CN105808802B - A kind of lead core rubber support equivalent linearization modeling method and its isolation bridge application - Google Patents
A kind of lead core rubber support equivalent linearization modeling method and its isolation bridge application Download PDFInfo
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Abstract
The present invention relates to a kind of lead core rubber support equivalent linearization model modelling approach and the lead core rubber support bridge damping design method based on this equivalent inearized model, equivalent linearization empirical model is fitted using the Artificial Seismic Wave to match with Bridges in Our Country earthquake resistant design code, and using this equivalent linearization empirical model as committed step, bridge damping design is carried out using iterative calculation method.Compared with prior art, the present invention is under the premise of ensureing that bridge lead core rubber support shock design result is reliable, have many advantages, such as that design accuracy is high, advantageously reduce design work difficulty, it is relatively low can effectively to solve the problems, such as that existing lead core rubber support equivalent linearization model calculates accuracy under Bridges in Our Country earthquake resistant design code system.
Description
Technical field
The invention belongs to bridge earthquake resistance technical fields, are related to a kind of bridge structure shock design method, more particularly, to one
Plant the lead core rubber support equivalent linearization model being fitted based on Artificial Seismic Wave and use this model progress bridge structure shock insulation
Design method.
Background technology
Bridge structure shock design is extending structure natural vibration period to weaken seismic energy by the way that horizontal seismic isolation bearing is arranged
It transmits, reduces the structural response under geological process, to ensure the seismic seeurity of bridge to the full extent.Geological process
Under, shock isolating pedestal enters non-linear force state, and accurate solution need to be obtained by Nonlinear time-history analysis.But Nonlinear time-history
Analysis method comparison is complicated, is not easy to be grasped by bridge technology personnel, therefore it is necessary to do the nonlinear characteristic of shock isolating pedestal
Linearization process is imitated, and then bridge damping design is carried out using linear analysis method.
The equivalent linearization of shock isolating pedestal is rigid with equivalent level in the sense that bearing horizontal shear deflection is suitable
Degree and damping ratio consume energy to consider that bearing post-yield stiffness is degenerated with plasticity, to convert nonlinear problem to linear problem.
In view of its explicit physical meaning, using easy feature, the earthquake resistant code of China and foreign countries all introduces equivalent linearization side
Method.At present, it has been suggested that equivalent linear method can be classified as two classes, one kind is the theoretical model derived from concept, another kind of
It is the empirical model returned by statistical analysis.On the whole, the accuracy of empirical model is than theoretical model higher.But
Empirical model also has its applicable elements, not can obtain more accurately result of calculation to any geological process, because having
Empirical model is fitted by limited amount and with the natural seismic wave for being different from design acceleration reaction spectrum signature.It is real
In the engineering of border, Bridge Earthquake Resistance Design is carried out frequently with artificial synthesized seismic wave, Artificial Seismic Wave is with natural seismic wave in acceleration
There are significant differences in reaction spectrum signature, will necessarily be reduced using the accuracy of existing empirical model.
Invention content
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide a kind of lead core rubber supports
Equivalent linearization model modelling approach and its isolation bridge application solve existing lead core rubber support equivalent linearization empirical model
Deficiency, have many advantages, such as that design accuracy is high, reduces design work difficulty.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of lead core rubber support equivalent linearization model modelling approach, includes the following steps：
1) elasto-plastic system is used to describe the mechanical characteristics of lead core rubber support；
2) Artificial Seismic Wave is synthesized according to Bridge Earthquake Resistance Design specification, obtains elasto-plastic system and makees in the Artificial Seismic Wave
Elastic-plastic Displacement spectrum under；
3) error function that the parameter of construction pair equivalent linear system corresponding with elasto-plastic system is identified：
4) using the parameter of modified Gauss-Newton algorithm identification equivalent linear system；
5) according to the parameter identified, the equivalent linearization model of lead core rubber support is fitted.
In the step 3), the error function of construction is specially：
In formula, SdFor the displacement spectra of equivalent linear system, SμIt is the Elastic-plastic Displacement spectrum for the elasto-plastic system that ductility ratio is μ,
T0,iFor elasto-plastic system initial natural vibration period, n is to count in the period of displacement spectra, β1=Te/T0For ratio natural vibration period, TeIt is equivalent
Natural vibration period, T0For elasto-plastic system initial natural vibration period, β2=ξeFor equivalent damping ratio, β1With β2The as equivalent line of being identified
The parameter of sexual system.
The equivalent linearization model of the step 5), lead core rubber support is specially：
Wherein, KeFor equivalent stiffness, ξeFor equivalent damping ratio, K0For the initial stiffness of lead core rubber support, μ is lead for retractable pencil rubber
The ductility ratio of glue bearing.
A kind of lead core rubber support bridge damping design method based on equivalent linearization model, includes the following steps：
Step S1：Bridge structure global finite element model is established, lead core rubber support control of horizontal displacement target is set
Δobj；
Step S2：It is preliminary to choose lead core rubber support parameter；
Step S3：Set lead core rubber support horizontal displacement initial value Δi；
Step S4：Calculating and ΔiCorresponding lead core rubber support ductility ratio μ, according to μ and above-mentioned equivalent linearization model,
Calculate lead core rubber support equivalent stiffness KeWith equivalent damping ratio ξe；
Step S5：The horizontal displacement value for calculating lead core rubber support under geological process, is maximized as Δn；
Step S6：Judge ΔiWith ΔnDeviation whether be more than feasible value, if so, with ΔnFor horizontal displacement initial value,
Return to step S4, if it is not, then by ΔnReal standard displacement maximum value as lead core rubber support；
Step S7：Judge ΔnWhether Δ is metn> Δsobj, if so, adjusting lead core rubber support parameter, return to step
S3, if it is not, then lead core rubber support parameter at this time is final design parameter.
In the step S5, the horizontal displacement of lead core rubber support under geological process is calculated using linear Time-History Analysis Method
Value.
The bridge structure includes any one of the bowstring arch bridge of simply supported girder bridge, continuous bridge, external freely-supported.
Compared with prior art, the invention has the advantages that：
1, lead core rubber support equivalent line is fitted using the Artificial Seismic Wave to match with Bridges in Our Country earthquake resistant design code
Property model, improve lead core rubber support bridge damping design result accuracy；
2, the equivalent linearization model based on the present invention may be used linear analysis method and carry out bridge damping design, drop
The low work difficulty of bridge technology personnel, is conducive to the popularization of seismic isolation technology, to improve the antidetonation energy of Bridges in Our Country structure
Power reduces earthquake disaster damage.
Description of the drawings
Fig. 1 is shock insulation parameter designing flow diagram of the present invention；
Fig. 2 is the Artificial Seismic Wave timeamplitude map that the embodiment of the present invention is selected；
Fig. 3 is the acceleration response spectrum of Artificial Seismic Wave and corresponding design acceleration response spectrum comparison diagram in Fig. 2；
Fig. 4 is the T of the present inventione/T0With μ relationship matched curve schematic diagrames；
Fig. 5 is the ξ of the present inventioneWith μ relationship matched curve schematic diagrames；
Fig. 6 is the bridge structure FEM model schematic diagram of the embodiment of the present invention.
Specific implementation mode
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention
Premised on implemented, give detailed embodiment and specific operating process, but protection scope of the present invention is not limited to
Following embodiments.
A kind of lead core rubber support equivalent linearization model modelling approach, theoretical foundation are that the mechanics of lead core rubber support is special
Sign can be described with elasto-plastic system, etc. Elastic-plastic Displacement spectrum under the conditions of ductility ratios can be by the displacement of an elastic systems
Spectrum is come approximate, which is exactly required equivalent linear system.The modeling method specifically comprises the steps of：
1) elasto-plastic system is used to describe the mechanical characteristics of lead core rubber support, the surrender rigidity folding of the elasto-plastic system
Subtract that coefficient is 0.155, material damping ratio is 0.05.
2) Artificial Seismic Wave is synthesized according to Bridge Earthquake Resistance Design specification, as shown in Fig. 2, obtaining elasto-plastic system artificially
Elasto-plastic response spectrum under seismic wave effect.
According to the division of the large, medium and small shake fortification in 6~9 degree of areas that set up defences of Bridges in Our Country earthquake resistant design code pair, choose
Earthquake motion peak acceleration include 0.025g, 0.05g, 0.1g, 0.125g, 0.2g, 0.22g, 0.4g and 0.62g, according to me
Division of state's Bridge Earthquake Resistance Design specification to site category, by be uniformly distributed principle selection eigenperiod include 0.25s,
Above-mentioned earthquake motion peak acceleration and eigenperiod are combined by 0.35s, 0.45s, 0.55s, 0.65s, 0.75s and 0.9s,
Artificial Seismic Wave is synthesized as design acceleration response spectrum controling parameter, amounts to 56.
Obtain Elastic-plastic Displacement time spectrum of the elasto-plastic system under Artificial Seismic Wave effect, by ductility ratio μ be respectively 2,4,
6,8,10,12,14,16,18,20,24,28,32,36,40,45 and 50, and initial 0.2~2s of range natural vibration period, interval
For 0.1s, as controling parameter.
3) the error function F (β that the parameter of construction pair equivalent linear system corresponding with elasto-plastic system is identified1,
β2)：
In formula, SdFor the displacement spectra of equivalent linear system, SμIt is the Elastic-plastic Displacement spectrum for the elasto-plastic system that ductility ratio is μ,
T0,iFor elasto-plastic system initial natural vibration period, n is to count in the period of displacement spectra, β1=Te/T0For ratio natural vibration period, TeIt is equivalent
Natural vibration period, T0For elasto-plastic system initial natural vibration period, β2=ξeFor equivalent damping ratio, β1With β2The as equivalent line of being identified
The parameter of sexual system.
4) using the parameter of modified Gauss-Newton algorithm identification equivalent linear system.
5) according to the parameter beta identified1、β2And its distribution characteristics, period ratio~ductility ratio and equivalent damping are fitted respectively
Than the curve and relational expression of~ductility ratio, as shown in Figure 4 and Figure 5：
According to rigidity than with the period than relationship Ke/K0=(Te/T0)-2, can obtain：
Wherein, KeFor equivalent stiffness, ξeFor equivalent damping ratio, K0For the initial stiffness of lead core rubber support, μ is lead for retractable pencil rubber
The ductility ratio of glue bearing.
Relational expression Ke/K0And ξeThe as equivalent linearization model of lead core rubber support.
As shown in Figure 1, the lead core rubber support bridge damping design method based on above-mentioned equivalent linearization model, including with
Lower step：
Step S1：Bridge structure global finite element model is established, lead core rubber support control of horizontal displacement target is set
Δobj。
Step S2：It is preliminary to choose lead core rubber support parameter.
Step S3：Set lead core rubber support horizontal displacement initial value Δi。
Step S4：Calculating and ΔiCorresponding lead core rubber support ductility ratio μ, according to μ and the lead core rubber support etc. of foundation
Inearized model is imitated, lead core rubber support equivalent stiffness K is calculatedeWith equivalent damping ratio ξe。
Step S5：The horizontal displacement value that lead core rubber support under geological process is calculated using linear Time-History Analysis Method, is taken
Maximum value is Δn。
Step S6：Judge ΔiWith ΔnDeviation whether be more than feasible value tol, if so, with ΔnIt is initial for horizontal displacement
Value, return to step S4, if it is not, then by ΔnReal standard displacement maximum value as lead core rubber support.
Step S7：Judge ΔnWhether Δ is metn> Δsobj, if so, adjusting lead core rubber support parameter, return to step
S3, if it is not, then lead core rubber support parameter at this time is final design parameter.
It is described further using an example.
One 3 × 30m small box girder bridge, superstructure are 4 small box girders, beam away from 3m, substructure bent cap section 2 ×
2.5m, 1.6 × 2.5m of pier stud section, height 5m, cushion cap height 2m, small box girder strength grade of concrete C50, bent cap C50, pier stud
C40, cushion cap C30, lead core rubber support vertical rigidity 1 × 108KN/m, horizontal initial stiffness 20600kN/m surrender Stiffness degradation
Coefficient 0.155, level surrender bearing capacity 134kN.The global finite element model of above-mentioned bridge structure is as shown in Figure 6.
Lead core rubber support equivalent linearization model is established using above-mentioned modeling method, wherein when selecting Artificial Seismic Wave
Journey curve as shown in Fig. 2, its peak accelerator be 0.2g, eigenperiod 0.45s, the acceleration response spectrum of the Artificial Seismic Wave
It is as shown in Figure 3 with the comparison of corresponding design acceleration response spectrum.
The process that shock design is carried out based on above-mentioned lead core rubber support equivalent linearization model is as follows：
(1) assume lead core rubber support initial level shift value Δi=0.2m, calculate corresponding ductility ratio μ=
30.7。
(2) according to ductility ratio μ=30.7 and equivalent linearization model, the equivalent stiffness K of lead core rubber support is calculatede=
3564kN/m, equivalent damping ratio ξe=0.239, and then damped coefficient c=517kNs/m can be obtained.
(3) horizontal displacement of lead core rubber support under geological process, maximum value are calculated using linear Time-History Analysis Method
For Δn=0.158m.The peak accelerator of input-to-state stabilization be 0.62g, eigenperiod 0.45s.
(4)ΔiWith ΔnDeviation be more than feasible value 0.001m, then by Δi=0.158m is repeated as initial level displacement
The above calculating process, until ΔiWith ΔnDeviation be less than or equal to feasible value 0.001m.Finally, lead core rubber support horizontal displacement
Calculated value converges on 0.148m, this value is lead core rubber support horizontal displacement maximum value.
Use the lead core rubber support horizontal displacement maximum actual value that nonlinear time-history analysis method is calculated for
0.131m, it can be seen that very close using the result of calculation and actual value of the present invention, accuracy can meet Bridge Design
It is required that.
Claims (6)
1. a kind of lead core rubber support equivalent linearization model modelling approach, which is characterized in that include the following steps：
1) elasto-plastic system is used to describe the mechanical characteristics of lead core rubber support；
2) Artificial Seismic Wave is synthesized according to Bridge Earthquake Resistance Design specification, obtains elasto-plastic system under Artificial Seismic Wave effect
Elastic-plastic Displacement spectrum；
3) error function that the parameter of construction pair equivalent linear system corresponding with elasto-plastic system is identified；
4) using the parameter of modified Gauss-Newton algorithm identification equivalent linear system；
5) according to the parameter identified, the equivalent linearization model of lead core rubber support is fitted：
Wherein, KeFor equivalent stiffness, ξeFor equivalent damping ratio, K0For the initial stiffness of lead core rubber support, μ is lead-rubber branch
The ductility ratio of seat.
2. lead core rubber support equivalent linearization model modelling approach according to claim 1, which is characterized in that the step
It is rapid 3) in, the error function of construction is specially：
In formula, SdFor the displacement spectra of equivalent linear system, SμIt is the Elastic-plastic Displacement spectrum for the elasto-plastic system that ductility ratio is μ, T0,i
For elasto-plastic system initial natural vibration period, n is to count in the period of displacement spectra, β1=Te/T0For ratio natural vibration period, TeFor it is equivalent from
It shakes the period, T0For elasto-plastic system initial natural vibration period, β2=ξeFor equivalent damping ratio, β1With β2For the equivalent linear of being identified system
The parameter of system.
3. a kind of lead core rubber support bridge damping design method based on equivalent linearization model, which is characterized in that including with
Lower step：
Step S1：Bridge structure global finite element model is established, lead core rubber support control of horizontal displacement target Δ is setobj；
Step S2：It is preliminary to choose lead core rubber support parameter；
Step S3：Set lead core rubber support horizontal displacement initial value Δi；
Step S4：Calculating and ΔiCorresponding lead core rubber support ductility ratio μ, according to μ and equivalent linearization described in claim 1
Model calculates lead core rubber support equivalent stiffness KeWith equivalent damping ratio ξe；
Step S5：The horizontal displacement value for calculating lead core rubber support under geological process, is maximized as Δn；
Step S6：Judge ΔiWith ΔnDeviation whether be more than feasible value, if so, with ΔnFor horizontal displacement initial value, return
Step S4, if it is not, then by ΔnReal standard displacement maximum value as lead core rubber support；
Step S7：Judge ΔnWhether Δ is metn> Δsobj, if so, lead core rubber support parameter is adjusted, return to step S3, if
No, then lead core rubber support parameter at this time is final design parameter.
4. the lead core rubber support bridge damping design method according to claim 3 based on equivalent linearization model,
It is characterized in that, lead core rubber support shock design parameter includes horizontal initial stiffness, horizontal surrender bearing capacity.
5. the lead core rubber support bridge damping design method according to claim 3 based on equivalent linearization model,
It is characterized in that, in the step S5, the horizontal position of lead core rubber support under geological process is calculated using linear Time-History Analysis Method
Shifting value.
6. the lead core rubber support bridge damping design method according to claim 3 based on equivalent linearization model,
It is characterized in that, the bridge structure includes any one of the bowstring arch bridge of simply supported girder bridge, continuous bridge, external freely-supported.
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| CN114444191B (en) * | 2022-02-11 | 2022-12-09 | 四川大学 | Lead core rubber shock insulation support parameter design method for heavy storage bin equipment |
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| CN101881089A (en) * | 2010-06-29 | 2010-11-10 | 哈尔滨工业大学深圳研究生院 | Evaluation method of earthquake resistant performance of steel tube concrete building and application |
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| CN101881089A (en) * | 2010-06-29 | 2010-11-10 | 哈尔滨工业大学深圳研究生院 | Evaluation method of earthquake resistant performance of steel tube concrete building and application |
Non-Patent Citations (2)
| Title |
|---|
| An equivalent linear model of lead-rubber seismic isolation bearings;J.S.Hwang 等;《Engineering Structures》;19960731;第18卷(第7期);530-533 * |
| 减隔震连续梁桥非经典阻尼问题与地震响应简化分析;彭伟 等;《振动与冲击》;20090131;第28卷(第1期);146-151 * |
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