JP3836645B2 - Modeling method of restoring force characteristics of steel - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for modeling a restoring force characteristic of a steel material, and more particularly, to a method for modeling a restoring force characteristic of a steel material in a structural analysis for improving accuracy related to structural evaluation of a building.
[0002]
[Prior art]
Conventionally, restoring force characteristics of steel materials have been modeled when evaluating the structural performance of buildings. For example, a bi-linear type (bilinear type), a model using a bilinear type (hereinafter referred to as bilinear type-M), and a model using a bilinear type (hereinafter referred to as bilinear type-K). ), Tri-linear type (trilinear type), Ramberg-Osgood type (Lambag Osgood type), and modeling of restoring force characteristics of steel materials such as split type divided into skeleton part, softened part and unloading part A method has been proposed.
[0003]
The bilinear type restoring force characteristic modeling method is the simplest model in which the elastic-plastic behavior of a steel material is expressed by two straight lines indicating an initial elastic gradient and a strain hardening gradient after plasticization. FIG. 7 shows the bilinear stress-strain relationship. In FIG. 7, the law of repetitive behavior is that the magnitude of the elastic load until the load is elastically unloaded and plasticized again by loading on the opposite side load is twice the load caused by kinematic hardening. Yes.
[0004]
Further, the method for modeling the restoring force characteristic of the bilinear type-M models a phenomenon in which the proof stress increases when repeatedly loaded with gradually increasing displacement. FIG. 8 shows a hysteresis law of a shearing force-deformation relationship. In FIG. 8, the load when the load is elastically unloaded and plasticized again by loading on the opposite side is the point where it intersects the DD ′ or EE ′ line.
[0005]
The method for modeling the restoring force characteristics of the bilinear type-K models a phenomenon in which the yield strength rises when repeatedly loading with gradually increasing displacement amplitude and an actual behavior that undergoes unsteady repetition. FIG. 9 shows a bilinear-K history model. As shown in FIG. 9, the bilinear-K hysteresis model is not limited to the increase / decrease of the displacement amplitude as compared with the bilinear-M restoring force characteristic modeling method. In the deformation relationship, the unloading plasticization start point after unloading for the unsteady repetition in which the load is unloaded in the same quadrant is set to the second and fourth points similarly to the DD ′ and EE ′ lines of the incremental loading. The quadrant is set as DD ′ and EE ′ lines.
[0006]
The modeling method of the restoring force characteristic of the trilinear type is a method in which linear approximation is also performed for the softened portion of the Bausinger effect. FIG. 10 shows the stress-strain relationship of the modeling method of the trilinear restoring force characteristic. In FIG. 10, the starting point of the second gradient where the load is elastically unloaded and softened by loading on the opposite side is set to 75%, which is twice the load generated by kinematic hardening.
[0007]
The method of modeling the restoring force characteristic of the Rambagh Osgood shape reproduces a repeated history curve using an exponential function. For example, the history model is as shown in FIG.
[0008]
In the split-type restoring force characteristic modeling method divided into a skeleton part, a softening part, and an unloading part, the restoring force characteristic is shown in FIG. 12 with the Bausinger effect as the softening part and the subsequent strain hardening part as the skeleton. It is expressed as a history model in which the softened part is expressed as a hyperbola and the skeleton part is expressed as a logarithm.
[0009]
A technique described in Japanese Patent Laid-Open No. 8-171403 has been proposed as a modeling method for an elastic structure, and a method for analyzing an earthquake response of a base-isolated structure has been proposed in Japanese Patent Laid-Open No. 9-113403. ing.
[0010]
In the technique described in Japanese Patent Laid-Open No. 8-171403, a plurality of elastic structures arranged side by side are connected to each other with an actuator, and the elastic structure is controlled in order to control vibration by exerting a force through the actuator. In modeling, each elastic structure is hypothesized as a distributed constant structure.
[0011]
The technique described in Japanese Patent Application Laid-Open No. 9-113403 is based on the fact that the seismic isolation device has both elastic and plastic characteristics, and its hysteresis characteristics are nonlinear characteristics and show complex behavior. Modeling is performed by combining elements with both characteristics.
[0012]
[Problems to be solved by the invention]
However, in the conventional method for modeling the restoring force characteristics of steel materials, except for the bilinear type-K restoring force characteristic modeling method, the magnitude of the displacement amplitude is arbitrarily increased or decreased, and the same in the load-deformation relationship. There is a problem that the hysteresis curve is not modeled for unsteady repetitive behavior in which the load is unloaded in the quadrant.
[0013]
In addition, there is a problem that the method of modeling the restoring force characteristics of the Lamberg Osgood type and the split type is complicated and not practical for use in the structural design program.
[0014]
The method for modeling the restoring force characteristics of the bilinear type-K is based on the elasto-plastic load (τ) -deformation (γ) relationship (actual history curve) shown by the broken line in FIG. The load at the first break point C, which is the starting point from the elastic gradient to the strain hardening gradient, is approximated by a broken line consisting of the following points: The tangential stiffness of the actual hysteresis curve is 1/50 of the initial elastic gradient stiffness. A straight line connecting point C and load point D with the maximum amplitude of the hysteresis curve is defined as a second broken line indicating a strain hardening gradient. Then, the slope (β) of the first broken point and the second broken line is obtained from an arbitrary hysteresis curve and experimental values of points B and D with respect to the maximum amplitude, and the first broken point is a straight line proportional to the magnitude of the amplitude. As shown in FIG. 14, it is expressed for each quadrant, and the gradient β is set to a constant value regardless of the magnitude of the amplitude. FIG. 15 shows the secondary gradient β for each amplitude of each specimen (B-1, B-2, B-3). The vertical axis is made dimensionless by dividing the secondary gradient β by the elastic gradient G, and the horizontal axis shows the number of cycles.
[0015]
As shown in FIG. 14, the bilinear-K model performs non-stationary repetition by giving a straight line at the first break point to the first and third quadrants in order to reproduce a hysteresis curve subjected to partial swing. Although the actual behavior is modeled, in the unsteady state of partial swing where the center of the amplitude of the repeated behavior deviates from the origin, the load when plasticizing defined by the first breakpoint is high, and the bilinear type However, it is larger than the history curve of the experiment, and there is a problem that the history curve peculiar to steel materials having a Bauschinger effect cannot be reproduced.
[0016]
In addition, the techniques described in Japanese Patent Application Laid-Open Nos. 8-171403 and 9-113403 also have a problem that modeling considering the Bauschinger effect is not performed.
[0017]
The present invention has been made to solve the above problem, and can restore the restoring force characteristics of the steel material with sufficient accuracy in design, and can restore the structural performance of the building with high accuracy. The purpose is to provide a method for modeling force characteristics.
[0018]
[Means for Solving the Problems]
In order to achieve the above object, the invention according to claim 1 is characterized in that the elastic-plastic behavior of a steel material is obtained by using two straight lines indicating an initial elastic gradient and a strain hardening gradient after plasticization. This is a method for modeling the restoring force characteristics of a steel material that represents a curve, and for repetitive behavior, a partial swing where the center of amplitude has moved from the origin of the hysteresis curve in a steady state where the center of amplitude is a complete swing. The hysteresis curve is expressed by moving to the origin of the unsteady state.
[0019]
According to the first aspect of the present invention, the model representing the hysteresis curve of the restoring force characteristic of the steel using two straight lines indicating the initial elastic gradient and the strain hardening gradient after plasticizing the elastic-plastic behavior of the steel ( The restoring force characteristics of the steel material are modeled using a so-called bilinear model. In the bilinear model, assuming that the hysteresis curve of a steel material hardens when the amplitude increases gradually and softens when the amplitude decreases, the origin of the history curve in a steady state is assumed for repeated behavior. Is moved to the origin of the unsteady state, and the origin is moved so as to always represent the steady state, and the history curve is represented. By doing in this way, the bauschinger effect of steel materials can be considered. Therefore, the restoring force characteristic of the steel material can be modeled with sufficient accuracy in design, and the structural performance of the building can be evaluated with high accuracy.
[0020]
The invention according to claim 2 is the invention according to claim 1, wherein the first folding point represented by the intersection of the two straight lines and the straight line representing the strain hardening gradient after plasticization are provided for each steel material type. It is characterized by setting.
[0021]
According to the invention described in claim 2, in the invention described in claim 1, the first folding point represented by the intersection of the two straight lines in the bilinear model and the straight line representing the strain gradient after plasticization are obtained. By setting for each steel material type, a history model corresponding to the steel material type can be set.
[0022]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an example of an embodiment of the present invention will be described in detail with reference to the drawings.
[0023]
The hysteresis curve for steady and unsteady cyclic behavior of steel is expressed using a simple bilinear model.
[0024]
It is considered that the hysteresis curve of a steel material hardens when the amplitude gradually increases, and softens when the amplitude gradually decreases in consideration of the Bausinger effect because the steel material has a Bauschinger effect.
[0025]
The amplitude range is also increased for the behavior of gradually increasing / decreasing amplitude (see Fig. 1) that varies from full swing, which is a steady repetitive behavior, to partial swing, where the center of the amplitude is an unsteady repetitive behavior. Hardens or softens depending on the thickness. This means that the origin of the history curve in the steady state is moved to the origin of the history curve in the non-stationary state, and the origin is moved so as to always represent the steady state to represent the history curve. The amplitude range is the difference between the maximum value and the minimum value of the amplitude as shown in FIG.
[0026]
The bilinear hysteresis model targets a shear system (for example, a panel or a wall) and an axial force system (for example, a brace or a cane) and does not buckle. In this case, since the inherent property of the material is substantially the same for each steel material type, a history model corresponding to each steel material type can be set.
[0027]
The hysteresis curve of steel when subjected to unsteady repeated deformation is defined as follows.
[0028]
In FIG. 2, the vertical axis represents the load F and the horizontal axis represents the deformation u. The straight line at the first break point for obtaining the load F ^* and the deformation u ^* at the plasticizing start point is shown in FIG. F = Yu + F ₀ for each of the first to fourth quadrants (1)
F = −Yu + F ₀ (2)
F = Yu−F ₀ (3)
F = −Yu−F ₀ (4)
Represented by Here, F ₀ is the value of the intersection of the straight line at the first break point and the vertical axis, and Y is the slope of the straight line, each representing a positive value.
[0029]
The elastic behavior of the load-deformation relationship can be expressed by the following equation.
F = Ke (u−u ₀ ) (5)
Here, Ke represents elastic rigidity, and is common during any loading and unloading. u ₀ represents the deformation when the history curve intersects the horizontal axis. Therefore, the elastic behavior at the time of virgin loading is
F = Keu (6)
It becomes.
[0030]
Next, the load F ^* and deformation u ^* at the plasticizing start point are obtained. During virgin loading, positive loading and negative loading are in the first and third quadrants, respectively. From each of the expressions (1) and (6) and the expressions (3) and (6), u ^* = ± F ₀ / (Ke−Y) (7)
F ^* = ± (KeF ₀ ) / (Ke−Y) (8)
It becomes. Here, + of the sign represents a case of loading on the positive side, and − represents a case of loading on the negative side. Further, when loaded after elastic unloading in the positive or negative direction in response to the n-th repeated deformation in the steady state, the load F ^* and the deformation u ^{* at} the plasticizing start point are the second and fourth, respectively. In the quadrant, u ^* = (Keu ₀ ± F ₀ ) / (Ke + Y) (9) from Expression (2) and Expression (5), and Expression (4) and Expression (5), respectively.
F ^* = Ke (± F ₀ −Yu ₀ ) / (Ke + Y) (10)
It becomes. Here, the sign relating to F ₀ represents a case where the load is positive on the positive side and negative on the negative side.
[0031]
The second broken line that models the increase in yield strength due to strain hardening of the hysteresis curve after plasticization is expressed as follows.
F = Kst (u−u ^* ) + F ^* (11)
It can be expressed as. Equation (11) is common to the positive side and the negative side.
[0032]
Next, the hysteresis curve is modeled in an unsteady state. The unsteady repetitive behavior is that _n-1 intersects the horizontal axis when the deformation _n u ^*, which is the plasticization start point of the _nth history curve, reaches the maximum amplitude of the (n-1) th history curve and is unloaded. It is defined as a state having the same sign as u ₀ . In this case, if the coordinate axis is moved to the intersection _n u ₀ with the horizontal axis at the n-th unloading and the origin is set, the subsequent hysteresis curve can be expressed by Expression (6) and Expression (11). .
[0033]
FIG. 3 shows an arbitrary path including a non-stationary repetitive behavior of a history curve drawn based on the modeling formula defined as described above.
[0034]
Next, the history curve modeled as described above and shown in FIG. 3 will be described.
[0035]
When the repetitive behavior starts, the balance path between the load F and the deformation u follows from the origin 0 to the intersection “1” with the straight line indicating the first folding point on the positive side, and then the deformation returns along the gradient of the second folding line. It reaches point “2”.
[0036]
When unloading from the deformation return point “2”, it reaches the first folding point “3” on the negative side along a path parallel to the straight line “01”, and reaches the deformation return point “4” along the second folding line. .
[0037]
Thereafter, when the displacement amplitude increases or decreases around the origin, the repetitive path is changed in the order of “4” → “5” → “6” → “7” → “8” → “9”. In this case, _n u ^* and _n−1 u ₀ have different signs and are in a steady state.
[0038]
Subsequently, when returning from the position “10” before the displacement exceeds the origin, _n u ^* and _n−1 u ₀ have the same sign, and an unsteady state is obtained. Here, a point where the return path intersects the horizontal axis with a load of 0 is set as a new origin 0 ′, and a repetitive behavior in a steady state starts from the new origin 0 ′ (“A” → “in FIG. 3). B) → “c” → “d” → “e”.
[0039]
Moreover, transition to a new when not displaced to the origin 0 'is returned is unloaded from the "to" in Figure 3 begins _(n u ^* and _n-1 u ₀ is the sign) origin more new origin 0'' Similarly, starting from a new origin 0 ″, a repetitive path in a steady state changes from “a” → “b” → “c” → “d” → “e”.
[0040]
FIG. 4 shows the relationship between the amplitude and the loading cycle in the experiment. As shown in FIG. 4, loading is repeated five times for each amplitude with complete double swing of the increasing amplitude, and the amplitude is decreased and repeated, and then the maximum amplitude is repeated twice.
[0041]
Then, after loading up to the maximum amplitude of the first quadrant, the displacement is returned to 1/2 of the maximum amplitude on one side in the fourth quadrant and the unloading is performed.
[0042]
Next, transition to partial shoulder loading is performed, and a repetition in which ½ of the maximum amplitude on one side is set to the amplitude range (Δ) is loaded. In the fourth quadrant, the displacement is returned to the point of 0 and repeated in the amplitude range of Δ. Then, it is deformed to the amplitude −Δ in the third quadrant and repeatedly loaded in the amplitude range Δ, and is deformed to the amplitude −2Δ in the third quadrant and repeatedly loaded in the amplitude range Δ.
[0043]
FIG. 5 shows the relationship between the amplitude and the loading cycle in the experiment conducted as described above. In FIG. 5, the thin dotted line indicates the repeated behavior of the experiment, the thick line indicates the model curve, the dotted line indicates the path of the gradually increasing and decreasing amplitude (between A and B in FIG. 4), and the solid line indicates the subsequent non-stationary partial swing. The path for repeated behavior (between B and C in Fig. 4) is shown.
[0044]
FIG. 6 shows a comparison of the repeat curve and the bilinear-K history model of the same experiment shown in FIG. In the bilinear type-K model, the load at the first break point becomes higher than the experimental value when moving away from the origin for partial swinging within the same amplitude range. Lower than the value. However, in the repeated curve obtained by the experiment, the load at the first break point is almost the same regardless of the position from the origin when the partial swing is in the same amplitude range due to the Bausinger effect.
[0045]
As shown in FIG. 5, the history model of the present invention gives a restoring force characteristic corresponding to such a behavior, and can reproduce a behavior having a Bausinger effect in an unsteady region.
[0046]
In addition, the bilinear model is a simple model, and the movement of the origin can be easily determined. Therefore, it can be easily incorporated into the structural design program.
[0047]
In the above description, the shear panel system of the extremely low yield point steel has been described. However, the same hysteresis rule is established in a range where no buckling occurs with respect to the axial force system. Moreover, if the gradient of a 1st fold point and a 2nd broken line is set according to steel material types, this historical model can be applied with respect to the restoring force characteristic for every steel material type.
[0048]
【The invention's effect】
As described above, according to the present invention, with respect to repetitive behavior, an unsteady state in which the center of the amplitude is moved in the steady state where the center of the amplitude is a complete swing is a partial swing in which the center of the amplitude is moved By representing the history curve by moving to the origin, it is possible to model the restoring force characteristics of the steel material with a system sufficient for design, and to accurately evaluate the structural performance of the building.
[0049]
In addition, there is an effect that the influence on the building can be verified by performing the time history response analysis once, and the design can be performed efficiently.
[Brief description of the drawings]
FIG. 1 is a diagram for explaining types of repetitive amplitudes.
FIG. 2 is a diagram for explaining how to determine a first break point;
FIG. 3 is a diagram for explaining a history rule according to the embodiment of the present invention.
FIG. 4 is a diagram showing a relationship between an amplitude and a loading cycle in an experiment.
FIG. 5 is a diagram showing a comparison between a repetition curve obtained in an experiment and a model according to an embodiment of the present invention.
FIG. 6 is a diagram showing a comparison between a repetitive curve obtained in an experiment and a model using a bilinear shape (bilinear shape-K model).
FIG. 7 is a diagram showing a stress-strain relationship of a method for modeling a bilinear restoring force characteristic.
FIG. 8 is a diagram showing a hysteresis law of a shearing force-deformation relationship in a method for modeling a restoring force characteristic of a model using a bilinear shape (bilinear shape-M).
FIG. 9 is a diagram illustrating a history model of a method for modeling a restoring force characteristic of a model using a bilinear shape (bilinear shape-K).
FIG. 10 is a diagram showing a stress-strain relationship of a method for modeling a restoring force characteristic of a trilinear type.
FIG. 11 is a diagram illustrating a history model of a method for modeling a restoring force characteristic of a Lamberg Osgood shape.
FIG. 12 is a diagram showing a history model of a method for modeling a split restoring force characteristic;
FIG. 13 is a diagram showing a part of the hysteresis curve on the normal loading side of the shear panel system.
FIG. 14 is a diagram showing a distribution of first break points in a method for modeling a bilinear restoring force characteristic.
FIG. 15 is a diagram showing amplitude / second-order gradient-number of cycles.
[Explanation of symbols]
0 Origin 0 'New origin 0 "New origin 1 First break point 2 Deformation return point (point on second break line)
3 First break point 4 Deformation return point (point on second break line)

Claims (2)

A method for modeling a restoring force characteristic of a steel material, which represents a hysteresis curve of a restoring force characteristic of a steel material by using two straight lines indicating an initial elastic gradient and a strain hardening gradient after plasticization, the elastic-plastic behavior of the steel material,
For repeated behavior, move the origin of the history curve in a steady state where the amplitude center is completely swinging to the origin of an unsteady state where the center of the amplitude is moved partially to represent the history curve. Modeling method for restoring force characteristics of steel. The restoring force characteristic of the steel material according to claim 1, wherein a first break point represented by an intersection of the two straight lines and a straight line representing the strain hardening gradient after plasticization are set for each steel material type. Modeling method.

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