Method for selecting reinforcement location of statically indeterminate structure
The method addresses the inefficiency in reinforcing RC rigid frame viaducts by using a material damage index to select critical columns for reinforcement, enhancing structural integrity and ductility.
Patent Information
- Application Number
- JP2024122396
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2024-07-29
- Publication Date
- 2026-02-10
AI Technical Summary
Existing methods for evaluating reinforced concrete (RC) beam members fail to assess the entire structure's load-bearing capacity in statically indeterminate structures like rigid-frame viaducts, and reinforcement is often inefficient due to obstacles, even if some columns reach their limit.
A method for selecting reinforcement points in statically indeterminate structures using a material damage index from nonlinear finite element analysis to identify critical columns, followed by reinforcement and re-analysis to confirm the effect on the entire structure.
Enables efficient and effective reinforcement of RC rigid frame viaducts by identifying and reinforcing critical columns, improving ductility without significant load reduction, and ensuring the structure maintains load-bearing capacity.
Smart Images
Figure 2026020824000001_ABST
Abstract
Description
[Technical Field]
[0001] The present invention relates to a method for selecting reinforcement points for a statically indeterminate structure, which targets a statically indeterminate structure having a plurality of reinforced concrete columns and a slab supported by the columns, and selects columns to be reinforced. [Background technology]
[0002] In Non-Patent Document 1, damage and destruction of reinforced concrete RC beam members are evaluated using a material damage index obtained from finite element analysis. In Non-Patent Document 1, normalized cumulative strain energy (W n ) and the second invariant of deviatoric strain (√J2). [Prior art documents] [Non-patent literature]
[0003] [Non-Patent Document 1] Saito et al., Damage Assessment of RC Beams Using Nonlinear Finite Element Analysis, Journal of the Japan Society of Civil Engineers, E2, Vol. 67, No. 2, pp. 166-180, 2011 Summary of the Invention [Problem to be solved by the invention]
[0004] However, Non-Patent Document 1 only evaluates the RC beam members individually, and does not evaluate the entire structure in which the RC beam members are arranged. In statically indeterminate structures such as rigid-frame viaducts, even if the load-bearing capacity of some of the column members reaches its limit, the load-bearing performance of the entire structure may not be lost.
[0005] Furthermore, when reinforcing the columns of an existing RC rigid frame viaduct, there are cases where reinforcement is difficult due to obstacles, etc. Even in such cases, if it is possible to select the columns that will cause critical damage to the existing RC rigid frame viaduct, it will be possible to carry out reinforcement efficiently and effectively.
[0006] Therefore, an object of the present invention is to provide a method for selecting reinforcement points of a statically indeterminate structure, which makes it possible to appropriately select columns that should be reinforced when viewed from the perspective of the entire statically indeterminate structure. [Means for solving the problem]
[0007] In order to achieve the above-mentioned object, the method for selecting reinforcement points for a statically indeterminate structure of the present invention is a method for selecting reinforcement points for a statically indeterminate structure that targets a statically indeterminate structure having a plurality of reinforced concrete columns and slabs supported by the columns, and selects columns to be reinforced.The method is characterized by comprising the steps of: selecting columns that cause a decrease in the load of the statically indeterminate structure using a material damage index of the concrete or reinforcing steel of the columns calculated by nonlinear finite element analysis using an analytical model of the statically indeterminate structure to be reinforced; and performing nonlinear finite element analysis again using an analytical model after reinforcement in which the selected columns are reinforced, and confirming the reinforcing effect of the entire statically indeterminate structure based on the results of the nonlinear finite element analysis after reinforcement.
[0008] Here, when confirming the reinforcing effect of the entire statically indeterminate structure, the validity of the selection of the columns can be confirmed in relation to the horizontal load acting on the statically indeterminate structure and the resulting horizontal displacement occurring in the slab.
[0009] Furthermore, when the material damage index is the normalized cumulative strain energy indicating compressive damage to concrete, the judgment criterion can be whether or not the normalized cumulative strain energy of the column calculated by the nonlinear finite element analysis exceeds a predetermined limit value.
[0010] Furthermore, if a column that causes a decrease in the load of the statically indeterminate structure is identified separately, it is preferable to select additional columns to reinforce and repeat the process of adding additional columns to reinforce the structure until the validity of the selection of the columns can be confirmed.
[0011] Furthermore, the nonlinear finite element analysis can be a pushover analysis in which a horizontal load perpendicular to the extension direction of the slab is gradually applied to the analytical model to evaluate the relationship with horizontal displacement. [Effects of the Invention]
[0012] In the method for selecting reinforcement points for a statically indeterminate structure of the present invention, which is configured as described above, the first step is to select columns that cause a decrease in the load of the statically indeterminate structure using a material damage index calculated by nonlinear finite element analysis.
[0013] Then, using the analytical model after reinforcing the selected columns, a nonlinear finite element analysis is performed again to confirm the reinforcement effect of the entire statically indeterminate structure, which allows appropriate selection of columns to be reinforced from the perspective of the entire statically indeterminate structure. [Brief explanation of the drawings]
[0014] [Figure 1] 1 is a flowchart illustrating the steps of a method for selecting reinforcement points for a statically indeterminate structure according to this embodiment. [Figure 2] This is an explanatory diagram showing the outline of the RC rigid frame viaduct. [Figure 3] This is a plan view explaining the configuration of the RC rigid frame viaduct. [Figure 4] This is an explanatory diagram showing the analysis results of the RC rigid frame viaduct before reinforcement. [Figure 5] FIG. 10 is an explanatory diagram showing the columns selected for reinforcement. [Figure 6] FIG. 6 is an explanatory diagram showing the analysis results of the reinforced analytical model of FIG. 5. [Figure 7] FIG. 10 is an explanatory diagram showing columns selected for additional reinforcement. [Figure 8] FIG. 8 is an explanatory diagram showing the analysis results of the re-reinforced analysis model of FIG. 7. DETAILED DESCRIPTION OF THE INVENTION
[0015] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Fig. 1 is a flowchart illustrating the procedure for selecting reinforcement points for a statically indeterminate structure according to this embodiment, and Fig. 2 is an explanatory diagram showing an outline of an RC rigid frame viaduct, which is a statically indeterminate structure.
[0016] Generally, when assessing the structural safety of a reinforced concrete (RC) structure, the limit state of the structure's structural safety is often considered to be when any one of its members reaches the limit state of destruction.However, RC rigid frame viaducts are statically indeterminate structures, and even if some parts or members are destroyed, it is thought that the structure will not immediately lose its load-bearing capacity.
[0017] Therefore, earthquake resistance diagnosis and reinforcement of existing RC rigid frame viaducts have been carried out with priority on columns prone to shear failure. In these earthquake resistance diagnosis, it is often confirmed that the shear force at the time of bending strength of the member does not exceed the shear strength. Shear failure is extremely brittle, and there is a certain degree of rationality in evaluating individual members.
[0018] On the other hand, in the case of bending failure, even if the member reaches its bending strength, a significant decrease in strength or axial deformation does not immediately occur. However, even in the case of bending failure, reinforcement is required if the deformation capacity is insufficient.
[0019] However, when reinforcing the columns of an existing RC rigid frame viaduct, reinforcement may be difficult due to obstacles, etc. Even in such cases, it is desirable to be able to select the columns that should be reinforced by taking advantage of the advantage that RC rigid frame viaducts are statically indeterminate structures.
[0020] Therefore, in the method for selecting reinforcement points for a statically indeterminate structure in this embodiment, columns that will cause critical damage to an RC rigid frame viaduct are selected, thereby enabling efficient and effective reinforcement.
[0021] An RC rigid frame viaduct, which is exemplified as a statically indeterminate structure in this embodiment, comprises multiple columns made of reinforced concrete and a slab supported by the columns, as shown in Fig. 2. An example of an RC rigid frame viaduct is a railway viaduct where trains run on tracks laid on the slab.
[0022] Figure 2 shows a three-span viaduct in which a slab is placed on top of multiple portal frame structures formed by pairs of columns and girders spaced apart on the left and right. In Figure 2, four rows of portal frame structures are shown along the extension direction of the slab, so starting from the first set of columns in the portal frame structure, they will be called L1 and R1 columns, L2 and R2 columns, L3 and R3 columns, and L4 and R4 columns.
[0023] Figure 3 is a plan view explaining the structure of an RC rigid frame viaduct. This RC rigid frame viaduct has a drum-shaped planar shape, with its width changing in the direction of the slab extension. Such an RC rigid frame viaduct is a statically indeterminate structure that is asymmetric with respect to the center of the structure (see the black circles ● indicating the displacement measurement positions), and even if one member is damaged, the stress is redistributed, allowing the structure to maintain its load-bearing capacity against horizontal forces.
[0024] Therefore, in this embodiment of the method for selecting reinforcement points for a statically indeterminate structure, some columns of the existing RC rigid frame viaduct are selected as reinforcement points so that the ductility can be improved without causing a significant reduction in the load on the existing RC rigid frame viaduct.
[0025] Next, the procedure for selecting reinforcement points for a statically indeterminate structure according to this embodiment will be described with reference to the flowchart of FIG.
[0026] First, in step S1, a target structure to be reinforced is identified. In this embodiment, the target structure is an RC rigid frame viaduct, which is a statically indeterminate structure shown in Figure 2. Then, in step S2, an analytical model is created.
[0027] Although the details are not shown in Figure 2, a 3D mesh was generated based on the external shape of the RC rigid frame viaduct to enable finite element analysis (FEM) and used as an analytical model. In the analytical model of the RC rigid frame viaduct, concrete was treated as a solid element, and the basic mesh size was 200 mm.
[0028] The stress-strain relationship of concrete was calculated using the Hordijk model on the tension side and the Parabolic model on the compression side, taking into account the softening gradient based on fracture energy.The crack surface was treated as a fixed crack model, and the AI-Mahaidi model, in which shear force decreases with crack width, was applied to the transmission of shear force at the crack surface.
[0029] On the other hand, the rebars were modeled using embedded rebar elements. The stress-strain relationship of the rebars was assumed to be linear up to the yield strength, after which a buckling model was applied to represent the buckling behavior. The buckling length was set to 400 mm, four times the spacing of the hoop rebars, and the elastic modulus was set to 200 kN / mm. 2 The piles were modeled as wire rods, and ground springs were placed in the horizontal and vertical directions.
[0030] Then, in step S3, a structural analysis is performed using the analytical model created in step S2. The three-dimensional nonlinear finite element analysis used in the structural analysis can evaluate the damage state of constituent parts and members, including the post-peak region, and is therefore a useful method for determining the load-bearing capacity of a structure.
[0031] Specifically, a pushover analysis is performed in which a horizontal load is applied to the analytical model in a direction perpendicular to the extension direction of the slab (perpendicular to the bridge axis). Pushover analysis is an analytical method in which a static seismic intensity (load) is gradually applied to the structure, and the seismic performance of the entire structure is evaluated based on the relationship between the applied seismic intensity (load) and horizontal displacement. Here, a horizontal seismic intensity is applied.
[0032] The loading method was load control, applying acceleration in one horizontal direction. Then, using the arc length increment method perpendicular to the bridge axis, the load was gradually increased until the balance calculation diverged. Additionally, the initial load was applied vertically as a line load, consisting of the bridge's own weight and a standard train load (EA-17). Half of the weight of the adjacent girder was applied near the support.
[0033] In the analysis, the failure mode of all columns was assumed to be shear failure, and the horizontal force was largely redistributed due to a significant decrease in the columns' rigidity.In evaluating the analysis results, as shown in Figure 3, the center of the slab was set as the displacement measurement position, and the horizontal and vertical displacements at this position were used to evaluate the entire structure.
[0034] First, in step S4, the results of the structural analysis are used to confirm the degree of damage to each column (L1 column, R1 column, L2 column, R2 column, L3 column, R3 column, L4 column, R4 column). The degree of damage to the columns can be confirmed using material damage indicators for concrete or rebar.
[0035] The material damage index for concrete is the normalized cumulative strain energy W n can be used. Normalized cumulative strain energy W n is an index expressing compressive damage to concrete, as defined in Non-Patent Document 1. The buckling level of the above-mentioned buckling model serves as an index of material damage to reinforcing bars.
[0036] In detail, the analysis results are used to examine the relationship between the horizontal seismic intensity and horizontal displacement of the RC rigid frame viaduct, and the normalized cumulative strain energy W of each column. n Figure 4 shows the analysis results of the RC rigid frame viaduct before reinforcement. Here, the normalized cumulative strain energy W n The research by Maki et al. (Maki et al., Numerical Analysis of Three-Dimensional Load-Resistant Mechanism of RC Members Using Concrete Damage Index, Journal of the Japan Society of Civil Engineers, Vol. 78, No. 1, pp. 121-137, 2022) has shown that the dependency of element division can be reduced by taking a weighted average. Therefore, in Figure 4, W nThe weighted average value is shown with an upper bar attached to it. In the following, the upper bar may be omitted for the sake of simplicity.
[0037] As shown in Fig. 4, the normalized cumulative strain energy W of the L4 and R4 columns at a horizontal displacement of approximately 60 mm n increased rapidly and reached the limit line (1500μ) indicating compressive damage. At almost the same time, the horizontal seismic intensity decreased. From the results of this pushover analysis, it can be determined that the cause of the decrease in the load of the RC rigid frame viaduct was compressive damage to the L4 and R4 columns. In addition, the normalized cumulative strain energy W of the other columns (L1 column, R1 column, L2 column, R2 column, L3 column, R3 column) n did not reach the limit line.
[0038] Therefore, in step S5, the normalized cumulative strain energy W n The L4 and R4 columns, where the values exceeded the limit value (1500μ), were judged to be columns that needed to be reinforced as they would affect the RC rigid frame viaduct.
[0039] Then, in step S51, L4 column and R4 column were selected as columns to be reinforced. Figure 5 is an explanatory diagram showing the columns selected for reinforcement. The selected columns are reinforced in the analysis model.
[0040] Specifically, shell elements with the properties of steel plates (6 mm) were used and rigidly connected to the solid elements of the L4 and R4 columns by interface elements. Here, to prevent the steel plates from contributing to the bending strength, it was decided not to place shell elements for one element from the end of the column.
[0041] Using the reinforced analytical model (step S2) created in this way, the steps from the structural analysis in step S3 to the confirmation of columns that need reinforcement in step S5 are carried out again. Figure 6 is an explanatory diagram showing the analysis results of the reinforced analytical model shown in Figure 5.
[0042] Looking at Figure 6, at a horizontal displacement of around 95 mm after the maximum load, the normalized cumulative strain energy W n It can be seen that the load reaches the limit value of 1500μ and drops significantly.
[0043] Therefore, in step S6, the validity of the selection of columns is confirmed in relation to the horizontal load acting on the RC rigid frame viaduct and the horizontal displacement that occurs in the slab as a result (see displacement measurement positions in Figure 3). In short, based on the analysis results in Figure 6, it can be said that reinforcement of columns L4 and R4 alone has caused a load reduction in the RC rigid frame viaduct, and that the reinforcement effect is insufficient.
[0044] Therefore, in step S7, it is determined that there are columns that need additional reinforcement, and in step S51, the columns to be reinforced are selected. Judging from the analysis results after reinforcement in Figure 6, the normalized cumulative strain energy W n The L1 column, whose value exceeded the limit, is also considered to be a column that will affect the RC rigid frame viaduct. Therefore, in the second step S51, the L1 column, located at the end of the RC rigid frame viaduct, and its paired R1 column were selected as columns to be reinforced, and the L1, R1, L4, and R4 columns were selected as columns to be reinforced.
[0045] Figure 7 is an explanatory diagram showing the columns selected for additional reinforcement. Then, in the third step S2, an analytical model after reinforcement is created. That is, shell elements with the properties of steel plates (6 mm) are added to the L1 and R1 columns newly selected for reinforcement.
[0046] Then, the steps from the structural analysis in step S3 to the confirmation of columns that need reinforcement in step S5 are carried out again. Fig. 8 is an explanatory diagram showing the analysis results of the analysis model after re-reinforcement shown in Fig. 7.
[0047] Looking at Figure 8, by reinforcing the L1, L4, R1, and R4 columns located at the ends of the RC rigid frame viaduct, the normalized cumulative strain energy W n It can be seen that the limit value (1500μ) was not reached.
[0048] Furthermore, in step S6, even when the reinforcement effect is checked in relation to the horizontal load acting on the RC rigid frame viaduct and the horizontal displacement of the slab, it is found that no reduction in load has occurred in the RC rigid frame viaduct.
[0049] In other words, by selecting and reinforcing the columns that affect the load reduction of the RC rigid frame viaduct, the large load reduction that occurred before reinforcement did not occur, and ductility was improved after the maximum horizontal seismic intensity.
[0050] Furthermore, as can be seen from Figure 8, when the horizontal displacement exceeded 130 mm, the normalized cumulative strain energy W n Although the load sometimes exceeds the limit value (1500μ), there is no significant load reduction in the RC rigid frame viaduct as a whole, which confirms that efficient and effective reinforcement has been achieved.
[0051] Therefore, in step S8, reinforcement is carried out on the columns that were selected to need reinforcement when the reinforcement effect was confirmed (L1 column, R1 column, L4 column, R4 column). As a result, the existing RC rigid frame viaduct has been reinforced to increase its ductility.
[0052] Next, the operation of the method for selecting reinforcement points for a statically indeterminate structure according to this embodiment will be described. In the method for selecting reinforcement points for a statically indeterminate structure configured as above, in the first step (S3-S5, S51), the material damage index (normalized cumulative strain energy W n Using the buckling of axial reinforcement, columns that cause a decrease in the load of a statically indeterminate RC rigid frame viaduct are selected.
[0053] Then, using the analytical model after reinforcement in which the selected columns have been reinforced, a nonlinear finite element analysis is performed again to confirm the reinforcement effect of the entire RC rigid frame viaduct, also based on the relationship between horizontal load and horizontal displacement (steps S6, S7).
[0054] This allows for the appropriate selection of columns to be reinforced from the perspective of the entire RC rigid-frame viaduct. For example, compared to uniformly reinforcing all columns that are likely to fail in shear, selecting columns that will be subject to critical damage to the RC rigid-frame viaduct allows for efficient and effective reinforcement.
[0055] Furthermore, even if there are areas among the columns of an existing RC rigid frame viaduct that are difficult to reinforce due to obstacles, etc., the RC rigid frame viaduct can be reinforced rationally as long as there are no restrictions on reinforcement due to obstacles, etc. on the selected columns.
[0056] The embodiments of the present invention have been described above in detail with reference to the drawings, but the specific configuration is not limited to this embodiment, and design changes that do not deviate from the gist of the present invention are included in the present invention.
[0057] For example, in the above embodiment, an RC rigid frame viaduct such as a railway viaduct was used as an example of a statically indeterminate structure, but the present invention is not limited to this, and can also be applied to statically indeterminate structures that suffer the same failure mode as an RC rigid frame viaduct.
Claims
1. A method for selecting reinforcement points of a statically indeterminate structure, the method being for selecting columns to be reinforced, the method being targeted at a statically indeterminate structure having a plurality of reinforced concrete columns and a slab supported by the columns, the method comprising: selecting columns that cause a decrease in the load of the statically indeterminate structure using a material damage index of the concrete or reinforcing steel of the columns calculated by nonlinear finite element analysis using an analytical model of the statically indeterminate structure to be reinforced; A method for selecting reinforcement points for a statically indeterminate structure, characterized by comprising the steps of: performing a nonlinear finite element analysis again using an analytical model after reinforcement in which the selected column has been reinforced; and confirming the reinforcement effect of the entire statically indeterminate structure based on the results of the nonlinear finite element analysis after reinforcement.
2. A method for selecting reinforcement points for a statically indeterminate structure, as described in claim 1, characterized in that, in confirming the reinforcing effect of the entire statically indeterminate structure, the validity of the selection of the columns is confirmed in relation to the horizontal load acting on the statically indeterminate structure and the resulting horizontal displacement occurring in the slab.
3. A method for selecting reinforcement points for a statically indeterminate structure as described in claim 1 or 2, characterized in that when the material damage index is normalized cumulative strain energy indicating compressive damage to concrete, the judgment criterion is whether or not the normalized cumulative strain energy of the column calculated by the nonlinear finite element analysis exceeds a predetermined limit value.
4. A method for selecting reinforcement points for a statically indeterminate structure as described in claim 1 or 2, characterized in that if a column that causes a decrease in the load of the statically indeterminate structure is separately identified, an additional column to be reinforced is selected, and the addition of the column to be reinforced is repeated until the validity of the selection of the column can be confirmed.
5. A method for selecting reinforcement points for a statically indeterminate structure as described in claim 1 or 2, characterized in that the nonlinear finite element analysis is a pushover analysis in which a horizontal load perpendicular to the extension direction of the slab is gradually applied to the analytical model to evaluate the relationship with horizontal displacement.