truss structure 120 are as shown in FIG.

  The simple truss structure 120 is modeled with a fiber model. Here, one member was divided into eight, and the joining condition between the members was rigid joining. In order to see the effect of element division, analysis was also performed in the case of fine element division (hereinafter referred to as “subdivision model”). The mass is defined not only at the member coupling portion but at all nodes. In addition, since the simple truss structure 120 is considered to be plasticized, the material constitutive law is a kinematic hardening law of a bilinear model with an elastic modulus of 2 × 10 MPa, yield stresses of 235 MPa and 355 MPa, and strain hardening of E / 100. did.

  Under such conditions, the behavior immediately after the diagonal member 128 was destroyed (deleted) from the state in which two types of loads of horizontal load 1500 kN and 3500 kN were applied to the upper left end portion of the simple truss structure 120 was specifically examined. . The dynamic analysis method is the same as in Example 2, and the time integration interval Δt is set to 0.0001 so that the Courant condition is satisfied. In the subdivision model, the time integration interval Δt is set to 0.00001.

<Preliminary analysis>
Prior to the response analysis by this analysis, a prior analysis is performed on the simplified truss structure 120. FIG. 24 is an axial force diagram in the preliminary analysis according to Example 3, where (a) is before the diagonal breakage, (b) is a structure without the diagonal, and (c) is the diagonal. A structure in which an impact load is applied to both ends of the part is shown. In the pre-analysis, when a horizontal load of 1500 kN is applied to the structure in a healthy state ((a) in FIG. 24) and the structure in which the diagonal member 128 does not exist from the beginning ((b) in FIG. 24). The axial force acting on each member is acquired.

  As shown in FIGS. 24A and 24B, in the simple truss structure 120 ′ in which the diagonal member 128 does not exist, the axial force of the diagonal member 129 is larger than that in the simple truss structure 120, and the vertical member 126. It can be seen that has come to bear the load.

  In FIG. 24 (c), the diagonal load of the simple truss structure 120 ′ without the diagonal member 128 is obtained by multiplying the axial load that was borne by the destroyed member by the impact coefficient 1.854. Static analysis was performed by acting on the positions of both ends of 128. The analysis for redundancy evaluation (hereinafter referred to as “conventional method”) performed in Non-Patent Document 1 described above is obtained by superimposing the results of (a) and (c) of FIG.

<Results of 1500kN load analysis>
(Overall consideration)
FIG. 25 is a graph showing an axial force history in a simple truss analysis relating to a 1500 kN load of Example 3, where (a) is an upper chord material, (b) is a vertical material, and (c) is an oblique material. . As shown in FIG. 25, the behavior after the oblique member 128 was broken was considered for the upper chord member 121, the vertical member 126, and the oblique member 129 that generate a large axial force.

  Among the response values of each graph, the response value with “a” at the end of the sign indicates the analysis result by this analysis, and the response value with “b” is the response value of each member without the diagonal member 128 from the beginning. The axial force (corresponding to (b) in FIG. 24) is shown, and the response value with “c” shows the analysis result by the conventional method.

  As shown in the response values 121a, 126a, and 129a, the analysis result according to the present invention shows that the diagonal material 128 vibrates around the response values 121b, 126b, and 129b that indicate a state in which there is no initial material. In this analysis, all members were elastic responses.

  As shown in FIG. 25A, it can be seen that the upper chord material 121 has about half the axial force and the amplitude is smaller than that of the diagonal material 129. In addition, since the response value 121b indicating that the diagonal member 128 is not present from the beginning overlaps with the response value 121c indicating the conventional method, it can be understood that the conventional method cannot express the behavior due to the impact. That is, in the conventional method, the influence due to the vibration after the diagonal member 128 is broken cannot be considered, but in the present analysis, the influence can be taken into consideration.

  As shown in FIG. 25B, the maximum value of the response value 126a of the vertical member 126 is smaller than the response value 126c of the conventional method. That is, it can be seen that the conventional method tends to be overestimated.

  On the other hand, as shown in FIG. 25C, the maximum value of the response value 129a of the diagonal member 129 is substantially equal to the value of the response value 129c of the conventional method.

  Here, the difference between the conventional method and this analysis will be further considered. FIG. 26 is a schematic diagram showing a deformation state when the axial force of the vertical member is maximum in the simple truss analysis according to the 1500 kN load of Example 3, where (a) is the present analysis, and (b) is the conventional analysis. Show the law. In FIG. 26, a bold part represents a state after deformation.

  When comparing (a) and (b) of FIG. 26, the diagonal member 129 of this analysis is deformed into an S-shape. In contrast, the oblique material 129 ″ according to the conventional method has a different deformation state. In the conventional method, it can be seen that the diagonal member 129 ″ itself vibrates.

(About longitudinal vibration of each member)
When the tendency of vibration generated in each member after the diagonal member 128 is broken is compared, the diagonal member 129 disposed in a direction substantially perpendicular to the diagonal member 128 to be broken is shown in FIG. In addition, it can be seen that high frequency vibration components are not included so much.
On the other hand, as shown in FIGS. 25A and 25B, the upper chord member 121 and the vertical member 126 contain a large amount of high-frequency vibration components. It can also be seen that these high-frequency vibrations become smaller as time elapses. From these, it can be said that the high-frequency component of the axial force generated in each member due to the destruction of the diagonal member 128 is due to the longitudinal vibration in each member, and has little influence on the generated maximum axial force. That is, the axial force (cross-sectional force) generated in each member is considered to be due to the flexural vibration of each member.

(About transmission of axial force in each member)
In order to clarify the transmission of vibration (axial force) in one member, attention was paid to the vertical member 126 (see FIG. 24B) of the simplified truss structure 120 ′ in which the diagonal member 128 does not exist. FIG. 27 is a graph showing axial force histories at three locations of a vertical member at a load of 1500 kN in Example 3.
As shown in FIG. 27, it can be seen that the central portion and both ends of the vertical member 126 vibrate substantially in the same manner. Further, it can be seen that the influence of longitudinal vibration in the member varies depending on the position in the member. Further, as shown in FIG. 27, it can be seen that a phase difference appears in one member at the rising time (0 to 0.002 seconds) of the response history of the axial force. It was confirmed that the magnitude of this phase difference coincided with the theoretical calculation.

(Effect of component element division)
The results so far are obtained by dividing one member into eight parts (hereinafter referred to as “normal division”) in each member constituting the simple truss structure 120. This division is intended to model the entire target bridge. In order to investigate the influence of the division, an analysis was performed when one member was divided into 100 elements (hereinafter referred to as “subdivision”). FIG. 28 is a graph showing the axial force history in the vertical subdivision analysis at the 1500 kN load of Example 3. In the drawing, the normal division is represented by a response value 126a, and the subdivision is represented by a response value 126d.

  As shown in FIG. 28, it can be seen that the normal division (response value 126a) and the subdivision (response value 124d) coincide with each other up to about one cycle of the response value, but the difference appears with time. In the structural analysis method according to the present invention, the first cycle in which the maximum value appears in the history of the axial force is important.

<Analysis result of 3500kN load>
Similarly to the above-described 1500 kN load, the diagonal material 128 was broken (deleted) from the state where the horizontal load was 3500 kN with respect to the simple truss structure 120 (see FIG. 23B), and the dynamic analysis was performed. The horizontal load of 3500 kN is a load that does not plasticize all members even when applied to the simplified truss structure 120 ′ shown in FIG.

  FIG. 29 is a graph showing an analysis result relating to the 3500 kN load of Example 3, where (a) shows the axial force history of the vertical member, and (b) shows the stress-strain relationship of the vertical member. In the figure, the response value 126a ′ indicates the result of this analysis, the response value 126b ′ indicates the analysis result in a state where no diagonal material is present from the beginning (corresponding to FIG. 24B), and the response value 126c ′ indicates the conventional method. The results are shown.

  As shown in FIG. 29 (a), the response value 126a ′ of this analysis is different from the case of 1500 kN load, and the generated axial force oscillates around the response value 126b ′ of the simple truss structure in which no diagonal material exists from the beginning. It can be seen that after the maximum axial force is exceeded, the state is lowered.

  Further, as shown in FIG. 29B, it can be seen that the response value 126d 'has passed the yield point, and that the vertical member 126 is greatly plasticized. That is, it can be said that the vibration characteristics are changed due to plasticity of the member due to the impact of the destruction of the diagonal member 128. Here, although the publication of results other than the vertical member 126 is omitted, it has been confirmed that most members other than the vertical member 126 have become greatly plasticized.

FIG. 30 is a table summarizing the damage states acting on each member in Example 3 in the conventional method and the present analysis. The numerical value of FIG. 30 is obtained by normalizing the analysis result of the 3500 kN load by the yield strain ε _y . As shown in FIG. 30, whereas in the present analysis element other than top chord member is made larger plasticized, in the conventional method, only the diagonal members 129 is in the plastic of about 1.22ε _y. This is probably because the conventional method was a linear analysis, and the force distribution due to the plasticization of the member could not be accurately performed, and was underestimated.

  According to the third embodiment described above, according to the present analysis (the present invention), the behavior after the member failure can be accurately reproduced, whereas in the conventional method, the behavior after the member failure is within the elastic range. There is a tendency to overestimate the level. In the conventional method, when the response value becomes large and reaches the level in the plastic region, it is considered that there is a tendency to underestimate.

DESCRIPTION OF SYMBOLS 1 Memory | storage means 2 Arithmetic processing means 3 Input means 4 Display means 5 Bus | bath 11 Editor program 12 Basic model file 13 Constant loading analysis program 14 Static analysis program 15 Changed model file 16 Free vibration analysis program 17 Collapse judgment program 18 Result file 31 Structure Analytical model creation means 32 Constant load analysis means 33 Static analysis means 34 Automatic vibration analysis means 35 Collapse determination means

Claims (5)

A structure composed of multiple members is modeled with elements that can take into account the nonlinearity of each member, creating a model for structural analysis, and using this structural analysis model to analyze the failure phenomenon of the structure A structure analysis method for a structure
A static analysis step of performing a static analysis on the structural analysis model and acquiring stress acting on each member constituting the structural analysis model;
A change model creation step for newly creating a structural analysis model in a state where one of the members of the structural analysis model is deleted;
For the structural analysis model created in the modified model creation step, a free vibration analysis step for performing free vibration analysis by applying stress acting on each member immediately before deleting the member;
A destructive member determination step for determining whether or not there is a newly destroyed member in the free vibration analysis step;
When it is determined that there is no newly destroyed member in the destructive member determination step, static analysis is performed on the structural analysis model after the free vibration analysis is performed, and the structural analysis model is A collapse determination step for determining whether or not it has collapsed,
The structural analysis method for a structure is characterized in that the modified model creation step, the free vibration analysis step, and the destructive member determination step are repeated until it is determined in the destructive member determination step that there is no newly destroyed member. . In the static analysis step, static analysis is performed by applying an additional load obtained by multiplying the reference load by the variable α,
In the collapse determination step, when it is determined that the structural analysis model does not collapse, after increasing the variable α, the process proceeds to the static analysis step, and the structural analysis model is collapsed. 2. The structural analysis method for a structure according to claim 1, wherein the modification model creation step, the free vibration analysis step, the fracture member determination step, and the collapse determination step are repeated until the determination is made.   The structural analysis method for a structure according to claim 2, wherein when there is a member destroyed in the static analysis step, the member is selected as a member to be deleted first in the change model creation step. .   One member is arbitrarily selected from the structural analysis models after the analysis in the static analysis step, and this member is selected as a member to be deleted first in the modified model creation step. The structure analysis method for a structure according to claim 2. Before the static analysis step, further includes a constant loading analysis step of creating an initial state of the structural analysis model by performing a static analysis by constant loading.
The member to be deleted first in the change model creation step is selected based on the strain energy obtained in the constant loading analysis step among the members constituting the structure. Structure analysis method of the structure.

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