CN103364829A - Selection method for inputting earthquake waves in time-procedure analysis for earthquake resistance of complex structures - Google Patents

Abstract

The invention discloses a selection method for inputting earthquake waves in time-procedure analysis for earthquake resistance of complex structures to meet the earthquake-resistant requirements of the complex structures such as a high-pier long-span girder bridge, a cable-stayed bridge, a suspension bridge and a super high-rise building. The method comprises the steps that firstly, alternative earthquake waves which meet different site conditions such as earthquake magnitude, distance, an acceleration peak value and long cycle characteristics are selected in an American PEER strong earthquake record database, and a primary-selection database is formed; secondly, the minimum relative weighted average error of spectrum values of alternative earthquake wave response spectrums and design response spectrums in the primary-selection database near previous orders of periodic points of platforms stages and the complex structures is used as a double-control index according to site conditions, and the specific input earthquake waves are determined to meet the requirement that a time-procedure analysis result is in accordance with response spectrum analysis analytic statistics. According to the selection method, engineering realization is easy to achieve, and the method is compared with multiple mode decomposition reaction spectrum methods. In addition, due to the fact that the earthquake waves are selected in the appointed primary-selection database, similar classification of the site conditions is ensured, and the quality of input earthquake waves is ensured.

Description

The system of selection of labyrinth antidetonation time-history analysis input seismic event

Technical field

The present invention relates to a kind of system of selection of labyrinth antidetonation time-history analysis input seismic event.

Background technology

Poplar is broad waits the people in (poplar a surname, Li Yingmin, Lai Ming. the selection control index [J] of structure time history analysis method input seismic event. the civil engineering work journal, 2000,33(6): 33-37) propose to select wave method for the two-band control of structure time-history analysis, only considered the impact of response spectrum platform section and the Basic Period of Structure.

Qu Zhe and blade row equality (Qu Zhe, blade row is flat, Pan Peng. the comparative studies [J] of earthquake motion record choosing method in the building structure elasto-plastic time history analysis. the civil engineering work journal, 2011,44(7): 10-21) domestic and international building structure time-history analysis selecting input earthquake wave method has been carried out summing up and comparing, comprised based on station information (earthquake magnitude, distance, fault feature etc.), move the wave method that selects that 3 classes are applied to the structure time-history analysis based on design spectrum frequency range and least favorable design earthquake.

In above-mentioned 2 kinds of methods, the impact of high order mode is considered not enough, therefore not bery applicable for Analysis of complex structures such as large span beam bridge with high pier, cable-stayed bridge, suspension bridge, high-rise buildings.

Summary of the invention

The technical problem to be solved in the present invention provides a kind of system of selection for labyrinth antidetonation time-history analysis input seismic event of introducing high vibration shape impact.

For reaching above purpose, be achieved through the following technical solutions:

The system of selection of labyrinth antidetonation time-history analysis input seismic event:

Step 1, based on the alternatively seismic wave of the different site conditions of selecting to satisfy earthquake magnitude, distance, acceleration peak value and long period characteristic in the U.S. PEER STRONG MOTION DATA database, the analysis of formation earthquake resistant engineering is with small-sized strong-motion data storehouse;

The earthquake resistant engineering analysis is selected from the disclosed PEER database of the U.S. with small-sized strong-motion data storehouse, this database, and its selection principle is:

The alternatively seismic wave of the different site conditions of earthquake magnitude, distance, acceleration peak value and long period characteristic is satisfied in selection in U.S. PEER STRONG MOTION DATA database, forms the primary election database.Selectively the principle of seismic wave is as follows in the database: (1) magnitude of earthquake (Ms) is more than 6 grades; (2) epicentral distance or tomography are apart between 20km～40km; (3) acceleration peak value is more than 0.15g; (4) the high-pass filtering cutoff frequency is below 0.2Hz.Because being subjected to the seismologic record restricted number, the seismic event that not exclusively satisfies on a small quantity above-mentioned condition is also at the row of selection.The purpose of way is like this: (1) earthquake can make the structure failure; (2) reduce earthquake magnitude, epicentral distance and the moving effects of nearly fault earthquake; (3) computational accuracy of assurance long period response spectrum (to 5s).

This toy data base place be divided into pan soil, in hard (soft) soil and weak soil three classes, corresponding soil layer (30m) average shear velocity of wave is Vs=360-750m/s, Vs=180-360m/s and Vs＜180m/s, corresponding to the category-B among the U.S. USGS, C class and D class, the I(II of approximate corresponding " Seismic Design of Highway Bridges detailed rules and regulations " (JTG/T B02-01-2008)) class, III class and IV class.Subordinate list 1-subordinate list 3 has provided the seismic event situation of selecting according to site condition, every class place consists of (20 seismic event) by 10 groups of two-way seismic events, contained the Northridge earthquake, Kobe earthquake, the collection that cause a large amount of modern project structural failures as far as possible and collected the events such as earthquake, so that focus (tomography) characteristic is close to stochastic distribution.

Whole process is selected in small-sized strong-motion data storehouse in the earthquake resistant engineering analysis of appointment, can guarantee the quality of the close and input seismic event of site condition classification.

The subordinate list explanation:

Table 1 is earthquake resistant engineering analysis of the present invention with stiff clay seismologic record in the small-sized strong-motion data storehouse.

Table 2 is earthquake resistant engineering analysis of the present invention with hard (soft) soil site seismologic record in the small-sized strong-motion data storehouse.

Table 3 is earthquake resistant engineering analysis of the present invention with weak soil place seismologic record in the small-sized strong-motion data storehouse.

Subordinate list 1 stiff clay seismologic record

Hard (soft) soil site seismologic record in the subordinate list 2

Subordinate list 3 weak soil place seismologic records

Step 2, based on the earthquake resistant engineering analysis with small-sized strong-motion data storehouse, seismic wave selectively, according to site condition with the earthquake resistant engineering analysis with alternatively seismic wave response spectrum and design response spectrum in the small-sized strong-motion data storehouse, the relative weighted average error minimum of spectrum value is the dual control index near the periodic point of the former rank of platform section and labyrinth, determine that concrete input seismic event is to realize time-history analysis result and response spectrum analytic statistics coherence request, select the high vibration shape impact of introducing in the wave method in multiband control, adopt the mean value error of platform section response spectrum and near the weighted mean of the larger former rank mean value error of the response spectrum cycle of labyrinth impact is controlled, namely by (1) formula:

$\left\{\begin{array}{cc}{\mathrm{\ϵ}}_w=({\stackrel{\‾}{\mathrm{\β}}}_w\left(T\right)-\stackrel{\‾}{\mathrm{\β}}\left(T\right))/\stackrel{\‾}{\mathrm{\β}}\left(T\right)\×100\%,& T=[0.1,T_g]\\ {\mathrm{\ϵ}}_T=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{\mathrm{\ϵ}}_{\mathrm{Ti}}}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i|{\stackrel{\‾}{\mathrm{\β}}}_{\mathrm{Ti}}\left(T\right)-{\stackrel{\‾}{\mathrm{\β}}}_i\left(T\right)|/{\stackrel{\‾}{\mathrm{\β}}}_i\left(T\right)}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i}\×100\%,& T=[T_i-\mathrm{\Δ}{T}_1,T_i+\mathrm{\Δ}{T}_2]\end{array}\right.$

Choose the seismic event for labyrinth;

Wherein, in (1) formula:

ε _TWeighted mean near the average relative error of spectrum value each rank periodic point of structure;

Be seismic wave amplification coefficient spectrum average in [0.1, Tg] scope;

Be standard amplification coefficient spectrum plateau value in [0.1, Tg] scope;

ε _TiBe structure i rank T natural vibration period _iNear the relative error of spectrum value average;

Be structure i rank T natural vibration period _iNear seismic wave amplification coefficient spectrum average;

Be structure i rank T natural vibration period _iNear standard amplification coefficient spectrum average; The structure vibration shape number of N for considering generally got the larger former first order modes of contribution;

λ _iBe structure i rank T natural vibration period _iThe weights of corresponding mean value error can be taken as normalized vibration shape participation coefficient and represent;

[T _i-⊿ T ₁, T _i-⊿ T ₂] be structure i rank T natural vibration period _iNear span ， Qu ⊿ T ₁=0.2s ， ⊿ T ₂=0.5s, T _gBe characteristic periods of response spectra;

(1) weighting coefficient λ in the formula _i: because vibration shape participation coefficient and vibration shape method for normalizing (Hu Yuxian. earthquake engineering [M]. Beijing: Earthquake Press, 1988) relevant, it can be just, can bear and according to vibration shape lack of alignment, by the dimensionless vibration shape calculate (Hu Yuxian. earthquake engineering [M]. Beijing: Earthquake Press, 1988) normalization vibration shape participation coefficient λ ^* _i, formula (2):

${{\mathrm{\λ}}^{*}}_i{{=M}_i}^{*}/\underset{j}{\mathrm{\Σ}}{m}_j$

(2) in the formula:

M _i ^*Generalized mass for the i vibration shape calculated by the dimensionless vibration shape;

Be the structural system gross mass;

λ ^* _iPhysical significance be expressed as: if regard the i vibration shape as simple substance point system, the ratio of the generalized mass of system and structure gross mass then, and this ratio is permanent in just and according to the vibration shape increasing descending sort, reflected the relative size of each vibration shape to structural dynamic reaction contribution, therefore weighting coefficient is taken as λ in (1) formula _i=λ _i ^*

Step 3, with the seismic event input selected and carry out time-history analysis, to satisfy the seismic Calculation demand of the labyrinths such as large span beam bridge with high pier, cable-stayed bridge, suspension bridge, high-rise building, because formula (2) also is the theoretical foundation that the engineering softwares such as SAP2000 or MIDAS calculate vibration shape contribution rate, weighting coefficient etc. can directly can be found in the analysis of Free Vibration Characteristics destination file;

The impact and the correlation parameter that adopt the present invention of technique scheme to introduce high order mode have clear and definite physical significance, and can be calculated by earthquake resistant engineering analysis software commonly used, are easy to Project Realization and compare with (many) vibration shape decomposition reaction spectrometry.In addition because select in small-sized strong-motion data storehouse in the earthquake resistant engineering analysis of appointment, can guarantee that the site condition classification is close and input the quality of seismic event.

Above-mentioned explanation only is the general introduction of technical solution of the present invention, for can clearer understanding technological means of the present invention, and can be implemented according to the content of instructions, and for above and other purpose of the present invention, feature and advantage can be become apparent, below especially exemplified by preferred embodiment, and the cooperation accompanying drawing, be described in detail as follows.

Description of drawings

The present invention is totally 3 width of cloth accompanying drawings, wherein:

Fig. 1 is earthquake resistant engineering analysis of the present invention with the comparison schematic diagram of stiff clay response spectrum and I, II class Site Design response spectrum in the small-sized strong-motion data storehouse.

Fig. 2 is earthquake resistant engineering analysis of the present invention with the comparison schematic diagram of stiff clay response spectrum in the small-sized strong-motion data storehouse and III class Site Design response spectrum.

Fig. 3 is earthquake resistant engineering analysis of the present invention with the comparison of weak soil place response spectrum in the small-sized strong-motion data storehouse and IV class Site Design response spectrum.

Among the figure: A represents amplification coefficient; T indication cycle; A represents the response spectrum of stiff clay wall scroll ripple; B represents the mean value of I class place response spectrum; C represents that I class place level is to normal value; D represents that II class place level composes to standard; The response spectrum of stiff clay wall scroll ripple during e represents; F represents the mean value of III class place response spectrum; G represents that III class place level composes to standard; H represents the response spectrum of weak soil place wall scroll ripple; I represents the mean value of IV class place response spectrum; J represents that IV class place level composes to standard.

Embodiment

The system of selection of labyrinth antidetonation time-history analysis input seismic event:

Step 1, based on the alternatively seismic wave of the different site conditions of selecting to satisfy earthquake magnitude, distance, acceleration peak value and long period characteristic in the U.S. PEER STRONG MOTION DATA database, the analysis of formation earthquake resistant engineering is with small-sized strong-motion data storehouse;

The earthquake resistant engineering analysis is selected from the disclosed PEER database of the U.S. with small-sized strong-motion data storehouse, this database, and its selection principle is:

The alternatively seismic wave of the different site conditions of earthquake magnitude, distance, acceleration peak value and long period characteristic is satisfied in selection in U.S. PEER STRONG MOTION DATA database, forms the primary election database.Selectively the principle of seismic wave is as follows in the database: (1) magnitude of earthquake (Ms) is more than 6 grades; (2) epicentral distance or tomography are apart between 20km～40km; (3) acceleration peak value is more than 0.15g; (4) the high-pass filtering cutoff frequency is below 0.2Hz.Because being subjected to the seismologic record restricted number, the seismic event that not exclusively satisfies on a small quantity above-mentioned condition is also at the row of selection.The purpose of way is like this: (1) earthquake can make the structure failure; (2) reduce earthquake magnitude, epicentral distance and the moving effects of nearly fault earthquake; (3) computational accuracy of assurance long period response spectrum (to 5s).

This toy data base place be divided into pan soil, in hard (soft) soil and weak soil three classes, corresponding soil layer (30m) average shear velocity of wave is Vs=360-750m/s, Vs=180-360m/s and Vs＜180m/s, corresponding to the category-B among the U.S. USGS, C class and D class, the I(II of approximate corresponding " Seismic Design of Highway Bridges detailed rules and regulations " (JTG/T B02-01-2008)) class, III class and IV class.Subordinate list 1-subordinate list 3 has provided the seismic event situation of selecting according to site condition, every class place consists of (20 seismic event) by 10 groups of two-way seismic events, contained the Northridge earthquake, Kobe earthquake, the collection that cause a large amount of modern project structural failures as far as possible and collected the events such as earthquake, so that focus (tomography) characteristic is close to stochastic distribution.

Whole process is selected in small-sized strong-motion data storehouse in the earthquake resistant engineering analysis of appointment, can guarantee the quality of the close and input seismic event of site condition classification.

The subordinate list explanation:

Table 1 is earthquake resistant engineering analysis of the present invention with stiff clay seismologic record in the small-sized strong-motion data storehouse.

Table 2 is earthquake resistant engineering analysis of the present invention with hard (soft) soil site seismologic record in the small-sized strong-motion data storehouse.

Table 3 is earthquake resistant engineering analysis of the present invention with weak soil place seismologic record in the small-sized strong-motion data storehouse.

Subordinate list 1 stiff clay seismologic record

Hard (soft) soil site seismologic record in the subordinate list 2

Subordinate list 3 weak soil place seismologic records

The comparison of the average response spectrum that Fig. 1 to Fig. 3 has provided 20 seismic events of different site categories and corresponding " Seismic Design of Highway Bridges detailed rules and regulations " (JTG/T B02-01-2008) (amplification coefficient).On the whole: the two meets fine with III class, IV place respectively for Moderate stiff soil sites and weak soil place; The two meets stiff clay and II class place better; And I class Site Design spectrum meets with the stiff clay averaging spectrum in cycle 0.3-2s scope and is not fine, and latter's spectrum value is slightly high, and engineering is used and seen relatively safety.

Advise during actual complex structural seismic time-history analysis: to the I(II) place can be from stiff clay seismic wave selectively; Can distinguish therefrom in the pan soil and weak soil place selectively seismic wave to III class and IV class place.

Consider the selecting input earthquake wave criterion of high vibration shape impact:

Step 2, based on the earthquake resistant engineering analysis with small-sized strong-motion data storehouse, seismic wave selectively, according to site condition with the earthquake resistant engineering analysis with alternatively seismic wave response spectrum and design response spectrum in the small-sized strong-motion data storehouse, the relative weighted average error minimum of spectrum value is the dual control index near the periodic point of the former rank of platform section and labyrinth, determine that concrete input seismic event is to realize time-history analysis result and response spectrum analytic statistics coherence request, select the high vibration shape impact of introducing in the wave method in multiband control, adopt the mean value error of platform section response spectrum and near the weighted mean of the larger former rank mean value error of the response spectrum cycle of labyrinth impact is controlled, namely by (1) formula:

$\left\{\begin{array}{cc}{\mathrm{\&epsiv;}}_w=({\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_w\left(T\right)-\stackrel{\&OverBar;}{\mathrm{\&beta;}}\left(T\right))/\stackrel{\&OverBar;}{\mathrm{\&beta;}}\left(T\right)\&times;100\%,& T=[0.1,T_g]\\ {\mathrm{\&epsiv;}}_T=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{\mathrm{\&epsiv;}}_{\mathrm{Ti}}}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i|{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_{\mathrm{Ti}}\left(T\right)-{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i\left(T\right)|/{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i\left(T\right)}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i}\&times;100\%,& T=[T_i-\mathrm{\&Delta;}{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00003526981600011.png,HDA00003526981600031.png"\; state="\{\{state\}\}">T</figure-callout>}}_1,T_i+\mathrm{\&Delta;}{T}_2]\end{array}\right.$

Choose the seismic event for labyrinth;

Wherein, in (1) formula:

ε _TWeighted mean near the average relative error of spectrum value each rank periodic point of structure;

Be seismic wave amplification coefficient spectrum average in [0.1, Tg] scope;

Be standard amplification coefficient spectrum plateau value in [0.1, Tg] scope;

ε _TiBe structure i rank T natural vibration period _iNear the relative error of spectrum value average;

Be structure i rank T natural vibration period _iNear seismic wave amplification coefficient spectrum average;

Be structure i rank T natural vibration period _iNear standard amplification coefficient spectrum average; The structure vibration shape number of N for considering generally got the larger former first order modes of contribution;

λ _iBe structure i rank T natural vibration period _iThe weights of corresponding mean value error can be taken as normalized vibration shape participation coefficient and represent;

[T _i-⊿ T ₁, T _i-⊿ T ₂] be structure i rank T natural vibration period _iNear span ， Qu ⊿ T ₁=0.2s ， ⊿ T ₂=0.5s.T _gBe characteristic periods of response spectra;

(1) weighting coefficient λ in the formula _i: because vibration shape participation coefficient and vibration shape method for normalizing (Hu Yuxian. earthquake engineering [M]. Beijing: Earthquake Press, 1988) relevant, it can be just, can bear and according to vibration shape lack of alignment, by the dimensionless vibration shape calculate (Hu Yuxian. earthquake engineering [M]. Beijing: Earthquake Press, 1988) normalization vibration shape participation coefficient λ ^* _i, formula (2):

${{\mathrm{\&lambda;}}^{*}}_i{{=M}_i}^{*}/\underset{j}{\mathrm{\&Sigma;}}{m}_j$

(2) in the formula:

M _i ^*Generalized mass for the i vibration shape calculated by the dimensionless vibration shape;

Be the structural system gross mass;

λ ^* _iPhysical significance be expressed as: if regard the i vibration shape as simple substance point system, the ratio of the generalized mass of system and structure gross mass then, and this ratio is permanent in just and according to the vibration shape increasing descending sort, reflected the relative size of each vibration shape to structural dynamic reaction contribution, therefore weighting coefficient is taken as λ in (1) formula _i=λ _i ^*

Step 3, satisfy two formula conditions of step 2, be matchingly seismic wave of the labyrinths such as large span beam bridge with high pier, cable-stayed bridge, suspension bridge, high-rise building, then with the seismic event input selected and carry out time-history analysis, to satisfy the seismic Calculation demand of the labyrinths such as large span beam bridge with high pier, cable-stayed bridge, suspension bridge, high-rise building, because formula (2) also is the theoretical foundation that the engineering softwares such as SAP2000 or MIDAS calculate vibration shape contribution rate, weighting coefficient etc. can directly can be found in the analysis of Free Vibration Characteristics destination file.

The impact and the correlation parameter that adopt the present invention of technique scheme to introduce high order mode have clear and definite physical significance, and can be calculated by earthquake resistant engineering analysis software commonly used, are easy to Project Realization and compare with (many) vibration shape decomposition reaction spectrometry.In addition because select in small-sized strong-motion data storehouse in the earthquake resistant engineering analysis of appointment, can guarantee that the site condition classification is close and input the quality of seismic event.

The above, it only is preferred embodiment of the present invention, be not that the present invention is done any pro forma restriction, although the present invention discloses as above with preferred embodiment, yet be not to limit the present invention, any those skilled in the art are not within breaking away from the technical solution of the present invention scope, appeal the equivalent embodiment that the technology contents that discloses is made a little change or is modified to equivalent variations when utilizing, in every case be the content that does not break away from technical solution of the present invention, any simple modification that foundation technical spirit of the present invention is done above embodiment, equivalent variations and modification all still belong in the scope of technical solution of the present invention.

Claims (1)

1. the system of selection of labyrinth antidetonation time-history analysis input seismic event is characterized in that:

Step 1, based on the alternatively seismic wave of the different site conditions of selecting to satisfy earthquake magnitude, distance, acceleration peak value and long period characteristic in the U.S. PEER STRONG MOTION DATA database, the analysis of formation earthquake resistant engineering is with small-sized strong-motion data storehouse;

Step 2, based on the earthquake resistant engineering analysis with small-sized strong-motion data storehouse, seismic wave selectively, according to site condition with the earthquake resistant engineering analysis with alternatively seismic wave response spectrum and design response spectrum in the small-sized strong-motion data storehouse, the relative weighted average error minimum of spectrum value is the dual control index near the periodic point of the former rank of platform section and labyrinth, determine that concrete input seismic event is to realize time-history analysis result and response spectrum analytic statistics coherence request, select the high vibration shape impact of introducing in the wave method in multiband control, adopt the mean value error of platform section response spectrum and near the weighted mean of the larger former rank mean value error of the response spectrum cycle of labyrinth impact is controlled, namely by (1) formula:

$\left\{\begin{array}{cc}{\mathrm{\&epsiv;}}_w=({\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_w\left(T\right)-\stackrel{\&OverBar;}{\mathrm{\&beta;}}\left(T\right))/\stackrel{\&OverBar;}{\mathrm{\&beta;}}\left(T\right)\&times;100\%,& T=[0.1,T_g]\\ {\mathrm{\&epsiv;}}_T=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{\mathrm{\&epsiv;}}_{\mathrm{Ti}}}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i|{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_{\mathrm{Ti}}\left(T\right)-{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i\left(T\right)|/{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i\left(T\right)}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i}\&times;100\%,& T=[T_i-\mathrm{\&Delta;}{T}_1,T_i+\mathrm{\&Delta;}{T}_2]\end{array}\right.$ Choose the seismic event for labyrinth;

Wherein, in (1) formula:

ε _wAverage relative error for response spectrum platform section;

ε _TWeighted mean near the average relative error of spectrum value each rank periodic point of structure;

Be seismic wave amplification coefficient spectrum average in [0.1, Tg] scope;

Be standard amplification coefficient spectrum plateau value in [0.1, Tg] scope;

ε _TiBe structure i rank T natural vibration period _iNear the relative error of spectrum value average;

Be structure i rank T natural vibration period _iNear seismic wave amplification coefficient spectrum average;

Be structure i rank T natural vibration period _iNear standard amplification coefficient spectrum average; The structure vibration shape number of N for considering generally got the larger former first order modes of contribution;

λ _iBe structure i rank T natural vibration period _iThe weights of corresponding mean value error can represent with normalized vibration shape participation coefficient;

[T _i-⊿ T ₁, T _i-⊿ T ₂] be structure i rank T natural vibration period _iNear span ， Qu ⊿ T ₁=0.2s ， ⊿ T ₂=0.5s, T _gBe characteristic periods of response spectra;

(1) weighting coefficient λ in the formula _i: be taken as the normalization vibration shape participation coefficient λ that the dimensionless vibration shape is calculated _i, formula (2):

${{\mathrm{\&lambda;}}^{*}}_i{{=M}_i}^{*}/\underset{j}{\mathrm{\&Sigma;}}{m}_j$

(1) in the formula:

M _i ^*Generalized mass for the i vibration shape calculated by the dimensionless vibration shape;

Be the structural system gross mass;

λ ^* _iPhysical significance be expressed as: if regard the i vibration shape as simple substance point system, the ratio of the generalized mass of system and structure gross mass then, and this ratio is permanent in just and according to the vibration shape increasing descending sort, reflected the relative size of each vibration shape to structural dynamic reaction contribution, therefore weighting coefficient is taken as λ in (1) formula _i=λ _i ^*

Step 3 is with the seismic event input selected and carry out time-history analysis, to satisfy the seismic Calculation demand of the labyrinths such as large span beam bridge with high pier, cable-stayed bridge, suspension bridge, high-rise building.

Images