CN114611186B - Y-shaped cast steel node anti-seismic performance design method based on capability spectrum method - Google Patents
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Abstract
The invention relates to a method for designing the anti-seismic performance of a Y-shaped cast steel node based on a capacity spectrum method, which comprises the following steps: establishing a ductility capability curve of the node; establishing a ductility requirement curve of the node; and calculating the performance points of the nodes according to the capability spectrum method. The method provided by the invention has certain universal applicability and can be used for designing the earthquake resistance of the more regular cast steel nodes.
Description
Technical Field
The invention relates to the field of seismic performance design of cast steel nodes, in particular to a method for designing the seismic performance of a Y-shaped cast steel node based on a capability spectrum method.
Background
The energy consumption and the deformation capacity of the cast steel node in the earthquake have great influence on the earthquake resistance of the whole structure. Especially for some large public buildings (airports, station houses and the like), due to the characteristics of complex structure, large space span, high crowd density and the like, serious social influence can be caused by structural failure. The existing earthquake-proof design method has the defects that the deformation capacity of the node in the earthquake is not considered enough, the safety of the node is not facilitated, and the deformation of the whole structure in the earthquake is not controlled. For some key nodes in large public buildings, not only bearing capacity design but also earthquake resistance design are needed.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a Y-shaped cast steel node anti-seismic performance design method based on a capability spectrum method, which can solve the problem that the anti-seismic performance design method of the cast steel node is lacked in the prior art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention provides a method for designing the anti-seismic performance of a Y-shaped cast steel node based on a capacity spectrum method, which comprises the following steps:
s1: establishing a bearing capacity formula of the node:
Under the action of the axle center or small eccentric pressure, the Y-shaped node yields at the intersection of the branch pipe and the main pipe, buckling instability damage can occur at the joint of the branch pipe and the main pipe along with the increase of load, and the bearing capacity of the instability damage node is related to the geometric dimension and is irrelevant to the strength of the material. In addition, since the node branch and the main pipe intersect after yielding to start to be unstable and damaged, the yielding state can be regarded as a critical state that the node is about to enter into the unstable and damaged state. The bearing capacity formula of the yield of the node is assumed to be the same as the bearing capacity of the limit, the bearing capacity formula of the hollow ball node is analogized, and according to the existing research results, the compression bearing capacity formula of the Y-shaped cast steel node under the action of the axial center and the small eccentric pressure is assumed to be written as,
In the method, in the process of the invention,Is yield compression bearing capacity of the node/(The ultimate compressive bearing capacity of the node; f is the design value of tensile strength, compressive strength and bending strength of cast steel; d is the outer diameter of the branch pipe of the node; d is the outer diameter of the main pipe hollow sphere; t is the wall thickness of the main pipe; the outside chamfer radius r of the branch pipe; a 1,A2,B1 and B 2 are regression coefficients; /(I)The influence coefficient of bending moment effect is considered when the axial force is designed; /(I)The influence coefficient of the axial force is considered when the bending moment is designed.
And/>The relation of the bending moment and the axial pressure of the node can be obtained according to the relation of the bending moment and the axial pressure of the node,，/>. It is noted that since the node yield load capacity formulation is derived from the destabilization failure, the calculated node yield load capacity will be slightly greater than the actual load capacity.
Sampling the geometrical parameters of the nodes by using Latin hypercube sampling, and establishing an analysis sample of the bearing capacity of the nodes;
Establishing a finite element model of the node, and analyzing a failure mode of the node under the action of the axle center and the small eccentric pressure;
calculating a load-displacement curve of the node under the action of axle center pressure by an arc length iteration method, and taking the load when the rigidity is reduced for the first time as the yield bearing capacity of the node; taking the load when the rigidity is reduced to 10% of the initial rigidity for the first time as the limit load of the node; respectively adopt to And/>Taking a non-dimensionalized variable of pi tdf as an ordinate of a node yield and ultimate compressive bearing capacity regression equation, and taking D/D as an abscissa; regression coefficients A 1,A2,B1 and B 2 are obtained through regression of the node compressive bearing capacity formula;
S2: establishing a ductility capability curve of the node:
The invention adopts ductility as an anti-seismic performance index of the node, and establishes a ductility capacity curve of the node according to the yield strength coefficient. Coefficient of yield strength It is defined that the first and second components,
In the method, in the process of the invention,The maximum elastoplastic internal force is under the action of earthquake; /(I)Is the yield bearing capacity.
In order to consider the plastic development of the node under the action of an earthquake, the application takes the ultimate bearing capacity of the node as the maximum elastoplastic internal force under the action of the earthquake. For the Y-shaped cast steel node with the axle center and small eccentric compression, adopting the compression bearing capacity to calculate the yield strength coefficient; the yield strength coefficient formula of the Y-shaped cast steel node, namely the ductility capability curve of the Y-shaped node, can be deduced from the yield bearing capacity formula and the ultimate bearing capacity of the node. The ductility curve of a Y-cast steel node can be expressed as,
In addition, the ductile capability curve of the node may also be defined by a yield level coefficient. Yield level coefficient for single degree of freedom systemsIt is defined that the first and second components,
Wherein m is the mass of a single degree of freedom system; PGA is the maximum ground acceleration under seismic action.
By definition, the yield strength coefficientCoefficient of yield level/>The relationship of (c) may be written as,
In the method, in the process of the invention,As the power amplification factor, in the current specification of China/>The value of (2) is 2.5.
S3: establishing a ductility requirement curve of the node:
Uncertainties in the ductile requirements of a structure fall into two categories: one type is uncertainty of earthquake motion, such as a seismic source mechanism, a seismic magnitude, a duration, a site condition and the like; the other is uncertainty of the structure itself, such as yield strength, damping ratio, hysteresis properties, etc. When the randomness of the earthquake motion is not considered, the coefficient of yield level is given And ductile requirement of structure/>, under the condition of structure self-oscillation period TObeying a lognormal distribution, the cumulative distribution function of which can be written as,
In the method, in the process of the invention,And/>Respectively/>And the conditional mean and conditional standard deviation of (2).
Ductility coefficientConditional mean/>And standard deviation of conditions/>Can be expressed as yield level coefficient/>And a function of the period T of the structure's natural vibration, which function can be written as,
Wherein E 1,…, E 7, F1,…, E 7 is a regression coefficient, and is calculated according to the elastoplastic time course analysis result of the single degree of freedom structure system.
And/>The regression coefficient value of (c) is related to the site category, for a particular site category,The distribution parameters in (1) can be defined by/>/>And (5) calculating to obtain the product. /(I)，/>/>A probabilistic model of the ductility requirement of the node is formed, at/>After the overrun probability is set, the ductility requirement curve under different overrun probabilities can be calculated.
S4: calculating the performance points of the nodes according to a capability spectrum method:
the basic idea of the capability spectroscopy is to use the same independent variables (typically basic variables of the structure) to build two curves: and the corresponding independent variable value is the design value.
Further, the argument in step S4 is D/D.
Further, in step S3The value of (2) is 2.5.
The Y-shaped cast steel node anti-seismic performance design method based on the capacity spectrum method provided by the invention can solve the problem that a quantized cast steel node anti-seismic performance design method is lacking in the prior art, and an optimization method of node design.
Drawings
FIG. 1 is a general flow chart of a method for designing the earthquake-resistant performance of a Y-shaped cast steel node based on a capacity spectrum method;
FIG. 2 is a schematic diagram of a Y-node according to an embodiment of the present invention;
FIG. 3 (a) is a schematic diagram of a Y-node axial compressive yield mode according to an embodiment of the present invention;
FIG. 3 (b) is a schematic diagram of a small eccentric compression yield mode of a Y-node according to an embodiment of the present invention;
FIG. 4 is a regression result of the formula of the compressive capacity of the Y-type node according to the embodiment of the present invention;
FIG. 5 is a graph of Y-node capability spectrum according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.
As shown in fig. 1: the invention provides a method for designing the anti-seismic performance of a Y-shaped cast steel node based on a capacity spectrum method, which comprises the following steps:
S1, establishing a bearing capacity formula of a node:
as shown in FIG. 2, the node is axisymmetric about the center line of the main pipe, the upper part of the main pipe is formed by splicing two partial spherical surfaces, the lower part of the main pipe is a truncated cone, and the outer diameter of the main pipe is 1100mm; the intersection angle of the central line of the branch pipe and the bottom surface of the main pipe is 52 .. The design parameters of the node are the outer diameter of the branch pipe, the outer diameter of the main pipe, the wall thickness of the branch pipe and the wall thickness of the main pipe. And calculating parameters in a node bearing capacity formula by adopting Monte Carlo simulation of the nodes through linear regression. Sampling the geometrical parameters of the nodes by using Latin hypercube sampling, and establishing an analysis sample of the bearing capacity of the nodes. The range of the values of the geometrical parameters of the nodes is shown in table 1.
Table 1 geometrical parameters and value ranges
| Node geometry parameters | Value range/mm | Original value/mm |
| Wall thickness t of main pipe | 35~65 | 55 |
| Outer diameter D of main pipe | 1170~1630 | 1246 |
| Outer diameter d of branch pipe | 300~500 | 500 |
Note that: the wall thickness of the branch pipe is 90% of the wall thickness of the main pipe; when the outer diameter of the branch pipe is changed, the axial direction of the branch pipe is not changed; in order to ensure that the extracted sample meets the design requirement of the node, the extracted sample model needs to meet the following conditions: the construction conditions of D/t is less than or equal to 35 and D/D is less than or equal to 0.2 and less than or equal to 0.4.
And establishing a finite element model of the node by adopting a 3D entity unit SOLID45 in universal finite element software ANSYS, and analyzing the damage mode of the node under the action of the axle center and small eccentric pressure. The finite element unit grid is divided by adopting hexahedron mapping, consolidation constraint is set at the bottom of the main pipe, the yield criterion adopts Von-Mises yield criterion, and the influence of geometrical nonlinearity of the node branch pipes is not considered. The node material is cast steel GS-20Mn5QT, and the constitutive relation adopts a two-fold line model considering linear reinforcement. According to the material property of cast steel, the elastic modulus in the constitutive relation is 2.06x10 5 MPa, the yield strength is 300MPa, the ultimate strength is 500MPa, the design strength value is 235MPa, the ultimate strain is 5.5x10 -5, the Poisson ratio is 0.27, and the line stiffness after yielding is 2% of the initial reference stiffness. .
As shown in fig. 3 (a) and fig. 3 (b), under the action of the axial center and small eccentric pressure, the Y-shaped node first yields at the intersection of the branch and the main pipe, buckling instability damage can occur at the joint of the branch and the main pipe along with the increase of load, and the bearing capacity is related to the geometric dimension of the node with instability damage, but is irrelevant to the strength of the material. In addition, since the node branch and the main pipe intersect after yielding to start to be unstable and damaged, the yielding state can be regarded as a critical state that the node is about to enter into the unstable and damaged state.
Calculating a load-displacement curve of the node under the action of axle center pressure by an arc length iteration method, and taking a load corresponding to a yield point as the yield bearing capacity of the node; according to the technical regulations for cast steel node application (CECS 235:2008) (the regulations for short), the load when the rigidity is reduced to 10% of the initial rigidity for the first time is taken as the limit load of the node. Respectively adopt toAndAnd taking the non-dimensionalized variable of pi tdf as the ordinate of a node yield and ultimate compressive bearing capacity regression equation, and taking D/D as the abscissa. The regression result of the node compressive capacity formula is shown in fig. 4.
S2, establishing a ductility capability curve of the node;
As shown in fig. 5, the ductility curve of the Y-cast steel node can be expressed as,
According to the result in FIG. 4 and the construction requirement of the node, the yield strength coefficient of the cast steel node can be calculated to be 0.49-0.52, and the ductility performance of the cast steel node is good.
S3, establishing a ductility requirement curve of the node;
Assuming a structural damping of 0.05, the field class is class I. Calculating node ductility requirement curve by using existing research results, and adopting And/>The equation of (2) is that,
According toAnd taking the ductility requirement curve with the overrun probability of 45% to calculate the performance point of the node, wherein the calculation result is shown in fig. 5. As shown in FIG. 5, both the ductility capability and the ductility requirement of the node decrease with increasing D/D, and the ductility requirement of the node decreases with increasing period; furthermore, according to the constructional requirements in procedure: D/D is more than or equal to 0.2 and less than or equal to 0.4, and when the self-vibration period of the integral structure is between 1.2s and 2.0s, the node has a performance point meeting the construction requirement.
Claims (1)
1. A design method of the anti-seismic performance of a Y-shaped cast steel node based on a capacity spectrum method comprises the following steps:
s1: establishing a bearing capacity formula of a Y-shaped cast steel node, and obtaining regression coefficients A 1、A2、B1 and B 2:
The compression bearing capacity formula of the Y-shaped cast steel node under the action of the axial center or small eccentric pressure is written as,
，
，
，
In the method, in the process of the invention,Is yield compression-resistant bearing capacity of Y-shaped cast steel nodeThe ultimate compressive bearing capacity of the Y-shaped cast steel node; f is the design value of tensile strength, compressive strength and bending strength of cast steel; d is the outer diameter of the branch pipe of the node; d is the outer diameter of the main pipe hollow sphere; t is the wall thickness of the main pipe; the outside chamfer radius r of the branch pipe; a 1、A2、B1 and B 2 are regression coefficients; /(I)The influence coefficient of bending moment effect is considered when the axial force is designed; /(I)The influence coefficient of the axial force is considered when the bending moment is designed;
Sampling the geometrical parameters of the nodes by using Latin hypercube sampling, and establishing an analysis sample of the bearing capacity of the nodes;
Establishing a finite element model of the node, and analyzing a failure mode of the node under the action of an axle center or small eccentric pressure;
calculating a load-displacement curve of the node under the action of axle center pressure by an arc length iteration method, and taking the load when the rigidity is reduced for the first time as the yield bearing capacity of the node; taking the load when the rigidity is reduced to 10% of the initial rigidity for the first time as the limit load of the node; respectively adopt to And/>Taking a non-dimensionalized variable of pi tdf as an ordinate of a node yield and ultimate compressive bearing capacity regression equation, and taking D/D as an abscissa; regression coefficients A 1,A2,B1 and B 2 are obtained through regression of the node compressive bearing capacity formula;
S2: establishing a ductility capability curve of the node:
Coefficient of yield strength It is defined that the first and second components,
，
In the method, in the process of the invention,The maximum elastoplastic internal force is under the action of earthquake; /(I)Is yield bearing capacity;
for the Y-shaped cast steel node pressed by the axle center or small eccentric, adopting the compressive bearing capacity to calculate the yield strength coefficient; the ductility curve of a Y-cast steel node can be expressed as,
；
S3: establishing a ductility requirement curve of the node:
At a given yield level coefficient And ductile requirement of structure/>, under the condition of structure self-oscillation period TObeys a log-normal distribution,
In the method, in the process of the invention,For structural ductility requirement/>At a given/>A lower cumulative distribution function; /(I)And/>Respectively/>The conditional mean and the conditional standard deviation of (2);
Wherein the coefficient of yield level ，/>Is the power amplification factor,/>The value of (2) is 2.5;
Ductility coefficient Conditional mean/>And standard deviation of conditions/>Expressed as coefficient of yield level/>And a function of the period T of the structure's natural vibration, written as,
，
，
Wherein, regression coefficients E1、E2、E3 、E4、E5、E6、E7, F1、F2、F3、F4、F5、F6 and F 7 are calculated according to the elastoplastic time course analysis result of the single degree of freedom structure system;
And/> The regression coefficient value in the method is related to the field category, and for the field category I, the regression coefficient value of the method is/is related to the field category IThe distribution parameters in (1) can be defined by/>/>Calculating to obtain; /(I)，/>/>A probabilistic model of the ductility requirement of the node is formed, at/>After the overrun probability is set, the ductility requirement curve under different overrun probabilities can be calculated;
s4: calculating the performance points of the nodes according to a capability spectrum method:
Two curves were established using the same argument: the method comprises the steps of a ductility capability curve and a ductility requirement curve, wherein the intersection point of the two curves is a performance point or a target ductility point of a node, and the corresponding independent variable value is a design value; the independent variable is D/D.
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