Continuous beam bridge beam optimization method and system based on stress safety uniformity

Abstract

The present invention relates to the field of civil engineering technology, and in particular to a method and system for optimizing the distribution of continuous beam bridges based on uniformity of stress safety. The present invention first formulates the structural dimensions of the continuous beam bridge and the facade style of the prestressed steel beam, establishes a finite element model, and selects several representative cross sections; sequentially calculates and extracts the stress values ​​generated by the tensioning unit steel beam on the representative cross sections in the order of the construction stages, and constructs a stress influence matrix; calculates and extracts the most unfavorable stress values ​​of the representative cross sections in the construction and operation stages of the non-prestressed structure according to the specifications, and constructs an initial stress vector; calculates the structural stress in the construction and operation stages using the superposition principle, and constructs a mathematical optimization model with the goal of making the stress safety in the operation stage the most uniform, and organizes the design variables, objective functions, and constraint equations; and then uses an optimization algorithm to solve the problem, and obtains a steel beam configuration that makes the structure meet the requirements of the specifications and has the most uniform stress safety, thereby improving the rationality of the force of the bridge structure and the design efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering, and in particular to a method and system for optimizing the beam distribution of a continuous beam bridge based on uniformity of stress safety. Background Art

[0002] In recent years, with the continuous improvement of material strength, the deepening of prestressed concrete design theory, and the continuous improvement of prestressing technology, prestressed concrete bridges have achieved rapid development, and their spans and construction technologies have made continuous breakthroughs. Continuous beam bridges occupy an important position in bridge construction due to their advantages such as high structural rigidity and gentle deformation curve of the main beam.

[0003] For the design of prestressed concrete continuous beam bridges, the traditional method is that designers mainly rely on experience to obtain a solution that meets the specifications through tedious and complex trial calculations. The general process is: based on experience, the bridge structure dimensions are preliminarily determined and static calculations are performed, then the steel bundle area is estimated and arranged, and finally the entire bridge is verified. If the specifications are not met, the design is continuously adjusted until the specifications are met. This repeated trial calculation method not only consumes a lot of time and manpower, but also has an infinite number of feasible solutions to meet the requirements of the specifications. The set of trial solutions obtained is not the optimal solution, and the rationality of the force of the structure needs to be improved. Summary of the invention

[0004] In order to overcome the time-consuming and labor-intensive design defects of concrete continuous beam bridges in the above-mentioned prior art, the present invention proposes a continuous beam bridge bundle optimization method based on stress safety uniformity, establishes a set of forward design processes for prestressed concrete continuous beam bridges, and guides the design with certain objectives, so as to quickly obtain a design scheme that meets the specifications and has reasonable stress.

[0005] The present invention proposes a method for optimizing the beam arrangement of a continuous beam bridge based on uniformity of stress safety, which comprises the following steps:

[0006] S1. Draft the structural dimensions of the continuous beam bridge and the facade style of the prestressed steel strands, establish a finite element model, and select several representative sections to represent the entire bridge; the representative sections are the sections pre-stored in the database;

[0007] S2. Calculate and extract the stress values ​​of the representative cross-sections caused by the tensioning unit steel strands in the order of the construction stages, and construct a stress influence matrix; calculate and extract the most unfavorable stress values ​​of the representative cross-sections in the construction and operation stages of the non-prestressed structure according to the specifications, and construct an initial stress vector;

[0008] S3. Use the superposition principle to calculate the structural stress during the construction and operation stages, build a mathematical optimization model with the goal of achieving the most uniform stress safety during the operation stage, and organize the design variables, objective functions, and constraint equations;

[0009] S4. Use the optimization algorithm to solve and obtain the steel bundle configuration that makes the structure meet the code requirements and has the most uniform stress safety.

[0010] Preferably, the stress influence matrix in S2 includes: the positive stress influence matrix of the upper and lower edges at each stage of construction Normal stress influence matrix of upper and lower edges at the bridge completion stage Normal stress influence matrix of principal stress calculation point in completed bridge state and the shear stress influence matrix Where s represents the construction stage number, L represents the left side of the representative section, R represents the right side of the representative section, T represents the upper edge of the representative section, B represents the lower edge of the representative section, and k represents the number of the principal stress calculation point;

[0011] Each stress influence matrix has n rows and G columns, where n is the number of representative cross sections and G is the type of tendon.

[0012] Preferably, the initial stress vector in S2 includes:

[0013] Normal stress vectors of the upper and lower edges of non-prestressed structures at various stages of construction

[0014] The most unfavorable normal stress vector of the upper and lower edges of the frequent combination during the operation stage The most unfavorable normal stress vector of the upper and lower edges of the standard combination And the most unfavorable normal stress vectors at the upper and lower edges of the quasi-permanent combination

[0015] Normal stress vectors of principal stress calculation points of each frequently encountered combination during the operation phase and the shear stress vector

[0016] Normal stress vectors of principal stress calculation points of each standard combination acting during the operation phase and the shear stress vector

[0017] Each initial stress vector has n rows, where n is the number of representative sections and j is the combination number.

[0018] Preferably, in S3, the design variables are the number of types of steel strands included in the bridge structure and the number of steel strands included in each type; the objective function is expressed as:

[0019]

[0020] Among them, min represents the minimum value function, F represents the safety variance of the most unfavorable compressive stress at the upper and lower edges of the representative section of the standard combination of the operation stage and the most unfavorable principal compressive stress at the principal stress calculation point; represents the mean safety of compressive stress and principal compressive stress, n represents the number of representative sections, and l represents the number of principal stress calculation points on a single representative section;

[0021] represents the safety degree of compressive stress at the upper and lower edges of the i-th representative section of the standard combination, It represents the principal compressive stress safety of the kth principal stress calculation point of the i-th representative section of the standard combination; the kth principal stress calculation point of the i-th representative section is the kth principal stress calculation point on the left side of the i-th representative section or the kth principal stress calculation point on the right side of the i-th representative section.

[0022] Preferably, and The calculation formula is as follows:

[0023]

[0024] Among them, [σ pc ] is the allowable compressive stress, is the most unfavorable compressive stress at the upper and lower edges of the i-th representative section of the standard combination; [σ pcp ] is the allowable principal compressive stress, It is the most unfavorable principal compressive stress at the kth principal stress calculation point of the i-th representative section of the standard combination.

[0025] Preferably, the constraint equations in S3 include: normal stress constraints in the construction phase, normal stress constraints in the operation phase, and principal stress constraints in the operation phase.

[0026] Preferably, the normal stress constraint formula during the construction phase is expressed as:

[0027]

[0028] Among them, {E ct} s is the allowable tensile stress vector of the structure at the sth construction stage, {E cc} s is the allowable compressive stress vector of the structure at the sth construction stage, {X} is the number vector of steel tendons;

[0029] is the normal stress vector of the upper and lower edges of the non-prestressed structure at each stage of construction, It is the influence matrix of the positive stress of the upper and lower edges at each stage of construction.

[0030] Preferably, the normal stress constraint formula in the operation stage is expressed as:

[0031]

[0032] in, is the most unfavorable normal stress vector of the structure under the frequently encountered combination of loads containing prestress, is the most unfavorable normal stress vector of the structure under the standard combination of loads containing prestress, is the most unfavorable normal stress vector of the structure under the quasi-permanent combination of loads with prestress, γ is the normal stress reduction factor of the prestress effect, {E pt},{E pt2},{E pc} are respectively the normal stress vectors allowed by the code;

[0033] is the most unfavorable normal stress vector of the upper and lower edges of the frequently encountered combination of non-prestressed structures during the operation stage, is the most unfavorable normal stress vector of the upper and lower edges of the standard combination of the action in the operation stage of the non-prestressed structure, is the most unfavorable normal stress vector of the upper and lower edges of the quasi-permanent combination of non-prestressed structures during the operation stage, It is the influence matrix of the positive stress of the upper and lower edges during the bridge formation stage.

[0034] Preferably, the principal stress constraint formula in the operation stage is expressed as:

[0035]

[0036]

[0037] in, is the principal tensile stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination, is the principal compressive stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination;

[0038] is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination, is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination of the non-prestressed structure; The positive stress influence matrix of the principal stress calculation point in the bridge state;

[0039] is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination of the non-prestressed structure, Shear stress influence matrix for principal stress calculation points in the bridge state;

[0040] is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination, is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination of the non-prestressed structure; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination of the non-prestressed structure;

[0041] {σ iYL,R} is the vertical normal stress, {E iptp} is the allowable principal tensile stress, {E ipcp} is the allowable principal compressive stress;

[0042] {X} is the type of steel strand; i} T is an n-column row vector with the i-th column element being 1 and the rest of the elements being 0.

[0043] The present invention proposes a continuous beam bridge bundle optimization system based on stress safety uniformity, including a memory and a processor, wherein a computer program is stored in the memory, and the processor is connected to the memory, and the processor is used to execute the computer program to implement the continuous beam bridge bundle optimization method based on stress safety uniformity.

[0044] The advantages of the present invention are:

[0045] (1) For prestressed concrete continuous beam bridges, a set of optimization design processes for prestressed steel tendons is proposed, which realizes the forward design of tendon distribution, changes the traditional design mode of continuous trial calculation, and improves design efficiency.

[0046] (2) The bundle distribution problem is transformed into an optimization problem, and the design direction is guided by the uniformity of stress safety. This makes the distribution of the structural normal stress and principal stress relatively uniform, and makes the stress safety of different sections of the bridge and different positions of the same section tend to be consistent, thereby improving the rationality of the structural force. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of the continuous beam bridge beam optimization method of the present invention;

[0048] FIG2( a ) is a schematic cross-section diagram of a support point of an embodiment;

[0049] FIG2( b ) is a schematic cross-sectional view of an embodiment;

[0050] Figure 3The figure is a schematic diagram of the steel bundle elevation style of the embodiment; wherein, W represents the web steel bundle in the cantilever construction stage, T represents the top plate steel bundle in the cantilever construction stage, MT represents the mid-span top plate steel bundle in the closure stage, MB represents the mid-span bottom plate steel bundle in the closure stage, ST represents the side span top plate steel bundle in the closure stage, and SB represents the side span bottom plate steel bundle in the closure stage. DETAILED DESCRIPTION

[0051] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0052] The present invention proposes a method for optimizing the beam arrangement of a continuous beam bridge based on uniformity of stress safety, which comprises the following steps:

[0053] S1. Draft the structural dimensions of the continuous beam bridge and the facade style of the prestressed steel strands, establish a finite element model, and select several representative sections; the representative sections are the sections pre-stored in the database;

[0054] In step S1, the structural dimensions and the steel bundle elevation arrangement are formulated according to design experience, specifications and actual needs. The finite element modeling takes into account various permanent and variable effects on the structure, and the selection of representative sections can characterize the entire bridge.

[0055] S2. Calculate and extract the stress values ​​of the representative cross-sections caused by the tensioning unit steel strands in the order of the construction stages, and construct a stress influence matrix; calculate and extract the most unfavorable stress values ​​of the representative cross-sections in the construction and operation stages of the non-prestressed structure according to the specifications, and construct an initial stress vector;

[0056] In step S2, the stress values ​​of the representative cross-sections generated by the tensioned unit steel strands are sequentially calculated and extracted during the construction phase. The stress influence matrix includes the positive stress influence matrix of the upper and lower edges at each construction phase. Normal stress influence matrix of upper and lower edges at the bridge completion stage Normal stress influence matrix of principal stress calculation point in completed bridge state and the shear stress influence matrix Where s represents the construction stage number, L / R represents the left or right side of the representative section, T / B represents the upper / lower edge of the representative section, k represents the number of the principal stress calculation point, each matrix has n rows and G columns, n is the number of representative sections, G is the type of steel strand; 1≤i≤n, 1≤g≤G;

[0057] The element in the i-th row and g-th column of is the normal stress value sequence of the i-th representative section at the s-th construction stage when one unit of the g-th steel strand is tensioned. The normal stress value sequence of the representative section includes the positive stress value of the upper edge on the left, the positive stress value of the lower edge on the left, the positive stress value of the upper edge on the right, and the positive stress value of the lower edge on the right of the representative section;

[0058] The element in the i-th row and g-th column of is the normal stress value sequence of the i-th representative section in the bridge completion stage when the g-th steel strand is tensioned by one unit;

[0059] The element of the i-th row and g-th column includes the normal stress value of the k-th principal stress calculation point on the left and the normal stress value of the k-th principal stress calculation point on the right on the i-th representative cross section at the bridge completion stage when the g-th steel strand is tensioned by one unit;

[0060] The elements in the i-th row and g-th column include the shear stress values ​​of the k-th principal stress calculation point on the left and the k-th principal stress calculation point on the right on the i-th representative cross section at the bridge completion stage when one unit of the g-th steel tendon is tensioned.

[0061] The initial stress vectors are all vectors of n rows, and the initial stress vectors include:

[0062] Normal stress vectors of the upper and lower edges of non-prestressed structures at various stages of construction The i-th row represents the positive stress value of the left upper edge, left lower edge, right upper edge, or right lower edge of the i-th representative section of the non-prestressed structure at the s-th construction stage.

[0063] The most unfavorable normal stress vector of the upper and lower edges of the non-prestressed structure is frequently encountered during the operation stage. The i-th row represents the most unfavorable normal stress sequence of the i-th representative section of the frequently encountered combination of the non-prestressed structure in the operation stage. The most unfavorable normal stress sequence of the representative section includes the most unfavorable normal stress value of the left upper edge, the most unfavorable normal stress value of the left lower edge, the most unfavorable normal stress value of the right upper edge and the most unfavorable normal stress value of the right lower edge of the representative section;

[0064] The most unfavorable normal stress vector of the upper and lower edges of the standard combination of non-prestressed structures in the operation stage Its i-th row represents the most unfavorable normal stress sequence of the i-th representative section of the standard combination of action of the non-prestressed structure in the operation stage;

[0065] The most unfavorable normal stress vectors of the upper and lower edges of the quasi-permanent combination of non-prestressed structures in the operation stage Its i-th row represents the most unfavorable normal stress sequence of the i-th representative section of the quasi-permanent combination of the non-prestressed structure during the operation stage;

[0066] Normal stress vectors of principal stress calculation points of various frequently encountered combinations of non-prestressed structures during the operation stage The i-th row includes the normal stress value of the k-th principal stress calculation point on the left side and the k-th principal stress calculation point on the right side of the i-th representative section of the j-th frequent combination of the non-prestressed structure in the operation stage.

[0067] Normal stress vectors of principal stress calculation points of each standard combination of non-prestressed structures during the operation stage The i-th row includes the normal stress value of the k-th principal stress calculation point on the left side and the k-th principal stress calculation point on the right side of the i-th representative section of the j-th standard combination of the non-prestressed structure in the operation stage.

[0068] Shear stress vectors of the principal stress calculation points of each frequently encountered combination of non-prestressed structures during the operation stage The i-th row includes the shear stress value of the k-th principal stress calculation point on the left side and the shear stress value of the k-th principal stress calculation point on the right side of the i-th representative section of the j-th frequent combination of non-prestressed structures in the operation stage.

[0069] Shear stress vectors of principal stress calculation points of each standard combination of non-prestressed structures during the operation stage The i-th row includes the shear stress value of the k-th principal stress calculation point on the left side and the shear stress value of the k-th principal stress calculation point on the right side of the i-th representative section of the j-th standard combination of the non-prestressed structure in the operation stage.

[0070] S3. Use the superposition principle to calculate the structural stress during the construction and operation stages, build a mathematical optimization model with the goal of achieving the most uniform stress safety during the operation stage, and organize the design variables, objective functions, and constraint equations;

[0071] In step S3, the design variable is the number of each steel bundle, and the constraint equation can specifically adopt the relevant stress constraints and other constraints in the "Highway Reinforced Concrete and Prestressed Concrete Bridge and Culvert Design Code JTG3362-2018" (hereinafter referred to as the Code).

[0072] In this implementation, the constraint equation is specifically as follows:

[0073] ① Normal stress constraint during construction phase:

[0074]

[0075] Among them, {E ct} s is the allowable tensile stress vector of the structure at the sth construction stage, {E cc} s is the allowable compressive stress vector of the structure at the sth construction stage, and {X} is the vector of the number of steel tendons.

[0076] ② Positive stress constraints in the operation phase:

[0077]

[0078] in, is the most unfavorable normal stress vector of the structure under the frequently encountered combination of loads containing prestress, is the most unfavorable normal stress vector of the structure under the standard combination of loads containing prestress, is the most unfavorable normal stress vector of the structure under the quasi-permanent combination of loads with prestress, γ is the normal stress reduction factor of the prestress effect, {E pt},{E pt2},{E pc} are the normal stress vectors allowed by the specification.

[0079] ③Principal stress constraints in the operation phase:

[0080]

[0081]

[0082] in, is the principal tensile stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination, is the principal compressive stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination; {σ iYL,R} is the vertical normal stress, {E iptp} is the allowable principal tensile stress, {E ipcp} is the allowable principal compressive stress;

[0083] is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination, is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination, calculated as follows:

[0084]

[0085] Among them, {e i} T is a single-row and n-column vector with the i-th column element being 1 and the rest of the elements being 0, where n represents the number of representative cross sections.

[0086] The meaning and calculation method of are similar to those of the standard combination, namely:

[0087]

[0088] is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination, is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination of the non-prestressed structure; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination; It is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination of the non-prestressed structure.

[0089] ④Other constraints:

[0090] It can be set arbitrarily according to actual needs.

[0091] In the step S3, the objective function is to minimize the safety variance of the most unfavorable compressive stress at the upper and lower edges of the representative cross section of the standard combination in the operation stage and the most unfavorable principal compressive stress at the principal stress calculation point, and the calculation formula is as follows:

[0092]

[0093] in, is the safety degree of compressive stress at the upper and lower edges of the i-th representative section of the standard combination, is the principal compressive stress safety factor of the kth principal stress calculation point of the i-th representative section of the standard combination, l is the number of principal stress calculation points on a single representative section, n is the total number of representative sections, is the mean safety degree of compressive stress and principal compressive stress. The safety degree is expressed as the ratio of the difference between the effect value and the allowable value to the allowable value. The calculation formula is as follows:

[0094]

[0095] Among them, [σ pc ] is the allowable compressive stress, [σ pcp ] is the allowable principal compressive stress;

[0096] is the most unfavorable compressive stress at the upper and lower edges of the i-th representative section of the standard combination, is the compressive stress at the upper and lower edges of the i-th representative section of the standard combination;

[0097] is the most unfavorable principal compressive stress at the kth principal stress calculation point of the i-th representative section of the standard combination, The elements of The maximum value of the same element on different representative sections.

[0098] The kth principal stress calculation point of the i-th representative section: includes the kth principal stress calculation point on the left side of the i-th representative section and the kth principal stress calculation point on the right side of the i-th representative section.

[0099] The upper and lower edges of the ith representative cross section: include the upper edge on the left side, the lower edge on the left side, the upper edge on the right side and the lower edge on the right side of the ith representative cross section.

[0100] S4. Use the optimization algorithm to solve and obtain the steel bundle configuration that makes the structure meet the code requirements and has the most uniform stress safety.

[0101] The algorithm optimization objectives include: the number of steel bundle types contained in each bridge structure and the number of steel bundles contained in each type; that is, traversing the number of steel bundle types contained in the bridge structure and the number of steel bundles contained in each type, and obtaining the steel bundle types and steel bundle numbers corresponding to the optimization objective function is the continuous beam bridge bundle optimization plan.

[0102] The above-mentioned continuous beam bridge beam optimization method based on stress safety uniformity is verified in combination with specific embodiments below.

[0103] This embodiment applies the above-mentioned continuous beam bridge beam optimization method based on stress safety uniformity to a three-span continuous rigid frame bridge with a main span of (95+173+95)m. The main beam adopts a single-box double-chamber section, C55 concrete, and the prestressed steel adopts a steel strand with a nominal diameter of 15.2mm. The standard value of tensile strength is 1860MPa.

[0104] according to Figure 1 The following steps are used to optimize the steel bundle arrangement. First, the structural dimensions and steel bundle elevation are determined based on experience, as shown in Figures 2(a), 2(b) and Figure 3 . The mid-span beam height a1=4.5m, the support beam height a2=10.0m, and the beam height changes according to the 2.0 parabola law. The top plate thickness a3=28cm, the web plate changes in three sections from the middle support to the mid-span, and the thickness changes from 85 to 65 to 50cm. The bottom plate thickness changes from 100cm at the support to 32cm in the mid-span according to the 2.0 parabola law. The cantilever casting construction method is adopted, and the order of closure is side span first and then middle span. There are 137 types of steel beams, and the representative sections are selected at the section changes and construction segment divisions, with a total of 115 representative sections. Considering the effects of self-weight, vehicle load, shrinkage creep, temperature effect and uneven settlement of supports, a spatial bar finite element model is established for Class A prestressed concrete components.

[0105] Secondly, the stress values ​​of the tensioned unit steel strands on the representative cross-sections are calculated and extracted in sequence according to the construction stages, and a stress influence matrix is ​​constructed, which includes 260 (65*4) positive stress influence matrices in the construction stages. Normal stress influence matrix of four bridge construction stages 12 (6*2) normal stress influence matrices of principal stress calculation points in the completed bridge state The shear stress influence matrix of 12 (6*2) principal stress calculation points in the bridge state Each influence matrix is ​​115*137. The most unfavorable stress values ​​of representative cross sections in the construction and operation stages of non-prestressed structures are calculated and extracted according to the specifications, and the initial stress vector is constructed, including 260 (65*4) positive stress vectors in the construction stage of non-prestressed structures. The most unfavorable normal stress vectors are frequently combined during the operation phase. The four most unfavorable normal stress vectors of the action standard combination in the operation stage Four most unfavorable normal stress vectors of quasi-permanent combination in operation stage 48 (8*6) normal stress vectors of principal stress calculation points of each frequently encountered combination during the operation phase and 48 (8*6) shear stress vectors 48 (8*6) normal stress vectors of principal stress calculation points acting on each standard combination during the operation phase and 48 (8*6) shear stress vectors Each vector is 115*1.

[0106] Then, the structural stresses in the construction and operation stages were calculated according to the superposition principle, and the design variables, objective functions and constraint equations were sorted out to construct a mathematical optimization model. The design variables are the number of 137 steel strands, and the constraint equations are established according to the normal stress in the construction stage and the normal and principal stress in the operation stage, including 520 (65*4*2) normal stress constraint equations in the construction stage, 12 (4*3) normal stress constraints in the operation stage, and 96 (48*2) principal stress constraints in the operation stage. According to the specifications, the design is based on Class A prestressed concrete components, γ = 1, construction stage: {E ct} s =-3.151MPa,{E cc} s =24.85MPa

[0107] Operational stage:

[0108] {E pt}=-1.918MPa,{E pt2}=0MPa,{E pc}=17.75MPa,

[0109] {E iptp}=-1.37MPa,{E ipcp =21.3MPa

[0110] The objective function is to minimize the safety variance of the most unfavorable compressive stress at the upper and lower edges of the representative section of the standard combination in the operation stage and the most unfavorable principal compressive stress at the principal stress calculation point.

[0111] Finally, the optimization algorithm was used to solve the problem, and the number of steel bundles obtained is shown in the following table.

[0112] Table 1 Optimized number of steel strands

[0113]

[0114] The scheme was brought into the finite element model and combined with the specification calculation. The most unfavorable compressive stress in the construction stage of the whole bridge was 13.01MPa, and the tensile stress was 1.43MPa; the most unfavorable tensile stress of the frequent combination in the operation stage was 0.94MPa, and the main tensile stress was 1.05MPa; the most unfavorable compressive stress of the standard combination was 12.97MPa, and the main compressive stress was 11.22Mpa; the most unfavorable compressive stress of the quasi-permanent combination was 0.98MPa, all of which met the requirements of the specification. The safety variance of the standard combination compressive stress and the main compressive stress was 0.0124, which was 55% lower than 0.0278 before optimization. The optimization effect was significant, proving that this method is feasible and effective.

[0115] Of course, it is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-limiting, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any reference numerals in the claims should not be regarded as limiting the claims involved.

[0116] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

[0117] The techniques, shapes, and structural parts not described in detail in the present invention are all well-known techniques.

Claims

1. A method for optimizing the beam arrangement of a continuous beam bridge based on uniformity of stress safety, characterized in that: It includes the following steps: S1. Draft the structural dimensions of the continuous beam bridge and the facade style of the prestressed steel strands, establish a finite element model, and select several representative sections to represent the entire bridge; the representative sections are the sections pre-stored in the database; S2. Calculate and extract the stress values ​​of the representative cross-sections caused by the tensioning unit steel strands in the order of the construction stages, and construct a stress influence matrix; calculate and extract the most unfavorable stress values ​​of the representative cross-sections in the construction and operation stages of the non-prestressed structure according to the specifications, and construct an initial stress vector; S3. Use the superposition principle to calculate the structural stress during the construction and operation stages, build a mathematical optimization model with the goal of achieving the most uniform stress safety during the operation stage, and organize the design variables, objective functions, and constraint equations; S4. Utilize the optimization algorithm to solve and obtain the steel bundle configuration that makes the structure meet the code requirements and has the most uniform stress safety; In S3, the design variables are the number of steel strand types contained in the bridge structure and the number of steel strands contained in each type; the objective function is expressed as: Among them, min represents the minimum value function, F represents the safety variance of the most unfavorable compressive stress at the upper and lower edges of the representative section of the standard combination of the operation stage and the most unfavorable principal compressive stress at the principal stress calculation point; represents the mean safety of compressive stress and principal compressive stress, n represents the number of representative sections, and l represents the number of principal stress calculation points on a single representative section; represents the safety degree of compressive stress at the upper and lower edges of the i-th representative section of the standard combination, It represents the safety degree of principal compressive stress of the kth principal stress calculation point of the i-th representative section of the standard combination; The kth principal stress calculation point of the i-th representative section is the kth principal stress calculation point on the left side of the i-th representative section or the kth principal stress calculation point on the right side of the i-th representative section.

2. The method for optimizing the continuous beam bridge beam arrangement based on uniformity of stress safety degree according to claim 1, characterized in that: The stress influence matrix in S2 includes: the positive stress influence matrix of the upper and lower edges at each stage of construction Normal stress influence matrix of upper and lower edges at the bridge completion stage Normal stress influence matrix of principal stress calculation point in completed bridge state and the shear stress influence matrix Where s represents the construction stage number, L represents the left side of the representative section, R represents the right side of the representative section, T represents the upper edge of the representative section, B represents the lower edge of the representative section, and k represents the number of the principal stress calculation point; Each stress influence matrix has n rows and G columns, where n is the number of representative cross sections and G is the type of tendon.

3. The method for optimizing the continuous beam bridge beam arrangement based on uniformity of stress safety degree according to claim 2, characterized in that: The initial stress vectors in S2 include: Normal stress vectors of the upper and lower edges of non-prestressed structures at various stages of construction The most unfavorable normal stress vector of the upper and lower edges of the frequent combination during the operation stage The most unfavorable normal stress vector of the upper and lower edges of the standard combination And the most unfavorable normal stress vectors at the upper and lower edges of the quasi-permanent combination Normal stress vectors of principal stress calculation points of each frequently encountered combination during the operation phase and the shear stress vector Normal stress vectors of principal stress calculation points of each standard combination acting during the operation phase and the shear stress vector Each initial stress vector has n rows, where n is the number of representative sections and j is the combination number.

4. The method for optimizing the continuous beam bridge beam arrangement based on uniformity of stress safety degree according to claim 1, characterized in that: and The calculation formula is as follows: Among them, [σ pc ] is the allowable compressive stress, is the most unfavorable compressive stress at the upper and lower edges of the i-th representative section of the standard combination; [σ pcp ] is the allowable principal compressive stress, It is the most unfavorable principal compressive stress at the kth principal stress calculation point of the i-th representative section of the standard combination.

5. The method for optimizing the continuous beam bridge beam arrangement based on uniformity of stress safety degree according to claim 4, characterized in that: The constraint equations in S3 include: normal stress constraint in the construction phase, normal stress constraint in the operation phase, and principal stress constraint in the operation phase.

6. The method for optimizing the continuous beam bridge beam arrangement based on uniformity of stress safety as claimed in claim 5, characterized in that: The normal stress constraint formula during the construction phase is expressed as: Among them, {E ct } s is the allowable tensile stress vector of the structure at the sth construction stage, {E cc } s is the allowable compressive stress vector of the structure at the sth construction stage, {X} is the number vector of steel tendons; is the normal stress vector of the upper and lower edges of the non-prestressed structure at each stage of construction, It is the influence matrix of the positive stress of the upper and lower edges at each stage of construction.

7. The method for optimizing the continuous beam bridge beam arrangement based on uniformity of stress safety degree according to claim 5, characterized in that: The normal stress constraint formula in the operation stage is expressed as: in, is the most unfavorable normal stress vector of the structure under the frequently encountered combination of loads containing prestress, is the most unfavorable normal stress vector of the structure under the standard combination of loads containing prestress, is the most unfavorable normal stress vector of the structure under the quasi-permanent combination of loads with prestress, γ is the normal stress reduction factor of the prestress effect, {E pt },{E pt2 },{E pc } are respectively the normal stress vectors allowed by the code; is the most unfavorable normal stress vector of the upper and lower edges of the frequently encountered combination of non-prestressed structures during the operation stage, is the most unfavorable normal stress vector of the upper and lower edges of the standard combination of the action in the operation stage of the non-prestressed structure, is the most unfavorable normal stress vector of the upper and lower edges of the quasi-permanent combination of non-prestressed structures during the operation stage, It is the influence matrix of the positive stress of the upper and lower edges during the bridge formation stage.

8. The method for optimizing the continuous beam bridge beam arrangement based on uniformity of stress safety as claimed in claim 5, characterized in that: The principal stress constraint formula in the operation stage is expressed as: in, is the principal tensile stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination, is the principal compressive stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination; is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination, is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination of the non-prestressed structure; The positive stress influence matrix of the principal stress calculation point in the bridge state; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth frequent combination of the non-prestressed structure, Shear stress influence matrix for principal stress calculation points in the bridge state; is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination, is the normal stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination of the non-prestressed structure; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination; is the shear stress vector of the kth principal stress calculation point of the ith representative section of the jth standard combination of the non-prestressed structure; {σ iYL,R } is the vertical normal stress, {E iptp } is the allowable principal tensile stress, {E ipcp } is the allowable principal compressive stress; {X} is the type of steel strand; i } T is an n-column row vector with the i-th column element being 1 and the rest of the elements being 0.

9. A continuous beam bridge beam optimization system based on stress safety uniformity, characterized in that: It includes a memory and a processor, the memory stores a computer program, the processor is connected to the memory, and the processor is used to execute the computer program to implement the continuous beam bridge bundle optimization method based on stress safety uniformity as described in any one of claims 1-8.

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