JP2008057204A - Method of analyzing behavior of reinforced concrete column subjected to repeated loading - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of analyzing the behavior of a reinforced concrete column subjected to repeated loading, for analyzing the behavior of the reinforced concrete column by using a computer according to the finite element method while adequately reflecting a deterioration mechanism of a load bearing ability by repeated loading in a plastic region of the reinforced concrete column. <P>SOLUTION: The method of analyzing the behavior of the reinforced concrete column is implemented by analyzing the behavior of the reinforced concrete column 10 subjected to the repeated loading in the plastic region, by using a computer according to the finite element method. In the method, a buckling model is incorporated in a structure side of axial reinforcements of the reinforced concrete column 10, and the behavior of the reinforced concrete column 10 in a region where a load bearing ability is lost after the load bearing ability reaches a peak, is analyzed. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a behavior analysis method for a reinforced concrete column in which the behavior of a reinforced concrete column subjected to repeated loading in a plastic region is analyzed using a computer by a finite element method.

  While there are concerns about the Tokai Earthquake, the Tonankai, and Nankai Earthquakes, performance design is becoming the mainstream in the design methods for reinforced concrete structures such as bridges. In performance design, it is necessary to accurately express the proof stress and dust performance of the structure, but there are unclear parts in the mechanism of deterioration of the load proof strength due to repeated loading of reinforced concrete structures in the plastic region, and the behavior is also expressed. Currently, no analysis method has been established.

On the other hand, in the field of civil engineering and construction, analysis methods using the finite element method (FEM) are widely used, and various structural analysis programs and design systems have been developed along with the development of computer technology (for example, (See Patent Document 1 and Patent Document 2).
JP 2003-20649 A JP-A-2005-299203

  For example, the reinforced concrete columns that make up the substructure of the bridge are, for example, the shear deformation of the core concrete surrounded by the axial reinforcement at the column base close to the footing foundation, the buckling of the axial reinforcement accompanying this, and the peeling of the covered concrete It is a common behavior to lose the load bearing capacity. In the conventional FEM analysis, when this behavior is to be expressed, it can be reproduced relatively well until the load bearing capacity reaches a peak, but the area that loses the load bearing capacity after reaching the peak (post-peak area). It could not be reproduced. That is, in the conventional FEM analysis, it has been difficult to appropriately reflect the deterioration mechanism of the load bearing capacity due to repeated loading in the plastic region of the reinforced concrete column including the post peak region.

  The present invention has been made by paying attention to such a conventional problem, and appropriately reflects the deterioration mechanism of the load bearing capacity due to repeated loading in the plastic region of the reinforced concrete column including the post-peak region, thereby providing a finite element. The purpose of this study is to provide a method for analyzing the behavior of reinforced concrete columns subjected to repeated loading that can be analyzed using a computer.

  The present invention relates to a reinforced concrete column behavior analysis method for analyzing the behavior of a reinforced concrete column subjected to repeated loading in a plastic region by using a computer by a finite element method, and a buckling model is provided on the component side of the axial rebar of the reinforced concrete column. Incorporating and analyzing the behavior of the reinforced concrete column in the region where the load bearing capacity is lost after the load bearing capacity reaches its peak, providing a method for analyzing the behavior of reinforced concrete columns subjected to repeated loading, thereby achieving the above object It is a thing.

  Further, according to the method of analyzing the behavior of a reinforced concrete column subjected to repeated loading according to the present invention, the repeated loading is horizontal loading, and the element of the axial reinforcing bar in which the buckling model is incorporated is compressed at the base of the reinforced concrete column. A single element on the side and on the tension side is preferred.

  Hereinafter, the method for analyzing the behavior of a reinforced concrete column subjected to repeated loading according to the present invention will be described in more detail. The behavior analysis method of a reinforced concrete column subjected to repeated loading according to the present invention is a behavior analysis method of a reinforced concrete column that analyzes the behavior of a reinforced concrete column subjected to repeated loading in a plastic region using a computer by a finite element method. A buckling model is incorporated on the component side of the axial rebar to analyze the behavior of the reinforced concrete column in the region where the load bearing capacity is lost after the load bearing capacity reaches a peak.

  According to the behavior analysis method of the present invention, the behavior of a reinforced concrete column subjected to repeated loading in a plastic region is determined by using various structural analysis programs by analysis software using a known finite element method (FEM) installed in a computer. Can be analyzed. As such FEM analysis software, for example, a well-known trade name “DIANA” (manufactured by TNO DIANA Co., Ltd., sales agent JIP Techno Science Co., Ltd.) can be preferably used as a general-purpose linear and nonlinear structure analysis system. DIANA is an advantageous analysis system in the civil engineering / construction field, especially for nonlinear analysis such as crack growth analysis of concrete, fatigue failure analysis / load-bearing analysis of steel structures, and ground stage construction analysis. In addition, DIANA models reinforcements in reinforced concrete structures as embedded reinforcement elements, so it is possible to place reinforcements and PC steel wires at any position without being aware of the concrete mesh shape, for example. It has various functions. Furthermore, DIANA has various constituent sides related to, for example, concrete and reinforcing bars, and also has a user subroutine function.

  In the present invention, for example, a user subroutine function of DIANA is used to incorporate a buckling model on the structural side of the axial rebar of the reinforced concrete column, thereby losing the load resistance after the load resistance reaches a peak. Analyze column behavior.

  Here, for example, as a buckling model incorporated into the structural side of the axial rebar of a reinforced concrete column using a user subroutine function, for example, the results of a buckling experiment using a single reinforcing bar showing the stress-strain relationship are shown in FIG. The proposed model proposed by Tagami et al. Can be preferably used (Kazuya Tagami, Hikaru Nakamura, Naruhiko Saito, Isamu Higaki: Research on buckling model of rebar subjected to repeated load, Structural engineering papers vol. .47A, 2001.3).

  In the user subroutine that incorporates the model proposed by Tagami et al. As a buckling model, as shown in FIG. 2, when the user subroutine is started, it becomes a trilinear model when it receives tensile stress (see OA-AB-BC in FIG. 1). ), When subjected to axial compression strain after tensile yielding, it is unloaded with an initial gradient (see CD in FIG. 1). When the compressive stress is subsequently applied, the buckling point (see D in FIG. 1) is reached. The buckling point can be obtained by a theoretical formula such as Euler or Engessa Kalman.

The behavior after buckling (see DE in FIG. 1) is expressed by the model of equation (1). That is, after buckling, the stress suddenly decreases, gradually becomes a gentle curve, and moves toward the residual stress. The behavior at the time of re-tension becomes an initial gradient while receiving compressive stress (see EF in FIG. 1), and the behavior after that (see FG in FIG. 1) is the compressive strain after buckling according to the equation (2). It becomes a straight line aiming at a point where the tensile stress is reduced according to the amount. That is, when a tensile strain is applied after buckling, it can be modeled by a straight line toward the point of (σ _{t, max} , σ _{t, i} ) shown in Equation (2).

Here, when the new cycle is performed with respect to the stress σ _{t, i −1} corresponding to the maximum tensile strain of the previous cycle, the expression (2) indicates that the tensile stress σ _t, It represents that _i decreases with the amount of incremental strain ε _b after buckling.

Furthermore, when recompressing from the point G, it is unloaded with an initial gradient (see GI in FIG. 1). At this time, when calculating the buckling stress at point I, the amount of stress reduction from point _C (stress at point _C : σ _C ) to point G (stress at point G: σ _G ) as shown in Equation (3). Assuming that the yield stress (σ _I ) at point _I is reduced, the yield stress is calculated, and the stress reduction due to repeated constant displacement is taken into account. Thereafter, calculation is sequentially performed according to the behavior after the buckling according to the stress state.

  According to the behavior analysis method of a reinforced concrete column subjected to repeated loading according to the present invention, a finite element method is used to appropriately reflect the deterioration mechanism of the load bearing capacity due to repeated loading in the plastic region of the reinforced concrete column including the post-peak region. Can be used for analysis.

  In the first preferred embodiment of the present invention, a reinforced concrete column 10 having a structure as shown in FIGS. 3A and 3B and FIGS. 4A and 4B simulating a railway viaduct that bends and breaks during an earthquake. In addition to conducting horizontal alternating loading experiments for the analysis target, the behavior analysis method of the reinforced concrete column of the present invention analyzes the behavior up to the area where the load bearing capacity is lost after the load bearing capacity reaches the peak (post peak area). (FEM) analysis was performed and compared with the experimental results from the horizontal alternating loading test.

  The reinforced concrete column 10 has a cross-sectional dimension of 50 × 50 cm and a height of 200 cm. By repeating horizontal loading with a height of 150 cm from the joint with the footing foundation 11 as an applied point. A horizontal alternating loading experiment was conducted. FIGS. 3A and 3B are structural diagrams of the reinforced concrete column 10, FIGS. 4A and 4B are bar arrangement diagrams of the reinforced concrete column 10, and Table 1 shows the specifications of the reinforced concrete column 10. FIG. In the horizontal alternating loading test, the reinforced concrete column 10 was repeatedly loaded in the horizontal direction, and at the column base adjacent to the footing foundation 11, the compression side concrete was crushed (buckling of the axial rebar, cover concrete protruding and peeling off). ) To cause bending fracture.

  On the other hand, in the FEM analysis, the above-mentioned trade name “DIANA” (manufactured by TNO DIANA Co., Ltd., sales agent JIP Techno Science Co., Ltd.) was used as analysis software by a finite element method installed in a computer. The analysis model was a two-dimensional model shown in FIGS. 5A and 5B, and the base was completely fixed. Further, as the analysis element, the quadruple element with four nodes was used for the concrete, the truss element was used for the axial rebar, and the embedded rebar element was used for the strip reinforcement.

  The concrete constitutive law is described in Vecchio and Collins (see FJVecchio, MPCollins: The modified compression field theory for reinforced concrete elements subjected to shear, ACI Journal 83, pp.219-231, 22 (1986)), and Selby and Vecchio. (See RGSelby, FJVecchio: Three-dimensional Constitutive Relations for Reinforced Concrete. Tech. Rep. 93-02, Univ. Toronto, dept. Civil Eng., Toronta, Canada, 1993.) Rotational crack model was used. The crack direction of this model rotates continuously with the main direction of the strain vector.

  The stress-strain relationship of concrete uses the nonlinear softening curve based on the tensile fracture energy of Hordijk (DAHordijk: Local approach to fatigue of concrete, PhD thesis, Delft University of Technology, 1991) on the tension side, and on the compression side. A nonlinear softening curve based on the compressive fracture energy of Feenstra (PHFeenstra: Computational Aspects of Biaxial Stress in Plain and Reinforced Concrete, PhD thesis, Delift University of Technology, 1993) was used. The tensile fracture energy is calculated by the method of the Japan Society of Civil Engineers Concrete Standards Specification (referred to by the Japan Society of Civil Engineers, Structural Performance Review, 2002), and the compressive fracture energy is calculated by Nakamura et al. (H. Nakamura, T. Higai). : Compressive Fracture Energy and Fracture Zone Length of Concrete, Seminar on Post-Peak Behavior of Structures Subjected to Seismic Loads, JCI, Vol.2, pp. 259-272, 1999.10.

  In the calculation step, after a predetermined vertical load was taken into consideration in the vertical force application point, a forced displacement was applied to the horizontal force application point in a 1/10 displacement step of 1δy (= 7.5 mm).

  The BFGS method was used as the solution method, the convergence error was 1/1000, the number of iterations was 50, and the error was carried over when it did not converge.

  In addition, the constitutive law of the reinforcing bars when the buckling of the axial reinforcing bars is not taken into account is elastoplastic, and the Von Mises criterion is used as the yield criterion.

  When incorporating the buckling model on the component side of the axial rebar, the above-mentioned DIANA user subroutine function is used, and the above proposed model by Tagami et al. Is used as the buckling model, and the axial rebar at the base of the reinforced concrete column 10 is used. A buckling model was incorporated into one element (element length 75 mm) on the compression side and the tension side. The other axial rebars were models that did not consider buckling.

  The buckling stress of the axial rebar was the yield stress of the rebar. This is approximate because the buckling length of the axial rebar in the horizontal alternating loading test is not more than 3 times the strip rebar spacing of 75 mm, and this buckling length is outside the scope of Euler's theoretical formula based on elasticity theory. It is determined in

  According to the first embodiment, in order to analyze the behavior of the reinforced concrete column 10 that is repeatedly loaded in the plastic region by FEM analysis using a computer, for example, as shown in FIG. Do. When the concrete element and the reinforcing bar element reach the nonlinear region, the nonlinear calculation at each loading step is continuously performed in consideration of each nonlinear characteristic, and a solution is obtained by convergence calculation.

  Further, in the first embodiment, since a buckling model is incorporated on the side of the axial reinforcing bar of the reinforced concrete column 10, a behavior analysis reflecting the occurrence of concrete crushing and buckling of the axial reinforcing bar is performed. Is called. When the load bearing capacity deteriorates due to concrete crushing or buckling of the axial rebar, and the load is reduced to, for example, about 50% or less of the maximum load as the yield load, the behavior analysis is terminated.

  In the first embodiment, as the behavior analysis of the reinforced concrete column 10 using DIANA, the analysis model based on the two-dimensional model shown in FIGS. We also performed an analysis without considering the above.

  FIG. 7 shows the behavior of the reinforced concrete column 10 subjected to repeated loading in the plastic region analyzed in the first embodiment as a relationship between the horizontal load loaded on the reinforced concrete column 10 and the horizontal displacement of the reinforced concrete column 10. This is shown in comparison with the experimental results from the loading experiment. According to the analysis result shown in FIG. 7, the analysis value when the buckling is not taken into account does not show a decrease in load like the experimental result even when the horizontal displacement reaches 75 mm. On the other hand, in the analysis value in consideration of buckling, the load decreases at 10δy (75 mm). In addition, the analysis value in consideration of buckling when the load is loaded is equivalent to the experimental load.

  As described above, as a result of performing FEM analysis for the reinforced concrete column 10 that receives and repeatedly receives a load in the plastic region and incorporates a buckling behavior on the component side of the axial rebar to reduce the load bearing capacity, the axial rebar is the result. If buckling is taken into consideration, the horizontal load-horizontal displacement relationship in the experimental results of the horizontal alternating loading test can be reproduced well until the load decreases. In addition, it has been proved effective to incorporate a buckling model on the component side of the axial rebar and analyze the post peak behavior of the reinforced concrete column 10 to be bent and fractured by FEM analysis.

  In the second preferred embodiment of the present invention, the reinforced concrete columns of FIGS. 3 (a), (b) and FIGS. 4 (a), (b) having the structure shown in FIGS. 8 (a) and 8 (b) are provided. In the same manner as in the first embodiment, a horizontal alternating loading test was performed on the reinforced concrete column 12 reinforced by a spiral winding method with a sprayed mortar thickness of 4 cm from the footing foundation 11 of 3 to 122 cm. As with the first embodiment, the behavior analysis of the reinforced concrete column according to the present invention is performed up to a region (post-peak region) where the load resistance is lost after reaching the peak, as in the first embodiment. FEM) analysis, and compared with the experimental results of horizontal alternating loading test.

  In the second embodiment, the analysis model is a three-dimensional model shown in FIGS. 9A and 9B. As analysis elements, the concrete is a four-node quadrilateral element, the axial reinforcement is a truss element, and the belt reinforcement. Used embedded reinforcement elements. The buckling model incorporated in the constituent side of the axial rebar was applied to the elements at both outer edges of the base axial rebar, and the other elements were bilinear. The buckling length was set as the strip rebar spacing, and the buckling stress was finally set to 1.5 times the yield stress. In the second embodiment, as in the first embodiment, as a behavior analysis of the reinforced concrete column 12 using DIANA, an analysis model based on the three-dimensional model shown in FIGS. 9A and 9B is used. The analysis without considering the buckling of the axial rebar as in the past was also performed.

  FIG. 10 shows the behavior of the reinforced concrete column 12 subjected to repeated loading in the plastic region, which is analyzed by incorporating a buckling model on the component side of the axial rebar in the second embodiment, and is loaded on the reinforced concrete column 12. The relationship between the horizontal load and the horizontal displacement of the reinforced reinforced concrete column 12 is shown in comparison with the experimental results of the horizontal alternating loading test. Further, FIG. 11 shows the behavior of the reinforced concrete column 12 subjected to repeated loading in the plastic region, which is analyzed by a conventional method in which buckling is not considered on the component side of the axial rebar in the second embodiment. 12 shows the relationship between the horizontal load loaded on the horizontal load 12 and the horizontal displacement of the reinforced reinforced concrete column 12 in comparison with the experimental results of the horizontal alternating loading test.

  According to the analysis results shown in FIGS. 10 and 11, the analysis value when the buckling is not taken into account does not show a decrease in load like the experimental result even when the horizontal displacement increases. On the other hand, in the analysis value when buckling is taken into account, the load decreases stepwise as the horizontal displacement increases, similar to the experimental result. In addition, the analysis value in consideration of buckling when the load is loaded is substantially equal to the load of the experimental value.

  Therefore, even in the second embodiment based on the three-dimensional model, if buckling is considered on the component side of the axial rebar, the horizontal load-horizontal displacement relationship of the experimental result by the horizontal alternating loading test is reduced until the load decreases. It turns out that it can be reproduced well. In addition, as a method for expressing the post-peak behavior of reinforced concrete columns by FEM analysis, it is proved effective to incorporate a buckling model on the component side of the axial rebar and analyze it.

  The present invention is not limited to the above-described embodiments, and various modifications can be made. For example, the finite element analysis software installed in the computer does not necessarily need to be DIANA, and other various finite element analysis software that can incorporate a buckling model on the side of the axial reinforcing bar. Can be used. Moreover, the constitutive law of concrete and the stress-strain relationship of concrete do not necessarily need to be based on the above-mentioned theory or standard specification.

It is a stress-strain relationship graph explaining an example of the buckling model incorporated in the component side of an axial rebar. It is a flowchart explaining an example of the user subroutine incorporating a buckling model. The structure of the reinforced concrete pillar used as the analysis object in 1st Embodiment is demonstrated, (a) is a front structural drawing, (b) is an upper surface structural drawing. The arrangement of reinforced concrete columns to be analyzed in the first embodiment will be described. (A) is a transverse arrangement diagram and (b) is a longitudinal arrangement diagram. In the first embodiment, used in FEM analysis, (a) is a two-dimensional analysis model of concrete, and (b) is a two-dimensional analysis model of reinforcing steel. It is a flowchart explaining the analysis procedure of the behavior of a reinforced concrete column by FEM analysis which incorporated the buckling model in the component side of an axial rebar. It is a graph which shows the behavior of the reinforced concrete column which receives repeated loading in the plastic zone analyzed in a 1st embodiment compared with the experimental result by a horizontal alternating loading experiment. The structure of a reinforced reinforced concrete column to be analyzed in the second embodiment will be described. (A) is a top structural view, and (b) is a front structural view. In the second embodiment, (a) is a three-dimensional analysis model of concrete, and (b) is a three-dimensional analysis model of reinforcing steel used in FEM analysis in the second embodiment. In the second embodiment, a graph showing the behavior of a reinforced concrete column subjected to repeated loading in a plastic region analyzed by incorporating a buckling model on the component side of the axial rebar in comparison with the experimental result by horizontal alternating loading test. is there. In the second embodiment, a graph showing the behavior of a reinforced concrete column subjected to repeated loading in a plastic region analyzed without considering buckling on the constituent side of the axial rebar in comparison with the experimental result by horizontal alternating loading test. is there.

Explanation of symbols

10 Reinforced concrete pillars 11 Footing foundation 12 Reinforced reinforced concrete pillars

Claims (2)

In the behavior analysis method for reinforced concrete columns, the behavior of reinforced concrete columns subjected to repeated loading in the plastic zone is analyzed using a computer by the finite element method.
Reinforced concrete subjected to repeated loading, characterized by incorporating a buckling model on the side of the axial reinforcing bar of the reinforced concrete column and analyzing the behavior of the reinforced concrete column in a region where the load bearing capacity is lost after the load bearing capacity reaches a peak Column behavior analysis method. The cyclic loading according to claim 1, wherein the cyclic loading is a horizontal loading, and the element of the axial rebar in which the buckling model is incorporated is one element on the compression side and the tension side in the base of the reinforced concrete column. Analysis method for reinforced concrete columns subjected to bending.

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