CN114707202B - Method and system for optimally designing arch bridge with suspender under moving load - Google Patents

Method and system for optimally designing arch bridge with suspender under moving load Download PDF

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CN114707202B
CN114707202B CN202210108984.XA CN202210108984A CN114707202B CN 114707202 B CN114707202 B CN 114707202B CN 202210108984 A CN202210108984 A CN 202210108984A CN 114707202 B CN114707202 B CN 114707202B
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force
arch
main arch
moving load
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CN114707202A (en
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周帅
于鹏
雷军
曾永平
谭芝文
狄谨
陈克坚
周建庭
刘安双
何昌杰
李水生
郑邦友
帅建国
罗桂军
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China Construction Fifth Engineering Bureau Co Ltd
China Construction Tunnel Construction Co Ltd
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    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D19/00—Structural or constructional details of bridges
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D19/00—Structural or constructional details of bridges
    • E01D19/02—Piers; Abutments ; Protecting same against drifting ice
    • E—FIXED CONSTRUCTIONS
    • E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
    • E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
    • E01D4/00—Arch-type bridges
    • G—PHYSICS
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Abstract

The invention relates to an optimal design method and a system for an arch bridge with a suspender under a moving load, comprising the following steps: s1, building a finite element model by drawing up the sizes of all members of an arch bridge; s2, based on linear static force calculation, calculating the bridge crane rod force to be used as a bridge crane rod force optimization initial value; s3, forming a moving load immobilized working condition based on the stability and strength effect of the main arch, and loading the moving load according to a fixed position; s4, based on nonlinear calculation, calculating a moving load and initial defects, and iteratively optimizing out an optimal lifting rod force; s5, completing the design of the rest components according to a conventional method; the system adopts the method of S1-S5; the method has the advantages that the main arch strength and stability are considered, the moving load and the initial defects are considered for iterative optimization, the optimal bridge forming hanging rod force is solved, the design result is closer to the actual condition of the bridge, the safety performance of the bridge is higher, the method is easy to realize in a programmed mode, the optimization speed can be changed in a self-adaptive mode, the method can be used for large-scale optimization design of a large-span arch bridge, and the method has higher economy.

Description

Method and system for optimally designing arch bridge with suspender under moving load
Technical Field
The invention relates to the technical field of arch bridge design, in particular to an optimal design method and system for an arch bridge with a suspender under a moving load.
Background
The arch bridge with a suspender can be divided into two types according to the stress sharing condition between beams and arches: the rigid-girder flexible arch bridge is a bridge with the main girder having rigidity larger than that of the main girder and bearing most of the load by the main girder, and the rigid-girder flexible arch bridge is a bridge with the main girder having rigidity larger than that of the main girder and bearing most of the load by the main girder. The currently used arch bridge with a boom, as shown in fig. 1, has a design process different from that of a general girder bridge: for the beam bridge structure, if the static load such as the structure size, the material, the second-stage constant load and the like is determined, the internal force of the static load of the structure is basically determined, and larger adjustment cannot be performed; however, for the arch bridge with the suspender, the bridge formation line and the internal force state can be obtained through the adjustment of the tension force of the suspender, so that the main work of the arch bridge with the suspender in the design stage is to determine the reasonable bridge formation force, and the reasonable bridge formation state of the arch bridge with the suspender is obtained by completing the design of other bridge components according to the reasonable bridge formation force and the conventional method.
Methods for determining reasonable bridge forming boom forces have been studied in suspension bridges and cable-stayed bridges, as in chinese patent "CN 201510312423-a suspension bridge cable force optimization method", "CN 202010851156-a cable-stayed bridge cable optimization method and system", and journal literature "Zhang Xi, chen Xingchong, wang Changfeng. Beam-arch combined bridge boom force optimization and engineering application [ J ]. Railway construction, 2014, (1)," official, chen Ziwei. Simplified calculation method of beam-arch combined bridge boom initial cable force [ J ]. Outer highway, 2017, (4), "165-170", "Zhang Yuping, liu Xuesong, li Chuanxi. Cable-stayed bridge cable force optimization analysis based on MOPSO algorithm [ J ]," civil and environmental engineering journal (chinese english), 2020, (2), "107-114.
The prior art comprises 8 methods of a rigid suspension rod method, a rigid support continuous beam method, a bending strain energy minimum method, a bending moment feasible region method, a zero displacement method, an influence matrix method and a force balance method, and when the methods are applied to suspension bridges, cable-stayed bridges and part-suspension rod arch bridges, the optimization of linear and internal force states is realized on the premise of only considering static loads, and the method has a good effect; however, the above methods are all based on linear superposition of load effect to perform boom force optimization, and the moving load relates to influence line analysis, which is also based on the linear superposition principle of load effect, so that the influence line analysis of the moving load cannot be considered in nonlinear calculation, and even if the problem of nonlinearity is not considered, the effect of the moving load is considered in the boom force optimization iteration because the combining difficulty of the boom force optimization process and the moving load influence line is too large to be realized, so that the prior art is abandoned; although the effect of the moving load is generally smaller than that of the non-moving load, the boom force obtained by the prior art by giving up the moving load is obviously not the optimal solution, and according to the proportion of the moving load to the total load of the bridge design, the boom force obtained by the prior art still has an optimization space in the range of 20% -50%.
In addition, for the stability problem of the arch bridge, the current standard only provides an inspection formula under the linear elastic buckling theory for the in-plane stability of the upper-bearing non-suspender arch bridge, the formula is approximately applicable to the in-plane stability problem of the rigid-arch flexible beam bridge, but along with popularization and application of the beam-arch bridge, more rigid-beam flexible arch bridges are also more and more developed at present, the arch section rigidity of the bridge is much smaller than the beam section rigidity, the ratio of the arch section height to the arch span is smaller, the linear rigidity of the arch is smaller, namely the generalized force required to be applied by the arch to generate unit vertical deformation is smaller, the nonlinear effect of the suspender rigid-beam flexible arch bridge is stronger, the load action causes the bending moment of the second-order effect to be brought after the main arch deviates from a reasonable arch axis, and thus the in-plane stability of the bridge is obviously reduced, and the in-plane stability inspection analysis method of the bridge is necessary. In the linear and nonlinear buckling analysis, the influence line of the moving load cannot be applied, the stability analysis in the prior art fails to consider the action of the moving load, the influence of the asymmetric deformation of the moving load on the initial defect is ignored, the influence is greatly different from the actual stability of the bridge, and the problem of unsafe calculation of the stability safety coefficient of the main arch exists.
For most single-rib arch bridges, the transverse bridge has weak linear rigidity and cannot exert the mechanical effect of the arch, the first-order buckling mode is usually out-of-plane buckling, the stability safety coefficient of the arch rib can be far lower than the strength safety coefficient, the suspension rod force at the moment plays a role in limiting the restoring force of out-of-plane instability, the suspension rod force optimization is an effective mode for improving out-of-plane stability, the suspension rod force optimization method in the prior art does not consider the stability problem of the arch, and the nonlinear buckling calculation is not realized in the suspension rod force optimization process, so that the problem of uneconomical performance that the stability safety coefficient is far lower than the strength safety coefficient can occur when the rigid beam flexible arch bridge is designed in the prior art, and the material strength performance can not be fully exerted to generate waste.
To sum up, the prior art has the following four problems:
1) The boom force optimization method in the prior art cannot consider the action effect of the moving load, so that the obtained bridge boom force is not an optimal solution, and an optimization space in the range of 20% -50% still exists;
2) The effect of the moving load cannot be considered in the bridge stability calculation in the prior art, the influence of the asymmetric deformation possibly generated by the moving load on the initial defect is ignored, the difference exists between the initial defect and the actual stability, and the problem of partial unsafety exists;
3) The boom force optimization method in the prior art does not consider the stability problem of an arch bridge, and also fails to realize nonlinear buckling calculation in the boom force optimization process, so that comprehensive optimization of bridge strength and stability cannot be considered, and the problem that the material strength is wasted due to the fact that the stability safety coefficient of some arch bridges is far lower than the strength safety coefficient can occur;
4) The boom force optimization algorithm in the prior art is usually subjected to iterative optimization at a constant speed, the mechanical property of a boom arch bridge and the effect guide of the boom force are not fully combined to improve the performance of the optimization algorithm in a targeted manner, and the optimization effect and the optimization speed are difficult to ensure simultaneously, so that a certain optimization effect is needed to be abandoned or a large amount of optimization man-hours are consumed in the large-scale boom force optimization of a large-span arch bridge.
Disclosure of Invention
In order to solve the four problems in the prior art, the invention provides the method and the system for optimizing the design of the arch bridge with the suspender under the moving load, which can realize the comprehensive optimization of the bearing capacity and the stability of the bridge by considering the influence of the moving load in the design process of the arch bridge with the suspender, take the safety coefficient of the main arch strength and the safety coefficient of the stability into consideration, and solve the more excellent bridge forming suspension rod force, so that the design result is more similar to the actual stability condition of the bridge, and the unreasonable design problem that the stability safety coefficient of the main arch is far lower than the strength safety coefficient is avoided; meanwhile, the realization difficulty of influencing line analysis and a large amount of needed time are avoided, the optimization speed can be adaptively changed according to the load effect, the balance of the optimization effect and the optimization speed is considered, and compared with the prior art, the arch bridge with the suspender designed by the method has higher economy, and the arch bridge with the suspender can be effectively applied to large-scale suspension rod force optimization of a large-span arch bridge.
In order to achieve the above object, the present invention provides the following technical solutions:
an optimization design method for a boom arch bridge under a moving load comprises the following steps: the optimal design method comprises the following steps of:
s1, according to the statistical data of the structural dimensions of the built arch bridge, combining the span arrangement of the built arch bridge and the bridge deck system local calculation model, planning the dimensions of each component, sequentially numbering the suspenders into 1,2,3 and … along the bridge,JwhereinJEstablishing a primary bridge finite element model for natural numbers;
s2, the suspender adopts truss units, the main arch, the main girder, the pier column and the foundation all adopt girder units, all constant loads are considered to carry out full-bridge line elastic static force analysis, and the design safety coefficient of the main arch is definedK]And the girder deflection limit value is used as a constraint condition, and on the premise of considering only the structural strength of the arch bridge, a set of bridge crane rod forces are calculated and used as optimized initial values, and the set of crane rod forces are expressed as vectors:T (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T J (0) ]；
s3, applying a moving load to the main arch, and finding out uniform distribution force in the moving load which makes the main arch stability check most unfavorable based on the main arch stability safety coefficientQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c), QAndPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the main arch stability check calculation least unfavorable b The method comprises the steps of carrying out a first treatment on the surface of the Similarly, a moving load is applied to the main arch, and based on the safety coefficient of the main arch strength, the uniform distribution force in the moving load which makes the main arch strength check most unfavorable is found outQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the main arch strength check calculation least unfavorable s ；
S4, the boom is changed into a rope unit, the bridge forming boom force of each boom is used as an independent variable, the optimization is carried out through iterative calculation, the smaller value of the main arch strength safety coefficient and the main arch stability safety coefficient is maximized, and the method is thatiThe optimal bridge forming hanging rod force is obtained after the round iterationT i() Corresponding main arch stability safety factorK b i() Safety coefficient of intensityK s i() The stress calculation in each round of optimization process adopts nonlinear finite element calculation,i≥0；
s5, recording the bridge crane rod forceT i() Bridge forming hanging rod force for stabilizing and comprehensively optimizing main arch strengthT * In the followingT * And applying a moving load according to a conventional influence line mode, determining the final boom size, the reinforcement and beam distribution design of each component and the auxiliary facility design of the bridge according to the full-bridge internal force state under the bridge design load combination and a conventional structural design method, setting the pre-camber according to the finite element deformation result to smooth the bridge deck, and ending the steps to obtain the optimized arch bridge with the boom.
The structural form suitable for the optimization design method comprises a rigid-girder flexible arch bridge and a rigid-girder flexible arch bridge, and in the step S1, the size of the main girder can be basically determined at the beginning no matter the rigid-girder flexible arch bridge or the rigid-girder flexible arch bridge: the main arch mainly plays a role in improving the rigidity of the main girder, is mainly used for railway bridges, the section size of the main girder is generally determined by the constant load of the main girder and the stress of the construction stage, and only the reinforcement and the beam allocation of the main girder are slightly influenced by the main arch; the latter adopts the construction of arch-first and beam-second, the girder mainly plays the role of bridge deck system and transfers force to the suspender, its section size is generally determined by the analysis of local loading by the concentrated force of the moving load, the girder design is not affected by the main arch basically. The structural size of the main arch can be drawn by referring to the statistics of the established bridge and the load concentration to be shared by the main arch, and the structural size of the pier column and the foundation can be determined by referring to the statistics of the established bridge and the self weight of the upper structure of the bridge and combining the constant active load proportion. The sectional area of the suspender is smaller than that of the main arch and the main girder, so that the influence of the suspender force on the stress of the bridge is larger, but the influence of the size of the suspender section on the stress of the bridge is not larger, and the size of the final suspender section can be finally determined after the optimizing calculation of the suspender force is completed.
Establishing a finite element model through the step S1, solving an optimal initial value of the bridge forming hanging rod force through the step S2, applying a moving load through the step S3 and forming a stationary working condition of the moving load, performing iterative optimization on the bridge forming hanging rod force on the basis of calculating a main arch strength safety coefficient and a stable safety coefficient through the step S4, and recording the optimal bridge forming hanging rod force through the step S5 to complete structural design; step S3 realizes the immobility of the moving load, namely the uniform force Q and the concentrated force P of the moving load are loaded according to fixed positions, so that the moving load can be counted in each iteration optimization of step S4 to carry out nonlinear static force calculation and nonlinear buckling calculation; the optimization process of the step S4 accounts for the influence of the moving load, so that the bridge forming hanging rod force which is better than the prior art can be obtained, and the obtained hanging rod force can enable the smaller value in the main arch strength and the stable safety coefficient to be improved by more than 20%; the optimization target of the step S4 considers the intensity safety coefficient and the stability safety coefficient of the main arch of the bridge, and the comprehensive optimization of the intensity and the stability safety performance in the process of designing the arch bridge with the suspender is realized; and S5, recording the optimal bridge forming hanging rod force, and completing the design of other bridge components according to the optimal bridge forming hanging rod force and a conventional method, thereby obtaining a reasonable bridge forming state of the arch bridge with the hanging rod, wherein the stability safety coefficient of the main arch is similar to the strength safety coefficient under the influence of the moving load.
In the preferred embodiment of the present invention, after each execution of the above step S4, the construction of the main arch is optimized according to the following steps:
s41, under the current main arch structure, if min #K s i() ,K b i() )>[K]S5, turning to the step; otherwise, taking the main arch structure and the corresponding main arch structure in the last optimizing processT i() S5, turning to S;
s42, if min%K s i() ,K b i() )-[K]>[△ K ]The main arch configuration is weakened by reducing the main arch cross-sectional profile size or the main arch cross-sectional sheet thickness, and then turning S3, [ △ K] optimizing convergence accuracy for a preset main arch structure; otherwise, go to S5.
After the boom force is optimized according to the steps S1-S4, the main arch strength and the main arch strength areThe smaller value of the stable safety factor is greatly improved, and the design safety factor is possibly separatedK]The main arch structure can be further optimized through the steps S41-S42, and the engineering cost is saved by weakening the main arch structure and combining with the optimization steps S3-S4 on the premise of meeting the design safety coefficient.
In the preferred embodiment of the present invention, the moving load immobilization LC that makes the main arch stability check most unfavorable is formed in the step S3 b The specific steps of (a) are as follows:
s301, judging whether the main arch structure has variation compared with the previous optimization process, if so, turning to S302, and if not, turning to S303;
S302, modifying main arch units and section parameters in the model, and then turning to S304;
s303, judging whether the working condition LC is formed for the first time under the current main arch structure b If yes, go to S304, otherwise go to S311;
s304, aiming at the primary bridge forming model of the arch bridge to be built, the cable units are modified into truss units, all bridge design loads except the moving load are applied, the girder nodes are numbered 1,2,3 and … one by one along the bridge direction,Ncarrying out full-bridge line elastic static force calculation to obtain a main arch stable safety coefficientK b (0) ；
S305, generating in the bearing capacity range of the suspender by adopting a Monte Carlo simulation methodMAssembling the boom force to enable the boom force to circulate variablem=1, girder node circulation variablen=1，m、n≥1；
S306, modifying the boom force of the finite element model intoMGroup hanging rod forcemThe values of the group are set in the first order of the primary arch if the primary arch is elastically flexed and not unstable in the out-of-plane directionnThe joints of the main beams are arrangedN v A unit load which is symmetrical or asymmetrical along the center line of the section, and respectively establishes loading working conditions,N v the number of lanes is designed; if the primary arch first-order line is elastically buckled into out-of-plane instability, then in the firstnOne side of the center line of the section at each girder node is arrangedN v Each unit load is minimum in transverse bridge direction according to standard requirements, and loading working conditions are respectively established Spacing arrangement;
s307, performing full-bridge line elastic buckling calculation according to 1-N v The minimum value of the combination of the calculation results of the working conditions is used for obtaining the stable safety coefficient of the main archK b m n(,) Order-makingK △b m n(,) =K b m n(,) -K b (0) ，K △b m n(,) Stabilization of positive and negative effect matrix for mobile loadmLine 1nA column of elements; by passing throughK △b m n(,) The positive and negative effects of the moving load stability are judged, and the boom force is taken as the firstmGroup and moving load is loaded on the firstnWhen the movable load plays a role in improving the stability of the bridge,K △b m n(,) positive, i.e., positive effect, when the moving load acts to reduce the stability of the bridge,K △b m n(,) negative, i.e. negative effect;
s308, ordern=n+1, ifn>NOrder in principlem=m+1, go to S309; otherwise, go to S306;
s309 ifm>MTurning to S310, otherwise turning to S306;
s310, from S306 to S309MLine XNColumn movement load stabilization positive-negative effect matrixK △b For a pair ofK △b After the average value is calculated column by column, the stable influence degree row vector is obtainedS b1 ，S b1 Reflecting the degree of strengthening or weakening the stability of the bridge when the moving load is loaded on each girder node under different boom force levels; will beK △b Count the number of positive elements in each column divided byMObtain stable influence significance row vectorS b2 ，S b2 Reflecting the probability of strengthening or weakening the stability of the bridge when the moving load is loaded on each girder node under different boom force levels; S b1 AndS b2 make up 2XNStable sensitive line matrix of columnS b ；
S311, extractingS b The first row of each column is less than 0 and the second row is less than the set significance levelα b To uniformly distribute force in moving loadQAll girder nodes loaded corresponding to the extracted columns are used for moving the concentrated force in the loadPLoading at the main beam node with the minimum first row value in the extracted column to obtain the movable load working condition LC with the least adverse main arch stability b 。
By adopting the steps S301-S311, the immobilization of the moving load based on the stability sensitive line matrix can be realized, namely the moving load uniform distribution force Q and the concentrated force P are loaded according to the fixed positions according to the negative effect condition of the moving load on the stability of the main arch, and the moving load immobilization working condition LC which makes the stability of the main arch least unfavorable is formed b In the process of (1), LC is formed under different boom force levels through Monte Carlo simulation and saliency test b Reliability of (C) formed LC b The loading device can be used for loading when the forces of all suspenders change greatly in the arch bridge optimization process; formation of LC b After that, the moving load is not needed to be considered according to the influence line loading, so that the problem that the moving load cannot be considered in boom force optimization iteration due to the fact that the influence line analysis cannot be performed simultaneously with buckling analysis or nonlinear static force calculation in the prior art is solved, and compared with the prior art, the method can obtain better bridge forming boom force, thereby providing higher bridge safety performance and further reducing bridge engineering cost; in addition, LC is formed b And then, a large amount of time required by line analysis is avoided, the time cost is obviously saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.
In a preferred embodiment of the present invention, after the step S311 is completed, if the stability positive and negative effects of each lane at the same girder node in S306 to S309 are different, the working condition LC is modified b The node of the main beam has negative effect and is smaller than the set significance test levelα b Uniformly distributing force for moving load on all lanes of vehicleQOr concentrate forcePLoading to obtain a modified working condition LC b 。
Comparing L obtained in the steps S301 to S311C b The modified working condition LC b The load can be carried out by considering the difference of stable positive and negative effects of each lane at the same girder node, and the modified working condition LC is adopted although a part of calculation workload is increased b The generated main arch stabilizing negative effect is more accurate, so that the boom force optimizing effect in the step S4 is further improved.
In the preferred embodiment of the present invention, the moving load immobilization LC that makes the main arch strength check most unfavorable is formed in the step S3 s The specific steps of (a) are as follows:
s321, judging whether the main arch structure has variation compared with the previous optimization process, if so, turning to S322, and if not, turning to S323;
S322, modifying main arch units and section parameters in the model, and then turning to S324;
s323, judging whether the working condition LC is formed for the first time under the current main arch structure s If yes, go to S324, otherwise go to S330;
s324, aiming at the primary bridge forming model of the arch bridge to be built, the cable units are modified into truss units, all bridge design loads except the moving load are applied, the girder nodes are numbered 1,2,3 and … one by one along the bridge direction,Ncarrying out full-bridge line elastic static force calculation to obtain the main arch strength safety coefficientK s (0) ；
S325, generating in the bearing capacity range of the suspender by adopting a Monte Carlo simulation methodMAssembling the boom force to enable the boom force to circulate variablem=1, girder node circulation variablen=1；
S326, modifying the finite element model boom force toMGroup hanging rod forcemThe values of the group, atnThe joints of the main beams are arrangedN v A unit load which is symmetrical or asymmetrical along the center line of the section, and respectively establishes loading working conditions,N v to design the number of lanes, then carrying out full-bridge line elastic static force calculation according to 1-1%N v The minimum value after the combination of the calculation results of the working conditions is used for obtaining the safety coefficient of the main arch strengthK s m n(,) Order-makingK △s m n(,) =K s m n(,) -K s (0) ；K △s m n(,) To move the positive and negative effect matrix of load intensitymA row(s),nBy listing elements ofK △b m n(,) The positive and negative effects of the moving load strength are judged, and the boom force is the first mGroup and moving load is loaded on the firstnWhen the moving load plays a role in improving the bearing capacity of the bridge,K △s m n(,) positive, i.e., positive effect, when the moving load has a decreasing effect on the bridge bearing capacity,K △s m n(,) negative, i.e. negative effect;
s327 ordern=n+1, ifn>NOrder in principlem=m+1, go to S328; otherwise, go to S326;
s328, ifm>MTurning to S329, otherwise turning to S326;
s329, from S326 to S328MLine XNPositive and negative effect matrix of column moving load intensityK △s For a pair ofK △s After column-by-column averaging, the intensity influence degree row vector is obtainedS s1 ，S s1 Reflecting the degree of strengthening or weakening the bridge bearing capacity when the moving load is loaded on each node under different boom force levels; will beK △s Count the number of positive elements in each column divided byMObtaining intensity-influencing significance row vectorsS s2 ，S s2 Reflecting the probability of strengthening or weakening the bridge bearing capacity when the moving load is loaded on each node under different boom force levels;S s1 andS s2 make up 2XNMatrix of intensity sensitive lines of columnsS s ；
S330, extractingS s The first row of each column is less than 0 and the second row is less than the set significance levelα s To uniformly distribute force in moving loadQAll nodes corresponding to the extracted columns are loaded, and the concentrated force in the load is movedPThe node with the minimum value of the first row loaded in the extracted column is obtained to obtain the most proved main arch strength Unfavorable moving load immobilization working condition LC s 。
The steps S321-S330 can be adopted to realize the immobilization of the moving load based on the intensity sensitive line matrix, and a moving load immobilization working condition LC which makes the main arch intensity check calculation the most unfavorable is formed s In the process of (1), LC is formed under different boom force levels through Monte Carlo simulation and saliency test s Reliability of (C) formed LC s When the forces of all suspenders change greatly in the arch bridge optimization process, the suspension rod can still be used for loading; formation of LC b After that, the moving load is not needed to be considered according to the influence line loading, so that the problem that the moving load cannot be considered in boom force optimization iteration due to the fact that the influence line analysis cannot be performed simultaneously with buckling analysis or nonlinear static force calculation in the prior art is solved, and compared with the prior art, the method can obtain better bridge forming boom force, thereby providing higher bridge safety performance and further reducing bridge engineering cost; in addition, LC is formed s And then, a large amount of time required by line analysis is avoided, the time cost is obviously saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.
In a preferred embodiment of the present invention, after the step S330 is completed, if the intensity positive and negative effects of each lane at the same girder node in S326-S328 are different, the LC is modified b Working conditions are that the main beam joint has negative effect and is smaller than the set significance test levelα s Uniformly distributing force for moving load on all lanes of vehicleQOr concentrate forcePLoading to obtain a modified working condition LC s 。
Comparing the LC obtained in the steps S321 to S330 s The modified working condition LC s The load can be carried out by considering the difference of positive and negative effects of the intensity of each lane at the same girder node, and the modified working condition LC is adopted although a part of calculation workload is increased b The generated main arch strength negative effect is more accurate, so that the boom force optimization effect in the step S4 is further improved.
In a preferred embodiment of the present invention, the specific steps of iterative optimization of the boom force in the step S4 are as follows:
s401 forJVector of individual boom forcesX，f(X) Representing the force per vector of each suspender of the arch bridgeXWhen taking value, the main arch strength safety coefficient obtained by full-bridge nonlinear finite element calculation is carried outK s And a main arch stability safety factorK b Smaller value of (3), calculatef(X) The finite element model suspender adopts a cable unit; pressing bridge hanging rod forceT (0) Calculated to obtainf(T (0) ) Wherein, the method comprises the steps of, wherein,T (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T J (0) ]the method comprises the steps of carrying out a first treatment on the surface of the Let the circulation variablej=1；
S402, willT (0) The first of (3)jThe value of the individual element increasing the unit force, i.eT (0) Becomes as followsT j (0) Calculated to obtainf(T j (0) ) The method comprises the steps of carrying out a first treatment on the surface of the If it isf(T j (0) )-f(T (0) )>0, boom force optimization direction vector dIs the first of (2)jElement fetchd(j) =1, otherwise letd(j)=-1；
S403, ifj<JOrder in principlej=j+1, go to S402; otherwise, letD J J× =diag(d) I.e. forming a boom force optimizing direction diagonal matrixD J J× The matrix reflects the primary arch after only a single boom force is increasedK s AndK b whether the smaller value of (a) plays a positive effect of lifting or a negative effect of lowering can be used for determining whether the optimization direction of each subsequent boom force is preferentially increased or preferentially decreased, and then the step S404 is performed;
s404 toT (0) As an optimization initial value, convergence accuracy of boom force fluctuation amount is setεGreater than or equal to 0, the fluctuation of the boom forceδ>εAcceleration coefficient of boom force variationα1 or more, deceleration coefficient of boom force variationβE (0, 1); order theH J1× To record the change of each suspender forceCompared with a variable which plays a positive effect or a negative effect before changing, the main archK s AndK b the smaller value of the product has positive effect when the product plays a role in lifting, otherwise has negative effect, and the initial value isH J1× =[0,0,0,...,0]The method comprises the steps of carrying out a first treatment on the surface of the External circulation variable for optimizing hanging rod forcei=0, internal circulation variablejBoom force intermediate variable =1F j() =T i() ；
S405, orderE j() =D(j,1:J) The method comprises the steps of carrying out a first treatment on the surface of the If it isf(F j() +δE j() )>f(T i() ) ThenH(j) =1, go to S406, otherwise go directly to S406;
s406, iff(F j() +δE j() )>f(F j() ) Order in principleF j(+1) =F j() +δE j() Turning to S407; otherwise, letF j(+1) =F j() Turning to S407;
s407, ifj<JOrder in principlej=j+1, go to S405; otherwise, go to S408;
s408, if each boom force is vector F j(+1) When the value is taken, the conventional design index and mechanical property of the main beam meet the design requirement, and the step S409 is carried out; otherwise, directly turning to S412;
s409, iff(F j(+1) )>f(T i() ) Turning to S410; otherwise, directly turning to S412;
s410 if sum @H)=JExplaining the basis of the forces of each boomD J J× After changing according to the respective positive effect direction, positive effects are generated on the main arch, namely, the nonlinear effect of the bridge is not strong at the moment, so that the fluctuation of the lifting rod force is increasedδTo accelerate convergence, i.e. orderδ=αδThen turning to S411; otherwise, the part of the hanging rod force is described according toD J J× The bridge has a significant nonlinear effect and thus has a negative effect on the main arch after changing according to the positive effect directionNo longer increases the fluctuation of the boom forceδAnd directly goes to S411;
s411, orderT i(+1) =F j(+1) The method comprises the steps of carrying out a first treatment on the surface of the Order thej=1，H J1× =[0,0,0,...,0]，F j() =T i(+1) ；i=i+1, go to S405;
s412, ifδ>εOrder-makingδ=βδReducing the fluctuation of the suspension rod forceδFine optimization is carried out; order thej=1，H J1× =[0,0,0,...,0]，F j() =T i() ，T i(+1) =T i() Order-makingi=i+1, go to S405; otherwise, the convergence accuracy of the fluctuation of the boom force is reached, the boom force optimization is terminated,T i() the bridge forming hanging rod force which enables the main arch to be stable and comprehensive and optimal is obtained.
The steps S401-S412 can be used for realizing arch bridge suspender force variable speed iterative optimization based on suspender force effect guiding and strength, stable comprehensive optimization, the iterative optimization method has rapid optimization convergence speed in the stage of weak bridge nonlinear effect, has fine optimization precision in the stage of strong bridge nonlinear effect, and considers the efficiency and precision of large-scale suspender force parameter optimization calculation, which is the variable speed optimization feature not possessed by the existing optimization algorithm in suspender force optimization iteration; in addition, the optimization process of the algorithm gives consideration to comprehensive optimization of bridge strength and stability, so that the problem that the stability safety coefficient is lower than the strength safety coefficient possibly occurs when the rigid-beam flexible arch bridge is designed in the prior art is avoided, the stability safety coefficient can be realized by adopting the algorithm to design, the mechanical property of the material is fully exerted, and the material strength waste caused by the stability problem is avoided.
In the preferred embodiment of the present invention, in the step S4, the main arch stability factor of safety is calculated each timeK b When in use, the method comprises the following steps:
s421, judging whether the main arch structure has variation compared with the previous optimization process, if so, turning to S422, and if not, turning to S423;
s422, modifying main arch units and section parameters in the model, and then turning to S424;
s423, judging whether buckling calculation is performed for the first time under the current main arch structure, if so, turning to S424, otherwise turning to S429;
s424, modifying a cable unit of a primary bridge forming finite element model of the arch bridge to be built into a truss unit, wherein the main arch position is according to an arch axis LS without initial defects 0 Modeling, namely applying all bridge design loads except the moving load, and then performing full-bridge line elastic buckling calculation, wherein all bridge design loads are set as variables during calculation;
s425, turning to S426 if the primary arch first-order buckling is out-of-plane instability; otherwise, turning to S427;
s426, initial defect amplitude of main arch shape under static loadδ 1 Is (1/300)L/φ，LThe span is calculated for the main arch and,φs main arch initial defect linear LS as axial compression component stability coefficient 1 Amplifying the linear corresponding to the first-order buckling mode to delta according to the amplitude 1 The resulting line shape; then the running line of the moving load is distributed at one side of the central line of the main girder according to the minimum transverse bridge spacing allowed by the specification, namely the moving load is distributed according to single side unbalanced load, the moving load is loaded along the bridge direction according to the influence line, the full bridge line elastic static force calculation is carried out, and the initial defect amplitude of the main arch line shape under the moving load is obtained δ 2 ，δ 2 Initial defect linear LS for maximum bridge displacement value of all nodes of main arch 2 To move under loadδ 2 The main arch transverse bridge is deformed and then is linear;
s427, initial defect amplitude of main arch shape under static loadδ 1 Is (1/300) &L a /2)/φ，L a For the length of the main arch axis,φinitial defect linear LS for axial compression component stability factor 1 Amplifying the first-order buckling line to the amplitude valueδ 1 The resulting line shape; then the movable load driving line transverse bridge directions are symmetrically distributed on two sides of the main beam central line, and the movable load is loaded along the bridge directions according to the influence line and entersCarrying out elastic static force calculation on the full bridge line to obtain initial defect amplitude of main arch line shape under moving loadδ 2 ，δ 2 Initial defect linear LS for maximum vertical displacement value of all nodes of main arch 2 To move under loadδ 2 The main arch is deformed vertically and then is linear;
s428, changing the main arch node coordinates into comprehensive initial defect linear LS, wherein the main arch comprehensive initial defect linear LS is LS 1 And LS 2 The boom is changed into a cable unit, and the moving load is changed into a working condition LC of the moving load immobilization in the step S3 b Loading, and performing nonlinear buckling calculation to obtain nonlinear buckling characteristic values, namely stable safety coefficients of the main archK b And ending the calculation of the stable safety coefficient.
In the above-described step S426,δ 1 fetch (1/300) ·L/φIs determined by combining a first-order buckling mode of a main arch, a conventional large-span steel structure stability theory and stress characteristics of a shaft pressing member; conventional long-span steel structure stability theory considers that the initial defect amplitude is preferable to be (1/300)L 0 ，L 0 Calculating a span for the frame beam; considering that the first-order buckling mode of the main arch is out-of-plane instability, the mechanical effect of the arch is hardly exerted, and can be regarded as a spanLIs characterized by that the frame beam is unstable,Lcalculating a span for the main arch; in addition, considering that the axial force of the main arch is also increased to destabilize the main arch when the main arch is deformed out of plane, the theory of the stress characteristics of the axial compression component is referred toLCalculated length coefficient of pressing memberφThe amplification is carried out and the amplification is carried out,φthe method can be determined by combining the existing standard table look-up according to the slenderness ratio and the end constraint condition of the main arch; to sum up, initial defect amplitudeδ 1 Fetch (1/300) ·L/φ. The influence line loading of the moving load cannot be performed when the buckling calculation is performed, so thatδ 2 The prior art is not considered in the calculation of the stability of various bridges; the prior art is not safe because the horizontal deformation of the main arch, which is caused by the unbalanced load of the moving load, is generated by the unbalanced load. The invention starts from the basic principle of stability problem and combines with the movable load transverse The mechanical property that the main arch can naturally generate horizontal displacement under the action of the single-side unbalanced load of the bridge, and the maximum transverse bridge displacement of the main arch under the moving load is obtained in a biased and safe wayδ 2 The main arch bridge is deformed in the shape of a line, and is considered as an initial defect generated by a moving load. In sum, consider at the same timeδ 1 、δ 2 Corresponding linear LS 1 、LS 2 As an initial defect, the nonlinear stability of the main arch can be analyzed more reliably.
In the above-mentioned step S427 of the present invention,δ 1 take (1/300) to take%L a /2)/φIs determined by combining a first-order buckling mode of a main arch, a conventional large-span steel structure stability theory and stress characteristics of a shaft pressing member; conventional long-span steel structure stability theory considers that the initial defect amplitude is preferable to be (1/300)L 0 ，L 0 Calculating a span for the frame beam; considering that the first-order buckling mode of the main arch is in-plane instability, the mechanical effect of the arch is fully exerted, and the first-order buckling mode in the plane is in-plane buckling mode of the half-span arch, and the other half-span arch is in-plane buckling mode, so the main arch can be regarded as a span of #L a The frame beam instability problem of/2),L a the arch axis length of the main arch; in addition, considering that the axial force of the main arch can also aggravate the instability of the main arch when the main arch is deformed out of plane, and the bending moment of the main arch is smaller when the main arch is designed according to the reasonable arch axis, the theory of the stress characteristics of the axial pressing component is consulted L a 2) calculating the length factor of the pressing memberφThe amplification is carried out and the amplification is carried out,φthe method can be determined by combining the existing standard table look-up according to the slenderness ratio and the end constraint condition of the main arch; to sum up, initial defect amplitudeδ 1 Take (1/300) to take%L a /2)/φ. The influence line loading of the moving load cannot be performed when the buckling calculation is performed, so thatδ 2 In the calculation of the stability of various bridges, the prior art is not considered; the horizontal deformation of the main arch and the other half-span arch caused by the unbalanced load of the moving load is what can actually happen, so that the prior art is unsafe. The invention starts from the basic principle of stability problem, and the main arch is bound to be under the action of loading along the bridge to the half-span by combining the moving loadThe mechanical property of horizontal displacement is generated, and the maximum vertical displacement of the main arch obtained by analysis of the moving load influence line is obtained in a safer wayδ 2 The main arch is deformed vertically and then is linear, and the main arch is considered as an initial defect generated by a moving load. In sum, consider at the same timeδ 1 、δ 2 Corresponding linear LS 1 、LS 2 As an initial defect, the nonlinear stability of the main arch can be analyzed more reliably.
By adopting the steps S421-S428, the arch bridge stability safety coefficient calculation can be realized by considering the initial defects of the moving load, the initial defects of the main arch can be determined by considering the influence of the static load and the moving load in the calculation process, the nonlinear stability of the main arch can be more practically analyzed, and the problem that the main arch stability safety coefficient is unsafe due to the fact that the moving load is ignored in the calculation of the main arch stability safety coefficient in the prior art is avoided.
In the preferred embodiment of the present invention, in the step S4, the main arch strength safety factor is calculated each timeK s When the moving load is in the working condition LC of the moving load immobilization in the step S3 s The load is applied to the container,K s the ratio of the section load bearing force at the position of the main arch where the main arch is stressed least to the section least adverse internal force.
At each time, the safety coefficient of the main arch strength is calculatedK s When the load is fixed according to the moving load working condition LC s The loading and the moving load are not needed to be considered according to the influence line loading, so that the problem that the moving load is discarded to be considered in boom force optimization iteration because the influence line analysis cannot be performed simultaneously with nonlinear static force calculation in the prior art is solved; meanwhile, a large amount of time required by line analysis is avoided, the time cost is remarkably saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.
The boom arch bridge optimal design system under the moving load adopts the boom arch bridge optimal design method under the moving load, and the optimal design system comprises a modeling module, a boom force initial value solving module, a moving load loading module, an iteration optimization module and a structural design module;
the modeling module is used for planningThe method comprises the steps of establishing a primary bridge formation finite element model according to the sizes of all components, and outputting a result to a boom force initial value calculating module; the initial value calculating module of the boom force is used for calculating the bridge forming boom force in the step S2, the moving load loading module is used for calculating the fixed loading position of the uniform force Q and the concentrated force P in the moving load which makes the main arch stability check most unfavorable, the fixed loading position of the uniform force Q and the concentrated force P in the moving load which makes the main arch strength check most unfavorable, and outputting the moving load immobilized working condition, and the iterative optimization module is used for calculating the optimal bridge forming boom force T i() Corresponding main arch stability safety factorK b i() Safety coefficient of intensityK s i() The structural design module is used for determining the size of the suspension rod, the reinforcement and beam distribution design of each component and the bridge auxiliary facility design according to the main arch strength, the stability and the comprehensive optimal bridge forming suspension rod force.
According to the optimal design system, the steps of an optimal design method can be realized according to each module, a bridge formation finite element model is established through a modeling module, a boom force optimal initial value is obtained through a boom force initial value obtaining module, a moving load immobilized working condition is obtained through a moving load loading module, an optimal bridge formation boom force is obtained through an iteration optimization module, final design is completed through a structural design module, comprehensive optimization of strength and stable safety performance during boom arch bridge design can be realized through output and execution steps of each module, and optimal design is finally completed.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the optimal design method, a finite element model is established through the step S1, an optimal initial value of the bridge forming hanging rod force is obtained through the step S2, a moving load is applied through the step S3, a moving load immobilized working condition is formed, the bridge forming hanging rod force is subjected to iterative optimization on the basis of calculating a main arch strength safety coefficient and a stable safety coefficient through the step S4, and the optimal bridge forming hanging rod force is recorded through the step S5, so that structural design is completed; step S3 realizes the immobility of the moving load, namely the uniform force Q and the concentrated force P of the moving load are loaded according to fixed positions, so that the moving load can be counted in each iteration optimization of step S4 to carry out nonlinear static force calculation and nonlinear buckling calculation; the optimization process of the step S4 accounts for the influence of the moving load, so that the bridge forming hanging rod force which is better than the prior art can be obtained, and the obtained hanging rod force can enable the smaller value in the main arch strength and the stable safety coefficient to be improved by more than 20%; the optimization target of the step S4 considers the intensity safety coefficient and the stability safety coefficient of the main arch of the bridge, and the comprehensive optimization of the intensity and the stability safety performance in the process of designing the arch bridge with the suspender is realized; and S5, recording the optimal bridge forming hanging rod force, and completing the design of other bridge components according to the optimal bridge forming hanging rod force and a conventional method, thereby obtaining a reasonable bridge forming state of the arch bridge with the hanging rod, wherein the stability safety coefficient of the main arch is similar to the strength safety coefficient under the influence of the moving load.
2. The method of the invention is adopted in step S3, the immobilization of the moving load based on the stable and intensity sensitive line matrix can be realized, and the moving load immobilization working condition LC which makes the main arch stability and intensity check most unfavorable is formed b And LC (liquid crystal display) s In the process of (1), LC is formed under different boom force levels through Monte Carlo simulation and combination of significance test b And LC (liquid crystal display) s Reliability of (C) formed LC b When the forces of all suspenders change greatly in the arch bridge optimization process, the suspension rod can still be used for loading; formation of LC b And LC (liquid crystal display) s After that, the moving load is not needed to be considered according to the influence line loading, so that the problem that the moving load is considered in the boom force optimization iteration because the influence line analysis cannot be carried out simultaneously with the buckling analysis or the nonlinear static force calculation in the prior art is solved, and compared with the prior art, the method can obtain better bridge forming boom force, thereby providing higher bridge safety performance and further reducing the bridge engineering cost; in addition, LC is formed b And LC (liquid crystal display) s And then, a large amount of time required by line analysis is avoided, the time cost is obviously saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.
3. The method step S4 can realize the arch bridge suspender force variable speed optimization based on the suspender force effect guiding and strength, stable and comprehensive optimization, the variable speed optimization method has rapid optimization convergence speed in the stage of weak bridge nonlinear effect, has fine optimization precision in the stage of strong bridge nonlinear effect, and considers the efficiency and precision of large-scale suspender force parameter optimization calculation, which is the variable speed optimization feature not possessed by the existing optimization algorithm in the suspender force optimization process; in addition, the optimization process of the algorithm gives consideration to comprehensive optimization of bridge strength and stability, so that the problem that the stability safety coefficient is far lower than the strength safety coefficient possibly occurs when the rigid-beam flexible arch bridge is designed in the prior art is avoided, the stability safety coefficient can be realized by adopting the algorithm to design, the mechanical property of the material is fully exerted, and the material strength waste caused by the stability problem is avoided.
4. The method step S4 of the invention can be used for calculating the stability and safety coefficient of the arch bridge by considering the initial defect of the moving load, and can simultaneously consider the influence of the static load and the moving load to determine the initial defect of the main arch in the calculation process, so that the nonlinear stability of the main arch can be more practically analyzed, and the problem of unsafe condition caused by neglecting the moving load when calculating the stability and safety coefficient of the main arch in the prior art is avoided.
5. The optimization design method is clear in flow, easy to realize in a programmed manner, and because the total freedom degrees of the beam unit and the cable unit model are less, the optimization of large-scale design parameters of the boom arch bridge developed by combining the nonlinear finite element analysis is still feasible, and the optimization convergence precision can be flexibly determined according to the computer hardware calculation force resources of the design party; the high-requirement optimization convergence precision can be set when the calculation force resource is high, the high-performance calculation resource can be fully exerted, so that the optimal design parameter is obtained, the requirement for the optimization convergence precision can be properly reduced when the calculation force resource is low, and the design parameter is optimized as much as possible under the reasonable time cost; therefore, the method has strong universality.
6. By adopting the optimal design method, under the same engineering cost, the designed arch bridge with the suspender has higher bridge safety performance compared with the prior art, and can generally realize the improvement of the safety performance of the main arch by more than 15 percent, thereby reducing the long-term operation and maintenance cost of the bridge; under the same safety performance, the designed arch bridge with the suspender has lower engineering cost compared with the prior art, can generally realize the reduction of the comprehensive cost of the main arch and the suspender by more than 8 percent, and can save hundreds of thousands of yuan to millions of yuan for common arch bridges with 100-300 m spans; in consideration of the fact that the time spent on optimizing calculation is only increased by days compared with the prior art, the time cost of days is very small compared with the construction period of the whole project for years, so that the economic benefit brought by the project cost saved after the optimization calculation is considerable, and the method for optimizing the design of the arch bridge with the suspender is very worth.
7. According to the optimization design system, a bridge forming finite element model is established through a modeling module, a boom force optimization initial value is obtained through a boom force obtaining module, a motionless working condition of a moving load is obtained through a loading module, an optimal bridge forming boom force is obtained through an iteration optimization module, final design is completed through a structural design module, output and execution of each module are carried out according to an optimization design method, steps of the optimization design method are carried out in a coordinated and unified mode according to a strict programming flow, comprehensive optimization of strength and stable safety performance when a boom arch bridge is designed can be achieved, optimization design is finally completed, optimization design efficiency of the boom arch bridge is improved, and manual operation time is saved.
Drawings
FIG. 1 is a schematic view of the major components of an arch bridge with a boom of the present invention;
FIG. 2 is a general step diagram of the present invention;
FIG. 3 shows a working condition LC formed by immobilizing a moving load based on a stability sensitive line matrix in embodiment 1 of the present invention b Is implemented as a flow chart;
FIG. 4 is a finite element model diagram of a underpinning rigid beam flexible arch bridge of example 1 of the present invention;
FIG. 5 shows a moving load immobilization condition LC for stabilizing and checking a main arch to be the least favorable in embodiment 1 of the present invention b A front view of the loading diagram;
FIG. 6 shows a moving load immobilization condition LC for stabilizing and checking a main arch to be the least favorable in embodiment 1 of the present invention b A top view of the loading diagram;
FIG. 7 is a graph showing the working condition LC formed by immobilizing a moving load based on an intensity sensitive line matrix in embodiment 2 of the present invention s Is implemented as a flow chart;
FIG. 8 is a moving load immobilization condition LC for minimizing adverse main arch strength check calculation in embodiment 2 of the present invention s A front view of the loading diagram;
FIG. 9 is a moving load immobilization condition LC for minimizing adverse main arch strength check in embodiment 2 of the present invention s A top view of the loading diagram;
FIG. 10 is a flowchart of an embodiment of the present invention for calculating the stability and safety factor of an arch bridge by considering initial defects of a moving load in embodiment 3;
FIG. 11 is a finite element model diagram of a underpinning rigid arch flexible bridge of example 3 of the present invention;
FIG. 12 is a first-order buckling mode diagram of the bridge according to embodiment 3 of the present invention;
FIG. 13 is a line LS of the initial defect of the main arch in example 3 of the present invention 2 Is a front view of (a);
FIG. 14 is a front view showing a line LS of the main arch composite initial defect in example 3 of the present invention;
FIG. 15 shows a moving load immobilization condition LC for stabilizing and checking a main arch to be the least favorable in embodiment 3 of the present invention b A front view of the loading diagram;
FIG. 16 is a general step diagram of embodiment 4 of the present invention;
FIG. 17 is a finite element model diagram of a soft arch bridge of a rigid middle-support beam according to example 4 of the present invention;
FIG. 18 is a first-order buckling mode diagram of the bridge according to embodiment 4 of the present invention;
FIG. 19 is a graph showing the moving load immobilization condition LC for stabilizing and checking the main arch to be the least favorable in embodiment 4 of the present invention b A front view of the loading diagram;
FIG. 20 is a graph showing the moving load immobilization condition LC for stabilizing and checking the main arch to be the least favorable in embodiment 4 of the present invention b A top view of the loading diagram;
FIG. 21 is a graph showing the moving load immobilization process for minimizing the adverse effect of main arch strength check in example 4 of the present inventionCondition LC s A front view of the loading diagram;
FIG. 22 is a graph showing the moving load immobilization condition LC for minimizing the adverse effect of the main arch strength check in example 4 of the present invention s A top view of the loading diagram;
FIG. 23 is a top view of a primary arch composite initial defect line LS of example 4 of the present invention;
FIG. 24 is a flowchart of an implementation of the arch bridge boom force variable speed iterative optimization based on boom force effect guidance and strength, stability comprehensive optimization in embodiment 5 of the present invention;
FIG. 25 is a chart showing the convergence process of iterative optimization calculation of the bridge crane rod force in embodiment 5 of the present invention;
FIG. 26 is a schematic diagram of an optimized design system for a arch bridge with a boom under moving loads in accordance with example 6 of the present invention;
The marks in the figure: 1-girder, 2-main arch, 3-suspender, 4-pier column, 5-foundation, 6-Q action range and 7-P action point.
Detailed Description
The present invention will be described in further detail with reference to test examples and specific embodiments. It should not be construed that the scope of the above subject matter of the present invention is limited to the following embodiments, and all techniques realized based on the present invention are within the scope of the present invention.
Example 1
Referring to fig. 3 to 4, in this embodiment, a rigid-girder flexible arch bridge (a boom arch bridge) with a certain span is set to (90+180+90) m, and the boom arch bridge includes: the main arch 2, the main girder 1, the suspender 3, the pier column 4 and the foundation 5 provide an optimal design method for the suspender arch bridge under the moving load, and elaborate the process of moving load immobilization based on a stable sensitive line matrix in the optimal design process of the bridge.
Referring to fig. 2, 3-6, the optimization design method includes the following steps:
s1, according to the statistical data of the structural dimensions of the built arch bridge, the dimensions of each component are planned by combining the span arrangement of the built arch bridge and the bridge deck system local calculation model, the boom 3 is numbered as 1,2,3 and … in sequence from root to root along the bridge, JJian (Chinese character of 'Jian')Establishing a primary bridge formation finite element model;
specifically, the main arch 2 of the bridge is a steel pipe concrete arch, the construction size of the initial main arch 2 and the construction size of other main components are determined according to the prior art, wherein the section of the main arch 2 is a dumbbell-shaped section, and a primary bridge forming model is established as shown in fig. 4; the boom 3 is numbered 1,2,3 and … in sequence from root to root along the bridge,J；J=18；
s2, the suspender 3 adopts truss units, the main arch 2, the main girder 1, the pier column 4 and the foundation 5 all adopt girder units, all constant loads are considered to carry out full-bridge line elastic static force analysis, and the design safety coefficient of the main arch 2 is defined [K]And the deflection limit value of the main beam 1, and as constraint conditions, under the premise of only considering the structural strength of the arch bridge, solving a set of bridge hanging rod forces, wherein the set of hanging rod forces are expressed as vectors:T (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T J (0) ]；
in particular, the design safety factor of the main arch 2 [K]=1.2, the main beam 1 deflection limit value is calculated according to the standard requirement, and the bridge forming boom force is obtained according to the rigid boom method in the prior artT (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T 18 (0) ]=[1160,1386, 1177, 2005, 1594, 2451, 1930, 1347, 2123, 2123, 1347, 1930, 2451, 1594, 2005, 1177, 1386, 1160]The number of units KN,T (0) i.e. as a subsequent boom force optimization initiation value.
S3, applying a moving load to the main arch 2, and finding out uniform distribution force in the moving load which makes the stability check of the main arch 2 most unfavorable based on the stability safety coefficient of the main arch 2QIs fixed in loading position and concentration force PIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the stability check calculation of the main arch 2 least unfavorable b The method comprises the steps of carrying out a first treatment on the surface of the Similarly, a moving load is applied to the main arch 2, and based on the intensity safety coefficient of the main arch 2, the uniform distribution force in the moving load which makes the intensity verification of the main arch 2 least unfavorable is found outQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the main arch 2 strength check calculation least unfavorable s ；
Specifically, the moving load is immobilized, namely, the moving load uniform distribution force Q and the concentrated force P are loaded according to fixed positions, the arch bridge has 2 lanes, the action range 6 of the uniform distribution force Q and the action point 7 of the concentrated force P are shown in fig. 6 on 2 lanes, each lane is 360m long, and the action point 7 of the concentrated force P is positioned at a corresponding girder node at the center of each lane; for the moving load immobilization condition LC formed in the step S3, which makes the stability check of the main arch 2 unfavorable b The specific implementation process of (1) is carried out according to the following steps S301-S312:
s301, judging whether the main arch 2 structure has variation compared with the previous optimization process, if so, turning to S302, and if not, turning to S303;
s302, modifying main arch 2 units and section parameters in the model, and then turning to S304;
Specifically, the present embodiment does not optimize the main arch 2 configuration, so it goes directly to S303.
S303, judging whether the working condition LC is formed for the first time under the current main arch 2 structure b If yes, go to S304, otherwise go to S311;
specifically, this embodiment is the first time that the operating condition LC is formed b So go to S304.
S304, aiming at the primary bridge forming model of the arch bridge to be built, the cable units are modified into truss units, all bridge design loads except the moving load are applied, the nodes of the main girder 1 are numbered 1,2,3 and … one by one according to the forward direction of the bridge,Ncarrying out full-bridge line elastic static force calculation to obtain a stable safety coefficient of the main arch 2K b (0) ；
Specifically, for the primary bridge forming model of the arch bridge to be built, the main beam 1 is uniformly divided into 360 units according to 1m segments, and the number of nodes of the main beam 1 is equalNAnd (361), the main girder 1 nodes are numbered 1,2,3, … and 361 one by one according to the forward bridge direction, and the full bridge line elastic static force calculation is carried out to obtain the main arch 2 strength safety coefficient without considering the moving loadK s (0) 1.6465, stability factor of safetyK b (0) =1.5512。
S305, generating in the bearing capacity range of the suspender 3 by adopting a Monte Carlo simulation methodMAssembling the boom force to enable the boom force to circulate variablem=1, girder 1 node circulation variablen=1，m、n≥1；
Specifically, the present embodiment is linear elastic finite element calculation, and the total degrees of freedom of the beam unit and the truss unit are small, so that the single calculation speed is fast, and the number of the suspenders 3 and the design accuracy are comprehensively considered, so M=10000。
S306, modifying the boom force of the finite element model intoMGroup hanging rod forcemThe values of the group are set to be the first order line of the main arch 2 if the elastic buckling is not unstable in the out-of-plane directionnThe 1 joints of the main beams are arrangedN v A unit load which is symmetrical or asymmetrical along the center line of the section, and respectively establishes loading working conditions,N v the number of lanes is designed; if the primary arch 2 first-order line elastically flexes to be out-of-plane unstable, then in the firstnOne side of the center line of the section at the node of each main girder 1 is arrangedN v The unit loads are arranged at minimum intervals in the transverse bridge direction according to the standard requirements, and loading working conditions are respectively established;
s307, performing full-bridge line elastic buckling calculation according to 1-N v The minimum value of the combination of the calculation results of the working conditions is used for obtaining the stable safety coefficient of the main arch 2K b m n(,) Order-makingK △b m n(,) =K b m n(,) -K b (0) ，K △b m n(,) Stabilization of positive and negative effect matrix for mobile loadmLine 1nA column of elements; by passing throughK △b m n(,) The positive and negative effects of the moving load stability are judged, and the boom force is taken as the firstmGroup and moving load is loaded on the firstnThe girder has 1 node, when the moving load plays a role in improving the stability of the bridge,K △b m n(,) positive, i.e., positive effect, when the moving load acts to reduce the stability of the bridge,K △b m n(,) negative, i.e. negative effect;
specifically, the primary arch 2 of the present embodiment elastically flexes to be out-of-plane instability due to the number of lanes of the bridge design N v The number of lanes is arranged at the minimum distance in the transverse bridge direction required by the specification on one side of the center line of the section, namely, the lane number is arranged at the minimum distance in the transverse bridge directionmGroup boom force firstnBefore full-bridge elastic buckling calculation is carried out on each node, two unit loads on one side of the node are arranged, the force of each load is 10KN, the direction is vertical downwards, each load corresponds to 1 load working condition independently, after full-bridge elastic buckling calculation is carried out, the minimum value after combination of unit load working condition results on 1-2 lanes is taken: namely, taking the value with the minimum stability safety coefficient of the main arch 2 under the three conditions of loading only the 1 st lane, loading only the 2 nd lane and loading both the 1 st and the 2 nd lanes asK b m n(,) Then calculateK △b m n(,) 。
S308, ordern=n+1, ifn>NOrder in principlem=m+1, go to S309; otherwise, go to S306;
s309 ifm>MTurning to S310, otherwise turning to S306;
s310, from S306 to S309MLine XNColumn movement load stabilization positive-negative effect matrixK △b For a pair ofK △b After the average value is calculated column by column, the stable influence degree row vector is obtainedS b1 ，S b1 Reflecting the degree of strengthening or weakening the stability of the bridge when the moving load is loaded on the node of each girder 1 under different boom force levels; will beK △b Count the number of positive elements in each column divided byMObtain stable influence significance row vector S b2 ，S b2 Reflecting the probability of strengthening or weakening the stability of the bridge when the moving load is loaded on the node of each girder 1 under different boom force levels;S b1 andS b2 make up 2XNStable sensitive line matrix of columnS b ；
Specifically, from S306-S309, 10000 rows×361 columns of stable positive and negative effects of moving loads can be obtainedStress matrixK △b For a pair ofK △b Column-by-column averaging to obtain stable influence degree row vectorS b1 For a pair ofK △b Count the number of positive elements in each column divided byMStability influencing significance row vectorS b2 ，S b1 AndS b2 make up 2XNStable sensitive line matrix of columnS b Because the result is too long, only listS b Representative results of these are shown in Table 1 below.
TABLE 1 stability sensitive line matrixS b Representative results of (3)
S311, extractingS b The first row of each column is less than 0 and the second row is less than the set significance levelα b To uniformly distribute force in moving loadQAll main girder 1 nodes loaded corresponding to the extracted columns are subjected to concentrated force in moving loadPThe movable load working condition LC which makes the stability of the main arch 2 least adverse is obtained by loading at the joint of the main beam 1 with the minimum first row value in the extracted column b ；
Specifically, the significance test level is obtained according to the common design accuracy requirement and the common statistical experience of the industryα b =0.05, so as to stabilize the main arch 2 and calculate the least favorable moving load immobilization condition LC b Due to LC b Many of the nodes loaded in the table are listed, with representative results only as shown in table 2 below.
TABLE 2 moving load immobilization condition LC for stabilizing and checking the main arch to be the least adverse b Is loaded with a node of (a)
S312, if the stable positive and negative effects of the lanes at the same girder 1 node in S306-S309 are different, modifying the working condition LC b The node of the main beam 1 has negative effect and is smaller than the set significance test levelα b Uniformly distributing force for moving load on all lanes of vehicleQOr concentrate forcePLoading to obtain a modified working condition LC b ；
Specifically, when each girder 1 node in S306-S309 is loaded on different lanes, the negative effects of the lanes are the same, so that the load is not applied to LC b Working condition is further modified, LC b The final loading diagram of (a) is shown in detail in fig. 5-6.
S4, the suspender 3 is changed into a rope unit, the bridge forming suspender force of each suspender 3 is used as an independent variable, and the optimization is carried out through iterative calculation, so that the smaller value of the intensity safety coefficient of the main arch 2 and the stability safety coefficient of the main arch 2 is maximized, and the bridge forming suspender is characterized in thatiThe optimal bridge forming hanging rod force is obtained after the round iterationT i() Corresponding main arch 2 stable safety factorK b i() Safety coefficient of intensityK s i() The stress calculation in each round of optimization process adopts nonlinear finite element calculation,i≥0；
specifically, under the current main arch 2 configuration, under iWhen=0, i.e. when no boom force optimization iteration is performed, the main arch 2 strength safety factorK s (23) Security coefficient of main arch 2 stability = 1.5386K b (23) = 1.2143; warp yarni=23 rounds of optimized convergence the optimal bridging rod force under the current main arch 2 configurationT (23) ，T (23) =[T 1 (23) ,T 2 (23) ,T 3 (23) , ...,T 18 (23) ]=[1250,1574, 1724, 1933, 1931, 1906, 1897, 1907, 1874, 1874, 1907, 1897, 1906, 1931, 1933, 1724, 1574, 1250]Unit KN, the main arch 2 strength safety factorK s (23) Security coefficient of main arch 2 stability = 1.4137K b (23) =1.4226。
In the above step S4, the main arch strength safety factor is calculated each timeK s When the moving load is in the working condition LC of the moving load immobilization in the step S3 s The load is applied to the container,K s the ratio of the section load capacity at the position of the main arch which is subjected to the least adverse loading to the least adverse internal force of the sectionA value; at each calculation of the main arch stability safety factorK b When the moving load is in the working condition LC of the moving load immobilization in the step S3 b Loading, and then carrying out nonlinear buckling calculation to obtain a nonlinear buckling characteristic value, namely a stable safety coefficient of the main archK b 。
S5, recording the bridge crane rod forceT i() To make the main arch 2 strength, stability and comprehensive optimum bridge-forming hanging rod forceT * In the followingT * Applying a moving load according to a conventional influence line mode, determining the size of a final suspender 3, the reinforcement and beam distribution design of each component and the auxiliary facility design of a bridge according to the full-bridge internal force state under the bridge design load combination and a conventional structural design method, setting a pre-camber according to a finite element deformation result to smooth a bridge deck, and ending the steps to obtain an optimized suspender arch bridge design;
Specifically, in step S4 described aboveT (30) Namely, the bridge forming hanging rod force which ensures the strength, stability, comprehensive and optimal of the main arch 2T * In the followingT * Determining the final boom 3 size, various concrete member reinforcement and beam distribution designs and bridge auxiliary facilities according to a conventional design method; the analysis of the result of S4 shows that after the optimization design is carried out by adopting the method of the invention, the comprehensive consideration of the strength and the safety coefficient after stabilization is improved from 1.2143 to 1.4137 compared with the prior art, namely the safety performance of the main arch 2 is improved by 16.4 percent.
In this embodiment, the steps S301 to S311 are adopted to implement immobilization of the moving load based on the stability sensitive line matrix, that is, the moving load uniform distribution force Q and the concentrated force P are loaded according to the fixed positions according to the negative effect condition of the moving load on the stability of the main arch 2, so as to form the moving load immobilization working condition LC that makes the stability of the main arch 2 least unfavorable b In the process of (1), LC is formed under different boom force levels through Monte Carlo simulation and saliency test b Reliability of (C) formed LC b The loading device can be used for loading when the forces of all suspenders change greatly in the arch bridge optimization process; formation of LC b After that, the moving load is not needed to be considered according to the influence line loading, thereby solving the problem of the prior art that the influence line exists The analysis cannot be carried out simultaneously with buckling analysis or nonlinear static force calculation, and the problem of considering the moving load is abandoned in boom force optimization iteration, so compared with the prior art, the invention can obtain better bridge forming boom force, thereby providing higher bridge safety performance and further reducing bridge engineering cost; in addition, LC is formed b And then, a large amount of time required by line analysis is avoided, the time cost is obviously saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.
Example 2
In this embodiment, steps S1 to S5 of embodiment 1 are adopted, which are different in that: in this embodiment, taking the proposed under-supported rigid-girder flexible arch bridge with the span of (90+180+90) m in embodiment 1 as an example, the process of moving load immobilization based on the intensity-sensitive line matrix involved in the process of optimizing the bridge design is described in detail.
Referring to fig. 2, 4, 7-9, a moving load immovable working condition LC that makes the main arch 2 strength check most unfavorable is formed in step S3 of the above embodiment 1 s The specific implementation process of (1) is carried out according to the following steps S321-S331:
s321, judging whether the structure of the main arch 2 has variation compared with the previous optimization process, if so, turning to S322, and if not, turning to S323;
S322, modifying main arch 2 units and section parameters in the model, and then turning to S324;
specifically, the present embodiment does not optimize the main arch 2 configuration, so it goes directly to S323.
S323, judging whether the working condition LC is formed for the first time under the current main arch 2 structure s If yes, go to S324, otherwise go to S330;
specifically, this embodiment is the first time that the operating condition LC is formed s So, go to S324.
S324, aiming at the primary bridge forming model of the arch bridge to be built, the cable units are modified into truss units, all bridge design loads except the moving load are applied, the nodes of the main girder 1 are numbered 1,2,3 and … one by one along the bridge direction,Ncarrying out full-bridge line elastic static force calculation to obtain the intensity safety coefficient of the main arch 2K s (0) ；
Specifically, the primary bridge forming model of the arch bridge is shown in fig. 4, the girder 1 is uniformly divided into 360 units according to 1m section, and the girder 1 has the node numberNAnd (361), the main girder 1 nodes are numbered 1,2,3, … and 361 one by one according to the forward bridge direction, and the full bridge line elastic static force calculation is carried out to obtain the main arch 2 strength safety coefficient without considering the moving loadK s (0) 1.6465, stability factor of safetyK b (0) =1.5512。
S325, generating in the bearing capacity range of the suspender 3 by adopting a Monte Carlo simulation methodMAssembling the boom force to enable the boom force to circulate variablem=1, girder 1 node circulation variable n=1；
Specifically, the present embodiment is linear elastic finite element calculation, and the total degrees of freedom of the beam unit and the truss unit are small, so that the single calculation speed is fast, and the number of the suspenders 3 and the design accuracy are comprehensively considered, soM=10000。
S326, modifying the finite element model boom force toMGroup hanging rod forcemThe values of the group, atnThe 1 joints of the main beams are arrangedN v A unit load which is symmetrical or asymmetrical along the center line of the section, and respectively establishes loading working conditions,N v to design the number of lanes, then carrying out full-bridge line elastic static force calculation according to 1-1%N v The minimum value of the combination of the calculation results of the working conditions is used for obtaining the intensity safety coefficient of the main arch 2K s m n(,) Order-makingK △s m n(,) =K s m n(,) -K s (0) ；K △s m n(,) To move the positive and negative effect matrix of load intensitymA row(s),nBy listing elements ofK △b m n(,) The positive and negative effects of the moving load strength are judged, and the boom force is the firstmGroup and moving load is loaded on the firstnThe girder has 1 node, when the moving load plays a role in improving the bearing capacity of the bridge,K △s m n(,) positive, i.e. positive effect, when the moving load is carried by the bridgeWhen the force is to be applied in a decreasing action,K △s m n(,) negative, i.e. negative effect;
specifically, the bridge design lane number of the present embodiment isN v The number of lanes is symmetrically arranged along the center line of the section, namely, every time the lane is aligned with the first lane mGroup boom force firstnBefore the full-bridge line elastic static force calculation is carried out on each node, two unit loads symmetrical along the node are arranged, the force of each load is 10KN, the direction is vertical downwards, each load corresponds to 1 load working condition independently, after the full-bridge line elastic static force calculation is carried out, the minimum value after combination of unit load loading working condition results on 1-2 lanes is taken: namely taking the value with the minimum safety coefficient of the strength of the main arch 2 under the three conditions of loading only the 1 st lane, loading only the 2 nd lane and loading both the 1 st and the 2 nd lanes asK s m n(,) Then calculateK △s m n(,) 。
S327 ordern=n+1, ifn>NOrder in principlem=m+1, go to S328; otherwise, go to S326;
s328, ifm>MTurning to S329, otherwise turning to S326;
s329, from S326 to S328MLine XNPositive and negative effect matrix of column moving load intensityK △s For a pair ofK △s After column-by-column averaging, the intensity influence degree row vector is obtainedS s1 ，S s1 Reflecting the degree of strengthening or weakening the bridge bearing capacity when the moving load is loaded on each node under different boom force levels; will beK △s Count the number of positive elements in each column divided byMObtaining intensity-influencing significance row vectorsS s2 ，S s2 Reflecting the probability of strengthening or weakening the bridge bearing capacity when the moving load is loaded on each node under different boom force levels;S s1 and S s2 Make up 2XNMatrix of intensity sensitive lines of columnsS s ；
Specifically, from S326-S328, 10000 rows×361 columns of positive and negative effect matrices of the moving load intensity can be obtainedK △s For a pair ofK △s Column-by-column averaging to obtain intensity influence degree row vectorS s1 For a pair ofK △s Count the number of positive elements in each column divided byMIntensity-influencing significance row vectorS s2 ，S s1 AndS s2 make up 2XNMatrix of intensity sensitive lines of columnsS s Because the result is too long, only listS s Representative results of these are shown in Table 3 below.
TABLE 3 matrix of intensity sensitive linesS s Representative results of (3)
S330, extractingS s The first row of each column is less than 0 and the second row is less than the set significance levelα s To uniformly distribute force in moving loadQAll nodes corresponding to the extracted columns are loaded, and the concentrated force in the load is movedPThe node with the smallest first row value loaded in the extracted column is used for obtaining the moving load immobilized working condition LC which makes the checking calculation of the main arch 2 strength least unfavorable s ；
Specifically, the significance test level is obtained according to the common design accuracy requirement and the common statistical experience of the industryα s =0.05, so that the moving load immobilization condition LC that makes the main arch 2 strength check most unfavorable s Due to LC s Many nodes loaded in the network, only representative results are listed in table 4 below.
TABLE 4 moving load immobilization conditions LC for minimizing Main arch Strength check s Is loaded with a node of (a)
S331, if the intensity positive and negative effects of the lanes at the same girder 1 node in S326-S328 are different, modifying LC b Working conditions are that the node of the main beam 1 has negative effect and is smaller than the set significance test levelα s Uniformly distributing force for moving load on all lanes of vehicleQOr concentrate forcePLoading to obtain a modified working condition LC s The arch bridge is provided with 2 lanes, the action range 6 of the uniform force Q and the action point 7 of the concentrated force P are shown in fig. 9, the 1 st lane is 89m, the 2 nd lane is 144m, the 2 lanes in the range are the action range 6 of the uniform force Q, the action point 7 of the concentrated force P corresponds to a girder node at the center of the 1 st lane, and the action position of the action point P on the 2 nd lane is the same as the action position of the action point P on the 1 st lane in the bridge length direction;
specifically, in S326-S328, it is found that the negative effects of nodes 90-145 are different when loading on different lanes, thus the method is suitable for LC s 、LC b The working condition is further modified, nodes with negative effects and less than the set significance test level in each lane are all loaded, so that the forward loading ranges of the 2 lanes are different, the method can analyze by considering the space effect of the bridge, and LC s The final loading diagram of (a) is shown in detail in fig. 8-9.
In this embodiment, the steps S321 to S330 are adopted to implement immobilization of the moving load based on the intensity-sensitive line matrix, so as to form the moving load immobilization working condition LC that makes the main arch 2 intensity check calculation least unfavorable s In the process of (1), LC is formed under different boom force levels through Monte Carlo simulation and saliency test s Reliability of (C) formed LC s When the forces of all suspenders change greatly in the arch bridge optimization process, the suspension rod can still be used for loading; formation of LC b After that, the moving load is not needed to be considered according to the influence line loading, so that the problem that the moving load cannot be considered in boom force optimization iteration due to the fact that the influence line analysis cannot be performed simultaneously with buckling analysis or nonlinear static force calculation in the prior art is solved, and compared with the prior art, the method can obtain better bridge forming boom force, thereby providing higher bridge safety performance and further reducing bridge engineering cost; in addition, LC is formed s And then, a large amount of time required by line analysis is avoided, the time cost is obviously saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.
Example 3
In this embodiment, the same members with boom arch bridges as in embodiments 1-2 are adopted, and referring to fig. 10-11, in this embodiment, a planned under-building rigid-arch flexible bridge with a span of 1×100m is taken as an example, so as to provide an optimized design method for a boom arch bridge under a moving load, and further, a process of taking initial defects of the moving load into consideration in the optimized design process of the bridge for calculating an arch bridge stability safety coefficient is described in detail.
Referring to fig. 2 and 10-15, the optimization design method includes the following steps:
s1, according to the statistical data of the structural dimensions of the built arch bridge, the dimensions of each component are planned by combining the span arrangement of the built arch bridge and the bridge deck system local calculation model, the boom 3 is numbered as 1,2,3 and … in sequence from root to root along the bridge,Jestablishing a primary bridge finite element model;
specifically, the main arch 2 of the bridge is a pure steel structure arch, the construction size of the initial main arch 2 and the construction size of other main components are determined according to the prior art, wherein the section of the main arch 2 is a rectangular steel box section, and a primary bridge forming model is established, as shown in fig. 11; the boom 3 is numbered 1,2,3 and … in sequence from root to root along the bridge,J；J=15；
s2, the suspender 3 adopts truss units, the main arch 2, the main girder 1, the pier column 4 and the foundation 5 all adopt girder units, all constant loads are considered to carry out full-bridge line elastic static force analysis, and the design safety coefficient of the main arch 2 is defined [ K]And the deflection limit value of the main beam 1, and as constraint conditions, under the premise of only considering the structural strength of the arch bridge, solving a set of bridge hanging rod forces, wherein the set of hanging rod forces are expressed as vectors:T (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T J (0) ]；
in particular, the design safety factor of the main arch 2 [K]=1.2, the main beam 1 deflection limit value is calculated according to the standard requirement, and the bridge forming boom force is obtained according to the rigid boom method in the prior artT (0) ，T (0) I.e. as a subsequent boom force optimization initiation value.
S3, applying to the main arch 2Moving load, based on the stability safety coefficient of the main arch 2, finding out the uniform distribution force in the moving load which makes the stability check of the main arch 2 most unfavorableQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the stability check calculation of the main arch 2 least unfavorable b The method comprises the steps of carrying out a first treatment on the surface of the Similarly, a moving load is applied to the main arch 2, and based on the intensity safety coefficient of the main arch 2, the uniform distribution force in the moving load which makes the intensity verification of the main arch 2 least unfavorable is found outQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the main arch 2 strength check calculation least unfavorable s ；
Specifically, the moving load is immobilized, that is, the moving load uniform force Q and the concentrated force P are applied at fixed positions, and the moving load immobilized condition LC is formed in the step S3, which makes the stability check of the main arch 2 unfavorable b The specific implementation process of (1) can refer to steps S301-S311 of embodiment 1 to form the moving load immovable working condition LC which makes the stability check of the main arch 2 least unfavorable s The specific implementation process of (a) can refer to steps S321 to S330 of embodiment 2.
S4, the suspender 3 is changed into a rope unit, the bridge forming suspender force of each suspender 3 is used as an independent variable, and the optimization is carried out through iterative calculation, so that the smaller value of the intensity safety coefficient of the main arch 2 and the stability safety coefficient of the main arch 2 is maximized, and the bridge forming suspender is characterized in thatiThe optimal bridge forming hanging rod force is obtained after the round iterationT i() Corresponding main arch 2 stable safety factorK b i() Safety coefficient of intensityK s i() The stress calculation in each round of optimization process adopts nonlinear finite element calculation,i≥0，iturning to S5 after the round iteration is completed;
specifically, under the current main arch 2 configuration, viaiAfter 19 rounds of optimization, converging to obtain the optimal bridge forming hanging rod force under the current main arch 2 structureT (19) At the same time, the intensity safety factor of the main arch 2 is obtainedK s (19) Stable safety factor of main arch 2K b (19) ；
Specifically, in the above step S4, the stability factor of safety of the main arch 2 is calculated each timeK b When in use, the method comprises the following steps:
s421, judging whether the main arch 2 structure has variation compared with the previous optimization process, if so, turning to S422, and if not, turning to S423;
s422, modifying main arch 2 units and section parameters in the model, and then turning to S424;
Specifically, the present embodiment does not optimize the main arch 2 configuration, so it goes directly to S423.
S423, judging whether buckling calculation is performed for the first time under the current main arch 2 structure, if yes, turning to S424, otherwise turning to S429;
specifically, the present embodiment calculates the first buckling calculation for the main arch 2 structure, so it goes to S424.
S424, modifying a cable unit of a primary bridge forming finite element model of the arch bridge to be built into a truss unit, and positioning a main arch 2 according to an arch axis LS without initial defects 0 Modeling, namely applying all bridge design loads except the moving load, and then performing full-bridge line elastic buckling calculation, wherein all bridge design loads are set as variables during calculation;
specifically, for a primary bridge forming model of an arch bridge to be built, the applied bridge design load is the dead weight of the structure, the constant load in the second period, the whole temperature change and the tension of a cable structure.
S425, turning to S426 if the primary arch 2 is in the first-order buckling mode to be unstable out of plane; otherwise, turning to S427;
s426, initial defect amplitude of main arch 2 linear shape under static loadδ 1 Is (1/300)L/φ，LThe span is calculated for the main arch 2,φinitial defect linear LS of main arch 2 as stability factor of axial compression component 1 Amplifying the linear corresponding to the first-order buckling mode to delta according to the amplitude 1 The resulting line shape; then the running line of the moving load is distributed on one side of the center line of the main girder 1 according to the minimum transverse bridge direction interval allowed by the specification, namely the moving load is distributed according to single side unbalanced load, the moving load is loaded along the bridge direction according to the influence line, the full bridge line elastic static force calculation is carried out, and the initial defect amplitude of the main arch 2 line shape under the moving load is obtained δ 2 ，δ 2 Initial defect linear LS for maximum bridge displacement value of all nodes of main arch 2 2 To move under loadδ 2 The transverse bridge of the main arch 2 is deformed and then is linear;
specifically, the first-order buckling mode of the bridge is shown in fig. 12, and is in-plane instability, so it goes to S427.
S427, initial defect amplitude of main arch 2 linear shape under static loadδ 1 Is (1/300) &L a /2)/φ，L a For the main arch 2 to be long in axis,φinitial defect linear LS for axial compression component stability factor 1 Amplifying the first-order buckling line to the amplitude valueδ 1 The resulting line shape; then the transverse bridge directions of the moving load driving lines are symmetrically distributed on two sides of the central line of the main girder 1, the moving load is loaded along the bridge directions according to the influence line, the full-bridge line elastic static force calculation is carried out, and the initial defect amplitude of the main arch 2 line shape under the moving load is obtainedδ 2 ，δ 2 Initial defect linear LS for maximum vertical displacement value of all nodes of main arch 2 2 To move under loadδ 2 The main arch 2 is deformed vertically and then is linear;
specifically, the main arch 2 of the bridge has long axisL a = 104.94m, calculating stability factor from two-end consolidated axial compression memberφ=0.682, soδ 1 =(1/300)·(L a /2)/φ= (1/300) × (104.94/2)/0.682=0.256 m, initial defect line shape LS 1 Amplifying the first-order buckling line to the amplitude valueδ 1 The resulting line shape; then the transverse bridge directions of the moving load driving lines are symmetrically distributed on two sides of the central line of the main girder 1, the moving load is loaded along the bridge directions according to the influence lines, the full-bridge line elastic static force calculation is carried out, and the maximum vertical displacement value of all the nodes of the main arch 2 under the moving load is obtained to be about 1/4 span, and the initial defect amplitude value of the main arch 2 is linear δ 2 =0.051 m, initial defect due to moving load is seenδ 2 Is of a size of (a)δ 1 Is also a value which is not suitable to be ignored, initial defect linear LS 2 To move under loadδ 2 The main arch 2 is deformed vertically and then is linear, as shown in figure 13;
in the above-mentioned step S427 of the present invention,δ 1 take (1/300) to take%L a /2)/φIs determined by combining a first-order buckling mode of the main arch 2, a conventional large-span steel structure stability theory and stress characteristics of the axial compression member; conventional long-span steel structure stability theory considers that the initial defect amplitude is preferable to be (1/300)L 0 ，L 0 Calculating a span for the frame beam; considering that the first-order buckling mode of the main arch 2 is in-plane instability, the mechanical effect of the arch is fully exerted, and the first-order buckling mode in the plane is the mode of half-span arch downwarping and the other half-span arch upturning, the method can be regarded as a span of #L a The frame beam instability problem of/2),L a is the arch axis length of the main arch 2; in addition, considering that the axial force of the main arch 2 can also aggravate the instability of the main arch 2 when the main arch 2 deforms out of plane, and the bending moment of the main arch 2 is smaller when the main arch 2 is designed according to the reasonable arch axis generally, the theory of the stress characteristics of the axial compression component is consultedL a 2) calculating the length factor of the pressing memberφThe amplification is carried out and the amplification is carried out,φcan be determined by combining the existing standard table look-up according to the slenderness ratio and the end constraint condition of the main arch 2; to sum up, initial defect amplitude δ 1 Take (1/300) to take%L a /2)/φ. The influence line loading of the moving load cannot be performed when the buckling calculation is performed, so thatδ 2 In the calculation of the stability of various bridges, the prior art is not considered; the prior art is not safe because the horizontal deformation of the main arch 2 caused by the offset load of the moving load and the horizontal deformation of the upper arch of the other half span is actually happening. The invention starts from the basic principle of stability problem, combines the mechanical property that the main arch 2 can naturally generate horizontal displacement under the action of the loading of the moving load along the bridge to the half-span, and obtains the maximum vertical displacement of the main arch 2 obtained by analyzing the moving load influence line to reach the aim ofδ 2 The main arch 2 is deformed vertically and then is linear, and the initial defect generated by the moving load is considered. In sum, consider at the same timeδ 1 、δ 2 Corresponding linear LS 1 、LS 2 As an initial defect, the nonlinear stability of the main arch 2 can be analyzed more reliably.
S428、Changing the node coordinates of the main arch 2 into the comprehensive initial defect linear LS, wherein the comprehensive initial defect linear LS of the main arch 2 is LS 1 And LS 2 The boom 3 is changed into a cable unit, and the moving load is according to the moving load immovable working condition LC in the step S3 b Loading, and performing nonlinear buckling calculation to obtain nonlinear buckling characteristic values, namely stable safety coefficients of the main arch 2 K b ；
Specifically, the comprehensive initial defect linear LS of the bridge main arch 2 is obtained by linearly superposing node coordinate values corresponding to LS1 and LS2, and the shape of LS is shown in figure 14; after the node coordinates of the main arch 2 of the bridge are changed into the comprehensive initial defect linear LS, the moving load immovable working condition LC with the least unfavorable stability of the main arch 2 is realized b Is shown in fig. 15; nonlinear buckling calculation is carried out to obtain a nonlinear buckling characteristic value, namely the stability and safety coefficient of the main arch 2 calculated at the timeK b And ending the calculation of the stable safety coefficient.
S5, recording the bridge crane rod forceT i() To make the main arch 2 strength, stability and comprehensive optimum bridge-forming hanging rod forceT * In the followingT * Applying a moving load according to a conventional influence line mode, determining the size of a final suspender 3, the reinforcement and beam distribution design of each component and the design of auxiliary facilities of a bridge according to the full-bridge internal force state under the bridge design load combination and a conventional structural design method, and setting a pre-camber according to a finite element deformation result to smooth the bridge deck;
specifically, in step S4 described aboveT (19) Namely, the bridge forming hanging rod force which ensures the strength, stability, comprehensive and optimal of the main arch 2T * In the followingT * And determining the final boom 3 size, various concrete member reinforcement and beam distribution designs and bridge auxiliary facilities according to a conventional design method, setting pre-camber according to a finite element deformation result to smooth the bridge deck, and ending the steps to obtain the optimized boom arch bridge design.
In this embodiment, the steps S421 to S428 are adopted to implement arch bridge stability and safety coefficient calculation by considering the initial defect of the moving load, and the initial defect of the main arch 2 can be determined by considering the influence of the static load and the moving load during the calculation process, so that the nonlinear stability of the main arch 2 can be more truly analyzed, and the problem of unsafe condition caused by neglecting the moving load when calculating the stability and safety coefficient of the main arch 2 in the prior art is avoided.
Example 4
In this embodiment, the same members with boom arch bridges as in embodiments 1 to 3 are adopted, and referring to fig. 16 to 17, in this embodiment, a temporary rigid-girder flexible arch bridge with a certain span of (40+40+168+40+40) m is taken as an example, so as to provide an optimized design method for a boom arch bridge under a moving load.
Referring to fig. 2 and 16-23, the optimization design method includes the following steps:
s1, according to the statistical data of the structural dimensions of the built arch bridge, the dimensions of each component are planned by combining the span arrangement of the built arch bridge and the bridge deck system local calculation model, the boom 3 is numbered as 1,2,3 and … in sequence from root to root along the bridge,Jestablishing a primary bridge finite element model;
specifically, the main arch 2 of the bridge is a steel structure arch, the construction size of the initial main arch 2 and the construction size of other main components are determined according to the prior art, wherein the section of the main arch 2 is a rectangular steel box section, the dimensions are 3000mm wide by 2500mm high by 32mm thick, and a primary bridge forming model is established as shown in figure 17; the boom 3 is numbered 1,2,3 and … in sequence from root to root along the bridge, J；J=25；
In the above step S1, for a rigid-girder flexible arch bridge, the dimensions of the girder 1 may be basically determined at the beginning: the bridge is constructed by adopting a beam first and an arch second, the main arch 2 mainly plays a role in improving the rigidity of the main girder 1, the section size of the main girder 1 is generally determined by the constant load of the main girder 1 and the stress in the construction stage, and only the reinforcement and the beam distribution of the main girder 1 are slightly influenced by the main arch 2; the structural size of the main arch 2 can be drawn by referring to the statistical information of the established bridge and the load concentration to be shared by the main arch 2, and the structural sizes of the pier column 4 and the foundation 5 can be drawn by referring to the statistical information of the established bridge and the self weight of the upper structure of the bridge and then combined with the constant load proportion; the cross section area of the hanger rod 3 is smaller than that of the main arch 2 and the main girder 1, so that the hanger rod force has a larger influence on the stress of the bridge, but the size of the cross section of the hanger rod 3 has a smaller influence on the stress of the bridge, and the size of the cross section of the final hanger rod 3 can be finally determined after the optimization calculation of the hanger rod force is completed.
S2, the suspender 3 adopts truss units, the main arch 2, the main girder 1, the pier column 4 and the foundation 5 all adopt girder units, all constant loads are considered to carry out full-bridge line elastic static force analysis, and the design safety coefficient [ K ] of the main arch 2 is defined]And the deflection limit value of the main beam 1, and as constraint conditions, under the premise of only considering the structural strength of the arch bridge, solving a set of bridge hanging rod forces, wherein the set of hanging rod forces are expressed as vectors: T (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T J (0) ]；
In particular, the design safety factor of the main arch 2 [K]=1.2, the main beam 1 deflection limit value is calculated according to the standard requirement, and the bridge forming boom force is obtained according to the rigid boom method in the prior artT (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T 25 (0) ]=[872, 907,873, 904, 843, 862, 839, 852, 884, 860, 863, 864, 869, 864, 863, 860, 884, 852, 839, 862, 843, 904, 873, 907, 872]The number of units KN,T (0) i.e. as a subsequent boom force optimization initiation value.
S3, applying a moving load to the main arch 2, and finding out uniform distribution force in the moving load which makes the stability check of the main arch 2 most unfavorable based on the stability safety coefficient of the main arch 2QIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the stability check calculation of the main arch 2 least unfavorable b The method comprises the steps of carrying out a first treatment on the surface of the Similarly, a moving load is applied to the main arch 2, and based on the intensity safety coefficient of the main arch 2, the uniform distribution force in the moving load which makes the intensity verification of the main arch 2 least unfavorable is found outQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the main arch 2 strength check calculation least unfavorable s The arch bridge has 6 lanes, and the action range 6 of the uniform force Q and the action point 7 of the concentrated force P are shown in figure 20, and the action range of each lane in the bridge length directionThe surrounding areas are 328m, 6 lanes in the range are the application range 6 for uniformly distributing the force Q, and the application point 7 for concentrating the force P corresponds to a girder node at the center of each lane from the 1 st lane to the 5 th lane;
Specifically, the so-called moving load immobilization, namely, loading the moving load uniform distribution force Q and the concentrated force P according to fixed positions, and the specific implementation process of the step S3 can refer to the embodiment 1 and the embodiment 2; in the embodiment, the girder 1 is uniformly divided into 328 units according to 1m sections, and the girder 1 has a node numberN=329, the girder 1 nodes are numbered 1,2,3, …,329 one by one in the forward direction; generation in boom 3 bearing capacity range based on Monte Carlo simulationMThe force of the hanging rod is assembled,M=10000; the bridge cross section is arranged as follows: 3.5m (sidewalk) +2.5m (non-motorized road) +0.5m (separator) +11.5m (motorized road) +4m (central separator) +11.5m (motorized road) +0.5m (separator) +2.5m (non-motorized road+3.5 m (sidewalk) =40m, and since the main arch 2 is a single rib arch, the moving load immobilization condition LC that makes the main arch 2 least unfavorable in terms of strength check is determined s When the vehicle is in a vehicle, the number of lanes is symmetrically arranged along the center line of the section; the first-order linear elastic buckling of the main arch 2 is calculated to be out-of-plane instability, as shown in figure 18, so that the moving load immobilization working condition LC which makes the stability of the main arch 2 least favorable is determined b The number of lanes is arranged at the single side of the center line of the section and at the minimum distance along the transverse bridge direction according to the standard requirement, and the main arch 2 and the suspension rod 3 play a role in separation due to the wider central separation band, so that the moving load of the other half bridge is not considered when the unbalanced loading lanes are arranged, namely the automobile load, the non-motor vehicle load and the crowd load of the other half bridge are not considered; finally, LC is obtained according to steps S301 to S311 of example 1 b The loading diagrams of (a) are shown in FIG. 19-FIG. 20, and LC is obtained according to steps S321-S330 of example 2 s The loading diagram of (2) is shown in fig. 21-22.
S4, the suspender 3 is changed into a rope unit, the bridge forming suspender force of each suspender 3 is used as an independent variable, and the optimization is carried out through iterative calculation, so that the smaller value of the intensity safety coefficient of the main arch 2 and the stability safety coefficient of the main arch 2 is maximized, and the bridge forming suspender is characterized in thatiThe optimal bridge forming hanging rod force is obtained after the round iterationT i() Corresponding main arch 2 stable safety factorK b i() Safety coefficient of intensityK s i() The stress calculation in each round of optimization process adopts nonlinear finite element calculation,inot less than 0, and then turning to S41;
specifically, the main arch strength safety factor is calculated each timeK s When the moving load is in the working condition LC of the moving load immobilization in the step S3 s The load is applied to the container,K s the ratio of the section bearing force at the position of the main arch where the main arch is stressed at the least adverse loading position to the least adverse internal force of the section; at each calculation of the main arch stability safety factorK b When the moving load is in the working condition LC of the moving load immobilization in the step S3 b Loading, and then carrying out nonlinear buckling calculation to obtain a nonlinear buckling characteristic value, namely a stable safety coefficient of the main archK b ；
Specifically, under the initial main arch 2 configuration, viaiAfter being optimized, 30 rounds of optimization are converged to obtain the optimal bridge forming hanging rod force under the current main arch 2 structure T (30) ，T (30) =[T 1 (30) ,T 2 (30) ,T 3 (30) , ...,T 25 (30) ]=[1353, 1147,1030, 982, 963, 948, 920, 882, 838, 786, 736, 691, 675, 691, 736, 786, 838, 882, 920, 948, 963, 982, 1030, 1147, 1353]Unit KN, the main arch 2 strength safety factorK s (30) Security coefficient of main arch 2 stability = 1.4146K b (30) =1.3977；
In addition, the stable safety factor of the main arch 2 is calculated each time in the above step S4K b In the process, the specific implementation process is shown in steps S421 to S428 of embodiment 3; the first-order buckling mode of the bridge is shown in fig. 18, and the main arch 2 of the bridge calculates the span for out-of-plane instabilityL=168 m, calculated stability factor for two-end consolidated axial compression memberφ=0.563, soδ 1 =(1/300)·L/φ= (1/300) ×168/0.563=0.995 m, initial defect linear LS 1 Amplifying the first-order buckling line to the amplitude valueδ 1 The resulting line shape; then the transverse bridges of the moving load driving line are symmetrically distributed on one side of the central line of the main girder 1 and are arranged at minimum intervals according to the transverse bridge directions required by the specification, and the main arch 2 is arranged due to the wider central separation belt,The suspension rods 3 play a role in separation, and the moving load of the other half-width bridge is not considered when the unbalanced load lane is arranged, namely the automobile load, the non-motor vehicle load and the crowd load of the other half-width bridge are not considered; the moving load is loaded along the bridge direction according to the influence line, full-bridge line elastic static force calculation is carried out, and the maximum vertical displacement value of all nodes of the main arch 2 under the moving load is obtained to be about 1/4 span, and the initial defect amplitude value of the main arch 2 is obtainedδ 2 =0.193 m, initial defect due to moving load is seen δ 2 Is of a size of (a)δ 1 Is also a value which is not suitable to be ignored, initial defect linear LS 2 To move under loadδ 2 The main arch 2 is deformed vertically and then is linear; the comprehensive initial defect line shape LS of the bridge main arch 2 is obtained by linearly superposing node coordinate values corresponding to LS1 and LS2, and the shape of LS is shown in figure 23.
After the optimization process in step S4 is performed, the configuration of the main arch 2 is optimized as follows:
s41, under the current structure of the main arch 2, if min #K s i() ,K b i() )>[K]S5, turning to the step; otherwise, the main arch 2 structure and the corresponding structure of the last optimizing process are takenT i() S5, turning to S;
s42, if min%K s i() ,K b i() )-[K]>[△ K ]The main arch 2 configuration is weakened by reducing the main arch 2 cross-sectional profile size or the main arch 2 cross-sectional sheet thickness, and then turning S3, [ △ K] optimizing convergence accuracy for the main arch 2 structure of the preset s; otherwise, go to S5.
Specifically, after comprehensively considering the design precision requirement and the optimization calculation cost, taking [ △ K] =0.05; min under the initial main arch 2 structureK s i() ,K b i() )-[K]=1.3977-1.2=0.1977>[△ K ]It can be seen that the safety factor under the initial main arch 2 structure s has a higher margin than the actual design requirement, and the main arch 2 structure can be further weakened to save the engineering cost, so the repeated pressing is performedS3-S42, saving and optimizing the structure of the main arch 2, wherein the optimizing process of the structure of the main arch 2 is shown in the following table 5, and the thickness of the main arch 2 is only changed when the structure of the main arch 2 is optimized because the width and the height of the section of the main arch 2 of the steel box are generally determined by the transverse and longitudinal section arrangement of the bridge; as is clear from Table 1, since the thickness of the steel plate for the bridge is not 27mm and 26mm, the thickness of the steel plate can be 25mm only when the boom force is optimized for the 4 th time according to the present invention, and the thickness is min @ K s i() ,K b i() ) Has not satisfied [ [K]The requirement of being greater than 1.2 is that the last main arch 2 structure is taken as the optimized final value, the corresponding section size is 3000mm wide by 2500mm high by 28mm thick, and the corresponding bridge forming hanging rod force isT i() =T (30) =[T 1 (30) ,T 2 (30) ,T 3 (30) , ...,T 25 (30) ]=[1288, 1098,992, 952, 940, 931, 909, 877, 838, 791, 746, 705, 693, 705, 746, 791, 838, 877, 909, 931, 940, 952, 992, 1098, 1288]Unit KN, at this time min%K s i() ,K b i() )=1.2295>[K]=1.2, and not exceed [ [K]Too much, the construction and construction of the main arch 2 corresponding to the optimized final value into the bridge crane rod force design value is economical and reasonable.
TABLE 5 partial detailed procedure for optimized calculation of the force of the bridge crane in this embodiment
S5, recording the bridge crane rod forceT i() To make the main arch 2 strength, stability and comprehensive optimum bridge-forming hanging rod forceT * In the followingT * Applying a moving load according to a conventional influence line mode, determining the size of a final suspender 3, the reinforcement and beam distribution design of each component and the auxiliary facility design of a bridge according to the full-bridge internal force state under the bridge design load combination and a conventional structural design method, setting a pre-camber according to a finite element deformation result to smooth a bridge deck, and ending the steps to obtain an optimized suspender arch bridge design;
specifically, in step S42 described aboveT (30) Namely, the bridge forming hanging rod force which ensures the strength, stability, comprehensive and optimal of the main arch 2T * In the followingT * After the final boom 3 size, various concrete member reinforcement and beam distribution designs and bridge auxiliary facilities are determined according to the conventional design method, the following table 5 is combined to show that:
1) Considering that the weight of the weld seam is generally calculated according to 1.5% of the weight of the steel structure, the steel consumption per unit length of the initial main arch 2 structure obtained according to the prior art is (1+0.015) (3000×32×2+2500×32×2)/1000/1000×78.5= 28.05t/m, the final structure obtained according to the invention is (1+0.015) (3000×28×2+2500×28×2)/1000/1000×78.5=24.54 t/m, and the steel consumption of the main arch 2 is reduced by 12.5% compared with the prior art after the adoption of the invention, the total steel consumption of the boom 3 is increased from 680.7t to 709.3t by about 4.2% after the measurement, and the material consumption of the main beam 1 is basically unchanged;
2) According to the length of an arch axis of a steel structure part of the main arch 2 of 159.9m, the budget unit price of the steel of the main arch 2 of 1.1 ten thousand yuan/t, the budget unit price of the steel of the suspender 3 of 1.6 times of that of the steel of the main arch 2, the total construction cost of the main arch 2 and the suspender 3 obtained according to the prior art is about 28.05 x 159.9 x 1.1+680.7 x 1.1 x 1.6=6132 ten thousand yuan, the total construction cost of the main arch 2 and the suspender 3 obtained according to the invention is about 24.54 x 159.9 x 1.1+709.3 x 1.1 x 1.6=5565 ten thousand yuan, so that the construction cost 567 ten thousand yuan can be saved after the optimized design of the suspender arch bridge according to the method, and the comprehensive construction cost of the main arch 2 and the suspender 3 can reach 9.25 percent;
3) The comprehensive consideration of the engineering quantity change condition and the safety coefficient change condition of each component of the bridge proves that the construction cost of the bridge designed by adopting the method of the invention is obviously reduced compared with the prior art, and the comprehensive consideration of the strength and the stable safety coefficient is also improved compared with the prior art.
Example 5
In this embodiment, steps S1 to S5 of embodiment 4 are adopted, which are different in that: in this embodiment, taking the construction of the rigid-girder flexible arch bridge with the span of (40+40+168+40+40) m as an example in embodiment 4, the process of arch bridge boom force variable speed iterative optimization based on boom force effect guiding and strength, stable comprehensive optimization involved in the process of optimizing the bridge design is described in detail.
Referring to fig. 2, 17 and 24-25, for the specific implementation process of the iterative optimization calculation of the bridge crane rod force in step S4 of the above embodiment 4, the following steps S401-S412 are performed:
s401 forJVector of individual boom forcesX，f(X) Representing the force per vector of each suspender of the arch bridgeXWhen taking value, the main arch 2 strength safety coefficient obtained by full-bridge nonlinear finite element calculation is carried outK s And the main arch 2 stabilizes the safety coefficientK b Smaller value of (3), calculatef(X) The finite element model suspender 3 adopts a rope unit; pressing bridge hanging rod force T (0) Calculated to obtainf(T (0) ) Wherein, the method comprises the steps of, wherein,T (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T J (0) ]the method comprises the steps of carrying out a first treatment on the surface of the Let the circulation variablej=1；
Specifically, the boom 3 is numbered 1,2,3 and … in sequence from root to root along the bridge,J，J=25; for convenience of description and distinction, the boom 3 numbers in this embodiment are represented by circled numbers in order: (1) (2), (3), …; obtaining the force of the bridge-forming suspension rod by the rigid suspension rod method in the prior artT (0) =[T 1 (0) ,T 2 (0) ,T 3 (0) , ...,T 25 (0) ]=[872, 907,873, 904, 843, 862, 839, 852, 884, 860, 863, 864, 869, 864, 863, 860, 884, 852, 839, 862, 843, 904, 873, 907, 872]The unit KN is calculated by the full-bridge nonlinear finite element to obtain the intensity safety coefficient of the main arch 2K s Security coefficient of main arch 2 stability = 1.5523K b = 1.1211, sof(T (0) )=1.1211。
S402, willT (0) The first of (3)jThe value of the individual element increasing the unit force, i.eT (0) Becomes as followsT j (0) Calculated to obtainf(T j (0) ) The method comprises the steps of carrying out a first treatment on the surface of the If it isf(T j (0) )-f(T (0) )>0, boom force optimization direction vectordIs the first of (2)jElement fetchd(j) =1, otherwise letd(j)=-1；
S403, ifj<JOrder in principlej=j+1, go to S402; otherwise, letD J J× =diag(d) I.e. forming a boom force optimizing direction diagonal matrixD J J× The matrix reflects the increase in single boom force to the main arch 2K s AndK b whether the smaller value of (a) plays a positive effect of lifting or a negative effect of lowering can be used for determining whether the optimization direction of each subsequent boom force is preferentially increased or preferentially decreased, and then the step S404 is performed;
specifically, boom force optimization direction diagonal matrixD J J× The values of the elements in the table 6 are shown in the table 6, wherein the unit grid value of 1 represents the main arch 2 after the force of a single hanging rod is increased K s AndK b smaller values between are positive effects that act as a boost, while a value of-1 indicates that act as a negative effect that is a decrease.
TABLE 6 boom force optimization direction diagonal matrixD J J× Values of elements in (a)
1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 0 0
0 0 0 0 0 0 0 0 0 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 -1
S404 toT (0) As an optimization initial value, convergence accuracy of boom force fluctuation amount is setεGreater than or equal to 0, the fluctuation of the boom forceδ>εAcceleration coefficient of boom force variationα1 or more, deceleration coefficient of boom force variationβE (0, 1); order theH J1× To record the variables that have positive or negative effects after each boom force change and before the change, the main arch 2 is subjected toK s AndK b the smaller value of the product has positive effect when the product plays a role in lifting, otherwise has negative effect, and the initial value isH J1× =[0,0,0,...,0]The method comprises the steps of carrying out a first treatment on the surface of the External circulation variable for optimizing hanging rod forcei=0, internal circulation variablejBoom force intermediate variable =1F j() =T i() ；
Specifically, the present embodiment sets the convergence accuracy of the fluctuation amount of the boom force after comprehensively considering the design accuracy requirement and the optimization calculation costεThe initial value of the boom force variation is =1KNδAcceleration coefficient of boom force variation =4knαDeceleration coefficient of boom force variation =2.0β=0.5。
S405, orderE j() =D(j,1:J) The method comprises the steps of carrying out a first treatment on the surface of the If it isf(F j() +δE j() )>f(T i() ) ThenH(j) =1, go to S406, otherwise go directly to S406;
s406, iff(F j() +δE j() )>f(F j() ) Order in principleF j(+1) =F j() +δE j() Turning to S407; otherwise, letF j(+1) =F j() Turning to S407;
s407, ifj<JOrder in principlej=j+1, go to S405; otherwise, go to S408;
s408, if each boom force is vector F j(+1) When the value is taken, the conventional design index and the mechanical property of the main beam 1 meet the design requirement, and the step S409 is carried out; otherwise, directly turning to S412;
s409, iff(F j(+1) )>f(T i() ) Turning to S410; otherwise, directly turning to S412;
s410 if sum @H)=JExplaining the basis of the forces of each boomD J J× After changing according to the respective positive effect direction, positive effects are generated on the main arch 2, namely, the nonlinear effect of the bridge is not strong at the moment, so that the fluctuation of the lifting rod force is increasedδTo accelerate convergence, i.e. orderδ=αδThen turning to S411; otherwise, the part of the hanging rod force is described according toD J J× According to the positive effect directionThe main arch 2 is subjected to negative effect after movement, namely the nonlinear effect of the bridge is obvious at the moment, so that the fluctuation of the boom force is not increased any moreδAnd directly goes to S411;
s411, orderT i(+1) =F j(+1) The method comprises the steps of carrying out a first treatment on the surface of the Order thej=1，H J1× =[0,0,0,...,0]，F j() =T i(+1) ；i=i+1, go to S405;
s412, ifδ>εOrder-makingδ=βδReducing the fluctuation of the suspension rod forceδFine optimization is carried out; order thej=1，H J1× =[0,0,0,...,0]，F j() =T i() ，T i(+1) =T i() Order-makingi=i+1, go to S405; otherwise, the convergence accuracy of the fluctuation of the boom force is reached, the boom force optimization is terminated,T i() the bridge forming hanging rod force which enables the main arch 2 to be stable and comprehensive and optimal is adopted;
specifically, in the steps S405 to S412, the internal circulation variablejThe inner loop is completed from 1 to 13, and the fluctuation of the boom force in each iteration of each inner loopδIs a constant value; external circulation variable iEach increment of 1 performs an outer loop iteration,δthe iterative process and the optimization convergence progress of the outer loop can be adaptively changed; the optimization calculation process of the bridge forming hanging rod force in the embodiment is shown in tables 7-8 and fig. 25, and only half-span hanging rod forces are listed in table 8 because the bridge is of a symmetrical structure; as can be seen from fig. 25, iniWhen=1 to 15, the convergence rate is high, and the following is the resultδContinuously reducing to enter a fine optimizing stage, and slowing down the convergence speed; when (when)iWhen the value of the ratio is =30,δ=1kn, achieve convergence accuracyεThe optimization calculation of the bridge forming hanging rod force under the current main arch 2 structure is completed,T (30) namely, the bridge forming hanging rod force which ensures that the main arch 2 is stable and comprehensive and optimal,T (30) =[T 1 (30) ,T 2 (30) ,T 3 (30) , ...,T 25 (30) ]=[1353, 1147,1030, 982, 963, 948, 920, 882, 838, 786, 736, 691, 675, 691, 736, 786, 838, 882, 920, 948, 963, 982, 1030, 1147, 1353]unit KN, the main arch 2 strength safety factorK s (30) Security coefficient of main arch 2 stability = 1.4146K b (30) = 1.3977, sof(T (30) ) As shown in 1.3977, after the comprehensive optimization of the strength and stability under the moving load is comprehensively considered according to the invention, the safety coefficient of the bridge is improved to 1.3977 as compared with 1.1211 in the prior art, the improvement range is 24.7%, and compared with the prior art, the safety coefficient is obviously improved, and if the actual design does not require such high safety coefficient, the construction of the main arch 2 can be further weakened so as to save the engineering cost.
TABLE 7 general Process of optimization calculation of the force of the bridge crane in this embodiment
External circulation variablei f(T (i) ) Fluctuation amountδ External circulation variablei f(T (i) ) Fluctuation amountδ
0 1.1211 —
1 1.1308 4 16 1.3607 32
2 1.1500 8 17 1.3684 32
3 1.1761 16 18 1.3684 16
4 1.2012 32 19 1.3742 16
5 1.2254 32 20 1.3796 8
6 1.2476 32 21 1.3844 8
7 1.2679 32 22 1.3844 8
8 1.2863 32 23 1.3873 8
9 1.3027 32 24 1.3897 4
10 1.3172 32 25 1.3897 4
11 1.3298 32 26 1.3916 4
12 1.3404 32 27 1.3936 2
13 1.3491 32 28 1.3955 2
14 1.3559 32 29 1.3974 2
15 1.3607 32 30 1.3977 1
TABLE 8 partial detailed procedure for optimized calculation of the force of the bridge crane in this embodiment
In the embodiment, the steps S401-S412 can be adopted to realize arch bridge boom force variable speed iterative optimization based on boom force effect guidance and strength, stability and comprehensive optimization, the iterative optimization method has rapid optimization convergence speed in the stage of weak bridge nonlinear effect, and fine optimization precision in the stage of strong bridge nonlinear effect, so that the efficiency and precision of large-scale boom force parameter optimization calculation are considered, and the variable speed optimization characteristics which are not possessed by the existing optimization algorithm in boom force optimization iteration are considered; in addition, the optimization process of the algorithm gives consideration to comprehensive optimization of bridge strength and stability, so that the problem that the stability safety coefficient is lower than the strength safety coefficient possibly occurs when the rigid-beam flexible arch bridge is designed in the prior art is avoided, the stability safety coefficient can be realized by adopting the algorithm to design, the mechanical property of the material is fully exerted, and the material strength waste caused by the stability problem is avoided.
Example 6
The embodiment provides an optimal design system for an arch bridge with a suspender under a moving load, and the optimal design system can apply an optimal design method for an arch bridge with a suspender under a moving load, and can perform optimal design by adopting steps S1 to S5 in embodiments 1 to 5.
Referring to fig. 26, the optimization design system includes a modeling module, an initial boom force calculating module, a mobile load loading module, an initial defect loading module, an iterative optimization module, a structural design module, an input module, a display module and a storage module, wherein the modeling module, the boom force calculating module, the mobile load loading module, the initial defect loading module, the iterative optimization module and the structural design module are respectively implanted with corresponding steps and calculation processes of the optimization design method, functions of each module can be realized through module division of software, the storage module can adopt a hardware memory, a virtual software storage module can also be adopted, the input module can adopt an interface in software, hardware such as a keyboard can also be adopted, the display module adopts a display, a display screen can also be adopted, the input module is used for inputting data by a user, the storage module is used for storing data output by each module, the display module is used for displaying results of steps S1-S5, and each module can be executed according to the steps to complete the optimization design.
The modeling module is used for drawing up the sizes of all the components, building a primary bridge forming finite element model, executing the step S1, collecting statistical data of the structural sizes of the built arch bridge, the sizes of all the components and the like through the input module, and outputting the result to the boom force initial value calculating module; the initial value module for solving the boom force executes the step S2, is used for calculating the bridge forming boom force in the step S2, and outputs the result to the mobile load loading module and the initial defect loading module; the loading module executes the step S3, and is used for calculating fixed loading positions of the uniform force Q and the concentrated force P in the moving load which make the stability check of the main arch 2 least unfavorable, the fixed loading positions of the uniform force Q and the concentrated force P in the moving load which make the strength check of the main arch 2 least unfavorable, and outputting the moving load immovable state to the iterative optimization module; the iterative optimization module executes the step S4, and the iterative optimization module is used for calculating the optimal bridge crane rod force T i() Corresponding main arch stability safety factorK b i() Safety coefficient of intensityK s i() Outputting the result to a structural design module; in the execution process of the iterative optimization module, each time of calculationK b The initial defect loading module is called to correct the main arch node coordinates; and S5, the structural design module is used for determining the size of the suspender 3, the reinforcement and beam distribution design of each component and the bridge auxiliary facility design according to the strength of the main arch 2 and the stable comprehensive optimal bridge forming suspender force. Through the optimal design system, the steps of an optimal design method can be realized according to each module, a bridge forming finite element model is established through a modeling module, a boom force optimal initial value is obtained through a boom force initial value obtaining module, a moving load immobilized working condition is obtained through a moving load loading module, a main arch stable safety coefficient can be accurately calculated through an initial defect loading module, an optimal bridge forming boom force is obtained through an iterative optimization module, final design is completed through a structural design module, and the realization of the steps of outputting and executing of each module can be realizedThe comprehensive optimization of the strength and the stable safety performance is realized when the suspender arch bridge is designed, and finally the optimization design is completed.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.

Claims (8)

1. An optimization design method for an arch bridge with a suspender under a moving load is characterized in that the arch bridge with the suspender comprises the following components: the design method comprises the following steps of:
s1, according to the statistical data of the structural dimensions of the built arch bridge, combining the span arrangement of the built arch bridge and the bridge deck system local calculation model, planning the dimensions of each component, sequentially numbering the suspenders into 1,2,3 and … along the bridge,Jestablishing a primary bridge finite element model;
s2, the suspender adopts truss units, the main arch, the main girder, the pier column and the foundation all adopt girder units, all constant loads are considered to carry out full-bridge line elastic static force analysis, and the design safety coefficient of the main arch is definedK]And the girder deflection limit value is used as a constraint condition, and on the premise of considering only the structural strength of the arch bridge, a set of bridge crane rod forces are calculated and used as optimized initial values, and the set of crane rod forces are expressed as vectors:T (0) =[T 1 (0) , T 2 (0) , T 3 (0) , ..., T J (0) ]；
s3, applying a moving load to the main arch, and finding out uniform distribution force in the moving load which makes the main arch stability check most unfavorable based on the main arch stability safety coefficientQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the main arch stability check calculation least unfavorable b The method comprises the steps of carrying out a first treatment on the surface of the Similarly, a moving load is applied to the main arch, and based on the safety coefficient of the main arch strength, the uniform distribution force in the moving load which makes the main arch strength check most unfavorable is found outQIs fixed in loading position and concentration forcePIs arranged at the fixed loading position of the (c),QandPloading according to the fixed loading position to form a moving load immovable working condition LC which makes the main arch strength check calculation least unfavorable s ；
Forming a moving load immobilization working condition LC which makes the checking calculation of the stability of the main arch least unfavorable b The specific steps of (a) are as follows:
s301, judging whether the main arch structure has variation compared with the previous optimization process, if so, turning to S302, and if not, turning to S303;
s302, modifying main arch units and section parameters in the model, and then turning to S304;
s303, judging whether the working condition LC is formed for the first time under the current main arch structure b If yes, go to S304, otherwise go to S311;
s304, aiming at the primary bridge forming model of the arch bridge to be built, the cable units are modified into truss units, all bridge design loads except the moving load are applied, the girder nodes are numbered 1,2,3 and … one by one along the bridge direction,Ncarrying out full-bridge line elastic static force calculation to obtain a main arch stable safety coefficientK b (0) ；
S305, generating in the bearing capacity range of the suspender by adopting a Monte Carlo simulation methodMAssembling the boom force to enable the boom force to circulate variable m=1, girder node circulation variablen=1；
S306, modifying the boom force of the finite element model intoMGroup hanging rod forcemThe values of the group are set in the first order of the primary arch if the primary arch is elastically flexed and not unstable in the out-of-plane directionnThe joints of the main beams are arrangedN v A unit load which is symmetrical or asymmetrical along the center line of the section, and respectively establishes loading working conditions,N v the number of lanes is designed; if the primary arch first-order line is elastically buckled into out-of-plane instability, then in the firstnOne side of the center line of the section at each girder node is arrangedN v The unit loads are arranged at minimum intervals in the transverse bridge direction according to the standard requirements, and loading working conditions are respectively established;
s307, performing full-bridge line elastic buckling calculation according to 1-N v The minimum value of the combination of the calculation results of the working conditions is used for obtaining the stable safety coefficient of the main archK b m n(,) Order-makingK △b m n(,) =K b m n(,) -K b (0) ，K △b m n(,) Stabilization of positive and negative effect matrix for mobile loadmLine 1nA column of elements; by passing throughK △b m n(,) The positive and negative effects of the moving load stability are judged, and the boom force is taken as the firstmGroup and moving load is loaded on the firstnWhen the movable load plays a role in improving the stability of the bridge,K △b m n(,) positive, i.e., positive effect, when the moving load acts to reduce the stability of the bridge,K △b m n(,) negative, i.e. negative effect;
s308, ordern=n+1, ifn>NOrder in principle m=m+1, go to S309; otherwise, go to S306;
s309 ifm>MTurning to S310, otherwise turning to S306;
s310, from S306 to S309MLine XNColumn movement load stabilization positive-negative effect matrixK △b For a pair ofK △b After the average value is calculated column by column, the stable influence degree row vector is obtainedS b1 ，S b1 Reflecting the degree of strengthening or weakening the stability of the bridge when the moving load is loaded on each girder node under different boom force levels; will beK △b Count the number of positive elements in each column divided byMObtain stable influence significance row vectorS b2 ，S b2 Reflecting the probability of strengthening or weakening the stability of the bridge when the moving load is loaded on each girder node under different boom force levels;S b1 andS b2 make up 2XNStable sensitive line matrix of columnS b ；
S311, extractingS b The first row of each column is less than 0 and the second row is less than the set significance levelα b To uniformly distribute force in moving loadQLoading all girder nodes corresponding to the extracted columns,concentrate forces in moving loadsPLoading at the main beam node with the minimum first row value in the extracted column to obtain the movable load working condition LC with the least adverse main arch stability b ；
Forming a moving load immobilization working condition LC which makes the main arch strength check calculation least unfavorable s The specific steps of (a) are as follows:
s321, judging whether the main arch structure has variation compared with the previous optimization process, if so, turning to S322, and if not, turning to S323;
S322, modifying main arch units and section parameters in the model, and then turning to S324;
s323, judging whether the working condition LC is formed for the first time under the current main arch structure s If yes, go to S324, otherwise go to S330;
s324, aiming at the primary bridge forming model of the arch bridge to be built, the cable units are modified into truss units, all bridge design loads except the moving load are applied, the girder nodes are numbered 1,2,3 and … one by one along the bridge direction,Ncarrying out full-bridge line elastic static force calculation to obtain the main arch strength safety coefficientK s (0) ；
S325, generating in the bearing capacity range of the suspender by adopting a Monte Carlo simulation methodMAssembling the boom force to enable the boom force to circulate variablem=1, girder node circulation variablen=1；
S326, modifying the finite element model boom force toMGroup hanging rod forcemThe values of the group, atnThe joints of the main beams are arrangedN v A unit load which is symmetrical or asymmetrical along the center line of the section, and respectively establishes loading working conditions,N v to design the number of lanes, then carrying out full-bridge line elastic static force calculation according to 1-1%N v The minimum value after the combination of the calculation results of the working conditions is used for obtaining the safety coefficient of the main arch strengthK s m n(,) Order-makingK △s m n(,) =K s m n(,) -K s (0) ；K △s m n(,) To move the positive and negative effect matrix of load intensitymA row(s),nList of elements, general purposePassing throughK △b m n(,) The positive and negative effects of the moving load strength are judged, and the boom force is the first mGroup and moving load is loaded on the firstnWhen the moving load plays a role in improving the bearing capacity of the bridge,K △s m n(,) positive, i.e., positive effect, when the moving load has a decreasing effect on the bridge bearing capacity,K △s m n(,) negative, i.e. negative effect;
s327 ordern=n+1, ifn>NOrder in principlem=m+1, go to S328; otherwise, go to S326;
s328, ifm>MTurning to S329, otherwise turning to S326;
s329, from S326 to S328MLine XNPositive and negative effect matrix of column moving load intensityK △s For a pair ofK △s After column-by-column averaging, the intensity influence degree row vector is obtainedS s1 ，S s1 Reflecting the degree of strengthening or weakening the bridge bearing capacity when the moving load is loaded on each node under different boom force levels; will beK △s Count the number of positive elements in each column divided byMObtaining intensity-influencing significance row vectorsS s2 ，S s2 Reflecting the probability of strengthening or weakening the bridge bearing capacity when the moving load is loaded on each node under different boom force levels;S s1 andS s2 make up 2XNMatrix of intensity sensitive lines of columnsS s ；
S330, extractingS s The first row of each column is less than 0 and the second row is less than the set significance levelα s To uniformly distribute force in moving loadQAll nodes corresponding to the extracted columns are loaded, and the concentrated force in the load is movedPThe node with the smallest first row value loaded in the extracted column is used for obtaining the moving load immovable working condition LC which makes the main arch strength check calculation least unfavorable s ；
S4, the boom is replaced by a rope unit, the bridge-forming boom force of each boom is used as an independent variable, and the main arch strength safety coefficient are optimized through iterative calculationThe smaller value of the arch stability safety coefficient is maximized iniThe optimal bridge forming hanging rod force is obtained after the round iterationT i() Corresponding main arch stability safety factorK b i() Safety coefficient of intensityK s i() The stress calculation in each round of optimization process adopts nonlinear finite element calculation;
s5, recording the bridge crane rod forceT i() Bridge forming hanging rod force for stabilizing and comprehensively optimizing main arch strengthT * In the followingT * And applying a moving load according to a conventional influence line mode, determining the final boom size, the reinforcement and beam distribution design of each component and the auxiliary facility design of the bridge according to the full-bridge internal force state under the bridge design load combination and a conventional structural design method, setting the pre-camber according to the finite element deformation result to smooth the bridge deck, and ending the steps to obtain the optimized arch bridge with the boom.
2. The method for optimizing an arch bridge with a boom under a moving load according to claim 1, wherein the construction of the main arch is optimized by the following steps after each execution of step S4:
s41, under the current main arch structure, if min # K s i() ,K b i() )>[K]S5, turning to the step; otherwise, taking the main arch structure and the corresponding main arch structure in the last optimizing processT i() S5, turning to S;
s42, if min%K s i() ,K b i() )-[K]>[△ K ]The main arch configuration is weakened by reducing the main arch cross-sectional profile size or the main arch cross-sectional sheet thickness, and then turning S3, [ △ K] optimizing convergence accuracy for a preset main arch structure; otherwise, go to S5.
3. The method for optimizing design of arch bridge with boom under moving load according to claim 1, wherein after the step S311 is completed, if the same main beam is in S306-S309The stable positive and negative effects of each lane at the node are different, and the working condition LC is modified b The node of the main beam has negative effect and is smaller than the set significance test levelα b Uniformly distributing force for moving load on all lanes of vehicleQOr concentrate forcePLoading to obtain a modified working condition LC b 。
4. The method for optimizing design of arch bridge with boom under moving load according to claim 1, wherein after the step S330 is completed, if the positive and negative effects of the intensities of the lanes at the same girder node in S326-S328 are different, LC is modified b Working conditions are that the main beam joint has negative effect and is smaller than the set significance test levelα s Uniformly distributing force for moving load on all lanes of vehicleQOr concentrate forcePLoading to obtain a modified working condition LC s 。
5. The method for optimizing the design of the arch bridge with the boom under the moving load according to claim 1, wherein the specific steps of iterative optimization of the boom force in the step S4 are as follows:
s401 forJVector of individual boom forcesX，f(X) Representing the force per vector of each suspender of the arch bridgeXWhen taking value, the main arch strength safety coefficient obtained by full-bridge nonlinear finite element calculation is carried outK s And a main arch stability safety factorK b Smaller value of (3), calculatef(X) The finite element model suspender adopts a cable unit; pressing bridge hanging rod forceT (0) Calculated to obtainf(T (0) ) Wherein, the method comprises the steps of, wherein,T (0) =[T 1 (0) , T 2 (0) , T 3 (0) , ..., T J (0) ]the method comprises the steps of carrying out a first treatment on the surface of the Let the circulation variablej=1；
S402, willT (0) The first of (3)jThe value of the individual element increasing the unit force, i.eT (0) Becomes as followsT j (0) Calculated to obtainf(T j (0) ) The method comprises the steps of carrying out a first treatment on the surface of the If it isf(T j (0) )-f(T (0) )>0, boom force optimization direction vectordIs the first of (2)jElement fetchd(j) =1, otherwise letd(j)=-1；
S403, ifj<JOrder in principlej=j+1, go to S402; otherwise, letD J J× =diag(d) I.e. forming a boom force optimizing direction diagonal matrixD J J× Then turning to S404;
s404 toT (0) As an optimization initial value, convergence accuracy of boom force fluctuation amount is setεGreater than or equal to 0, the fluctuation of the boom forceδ>εAcceleration coefficient of boom force variationα1 or more, deceleration coefficient of boom force variationβE (0, 1); order theH J1× To record the variables with positive effect or negative effect after the change of each suspender force and before the change, the main arch is provided with a plurality of main arches K s AndK b the smaller value of the product has positive effect when the product plays a role in lifting, otherwise has negative effect, and the initial value isH J1× =[0,0,0,...,0]The method comprises the steps of carrying out a first treatment on the surface of the External circulation variable for optimizing hanging rod forcei=0, internal circulation variablejBoom force intermediate variable =1F j() =T i() ；
S405, orderE j() =D(j,1:J) The method comprises the steps of carrying out a first treatment on the surface of the If it isf(F j() +δE j() )>f(T i() ) ThenH(j) =1, go to S406, otherwise go directly to S406;
s406, iff(F j() +δE j() )>f(F j() ) Order in principleF j(+1) =F j() +δE j() Turning to S407; otherwise, letF j(+1) =F j() Turning to S407;
s407, ifj<JOrder in principlej=j+1, go to S405; otherwise, go to S408;
s408, if each boom force is vectorF j(+1) When the value is taken, the conventional design index and mechanical property of the main beam meet the design requirement, and the step S409 is carried out; otherwise, directly turning to S412;
s409, iff(F j(+1) )>f(T i() ) Turning to S410; otherwise, directly turning to S412;
s410 if sum @H)=JOrder-makingδ=αδThen turning to S411; otherwise, directly switching to S411;
s411, orderT i(+1) =F j(+1) The method comprises the steps of carrying out a first treatment on the surface of the Order thej=1，H J1× =[0,0,0,...,0]，F j() =T i(+1) ；i=i+1, go to S405;
s412, ifδ>εOrder-makingδ=βδ，j=1，H J1× =[0,0,0,...,0]，F j() =T i() ，T i(+1) =T i() Order-makingi=i+1, go to S405; otherwise, the convergence accuracy of the fluctuation of the boom force is reached, the boom force optimization is terminated,T i() the bridge forming hanging rod force which enables the main arch to be stable and comprehensive and optimal is obtained.
6. The method for optimizing design of arch bridge with boom under moving load according to claim 1, wherein in step S4, the main arch stability safety factor is calculated each timeK b When in use, the method comprises the following steps:
S421, judging whether the main arch structure has variation compared with the previous optimization process, if so, turning to S422, and if not, turning to S423;
s422, modifying main arch units and section parameters in the model, and then turning to S424;
s423, judging whether buckling calculation is performed for the first time under the current main arch structure, if so, turning to S424, otherwise turning to S429;
s424, modifying a cable unit of a primary bridge forming finite element model of the arch bridge to be built into a truss unit, wherein the main arch position is according to an arch axis LS without initial defects 0 Modeling, namely applying all bridge design loads except the moving load, and then performing full-bridge line elastic buckling calculation, wherein all bridge design loads are set as variables during calculation;
s425, turning to S426 if the primary arch first-order buckling is out-of-plane instability; otherwise, turning to S427;
s426, initial defect amplitude of main arch shape under static loadδ 1 Is (1/300)L/φ，LThe span is calculated for the main arch and,φline-shaped LS of initial defect of main arch for stabilizing coefficient of axial compression component 1 Amplifying the linear corresponding to the first-order buckling mode to delta according to the amplitude 1 The resulting line shape; then the running line of the moving load is distributed at one side of the central line of the main girder according to the minimum transverse bridge spacing allowed by the specification, namely the moving load is distributed according to single side unbalanced load, the moving load is loaded along the bridge direction according to the influence line, the full bridge line elastic static force calculation is carried out, and the initial defect amplitude of the main arch line shape under the moving load is obtained δ 2 ，δ 2 Initial defect linear LS for maximum bridge displacement value of all nodes of main arch 2 To move under loadδ 2 The main arch transverse bridge is deformed and then is linear;
s427, initial defect amplitude of main arch shape under static loadδ 1 Is (1/300) &L a /2)/φ，L a For the length of the main arch axis,φinitial defect linear LS for axial compression component stability factor 1 Amplifying the first-order buckling line to the amplitude valueδ 1 The resulting line shape; then the transverse bridge directions of the moving load driving lines are symmetrically distributed on two sides of the central line of the main girder, the moving load is loaded along the bridge directions according to the influence lines, the full-bridge line elastic static force calculation is carried out, and the initial defect amplitude of the main arch shape under the moving load is obtainedδ 2 ，δ 2 Initial defect linear LS for maximum vertical displacement value of all nodes of main arch 2 To move under loadδ 2 The main arch is deformed vertically and then is linear;
s428, changing the main arch node coordinates into comprehensive initial defect linear LS, wherein the main arch comprehensive initial defect linear LS is LS 1 And LS 2 Is changed into a cable unit and movedThe dynamic load is according to the moving load immobilized working condition LC in the step S3 b Loading, and performing nonlinear buckling calculation to obtain nonlinear buckling characteristic values, namely stable safety coefficients of the main archK b And ending the calculation of the stable safety coefficient.
7. The method for optimizing design of arch bridge with boom under moving load according to claim 1, wherein in step S4, the main arch strength safety factor is calculated each timeK s When the moving load is in the working condition LC of the moving load immobilization in the step S3 s The load is applied to the container,K s the ratio of the section load bearing force at the position of the main arch where the main arch is stressed least to the section least adverse internal force.
8. An optimized design system for a boom arch bridge under a moving load is characterized in that the optimized design method for the boom arch bridge under the moving load is adopted, and the optimized design system comprises a modeling module, a boom force initial value solving module, a moving load loading module, an iterative optimization module and a structural design module;
the modeling module is used for drawing up the sizes of all the components, building a primary bridge formation finite element model and outputting the result to the boom force initial value solving module; the initial boom force calculating module is used for calculating the bridge forming boom force in the step S2, the moving load loading module is used for calculating fixed loading positions of uniform force Q and concentrated force P in moving load with the most unfavorable main arch stability checking calculation, fixed loading positions of uniform force Q and concentrated force P in moving load with the most unfavorable main arch strength checking calculation, and outputting moving load immobilized working conditions, and the iterative optimization module is used for calculating the optimal bridge forming boom force T i() Corresponding main arch stability safety factorK b i() Safety coefficient of intensityK s i() The structural design module is used for determining the size of the suspension rod, the reinforcement and beam distribution design of each component and the bridge auxiliary facility design according to the bridge-forming suspension rod force with stable main arch and comprehensive optimal strength.
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