CN114707202A

CN114707202A - Method and system for optimally designing arch bridge with suspender under mobile load

Info

Publication number: CN114707202A
Application number: CN202210108984.XA
Authority: CN
Inventors: 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
Original assignee: China Construction Fifth Engineering Bureau Co Ltd; China Construction Tunnel Construction Co Ltd
Current assignee: China Construction Fifth Engineering Bureau Co Ltd; China Construction Tunnel Construction Co Ltd
Priority date: 2022-01-28
Filing date: 2022-01-28
Publication date: 2022-07-05
Anticipated expiration: 2042-01-28
Also published as: CN114707202B

Abstract

The invention relates to an optimization design method and a system of an arch bridge with a suspender under a mobile load, which comprises the following steps: s1, drawing up the dimensions of each component of the arch bridge, and establishing a finite element model; s2, calculating the force of the crane jib of the finished bridge based on linear static force calculation to be used as an initial optimization value of the force of the crane jib of the finished bridge; s3, forming a moving load immobility working condition based on the stability and strength effect of the main arch, and realizing the loading of the moving load according to a fixed position; s4, calculating the moving load and the initial defects based on nonlinear calculation, and iteratively optimizing the optimal boom force; s5, finishing the design of the rest components according to a conventional method; the system adopts the method of S1-S5; the method gives consideration to the strength and stability of the main arch, iterative optimization is carried out by considering the moving load and the initial defect, a better bridge forming crane rod force is solved, the design result is closer to the actual situation 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 change in a self-adaptive mode, and the method can be used for large-scale optimization design of a large-span arch bridge and has higher economical efficiency.

Description

Optimization design method and system for arch bridge with suspender under moving load

Technical Field

The invention relates to the technical field of arch bridge design, in particular to an optimization design method and system of an arch bridge with a suspender under a moving load.

Background

The arch bridge with the suspender can be divided into two types according to the stress sharing condition between the beam and the arch: the rigid-beam flexible arch bridge is a bridge with a girder of which the rigidity is greater than that of a main arch and most of load is borne by the girder, and the rigid-arch flexible bridge is a bridge with a main arch of which the rigidity is greater than that of the girder and most of load is borne by the main arch. The arch bridge with a boom currently used is designed in a process different from that of a general beam bridge as shown in fig. 1: for the beam type bridge structure, if the structure size, the material, the second-stage constant load and other static loads are determined, the internal force of the static load of the structure is also basically determined, and large adjustment cannot be carried out; however, for the arched bridge with the suspender, the bridge forming line shape and the internal force state can be obtained by adjusting the tensioning force of the suspender, so the main work of the arched bridge with the suspender in the design stage is to determine the reasonable bridge forming suspender force, and the reasonable bridge forming state of the arched bridge with the suspender is obtained by completing the design of other bridge components according to the reasonable bridge forming suspender force and a conventional method.

A method for determining reasonable bridge-forming suspender force is researched more in a suspension bridge and a cable-stayed bridge, such as Chinese patent 'CN 201510312423-a suspension bridge cable force optimization method', 'CN 202010851156-a cable-stayed bridge cable optimization method and system', and journal document 'Zhang-Yin, Chengxing, Wang-Chang-Feng, Beam-arch combined bridge suspender force optimization and engineering application [ J ]. railway building, 2014, (1), 4-6.', 'Guanhua, Cumin, simplified calculation method for initial cable force of beam-arch combined bridge suspender bridge-forming initial cable force [ J ]. China and foreign road, 2017, (4), 165 and 170.', 'Zhang-Yuping, Liuxue, biography, and analysis [ J ]. civil and environmental engineering report (Chinese and English) based on MOPSO algorithm, (2)' 107-114.

The prior art comprises 8 types of methods including a rigid suspender 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 a suspension bridge, a cable-stayed bridge and a part of arched bridges with suspenders, the optimization of linear and internal force states is realized on the premise of only considering static load, so that the method has a good effect; however, the above methods are all based on linear superposition of load effects to optimize the boom force, while the moving load involves influence line analysis, which is also based on the linear superposition principle of load effects, 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 method is difficult to realize due to the large difficulty in combining the boom force optimization process and the moving load influence line, so the prior art abandons the consideration of the action effect of the moving load in boom force optimization iteration; although the action effect of the moving load is generally smaller than that of the non-moving load, the boom force obtained after abandoning the moving load in the prior art is obviously not an optimal solution, and the boom force obtained in the prior art still has an optimization space in the range of 20% -50% according to the proportion of the moving load in the total load of the bridge design.

In addition, for the stability problem of the arch bridge, the current specification only provides a checking formula under the linear elastic buckling theory for the in-plane stability of the deck type non-suspender arch bridge, the formula is approximately applicable to the problem of in-plane stability of the rigid-arch flexible beam bridge, but along with popularization and application of the beam-arch bridge, more and more rigid-arch flexible beam bridges appear at present, the rigidity of the arch section of the bridge is much lower than that of the beam section, the height of the arch section is smaller than the span of the arch, the linear rigidity of the arch is smaller, namely, the generalized force required to be applied when the arch generates unit vertical deformation is smaller, so that the nonlinear effect of the suspender rigid-beam flexible arch bridge is stronger, the load action causes the main arch to deviate from the reasonable arch axis and then bring bending moment of second-order effect, therefore, the in-plane stability of the arch is obviously reduced, and therefore a nonlinear buckling analysis method is necessary to be adopted for the in-plane stability checking calculation of the bridge. During linear and nonlinear buckling analysis, the influence line of the moving load cannot be applied, the stability analysis in the prior art cannot consider the action of the moving load, the influence of asymmetric deformation of the moving load on initial defects is neglected, the difference from the actual stability condition of the bridge is large, and the problem of partial insecurity exists during the calculation of the main arch stability safety coefficient.

For the out-of-plane stability checking method of the arch, the current specification is not given, and for most single-rib arch bridges, the rigidity of the transverse bridge direction line is very weak, the transverse bridge direction cannot play 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 is possibly far lower than the strength safety coefficient, the boom force at this time acts as a restoring force that limits out-of-plane instability, optimization of the boom force is an effective way to improve out-of-plane stability, the boom force optimization method in the prior art does not consider the stability problem of the arch, and also does not realize nonlinear buckling calculation in the boom force optimization process, therefore, the prior art may have the problem of uneconomical property that the stability safety coefficient is far lower than the strength safety coefficient when the rigid-beam flexible arch bridge is designed, and the material strength performance cannot be fully exerted to cause waste.

In summary, the prior art has the following four problems:

1) in the prior art, the effect of the moving load cannot be considered in the boom force optimization method, so that the obtained bridge-forming boom force is not an optimal solution and an optimization space in the range of 20-50% is still available;

2) in the prior art, the bridge stability calculation fails to consider the action effect of the moving load, neglects the influence of the asymmetric deformation possibly generated by the moving load on the initial defect, and has the problem of unsafe situation compared with the actual stability;

3) the boom force optimization method in the prior art does not consider the stability problem of the arch bridge, does not realize nonlinear buckling calculation in the boom force optimization process, cannot give consideration to the comprehensive optimization of the strength and stability of the bridge, and can cause the problem of material strength waste caused by the fact that the stability safety coefficient of some arch bridges is far lower than the strength safety coefficient;

4) in the prior art, the boom force optimization algorithm is usually optimized iteratively at a constant speed, the mechanical characteristics of the boom arch bridge and the effect guidance of the boom force are not fully combined to improve the performance of the optimization algorithm pertinently, and the optimization effect and the optimization speed are difficult to ensure at the same time, so that a certain optimization effect needs to be abandoned or a large amount of optimization working hours needs to be consumed in the large-scale boom force optimization of the large-span arch bridge.

Disclosure of Invention

In order to solve the four problems in the prior art, the invention provides an optimization design method and system for an arch bridge with a suspender under a moving load, which can realize the comprehensive optimization of the bearing capacity and stability of the bridge by considering the influence of the moving load in the design process of the arch bridge with the suspender, give consideration to the main arch strength safety coefficient and the stability safety coefficient of the bridge, solve a better bridge-forming suspender force, enable the design result to be closer to the actual stability condition of the bridge, and avoid the unreasonable design problem that the main arch stability safety coefficient is far lower than the strength safety coefficient; meanwhile, the method avoids the realization difficulty of influence line analysis and large required time consumption, can adaptively change the optimization speed according to the load effect, and considers the balance of the optimization effect and the optimization speed.

In order to achieve the purpose, the invention provides the following technical scheme:

an optimized design method of a suspender arch bridge under a mobile load comprises the following components: the optimization design method comprises the following steps:

s1, according to the statistical data of the structure size of the built arch bridge, combining the span arrangement of the built arch bridge and a bridge deck local calculation model, drawing up the size of each component, sequentially numbering the suspender one by one along the bridge direction as 1,2,3, … and J, wherein J is a natural number, and establishing a one-time bridge finite element model;

s2, adopting truss units as the hanger rods, adopting beam units as the main arch, the main beam, the pier column and the foundation, considering all the dead loads to carry out full-bridge linear elastic static force analysis, and defining the design safety factor [ K ] of the main arch]And a main beam deflection limit value, and as a constraint condition, on the premise of only considering the structural strength of the arch bridge, a group of crane rod forces of the bridge are solved and used as an initial optimization value, and the group of crane rod forces are expressed by vectors as follows: t is⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T_J ⁽⁰⁾]；

S3, applying a moving load to the main arch, and finding out a test for enabling the stability of the main arch to be stable based on the stability safety coefficient of the main archCalculating the fixed loading position of uniform force Q and the fixed loading position of concentrated force P in the worst moving load, and loading Q and P according to the fixed loading positions to form the immovable working condition LC of the moving load which enables the stability of the main arch to be checked and calculated to be worst_b(ii) a Similarly, a moving load is applied to the main arch, a fixed loading position for uniformly distributing force Q in the moving load and a fixed loading position for concentrating force P in the moving load when the main arch strength is most unfavorable to be checked are found out based on the strength safety coefficient of the main arch, and Q and P are loaded according to the fixed loading positions to form a moving load immotilization working condition LC (inductance capacitance) which enables the main arch strength to be most unfavorable to be checked_s；

S4, changing the hanger rods into cable units, taking the bridge-forming hanger rod force of each hanger rod as an independent variable, optimizing through iterative calculation to maximize the smaller value of the main arch strength safety coefficient and the main arch stability safety coefficient, and converging to obtain the optimal bridge-forming hanger rod force T after i rounds of iteration⁽ⁱ⁾And corresponding main arch stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾The stress calculation in each round of optimization process adopts nonlinear finite element calculation, and i is more than or equal to 0;

s5, recording the force T of the bridge boom⁽ⁱ⁾Bridging hanging rod force T for comprehensively optimizing main arch strength and stability^*At T^*And applying a moving load according to a conventional influence line mode, determining the final size of the suspender, the reinforcement and beam distribution design of each component and the design of the bridge auxiliary facilities according to the full-bridge internal force state and a conventional structure design method under the bridge design load combination, setting the pre-camber according to the finite element deformation result to smooth the bridge floor, and finishing the step to obtain the optimized arched bridge design with the suspender.

The structural form applicable to the optimal design method comprises a rigid-girder flexible arch bridge and a rigid-arch flexible girder bridge, and in the step S1, the size of the main girder can be basically determined at the beginning no matter whether the rigid-girder flexible arch bridge or the rigid-arch flexible girder bridge is adopted: the main arch mainly plays a role in improving the rigidity of a main beam and is mainly used for railway bridges, the section size of the main beam is generally determined by the constant load of the main beam and the stress at the construction stage, and only the main beam reinforcement and the beam arrangement are slightly influenced by the main arch; the latter adopts the first arch and the second girder construction, the main girder mainly plays the role of a bridge deck system and transmits force to the suspender, the section size of the main girder is generally determined by local loading analysis of the concentrated force of the moving load, and the design of the main girder is basically not influenced by the main arch. The structural size of the main arch can be drawn up by referring to the statistical data of the built 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 statistical data of the built bridge and the self weight of the upper structure of the bridge and combining the constant live load proportion. The sectional area of the suspender is small relative to the main arch and the main beam, so that although the force of the suspender has great influence on the stress of the bridge, the size of the section of the suspender has little influence on the stress of the bridge, and the size of the section of the final suspender can be finally determined after the optimized calculation of the force of the suspender is completed.

Establishing a finite element model through step S1, calculating an optimized initial value of the bridge forming boom force through step S2, applying a moving load and forming an unmovable working condition of the moving load through step S3, performing iterative optimization on the bridge forming boom force on the basis of calculating a main arch strength safety coefficient and a stability safety coefficient through step S4, recording the optimal bridge forming boom force through step S5, and completing structural design; step S3 realizes the immobilization of the moving load, namely, the uniform distribution force Q and the concentrated force P of the moving load are loaded according to fixed positions, so that the moving load can be included in each iterative optimization of step S4 to carry out nonlinear static force calculation and nonlinear buckling calculation; the optimization process of the step S4 takes the influence of the moving load into account, so that better bridge-forming boom force than the prior art can be obtained, and the obtained boom force can improve the smaller value of the main arch strength and the stability safety coefficient by more than 20%; the optimization target of the step S4 takes the strength safety factor and the stability safety factor of the main arch of the bridge into consideration, and the comprehensive optimization of the strength and the stability safety performance during the design of the arch bridge with the suspender is realized; and step S5, recording the optimal bridge forming suspender force, and completing the design of other bridge members according to the optimal bridge forming suspender force and a conventional method, thereby obtaining a reasonable bridge forming state of the arch bridge with the suspender, wherein the stability safety coefficient and the strength safety coefficient of the main arch are close to each other under the influence of the moving load.

In the preferred embodiment of the present invention, after the above step S4 is performed, the structure of the main arch is optimized according to the following steps:

s41, under the structure of the current main arch, if min (K)_s ⁽ⁱ⁾,K_b ⁽ⁱ⁾)>[K]Then go to S5; otherwise, taking the main arch structure of the last optimization process and the corresponding T⁽ⁱ⁾Go to S5;

s42, if min (K)_s ⁽ⁱ⁾,K_b ⁽ⁱ⁾)-[K]>[△_K]Weakening the main arch structure by reducing the main arch section profile size or the main arch section plate thickness, and then turning to S3, a_KOptimizing 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 smaller value of the main arch strength and the stability safety factor is greatly improved, and at the moment, the design safety factor [ K ] may be more margin, so the structure of the main arch can be further optimized through the steps S41-S42, the structure of the main arch is weakened on the premise of meeting the design safety factor, and the construction cost is saved by combining the optimization steps S3-S4.

In a preferred embodiment of the present invention, the above step S3 forms the moving load immobility condition LC that makes the main arch stability check most unfavorable_bThe method comprises the following specific steps:

s301, judging whether the main arch structure changes compared with the last 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 a working condition LC is formed for the first time under the current main arch structure_bIf yes, turning to S304, otherwise turning to S311;

s304, aiming at a primary bridge forming model of the arch bridge to be built, modifying a cable unit into a truss unit, applying all bridge design loads except the moving load, numbering the main beam nodes as 1,2,3, … and N one by one along the bridge direction, and performing full-bridge linear elastic static calculation to obtain a main arch stability safety coefficient K_b ⁽⁰⁾；

S305, generating M groups of boom forces in the range of the bearing capacity of the boom by adopting a Monte Carlo simulation method, and enabling a boom force circulation variable M to be 1 and a main beam node circulation variable n to be 1, wherein M and n are more than or equal to 1;

s306, modifying the finite element model lifting rod force into the value of the M group of lifting rod forces, and if the main arch first-order line elastic buckling non-out-of-plane instability exists, arranging N at the node of the nth main beam_vUnit loads which are symmetrical or asymmetrical along the central line of the section and respectively establish loading conditions, N_vDesigning the number of lanes; if the first-order line elastic buckling of the main arch is out-of-plane instability, arranging N on one side of the section center line at the nth main beam node_vRespectively establishing loading working conditions for unit loads, wherein the unit loads are arranged at minimum intervals in the transverse bridge direction according to the standard requirement;

s307, calculating the elastic buckling of the full bridge wire according to the ratio of 1-N_vThe minimum value of the combined calculation results of the working conditions is used for obtaining the main arch stability safety coefficient K_b ^(m,n)Let K be_△b ^(m,n)＝K_b ^(m,n)-K_b ⁽⁰⁾，K_△b ^(m,n)Stabilizing the mth row and nth column elements of the positive and negative effect matrix for the moving load; by K_△b ^(m,n)Positive and negative judgment of moving load stabilizes positive and negative effect, the jib force is taken the mth group and the moving load is loaded at the nth girder node, when the moving load plays a role in improving the stability of the bridge, K_△b ^(m,n)For positive, i.e. positive effect, K when the moving load has a reducing effect on the stability of the bridge_△b ^(m,n)Is negative, i.e. negative effect;

s308, if N is equal to N +1, if N is greater than N, then m is equal to m +1, go to S309; otherwise, turning to S306;

s309, if M is larger than M, turning to S310, otherwise, turning to S306;

s310, obtaining a moving load stable positive and negative effect matrix K with M rows multiplied by N columns from S306 to S309_△bTo K, pair_△bAfter the row-by-row average value is obtained, the row vector S of the stable influence degree is obtained_b1，S_b1Reflecting the degree of strengthening or weakening the stability of the bridge when the moving load is loaded on each girder node under different suspender force levels; will K_△bCounting the number of positive value elements in each row and dividing the number by M to obtain a stability influence significance row vector S_b2，S_b2Horizontal moving load adding for reflecting different boom forcesThe probability of reinforcing or weakening the stability of the bridge when the bridge is loaded on each girder node; s. the_b1And S_b2Stable sensitive line matrix S composed of 2 rows by N columns_b；

S311, extracting S_bThe first row in each column is less than 0 and the second row is less than the set significance level α_bLoading the uniform force Q in the moving load on all the main beam nodes corresponding to the extracted row, and loading the concentrated force P in the moving load on the main beam node with the minimum first row value in the extracted row, namely obtaining the moving load working condition LC with the worst main arch stability_b。

The steps S301 to S311 can realize the immobility of the moving load based on the stable sensitive line matrix, namely, the uniform distribution force Q and the concentrated force P of the moving load are loaded according to the fixed position according to the negative effect condition of the moving load on the stability of the main arch, and the immobility working condition LC of the moving load, which makes the main arch stability check most unfavorable, is formed_bIn the process, the Monte Carlo simulation is combined with the significance test to ensure that LC is formed under different suspender force levels_bReliability of, LC formed_bThe force of each suspender can still be used for loading when being greatly changed in the optimization process of the arch bridge; form LC_bThen, the moving load does not need to be considered according to influence line loading, and the problem that in the prior art, because influence line analysis cannot be carried out simultaneously with buckling analysis or nonlinear static calculation, moving load is abandoned to be considered in optimization iteration of the suspender force is solved, so that compared with the prior art, the invention can obtain better bridge-forming suspender force, thereby providing higher bridge safety performance and further reducing the bridge engineering cost; in addition, LC is formed_bAnd then, the time consumption required by influence line analysis is greatly 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 positive and negative effects of the lane at the same main beam node in S306 to S309 are different, the working condition LC is modified_bIf the node of the main beam has negative effect and is less than the set significance test level alpha_bAll lanes of the vehicle are movingLoading the uniform distribution force Q or the concentration force P to obtain the modified working condition LC_b。

LC obtained in step S301 to S311_bModified operating conditions LC_bThe loading can be carried out by considering the difference of the positive and negative effects of the stability of each lane at the same main beam node, although part of the calculation workload is increased, the modified working condition LC_bThe resulting negative effect of main arch stabilization is more accurate, thereby further enhancing the boom force optimization effect in step S4.

In a preferred embodiment of the present invention, the above step S3 forms the immobile condition LC of the moving load that makes the main arch strength check most unfavorable_sThe method comprises the following specific steps:

s321, judging whether the main arch structure changes compared with the last optimization process, if so, turning to S322, and if not, turning to S323;

s322, modifying the main arch unit and the section parameters in the model, and then turning to S324;

s323, judging whether a working condition LC is formed for the first time under the current main arch structure_sIf yes, go to S324, otherwise go to S330;

s324, aiming at the primary bridge forming model of the arch bridge to be built, modifying the cable units into truss units, applying all bridge design loads except the moving load, numbering the main beam nodes as 1,2,3, … and N one by one along the bridge direction, and performing full-bridge linear elastic static calculation to obtain a main arch strength safety coefficient K_s ⁽⁰⁾；

S325, generating M groups of boom forces in the range of the bearing capacity of the boom by adopting a Monte Carlo simulation method, and enabling a boom force circulation variable M to be 1 and a main beam node circulation variable n to be 1;

s326, modifying the finite element model lifting rod force into the value of the mth group in the M groups of lifting rod forces, and arranging N at the nth main beam node_vUnit loads which are symmetrical or asymmetrical along the central line of the section and respectively establish loading conditions, N_vIn order to design the number of lanes, then performing elastic static calculation of the whole bridge line according to the ratio of 1-N_vThe minimum value of the combined working condition calculation results is used for obtaining the main arch strength safety coefficient K_s ^(m,n)Let K_△s ^(m,n)＝K_s ^(m,n)-K_s ⁽⁰⁾；K_△s ^(m,n)For moving the m row and n column elements of the load intensity positive and negative effect matrix, pass K_△b ^(m,n)Positive and negative judgment of moving load strength positive and negative effect, the lifting rod force is the mth group and the moving load is loaded on the nth main beam node, and when the moving load plays a role in improving the bearing capacity of the bridge, K_△s ^(m,n)For positive, i.e. positive effect, K when the moving load has a decreasing effect on the bridge load-bearing capacity_△s ^(m,n)Is negative, i.e. negative effect;

s327, if N is equal to N +1, if N > N, then m is equal to m +1, go to S328; otherwise, go to S326;

s328, if M is greater than M, turning to S329, otherwise, turning to S326;

s329, obtaining a matrix K of M rows by N columns of positive and negative effect of the moving load strength from S326 to S328_△sTo K for_△sAfter the column-by-column average value is obtained, the strength influence degree row vector S is obtained_s1，S_s1Reflecting the degree of strengthening or weakening the bearing capacity of the bridge when the moving load is loaded on each node under different suspender force levels; will K_△sCounting the number of positive value elements in each row and dividing the positive value elements by M to obtain a strength influence significance row vector S_s2，S_s2Reflecting the probability of strengthening or weakening the bearing capacity of the bridge when the moving load is loaded on each node under different suspender force levels; s. the_s1And S_s2Forming a matrix S of 2 rows by N columns of intensity sensitive lines_s；

S330, extracting S_sThe first row in each column is less than 0 and the second row is less than the set significance level α_sLoading the uniform distribution force Q in the moving load on all nodes corresponding to the extracted row, and loading the concentrated force P in the moving load on the node with the minimum first row value in the extracted row, namely obtaining the unmoved working condition LC of the moving load which makes the main arch strength check calculation most unfavorable_s。

The steps S321 to S330 can realize immobility of the moving load based on the strength sensitive line matrix, and form the working condition LC of immobility of the moving load which makes the main arch strength check calculation most unfavorable_sIn the process of (1), by means of a Monte cardThe combination of Rou simulation and significance test ensures LC formation under different boom force levels_sReliability of, LC formed_sWhen the force of each suspender is greatly changed in the optimization process of the arch bridge, the suspender can still be used for loading; form LC_bThen, the moving load does not need to be considered according to influence line loading, and the problem that in the prior art, because influence line analysis cannot be carried out simultaneously with buckling analysis or nonlinear static calculation, moving load is abandoned to be considered in optimization iteration of the suspender force is solved, so that compared with the prior art, the invention can obtain better bridge-forming suspender force, thereby providing higher bridge safety performance and further reducing the bridge engineering cost; in addition, LC is formed_sAnd then, the time consumption required by influence line analysis is greatly 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 positive and negative effects of the strength of each lane at the same main beam node in S326-S328 are different, the LC is modified_bWorking condition, and enabling the node of the main beam to have negative effect which is smaller than the set significance test level alpha_sAll lanes of the system are loaded with uniform force Q or concentrated force P of the moving load to obtain the modified working condition LC_s。

Compared with LC obtained in steps S321 to S330_sModified operating conditions LC_sThe loading can be carried out by considering the difference of positive and negative effects of the strength of each lane at the same main beam node, although part of calculation workload is increased, the modified working condition LC_bThe resulting negative effect of the main arch strength is more accurate, thereby further enhancing the boom force optimization effect in step S4.

In a preferred embodiment of the present invention, the step S4 of iteratively optimizing the boom force includes the following specific steps:

s401, when a vector X consisting of N suspender forces, f (X) represents that each suspender force of the arch bridge takes a value according to the vector X, a main arch strength safety coefficient K obtained by full-bridge nonlinear finite element calculation is obtained_sAnd main arch stability safety factor K_bThe lower value of the (f), (X) is calculated by using a rope as a finite element model suspenderA unit; force T of crane rod for pressing bridge⁽⁰⁾Calculated f (T)⁽⁰⁾) Wherein, T⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T_J ⁽⁰⁾](ii) a Let the cyclic variable j equal to 1;

s402, mixing T⁽⁰⁾The value of the j-th element in (a) increases by unit force, i.e. T⁽⁰⁾Is changed into T_j ⁽⁰⁾Calculating f (T)_j ⁽⁰⁾) (ii) a If f (T)_j ⁽⁰⁾)-f(T⁽⁰⁾)>0, the first j element of the boom force optimization direction vector d is d (j) equal to 1, otherwise d (j) is equal to-1;

s403, if j<J, if J is J +1, go to S402; otherwise, let D_J×JForming a boom force optimization direction diagonal matrix D_J×JThe matrix reflects the main arch K after the force of only a single suspender is increased_sAnd K_bThe smaller value of the two is a positive effect of lifting or a negative effect of reduction, and the smaller value can be used for determining whether the optimization direction of each subsequent lifting rod force is preferentially increased or preferentially decreased, and then the step S404 is executed;

s404, taking T⁽⁰⁾As an initial value for optimization, the convergence accuracy ε of the boom fluctuation amount is set to be not less than 0 and δ of the boom fluctuation amount>Epsilon, the acceleration coefficient alpha of the change of the suspender force is more than or equal to 1, and the deceleration coefficient beta of the change of the suspender force belongs to (0, 1); let H_1×JFor recording the positive or negative effect of the variable after the change of the force of each boom, relative to the main arch K_sAnd K_bThe smaller value of the two has a positive effect when the lifting action is performed, and has a negative effect when the lifting action is not performed, and the initial value of the lifting action is H_1×J＝[0,0,0,...,0](ii) a The outer circulation variable i of the boom force optimization is equal to 0, the inner circulation variable j is equal to 1, and the intermediate variable F of the boom force^(j)＝T⁽ⁱ⁾；

S405, order E^(j)D (J,1: J); if F (F)^(j)+δE^(j))>f(T⁽ⁱ⁾) If h (j) is 1, go to S406, otherwise go to S406 directly;

s406, if F (F)^(j)+δE^(j))>f(F^(j)) Then order F^(j+1)＝F^(j)+δE^(j)Go to S407; otherwise, let F^(j+1)＝F^(j)Go to S407;

s407, if J < J, making J equal to J +1, and going to S405; otherwise, go to S408;

s408, if each suspender force is according to the vector F^(j+1)During value taking, if the conventional design index and the mechanical property of the main beam meet the design requirement, S409 is switched; otherwise, go directly to S412;

s409, if F (F)^(j+1))>f(T⁽ⁱ⁾) Go to S410; otherwise, go directly to S412;

s410, if sum (h) is J, the respective boom forces are described according to D_J×JThe main arches are all subjected to positive effects after being changed according to respective positive effect directions, namely, the nonlinear effect of the bridge is not strong at the moment, so that the force change quantity delta of the lifting rod is increased to accelerate convergence, namely, delta is made to be alpha delta, and then S411 is turned; otherwise, part of the boom force is stated according to D_J×JThe change according to its positive effect direction has produced the negative effect to the main arch, namely the bridge nonlinear effect is obvious at this moment, so does not increase the boom force variation delta any more, but directly shift to S411;

s411, order T⁽ⁱ⁺¹⁾＝F^(j+1)(ii) a Let j equal 1, H_1×J＝[0,0,0,...,0]，F^(j)＝T⁽ⁱ⁺¹⁾(ii) a i +1, turning to S405;

s412, if delta>E, changing delta to beta delta, and reducing the force variation delta of the lifting rod to perform fine optimization; let j equal 1, H_1×J＝[0,0,0,...,0]，F^(j)＝T⁽ⁱ⁾，T⁽ⁱ⁺¹⁾＝T⁽ⁱ⁾Turning to S405 when i is i + 1; otherwise, the convergence precision of the variation amount of the suspender force is achieved, the optimization of the suspender force is ended, and T⁽ⁱ⁾Namely the bridge-forming hoisting rod force which enables the strength and the stability of the main arch to be comprehensively optimal.

By adopting the steps S401-S412, the arch bridge suspender force variable speed iterative optimization based on suspender force effect guidance and strength, stability and comprehensive optimization can be realized, the iterative optimization method has rapid optimization convergence speed at the stage of weak bridge nonlinear effect, has fine optimization precision at the stage of strong bridge nonlinear effect, and considers the efficiency and precision of large-scale suspender force parameter optimization calculation, which is a variable speed optimization characteristic that the existing optimization algorithm does not have in suspender force optimization iteration; in addition, the optimization process of the algorithm gives consideration to the comprehensive optimization of the strength and stability of the bridge, the problem that the stability safety coefficient is lower than the strength safety coefficient and is not economical when a rigid-beam flexible arch bridge is designed in the prior art is solved, and the stability safety coefficient is not lower than the strength safety coefficient by adopting the algorithm, so that 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 safety factor K is calculated each time_bThe method comprises the following steps:

s421, judging whether the main arch structure changes compared with the last optimization process, if so, turning to S422, and if not, turning to S423;

s422, modifying the main arch unit and the section parameters in the model, and then turning to S424;

s423, judging whether buckling calculation is carried out for the first time under the current main arch structure, if so, turning to S424, and if not, turning to S429;

s424, aiming at a primary bridging finite element model of the proposed arch bridge, a cable unit is modified into a truss unit, and the position of a main arch is determined according to an arch axis LS without initial defects₀Modeling, 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, if the first-order buckling of the main arch is out-of-plane instability, turning to S426; otherwise, turning to S427;

s426, initial defect amplitude delta of main arch line shape under static load₁Is composed of

L is the main arch calculation span, and the initial defect linear LS of the main arch₁Amplifying the linear shape corresponding to the first-order buckling mode to delta according to the amplitude value₁The resulting line shape; then, the moving load driving line is distributed on one side of the central line of the main beam according to the minimum transverse bridge direction interval allowed by the specification, namely, the moving load is distributed according to the offset load on one side, the moving load is loaded according to the influence line along the bridge direction, the full-bridge line elasticity static calculation is carried out, and the main beam under the moving load is obtainedInitial defect amplitude delta of the camber line₂，δ₂Initial defect linear LS for maximum lateral bridge displacement value of all nodes of main arch₂To move the load by delta₂The main arch transverse bridge is deformed in the longitudinal direction and then is in a linear shape;

s427, initial defect amplitude delta of main arch line shape under static load₁Is composed of

L_aThe axial line of the main arch is long,

initial defect line shape LS for stability factor of axial compression member₁Amplifying to delta according to amplitude for first-order buckling line shape₁The resulting line shape; then, the travelling line of the moving load is symmetrically distributed on two sides of the central line of the main beam along the transverse bridge direction, 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 initial defect amplitude value delta of the main arch line shape under the moving load is obtained₂，δ₂Is the maximum vertical displacement value of all nodes of the main arch, and the initial defect linear LS₂To move the load by delta₂The main arch is vertically deformed and then is linear;

s428, changing the coordinates of the main arch node into a comprehensive initial defect linear LS (least squares) which is the LS₁And LS₂The boom is changed into a cable unit, and the moving load is fixed on the working condition LC according to the moving load in the step S3_bLoading, and carrying out nonlinear buckling calculation to obtain a nonlinear buckling characteristic value, namely a stability safety coefficient K of the main arch_bAnd finishing the calculation of the stability safety coefficient.

In the above step S426, δ₁Get

The method is determined by combining a first-order buckling mode of a main arch, a conventional large-span steel structure stability theory and the stress characteristic of an axial compression component; the conventional long-span steel structure stabilization theory considers that the initial defect amplitude can be (1/300). L₀，L₀Calculating the span for the frame beam;considering that the mechanical effect of the main arch can hardly be exerted when the first-order buckling mode of the main arch is out-of-plane instability, the problem of instability of the frame beam with a span L can be considered, and the span L is calculated by 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 generates out-of-plane deformation, the L is calculated according to the calculated length coefficient of the axial compression component by referring to the stress characteristic theory of the axial compression component

The amplification is carried out, and the amplification is carried out,

the length-slenderness ratio and the end constraint conditions of the main arch can be determined by combining the current standard table look-up; in summary, the initial defect amplitude δ₁Get

The influence line loading on the moving load cannot be carried out when the buckling calculation is carried out, so that the influence line loading is different for delta₂The prior art is not considered in the stability calculation of various bridges; however, it is actually the case that the horizontal deformation of the main arch to one side due to the unbalanced load of the moving load occurs, and thus the prior art is not safe. The invention is based on the basic principle of stability problem, combines the mechanical property that the main arch inevitably generates horizontal displacement under the action of the lateral offset load of the moving load transverse bridge to one side, and safely obtains that the maximum lateral bridge displacement of the main arch under the moving load reaches delta₂The main arch transverse bridge is deformed to be linear and considered as an initial defect generated by the moving load. To sum up, δ is considered at the same time₁、δ₂Corresponding linear LS₁、LS₂As an initial defect, the nonlinear stability of the main arch can be more reliably analyzed.

In the above step S427, δ₁Get

The method is determined by combining a first-order buckling mode of a main arch, a conventional large-span steel structure stability theory and the stress characteristic of an axial compression component; conventional large-span steel structure stability theoryFor the initial defect amplitude, L (1/300) may be taken₀，L₀Calculating the span of the frame beam; considering that the first-order buckling mode of the main arch is unstable in a plane, the mechanical effect of the arch is fully exerted, and the first-order buckling mode in the plane is a mode of half-span arch downwarping and the other half-span arch upwarping, so that the main arch can be regarded as one span of (L)_a[ 2 ] instability problem of the frame Beam, L_aIs 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 generates out-of-plane deformation, and the bending moment of the main arch is smaller when the main arch is designed according to a reasonable arch axis, the theory of the stress characteristic of the reference axial compression component is (L)_aPer 2) calculated length factor of the member pressed against the shaft

The amplification is carried out, and the amplification is carried out,

The influence line loading on the moving load cannot be carried out when the buckling calculation is carried out, so that the influence line loading is different for delta₂The prior art does not take the determination into consideration in the calculation of the stability of various bridges; the horizontal deformation of the main arch caused by the shifting load unbalance loading to generate half-span downward deflection and the other half-span upward deflection can be actually happened, so the prior art is unsafe. The invention is based on the basic principle of stability, combines the mechanical property that the main arch inevitably generates horizontal displacement under the action of the load along the bridge to the half span, and safely obtains the maximum vertical displacement of the main arch which is obtained by analyzing the influence line of the load to delta₂The linear shape of the main arch after vertical deformation is considered as the initial defect generated by the moving load. To sum up, δ is considered at the same time₁、δ₂Corresponding linear LS₁、LS₂As an initial defect, the nonlinear stability of the main arch can be more reliably analyzed.

By adopting the steps S421 to S428, the initial defect of the moving load can be considered to calculate the stability safety coefficient of the arch bridge, the initial defect of the main arch can be determined by simultaneously 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 stability safety coefficient of the main arch is unsafe due to neglecting the moving load in the prior art is solved.

In the preferred embodiment of the present invention, in the step S4, the main arch strength safety factor K is calculated each time_sIn the meantime, the moving load is the moving load immobilizer condition LC in step S3_sLoading, K_sThe ratio of the section bearing capacity at the position where the main arch is stressed by the most unfavorable loading position to the least unfavorable internal force of the section.

Calculating the main arch strength safety coefficient K each time_sWorking condition LC of being immobilized according to moving load_sLoading, namely moving load does not need to be considered according to influence line loading, so that the problem that the moving load is abandoned and considered in the optimization iteration of the suspender force because influence line analysis cannot be carried out simultaneously with nonlinear static calculation in the prior art is solved; meanwhile, a large amount of time needed by influence line analysis is avoided, time cost is obviously saved in each optimization iteration, and time efficiency of large-scale optimization calculation is guaranteed.

An optimized design system of a suspender arch bridge under a mobile load adopts the optimized design method of the suspender arch bridge under the mobile load, and the optimized design system comprises a modeling module, a suspender force initial value calculating module, a mobile load loading module, an iterative optimization module and a structural design module;

the modeling module is used for drawing up the size of each component, establishing a primary bridging finite element model and outputting the result to the initial value calculating module of the boom force; the initial value module of the boom force is used for calculating the boom force of the finished bridge in S2, the moving load loading module is used for calculating the fixed loading positions of the uniform distribution force Q and the concentrated force P in the moving load when the main arch stability is tested to be the worst, the fixed loading positions of the uniform distribution force Q and the concentrated force P in the moving load when the main arch strength is tested to be the worst, and outputting the unmovable working condition of the moving load, the iterative optimization module is used for calculating the optimal boom force T of the finished bridge⁽ⁱ⁾And corresponding main arch stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾The structural design module is used for determining the size of a suspender, the reinforcement and beam distribution design of each component and the design of auxiliary facilities of the bridge according to the main arch strength and the stable and comprehensive optimal bridge-forming suspender force.

Through the optimization design system, each step of the optimization design method can be realized according to each module, a finite element model of the finished bridge is established through a modeling module, an initial value of the suspender force is obtained through a module for obtaining the initial value of the suspender force, the immobilized working condition of the mobile load is obtained through a mobile load loading module, the optimal finished bridge suspender force is obtained through an iteration optimization module, the final design is completed through a structural design module, the comprehensive optimization of the strength and the stable safety performance during the design of the arched bridge with the suspender can be realized through the output and execution steps of each module, and the optimization design is finally completed.

Compared with the prior art, the invention has the following beneficial effects:

1. the optimization design method comprises the steps of establishing a finite element model through step S1, obtaining an optimized initial value of the force of the bridge crane through step S2, applying a moving load and forming an immobilized working condition of the moving load through step S3, carrying out iterative optimization on the force of the bridge crane on the basis of calculating the strength safety factor and the stability safety factor of a main arch through step S4, recording the optimal force of the bridge crane through step S5, and completing structural design; step S3 realizes immobilization of the moving load, namely uniform distribution force Q and concentrated force P of the moving load are loaded according to fixed positions, so that the moving load can be included in each iterative optimization of step S4 to carry out nonlinear static calculation and nonlinear buckling calculation; the optimization process of the step S4 takes the influence of the moving load into account, so that better bridge-forming boom force than the prior art can be obtained, and the obtained boom force can improve the smaller value of the main arch strength and the stability safety coefficient by more than 20%; the optimization target of the step S4 takes the strength safety factor and the stability safety factor of the main arch of the bridge into consideration, and the comprehensive optimization of the strength and the stability safety performance during the design of the arch bridge with the suspender is realized; and step S5, recording the optimal bridge forming suspender force, and completing the design of other bridge members according to the optimal bridge forming suspender force and a conventional method, thereby obtaining a reasonable bridge forming state of the arch bridge with the suspender, wherein the stability safety coefficient and the strength safety coefficient of the main arch are close to each other under the influence of the moving load.

2. By adopting the method of the invention, the step S3, the immobility of the moving load can be realized based on the stable and strength sensitive line matrix, and the working condition LC of immobility of the moving load which makes the main arch stability and strength check calculation most unfavorable is formed_bAnd LC_sIn the process, the formation of LC under different suspender force levels is ensured by Monte Carlo simulation and combined with significance test_bAnd LC_sReliability of, LC formed_bWhen the force of each suspender is greatly changed in the optimization process of the arch bridge, the suspender can still be used for loading; form LC_bAnd LC_sThen, the moving load does not need to be considered according to influence line loading, the problem that the influence line analysis cannot be simultaneously carried out with buckling analysis or nonlinear static calculation in the prior art, and the moving load is discarded and considered in optimization iteration of the suspender force is solved, and compared with the prior art, better bridge forming suspender force can be obtained, so that higher bridge safety performance is provided, and the bridge engineering cost can be further reduced; in addition, LC is formed_bAnd LC_sAnd then, the time consumption required by influence line analysis is greatly avoided, the time cost is obviously saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.

3. By adopting the method of the invention, step S4, the arch bridge suspender force variable speed optimization based on suspender force effect guidance and strength and stable comprehensive optimization can be realized, the variable speed optimization method has rapid optimization convergence speed at the stage of weak bridge nonlinear effect, has fine optimization precision at the stage of strong bridge nonlinear effect, and considers the efficiency and precision of large-scale suspender force parameter optimization calculation, which is a variable speed optimization characteristic that the existing optimization algorithm does not have in the suspender force optimization process; in addition, the optimization process of the algorithm gives consideration to the comprehensive optimization of the strength and stability of the bridge, the problem that the stability safety factor of the rigid-beam flexible arch bridge is far lower than the strength safety factor when the rigid-beam flexible arch bridge is designed in the prior art is solved, and the stability safety factor is not lower than the strength safety factor when the algorithm is adopted for design, so that the mechanical property of the material is fully exerted, and the material strength waste caused by the stability problem is avoided.

4. By adopting the method of the invention, the step S4, the initial defect of the moving load can be considered to calculate the stability safety coefficient of the arch bridge, the influence of the static load and the moving load can be considered simultaneously in the calculation process to determine the initial defect of the main arch, the nonlinear stability of the main arch can be analyzed more practically, and the problem of unsafe situation caused by neglecting the moving load when the stability safety coefficient of the main arch is calculated in the prior art is avoided.

5. The optimization design method has clear flow and is easy to realize by programming, and because the total degree of freedom of the beam unit and cable unit models is less, the large-scale design parameter optimization of the arch bridge with the suspender by combining the nonlinear finite element analysis is still feasible, and the optimization convergence precision can be flexibly determined according to the computational power resources of computer hardware of a design party; when the computational resources are high, the high-requirement optimization convergence precision can be set, so that the high-performance computational resources can be fully exerted, the optimal design parameters can be obtained, when the computational resources are low, the requirement on the optimization convergence precision can be properly reduced, and the design parameters can be optimized as far as possible at reasonable time cost; therefore, the method has stronger universality.

6. By adopting the optimized design method, under the same construction cost, compared with the prior art, the arch bridge with the suspender designed by the invention has higher bridge safety performance, 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; compared with the prior art, the arched bridge with the suspender designed by the invention has lower construction cost under the same safety performance, can generally realize the amplitude reduction of the comprehensive construction cost of the main arch and the suspender by more than 8 percent, and can save the construction cost from dozens of ten thousand yuan to hundreds of thousand yuan for the common arched bridge with the suspender and the span of 100-300 m; considering that the time spent on the optimization calculation of the invention is only increased by days compared with the prior art, and the time cost of days is less than the construction period of the whole project for years, the economic benefit brought by the construction cost saved after the optimization calculation is considerable, and the method of the invention is very worthy of the optimization design of the arched bridge with the suspender.

7. According to the optimized design system, a finite element model of a finished bridge is established through a modeling module, an initial value of boom force optimization is obtained through a boom force obtaining module, the immobilized working condition of a moving load is obtained through a loading module, the optimal finished bridge boom force is obtained through an iteration optimization module, the final design is completed through a structural design module, the output and the execution of each module are carried out according to an optimized design method, all the steps of the optimized design method are coordinately and uniformly executed according to a strict programmed flow, the comprehensive optimization of strength and stable safety performance during the design of the arched bridge with the boom can be realized, the optimized design is finally completed, the optimized design efficiency of the arched bridge with the boom is improved, and the manual operation time is saved.

Drawings

FIG. 1 is a schematic view of the major components of a boom arch bridge of the present invention;

FIG. 2 is a general step diagram of the present invention;

FIG. 3 shows working conditions LC formed after a moving load is immobilized based on a stable sensitive line matrix in embodiment 1 of the present invention_bA flow chart of the implementation of (1);

FIG. 4 is a finite element model diagram of a soft arch bridge with a bottom-supported rigid beam according to embodiment 1 of the present invention;

FIG. 5 shows the unmoved moving load condition LC that minimizes the main arch stability verification in example 1 of the present invention_bA front view of the loading diagram;

FIG. 6 shows the unmoved moving load condition LC that minimizes the main arch stability verification in example 1 of the present invention_bA top view of the loading diagram;

FIG. 7 shows working conditions LC formed after immobilization of moving loads based on the intensity-sensitive line matrix in embodiment 2 of the present invention_sA flow chart of the implementation of (1);

FIG. 8 shows the unmoving condition LC of the moving load for minimizing the main arch strength verification in embodiment 2 of the present invention_sA front view of the loading diagram;

FIG. 9 shows the unmoving condition LC of the moving load for minimizing the main arch strength verification in embodiment 2 of the present invention_sTop view of loading diagram；

Fig. 10 is an implementation flowchart of the calculation of the arch bridge stability safety factor in consideration of the initial defect of the moving load in embodiment 3 of the present invention;

FIG. 11 is a finite element model diagram of a through rigid-arch flexible girder bridge according to embodiment 3 of the present invention;

fig. 12 is a first-order buckling modal diagram of a bridge according to embodiment 3 of the present invention;

FIG. 13 is a line LS of primary defect lines of the main arch in example 3 of the present invention₂A front view of;

FIG. 14 is a front view of a main arch integrated initial defect line shape LS in embodiment 3 of the present invention;

FIG. 15 shows the unmoving condition LC of the moving load for minimizing the main arch stability verification in embodiment 3 of the present invention_bA front view of the loading diagram;

FIG. 16 is a diagram showing the general steps in embodiment 4 of the present invention;

FIG. 17 is a finite element model diagram of a half-through rigid-girder flexible arch bridge according to embodiment 4 of the present invention;

fig. 18 is a first-order buckling modal diagram of a bridge according to embodiment 4 of the present invention;

FIG. 19 shows the unmoving condition LC of the moving load for minimizing the main arch stability verification in embodiment 4 of the present invention_bA front view of the loading diagram;

FIG. 20 shows the unmoving condition LC of the moving load for minimizing the main arch stability verification in example 4 of the present invention_bA top view of the loading diagram;

FIG. 21 shows the unmoving condition LC of the moving load for minimizing the main arch strength verification in example 4 of the present invention_sA front view of the loading diagram;

FIG. 22 shows the unmoving condition LC of the moving load for minimizing the main arch strength verification in example 4 of the present invention_sA top view of the loading diagram;

FIG. 23 is a top view of the main arch integrated initial defect line shape LS in example 4 of the present invention;

fig. 24 is a flowchart illustrating an implementation of iterative optimization of arch bridge boom force shift based on boom force effect guidance and strength, stability, and comprehensive optimization in embodiment 5 of the present invention;

FIG. 25 is a diagram illustrating a convergence process of an iterative optimization calculation of the force of the boom for a middle bridge in embodiment 5 of the present invention;

FIG. 26 is a schematic view of an optimum design system for a suspension rod arch bridge under a moving load in embodiment 6 of the present invention;

the labels in the figure are: 1-main beam, 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 be understood that the scope of the above-described subject matter is not limited to the following examples, and any techniques implemented based on the disclosure of the present invention are within the scope of the present invention.

Example 1

Referring to fig. 3 to 4, in the present embodiment, a proposed through-put rigid-girder flexible arch bridge (with a boom arch bridge) with a certain span arrangement of (90+180+90) m is taken as an example, and the boom arch bridge includes components: the main arch 2, the main beam 1, the suspender 3, the pier stud 4 and the foundation 5 provide an optimization design method of the arch bridge with the suspender under the moving load, and elaborate the process of carrying out the immobility of the moving load based on the stable sensitive line matrix in the optimization design process of the bridge.

Referring to fig. 2,3 to 6, the optimal design method includes the following steps:

s1, according to the statistical data of the structure size of the built arch bridge, combining the span arrangement of the built arch bridge and a bridge deck local calculation model, drawing up the size of each component, sequentially numbering 1,2,3, … and J from one bridge to the next by a suspender 3, and establishing a primary bridge formation finite element model;

specifically, the main arch 2 of the bridge is a concrete-filled steel tube arch, the structural dimension of the initial main arch 2 and the structural dimensions 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 once-forming bridge model is established and is shown in figure 4; the hanger rods 3 are numbered as 1,2,3, … and J sequentially one by one along the bridge direction; j ═ 18;

s2, using a truss unit as a suspender 3, using a beam unit as a main arch 2, a main beam 1, a pier column 4 and a foundation 5, considering all dead loads to perform full-bridge linear elastic static force analysis, and defining the main arch 2Design factor of safety [ K ]]And the deflection limit value of the main beam 1, and as a constraint condition, on the premise of only considering the structural strength of the arch bridge, a group of crane rod forces of the bridge are solved and used as an initial optimization value, and the group of crane rod forces are expressed by vectors as follows: t is⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T_J ⁽⁰⁾]；

In particular, the design safety factor [ K ] of the main arch 2]1.2, the deflection limit value of the main beam 1 is selected according to the standard requirement, and the finished bridge hanging rod force T is obtained according to the rigid hanging rod method in the prior art⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T₁₈ ⁽⁰⁾]＝[1160,1386,1177,2005,1594,2451,1930,1347,2123,2123,1347,1930,2451,1594,2005,1177,1386,1160]Unit of KN, T⁽⁰⁾I.e. as a subsequent initial value for boom force optimization.

S3, applying a moving load to the main arch 2, finding out a fixed loading position of uniform force Q and a fixed loading position of concentrated force P in the moving load when the stability of the main arch 2 is checked to be the worst based on the stability safety coefficient of the main arch 2, and loading Q and P according to the fixed loading positions to form a moving load immobility working condition LC (inductance capacitance) which enables the stability of the main arch 2 to be checked to be the worst_b(ii) a Similarly, a moving load is applied to the main arch 2, a fixed loading position of uniform force Q and a fixed loading position of concentrated force P in the moving load when the main arch 2 is subjected to strength checking calculation to be the most unfavorable are found out based on the strength safety factor of the main arch 2, and Q and P are loaded according to the fixed loading positions to form a moving load immobility working condition LC (liquid Crystal Circuit) which enables the main arch 2 to be subjected to strength checking calculation to be the most unfavorable_s；

Specifically, the moving load immobilization is to load the uniform distribution force Q and the concentrated force P of the moving load according to fixed positions, the arch bridge has 2 lanes, on the 2 lanes, the action range 6 of the uniform distribution force Q and the action point 7 of the concentrated force P are as shown in fig. 6, each lane is 360m long, and the action point 7 of the concentrated force P is located at the corresponding main beam node at the center of each lane; the stationary behavior LC of the moving load that makes the stability verification of the main arch 2 most unfavorable is formed in the above step S3_bThe specific implementation process of (1) is performed according to the following steps S301 to S312:

s301, judging whether the structure of the main arch 2 changes compared with the last optimization process, if so, turning to S302, and if not, turning to S303;

s302, modifying a main arch 2 unit and section parameters in the model, and then turning to S304;

specifically, in the present embodiment, the structure of the main arch 2 is not optimized, and therefore, the operation goes directly to S303.

S303, judging whether a working condition LC is formed for the first time under the current main arch 2 structure_bIf yes, then go to S304, otherwise go to S311;

specifically, the present embodiment forms the operating condition LC for the first time_bTherefore, the process goes to S304.

S304, aiming at a primary bridge forming model of the arch bridge to be built, cable units are modified into truss units, all bridge design loads except moving loads are applied, the nodes of the main beam 1 are numbered as 1,2,3, … and N one by one along the bridge direction, full-bridge linear elasticity static calculation is carried out, and stability safety factors K of the main arch 2 are obtained_b ⁽⁰⁾；

Specifically, for a primary bridge forming model of an arch bridge to be built, a main beam 1 is uniformly divided into 360 units according to 1m sections, the number of nodes N of the main beam 1 is 361, the nodes of the main beam 1 are numbered 1,2,3, … and 361 one by one along the bridge direction, full-bridge linear elastic static calculation is carried out, and the strength safety coefficient K of a main arch 2 without considering the moving load is obtained_s ⁽⁰⁾1.6465, stable safety factor K_b ⁽⁰⁾＝1.5512。

S305, generating M groups of boom forces in the range of the bearing capacity of the boom 3 by adopting a Monte Carlo simulation method, and enabling a boom force circulation variable M to be 1, a main beam 1 node circulation variable n to be 1, wherein M and n are more than or equal to 1;

specifically, the present embodiment is a linear elastic finite element calculation, and the total degree of freedom of the beam unit and the truss unit is small, so the rate of single calculation is fast, and the number of the suspenders 3 and the requirement of design accuracy are comprehensively considered, so M is 10000.

S306, modifying the finite element model lifting rod force into the value of the M group of lifting rod forces, and if the main arch 2 is subjected to first-order linear elastic buckling and non-out-of-plane instability, arranging N at the node 1 of the nth main beam_vUnit loads which are symmetrical or asymmetrical along the central line of the section and are respectively establishedLoad condition, N_vDesigning the number of lanes; if the first-order line elastic buckling of the main arch 2 is out-of-plane instability, arranging N on one side of the section center line at the node of the nth main beam 1_vRespectively establishing loading working conditions for each unit load, wherein each unit load is arranged according to the minimum distance in the transverse bridge direction required by the specification;

s307, calculating the elastic buckling of the full bridge wire according to the ratio of 1-N_vThe minimum value of the combined working condition calculation results is used for obtaining the main arch 2 stability safety coefficient K_b ^(m,n)Let K_△b ^(m,n)＝K_b ^(m,n)-K_b ⁽⁰⁾，K_△b ^(m,n)Stabilizing the mth row and nth column elements of the positive and negative effect matrix for the moving load; by K_△b ^(m,n)Positive and negative judgment of moving load stabilizes positive and negative effect, the jib force is taken the mth group and the moving load is loaded at the nth main beam 1 node, when the moving load plays a role in improving the stability of the bridge, K_△b ^(m,n)Is positive, i.e. positive effect, K when the moving load has a reducing effect on the stability of the bridge_△b ^(m,n)Is negative, i.e. negative effect;

specifically, in this embodiment, the primary-line elastic buckling of the main arch 2 is out-of-plane instability, because the number of the designed lanes of the bridge is N _v2, the lane number is arranged to minimum interval at the unilateral horizontal bridge that requires according to the standard of cross-section central line, every time carry out full-bridge line elastic buckling to nth node under the m group jib power promptly and calculate before, arrange two unit loads at the node unilateral, the power of every load is 10KN, the direction is vertical downwards, each load corresponds 1 load operating mode alone, carry out full-bridge line elastic buckling and calculate the back, take the minimum after 1 ~ 2 lane unit load loading operating mode results combinations: namely, the value with the minimum stability safety factor of the main arch 2 under the three conditions of loading only on the 1 st lane, loading only on the 2 nd lane and loading both the 1 st lane and the 2 nd lane is taken as K_b ^(m,n)Then calculate K_△b ^(m,n)。

s309, if M is larger than M, turning to S310, otherwise, turning to S306;

s310, obtaining a moving load stable positive and negative effect matrix K with M rows and N columns from S306 to S309_△bTo K for_△bAfter the row-by-row average value is obtained, the row vector S of the stable influence degree is obtained_b1，S_b1Reflecting the degree of strengthening or weakening the stability of the bridge when the moving load is loaded on each main beam 1 node under different suspender force levels; will K_△bCounting the number of positive value elements in each row and dividing the positive value elements by M to obtain a row vector S with stable influence significance_b2，S_b2Reflecting the probability of strengthening or weakening the stability of the bridge when the moving load is loaded on each main beam 1 node under different suspender force levels; s. the_b1And S_b2Stable sensitive line matrix S composed of 2 rows by N columns_b；

Specifically, 10000 rows by 361 columns of moving load stable positive and negative effect matrix K can be obtained from S306 to S309_△bTo K for_△bObtaining a row vector S of stable influence degree after column-by-column averaging_b1To K for_△bCounting the number of positive value elements in each row and dividing the number by M to obtain a row vector S with stable influence significance_b2，S_b1And S_b2Stable sensitive line matrix S composed of 2 rows by N columns_bIf the result is too long, only S is listed_bRepresentative results of (a) are shown in table 1 below.

TABLE 1 Stable sensitive line matrix S_bResults of (1)

Node number	1	2	3	...	45	46	47	...	359	360	361
												S_s1	-6.56E-6	-1.31E-5	-1.97E-5	...	-1.16E-3	-1.18E-3	-1.16E-3	...	-1.97E-5	-1.31E-5	-6.56E-6
S_s2	0.000	0.000	0.000	...	0.000	0.000	0.000	...	0.000	0.000	0.000

S311, extracting S_bThe first row in each column is less than 0 and the second row is less than the set significance level α_bLoading the uniform force Q in the moving load on all the main beam 1 nodes corresponding to the extracted row, and loading the concentrated force P in the moving load on the main beam 1 node with the minimum first row value in the extracted row, namely obtaining the moving load working condition LC with the most unfavorable stability of the main arch 2_b；

Specifically, according to the design precision requirement and the general statistical experience in the industry, the significance test level is taken as alpha_bThe moving load immobility working condition LC which causes the main arch 2 to be most unfavorable for stable checking calculation is obtained when the moving load is 0.05_bDue to LC_bThere are many nodes loaded, and only representative results are listed in table 2 below.

TABLE 2 unmoving behavior LC of moving load that makes the main arch stability check the most unfavorable_bLoad node of

Node number

1

2

3

...

45

46

47

...

359

360

361

S_b1<0？

Is that

S_b2<α_b？

Is that

Add uniform force?

Is that

Add a concentration force?

Whether or not

Is that

Whether or not

S312, if the stable positive and negative effects of all lanes at the same main beam 1 node in the S306-S309 are different, modifying the working condition LC_bIf the node of the main beam 1 has negative effect and is less than the set significance test level alpha_bAll lanes are loaded with uniform force Q or concentrated force P of moving load to obtain modified working condition LC_b；

Specifically, when each main beam 1 node in S306 to S309 is loaded at different lanes, the negative effects of the lanes are the same, and therefore, the LC is not influenced_bFurther modification of the operating conditions, LC_bSee fig. 5-6 for details of the final loading diagram.

S4, changing the hanger rods 3 into cable units, taking the bridge-forming hanger rod force of each hanger rod 3 as an independent variable, optimizing through iterative calculation to maximize the smaller value of the main arch 2 strength safety coefficient and the main arch 2 stability safety coefficient, and converging to obtain the optimal bridge-forming hanger rod force T after i rounds of iteration⁽ⁱ⁾And corresponding main arch 2 stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾The stress calculation in each round of optimization process adopts nonlinear finite element calculation, and i is more than or equal to 0;

in particular, with the current main arch 2 configuration, when i is 0, i.e. when no jib force optimization iteration is performed, the main arch 2 strength safety factor K_s ⁽²³⁾1.5386, main arch 2 stability factor of safety K_b ⁽²³⁾1.2143; optimized by 23 rounds of i-23 to converge the optimal bridge forming hanger rod force T under the current main arch 2 construction⁽²³⁾，T⁽²³⁾＝[T₁ ⁽²³⁾,T₂ ⁽²³⁾,T₃ ⁽²³⁾,...,T₁₈ ⁽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 factor K at this time_s ⁽²³⁾1.4137, main arch 2 stability factor of safety K_b ⁽²³⁾＝1.4226。

In step S4, the main arch strength safety factor K is calculated each time_sIn the meantime, the moving load is the moving load immobilizer condition LC in step S3_sLoading, K_sThe ratio of the section bearing capacity at the loading position where the main arch is stressed most unfavorably to the section most unfavorably internal force is defined; calculating the main arch stability safety coefficient K each time_bIn the meantime, the moving load is the moving load immobilizer condition LC in step S3_bLoading, and then carrying out nonlinear buckling calculation to obtain a nonlinear buckling characteristic value, namely a stability safety coefficient K of the main arch_b。

S5, recording the force T of the bridge boom⁽ⁱ⁾Bridge-forming hoisting rod force T comprehensively optimizing strength and stability of main arch 2^*At T^*Applying a moving load according to a conventional influence line mode according to a bridgeDetermining the final size of a suspender 3, the reinforcement and beam distribution design of each component and the design of bridge auxiliary facilities by using a full-bridge internal force state and a conventional structure design method under the condition of load-measuring combination, setting the pre-camber according to a finite element deformation result to smooth the bridge deck, and finishing the steps to obtain the optimized arched bridge design with the suspender;

specifically, T in the above-described step S4⁽³⁰⁾Namely the bridging suspender force T which comprehensively optimizes the strength and stability of the main arch 2^*At T^*Determining the final size of the suspender 3, the reinforcement and beam design of various concrete members and bridge auxiliary facilities according to a conventional design method; the result of S4 analysis shows that after the method is adopted for optimization design, the safety coefficient after comprehensive consideration of the strength and the stability is improved to 1.4137 from 1.2143 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 realize immobility of the moving load based on the stable sensitive line matrix, that is, the uniform moving load force Q and the concentrated moving load force P are loaded at fixed positions according to the negative effect of the moving load on the stability of the main arch 2, and the immobility condition LC of the moving load is formed to make the stability check of the main arch 2 most unfavorable_bIn the process, the formation of LC under different suspender force levels is ensured by combining Monte Carlo simulation with significance test_bReliability of, LC formed_bThe force of each suspender can still be used for loading when being greatly changed in the optimization process of the arch bridge; form LC_bThen, the moving load does not need to be considered according to influence line loading, and the problem that in the prior art, because influence line analysis cannot be carried out simultaneously with buckling analysis or nonlinear static calculation, moving load is abandoned to be considered in optimization iteration of the suspender force is solved, so that compared with the prior art, the invention can obtain better bridge-forming suspender force, thereby providing higher bridge safety performance and further reducing the bridge engineering cost; in addition, LC is formed_bAnd then, the time consumption required by influence line analysis is greatly avoided, the time cost is obviously saved in each optimization iteration, and the time efficiency of large-scale optimization calculation is ensured.

Example 2

This embodiment adopts steps S1 to S5 of embodiment 1, except that: in this embodiment, a proposed through-put rigid-girder flexible arch bridge with span-diameter arrangement of (90+180+90) m in example 1 is taken as an example, and a process of performing immobile moving load based on a strength sensitive line matrix involved in the bridge optimization design process is described in detail.

Referring to fig. 2, 4, and 7 to 9, in step S3 of example 1, a moving load immobilizer condition LC is formed to minimize the verification of the main arch 2 strength_sThe specific implementation process of (3) is performed according to the following steps S321 to S331:

s321, judging whether the structure of the main arch 2 changes compared with the last optimization process, if so, turning to S322, and if not, turning to S323;

s322, modifying the main arch 2 unit and the section parameters in the model, and then turning to S324;

specifically, in the present embodiment, the structure of the main arch 2 is not optimized, and therefore, the operation is directly switched to S323.

S323, judging whether the working condition LC is formed for the first time under the current main arch 2 structure_sIf yes, go to S324, otherwise go to S330;

specifically, the embodiment is to form the working condition LC for the first time_sTherefore, go to S324.

S324, aiming at the one-time bridge forming model of the arch bridge to be built, cable units are modified into truss units, all bridge design loads except the moving load are applied, the nodes of the main beam 1 are numbered as 1,2,3, … and N one by one along the bridge direction, full-bridge linear elasticity static calculation is carried out, and the strength safety coefficient K of the main arch 2 is obtained_s ⁽⁰⁾；

Specifically, a primary bridge forming model of the arch bridge to be built is shown in fig. 4, a main beam 1 is uniformly divided into 360 units according to 1m sections, the number of nodes N of the main beam 1 is 361, the nodes of the main beam 1 are numbered as 1,2,3, … and 361 one by one along the bridge direction, full-bridge linear elastic static calculation is carried out, and a main arch 2 strength safety coefficient K without considering the moving load is obtained_s ⁽⁰⁾1.6465, stable safety factor K_b ⁽⁰⁾＝1.5512。

S325, generating M groups of boom forces in the range of the bearing capacity of the boom 3 by adopting a Monte Carlo simulation method, and enabling a boom force circulation variable M to be 1 and a main beam 1 node circulation variable n to be 1;

S326, modifying the finite element model lifting rod force into the value of the mth group in the M groups of lifting rod forces, and arranging N at the node of the nth main beam 1_vUnit loads which are symmetrical or asymmetrical along the central line of the section and respectively establish loading conditions, N_vIn order to design the number of lanes, then performing elastic static calculation of the whole bridge line according to the ratio of 1-N_vThe minimum value of the combined working condition calculation results is used for obtaining the strength safety coefficient K of the main arch 2_s ^(m,n)Let K_△s ^(m,n)＝K_s ^(m,n)-K_s ⁽⁰⁾；K_△s ^(m,n)For moving the m row and n column elements of the load intensity positive and negative effect matrix, pass K_△b ^(m,n)Positive and negative effect of moving load strength is judged, the lifting rod force is taken from the mth group, the moving load is loaded on the nth main beam 1 node, and when the moving load improves the bridge bearing capacity, K_△s ^(m,n)Is positive, i.e. positive effect, when the moving load has a decreasing effect on the bridge bearing capacity, K_△s ^(m,n)Is negative, i.e. negative effect;

specifically, the number of the designed lanes of the bridge of the embodiment is N _v2, the lane number is according to following cross-section central line symmetrical arrangement, before carrying out full-bridge line elasticity static calculation to nth node under the jib power of mth group promptly at every turn, arranges two along the symmetrical unit loads of node pair, the power of every load is 10KN, the direction is vertical downwards, each load corresponds 1 load operating mode alone, carries out full-bridge line elasticity static calculation back, takes the minimum after unit load loading operating mode result makes up on 1 ~ 2 lanes: namely, the value with the minimum safety factor of the strength of the main arch 2 under the three conditions of loading only on the 1 st lane, loading only on the 2 nd lane and loading both the 1 st lane and the 2 nd lane is taken as K_s ^(m,n)Then calculate K_△s ^(m,n)。

S327, if N is greater than N, then m is equal to m +1, and go to S328; otherwise, go to S326;

s328, if M is larger than M, turning to S329, otherwise, turning to S326;

s329, obtaining a matrix K of M rows by N columns of positive and negative effect of the moving load strength from S326 to S328_△sTo K for_△sAfter the column-by-column average value is obtained, the strength influence degree row vector S is obtained_s1，S_s1Reflecting the degree of strengthening or weakening the bearing capacity of the bridge when the moving load is loaded on each node under different suspender force levels; will K_△sCounting the number of positive value elements in each row and dividing the number by M to obtain a strength influence significance row vector S_s2，S_s2Reflecting the probability of strengthening or weakening the bearing capacity of the bridge when the moving load is loaded on each node under different suspender force levels; s_s1And S_s2Forming a matrix S of 2 rows by N columns of intensity sensitive lines_s；

Specifically, 10000 rows by 361 columns of positive and negative effect matrixes K of moving load intensity can be obtained from S326 to S328_△sTo K for_△sObtaining the strength influence degree row vector S after the column-by-column average value_s1To K for_△sCounting the number of positive value elements in each row and dividing the number by M to obtain an intensity influence significance row vector S_s2，S_s1And S_s2Forming a matrix S of 2 rows by N columns of intensity sensitive lines_sIf the result is too long, only S is listed_sRepresentative results are shown in table 3 below.

TABLE 3 intensity sensitive line matrix S_sResults of (1)

Node number	1	2	...	45	46	47	...	89	...	144	145	146	147
														S_s1	-4.86E-5	-9.72E-5	...	-2.10E-3	- 2.19E- 3	-2.10E- 3	...	- 9.72E -5	...	-9.72E-5	-4.86E-5	-4.91E-6	9.72E-5
S_s2	0.000	0.000	...	0.000	0.000	0.000	...	0.000	...	0.017	0.063	0.177	0.523

S330, extracting S_sThe first row in each column is less than 0 and the second row is less than the set significance level α_sLoading the uniform distribution force Q in the moving load on all nodes corresponding to the extracted row, and loading the concentrated force P in the moving load on the node with the minimum first row value in the extracted row, namely obtaining the unmoved working condition LC of the moving load which makes the main arch 2 with the worst intensity check calculation_s；

Specifically, according to the design accuracy requirement and the general statistical experience in the industry, the significance test level is taken as alpha_sThe moving load immobility working condition LC which makes the main arch 2 strength check calculation most unfavorable is obtained when the moving load is 0.05_sDue to LC_sThere are many nodes loaded, and only representative results are listed below in table 4.

TABLE 4 unmovable operating mode LC for making the main arch strength check calculation the most unfavorable_sLoad node of

Node number

1

2

...

45

46

47

...

89

...

144

145

146

147

S_s1<0？

Is that

Whether or not

S_s2<α_s？

Is that

Whether or not

Add uniform force?

Is that

Whether or not

Add a concentration force?

Whether or not

Is that

Whether or not

S331, if the positive and negative effects of the intensity of each lane at the same main beam 1 node in S326-S328 are different, modifying LC_bWorking condition, the node of the main beam 1 has negative effect and is smaller than the set significance test level alpha_sAll lanes are loaded with uniform force Q or concentrated force P of moving load to obtain modified working condition LC_sThe arch bridge comprises 2 lanes, on the 2 lanes, the action range 6 of the uniform distribution force Q and the action point 7 of the concentration force P are shown in fig. 9, the 1 st lane is 89m, the 2 nd lane is 144m, the 2 lanes in the above range are the action range 6 of the uniform distribution force Q, the corresponding main beam node of the action point 7 of the concentration force P at the center of the 1 st lane, the action point of the P on the 2 nd lane and the action point of the P on the 1 st lane are the same in action position in the bridge length direction;

in particular, it is found in S326-S328 that the negative effects of nodes No. 90-145 are different when the nodes are loaded at different lanes, and therefore, the negative effects are different for the LC_s、LC_bThe working condition is further modified, all nodes with negative effects in each lane and less than the set significance test level are loaded, so that the forward loading ranges of the 2 lanes are different, the method is also embodied in that the space effect of the bridge can be considered for analysis, and LC_sSee fig. 8-9 for details of the final loading diagram.

In this embodiment, the steps S321 to S330 can be adoptedThe immobilized moving load is carried out based on the intensity sensitive line matrix, and the immobilized moving load working condition LC which makes the intensity check calculation of the main arch 2 most unfavorable is formed_sIn the process, the Monte Carlo simulation is combined with the significance test to ensure that LC is formed under different suspender force levels_sReliability of, LC formed_sWhen the force of each suspender is greatly changed in the optimization process of the arch bridge, the suspender can still be used for loading; form LC_bThen, the moving load does not need to be considered according to influence line loading, and the problem that in the prior art, because influence line analysis cannot be carried out simultaneously with buckling analysis or nonlinear static calculation, moving load is abandoned to be considered in optimization iteration of the suspender force is solved, so that compared with the prior art, the invention can obtain better bridge-forming suspender force, thereby providing higher bridge safety performance and further reducing the bridge engineering cost; in addition, LC is formed_sAnd then, the time consumption required by influence line analysis is greatly 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 the present embodiment, a member with a boom arch bridge, which is the same as that in embodiments 1 to 2, is adopted, referring to fig. 10 to 11, and in the present embodiment, a proposed through-put rigid-arch flexible girder bridge with a span of 1 × 100m is taken as an example, a method for optimally designing an arch bridge with a boom under a moving load is provided, and a process of calculating a stable safety coefficient of the arch bridge in consideration of an initial defect of the moving load involved in the bridge optimal design process is described in detail.

Referring to fig. 2, 10 to 15, the optimal design method includes the following steps:

specifically, the main arch 2 of the bridge is a pure steel structure arch, the structural dimension of the initial main arch 2 and the structural dimensions of other main components are determined according to the prior art, wherein the section of the main arch 2 is the section of a rectangular steel box, and a primary bridge forming model is established and is shown in figure 11; the hanger rods 3 are numbered as 1,2,3, … and J sequentially one by one along the bridge direction; j15;

s2, the hanger rods 3 adopt truss units, the main arches 2, the main beams 1, the pier columns 4 and the foundation 5 all adopt beam units, full-bridge linear elastic static force analysis is carried out by considering all dead loads, and the design safety factor [ K ] of the main arches 2 is defined]And the deflection limit value of the main beam 1, and as a constraint condition, on the premise of only considering the structural strength of the arch bridge, a group of crane rod forces of the bridge are solved and used as an initial optimization value, and the group of crane rod forces are expressed by vectors as follows: t is⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T_J ⁽⁰⁾]；

In particular, the design safety factor [ K ] of the main arch 2]1.2, the deflection limit value of the main beam 1 is selected according to the standard requirement, and the finished bridge hanging rod force T is obtained according to the rigid hanging rod method in the prior art⁽⁰⁾，T⁽⁰⁾I.e. as a subsequent initial value for boom force optimization.

Specifically, the so-called moving load immobilizer is to load the uniform moving load force Q and the concentrated moving load force P at fixed positions, and the moving load immobility condition LC that makes the main arch 2 stability check least favorable is formed in the above step S3_bThe specific implementation process of (3) can refer to steps S301 to S311 of embodiment 1 to form a moving load immobility working condition LC that makes the main arch 2 stability check calculation most unfavorable_sReference is made to steps S321 to S330 in embodiment 2.

S4 change the hanger rod 3 into the rope sheetThe force of each suspension rod 3 for forming the bridge is taken as an independent variable, optimization is carried out through iterative calculation, the value of the smaller value of the strength safety coefficient of the main arch 2 and the stability safety coefficient of the main arch 2 is maximized, and the optimal force T for forming the bridge suspension rod is obtained after i-round iteration and convergence⁽ⁱ⁾And corresponding main arch 2 stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾The stress calculation in each round of optimization process adopts nonlinear finite element calculation, i is more than or equal to 0, and S5 is turned after i rounds of iteration are finished;

specifically, under the current main arch 2 configuration, the optimal bridging boom force T under the current main arch 2 configuration is converged after i-19 rounds of optimization⁽¹⁹⁾And simultaneously obtaining the strength safety coefficient K of the main arch 2 at the moment_s ⁽¹⁹⁾And main arch 2 stability safety factor K_b ⁽¹⁹⁾；

Specifically, in step S4 described above, the main arch 2 stability factor K is calculated every time the main arch 2 stability factor K is calculated_bThe method comprises the following steps:

s421, judging whether the structure of the main arch 2 changes compared with the last optimization process, if so, turning to S422, and if not, turning to S423;

s422, modifying the main arch 2 unit and the section parameters in the model, and then turning to S424;

specifically, in the present embodiment, the structure of the main arch 2 is not optimized, and therefore, the operation goes directly to S423.

S423, judging whether buckling calculation is carried out for the first time under the current main arch 2 structure, if so, turning to S424, and if not, turning to S429;

specifically, the present embodiment calculates the first buckling of the main arch 2, so S424 is performed.

S424, aiming at a primary bridging finite element model of the proposed arch bridge, a cable unit is modified into a truss unit, and the position of a main arch 2 is determined according to an arch axis LS without initial defects₀Modeling, 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, aiming at a primary bridge forming model of a proposed arch bridge, the applied bridge design load is the structure dead weight, the second-stage dead load, the integral temperature change and the cable structure tension.

S425, if the first-order buckling of the main arch 2 is out-of-plane instability, turning to S426; otherwise, turning to S427;

s426, initial defect amplitude delta of main arch 2 line shape under static load₁Is composed of

L is the calculated span of the main arch 2, and the initial defect linear LS of the main arch 2₁Amplifying the linear shape corresponding to the first-order buckling mode to delta according to the amplitude value₁The resulting line shape; then, a moving load driving line is distributed on one side of the central line of the main beam 1 according to the minimum transverse bridge direction interval allowed by the specification, namely, the moving load is distributed according to the offset load on one side, the moving load is loaded according to the influence line along the bridge direction, the full-bridge linear elasticity static calculation is carried out, and the linear initial defect amplitude delta of the main arch 2 under the moving load is obtained₂，δ₂Is the maximum transverse bridge displacement value of all nodes of the main arch 2, and the initial defect linear LS₂To move the load by delta₂The transverse bridge of the main arch 2 is deformed in a linear shape;

specifically, the first-order buckling mode of the present bridge is shown in fig. 12, which is an in-plane instability, and therefore turns to S427.

S427, initial defect amplitude delta of main arch 2 line shape under static load₁Is composed of

L_aIs the length of the 2-axis of the main arch,

initial defect line shape LS for stability factor of axial compression member₁Amplifying to delta according to amplitude for first-order buckling line shape₁The resulting line shape; then, the moving load driving lines are symmetrically distributed on two sides of the central line of the main beam 1 in the transverse bridge direction, the moving load is loaded along the bridge direction according to the influence line, full-bridge line elastic static calculation is carried out, and the linear initial defect amplitude delta of the main arch 2 under the moving load is obtained₂，δ₂Is the maximum vertical displacement value of all nodes of the main arch 2 and the initial defect linear LS₂To move the load by delta₂The main arch 2 is vertically deformed and then is linear;

specifically, the main arch 2 of the bridge has an axial length L_a104.94m, the stability factor is calculated according to the axial compression member fixed at both ends

Therefore, it is

Initial defect line shape LS₁Amplifying to delta according to amplitude for first-order buckling line shape₁The resulting line shape; then, the moving load driving lines are symmetrically distributed on two sides of the central line of the main beam 1 in the transverse bridge direction, the moving load is loaded along the bridge direction according to the influence line, full-bridge line elastic static calculation is carried out, the maximum vertical displacement value of all nodes of the main arch 2 under the moving load is obtained and is close to 1/4 span, and the linear initial defect amplitude delta of the main arch 2 is obtained₂0.051m, the initial defect delta generated by the moving load can be seen₂Size ratio of delta₁Is also a value which is not suitable for being ignored, initial defect line shape LS₂To move the load by delta₂The main arch 2 is vertically deformed and then is linear, as shown in figure 13;

in the above step S427, δ₁Get

The method is determined by combining the first-order buckling mode of the main arch 2, the conventional large-span steel structure stability theory and the stress characteristic of the axial compression component; the conventional long-span steel structure stabilization theory considers that the initial defect amplitude can be (1/300). L₀，L₀Calculating the span of the frame beam; considering that the first-order buckling mode of the main arch 2 is unstable in a plane, the mechanical effect of the arch is fully exerted, and the first-order buckling mode in the plane is a mode of half-span arch downwarping and the other half-span arch upwarping, so that the main arch can be regarded as one span of (L)_a[ 2 ] instability problem of the frame Beam, L_aIs 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 out-of-plane deformation occurs on the main arch 2, and the bending moment of the main arch 2 is smaller when the reasonable arch axis is designed, the theory of the stress characteristic of the reference axial compression component is (L)_aPer 2) calculated length factor of the member pressed against the shaft

The amplification is carried out, and the amplification is carried out,

the length-slenderness ratio and the end constraint conditions of the main arch 2 can be determined by combining the current standard table look-up; in summary, the initial defect amplitude δ₁Get

The influence line loading on the moving load cannot be carried out when the buckling calculation is carried out, so that the influence line loading is different for delta₂The determination of (1) is that the prior art does not take the stability calculation of various bridges into consideration; the horizontal deformation of the main arch 2 caused by the unbalanced load of the moving load in the half-span downward deflection and the other half-span upward deflection can actually happen, so the prior art is unsafe. The invention is based on the basic principle of stability, combines the mechanical property that the main arch 2 inevitably generates horizontal displacement under the action of the load along the bridge to the half span, and safely obtains the maximum vertical displacement of the main arch 2 which is obtained by analyzing the influence line of the moving load and reaches delta₂The main arch 2 is vertically deformed and then is linear, and the initial defect generated by the moving load is considered. To sum up, δ is considered at the same time₁、δ₂Corresponding linear LS₁、LS₂As an initial defect, the nonlinear stability of the main arch 2 can be more reliably analyzed.

S428, changing the node coordinates of the main arch 2 into a comprehensive initial defect linear LS, wherein the comprehensive initial defect linear LS of the main arch 2 is LS₁And LS₂The boom 3 is changed into a cable unit, and the moving load is immobilized on the working condition LC according to the moving load in step S3_bLoading, and carrying out nonlinear buckling calculation to obtain a nonlinear buckling characteristic value, namely a stability safety coefficient K of the main arch 2_b；

Specifically, the comprehensive initial defect linear LS of the bridge main arch 2 is obtained by linearly superposing the node coordinate values corresponding to LS1 and LS2, and the shape of the LS is shown in the attached figure 14; after the node coordinates of the main arch 2 of the bridge are changed into the linear LS with the comprehensive initial defects, the moving load which causes the main arch 2 to have the worst stabilityImmobilized operating mode LC_bSee fig. 15; performing nonlinear buckling calculation to obtain a nonlinear buckling characteristic value, namely the stable safety coefficient K of the main arch 2 calculated this time_bAnd finishing the calculation of the stable safety coefficient.

S5, recording the force T of the bridge boom⁽ⁱ⁾Bridge-forming hoisting rod force T for comprehensively optimizing strength and stability of main arch 2^*At T^*Applying a moving load according to a conventional influence line mode, determining the final size of the suspender 3, the reinforcement and beam arrangement design of each component and the design of bridge auxiliary facilities according to the full-bridge internal force state and a conventional structure design method under the bridge design load combination, and setting the pre-camber according to the finite element deformation result to smooth the bridge deck;

specifically, T in the above-described step S4⁽¹⁹⁾Namely the bridging suspender force T which comprehensively optimizes the strength and stability of the main arch 2^*At T^*And determining the size of the final suspender 3, the reinforcement and beam matching design of various concrete members and bridge auxiliary facilities according to a conventional design method, setting the pre-camber according to a finite element deformation result to smooth the bridge deck, and finishing the step to obtain the optimized arched bridge design with the suspender.

In this embodiment, the steps S421 to S428 may be adopted to calculate the arch bridge stability safety coefficient by considering the initial defect of the moving load, and the initial defect of the main arch 2 may be determined by considering the influence of the static load and the moving load simultaneously in the calculation process, so that the nonlinear stability of the main arch 2 may be more practically analyzed, and the problem of the prior art that the main arch 2 is unsafe due to neglecting the moving load when calculating the stability safety coefficient is avoided.

Example 4

In the present embodiment, the same members of the arch bridge with the boom as in embodiments 1 to 3 are adopted, and referring to fig. 16 to 17, the present embodiment takes a simulated through-put rigid-beam flexible arch bridge with a certain span arranged as (40+40+168+40+40) m as an example, and provides an optimal design method for the arch bridge with the boom under a moving load.

Referring to fig. 2, 16 to 23, the optimal design method includes the following steps:

s1, according to the statistical data of the structure size of the built arch bridge, combining the span arrangement of the built arch bridge and a bridge deck system local calculation model, drawing up the size of each component, sequentially numbering the suspender 3 as 1,2,3, … and J along the bridge direction one by one, and establishing a primary bridge finite element model;

specifically, the main arch 2 of the bridge is a steel structure arch, the structural dimension of the initial main arch 2 and the structural dimension of other main components are determined according to the prior art, wherein the section of the main arch 2 is the section of a rectangular steel box, the dimension is 3000mm in width, 2500mm in height and 32mm in thickness, and a once-forming bridge model is established and is shown in figure 17; the hanger rods 3 are numbered 1,2,3, … and J sequentially along the bridge direction; j is 25;

in step S1, for the rigid-girder flexible arch bridge, the size of the main girder 1 can be basically determined at the beginning: the bridge is constructed by adopting a first girder and a second arch, 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 reinforcing bars and the reinforcing bundles of the main girder 1 are slightly influenced by the main arch 2; the structural size of the main arch 2 can be drawn up by referring to the statistical data of the built bridge and the load concentration to be shared by the main arch 2, and the structural sizes of the pier stud 4 and the foundation 5 are determined by referring to the statistical data of the built bridge and the self weight of the upper structure of the bridge and combining the constant live load proportion; the sectional area of the suspender 3 is very small relative to the main arch 2 and the main beam 1, so that although the force of the suspender has a large influence on the stress of the bridge, the size of the section of the suspender 3 has little influence on the stress of the bridge, and the size of the section of the final suspender 3 can be finally determined after the optimized calculation of the force of the suspender is completed.

In particular, the design safety factor [ K ] of the main arch 2]1.2, the deflection limit value of the main beam 1 is taken according to the standard requirement and the prior artMethod for obtaining finished bridge boom force T by using rigid boom⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T₂₅ ⁽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]Unit of KN, T⁽⁰⁾I.e. as a subsequent initial value for boom force optimization.

S3, applying a moving load to the main arch 2, finding out a fixed loading position of uniform force Q and a fixed loading position of concentrated force P in the moving load when the stability of the main arch 2 is checked to be the worst based on the stability safety coefficient of the main arch 2, and loading Q and P according to the fixed loading positions to form a moving load immobility working condition LC (inductance capacitance) which enables the stability of the main arch 2 to be checked to be the worst_b(ii) a Similarly, a moving load is applied to the main arch 2, based on the strength safety coefficient of the main arch 2, a fixed loading position for uniformly distributing force Q in the moving load and a fixed loading position for concentrating force P when the main arch 2 is tested to be the worst in strength are found out, and Q and P are loaded according to the fixed loading positions to form a moving load immotilization working condition LC (liquid Crystal) which enables the main arch 2 to be tested to be the worst in strength_sThe arch bridge comprises 6 lanes, on the 6 lanes, the action range 6 of the uniform distribution force Q and the action point 7 of the concentration force P are shown in fig. 20, the action range of each lane in the length direction of the bridge is 328m, the 6 lanes in the range are the action range 6 of the uniform distribution force Q, and the action point 7 of the concentration force P is a corresponding main beam node at the center of each lane from the 1 st lane to the 5 th lane;

specifically, the so-called moving load immobilization is to load the uniform moving load force Q and the concentrated moving load force P at fixed positions, and the specific implementation process of step S3 can refer to embodiment 1 and embodiment 2; in this embodiment, the main beam 1 is uniformly divided into 328 units according to 1m segments, the number of the nodes of the main beam 1 is N equals to 329, and the nodes of the main beam 1 are numbered as 1,2,3, … and 329 one by one along the bridge direction; generating M groups of lifting rod forces in the range of the bearing capacity of the lifting rod 3 based on Monte Carlo simulation, wherein M is 10000; the bridge is arranged in cross section: 3.5m (sidewalk) +2.5m (non-motor lane) +0.5m (partition) +11.5m (motor lane) +4m (central partition) +11.5m (motor lane) +0.5m (partition) +2.5m (non-motor lane +3.5m (sidewalk) ═ 40 m), because the main arch 2 is a single-rib arch, it is determined that the main arch 2 is the most unfavorable for the calculation of strengthMoving load immobility working condition LC_sWhen the vehicle is running, the number of lanes is symmetrically arranged along the central line of the section; the first-order elastic buckling of the main arch 2 is calculated to be out-of-plane instability, as shown in figure 18, so that the immovable working condition LC of the moving load which causes the most unfavorable stability of the main arch 2 is determined_bWhen the number of lanes is arranged on one side of the central line of the section according to the minimum distance in the direction of the cross bridge required by the specification, and because the central division belt is wide and the main arch 2 and the suspender 3 play a role in division, the moving load of the other half bridge is not considered when the offset load lane is arranged, namely the automobile load, the non-motor vehicle load and the crowd load of the other half bridge are not considered; finally, LC was obtained in steps S301 to S311 of example 1_bFIGS. 19 to 20, and the LC obtained in accordance with steps S321 to S330 of example 2_sSee fig. 21-22 for loading diagrams.

S4, changing the hanger rods 3 into cable units, taking the bridge-forming hanger rod force of each hanger rod 3 as an independent variable, optimizing through iterative calculation to maximize the smaller value of the main arch 2 strength safety coefficient and the main arch 2 stability safety coefficient, and converging to obtain the optimal bridge-forming hanger rod force T after i rounds of iteration⁽ⁱ⁾And corresponding main arch 2 stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾Calculating the stress in each round of optimization process by adopting a nonlinear finite element, wherein i is more than or equal to 0, and then turning to S41;

specifically, the main arch strength safety factor K is calculated every time_sIn the meantime, the moving load is according to the moving load immobilizer condition LC in step S3_sLoading, K_sThe ratio of the section bearing capacity at the loading position where the main arch is stressed most unfavorably to the section most unfavorably internal force is defined; calculating the main arch stability safety coefficient K each time_bIn the meantime, the moving load is the moving load immobilizer condition LC in step S3_bLoading, and then carrying out nonlinear buckling calculation to obtain a nonlinear buckling characteristic value, namely a stability safety coefficient K of the main arch_b；

Specifically, under the initial main arch 2 configuration, the optimal bridging boom force T under the current main arch 2 configuration is converged after i-30 rounds of optimization⁽³⁰⁾，T⁽³⁰⁾＝[T₁ ⁽³⁰⁾,T₂ ⁽³⁰⁾,T₃ ⁽³⁰⁾,...,T₂₅ ⁽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 factor K at this time_s ⁽³⁰⁾1.4146, main arch 2 stability safety factor K_b ⁽³⁰⁾＝1.3977；

In addition, the main arch 2 stability factor K is calculated every time in step S4 described above_bThe specific implementation process is shown in steps S421 to S428 of embodiment 3; the first-order buckling mode of the bridge is shown in figure 18, the instability outside the plane is shown, the span L of the main arch 2 of the bridge is 168m, and the stability coefficient is calculated according to the axle pressing components fixed at the two ends

Therefore, it is

Initial defect line shape LS₁Amplifying to delta according to amplitude for first-order buckling line shape₁The resulting line shape; then, the moving load driving lines are symmetrically distributed on one side of the central line of the main beam 1 in the transverse bridge direction and are arranged according to the minimum distance of the transverse bridge direction required by the specification, and because the central separation belt is wide and the main arch 2 and the suspender 3 play a role in separation, the moving load of the other half bridge is not considered when the offset load lane is arranged, namely the automobile load, the non-motor vehicle load and the crowd load of the other half bridge are not considered; loading the moving load along the bridge direction according to the influence line, performing full-bridge linear elastic static calculation to obtain that the maximum vertical displacement value of all nodes of the main arch 2 under the moving load is close to 1/4 span, and the linear initial defect amplitude delta of the main arch 2₂0.193m, the initial defect delta produced by the moving load is visible₂Size ratio of delta₁Also a value which is not easy to ignore, initial defect line shape LS₂To move the load by delta₂The main arch 2 is vertically deformed and then is linear; the comprehensive initial defect linear LS of the bridge main arch 2 is obtained by linearly superposing the node coordinate values corresponding to LS1 and LS2, and the shape of the LS is shown in figure 23.

After the optimization process in step S4 is completed, the structure 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]If yes, go to S5; otherwise, taking the main arch 2 structure of the last optimization process and the corresponding T⁽ⁱ⁾Go to S5;

s42, if min (K)_s ⁽ⁱ⁾,K_b ⁽ⁱ⁾)-[K]>[△_K]The construction of the main arch 2 is weakened by reducing the sectional profile size of the main arch 2 or the thickness of the sectional plate material of the main arch 2, and then the steps S3, Delta_KConstructing an optimized convergence precision for a preset main arch 2; otherwise, go to S5.

Specifically, after design precision requirements and optimized calculation cost are comprehensively considered, the Delta is taken_K0.05; min (K) under initial Main Arch 2 configuration_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 has higher margin than the actual design requirement, and the main arch 2 structure can be further weakened to save the engineering cost, so the steps S3-S42 are repeated to save and optimize the main arch 2 structure, the optimization process of the main arch 2 structure is as the following table 5, because the width and the height of the section of the main arch 2 of the steel box are generally determined by the arrangement of the transverse and longitudinal sections of the bridge, the plate thickness of the main arch 2 is only changed when the main arch 2 structure is optimized; as can be seen from Table 1, the thickness of the steel plate for bridges is not 27mm or 26mm, and the thickness of the steel plate at the time of the new structure lower hanger bar force is 25mm or less according to the specification of the steel plate thickness at the time of the 4 th optimization of the present invention, which is min (K) at this time_s ⁽ⁱ⁾,K_b ⁽ⁱ⁾) Has not satisfied [ K]Greater than 1.2, so the last structure of the main arch 2 is taken as the optimized final value, the corresponding cross-sectional dimension is 3000mm wide, 2500mm high, 28mm thick, the corresponding bridge-forming crane rod force T⁽ⁱ⁾＝T⁽³⁰⁾＝[T₁ ⁽³⁰⁾,T₂ ⁽³⁰⁾,T₃ ⁽³⁰⁾,...,T₂₅ ⁽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, min (K) at this time_s ⁽ⁱ⁾,K_b ⁽ⁱ⁾)＝1.2295>[K]1.2, and not exceeding [ K]Too many, the design values of the main arch 2 structure and the bridge crane rod force corresponding to the optimized final value are economic and reasonableIn (1).

Table 5 this example is part of the detailed process for bridge boom force optimization calculation

S5, recording the force T of the bridge boom⁽ⁱ⁾Bridge-forming hoisting rod force T for comprehensively optimizing strength and stability of main arch 2^*At T^*Applying a moving load according to a conventional influence line mode, determining the final size of the suspender 3, the reinforcement and beam distribution design of each component and the design of bridge auxiliary facilities according to the full-bridge internal force state and a conventional structure design method under the bridge design load combination, setting the pre-camber according to the finite element deformation result to smooth the bridge deck, and finishing the step to obtain the optimized arched bridge design with the suspender;

specifically, T in the above-described step S42⁽³⁰⁾Namely the bridge-forming hoisting rod force T which comprehensively optimizes the strength and stability of the main arch 2^*At T^*After the final dimensions of the suspender 3, the reinforcement and beam design of various concrete members and the auxiliary facilities of the bridge are determined according to the conventional design method, the following can be known by combining the table 5:

1) considering that the weight of the weld bead is generally calculated as 1.5% of the weight of the steel structure, the steel amount 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)/1000/1000.5 ═ 28.05t/m, and the final structure obtained according to the present invention is (1+0.015) ((3000 × 28 + 2+2500 × 28 × 2)/1000/1000 × 78.5 ═ 24.54t/m, it can be seen that the steel amount of the main arch 2 is reduced by 12.5% compared with the prior art, while the total steel amount of the hanger rod 3 obtained according to the present invention is increased by about 4.2% from 680.7t 709.3t, and the material amount of the main beam 1 is not changed substantially;

2) the length of the arch axial line of the steel structure part of the main arch 2 is 159.9m, the budget unit price of the steel material of the main arch 2 is 1.1 ten thousand yuan/t, the budget unit price of the steel material of the suspender 3 is generally 1.6 times of that of the steel material 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 28.05 159.9, 1.1+680.7, 1.1, 6 is 6132 ten thousand yuan, the total construction cost of the main arch 2 and the suspender 3 obtained according to the invention is 24.54 159.9, 1.1+709.3, 1.1, 6 is 5565 ten thousand yuan, so that the construction cost can be saved by 567 ten thousand yuan after the optimized design of the suspender bridge is carried out according to the method of the invention, and the comprehensive construction cost of the main arch 2 and the suspender 3 can be saved by 9.25%;

3) the change situation of the engineering quantity and the change situation of the safety coefficient of each component of the bridge are comprehensively considered, the bridge engineering cost designed by the method is obviously reduced compared with the prior art, and the safety coefficient after the comprehensive consideration of the strength and the stability is also improved compared with the prior art.

Example 5

This embodiment adopts steps S1 to S5 of embodiment 4, except that: the present embodiment takes a proposed through-put rigid-girder flexible arch bridge with span-diameter arrangement of (40+40+168+40+40) m in example 4 as an example, and details an arch bridge boom force variable speed iterative optimization process based on optimal stability synthesis and boom force effect guidance and strength involved in the bridge optimization design process.

Referring to fig. 2, 17, 24 to 25, the concrete implementation process of the iterative optimization calculation of the bridge boom force in step S4 of the above embodiment 4 is performed according to the following steps S401 to S412:

s401, when a vector X consisting of N suspender forces, f (X) represents that each suspender force of the arch bridge takes a value according to the vector X, carrying out full-bridge nonlinear finite element calculation to obtain a main arch 2 strength safety coefficient K_sAnd main arch 2 stability safety factor K_bThe lower value of f (X), the finite element model suspender 3 adopts a cable unit when calculating f (X); force T of crane rod for pressing bridge⁽⁰⁾Calculated f (T)⁽⁰⁾) Wherein, T⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T_J ⁽⁰⁾](ii) a Let the cyclic variable j equal to 1;

specifically, the hanger rods 3 are numbered 1,2,3, …, J being 25 sequentially one by one along the bridge direction; for convenience of description and distinction, the numbers of the suspension rods 3 in the embodiment are sequentially represented by circled numbers as follows: (ii) …; obtaining a finished bridge boom force T according to a rigid boom method of the prior art⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T₂₅ ⁽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]Unit KN, the safety coefficient K of the strength of the main arch 2 is calculated by the full-bridge nonlinear finite element at the moment_s1.5523, main arch 2 stability factor of safety K_b1.1211, so f (T)⁽⁰⁾)＝1.1211。

S402, mixing T⁽⁰⁾The value of the j-th element in (a) increases by unit force, i.e. T⁽⁰⁾Is changed into T_j ⁽⁰⁾Calculating f (T)_j ⁽⁰⁾) (ii) a If f (T)_j ⁽⁰⁾)-f(T⁽⁰⁾)>0, the j element of the boom force optimization direction vector d is d (j) equal to 1, otherwise d (j) is equal to-1;

s403, if j<J, if J is J +1, go to S402; otherwise, let D_J×JForming a boom force optimization direction diagonal matrix D_J×JThe matrix reflects K for the main arch 2 after only a single boom force is increased_sAnd K_bThe smaller value of the two is a positive effect of lifting or a negative effect of reduction, and the smaller value can be used for determining whether the optimization direction of each subsequent lifting rod force is preferentially increased or preferentially decreased, and then the step S404 is executed;

in particular, the boom force optimized direction diagonal matrix D_J×JThe values of the elements are shown in the following table 6, wherein the cell value of 1 in the table represents K of the main arch 2 after the force of a single lifting rod is increased_sAnd K_bThe smaller value between is a positive effect to act as a boost, and a-1 indicates a negative effect to act as a reduction.

TABLE 6 boom force optimization direction diagonal matrix D_J×JValue of each element in

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, using T⁽⁰⁾As an initial value for optimization, the convergence accuracy ε of the boom fluctuation amount is set to be not less than 0 and δ of the boom fluctuation amount>Epsilon, the acceleration coefficient alpha of the change of the suspender force is more than or equal to 1, and the deceleration coefficient beta of the change of the suspender force belongs to (0, 1); let H_1×JTo record eachThe variable having a positive or negative effect on the main arch 2 after the change of the boom force compared to the variable before the change_sAnd K_bThe smaller value of the two has a positive effect when the lifting action is performed, and has a negative effect when the lifting action is not performed, and the initial value of the lifting action is H_1×J＝[0,0,0,...,0](ii) a The outer circulation variable i of the boom force optimization is equal to 0, the inner circulation variable j is equal to 1, and the intermediate variable F of the boom force^(j)＝T⁽ⁱ⁾；

Specifically, in the present embodiment, after the design accuracy requirement and the optimization calculation cost are considered in combination, the convergence accuracy ∈ of the boom force fluctuation amount is set to 1KN, the initial value δ of the boom force fluctuation amount is set to 4KN, the acceleration coefficient α of the boom force change is set to 2.0, and the deceleration coefficient β of the boom force change is set to 0.5.

s408, if each suspender force is according to the vector F^(j+1)During value taking, if the conventional design index and the mechanical property of the main beam 1 meet the design requirement, S409 is switched; otherwise, go directly to S412;

s409, if F (F)^(j+1))>f(T⁽ⁱ⁾) Go to S410; otherwise, go directly to S412;

s410, if sum (h) is J, the boom forces are described as D_J×JAfter changing according to the respective positive effect directions, 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 force change quantity delta of the lifting rod is increased to accelerate convergence, namely delta is made to be alpha delta, and then S411 is turned; otherwise, part of the boom force is stated according to D_J×JThe change according to its positive effect direction has produced the negative effect to the main arch 2, namely the bridge nonlinear effect is obvious at this moment, so does not increase the boom force variation delta any more, but directly shift to S411;

s412, if delta>E, changing delta to beta delta, and reducing the change delta of the lifting rod force to perform fine optimization; let j equal 1, H_1×J＝[0,0,0,...,0]，F^(j)＝T⁽ⁱ⁾，T⁽ⁱ⁺¹⁾＝T⁽ⁱ⁾Turning to S405 when i is i + 1; otherwise, the convergence precision of the variation amount of the suspender force is achieved, the optimization of the suspender force is ended, and T⁽ⁱ⁾Namely the optimal force of the forming bridge crane rod for the stability and the synthesis of the strength of the main arch 2 and the main arch 2;

specifically, in the steps S405 to S412, one internal cycle is completed every time the internal cycle variable j is increased from 1 to 13, and the boom force variation δ is a constant value in each iteration of each internal cycle; the outer loop iteration is performed once every time the outer loop variable i is increased by 1, and the delta can be changed in a self-adaptive manner along with the iteration process and the optimized convergence progress of the outer loop; the optimal calculation process of the bridge-forming lifting rod force of the embodiment is shown in tables 7-8 and FIG. 25, and only half-span lifting rod force is listed in the table 8 because the bridge is of a symmetrical structure; as can be seen from fig. 25, the optimized convergence rate is fast when i is 1 to 15, and then the convergence rate is slowed down when δ is continuously decreased to enter the fine optimization stage; when i is equal to 30, delta is equal to 1KN, convergence accuracy epsilon is achieved, the optimized calculation of the force of the formed bridge crane rod under the construction of the current main arch 2 is finished, and T is⁽³⁰⁾I.e. the bridging boom force T for comprehensively optimizing the strength and stability of the main arch 2⁽³⁰⁾＝[T₁ ⁽³⁰⁾,T₂ ⁽³⁰⁾,T₃ ⁽³⁰⁾,...,T₂₅ ⁽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 factor K at this time_s ⁽³⁰⁾1.4146, main arch 2 stability factor of safety K_b ⁽³⁰⁾1.3977, so f (T)⁽³⁰⁾) 1.3977, it can be seen that the safety factor of the bridge is improved to 1.3977 compared with 1.1211 in the prior art, the improvement range is 24.7%, compared with the prior art, after the comprehensive consideration of the strength and stability under the moving load is optimized, the invention has obvious improvement, if the actual design does not require the high safety factorThe main arch 2 configuration can be further weakened to save construction costs.

Table 7 the overall process of variation for optimized calculation of bridge boom force in this embodiment

Variable of extrinsic cycle i	f(T⁽ⁱ⁾)	Variation delta	Variable of extrinsic cycle i	f(T⁽ⁱ⁾)	Variation delta
						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 this example becomes part of the detailed process of the bridge boom force optimization calculation

In this embodiment, the step S401 to S412 are adopted to realize stable, comprehensive and optimal arch bridge suspender force variable speed iterative optimization based on suspender force effect guidance and strength, the iterative optimization method has a fast optimization convergence speed at a stage when the bridge nonlinear effect is not strong, has a fine optimization precision at a stage when the bridge nonlinear effect is strong, and considers efficiency and precision of large-scale suspender force parameter optimization calculation, which is a variable speed optimization feature that the existing optimization algorithm does not have in suspender force optimization iteration; in addition, the optimization process of the algorithm gives consideration to the comprehensive optimization of the strength and stability of the bridge, the problem that the stability safety coefficient is lower than the strength safety coefficient and is not economical when a rigid-beam flexible arch bridge is designed in the prior art is solved, and the stability safety coefficient is not lower than the strength safety coefficient by adopting the algorithm, so that 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 boom under a moving load, the optimal design system can apply the optimal design method for the arch bridge with the boom under the moving load, and the optimal design system can adopt the steps S1 to S5 in the embodiments 1 to 5 to carry out optimal design.

Referring to fig. 26, the optimization design system includes a modeling module, a boom force initial value calculating module, a moving 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 moving load loading module, the initial defect loading module, the iterative optimization module and the structural design module are respectively embedded in corresponding steps and calculation processes of the optimization design method, functions of the modules can be realized by module division of software, the storage module can adopt a hardware memory or a virtual software storage module, the input module can adopt an interface in the software or hardware such as a keyboard, the display module adopts hardware, the display module adopts a display or a display screen, the input module is used for a user to input data, and the storage module is used for storing data output by the modules, the display module is used for displaying the results of the 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 sizes of all components and establishing a primary bridging finite element model, the modeling module executes the step S1, the statistical data of the sizes of the built arch bridge structure, the sizes of all the components and the like are collected through the input module, and the result is output to the initial value calculating module of the suspender force; force of hanger rodThe value module executes step S2 for calculating the bridging boom force in step S2 and outputting the result to the moving load loading module and the initial defect loading module; the loading module executes the step S3, and is used for calculating the fixed loading positions of the uniform distribution force Q and the concentrated force P in the moving load when the main arch 2 is subjected to the stability checking calculation to the worst condition, calculating the fixed loading positions of the uniform distribution force Q and the concentrated force P in the moving load when the main arch 2 is subjected to the strength checking calculation to the worst condition, and outputting the unmoving working condition of the moving load to the iterative optimization module; the iterative optimization module for calculating the optimal bridging boom force T performs step S4⁽ⁱ⁾And corresponding main arch stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾And outputting the result to the structure design module; during the execution of the iterative optimization module, K is calculated each time_bAn initial defect loading module is called to correct the coordinates of the main arch nodes; and the step S5 is executed by a structural design module, and the structural design module is used for determining the size of the suspender 3, the reinforcement and distribution design of each component and the design of bridge affiliated facilities according to the strength of the main arch 2 and the optimal stable and comprehensive bridging suspender force. Through the optimization design system, each step of the optimization design method can be realized according to each module, a finite element model of a finished bridge is established through a modeling module, an initial value of the suspender force is obtained through a suspender force obtaining module, the immobility working condition of the moving load is obtained through a moving load loading module, the main arch stability safety coefficient can be accurately calculated through an initial defect loading module, the optimal force of the finished bridge suspender is obtained through an iteration optimization module, the final design is completed through a structural design module, the comprehensive optimization of the strength and the stable safety performance during the design of the arched bridge with the suspender can be realized through the output and execution steps of each module, and the optimization design is finally completed.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims

1. An optimized design method of a suspender arch bridge under moving load is characterized in that the suspender arch bridge comprises components: the design method comprises the following steps:

s1, according to the statistical data of the structure size of the built arch bridge, combining the span arrangement of the built arch bridge and a bridge deck local calculation model, drawing up the size of each component, sequentially numbering the suspenders 1,2,3, … and J one by one along the bridge direction, and establishing a primary bridge formation finite element model;

s2, adopting truss units as the hanger rods, adopting beam units as the main arch, the main beam, the pier column and the foundation, considering all the dead loads to carry out full-bridge linear elastic static force analysis, and defining the design safety factor [ K ] of the main arch]And a main beam deflection limit value, and as a constraint condition, on the premise of only considering the structural strength of the arch bridge, a group of crane rod forces of the bridge are solved and used as an initial optimization value, and the group of crane rod forces are expressed by vectors as follows: t is a unit of⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T_J ⁽⁰⁾]；

S3, applying a moving load to the main arch, based on the main arch stability safety coefficient, finding out the fixed loading position of uniform force Q and the fixed loading position of concentrated force P in the moving load when the main arch stability check is worst, and loading Q and P according to the fixed loading positions to form the moving load immobility working condition LC which makes the main arch stability check is worst_b(ii) a Similarly, a moving load is applied to the main arch, a fixed loading position of uniform force Q and a fixed loading position of concentrated force P in the moving load when the main arch strength inspection is most unfavorable are found out based on the main arch strength safety coefficient, and Q and P are loaded according to the fixed loading positions to form a moving load immobility working condition LC (liquid Crystal capacitor) which enables the main arch strength inspection to be most unfavorable_s；

S4, changing the hanger rods into cable units, taking the bridge-forming hanger rod force of each hanger rod as an independent variable, optimizing through iterative calculation to maximize the smaller value of the main arch strength safety coefficient and the main arch stability safety coefficient, and converging to obtain the optimal bridge-forming hanger rod force T after i rounds of iteration⁽ⁱ⁾And corresponding main arch stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾The stress calculation in each round of optimization process adopts nonlinear limitPerforming element calculation;

2. The method for optimally designing a boom arch bridge under moving load according to claim 1, wherein the construction of the main arch is optimized according to the following steps after the step S4 is executed each time:

3. The method of claim 1, wherein said step S3 is performed to form a moving load immobilization condition LC that minimizes the primary arch stability check_bThe method comprises the following specific steps:

S305, generating M groups of boom forces in a boom bearing capacity range by adopting a Monte Carlo simulation method, and enabling a boom force circulation variable M to be 1 and a main beam node circulation variable n to be 1;

s306, modifying the finite element model lifting rod force into the value of the M group of lifting rod forces, and if the main arch first-order line elastic buckling non-out-of-plane instability exists, arranging N at the node of the nth main beam_vUnit loads which are symmetrical or asymmetrical along the central line of the section and respectively establish loading conditions, N_vDesigning the number of lanes; if the first-order line elastic buckling of the main arch is out-of-plane instability, arranging N on one side of the section center line at the nth main beam node_vRespectively establishing loading working conditions for each unit load, wherein each unit load is arranged according to the minimum distance in the transverse bridge direction required by the specification;

s307, calculating the elastic buckling of the full bridge wire according to the ratio of 1-N_vThe minimum value of the combined calculation results of the working conditions is used for obtaining the main arch stability safety coefficient K_b ^(m,n)Let K_△b ^(m,n)＝K_b ^(m,n)-K_b ⁽⁰⁾，K_△b ^(m,n)Stabilizing the mth row and nth column elements of the positive and negative effect matrix for the moving load; by K_△b ^(m,n)Positive and negative judgment of moving load stabilizes positive and negative effect, and the jib power is got the mth group and is removed the load loading and at nth girder node, when removing the load and playing the improvement effect to bridge stability, K_△b ^(m,n)For positive, i.e. positive effect, K when the moving load has a reducing effect on the stability of the bridge_△b ^(m,n)Is negative, i.e., a negative effect;

s309, if M is larger than M, turning to S310, otherwise, turning to S306;

s310, obtaining a moving load stable positive and negative effect matrix K with M rows multiplied by N columns from S306 to S309_△bTo K for_△bAfter the column-by-column average value is calculated, a row vector S of the stable influence degree is obtained_b1，S_b1Reflecting the degree of strengthening or weakening the stability of the bridge when the moving load is loaded on each girder node under different suspender force levels; will K_△bCounting the number of positive value elements in each row and dividing the positive value elements by M to obtain a row vector S with stable influence significance_b2，S_b2Reflecting the probability of strengthening or weakening the stability of the bridge when the moving load is loaded on each main beam node under different suspender force levels; s_b1And S_b2Stable sensitive line matrix S composed of 2 rows by N columns_b；

4. The method for optimally designing the arch bridge with the suspender under the moving load as claimed in claim 3, wherein after the step S311 is completed, if the stable positive and negative effects of all lanes at the same main beam node in S306-S309 are different, the working condition LC is modified_bIf the node of the main beam has negative effect and is less than the set significance test level alpha_bAll lanes of the system are loaded with uniform force Q or concentrated force P of the moving load to obtain the modified working condition LC_b。

5. The method for optimally designing a arch bridge with a boom under a moving load according to claim 1, wherein the step S3 is performed to form a moving load immobility condition LC that minimizes the main arch strength check_sThe method comprises the following specific steps:

s326, modifying the finite element model lifting rod force into the value of the mth group in the M groups of lifting rod forces, and arranging N at the nth main beam node_vUnit loads which are symmetrical or asymmetrical along the central line of the section and respectively establish loading conditions, N_vIn order to design the number of lanes, then performing elastic static calculation of the whole bridge line according to the ratio of 1-N_vThe minimum value of the combined working condition calculation results is used for obtaining the main arch strength safety coefficient K_s ^(m,n)Let K_△s ^(m,n)＝K_s ^(m,n)-K_s ⁽⁰⁾；K_△s ^(m,n)For moving the m row and n column elements of the load intensity positive and negative effect matrix, pass K_△b ^(m,n)Positive and negative effect of moving load strength is judged, the lifting rod force is taken the mth group and the moving load is loaded on the nth main beam node, and when the moving load plays a role in improving the bearing capacity of the bridge, K_△s ^(m,n)For positive, i.e. positive effect, K when the moving load has a decreasing effect on the bridge load-bearing capacity_△s ^(m,n)Is negative, i.e. negative effect;

s328, if M is larger than M, turning to S329, otherwise, turning to S326;

s329, obtaining a matrix K of M rows by N columns of positive and negative effect of the moving load strength from S326 to S328_△sTo K for_△sAfter the column-by-column average value is obtained, the strength influence degree row vector S is obtained_s1，S_s1Reflecting the degree of strengthening or weakening the bearing capacity of the bridge when the moving load is loaded on each node under different suspender force levels; will K_△sCounting the number of positive value elements in each row and dividing the positive value elements by M to obtain a strength influence significance row vector S_s2，S_s2Reflecting the probability of strengthening or weakening the bearing capacity of the bridge when the moving load is loaded on each node under different suspender force levels; s_s1And S_s2Forming a matrix S of 2 rows by N columns of intensity sensitive lines_s；

6. The method of claim 5, wherein after step S330, if the positive and negative effects of the strength of each lane at the same main beam node are different from each other in S326-S328, the LC is modified_bWorking condition, and enabling the node of the main beam to have negative effect and be smaller than the set significance test level alpha_sAll lanes are loaded with uniform force Q or concentrated force P of moving load to obtain modified working condition LC_s。

7. The method for optimally designing the arch bridge with the boom under the moving load according to claim 1, wherein the step S4 of iteratively optimizing the boom force comprises the following specific steps:

s401, when a vector X consisting of N suspender forces, f (X) represents that each suspender force of the arch bridge takes a value according to the vector X, a main arch strength safety coefficient K obtained by full-bridge nonlinear finite element calculation is obtained_sAnd main arch stability safety factor K_bThe lower value of f (X) is calculated, and the finite element model suspender adopts a cable unit; force T of crane rod for pressing bridge⁽⁰⁾Calculated f (T)⁽⁰⁾) Wherein, T⁽⁰⁾＝[T₁ ⁽⁰⁾,T₂ ⁽⁰⁾,T₃ ⁽⁰⁾,...,T_J ⁽⁰⁾](ii) a Let the cyclic variable j equal to 1;

s403, if j<J, if J is J +1, go to S402; otherwise, let D_J×JForming a boom force optimization direction diagonal matrix D_J×JThen go to S404;

s404, using T⁽⁰⁾As an initial value for optimization, the convergence accuracy ε of the boom fluctuation amount is set to be not less than 0 and δ of the boom fluctuation amount>Epsilon, the acceleration coefficient alpha of the change of the suspender force is more than or equal to 1, and the deceleration coefficient beta of the change of the suspender force belongs to (0, 1); let H_1×JFor recording the variable with positive or negative effect after the force of each boom changes compared with the variable before the change, the main arch K is aligned_sAnd K_bThe smaller value of the two has a positive effect when the lifting action is performed, and has a negative effect when the lifting action is not performed, and the initial value of the lifting action is H_1×J＝[0,0,0,...,0](ii) a The outer circulation variable i of the boom force optimization is equal to 0, the inner circulation variable j is equal to 1, and the intermediate variable F of the boom force^(j)＝T⁽ⁱ⁾；

s406, if F (F)^(j)+δE^(j))>f(F^(j)) Then let F^(j+1)＝F^(j)+δE^(j)Go to S407; otherwise, let F^(j+1)＝F^(j)Go to S407;

s408, if each suspender force is according to the vector F^(j+1)During value taking, if the conventional design index and the mechanical property of the main beam meet the design requirement, S409 is switched; whether or notGo directly to S412;

s409, if F (F)^(j+1))>f(T⁽ⁱ⁾) Go to S410; otherwise, go directly to S412;

s410, if sum (h) ═ J, let δ be α δ, then go to S411; otherwise, directly switching to S411;

s412, if delta>E, let δ be β δ, j be 1, H_1×J＝[0,0,0,...,0]，F^(j)＝T⁽ⁱ⁾，T⁽ⁱ⁺¹⁾＝T⁽ⁱ⁾Turning to S405 when i is i + 1;

otherwise, the convergence precision of the variation amount of the suspender force is achieved, the optimization of the suspender force is ended, and T⁽ⁱ⁾Namely the bridge-forming hoisting rod force which enables the strength and the stability of the main arch to be comprehensively optimal.

8. The method for optimally designing a boom-under-moving-load arch bridge according to claim 1, wherein in the step S4, the main arch stability safety factor K is calculated every time_bThe method comprises the following steps:

s426, primary arch line shape under static loadInitial defect amplitude delta₁Is composed of

L is the main arch calculation span, and the initial defect linear LS of the main arch₁Amplifying the linear shape corresponding to the first-order buckling mode to delta according to the amplitude value₁The resulting line shape; then distributing a moving load driving line on one side of a main beam central line according to a minimum transverse bridge direction interval allowed by a specification, namely arranging the moving load according to a single-side unbalance load, loading according to an influence line along the bridge direction, and performing full-bridge linear elastic static calculation to obtain an initial defect amplitude value delta of a main arch line shape under the moving load₂，δ₂Initial defect linear LS for maximum lateral bridge displacement value of all nodes of main arch₂To move the load by delta₂The main arch transverse bridge is deformed in the longitudinal direction and then is in a linear shape;

L_aThe axial line of the main arch is long,

initial defect linear LS for stability factor of axial compression component₁Amplifying to delta according to amplitude for first-order buckling line shape₁The resulting line shape; then, the moving load driving lines are symmetrically distributed on two sides of the central line of the main beam in the transverse bridge direction, the moving load is loaded along the bridge direction according to the influence line, full-bridge line elastic static calculation is carried out, and the initial defect amplitude delta of the main arch line under the moving load is obtained₂，δ₂Is the maximum vertical displacement value of all nodes of the main arch, and the initial defect linear LS₂To move the load by delta₂The main arch is vertically deformed and then is linear;

s428, changing the coordinates of the main arch node into a comprehensive initial defect linear LS (least squares) which is the LS₁And LS₂The boom is changed into a cable unit, and the moving load is fixed on the working condition LC according to the moving load in the step S3_bLoading, and calculating the nonlinear buckling to obtainGiving out a characteristic value of non-linear buckling, i.e. the stability factor of safety K of the main arch_bAnd finishing the calculation of the stability safety coefficient.

9. The method for optimally designing a boom-under-moving-load arch bridge according to claim 1, wherein in the step S4, the main arch strength safety factor K is calculated every time_sIn the meantime, the moving load is the moving load immobilizer condition LC in step S3_sLoading, K_sThe ratio of the section bearing capacity at the position where the main arch is stressed with the most unfavorable load to the section internal force is determined.

10. An optimal design system of an arch bridge with a suspender under a moving load is characterized in that the optimal design method of the arch bridge with the suspender under the moving load according to any one of claims 1 to 8 is adopted, and the optimal design system comprises a modeling module, a suspender force initial value calculating module, a moving load loading module, an iterative optimization module and a structural design module;

the modeling module is used for drawing up the size of each component, establishing a primary bridging finite element model and outputting the result to the initial value calculating module of the suspender force; the initial value calculating module is used for calculating the bridge-forming boom force in S2, the moving load loading module is used for calculating the fixed loading position of the uniform distribution force Q and the concentrated force P in the moving load when the main arch stability is tested and calculated to be the worst, the fixed loading position of the uniform distribution force Q and the concentrated force P in the moving load when the main arch strength is tested and calculated to be the worst, and the working condition of unmoving the moving load is output, and the iterative optimization module is used for calculating the optimal bridge-forming boom force T⁽ⁱ⁾And corresponding main arch stability safety factor K_b ⁽ⁱ⁾Strength safety factor K_s ⁽ⁱ⁾The structural design module is used for determining the size of a suspender, the reinforcement and beam matching design of each component and the design of auxiliary facilities of the bridge according to the comprehensive optimal force of the main arch to form the bridge suspender, wherein the comprehensive optimal strength of the main arch is stable.