CN108170913A - A kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy - Google Patents
A kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy Download PDFInfo
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- CN108170913A CN108170913A CN201711369929.1A CN201711369929A CN108170913A CN 108170913 A CN108170913 A CN 108170913A CN 201711369929 A CN201711369929 A CN 201711369929A CN 108170913 A CN108170913 A CN 108170913A
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- G06F30/00—Computer-aided design [CAD]
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- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
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Abstract
The present invention provides a kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy, this method is in order to avoid the arbitrariness drawback of the initial interval of hypothesis beam-ends drag-line tangent slope in solution procedure is calculated, the linear functional arrangement with beam-ends drag-line tangent slope of drag-line is drawn by graphic-arts technique, effective interval is quickly determined from figure, and combine dichotomy program, the beam-ends tangent slope in drag-line linear equations can more accurately be solved, it is long further to solve rope, tower end drag-line tangent slope, the related drag-line parameter such as beam-ends and tower end cable tension power.Certain Changjiang River Highway Bridge suspension cable parameter result of calculation is shown by the method for the present invention to calculate based on graphic-arts technique and the cable-stayed bridge cable parameter of dichotomy simpler, intuitive and accurate.In addition, this method can also control computational accuracy according to actual demands of engineering so that it is accurately calculated, it is more efficient.
Description
Technical field
The invention belongs to science of bridge building field more particularly to a kind of cable-stayed bridge cable parameters based on graphic-arts technique and dichotomy
Computational methods.
Background technology
Suspension cable is the Force transmission parts of cable-stayed bridge, and suspension cable will act at live load (vehicular load and crowd on bridge floor
Load) and bridge dead weight dead load etc. be transmitted to bridge tower, then pass to bridge pier, basis, finally pass on ground.The design of suspension cable is whole
It is played a very important role in the design of a cable-stayed bridge, and linear determining of the static(al) of suspension cable directly affects anchor plate and drawing
The installation of cable guide pipe.Therefore, it is very necessary that it is linear, which to be accurately determined drag-line,.
It is mainly catenary theory to study the linear method of suspension cable static(al).Although the linear table of static(al) derived using stretched wire lineation
Up to formula, more complicated but precision is higher.The drag-line that is derived in detail based on catenary theory is linear, beam-ends drag-line tangent slope, rope
The expression formula of the associated arguments such as long, and carry out the calculating of cable-stayed bridge cable relevant parameter.In calculating process, need to assume first that
The initial interval of beam-ends drag-line tangent slope, and it is iterated operation.However, the initial interval of arbitrary assumption will be brought
The drawbacks of in computational efficiency.
Invention content
The purpose of the present invention is to provide a kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy, purports
In the arbitrariness drawback for solving the initial interval for assuming in solution procedure is calculated beam-ends drag-line tangent slope, realize more
Simply, intuitive and accurate cable-stayed bridge cable parameter effectively calculates.
The invention is realized in this way a kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy, including with
Lower step：
Step (S1) draws inclined cable shape function by graphic-arts techniqueFigure, find functional image with's
Then intersection point determines the nearest left and right two of ion-exchange pointValue, and be assumed to initial value、, above and below dichotomy
Limit.
Step (S2) according to the characteristics of dichotomy, takes the intermediate value of bound, substituted into inclined cable shape
It is obtained in functionValue, then compareWith 0 magnitude relationship.
Step (S3), if, then zero value section [,] between, it enables=.If, then zero value section [,] between, it enables=.Repeat step (S2), (S3).
Step (S4), when(accuracy value of permission) enables, as functionSection [,]
Null solution, be exactly A ends slope, and solve suspension cable A ends pulling forceT A , B ends slopek B , B ends pulling forceT B And always rope is longS。
In above-mentioned steps, inclined cable shape function, A ends pulling forceT A , B ends slopek B , B ends pulling forceT B And always rope is longSRespectively
For：
In formula:Vertical force component for drag-line A ends pulling force；ch（）For cosine function more than hyperbolic；arsh（）For asinh
Function；sh（）For hyperbolic sine function；Mass density for drag-line unit length；For acceleration of gravity；For drag-line A ends
Tangent line oblique pull；Floor projection distance for drag-line both ends；Vertical projection distance for drag-line both ends.
The advantageous effect that the present invention reaches：1. in terms of the complexity of method, can intuitively and easily be determined tiltedly by graphic-arts technique
Draw effective initial interval of bridge drag-line slope；2. in terms of the timeliness of method, because the present invention is determined by graphic-arts technique
The initial interval of cable-stayed bridge cable oblique pull intuitively, conveniently, effectively, avoids the invalid initial section that arbitrary value is brought,
So as to eliminate the processing time in invalid initial section, the computational efficiency of the method for the present invention is improved；3. in the calculating essence of method
In terms of degree, can computational accuracy be controlled according to actual demands of engineering so that it is accurately calculated, it is more efficient.
Description of the drawings
Fig. 1 is the step flow chart of the cable-stayed bridge cable calculation method of parameters the present invention is based on graphic-arts technique and dichotomy；
Fig. 2 be in the embodiment of the present invention No. 3 piers of Tongling Changjiang River Highway Bridge to No. 6 pier drag-line layout drawings
Fig. 3 is A1 drag-lines k in the embodiment of the present inventionA- F relational graphs
Fig. 4 is A2 drag-lines k in the embodiment of the present inventionA- F relational graphs
Fig. 5 is A3 drag-lines k in the embodiment of the present inventionA- F relational graphs
Fig. 6 is A16 drag-lines k in the embodiment of the present inventionA- F relational graphs
Fig. 7 is J1 drag-lines k in the embodiment of the present inventionA- F relational graphs
Fig. 8 is J2 drag-lines k in the embodiment of the present inventionA- F relational graphs
Fig. 9 is J3 drag-lines k in the embodiment of the present inventionA- F relational graphs
Figure 10 is J16 drag-lines k in the embodiment of the present inventionA- F relational graphs
Figure 11 is J22 drag-lines k in the embodiment of the present inventionA- F relational graphs
Figure 12 is J26 drag-lines k in the embodiment of the present inventionA- F relational graphs
Specific embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, it is right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
The present invention provides a kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy, as shown in Figure 1, including
Following steps：
Step (S1) draws inclined cable shape function by graphic-arts techniqueFigure, find functional image with's
Then intersection point determines the nearest left and right two of ion-exchange pointValue, and be assumed to initial value、, above and below dichotomy
Limit.
In S1, according to the vertical force component of drag-line A ends pulling force, the mass density of drag-line unit length, acceleration of gravity
, the floor projection distance at drag-line both endsWith vertical projection distance, inclined cable shape function is drawn by graphic-arts technique
Figure, you can tentatively can intuitively and easily by graphic-arts technique determine cable-stayed bridge cable slope effective initial interval [,], which will be as the initial bound of dichotomy.
Step (S2) according to the characteristics of dichotomy, takes the intermediate value of bound, substituted into inclined cable shape
It is obtained in functionValue, then compareWith 0 magnitude relationship.
It, will in S2WithIt substitutes into inclined cable shape function, is obtained corresponding respectivelyValue, i.e.,With.Due to,It is two values taken in zero or so, therefore exists。
Step (S3), if, then zero value section [,] between, it enables=.If, then zero value section [,] between, it enables=.Repeat step (S2), (S3).
Step (S4), when(accuracy value of permission) enables, as functionSection [,]
Null solution, be exactly A ends slope, and solve suspension cable A ends pulling forceT A , B ends slopek B , B ends pulling forceT B And always rope is longS。
The present invention is based on graphic-arts techniques and the application case of the cable-stayed bridge cable calculation method of parameters of dichotomy：With built Anhui
For Tongling Changjiang River Highway Bridge of province Tongling Yang Shanji.
Tongling Changjiang River Highway Bridge is put into operation in December, 1991, and December 26 nineteen ninety-five builds up.The bridge bridge type is prestressing force
Reinforced Concrete Double Tasso face cable-stayed bridge, 2592 meters of overall length, main bridge overall length 1152m are 80+90+190+432+190+90+80m
7 holes continuously arrange, by the end bay institute group of the double rope face prestressed concrete cable-stayed bridge of the double tower of main span 432m and the firm structure of continuous T type
Into.The bridge bridge tower uses H-type door type structure, and box section, tower height 153.65m, suspension cable is fan-shaped arrangement, and each covering of the fan has 26
To rope, rope is away from 8 meters.Each drag-line arrangement on the bridge No. 3 piers to No. 6 piers is as shown in Figure 2.In order to carry out comparative study, case choosing
10 drag-line A1, A2, A3, A16, J1, J2, J3, J16, J22, J26 ropes is taken to be checked, the of substantially known parameter of each drag-line
As shown in table 1.
Each suspension cable relevant parameter of 1 Tongling Changjiang River Highway Bridge of table
Tab.1 The cable related parameters of Tongling Yangtze river highway
bridge
2 each drag-line beam-ends slope of tablek A Interval
Tab.2 The region taking value of beam-end slope kA
| A1 | A2 | A3 | A16 | J1 | J2 | J3 | J16 | J22 | J26 | |
| k A Interval | [4,4.5] | [2.5,3] | [2,2.5] | [0.5,1] | [4,4.5] | [2.5,3] | [2,2.5] | [0.5,1] | [0,1] | [0,1] |
During drag-line parametric solution is carried out, the initial interval of beam-ends drag-line tangent slope need to be assumed, and be iterated
Operation.In order to avoid there is invalid hypothesis section, depict that each drag-line is linear to be cut with beam-ends drag-line by graphic-arts technique first
The functional arrangement of line slope, and determine effective interval of each drag-line beam-ends tangent slope.Due to beam-ends drag-line and horizontal direction
Angle be more than 0 °, i.e.,>0.Only when Stayed Cable Bridge is when 10000m is reached, beam-ends drag-line tangent slope can just be equal to zero.
And nowadays, cable-stayed bridge longest across footpath just breaks through km, and myriametre is not achieved, therefore,k A Lower limiting value can take zero, i.e., under
Limit value isk A =0.Upper limit value can take the slope of that the root drag-line string of a musical instrument nearest from bridge tower=4.44, take 4.5.Due to more
Close to the drag-line of bridge tower, the tangent slope of beam-ends is bigger, and drag-line is under the influence of gravity, the physical location meeting of drag-line
Deviate the string of a musical instrument, thereforek A Upper limit value can takek A =4.5, physical location is lower than the string of a musical instrument.Each drag-line is drawn using graphic-arts technique
'sk A - F is schemed as shown in Fig. 3 ~ 12, can further accurate dichotomy be solved according to figureUpper lower limit value, obtain each drag-line beam
The interval of tangent slope is held, the result is shown in tables 2.The effective of interval reduces the iterations that can reduce dichotomy,
Help to improve computational efficiency.By taking A1 drag-lines as an example, it can determine by graphic-arts techniqueSection where accurate solution ranging from [4,
4.5].10 can be calculated using the cable-stayed bridge cable calculation method of parameters provided by the invention based on graphic-arts technique and dichotomy-3Precision
's, solving only need to pass through 9 iteration.Therefore, graphic-arts technique can not only improve essence with being used in combination for dichotomy
Degree and the iterations that can control high precision computation, can effectively improve computational efficiency.
The static force solution of 3 each suspension cable of Tongling Changjiang River Highway Bridge of table
Tab.3 The static solution of each cable of Tongling Yangtze river highway
bridge
Note：A is desired value, and B is existing method calculated value, and C is the method for the present invention calculated value
4 beam-ends stretching force of tableT A With tower end stretching forceT B
Tab.4 The beam-end tension T A and the pylons-end tension T B
Note：B is existing method calculated value, and C is the method for the present invention calculated value
Each oblique pull parameter result of calculation of cable-stayed bridge is as shown in Table 3 and Table 4.Consideration is influenced by table length, and case is only to table
In beam-ends tangent slope carried out error comparing calculation.From the calculating of the A-B errors in table 3 and A-C errors：Existing side
The solution by iterative method beam-ends tangent slope worst error that method uses is drag-line J22, and error amount reaches 4.67%, and minimal error is
Drag-line J1, also there is 0.41%.And the method for the present invention calculates as a result, its max value of error is the 0.05% of drag-line J3, this error
Value is very small, can almost be neglected, and minimal error reaches 0%, and be the errors of most of drag-lines is 0%.Thus
It can be seen that the graphic-arts technique that the method for the present invention uses is combined with dichotomy, precision is very high.It can be with by the error calculation in table 4
Find out：Both there are certain error, J22 for the beam-ends cable tension power that methodical beam-ends cable tension power had been calculated with the method for the present invention
The beam-ends worst error of drag-line is 2.27%, and tower end worst error value is 5.41%, this is because existing method is calculating J22 drag-lines
Beam-ends tangent slope occurs caused by large error.Existing method is iterated operation by choosing an initial value,
In a way, initial value it is arbitrary choose may so that interative computation is invalid or obtain large error as a result, therefore existing
Method has certain limitation and uncertainty.
A kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy provided by the invention, this method can avoid tiltedly
The arbitrariness drawback of the initial interval of bridge end drag-line tangent slope is drawn, draws that drag-line is linear to be drawn with beam-ends by graphic-arts technique
The functional arrangement of rope tangent slope quickly determines effective interval from figure, and combines dichotomy program, can be more accurately
The beam-ends tangent slope in drag-line linear equations is solved, further solves rope length, tower end drag-line tangent slope, beam-ends and tower end
The correlation drag-line parameter such as cable tension power.By the method for the present invention to certain Changjiang River Highway Bridge suspension cable parameter result of calculation table
It is bright, it is calculated based on graphic-arts technique and the cable-stayed bridge cable parameter of dichotomy simpler, intuitive and accurate.In addition, this method may be used also
To control computational accuracy according to actual demands of engineering so that it is accurately calculated, it is more efficient.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, it is all the present invention spirit and
All any modification, equivalent and improvement made within principle etc., should all be included in the protection scope of the present invention.
Claims (3)
1. a kind of cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy, it is characterised in that include the following steps：
Step (S1) draws inclined cable shape function by graphic-arts techniqueFigure, find functional image withFriendship
Then point determines the nearest left and right two of ion-exchange pointValue, and be assumed to initial value、, above and below dichotomy
Limit；
Step (S2) according to the characteristics of dichotomy, takes the intermediate value of bound, substituted into inclined cable shape
It is obtained in functionValue, then compareWith 0 magnitude relationship；
Step (S3), if, then zero value section [,] between, it enables=；
If, then zero value section [,] between, it enables=；
Repeat step (S2), (S3)；
Step (S4), when(accuracy value of permission) enables, as functionSection [,]
Null solution, be exactly A ends slope, and solve suspension cable A ends pulling forceT A , B ends slopek B , B ends pulling forceT B And always rope is longS。
2. the cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy as described in claim 1, which is characterized in that
In step (S1), cable-stayed bridge cable shape function figure, quick, intuitive, effectively determining suspension cable drawing are drawn with graphic-arts technique
The initial section of rope slope, and as the initial bound of dichotomy.
3. the cable-stayed bridge cable calculation method of parameters based on graphic-arts technique and dichotomy as described in claim 1, which is characterized in that
In step (S4), due to combining using dichotomy, can computational accuracy be controlled according to actual demands of engineeringSo that oblique pull
Bridge drag-line parameter is accurately calculated, more efficient.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109374171A (en) * | 2018-10-31 | 2019-02-22 | 重庆交通大学 | Method for detecting in-service stay cable force |
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| CN101852600A (en) * | 2010-06-18 | 2010-10-06 | 武汉理工大学 | Method for precisely solving length of unstressed cable of cable-stayed bridge |
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