Method for calculating creep secondary force caused by steel beam

Abstract

The invention discloses a method for calculating creep secondary force caused by a steel beam. The method comprises the following steps: determining information of the steel beam participating in work at an initial moment, structural information, initial values of creep primary force and initial values of creep secondary force; calculating the elastic displacement of the bridge structure obtained by tensioning the steel beam; calculating a creep displacement value increased by tensioning of the steel beam; introducing a section characteristic conversion coefficient, and calculating specific numerical values corresponding to two ends of the unit; on the basis of the steps, the creep primary force is calculated; secondary creep force is calculated; and substituting the creep secondary force into the next stage, repeating the steps, and calculating the creep primary force and the creep secondary force in the next time period. According to the method, aiming at accurate characterization and rapid calculation of creep secondary force caused by steel beam tensioning in bridge engineering in the field of traffic transportation, a beam creep calculation problem in a steel beam tensioning physical process can be established, and an accurate mapping relation between a parameter space and a mechanical property space is established; and the limitation of the traditional method in the aspects of calculation dimension and efficiency is broken through.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge engineering in the transportation industry, and particularly relates to a method for calculating creep secondary forces caused by steel bundles. Background Art

[0002] Prestressed concrete structures are widely used in major projects such as long-span bridges and high-rise buildings due to their excellent crack resistance and bearing capacity. However, under long-term loads, the creep effect of concrete will cause a redistribution of internal forces in the structure, and the interaction between the prestressed steel strands and the concrete will further complicate this process, generating unpredictable "creep secondary forces." If the "creep secondary forces" are not accurately calculated, they may lead to excessive structural stress, uncontrolled prestress loss, and even induce crack expansion or excessive deformation, directly threatening the safety and durability of the project. In recent years, frequent accidents such as excessive bridge deflection and cracking of nuclear power plant containment caused by creep effects have occurred both at home and abroad, highlighting the urgency of technological breakthroughs in this field.

[0003] Traditional methods for calculating creep secondary forces (such as the age-adjusted effective modulus method and the piecewise linear superposition model) are mostly based on idealized assumptions and have significant limitations: First, the theoretical models are overly simplified and ignore the spatiotemporal heterogeneity of the coordinated deformation of steel tendons and concrete. In particular, in curved tendon distribution and variable cross-section structures, the dynamic coupling effect of interface slip and stress redistribution is difficult to characterize; second, the calculation accuracy is insufficient, and existing methods have deviations in the quantification of the coupling effects of multiple factors such as steel tendon relaxation and beam elastic compression; third, their engineering applicability is poor. For large-span prestressed concrete structures, they must rely on finite element iterative calculations, which is time-consuming and costly, and cannot meet the needs of modern engineering intelligent design.

[0004] As major projects like high-speed rail bridges place ever-higher demands on refined design, the error tolerances of traditional methods are no longer sufficient to meet the high safety requirements of high-speed rail bridges. Furthermore, with the trend toward green construction, reducing material redundancy through precise internal force control has become a key path to lowering carbon emissions.

[0005] Based on this, the present invention addresses this bottleneck by proposing a method for calculating the creep secondary force caused by steel strands. This method aims to accurately and rapidly calculate creep losses in prestressed concrete bridge structures caused by prestressing steel strands, while also ensuring engineering practicality. This method fills the gap in high-precision methods for calculating the creep secondary force caused by prestressing steel strands, providing core algorithmic support for structural health monitoring and intelligent bridge design and construction. It will advance prestressed concrete design from "empirical conservatism" to "precise prediction," with significant economic benefits and social value. Summary of the Invention

[0006] The present invention aims to provide a method for calculating the creep secondary forces caused by steel strands. This method enables accurate characterization and rapid calculation of the creep secondary forces caused by steel strand tensioning in transportation, such as railway, highway, and municipal bridge projects. This patented method addresses the problem of beam creep calculations during the physical process of steel strand tensioning, establishing a precise mapping between parameter space and mechanical property space, thus overcoming the computational dimensionality and efficiency limitations of traditional methods.

[0007] The present invention provides a method for calculating creep secondary force caused by steel bundles, and its technical solution is: a method for calculating creep secondary force caused by steel bundles, comprising the following steps:

[0008] Step A, determining the initial values ​​of the steel tendon information, structural information, creep primary force and creep secondary force involved in the work at the initial moment;

[0009] Step B, based on step A, calculating the elastic displacement of the bridge structure obtained by tensioning the steel tendons;

[0010] Step C, calculating the creep displacement value increased by the tensioning of the steel tendons;

[0011] Step D, introduce the cross-sectional property conversion coefficient and calculate the specific values ​​corresponding to the two ends of the unit;

[0012] Step E, calculating the creep primary force based on steps B to D;

[0013] Step F, calculating the creep secondary force based on steps B to E;

[0014] In step G, the creep secondary force is substituted into the next stage, and steps A to F are repeated to calculate the creep primary force and creep secondary force of the next time period.

[0015] Furthermore, step A determines the initial values ​​of the steel tendon information, structural information, creep primary force, and creep secondary force involved in the work at the initial moment. The specific process is as follows:

[0016] First, determine the information of the steel strands involved in the work, such as the tension force of the steel strand, the cross-sectional area of ​​the steel strand, the number of steel strands, the friction coefficient of the steel strand, the design coordinates of the steel strand, the rebound shrinkage of the steel strand, and the positional relationship between the steel strand and the beam element;

[0017] Secondly, determine the structural information involved in the work, such as unit number, restraint system, other loads besides tendon tension, construction stage, and concrete shrinkage and creep;

[0018] Finally, the primary creep force and secondary creep force of the structure at the initial moment are determined to be zero, which can be written as:

[0019]

[0020] Where f1 represents the primary creep force of the structure, and f2 represents the secondary creep force of the structure.

[0021] Furthermore, step B calculates the elastic displacement of the bridge structure obtained by tensioning the steel tendons based on step A. The specific process is as follows:

[0022] First, based on the information from step A, calculate the long-term loss and short-term loss values ​​of each steel strand;

[0023] Secondly, the effective tensile stress value of the steel tendon along the tendon coordinate is calculated;

[0024] Again, the equivalent load at each unit node is calculated and applied to the structural unit;

[0025] Finally, the overall stiffness matrix and load matrix of the structure are assembled to calculate the elastic displacement of each unit node of the structure.

[0026] Furthermore, step C calculates the creep displacement value added by tendon tensioning. The specific process is as follows:

[0027] First, the elastic displacement of the structure caused by the tensioning of the steel tendons is calculated;

[0028] Secondly, calculate the creep coefficient and increment corresponding to each time point and time history;

[0029] Finally, the creep displacement value increased by tendon tensioning is calculated, which is expressed as follows:

[0030]

[0031] Where Δu represents the elastic displacement of the structure caused by the tensioning of the steel tendons. It represents the creep coefficient increment, and du represents the creep displacement value increased by tendon tensioning.

[0032] Furthermore, step D introduces the cross-sectional property conversion coefficient and calculates the specific values ​​corresponding to the two ends of the unit. The specific calculation expression is as follows:

[0033]

[0034] Wherein, λ represents the cross-sectional characteristic conversion coefficient introduced in the present invention. When used for axial force calculation and bending moment calculation, the specific expressions are different. A0 and A all Represents the net concrete cross-sectional area and the equivalent converted area including the steel tendons, I0 and I all Represents the net moment of inertia of concrete and the equivalent converted moment of inertia including steel tendons.

[0035] Furthermore, step E calculates the creep force based on steps B to D. The calculation expression is as follows:

[0036]

[0037] Where f1 represents the creep force of the structure, K represents the elastic stiffness matrix of the structure, and f 固端 represents the equivalent fixed end force caused by the non-nodal load of the structure, Represents the creep coefficient of each unit of the structure from the initial time t0 to the calculation time t.

[0038] Furthermore, step F calculates the creep secondary force based on steps B to E. The specific calculation expression is as follows:

[0039]

[0040] Where f2 represents the creep secondary force of the structure, du represents the creep displacement increment, which is obtained by applying the creep primary force f1 to the structure; dF represents the elastic internal force increment caused by displacement, which can be expressed by the expression dF = K*Δu; Represents the creep coefficient increment.

[0041] Furthermore, step G substitutes the creep secondary force into the next stage and repeats steps A to F to calculate the creep primary force and creep secondary force of the next time period. The specific process is as follows:

[0042] The creep secondary force calculated by formula (8) replaces the initial value of the creep secondary force in formula (1), and then enters the next stage and calculates according to formulas (2) to (8) until the end of the stage.

[0043] The beneficial effects of the present invention are as follows:

[0044] This patented method accurately characterizes and rapidly calculates the creep secondary forces caused by steel strand tensioning in bridge projects in transportation sectors such as railways, highways, and municipal infrastructure. This method addresses the problem of beam creep calculations during the physical process of steel strand tensioning, establishing a precise mapping between parameter space and mechanical property space, thus overcoming the limitations of traditional methods in terms of computational dimensionality and efficiency. The algorithm balances engineering applicability with program compatibility, and its modular architecture facilitates integration into finite element kernel computing systems.

[0045] This invention will fill the gap in the high-precision calculation method of creep secondary force caused by prestressing of steel strands, provide core algorithm support for structural health monitoring, intelligent bridge design and construction, and promote the transition of prestressed concrete design from "empirical conservatism" to "accurate prediction", with significant economic benefits and social value. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the calculation process of the present invention;

[0047] Figure 2 This is a schematic diagram of the tensioning of steel strands in a prestressed concrete beam according to the present invention;

[0048] Figure 3 Schematic diagram of the relationship between the six loss components of the steel bundle of the present invention;

[0049] Figure 4 This is a schematic diagram of the decomposition of the equivalent load of prestressing when the steel bundle is tensioned according to the present invention;

[0050] Figure 5 Schematic diagram of the comparative calculation model of the three-span continuous beam of the present invention;

[0051] Figure 6 This is an axial comparison diagram of the creep secondary force of the present invention;

[0052] Figure 7 This is a vertical comparison diagram of creep secondary force of the present invention;

[0053] Figure 8 This is a comparison diagram of the creep secondary force and bending moment components of the present invention. DETAILED DESCRIPTION

[0054] Hereinafter, the present invention will be described in detail with reference to the accompanying drawings and embodiments:

[0055] like Figures 1 to 8 As shown, a method for calculating the creep secondary force caused by steel tendons includes the following steps:

[0056] Step A, determining the initial values ​​of the steel tendon information, structural information, creep primary force and creep secondary force involved in the work at the initial moment;

[0057] Step B, based on step A, calculating the elastic displacement of the bridge structure obtained by tensioning the steel tendons;

[0058] Step C, calculating the creep displacement value increased by the tensioning of the steel tendons;

[0059] Step D, introduce the cross-sectional property conversion coefficient and calculate the specific values ​​corresponding to the two ends of the unit;

[0060] Step E, calculating the creep primary force based on steps B to D;

[0061] Step F, calculating the creep secondary force based on steps B to E;

[0062] In step G, the creep secondary force is substituted into the next stage, and steps A to F are repeated to calculate the creep primary force and creep secondary force of the next time period.

[0063] Step A determines the initial values ​​of the steel tendon information, structural information, creep primary force, and creep secondary force involved in the work. The specific process is as follows:

[0064] First, determine the information of the steel strands involved in the work, such as the tension of the steel strands, the cross-sectional area of ​​the steel strands, the number of steel strands, the friction coefficient of the steel strands, the design coordinates of the steel strands, the rebound shrinkage of the steel strands, and the positional relationship between the steel strands and the beam elements, such as Figure 2 As shown;

[0065] Secondly, determine the structural information involved in the work, such as unit number, restraint system, other loads besides tendon tension, construction stage, and concrete shrinkage and creep;

[0066] Finally, the primary creep force and secondary creep force of the structure at the initial moment are determined to be zero, which can be written as:

[0067]

[0068] Where f1 represents the primary creep force of the structure, and f2 represents the secondary creep force of the structure.

[0069] Figure 2 In the figure, Z and X represent the axial direction and the vertical direction, respectively.

[0070] Step B is based on step A and calculates the elastic displacement of the bridge structure resulting from the tensioning of the steel tendons. The specific process is as follows:

[0071] First, based on the information from step A, calculate the long-term loss and short-term loss value of each steel strand, such as Figure 3 As shown;

[0072] Secondly, the effective tensile stress value of the steel tendon along the tendon coordinate is calculated;

[0073] Again, calculate the equivalent load at each unit node, such as Figure 4 As shown, and applied to the structural unit;

[0074] Finally, the overall stiffness matrix and load matrix of the structure are assembled to calculate the elastic displacement of each unit node of the structure.

[0075] Specifically, the effective tensile stress value is expressed as follows;

[0076] σ con =σ0-σ s -σ l (2)

[0077] Where σ con represents the effective tensile stress value of the steel tendon along the steel tendon coordinate, σ0 represents the tensile control stress value, σ s represents the short-term stress loss value of the steel tendon, σ l Indicates the long-term stress loss value of the steel tendon.

[0078] Attachment Figure 3 In thes1 , σ s2 , σ s3 , σ s4 , σ s5 , σ s6 They represent six different losses of steel tendon prestressing, and their physical meanings are marked in the figure respectively.

[0079] Specifically, the equivalent load of the steel tendon is expressed by the following two formulas:

[0080]

[0081] Where, subscripts i and j represent the cross-section numbers at both ends of each unit, respectively. i and P j Respectively represent the effective tension force of the steel strand at the two end sections, P i and P j The value of can be calculated from the effective tensile stress value of formula (2), θ i and θ j is the angle between the steel strand and the axis of the cross-section at both ends of the unit, e zi and e zj is the offset between the steel strand and the axis of the cross-section at both ends of the unit, P xi 、P zi 、m yi is the equivalent load of the steel tendon in different directions at section i, P xj 、P zj 、m yj is the equivalent load of the steel tendon in different directions at section j.

[0082] Step C calculates the creep displacement value added by tendon tensioning. The specific process is as follows:

[0083] First, the elastic displacement of the structure caused by the tensioning of the steel tendons is calculated;

[0084] Secondly, calculate the creep coefficient and increment corresponding to each time point and time history;

[0085] Finally, the creep displacement value increased by tendon tensioning is calculated, which is expressed as follows:

[0086]

[0087] Where Δu represents the elastic displacement of the structure caused by the tensioning of the steel tendons. It represents the creep coefficient increment, and du represents the creep displacement value increased by tendon tensioning.

[0088] Step D introduces the cross-sectional property conversion coefficient and calculates the specific values ​​corresponding to the two ends of the unit. The specific calculation expression is as follows:

[0089]

[0090] Wherein, λ represents the cross-sectional characteristic conversion coefficient introduced in the present invention. When used for axial force calculation and bending moment calculation, the specific expressions are different. A0 and A all Represents the net concrete cross-sectional area and the equivalent converted area including the steel tendons, I0 and I all Represents the net moment of inertia of concrete and the equivalent converted moment of inertia including steel tendons.

[0091] Step E calculates the creep force based on steps B to D. The calculation expression is as follows:

[0092]

[0093] Where f1 represents the creep force of the structure, K represents the elastic stiffness matrix of the structure, and f 固端 represents the equivalent fixed end force caused by the non-nodal load of the structure, Represents the creep coefficient of each unit of the structure from the initial time t0 to the calculation time t.

[0094] Step F calculates the creep secondary force based on steps B to E. The specific calculation expression is as follows:

[0095]

[0096] Where f2 represents the creep secondary force of the structure, du represents the creep displacement increment, which is obtained by applying the creep primary force f1 to the structure; dF represents the elastic internal force increment caused by displacement, which can be expressed by the expression dF = K*Δu; Represents the creep coefficient increment.

[0097] Step G substitutes the creep secondary force into the next stage and repeats steps A to F to calculate the creep primary force and creep secondary force for the next time period. The specific process is as follows:

[0098] The creep secondary force calculated by formula (8) replaces the initial value of the creep secondary force in formula (1), and then enters the next stage and calculates according to formulas (2) to (8) until the end of the stage.

[0099] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0100] Example 1

[0101] As attached Figure 5As shown, a three-span continuous beam of (94.5+166.4+107.9) m was established, and the pile foundation, pier cap, and pier structure were simulated simultaneously. The calculation model has 92 beam unit sections, including different types such as variable cross-section, middle-upper eccentricity, and PSC single-box single-chamber sections in the beam section. The concrete material of the continuous beam uses different grades of concrete in different parts. The beam body is C60 concrete, the pier is C40 concrete, and the foundation parts such as the pile foundation pier are C30 concrete. The entire construction process of the continuous beam and the bridge analysis process are simulated, considering the prestressed steel strands and shrinkage and creep effects of the concrete. There are three groups of steel strand characteristic values, 238 groups of steel strand shapes, and 40 groups of construction stages.

[0102] The algorithm of the present invention was incorporated into the self-developed, independently controllable finite element software Wolong System, and its accuracy was tested using the aforementioned engineering case. Back-to-back comparative calculations with the commercial finite element software Midas were used for verification. The creep secondary forces in the axial, vertical, and moment directions under the tensile forces of 238 steel strands during a typical analysis phase (ten years after completion) were extracted for comparison.

[0103] Attachment Figure 6 Comparison of creep secondary forces in the axial direction between the commercial finite element software Midas and the self-developed finite element software Wolong. Figure 7 The vertical creep secondary force comparison diagram of the commercial finite element software Midas and the self-developed finite element software Wolong is shown in the figure. Figure 8 A comparison chart showing the creep secondary force in the bending moment direction between the commercial finite element software Midas and the self-developed finite element software Wolong.

[0104] Attachment Figure 6 To the attached Figure 8 The symbols Fx, Fz, and My represent the creep secondary forces in the axial, vertical, and bending directions, respectively.

[0105] From the attached Figure 6 To the attached Figure 8 It can be seen that the calculation results of the commercial finite element software Midas and the self-developed finite element software Wolong are very close. In the three comparison figures, the curves drawn by the two software calculations are almost superimposed. A detailed analysis of the numerical values ​​shows that the maximum relative error in the creep secondary force among the three comparison results is 4%, and the maximum error is at the lower value of the calculated value.

[0106] Therefore, it can be seen from this calculation example that the calculation results of the creep secondary force calculation method caused by steel strands proposed in the present invention are reasonable and reliable, and meet the requirements of engineering design.

[0107] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating creep secondary forces caused by steel tendons, characterized by: The following steps are involved: Step A, determining the initial values ​​of the steel tendon information, structural information, creep primary force and creep secondary force involved in the work at the initial moment; Step B, based on step A, calculating the elastic displacement of the bridge structure obtained by tensioning the steel tendons; Step C, calculating the creep displacement value increased by the tensioning of the steel tendons; Step D, introduce the cross-sectional property conversion coefficient and calculate the specific values ​​corresponding to the two ends of the unit; Step E, calculating the creep primary force based on steps B to D; Step F, calculating the creep secondary force based on steps B to E; Step G, substitute the creep secondary force into the next stage, repeat steps A to F, and calculate the creep primary force and creep secondary force of the next time period.

2. The method for calculating creep secondary force caused by steel tendons according to claim 1, characterized in that: Step A determines the initial values ​​of the steel tendon information, structural information, creep primary force, and creep secondary force involved in the work. The specific process is as follows: First, determine the information of the steel strands involved in the work, such as the tension force of the steel strand, the cross-sectional area of ​​the steel strand, the number of steel strands, the friction coefficient of the steel strand, the design coordinates of the steel strand, the rebound shrinkage of the steel strand, and the positional relationship between the steel strand and the beam element; Secondly, determine the structural information involved in the work, such as unit number, restraint system, other loads besides tendon tension, construction stage, and concrete shrinkage and creep; Finally, the primary creep force and secondary creep force of the structure at the initial moment are determined to be zero, which can be written as: Where f1 represents the primary creep force of the structure, and f2 represents the secondary creep force of the structure.

3. The method for calculating creep secondary force caused by steel tendons according to claim 1, characterized in that: Step B is based on step A and calculates the elastic displacement of the bridge structure obtained by tensioning the steel tendons. The specific process is as follows: First, based on the information from step A, calculate the long-term loss and short-term loss values ​​of each steel strand; Secondly, the effective tensile stress value of the steel tendon along the tendon coordinate is calculated; Again, the equivalent load at each unit node is calculated and applied to the structural unit; Finally, the overall stiffness matrix and load matrix of the structure are assembled to calculate the elastic displacement of each unit node of the structure.

4. The method for calculating creep secondary force caused by steel tendons according to claim 1, characterized in that: Step C calculates the creep displacement value added by tendon tensioning. The specific process is as follows: First, the elastic displacement of the structure caused by the tensioning of the steel tendons is calculated; Secondly, calculate the creep coefficient and increment corresponding to each time point and time history; Finally, the creep displacement value increased by tendon tensioning is calculated, which is expressed as follows: Where Δu represents the elastic displacement of the structure caused by the tensioning of the steel tendons. It represents the creep coefficient increment, and du represents the creep displacement value increased by tendon tensioning.

5. The method for calculating creep secondary force caused by steel tendons according to claim 1, characterized in that: Step D introduces the cross-sectional property conversion coefficient and calculates the specific values ​​corresponding to the two ends of the unit. The specific calculation expression is as follows: Wherein, λ represents the cross-sectional characteristic conversion coefficient introduced in the present invention. When used for axial force calculation and bending moment calculation, the specific expressions are different. A0 and A all Represents the net concrete cross-sectional area and the equivalent converted area including the steel tendons, I0 and I all Represents the net moment of inertia of concrete and the equivalent converted moment of inertia including steel tendons.

6. The method for calculating creep secondary force caused by steel tendons according to claim 1, characterized in that: Step E calculates the creep force based on steps B to D. The calculation expression is as follows: Where f1 represents the creep force of the structure, K represents the elastic stiffness matrix of the structure, and f 固端 represents the equivalent fixed end force caused by the non-nodal load of the structure, Represents the creep coefficient of each unit of the structure from the initial time t0 to the calculation time t.

7. The method for calculating creep secondary force caused by steel tendons according to claim 1, characterized in that: Step F calculates the creep secondary force based on steps B to E. The specific calculation expression is as follows: Where f2 represents the creep secondary force of the structure, du represents the creep displacement increment, which is obtained by applying the creep primary force f1 to the structure; dF represents the elastic internal force increment caused by displacement, which can be expressed by the expression dF = K*Δu; Represents the creep coefficient increment.

8. The method for calculating creep secondary force caused by steel tendons according to claim 1, characterized in that: Step G substitutes the creep secondary force into the next stage and repeats steps A to F to calculate the creep primary force and creep secondary force for the next time period. The specific process is as follows: The creep secondary force calculated by formula (8) replaces the initial value of the creep secondary force in formula (1), and then enters the next stage and calculates according to formulas (2) to (8) until the end of the stage.

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