CN104947838B - Method for finding feasible prestress of cable-pole structure - Google Patents
Method for finding feasible prestress of cable-pole structure Download PDFInfo
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- CN104947838B CN104947838B CN201510320430.6A CN201510320430A CN104947838B CN 104947838 B CN104947838 B CN 104947838B CN 201510320430 A CN201510320430 A CN 201510320430A CN 104947838 B CN104947838 B CN 104947838B
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Abstract
The invention provides a method for finding feasible prestress of a cable-pole structure. The method comprises the steps that an analysis model including a load F, a prestress initial value P*, a calculation error epsilon n and a displacement calculation error epsilon d is established, a Newton iterative formula is established according to a fuzzy expression between the input value P of the prestress and the output value N of unit internal force and is used for iterative calculation on the prestress P until the error requirement is met; whether the feasible prestress of the cable-pole structure is found out or not and whether reasonable updating needs to be conducted on structure geometry are judged according to the structure self-stress modal number, the internal force of a cable and a pole and the displacement of the structure, during geometry updating, the structure deformation under the prestress P and the load F is directly stacked to an original geometry to be conducted, and the prestress iteration and geometry updating are circularly conducted until all index requirements are met. According to the method, in the process of finding the feasible prestress of the cable-pole structure, reasonable geometry updating can be conducted, and the load possibility of the structure can be taken into consideration.
Description
Art
The feasible prestressed computational methods of one kind according to the present invention, it is specifically a kind of can for finding cable-rod structure
The prestressed method of row, range of application includes cable dome structure, cable-truss structure, cable net structure and suspended-dome structure and Zhang Xian
The cable-strut system of girder construction bottom.
Background technology
In large-span space structure engineering field, Cable Structure, rope bar and rope bar girder construction are used as in stadiums, exhibitions
The roof system of the buildings such as the heart, Railway Passenger Stations and airport building is widely paid close attention to.Nineteen twenty-seven, Fuller was proposed first
The concept of tension integral structure, subsequent Snelson has built the model of first tension integral structure in the world.In tensioning entirety
On the basis of structure, Geiger arranges ring beam and has invented cable dome structure by the periphery in tension integral structure, Cable dome
Gymnasium successively in the Soul Olympic Games in 1986, the Redbird gymnasiuies of Illinois, America in 1988,1996 it is sub- special
Applied on the gymnasium of the blue big Olympic Games and the roof system of Chinese Erdos gymnasium.Cable-rod structure is due to without just
Beginning rigidity, the rigidity of structure must be produced by applying prestressing force.So prestressed searching is cable-rod structure design with design
In the step of key one.At present the pre-stress design to cable-rod structure, there is both at home and abroad certain research, but not yet finds both to examine
Considering load can carry out carrying out document and patent achievement that prestressing force finds design after rationalization renewal to unreasonable construction geometry again.
Research both domestic and external has, Pellegrino be equal to 1993《International Journal of Solids
and Structures》On article " the Structural Computations with the Singular Value that deliver
Decomposition of the Equilibrium Matrix " carry out singular value point by the balancing matrix to construction geometry
Solution, has obtained the self-stress modes of structure, but this method only just can be entered in construction geometry determination and under the premise of rational
OK, and outer load and the deadweight of structure can not be considered.YUAN in 2002 etc. exists《Computers and Structures》It is upper to send out
The article " Integral feasible pre-stress of cable domes " of table is symmetrical according to cable dome structure itself
Characteristic, it is proposed that the concept of structure integrity feasible prestress, and traditional singular value decomposition method is simplified, but use this side
Method carries out still considering structural load when prestressing force searching and design, and must determine in construction geometry and it is rational under the premise of
Just can carry out.Later Wang etc. existed《Journal of Constructional Steel Research》On the article delivered
“Simple approach for force finding analysis of circular Geiger domes with
Dead load is converted into that joint load given by node balance method by consideration of self-weight " can be with
Consider dead load simplified calculation method, but this method be only used in the Geiger domes with single self-stress modes and
On Levy domes, for other Cable dome forms of multi self-equilibrium stress mode have no the report of this method application, this side in addition
Method equally will determine in construction geometry and could apply on the basis of rational, consider to appoint while also having no and applying this method
Report on the pre-stress design of meaning form load.In addition Cao etc. exists《Engineering Structures》On the text delivered
Chapter " A simplified strategy for force finding analysis of suspendomes " describes one kind
For the prestressed localized design method of rope bar girder construction, Guo exists《Advances in Structural Engineering》On
Article " the A Simple Approach for Force Finding Analysis of Suspended-Domes for delivering
Based on the Superposition Principle " are described and are carried out prestressing force to rope bar girder construction using principle of stacking
The simple computational method of design, but above-mentioned both approaches are required to structure and there is rational geometric configuration could apply.For
Above-mentioned deficiency, the present invention proposes one kind for finding the feasible prestressed method of cable-rod structure, can set up cable-rod structure
Directly the load that structure may bear included during numerical model, and then is directly examined during feasible prestressing force is found
Consider the load that structure is possible to undertake；Formula X is utilized simultaneouslyi+1=Xi+DiCan to some cannot apply it is feasible it is prestressed not
Rational structure carries out construction geometry and rationalizes amendment, and designs the corresponding feasible prestressing force of searching, is only capable of to several compared with traditional method
What determines and rational structure can just carry out pre-stress design and have progress substantially；Additionally, constant in holding structure geometry
In the case of the prestressing force of structure is iterated, construction geometry renewal is then carried out after the completion of prestressing force iteration, do not stop
Repetition above-mentioned calculating circulation until meeting all indexs till this method overcome construction geometry and internal force intercouple it is right
The impact of pre-stress design.This method not only can carry out prestressed searching to the complicated cable-rod structure of Mechanical Builds, to knot
Structure constitute with the relatively simple rope bar girder construction of moulding in rope lever system and cable net structure can carry out it is feasible prestressed
Find design.
The content of the invention
It is an object of the invention to provide one kind had not only been contemplated that structural load but also unreasonable construction geometry can have been rationalized
The prestressing force finding method of amendment, i.e., it is a kind of to be used to find the feasible prestressed method of cable-rod structure.Realize outside carry, from recast
Found and design with the prestressing force of lower cable-rod structure, and entered to feasible prestressed unreasonable cable-rod structure geometry cannot be applied
Row geometry rationalizes amendment, and feasible prestressed searching and design are carried out to it.
The object of the present invention is achieved like this：
(1) according to the geometry X of cable-rod structureiThe numerical model comprising structure load F (5) is set up, and rope bar is tied
Lower oblique cord (1), upper oblique cord (2), strop (3) are initialized as P with the prestressing force of depression bar (4) in structure*=[Pc Ps], wherein, it is oblique
Rope (1), upper oblique cord (2), the prestressing force of strop (3) are the arbitrary value (P more than zeroc>0), the prestressing force of depression bar (4) is less than zero
Arbitrary value (Ps<0)。
(2) internal force of setting structure and minimum allowable error value ε of displacementnAnd εdAnd part lower oblique cord (1), upper oblique cord
(2), the internal force desired value of strop (3) or depression bar (4)
(3) with rope in cable-rod structure and the prestressing force P=P (p of bar1…pl…pb) as input value, calculate correspondence rope and bar
Internal force N=N (n1…nl…nb), and set up following input/output relation：
N=Φ (P)
Φ represents the transmission function between prestressing force P and internal force N in above formula, and b is the total quantity of rope and bar.
Provide the internal force desired value of lower oblique cord (1), upper oblique cord (2), strop (3) and depression bar (4)
With actual interior force value N=N (n1…nl…nb) difference function expression：
It is pre- l-th component of searching (for lower oblique cord (1), upper oblique cord (2), strop (3) or depression bar (4)) to be constructed using above formula
Stress plNewton iterative calculation formula：
In above formula,It is right for difference function f (P)First-order partial derivative, can as the following formula be entered in the form of difference
Row is calculated：
Calculate l-th component prestressing force plNewton iterative calculation formula it is as follows：
In above formulaFor l-th component the step of kth -1 and kth step iterative calculation when apply it is pre-
Stress value and internal force value of calculation.
As k=1, following oblique cord (1), upper oblique cord (2), strop (3) are with depression bar (4) in structural initial pre stress P* and load F
Prestressing force iterative initial value of interior force value N under effect as counterpart memberFor convenience of calculation
Force value in the target of l root ropes (or bar)Can be according to force value in the target of known membersCount as follows
Calculate：
Prestressed iterative calculation is carried out using above-mentioned formula, until lower oblique cord (1), upper oblique cord (2), strop (3) and pressure
The actual internal force (N) of bar (4) and target internal force ()) difference less than setting calculation error εnAfter obtain target
Prestress value
(3) target prestress value is judged by following indexWhether it is feasible prestressing force and construction geometry XiWhether need
Carry out rationalization amendment：
Index 1：Judge the geometry X with cable-rod structureiWhether corresponding structure self-stress modes number (S) is more than 0.
Index 2：Judge structure in load F and target prestressing forceUnder effect, all lower oblique cords (1), upper oblique cord (2), ring
Whether tension, all depression bars (4) are pressurized for rope (3), i.e. Nc＞ 0, Ns＜ 0.
Index 3：Judge structure in load F and prestressing forceIn the presence of displacement (Di) whether calculate error ε less than displacementd。
If while meeting index 1, index 2 and index 3, the target prestress value for searching outAs structure it is feasible it is pre- should
Power；As met index 1 simultaneously with index 2 but being unsatisfactory for index 3, then re-using newton iteration formula carries out prestressing force iteration meter
Calculate, now
If being unsatisfactory for index 1 or index 2, cannot be in the existing geometry X of structureiUnder conditions of search out the feasible pre- of structure
Stress, need to be to construction geometry XiCarry out rationalization amendment；In this case index 3 is such as unsatisfactory for, is then carried out by the present invention several
What rationalizes continually looks for the feasible prestressing force of structure after renewal；Such as meet index 3, then cannot pass through the displacement superposed of the present invention
Carrying out geometry rationalization renewal need to redesign to structure.
(4) the existing geometry X of structureiIn load F (5) and target prestressing forceDisplacement under effect is Di, such as need to be to structure
Geometry carries out rationalization amendment, directly by the displacement superposed in existing geometry X of structureiOn be updated to new construction geometry Xi+1,
I.e.：Xi+1=Xi+Di。
(5) present invention keeps first cable-rod structure XiThe feasible prestressing force iterative calculation that structure is carried out in the case of constant comes
Find the target prestressing force of lower oblique cord (1), upper oblique cord (2), strop (3) and depression bar (4)Basis after the completion of epicycle iterative calculation
Indicator conditions are on demand by construction geometry XiUpdate, then in new construction geometry Xi+1Next round target is carried out in the case of constant
Prestressing forceIterative calculation, the above-mentioned prestressing force of repetition finds the cycle calculations updated with geometry until meeting all index requests
Till, the target prestress value for searching outThe as feasible prestressing force of structure.
One kind that the present invention is provided is used to find the feasible prestressed method of cable-rod structure, overcomes existing method and in advance should
Power cannot directly consider that structure is possible to the shortcoming of imposed load when designing, and also breaching existing pre-stress design method can only
Geometry is determined and rational cable-rod structure can just carry out the restriction of pre-stress design, while also having without deliberately processing structure
The advantage that geometry and internal force intercouple.Concrete advantage includes：In the geometry X according to structureiWhen setting up numerical model, Ke Yizhi
Consideration structure load F (5) is connect, and load F (5) is directly considered when pre-stress design is calculated；Additionally, when by under
Oblique cord (1), upper oblique cord (2), strop (3) do not have applying feasible prestressed rationally several with the cable-rod structure that depression bar (4) is constituted
During what configuration, can be according to structure in load F (5) and target prestressing forceDisplacement D under effectiX is pressed to structurei+1=Xi+DiEnter
The rationalization amendment of row construction geometry, the maximum defect of the exactly existing pre-stress design method of this advantage；The last present invention is logical
Cross prestressing force iteration and geometry update carry out successively and circulating repetition method, overcome and solve what internal force and geometry intercoupled
Problem, flow process is simply easily achieved, and disclosure satisfy that the needs of practical engineering application.
Description of the drawings
Fig. 1 is to find feasible prestressed cable-rod structure schematic diagram using the present invention.
Fig. 2 is the flow chart of the present invention.
Fig. 3 is the iterative calculation block flow diagram of prestressing force P of the present invention.
Fig. 4 is that present configuration geometry updates computing module flow chart.
Specific embodiment
The specific embodiment of the present invention is described further below in conjunction with accompanying drawing：
With reference to Fig. 1～4, the present invention includes following step：
Step one：According to geometry XiSet up the cable-rod structure numerical value being made up of with depression bar 4 lower oblique cord 1, upper oblique cord 2, strop 3
Model, and apply all possible load (F) 5 for structure；And oblique cord 1, upper oblique cord 2, strop 3 will be descended in structure with depression bar 4
Prestressing force is initialized as P*=[Pc Ps], wherein, lower oblique cord 1, upper oblique cord 2, the prestressing force of strop 3 are the arbitrary value more than zero
(Pc>0), the prestressing force of depression bar 4 is minus arbitrary value (Ps<0)；The calculation of Prestress error ε of setting structurenAnd displacement meter
Calculate error εd, and according to the internal force desired value of oblique cord 1, upper oblique cord 2, strop 3 or depression bar 4 under design requirement setting section
Step 2：Prestressing force iterative calculation module into structure carries out target prestressing forceCalculating：
All lower oblique cords 1, upper oblique cord 2, strop 3 are initializing prestressing force P with depression bar 4 first in computation structure*And load
(F) the internal force N of the lower counterpart member of 5 effects, and as the prestressing force iterative initial value P of counterpart member1, and by iterative formula
P0With N0It is taken as 0.
Then by prestressing force PkCorresponding lower oblique cord 1, upper oblique cord 2, strop 3 and depression bar 4 are input into, each component correspondence is calculated
Internal force Nk, judging unit internal force NkWith target internal forceDifference whether be less than calculation of Prestress error εnThis
Indicator conditions, as being unsatisfactory for, renewal are iterated using following Newton iterative calculation formula (1) to the prestressing force of each component：
In formulaFor l-th component the step of kth -1 and kth step iterative calculation when apply it is pre- should
Force value and internal force value of calculation；Force value in l-th component target in formulaCan be according to force value in the target of known membersBy such as
Lower formula (2) calculates：
Prestressed iterative calculation is carried out using above-mentioned newton iteration formula, lower oblique cord 1, upper oblique cord 2, ring in structure
The actual internal force (N) of rope 3 and depression bar 4 and target internal force () difference be less than calculation of Prestress error εn, and obtain target in advance should
Force value
Step 3：According to following index, cable-rod structure geometry X is judgediWhether need to carry out rationalization amendment, and target
Prestressing forceWhether it is the feasible prestressing force of cable-rod structure：
Index 1：Judge the geometry X with cable-rod structureiWhether corresponding structure self-stress modes number (S) is more than 0, i.e.,：
S>0 (3)
Index 2：Judge structure in load (F) 5 and target prestressing forceUnder effect, all lower oblique cords 1, upper oblique cord 2, strop
Whether 3 whether whole tensions, all depression bars 4 are all pressurized, i.e.,:
Nc＞ 0, Ns＜ 0 (4)
Index 3：Computation structure is in load (F) 5 and target prestressing forceIn the presence of displacement D whether calculate less than displacement and miss
Difference εd, i.e.,：
| D | ＜ εd (5)
If while meet index 1, index 2 and index 3,The feasible prestressing force of cable-rod structure for as searching out.
If while meeting index 1 with index 2 but being unsatisfactory for index 3, carrying out prestressing force iterative calculation by step 2 again,
Now lower oblique cord 1, upper oblique cord 2, strop 3 are initialized as with the prestressing force of depression bar 4 in cable-rod structureI.e.
If being unsatisfactory for index 1 or index 2, the existing geometry X of structureiIt is unreasonable, it is impossible to search out the feasible pre- of structure
Stress, need to be to construction geometry XiCarry out rationalization amendment；In this case index 3 is such as met, due to displacement structure DiIt is zero, nothing
Method rationalizes renewal by the displacement superposed geometry that carries out of the present invention, and construction geometry need to be redesigned；Such case is such as
Index 3 is unsatisfactory for, then into geometry update module.
Step 4：Into the rationalization update module of geometry, the reasonable geometric of structure is found：
Computation structure is in load F and target prestressing forceThe lower displacement D for producing of effecti, by the displacement D of structureiIt is superimposed upon knot
The original geometry X of structureiIt is upper direct to geometry XiIt is updated, the construction geometry after renewal is Xi+1, geometry more new formula is：
Xi+1=Xi+Di (6)
Step 5：Till repeat step two, three, four is until meeting all indicator conditions, the target prestressing force for searching out
The as feasible prestressing force of structure.
Claims (3)
1. a kind of for finding the feasible prestressed method of cable-rod structure, it is characterized in that：
(1) according to the geometry X of cable-rod structureiThe numerical model comprising structure load F (5) is set up, under setting in cable-rod structure
The structural initial pre stress P of oblique cord (1), upper oblique cord (2), strop (3) and depression bar (4)*=[Pc Ps], wherein, lower oblique cord (1), it is upper tiltedly
Rope (2), the structural initial pre stress of strop (3) are the arbitrary value (P more than zeroc>0), the structural initial pre stress of depression bar (4) is minus
Arbitrary value (Ps<0)；The internal force of setting structure and minimum allowable error value ε of displacementnAnd εdAnd the lower oblique cord (1) in part, it is upper tiltedly
The internal force desired value of rope (2), strop (3) or depression bar (4)
(2) with rope in cable-rod structure and the prestressing force P=P (p of bar1…pl…pb) used as input value, output correspondence rope is interior with bar
Force value N=N (n1…nl…nb), and set up following input/output relation：
N=Φ (P)
Transmission function between Φ represents input and exports in above formula, b is the total quantity of rope and bar；
Lower oblique cord (1), upper oblique cord (2), strop (3) are available with the difference of the actual internal force of depression bar (4) and target internal force such as minor function
Expression：
L-th component (drag-line or depression bar) prestressing force p of searching is constructed using above formulalNewton iterative calculation formula：
In above formula,It is right for f (P)First-order partial derivative, calculated in the form of first-order difference,The prestress value applied for l-th step of component kth -1 and kth step and internal force value of calculation,For l-th structure
Force value can be according to known internal force desired value in the target of partFoundationThis formula is calculated；As k=1By lower oblique cord (1), upper oblique cord (2), strop (3) and depression bar (4) under structural initial pre stress P* and load F effects
Interior force value N=N (n1…nl…nb) as the prestressing force iterative initial value of counterpart member
The each component in lower oblique cord (1), upper oblique cord (2), strop (3) and depression bar (4) is carried out using calculation of Prestress formula pre-
The iterative calculation of stress, in the actual internal force (N) and target of lower oblique cord (1), upper oblique cord (2), strop (3) with depression bar (4)
PowerDifference be less than calculation of Prestress error εn, the prestressing force at this moment obtaining is target prestress value
Then following index is judged：
The geometry X of index 1, cable-rod structureiWhether corresponding structure self-stress modes number is more than 0；Index 2, structure is in load F
With target prestressing forceUnder effect, whether tension, all depression bars (4) for all lower oblique cords (1), upper oblique cord (2), strop (3)
It is pressurized；Index 3, structure is in load F and target prestressing forceIn the presence of displacement (Di) whether calculate error ε less than displacementd。
2. according to claim 1 a kind of for finding the feasible prestressed method of cable-rod structure, it is characterized in that：If while
Meet index 1, index 2 and index 3, then the target prestressing force for searching outThe as feasible prestressing force of cable-rod structure；As simultaneously
Index 1 is met with index 2 but be unsatisfactory for index 3, then re-using prestressed newton iteration formula carries out prestressing force iteration meter
Calculate, now by the target prestressing force for searching outIt is set as new structural initial pre stress P*, i.e.,If being unsatisfactory for index 1 or referring to
2 are marked, then the existing geometry X of structureiIt is unreasonable, rationalization amendment must be carried out to construction geometry；When rationalizing amendment, new structure
Geometry Xi+1For the displacement D of structureiWith original structure geometry XiSuperposition, computing formula is Xi+1=Xi+Di。
3. according to claim 1 and 2 a kind of for finding the feasible prestressed method of cable-rod structure, it is characterized in that：It is first
First keep cable-rod structure geometry XiCarry out the prestressed iteration of rope bar in the case of constant to calculate target prestressing forceThen root
Construction geometry X is carried out according to indicator conditionsiRenewal, in new geometry Xi+1It is lower to continue to iterate to calculateAbove-mentioned prestressing force iteration with
Till the cycle calculations that geometry updates are until meeting all index requests, the target prestressing force for now searching outAs rope bar is tied
The feasible prestressing force of structure.
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| CN106599509B (en) * | 2016-12-26 | 2020-06-19 | 河北建筑工程学院 | Method for simulating prestress application of suspended dome structure |
| CN107992707B (en) * | 2017-12-26 | 2021-05-04 | 中国建筑西南设计研究院有限公司 | Preloading resilience method for determining initial prestress distribution of tension cable bar structure |
| CN110700474B (en) * | 2018-07-09 | 2021-05-14 | 上海海事大学 | zero-Gaussian curvature cable dome |
| CN109826355B (en) * | 2019-01-17 | 2023-10-31 | 上海海事大学 | Rotary S-shaped curved cable dome |
| CN109826356B (en) * | 2019-01-17 | 2023-10-31 | 上海海事大学 | Rotary hyperboloid sunflower-type cable dome |
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| CN103924721B (en) * | 2014-04-25 | 2015-12-02 | 东南大学 | A kind of large-span cable bar tension force structural system of roof |
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