CN109977565A - A kind of Dynamic Property Analysis of Cable-stayed Bridge method based on FEA - Google Patents
A kind of Dynamic Property Analysis of Cable-stayed Bridge method based on FEA Download PDFInfo
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Abstract
The present invention relates to Dynamic Property Analysis of Cable-stayed Bridge technical fields, provide a kind of Dynamic Property Analysis of Cable-stayed Bridge method based on FEA, initially set up the finite element model of cable-stayed bridge to be analyzed；Then the boundary condition for changing finite element model, constructs the finite element model of half floating system, floating system, tower beam consolidation system cable-stayed bridge；Then a variety of basic load operating conditions are added in finite element model, each rank natural frequency of vibration of every kind of structural system cable-stayed bridge is obtained using multi-Ritz-Vectormethod, analyzes the relationship between structural system and the cable-stayed bridge natural frequency of vibration；Then construct every kind of structural system cable-stayed bridge without auxiliary pier finite element model, whether there is or not the relationships between auxiliary pier and each rank natural frequency of vibration of cable-stayed bridge for analysis；Finite element model of the different steel reinforced concretes of cable-stayed bridge to be analyzed than under is finally constructed, the relationship between the steel reinforced concrete rank natural frequency of vibration more each than cable-stayed bridge to be analyzed is analyzed.The present invention can analyze the integral dynamic properties of cable-stayed bridge, and high-efficient, result accuracy height.
Description
Technical field
The present invention relates to Dynamic Property Analysis of Cable-stayed Bridge technical fields, dynamic more particularly to a kind of cable-stayed bridge based on FEA
Force characteristic analysis method.
Background technique
Cable-stayed bridge has become most economical and beautiful bridge with quick speed of application to making full use of for material with it
One of pattern.With the increase of the service life, bridge structure will appear different degrees of damage and destruction, move to cable-stayed bridge
Force characteristic analysis, to understand different structural-system and structural parameters to the sensitivity of natural frequency of structures, to improvement cable-stayed bridge
Situation be of great significance.
In existing Dynamic Property Analysis of Cable-stayed Bridge method, lack the analysis to its integral dynamic properties, and mostly adopt
With economics analysis method, also bridge is simplified, is then solved by solving analytic equation in mathematics,
Its analysis efficiency is low, analysis result is not accurate enough.
Summary of the invention
In view of the problems of the existing technology, the present invention provides a kind of Dynamic Property Analysis of Cable-stayed Bridge method based on FEA,
The integral dynamic properties of cable-stayed bridge can be analyzed, and high-efficient, result accuracy height.
The technical solution of the present invention is as follows:
A kind of Dynamic Property Analysis of Cable-stayed Bridge method based on FEA, the cable-stayed bridge include king-tower, girder and pier stud,
It is characterized in that, includes the following steps:
Step 1: collecting the design drawing of cable-stayed bridge to be analyzed, construction note, final acceptance of construction data, supervision diary and all previous
Maintenance data establishes the finite element model of cable-stayed bridge to be analyzed using finite element software Midas/civil；
Step 2: on the basis of the finite element model of cable-stayed bridge to be analyzed, changing the finite element model of cable-stayed bridge to be analyzed
Boundary condition, construct the finite element model of three kinds of structural system cable-stayed bridges, three kinds of structural system cable-stayed bridges are half to float
System cable-stayed bridge, floating system cable stayed bridge, tower beam consolidation system cable-stayed bridge；
Step 3: in the finite element model of every kind of structural system cable-stayed bridge, basic load operating condition is added, and using more
Weight Ritz vector method obtain every kind of structural system cable-stayed bridge preceding 10 first order mode figure and each rank natural frequency of vibration, by comparing different knots
Each rank natural frequency of vibration of structure system cable-stayed bridge obtains the relationship between stayed-cable bridge structure system and the cable-stayed bridge natural frequency of vibration, by comparing
The time that the vertical drift vibration shape of different structural-system cable-stayed bridge occurs obtains between stayed-cable bridge structure system and cable-stayed bridge longitudinal rigidity
Relationship；
Step 4: on the basis of the finite element model of every kind of structural system cable-stayed bridge, constructing every kind of structural system cable-stayed bridge
Without auxiliary pier finite element model, in every kind of structural system cable-stayed bridge without being added and step 3 in auxiliary pier finite element model
In identical basic load operating condition, and using multi-Ritz-Vectormethod obtain every kind of structural system cable-stayed bridge without auxiliary pier when 10
First order mode figure and each rank natural frequency of vibration, by comparing every kind of structural system cable-stayed bridge, whether there is or not each rank natural frequencies of vibration when auxiliary pier to obtain
To whether there is or not the relationships between auxiliary pier and each rank natural frequency of vibration of cable-stayed bridge.
In the step 3, the basic load operating condition includes self weight, T1-T28, concrete box girder diaphragm plate, system liter
Temperature, system cooling, suspension cable heating, suspension cable cooling, secondary dead load, steel beam prestressing force, positive temperature gradient, negative temperature gradient,
End reaction, ballast, loop wheel machine, longitudinal righteous style and practice, lateral righteous style and practice, longitudinal negative wind, laterally negative wind, steel anchor box, access bridge dead load, access bridge vapour
Vehicle, access bridge tramcar, access bridge crowd, access bridge gradient increased temperature, access bridge gradient cooling, access bridge settle load, the basic load
All operating conditions in operating condition are added simultaneously.
The cable-stayed bridge to be analyzed is half floating system hybrid cable-stayed bridge, and the girder of the cable-stayed bridge to be analyzed is
Mix box beam, main span is all steel box beam, secondary end bay is steel box-girder, end bay is prestressed concrete box girder.
The above-mentioned Dynamic Property Analysis of Cable-stayed Bridge method based on FEA, further includes step 5: in the limited of cable-stayed bridge to be analyzed
On the basis of meta-model, finite element model of the different steel reinforced concretes of cable-stayed bridge to be analyzed than under is constructed, in the every of cable-stayed bridge to be analyzed
The addition and identical basic load operating condition in step 3 in the finite element model than under of kind steel reinforced concrete, and use multiple Ritz vector
Method obtains cable-stayed bridge to be analyzed in 10 first order mode figures of the every kind of steel reinforced concrete than under and each rank natural frequency of vibration, by comparing oblique pull to be analyzed
Bridge obtains the relationship between the steel reinforced concrete rank natural frequency of vibration more each than cable-stayed bridge to be analyzed in each rank natural frequency of vibration of the every kind of steel reinforced concrete than under.
In the step 5, the difference steel reinforced concrete ratio includes that steel box-girder length shortens 0.05 times, steel box-girder length shortening 0.15
Times.
The invention has the benefit that
The present invention is based on FEA to carry out Analysis of Dynamic Characteristics to cable-stayed bridge, on the basis of cable-stayed bridge finite element model to be analyzed
On, change boundary condition, constructs the finite element mould whether there is or not auxiliary pier and different steel reinforced concrete than lower different structural-system cable-stayed bridge
Type, by applying a variety of basic load operating conditions, obtain cable-stayed bridge 10 first order mode figures and each rank natural frequency of vibration, can be to cable-stayed bridge
Integral dynamic properties analyzed, obtain that stayed-cable bridge structure system, whether there is or not auxiliary pier, different steel reinforced concrete ratio and cable-stayed bridge self-vibrations frequently
Relationship between rate provides effective reference for subsequent bridge inspection and maintenance and engineering design, and analysis efficiency is high, analysis result accuracy
It is high.
Detailed description of the invention
Fig. 1 is that the present invention is based on the flow charts of the Dynamic Property Analysis of Cable-stayed Bridge method of FEA；
Fig. 2 is the finite element model structural schematic diagram of cable-stayed bridge to be analyzed in the embodiment of the present invention；
Fig. 3 is 1 first order mode figure of cable-stayed bridge to be analyzed in the embodiment of the present invention；
Fig. 4 is 3 first order mode figures of cable-stayed bridge to be analyzed in the embodiment of the present invention；
Fig. 5 is 5 first order mode figures of cable-stayed bridge to be analyzed in the embodiment of the present invention；
Fig. 6 is 9 first order mode figures of cable-stayed bridge to be analyzed in the embodiment of the present invention；
Fig. 7 is the preceding 10 rank natural frequency of vibration curve graph of three kinds of structural system cable-stayed bridges in the embodiment of the present invention；
Fig. 8 is that whether there is or not 10 rank natural frequency of vibration curves before when auxiliary pier for half floating system cable stayed bridge in the embodiment of the present invention
Figure；
Fig. 9 is that whether there is or not 10 rank natural frequency of vibration curve graphs before when auxiliary pier for floating system cable stayed bridge in the embodiment of the present invention；
Figure 10 is that whether there is or not the 10 rank natural frequencies of vibration before when auxiliary pier are bent for tower beam consolidation system cable-stayed bridge in the embodiment of the present invention
Line chart；
Figure 11 be the embodiment of the present invention in half floating system cable stayed bridge difference steel reinforced concrete than under before 10 rank natural frequency of vibration curves
Figure.
Specific embodiment
Below in conjunction with the drawings and specific embodiments, the invention will be further described.
As shown in Figure 1, for the present invention is based on the flow charts of the Dynamic Property Analysis of Cable-stayed Bridge method of FEA.Base of the invention
In the Dynamic Property Analysis of Cable-stayed Bridge method of FEA, the cable-stayed bridge includes king-tower, girder and pier stud, which is characterized in that including under
State step:
Step 1: collecting the design drawing of cable-stayed bridge to be analyzed, construction note, final acceptance of construction data, supervision diary and all previous
Maintenance data establishes the finite element model of cable-stayed bridge to be analyzed using finite element software Midas/civil.
The cable-stayed bridge to be analyzed is half floating system hybrid cable-stayed bridge, and the girder of the cable-stayed bridge to be analyzed is
Mix box beam, main span is all steel box beam, secondary end bay is steel box-girder, end bay is prestressed concrete box girder.
Wherein, finite element analysis (FEA, Finite Element Analysis) is using the method for mathematical approach to true
Physical system (geometry and load working condition) is simulated, and simple and interaction element (i.e. unit) is utilized, so that it may
Remove to approach the real system of unlimited unknown quantity with the unknown quantity of limited quantity.
In the present embodiment, cable-stayed bridge to be analyzed is Jiangwan Bridge, is located at Guangdong Province, overall length 1027m, main bridge is across footpath group
Close the hybrid cable-stayed bridge of 33+102+183=318m；Its girder is mixing box beam, and wherein main span is all steel box beam, secondary
End bay is steel box-girder, and end bay is prestressed concrete box girder；It uses half floating system of three stride continuous, the separation of tower beam, auxiliary pier
The isolated vase pier in selection left and right.Wherein, mixing box beam refers to the feelings being restricted in the ratio of cable-stayed bridge end bay and main span
Under condition, girder end bay and main span use different materials, and connecting portion is near bridge tower.According to the design drawing of Jiangwan Bridge
Etc. data, the finite element model of cable-stayed bridge to be analyzed is established by Midas/civil, as shown in Figure 2；Bridge model totally 2203
Node, 2115 units, 87 sections.
Step 2: on the basis of the finite element model of cable-stayed bridge to be analyzed, changing the finite element model of cable-stayed bridge to be analyzed
Boundary condition, construct the finite element model of three kinds of structural system cable-stayed bridges, three kinds of structural system cable-stayed bridges are half to float
System cable-stayed bridge, floating system cable stayed bridge, tower beam consolidation system cable-stayed bridge.
Wherein, half floating system uses Pylon pier consolidation form, and the position that girder passes through king-post sets vertical support on crossbeam；
Without general bearing under the girder of floating system, without constraint between girder and king-tower and bridge pier；The king-tower of tower beam consolidation system and master
For beam using rigid connection, king-tower, girder share a node, and king-tower, pier stud use elastic connection.
Step 3: in the finite element model of every kind of structural system cable-stayed bridge, basic load operating condition is added, and using more
Weight Ritz vector method obtain every kind of structural system cable-stayed bridge preceding 10 first order mode figure and each rank natural frequency of vibration, by comparing different knots
Each rank natural frequency of vibration of structure system cable-stayed bridge obtains the relationship between stayed-cable bridge structure system and the cable-stayed bridge natural frequency of vibration, by comparing
The time that the vertical drift vibration shape of different structural-system cable-stayed bridge occurs obtains between stayed-cable bridge structure system and cable-stayed bridge longitudinal rigidity
Relationship.
In the step 3, the basic load operating condition includes self weight, T1-T28, concrete box girder diaphragm plate, system liter
Temperature, system cooling, suspension cable heating, suspension cable cooling, secondary dead load, steel beam prestressing force, positive temperature gradient, negative temperature gradient,
End reaction, ballast, loop wheel machine, longitudinal righteous style and practice, lateral righteous style and practice, longitudinal negative wind, laterally negative wind, steel anchor box, access bridge dead load, access bridge vapour
Vehicle, access bridge tramcar, access bridge crowd, access bridge gradient increased temperature, access bridge gradient cooling, access bridge settle load, the basic load
All operating conditions in operating condition are added simultaneously.
In the present embodiment, static load operating condition has 54 kinds, obtains every kind of structural system oblique pull using multi-Ritz-Vectormethod
The preceding 10 first order mode figure of bridge and each rank natural frequency of vibration.Wherein, 1 rank, 3 ranks, 5 ranks of Jiangwan Bridge, 9 first order mode figures respectively as Fig. 3,
Shown in Fig. 4, Fig. 5, Fig. 6, the preceding 10 rank natural frequency of vibration and preceding 10 first order mode feature such as the following table 1 and Fig. 7 of 3 kinds of structural system cable-stayed bridges
It is shown.It can be seen that the basic cycle of (1) Jiangwan Bridge is 1.807s, fundamental natural frequency 0.554Hz, model self-vibration week
Phase changes to a very small extent after the 6th rank, and is gradually reduced, and illustrates that Jiangwan Bridge's model belongs to densely covered frequency spectrum；By one
First order mode, second_mode, three first order modes are it is found that the vertical and lateral stiffness of girder main span is small compared with the rigidity of side bar, the cross of king-tower
It is small compared with longitudinal rigidity to rigidity, girder generally longitudinally rigidity than laterally and vertical small；(2) natural frequency of vibration is according to the sequence successively decreased
Are as follows: tower beam consolidation system, half floating system, floating system, floating system are significantly greater than half floating system and Ta Liang natural vibration period
Consolidation system；(3) the single order natural frequency of vibration and period of tower beam consolidation and half floating system are close, and the floating system natural frequency of vibration is
0.1823Hz, about the 0.3 of half floating system times differ larger, this is because the girder of floating system and king-tower and bridge pier it
Between without constraint, overall stiffness is small: the vertical drift vibration shape of the girder of (4) floating system occurs more early, appears in first vibration mode, and partly floats
It is floating, consolidation system is later, in third and fourth vibration shape, it is seen that floating system longitudinal rigidity is than half floating and tower beam consolidation system
It is small, but half floating and floating system occur that internal force is comparatively much smaller when vertical drift, so both structures can reduce
Influence of the earthquake to structure.
Step 4: on the basis of the finite element model of every kind of structural system cable-stayed bridge, constructing every kind of structural system cable-stayed bridge
Without auxiliary pier finite element model, in every kind of structural system cable-stayed bridge without being added and step 3 in auxiliary pier finite element model
In identical basic load operating condition, and using multi-Ritz-Vectormethod obtain every kind of structural system cable-stayed bridge without auxiliary pier when 10
First order mode figure and each rank natural frequency of vibration, by comparing every kind of structural system cable-stayed bridge, whether there is or not each rank natural frequencies of vibration when auxiliary pier to obtain
To whether there is or not the relationships between auxiliary pier and each rank natural frequency of vibration of cable-stayed bridge.
Table 1
In the present embodiment, half floating system cable stayed bridge, floating system cable stayed bridge, whether there is or not auxiliary for tower beam consolidation system cable-stayed bridge
Preceding 10 rank natural frequency of vibration when pier is respectively as shown in Fig. 8, Fig. 9, Figure 10.It can be seen that (1), for half floating system, end bay is set
Setting auxiliary pier, vertically the curved natural frequency of vibration changes greatly in 1 rank girder, improves 24.5%, illustrates that auxiliary pier can significantly improve master
Beam vertical rigidity；End bay setting auxiliary pier is substantially unchanged in the horizontal curved natural frequency of vibration of 2 rank king-towers, illustrates auxiliary pier to king-tower
Lateral stiffness is substantially without influence；End bay auxiliary pier, which exists, improves the natural frequency of vibration, increase rate 10%-20%, and structure is integrally rigid
Degree increases；(2) for floating system and tower beam consolidation system, natural frequency of foundation is respectively increased in end bay setting auxiliary pier
11% and 23.9%, illustrate that end bay auxiliary pier influences the smallest to be floating system on natural frequency of foundation in three kinds of structural systems；
End bay be arranged auxiliary pier exist improve the natural frequency of vibration, increase rate is 10%-20% and 20%-30%, illustrate whether there is or not
Auxiliary pier influences maximum to tower beam consolidation system, and floating system and the influence of half floating system are taken second place.
Step 5: on the basis of the finite element model of cable-stayed bridge to be analyzed, constructing the different steel reinforced concrete ratios of cable-stayed bridge to be analyzed
Under finite element model, be added in finite element model than under in every kind of steel reinforced concrete of cable-stayed bridge to be analyzed identical with step 3
Basic load operating condition, and 10 first order mode figures of the cable-stayed bridge to be analyzed in every kind of steel reinforced concrete than under are obtained using multi-Ritz-Vectormethod
With each rank natural frequency of vibration, by comparing cable-stayed bridge to be analyzed each rank natural frequency of vibration of the every kind of steel reinforced concrete than under obtain steel reinforced concrete ratio with to
Analyze the relationship between each rank natural frequency of vibration of cable-stayed bridge.
In the present embodiment, half floating system cable stayed bridge difference steel reinforced concrete than under before the 10 rank natural frequencies of vibration it is as shown in figure 11.Its
In, the difference steel reinforced concrete ratio includes that steel box-girder length shortens 0.05 times, 0.15 times of steel box-girder length shortening.As can be seen that steel-is mixed
In hybrid beam, after reducing reinforcing bar beam length, low order frequency has a minor change, and middle order frequency is at being decreased obviously trend.
Obviously, above-described embodiment is only a part of the embodiments of the present invention, instead of all the embodiments.Above-mentioned implementation
Example for explaining only the invention, is not intended to limit the scope of the present invention..Based on the above embodiment, those skilled in the art
Member's every other embodiment obtained namely all in spirit herein and original without making creative work
Made all modifications, equivalent replacement and improvement etc., are all fallen within the protection domain of application claims within reason.
Claims (5)
1. a kind of Dynamic Property Analysis of Cable-stayed Bridge method based on FEA, the cable-stayed bridge includes king-tower, girder and pier stud, spy
Sign is, includes the following steps:
Step 1: collecting design drawing, construction note, final acceptance of construction data, supervision diary and all previous maintenance of cable-stayed bridge to be analyzed
Repair information establishes the finite element model of cable-stayed bridge to be analyzed using finite element software Midas/civil；
Step 2: on the basis of the finite element model of cable-stayed bridge to be analyzed, changing the side of the finite element model of cable-stayed bridge to be analyzed
Boundary's condition, constructs the finite element model of three kinds of structural system cable-stayed bridges, and three kinds of structural system cable-stayed bridges are half floating system
Cable-stayed bridge, floating system cable stayed bridge, tower beam consolidation system cable-stayed bridge；
Step 3: in the finite element model of every kind of structural system cable-stayed bridge, basic load operating condition is added, and using multiple
Ritz vector method obtain every kind of structural system cable-stayed bridge preceding 10 first order mode figure and each rank natural frequency of vibration, by comparing different structure
Each rank natural frequency of vibration of system cable-stayed bridge obtains the relationship between stayed-cable bridge structure system and the cable-stayed bridge natural frequency of vibration, by comparing not
The time occurred with the vertical drift vibration shape of structural system cable-stayed bridge obtains the pass between stayed-cable bridge structure system and cable-stayed bridge longitudinal rigidity
System；
Step 4: on the basis of the finite element model of every kind of structural system cable-stayed bridge, constructing the nothing of every kind of structural system cable-stayed bridge
Auxiliary pier finite element model, in every kind of structural system cable-stayed bridge without being added in auxiliary pier finite element model and phase in step 3
Same basic load operating condition, and 10 ranks vibration of the every kind of structural system cable-stayed bridge without auxiliary pier when is obtained using multi-Ritz-Vectormethod
Type figure and each rank natural frequency of vibration, by comparing every kind of structural system cable-stayed bridge, whether there is or not each rank natural frequencies of vibration when auxiliary pier to be had
Without the relationship between auxiliary pier and each rank natural frequency of vibration of cable-stayed bridge.
2. the Dynamic Property Analysis of Cable-stayed Bridge method according to claim 1 based on FEA, which is characterized in that the step 3
In, the basic load operating condition includes self weight, T1-T28, concrete box girder diaphragm plate, system heating, system cooling, suspension cable
Heating, suspension cable cooling, secondary dead load, steel beam prestressing force, positive temperature gradient, negative temperature gradient, end reaction, ballast, loop wheel machine,
Longitudinal righteous style and practice, longitudinal negative wind, lateral negative wind, steel anchor box, access bridge dead load, access bridge automobile, access bridge tramcar, is drawn at lateral righteous style and practice
Bridge crowd, access bridge gradient increased temperature, access bridge gradient cooling, access bridge settle load, and all operating conditions in the basic load operating condition are same
When be added.
3. the Dynamic Property Analysis of Cable-stayed Bridge method according to claim 2 based on FEA, which is characterized in that described wait divide
Analysis cable-stayed bridge is half floating system hybrid cable-stayed bridge, and the girder of the cable-stayed bridge to be analyzed is mixing box beam, main span
For all steel box beam, secondary end bay be steel box-girder, end bay is prestressed concrete box girder.
4. the Dynamic Property Analysis of Cable-stayed Bridge method according to claim 3 based on FEA, which is characterized in that further include step
Rapid 5: on the basis of the finite element model of cable-stayed bridge to be analyzed, constructing finite element of the different steel reinforced concretes of cable-stayed bridge to be analyzed than under
Model is added and identical basic load in step 3 in finite element model than under in every kind of steel reinforced concrete of cable-stayed bridge to be analyzed
Operating condition, and cable-stayed bridge to be analyzed is obtained in 10 first order mode figures of the every kind of steel reinforced concrete than under and each rank self-vibration using multi-Ritz-Vectormethod
Frequency obtains steel reinforced concrete ratio and cable-stayed bridge to be analyzed in each rank natural frequency of vibration of the every kind of steel reinforced concrete than under by comparing cable-stayed bridge to be analyzed
Relationship between each rank natural frequency of vibration.
5. the Dynamic Property Analysis of Cable-stayed Bridge method according to claim 4 based on FEA, which is characterized in that the step 5
In, the difference steel reinforced concrete ratio includes that steel box-girder length shortens 0.05 times, 0.15 times of steel box-girder length shortening.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110704894A (en) * | 2019-08-22 | 2020-01-17 | 中铁大桥勘测设计院集团有限公司 | Calculation method for seismic response of cable-stayed bridge tower |
| CN111797457A (en) * | 2020-07-15 | 2020-10-20 | 哈尔滨工业大学 | Steel-concrete combined continuous beam bridge natural vibration frequency rapid estimation method |
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| CN101937485A (en) * | 2010-10-11 | 2011-01-05 | 武汉理工大学 | Determination method of initial completion initial cable force of cable-stayed bridge |
| CN103696356A (en) * | 2013-12-16 | 2014-04-02 | 中交公路规划设计院有限公司 | Multi-tower diagonal cable bridge provided with double-row support system |
| CN203625762U (en) * | 2013-12-16 | 2014-06-04 | 中交公路规划设计院有限公司 | Multi-tower cable-stayed bridge provided with double rows of support systems |
| CN104933285A (en) * | 2015-03-05 | 2015-09-23 | 西南交通大学 | Bridge field static load test evaluation method |
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| CN101937485A (en) * | 2010-10-11 | 2011-01-05 | 武汉理工大学 | Determination method of initial completion initial cable force of cable-stayed bridge |
| CN103696356A (en) * | 2013-12-16 | 2014-04-02 | 中交公路规划设计院有限公司 | Multi-tower diagonal cable bridge provided with double-row support system |
| CN203625762U (en) * | 2013-12-16 | 2014-06-04 | 中交公路规划设计院有限公司 | Multi-tower cable-stayed bridge provided with double rows of support systems |
| CN104933285A (en) * | 2015-03-05 | 2015-09-23 | 西南交通大学 | Bridge field static load test evaluation method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110704894A (en) * | 2019-08-22 | 2020-01-17 | 中铁大桥勘测设计院集团有限公司 | Calculation method for seismic response of cable-stayed bridge tower |
| CN111797457A (en) * | 2020-07-15 | 2020-10-20 | 哈尔滨工业大学 | Steel-concrete combined continuous beam bridge natural vibration frequency rapid estimation method |
| CN111797457B (en) * | 2020-07-15 | 2021-03-23 | 哈尔滨工业大学 | Steel-concrete combined continuous beam bridge natural vibration frequency rapid estimation method |
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Application publication date: 20190705 |