CN103364829A - Selection Method of Input Seismic Waves for Seismic Time History Analysis of Complicated Structures - Google Patents

Abstract

The invention discloses a selection method for inputting seismic waves by time-course analysis of seismic resistance of a complex structure, which is used for meeting the seismic resistance requirements of complex structures such as a high-pier large-span beam bridge, a cable-stayed bridge, a suspension bridge and a super high-rise building. Firstly, selecting alternative seismic waves meeting different field conditions of magnitude, distance, acceleration peak value and long period characteristic from an American PEER strong earthquake record database to form a primary selection database. Secondly, according to the field conditions, the candidate seismic wave response spectrum and the design response spectrum in the primary selection database are used, the minimum relative weighted average error of the spectrum values around the platform section and the first few-order period points of the complex structure is used as a double-control index, and the specific input seismic wave is determined to meet the requirement of time-course analysis results and response spectrum analysis statistical consistency. The wave selection method is easy to realize engineering and is compared with a multi-vibration decomposition reaction spectrum method. In addition, the selection in the designated primary selection database can ensure that the field condition types are similar and the quality of the input seismic waves is ensured.

Description

Selection Method of Input Seismic Waves for Seismic Time History Analysis of Complicated Structures

technical field

The invention relates to a method for selecting input seismic waves for seismic time-history analysis of complex structures. the

Background technique

Yang Pu et al. (Yang Pu, Li Yingmin, Lai Ming. Structural time-history analysis method input seismic wave selection control index [J]. Chinese Journal of Civil Engineering, 2000, 33 (6): 33-37) proposed a method for structural time-history The analyzed dual-band control wave selection method only considers the influence of the response spectrum plateau and the fundamental period of the structure. the

Qu Zhe and Ye Lieping (Qu Zhe, Ye Lieping, Pan Peng. A comparative study on the selection methods of ground motion records in elastic-plastic time-history analysis of building structures [J]. Chinese Journal of Civil Engineering, 2011, 44 (7): 10-21) The selection methods of input seismic waves for time history analysis of building structures at home and abroad are summarized and compared, including three types based on station information (magnitude, distance, fault characteristics, etc.), based on design spectrum frequency bands and the most unfavorable design ground motions applied to structural time history. Analysis of wave selection methods. the

In the above two methods, the influence of high-order mode shapes is not considered enough, so it is not very suitable for the analysis of complex structures such as high-pier long-span girder bridges, cable-stayed bridges, suspension bridges, and super high-rise buildings. the

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for selecting input seismic waves for complex structure anti-seismic time-history analysis that introduces the influence of high mode shapes. the

In order to achieve the above purpose, it is achieved through the following technical solutions:

Selection method of input seismic wave for seismic time history analysis of complex structures:

Step 1: Based on the US PEER strong earthquake record database, select alternative seismic waves that meet the different site conditions of magnitude, distance, acceleration peak and long-period characteristics, and form a small strong earthquake database for engineering seismic analysis;

A small strong earthquake database for engineering seismic analysis, which is selected from the public PEER database in the United States. The selection principles are as follows:

In the US PEER strong motion record database, candidate seismic waves that meet different site conditions of magnitude, distance, peak acceleration and long-period characteristics are selected to form a primary selection database. The principles for selecting seismic waves in the database are as follows: (1) The earthquake magnitude (Ms) is above 6; (2) The epicentral distance or fault distance is between 20km and 40km; (3) The peak acceleration is above 0.15g; (4) High pass The filter cutoff frequency is below 0.2Hz. Due to the limitation of the number of seismic records, a small number of seismic waves that do not fully meet the above conditions are also selected. The purpose of this approach is: (1) The earthquake can damage the structure; (2) Reduce the impact of magnitude, epicentral distance and near-fault ground motion; (3) Ensure the calculation accuracy of the long-period response spectrum (up to 5s). the

The site of this small database is divided into three types: hard soil, medium hard (soft) soil and soft soil. 180m/s, corresponding to Class B, Class C and Class D in the USGS, approximately corresponding to Class I (II), Class III and Class IV of "Detailed Rules for Seismic Design of Highway Bridges" (JTG/T B02-01-2008) . Attached Tables 1 to 3 show the selected seismic waves according to site conditions. Each type of site is composed of 10 groups of two-way seismic waves (20 seismic waves), covering as much as possible the Northridge earthquake, Kobe earthquake, and concentrated Events such as earthquakes are aggregated so that the source (fault) properties are close to a random distribution. the

The whole process is selected in the specified small-scale strong earthquake database for engineering seismic analysis, which can ensure that the site condition category is similar and the quality of the input seismic wave is guaranteed. the

Attached table description:

Table 1 is the earthquake record of the hard soil site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Table 2 is the earthquake record of medium-hard (soft) soil site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Table 3 is the seismic records of the soft soil site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Attached Table 1 Seismic Records of Hard Soil Sites

Seismic records of hard (soft) soil sites in Attached Table 2

Attached Table 3 Seismic Records of Soft Soil Sites

Step 2. Based on the small strong earthquake database for engineering seismic analysis, select seismic waves, and use the alternative seismic wave response spectrum and design response spectrum in the small strong earthquake database for engineering seismic analysis according to the site conditions, and select the seismic wave response spectrum and design response spectrum at the platform section and the first few stages of the complex structure. The minimum relative weighted average error of the nearby spectral values is the dual control index. The specific input seismic wave is determined to achieve the statistical consistency requirements between the time history analysis results and the response spectrum analysis. The mean error of the segment response spectrum and the weighted average of the mean error of the response spectrum near the first few cycles that have a greater influence on the complex structure are controlled, that is, through the formula (1):

$\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 0.1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; ]</span>\\ {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; Ti</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; Ti</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; /</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>\end{array}\right.$

Select seismic waves for complex structures;

Among them, in formula (1):

ε _T is the weighted average of the relative error of the mean value of the spectral values near the periodic points of each order of the structure;

为[0.1，Tg]范围内地震波放大系数谱均值； 

is the mean value of the seismic wave amplification factor spectrum within the range of [0.1, Tg];

为[0.1，Tg]范围内规范放大系数谱平台值； 

is the platform value of the standard amplification factor spectrum within the range of [0.1, Tg];

ε _Ti is the relative error of the mean value of the spectral value near the i-th order natural vibration period T _i of the structure;

为结构第i阶自振周期T_i附近地震波放大系数谱均值； 

is the mean value of the seismic wave amplification factor spectrum near the i-th order natural vibration period T _i of the structure;

为结构第i阶自振周期T_i附近规范放大系数谱均值；N为考虑的结构振型数，一般取贡献较大的前几阶振型； 

is the mean value of the normative amplification factor spectrum near the i-th order natural vibration period T _i of the structure; N is the number of structural mode shapes considered, and generally the first few mode shapes with larger contributions are taken;

λ _i is the weight of the mean error corresponding to the i-th order natural vibration period T _i of the structure, which can be expressed as a normalized mode shape participation coefficient;

[T _i -⊿T ₁ , T _i -⊿T ₂ ] is the value range around the i-th order natural vibration period T _i of the structure, ⊿T ₁ =0.2s, ⊿T ₂ =0.5s, T _g is the response Spectrum characteristic period;

(1) Weighting coefficient λ _i in the formula: Since the mode shape participation coefficient is related to the mode normalization method (Hu Yuxian. Earthquake Engineering [M]. Beijing: Earthquake Press, 1988), it can be positive, negative and depends on The mode shapes are arranged in disorder, and the normalized mode shape participation coefficient λ ^* _i is calculated through dimensionless mode shapes (Hu Yuxian. Earthquake Engineering [M]. Beijing: Earthquake Press, 1988), formula (2):

${{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{<span\; class="notranslate">\; *</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{{<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

(2) where:

M _i ^* is the generalized mass of the i-th mode calculated from the dimensionless mode;

is the total mass of the structural system;

The physical meaning of λ ^* _i is expressed as: if the i-th vibration mode is regarded as a single-mass point system, the ratio of the generalized mass of the system to the total mass of the structure, and this ratio is always positive and arranged in descending order according to the increase of the vibration mode, reflecting the The relative size of the mode shape’s contribution to the structural dynamic response, so the weighting coefficient in (1) is taken as λ _i = λ _i ^* .

Step 3: Input the selected seismic waves and perform time-history analysis to meet the seismic calculation requirements of complex structures such as high-pier long-span girder bridges, cable-stayed bridges, suspension bridges, and super high-rise buildings. The theoretical basis of the engineering software to calculate the contribution rate of the mode shape, the weighting coefficient, etc. can be found directly in the natural vibration characteristic analysis result file;

The present invention adopting the above-mentioned technical scheme introduces the influence of high-order mode shapes and related parameters have clear physical meanings, and can be calculated by commonly used engineering anti-seismic analysis software, which is easy for engineering implementation and comparison with (multi-) mode-shape decomposition response spectrum method. In addition, because it is selected from the specified small-scale strong earthquake database for engineering seismic analysis, it can ensure that the site condition category is similar and the quality of the input seismic wave is guaranteed. the

The above description is only an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention, it can be implemented according to the contents of the description, and in order to make the above and other purposes, features and advantages of the present invention more obvious and understandable , the following preferred embodiments are specifically cited below, and are described in detail as follows in conjunction with the accompanying drawings. the

Description of drawings

The present invention has 3 drawings in total, in which:

Fig. 1 is a comparison schematic diagram of the response spectrum of hard soil site and the design response spectrum of class I and II sites in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Fig. 2 is a comparison schematic diagram of the response spectrum of medium-hard soil site and the design response spectrum of Class III site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Fig. 3 is a comparison between the response spectrum of soft soil site and the design response spectrum of Class IV site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

In the figure: A represents the amplification factor; T represents the period; a represents the response spectrum of a single wave on a hard soil site; b represents the average value of the response spectrum of a Class I site; c represents the horizontal standard value of a Class I site; d represents the level of a Class II site e represents the response spectrum of a single wave in a medium-hard soil site; f represents the average value of the response spectrum in a class III site; g represents the horizontal standard spectrum in a class III site; h represents the response spectrum of a single wave in a soft soil site; The average value of the response spectrum of a category IV site; j represents the horizontal specification spectrum of a category IV site. the

Detailed ways

Selection method of input seismic wave for seismic time history analysis of complex structures:

Step 1: Based on the US PEER strong earthquake record database, select alternative seismic waves that meet the different site conditions of magnitude, distance, acceleration peak and long-period characteristics, and form a small strong earthquake database for engineering seismic analysis;

A small strong earthquake database for engineering seismic analysis, which is selected from the public PEER database in the United States. The selection principles are as follows:

In the US PEER strong motion record database, candidate seismic waves that meet different site conditions of magnitude, distance, peak acceleration and long-period characteristics are selected to form a primary selection database. The principles for selecting seismic waves in the database are as follows: (1) The earthquake magnitude (Ms) is above 6; (2) The epicentral distance or fault distance is between 20km and 40km; (3) The peak acceleration is above 0.15g; (4) High pass The filter cutoff frequency is below 0.2Hz. Due to the limited number of seismic records, a small number of seismic waves that do not fully meet the above conditions are also selected. The purpose of this approach is: (1) The earthquake can damage the structure; (2) Reduce the impact of magnitude, epicentral distance and near-fault ground motion; (3) Ensure the calculation accuracy of the long-period response spectrum (up to 5s). the

The site of this small database is divided into three types: hard soil, medium hard (soft) soil and soft soil. 180m/s, corresponding to Class B, Class C and Class D in the USGS, approximately corresponding to Class I (II), Class III and Class IV of "Detailed Rules for Seismic Design of Highway Bridges" (JTG/T B02-01-2008) . Attached Tables 1 to 3 show the selected seismic waves according to site conditions. Each type of site is composed of 10 groups of two-way seismic waves (20 seismic waves), covering as much as possible the Northridge earthquake, Kobe earthquake, and concentrated Events such as earthquakes are aggregated so that the source (fault) properties are close to a random distribution. the

The whole process is selected in the specified small-scale strong earthquake database for engineering seismic analysis, which can ensure that the site condition category is similar and the quality of the input seismic wave is guaranteed. the

Attached table description:

Table 1 is the earthquake record of the hard soil site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Table 2 is the earthquake record of medium-hard (soft) soil site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Table 3 is the seismic records of the soft soil site in the small-scale strong earthquake database for engineering anti-seismic analysis of the present invention. the

Attached Table 1 Earthquake Records of Hard Soil Sites

Seismic records of hard (soft) soil sites in Attached Table 2

Attached Table 3 Seismic Records of Soft Soil Sites

Figures 1 to 3 show the comparison between the average response spectrum of 20 seismic waves in different site categories and the corresponding "Detailed Rules for Seismic Design of Highway Bridges" (JTG/T B02-01-2008) (magnification factor). On the whole: medium-hard sites and soft soil sites are in good agreement with Category III and IV sites respectively; hard soil sites are in good agreement with Category II sites; and the design spectrum of Category I sites is within the range of 0.3-2s It does not match well with the average spectrum of the hard soil site, and the spectrum value of the latter is slightly higher, and it will be safer for engineering applications. the

It is suggested in the seismic time-history analysis of actual complex structures: for I (II) sites, the seismic waves can be selected from the hard soil sites; for the III and IV types of sites, the seismic waves can be selected from the medium hard soil and soft soil sites, respectively. the

The selection criterion of input seismic wave considering the influence of high mode shape:

Step 2: Based on the small strong earthquake database for engineering seismic analysis, select seismic waves, and use the alternative seismic wave response spectrum and design response spectrum in the small strong earthquake database for engineering seismic analysis according to the site conditions, at the platform section and the first few stages of the complex structure. The minimum relative weighted average error of the nearby spectral values is the dual control index. The specific input seismic wave is determined to achieve the statistical consistency requirements of the time history analysis results and the response spectrum analysis. The mean error of the segment response spectrum and the weighted average of the mean error of the response spectrum near the first few cycles that have a greater influence on the complex structure are controlled, that is, through the formula (1):

$\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 0.1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; ]</span>\\ {\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; Ti</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; Ti</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; /</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; )</span>}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; 100</span>}<span\; class="notranslate">\; \%</span><span\; class="notranslate">\; ,</span>& \mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="T"\; filenames="HDA00003526981600011.png,HDA00003526981600031.png"\; state="\{\{state\}\}">T</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>\end{array}\right.$

Select seismic waves for complex structures;

Among them, in formula (1):

ε _T is the weighted average of the relative error of the mean value of the spectral values near the periodic points of each order of the structure;

为[0.1，Tg]范围内地震波放大系数谱均值； 

is the mean value of the seismic wave amplification factor spectrum within the range of [0.1, Tg];

为[0.1，Tg]范围内规范放大系数谱平台值； 

is the platform value of the standard amplification factor spectrum within the range of [0.1, Tg];

ε _Ti is the relative error of the mean value of the spectral value near the i-th order natural vibration period T _i of the structure;

为结构第i阶自振周期T_i附近地震波放大系数谱均值； 

is the mean value of the seismic wave amplification factor spectrum near the i-th order natural vibration period T _i of the structure;

为结构第i阶自振周期T_i附近规范放大系数谱均值；N为考虑的结构振型数，一般取贡献较大的前几阶振型； 

is the mean value of the normative amplification factor spectrum near the i-th order natural vibration period T _i of the structure; N is the number of structural mode shapes considered, and generally the first few mode shapes with larger contributions are taken;

λ _i is the weight of the mean error corresponding to the i-th order natural vibration period T _i of the structure, which can be expressed as a normalized mode shape participation coefficient;

[T _i -⊿T ₁ , T _i -⊿T ₂ ] is the value range around the i-th order natural vibration period T _i of the structure, ⊿T ₁ =0.2s, ⊿T ₂ =0.5s. T _g is the characteristic period of the response spectrum;

(1) Weighting coefficient λ _i in the formula: Since the mode shape participation coefficient is related to the mode normalization method (Hu Yuxian. Earthquake Engineering [M]. Beijing: Earthquake Press, 1988), it can be positive, negative and depends on The mode shapes are arranged in disorder, and the normalized mode shape participation coefficient λ ^* _i is calculated through dimensionless mode shapes (Hu Yuxian. Earthquake Engineering [M]. Beijing: Earthquake Press, 1988), formula (2):

${{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{<span\; class="notranslate">\; *</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{{<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$

(2) where:

M _i ^* is the generalized mass of the i-th mode calculated from the dimensionless mode;

is the total mass of the structural system;

The physical meaning of λ ^* _i is expressed as: if the i-th vibration mode is regarded as a single-mass point system, the ratio of the generalized mass of the system to the total mass of the structure, and this ratio is always positive and arranged in descending order according to the increase of the vibration mode, reflecting the The relative size of the mode shape’s contribution to the structural dynamic response, so the weighting coefficient in (1) is taken as λ _i = λ _i ^* .

Step 3: Satisfy the two calculation conditions of step 2, that is, match seismic waves for complex structures such as high-pier long-span girder bridges, cable-stayed bridges, suspension bridges, super high-rise buildings, etc., and then input the selected seismic waves and perform time-history analysis to satisfy For the seismic calculation requirements of complex structures such as high-pier long-span girder bridges, cable-stayed bridges, suspension bridges, and super high-rise buildings, since formula (2) is also the theoretical basis for calculating the mode contribution rate of engineering software such as SAP2000 or MIDAS, the weighting coefficients can be directly It can be found in the natural vibration characteristic analysis result file. the

The present invention adopting the above-mentioned technical scheme introduces the influence of high-order mode shapes and related parameters have clear physical meanings, and can be calculated by commonly used engineering anti-seismic analysis software, which is easy for engineering implementation and comparison with (multi-) mode-shape decomposition response spectrum method. In addition, because it is selected from the specified small-scale strong earthquake database for engineering seismic analysis, it can ensure that the site condition category is similar and the quality of the input seismic wave is guaranteed. the

The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, it is not intended to limit the present invention. Anyone familiar with this field Without departing from the scope of the technical solution of the present invention, the skilled person can use the technical content disclosed in the appeal to make some changes or modify it into an equivalent embodiment with equivalent changes, but any content that does not depart from the technical solution of the present invention, according to the present invention Any simple modifications, equivalent changes and modifications made to the above embodiments still fall within the scope of the technical solutions of the present invention. the

Claims (1)

1. The selection method of input seismic wave for seismic time-history analysis of complex structures is characterized in that: Step 1: Based on the US PEER strong earthquake record database, select alternative seismic waves that meet the different site conditions of magnitude, distance, acceleration peak value and long-period characteristics, and form a small strong earthquake database for engineering seismic analysis; Step 2. Based on the small strong earthquake database for engineering seismic analysis, select seismic waves, and use the alternative seismic wave response spectrum and design response spectrum in the small strong earthquake database for engineering seismic analysis according to the site conditions, and select the seismic wave response spectrum and design response spectrum at the platform section and the first few stages of the complex structure. The minimum relative weighted average error of the nearby spectral values is the dual control index. The specific input seismic wave is determined to achieve the statistical consistency requirements between the time history analysis results and the response spectrum analysis. The mean error of the segment response spectrum and the weighted average of the mean error of the response spectrum near the first few cycles that have a greater influence on the complex structure are controlled, that is, through formula (1): $\left\{\begin{array}{cc}{\mathrm{\&epsiv;}}_w=({\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_w\left(T\right)-\stackrel{\&OverBar;}{\mathrm{\&beta;}}\left(T\right))/\stackrel{\&OverBar;}{\mathrm{\&beta;}}\left(T\right)\&times;100\%,& T=[0.1,T_g]\\ {\mathrm{\&epsiv;}}_T=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{\mathrm{\&epsiv;}}_{\mathrm{Ti}}}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i|{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_{\mathrm{Ti}}\left(T\right)-{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i\left(T\right)|/{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i\left(T\right)}{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i}\&times;100\%,& T=[T_i-\mathrm{\&Delta;}{T}_1,T_i+\mathrm{\&Delta;}{T}_2]\end{array}\right.$ Select seismic waves for complex structures; Among them, in formula (1): ε _w is the mean relative error of the plateau segment of the response spectrum; ε _T is the weighted average of the relative error of the mean value of the spectral values near the periodic points of each order of the structure;

is the mean value of the seismic wave amplification factor spectrum within the range of [0.1, Tg];

is the platform value of the standard amplification factor spectrum within the range of [0.1, Tg]; ε _Ti is the relative error of the mean value of the spectral value near the i-th order natural vibration period T _i of the structure;

is the mean value of the seismic wave amplification factor spectrum near the i-th order natural vibration period T _i of the structure;

is the mean value of the normative amplification factor spectrum near the i-th order natural vibration period T _i of the structure; N is the number of structural mode shapes considered, and generally the first few mode shapes with larger contributions are taken; λ _i is the weight of the mean error corresponding to the i-th order natural vibration period T _i of the structure, which can be expressed by the normalized mode shape participation coefficient; [T _i -⊿T ₁ , T _i -⊿T ₂ ] is the value range around the i-th order natural vibration period T _i of the structure, ⊿T ₁ =0.2s, ⊿T ₂ =0.5s, T _g is the response Spectrum characteristic period; (1) The weighting coefficient λ _i in the formula: take it as the normalized mode shape participation coefficient λ _i calculated by the dimensionless mode shape, formula (2): ${{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{<span\; class="notranslate">\; *</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{{<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; /</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}$ (1) where: M _i ^* is the generalized mass of the i-th mode calculated from the dimensionless mode;

is the total mass of the structural system; The physical meaning of λ ^* _i is expressed as: if the i-th vibration mode is regarded as a single-mass point system, the ratio of the generalized mass of the system to the total mass of the structure, and this ratio is always positive and arranged in descending order according to the increase of the vibration mode, reflecting the The relative size of the mode shape’s contribution to the structural dynamic response, so the weighting coefficient in (1) is taken as λ _i = λ _i ^* ; Step 3: Input the selected seismic waves and perform time-history analysis to meet the seismic calculation requirements of complex structures such as high-pier long-span girder bridges, cable-stayed bridges, suspension bridges, and super high-rise buildings.

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