A prestressed friction loss calculation analysis method and system

Abstract

This invention proposes a method and system for calculating and analyzing prestressed friction loss, belonging to the field of friction loss calculation. The method includes acquiring preset coordinate data of the duct centerline and performing spatial geometric modeling of the duct to obtain its geometric parameters; segmenting the duct; establishing a dynamic friction coefficient model, which determines the stress range of prestress transfer based on the ratio of the current prestress value to the tension control stress; recursively calculating the prestress loss of each duct micro-segment starting from the tensioning end of the duct; determining the dynamic friction coefficient of each micro-segment based on the starting prestress value of each duct as the far end using the dynamic friction coefficient model; calculating the prestress loss of each micro-segment based on the dynamic friction coefficient and the geometric parameters of the micro-segment and transferring it to the next micro-segment, recursively extending to the end of the prestressing tendon duct to obtain the prestress distribution. This invention improves the accuracy and applicability of prestress loss calculation.

Description

Technical Field

[0001] This invention relates to the field of friction loss calculation technology, and in particular to a method and system for calculating and analyzing prestressed friction loss. Background Technology

[0002] In prestressed concrete structures, prestressing tendons typically pass through metal or plastic corrugated pipe ducts pre-embedded in the concrete. Tensioning equipment applies tension to the tendons at one or both ends of the member, anchoring them once the design prestress value is reached. During tensioning, frictional contact exists between the prestressing tendons and the inner wall of the duct. As the prestress is transmitted along the duct from the tensioning end to the non-tensioning end, it gradually attenuates due to overcoming friction; this phenomenon is called prestress friction loss.

[0003] However, recent engineering practices and scientific research have revealed the limitations of existing calculation methods. Studies have shown that the friction loss of prestressed tendons under low stress is significantly higher than that under high stress. When the tensile stress is lower than a certain proportion of the design strength, the actual friction loss can be several times the theoretically calculated value. The physical mechanism of this phenomenon is that the contact pressure between the prestressed tendon and the duct wall is relatively small under low stress. Uneven factors such as local bending of the prestressed tendon and entanglement between the strands of steel wire formed during the threading process have not been fully eliminated, leading to an abnormally high friction coefficient.

[0004] Chinese invention patent application number 201710080588.X discloses a method for accurately determining the friction coefficient of prestressed ducts. This method involves setting an active end and a passive end at both ends of the duct. First, the active end tensions the prestressing tendon, and then the passive end applies tension until the prestressing tendon detaches from the inner wall of the duct. The friction coefficient is then calculated based on the force value at the critical detachment state, thus achieving accurate measurement of the friction coefficient. However, this method focuses on obtaining a precise value for a single, fixed friction coefficient through specialized testing, without addressing the dynamic adjustment of the friction coefficient as the prestress level changes. It lacks specific methods to handle the differences in friction characteristics of prestressing tendons under different tensile stress states. Summary of the Invention

[0005] In view of this, the present invention proposes a method and system for calculating and analyzing prestressed friction loss, which can solve the problem of interaction between different batches of prestressing tendons in multi-stage tensioning construction in the prior art, and improve the accuracy and applicability of prestress loss calculation.

[0006] The technical solution of this invention is implemented as follows: On the one hand, the present invention provides a method for calculating and analyzing prestressed friction loss, comprising the following steps: S1. Obtain the preset coordinate data of the center line of the duct and perform spatial geometric modeling of the duct to obtain the geometric parameters of the duct; wherein, the duct is a pipe embedded in concrete for inserting prestressed tendons. S2. The channel is segmented to obtain multiple channel micro-segments and the geometric parameters of each channel micro-segment. S3. Establish a dynamic friction coefficient model. The dynamic friction coefficient model determines the stress range in which the prestress is transferred based on the ratio of the current prestress value to the tension control stress. Different friction coefficient correction factors are used for different stress ranges. S4. Starting from the tensioning end of the duct, perform recursive calculations on each duct micro-segment in sequence. Based on the starting prestress value of each duct as the far end, determine the dynamic friction coefficient of the micro-segment through the dynamic friction coefficient model. Calculate the prestress loss of the micro-segment based on the dynamic friction coefficient and the geometric parameters of the micro-segment, and transfer it to the next micro-segment. Recursively calculate to the end of the prestressing tendon duct to obtain the prestress distribution.

[0007] Based on the above technical solutions, preferably, step S3 specifically includes: Define stress ratio Current prestress value With tension control stress The ratio; According to stress ratio Dividing the prestress transmission process along the duct into three zones—low stress zone, normal stress zone, and high stress zone—the dynamic friction coefficient is then... for: ; in, For stress ratio The changing dynamic coefficient of friction, As the reference friction coefficient, It is a low-stress enhancement factor. As a high-stress adjustment factor, Stress ratio, Low stress threshold, For high stress threshold, This represents the maximum stress ratio threshold.

[0008] Based on the above technical solutions, preferably, step S4 specifically includes: S41, Regarding the first Each micro-element segment, based on the prestress value at the starting point of the micro-element segment. and tension control stress Calculated stress ratio And based on the stress ratio The dynamic friction coefficient of the micro-segment is determined using a dynamic friction coefficient model. ; S42, Based on the dynamic friction coefficient Angular change of the infinitesimal segment Deviation coefficient per unit length of the duct and the length of the infinitesimal segment Calculate the prestress loss of the micro-element segment ; S43. For single-stage tensioning, the prestress value... With prestress loss The difference is used as the final prestress value. And it is transferred to the next micro-element segment, from the tensioning end to the end of the duct, to obtain the prestress distribution; or, For multi-stage tensioning, during the first stage... During stage tensioning, read the first to the last... The prestress distribution of the prestressed duct in the first stage is taken as the initial state for the second stage. The prestress distribution of the newly tensioned duct is obtained through recursive calculation. Based on the prestress distribution of the newly tensioned duct, the resultant force and bending moment of the prestressing tendons in the new tensioned duct are calculated. The prestress distribution of the already tensioned duct is then obtained through iterative calculation based on the resultant force and bending moment. This process is repeated to obtain the prestress distribution after multiple stages of tensioning. It is a positive integer not less than 2.

[0009] Based on the above technical solutions, preferably, the formula for calculating the prestress loss is as follows: ; ; in, For the first The prestress value at the starting point of each micro-element segment, For the first The dynamic friction coefficient of each micro-element segment, For the first The change in angle of each infinitesimal segment This is the deviation coefficient per unit length of the channel. For the first The length of each infinitesimal segment Let be the radius of curvature of this infinitesimal segment.

[0010] Based on the above technical solutions, preferably, the calculation of the resultant force and bending moment of the prestressing tendons in the new tensioning duct based on the prestress distribution of the new tensioning duct specifically includes: For the For a newly tensioned duct, the average effective prestress of the duct is calculated based on the prestress distribution of each micro-element segment along the length of the duct. ; Based on the cross-sectional area of ​​the prestressing tendons and average effective prestress Calculate the resultant force of the prestressing tendons in this duct. and for the first The total resultant force of the prestressing tendons in the new tensioning ducts is obtained by summing the resultant forces of all newly tensioned ducts in each stage. : ; ; in For the first The collection of newly tensioned ducts in each stage, This represents the resultant force of the prestressing tendon in the j-th newly tensioned duct; For the For each newly tensioned duct in the stage, the bending moment generated by the prestressing tendons in the new tensioned duct is obtained by summing the results over all newly tensioned ducts: ; in, This represents the bending moment generated by the prestressing tendons in the newly tensioned duct. Indicates the index of the newly tensioned duct. Indicates the first The eccentricity of the centroid of the prestressing tendon in the new tensioning duct relative to the centroid of the component section.

[0011] Based on the above technical solutions, preferably, the iterative calculation specifically includes: Based on the resultant force of the prestressed tendons in the newly tensioned duct The elastic modulus of concrete in structural members and concrete cross-sectional area Calculate the axial compressive strain of the component : ; in, Indicates the number of iterations. The elastic modulus of concrete. The concrete cross-sectional area of ​​the component; Based on the bending moment generated by the prestressing tendons in the newly tensioned duct and the moment of inertia of the concrete section of the component Calculate the change in curvature : ; in, The moment of inertia of the concrete section of the component; For the The prestressed duct is tensioned based on the eccentricity of its prestressing tendon centroid relative to the centroid of the member section. Axial compressive strain and changes in curvature Calculate the longitudinal strain increment at this location. : ; Based on the elastic modulus of prestressed tendons and longitudinal strain increment Calculate the stress variation of the prestressed tendons in this duct: ; in, The elastic modulus of the prestressing tendon; Update the prestress values ​​of the tensioned prestressed tendons. Calculate the maximum absolute value of the stress change in the tensioned prestressed tendons: ; ; ; ; in, Indicates the first During the nth iteration The axial stress of the prestressed tendons has been reduced. Indicates the first During the nth iteration The axial stress of the prestressed tendons has been reduced. This represents the elastic modulus of prestressed tendons. This represents the total axial force in the newly tensioned duct. It represents the equivalent axial stiffness of the component. This represents the total bending moment of the newly tensioned duct. Indicates the first The eccentricity of the centroid of the prestressed tendon relative to the centroid of the member section. It represents the equivalent bending stiffness of a component. Indicates the area of ​​the tensioned reinforcing bars; Determine the maximum absolute value Is it less than the convergence tolerance? : If so, output the current prestress distribution of each duct; If not, proceed to the next step. Repeat the iterations until the convergence condition is met.

[0012] Based on the above technical solutions, preferably, step S1 specifically includes: Obtain preset coordinate data of the channel centerline, the coordinate data including the three-dimensional coordinates of each feature point on the channel centerline; Based on the coordinate data, a spatial geometric model of the channel is established, and the curvature and radius of curvature at each position along the channel are calculated.

[0013] Based on the above technical solutions, preferably, the channel includes a spatial curved channel and a planar curved channel, wherein, For a spatial curve channel, the curvature is obtained by calculating the rate of change of the tangent vector of the channel centerline using differential geometry methods, and the deflection is obtained by calculating the rotation rate of the principal normal vector of the channel centerline. The deflection is used to characterize the three-dimensional torsional features of the channel. For planar curved channels, identify the boundaries between straight segments, circular curve segments, and other curved segments in the channel, and extract the radius of curvature of each curved segment.

[0014] Furthermore, step S2 specifically includes: The length of the micro-element segment is determined based on the total length of the duct and the required calculation accuracy. ; The center line of the channel is divided equally according to the length of the micro-segment to obtain multiple channel micro-segments, and each channel micro-segment is numbered. For the Extract the arc length coordinates of the starting point of each infinitesimal segment. , End point arc length coordinates And calculate the length of the infinitesimal segment. ; Calculate the curvature at the midpoint of each infinitesimal element. and radius of curvature The geometric parameters of the midpoint of the infinitesimal segment are used as the geometric parameters of the infinitesimal segment.

[0015] On the other hand, the present invention provides a prestressed friction loss calculation and analysis system, which employs the prestressed friction loss calculation and analysis method described above, including: The parameter acquisition module is used to acquire the preset coordinate data of the center line of the duct and to perform spatial geometric modeling of the duct to obtain the geometric parameters of the duct; wherein, the duct is a pipe embedded in concrete for inserting prestressed tendons. The channel segmentation module is used to segment the channel to obtain multiple channel micro-segments and the geometric parameters of each channel micro-segment; The model building module is used to establish a dynamic friction coefficient model. The dynamic friction coefficient model determines the stress range in which the prestress is transferred based on the ratio of the current prestress value to the tension control stress. Different friction coefficient correction factors are used for different stress ranges. The calculation and analysis module is used to perform recursive calculations on each micro-segment of the duct starting from the tensioning end. Based on the starting prestress value of each duct as the far end, the dynamic friction coefficient of the micro-segment is determined by the dynamic friction coefficient model. Based on the dynamic friction coefficient and the geometric parameters of the micro-segment, the prestress loss of the micro-segment is calculated and transferred to the next micro-segment, and the process is repeated until the end of the prestressing tendon duct to obtain the prestress distribution.

[0016] The prestressed friction loss calculation and analysis method and system of the present invention have the following advantages over the prior art: (1) By establishing a dynamic friction coefficient model, the prestress transmission process is divided into three intervals: low stress zone, normal stress zone, and high stress zone according to the ratio of prestress value to tension control stress. Different friction coefficient correction factors are used for different intervals so that the friction coefficient can be dynamically adjusted with the prestress state, so that the calculation results can more realistically reflect the actual friction characteristics change law in the prestress transmission process along the duct. (2) By using an iterative algorithm to simulate the interaction process between the prestressed tendons and the components, the strain increment at the location of the tensioned prestressed tendons is calculated by the changes in axial compressive strain and bending curvature, and then the passive stress loss of the prestressed tendons is obtained. This ensures the calculation accuracy and convergence of the multi-stage interaction analysis, accurately assesses the cumulative stress loss in the batch tensioning construction, and provides a more reliable technical basis for ensuring the safety and durability of the structure in the long-term use stage. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a prestressed friction loss calculation and analysis method according to the present invention; Figure 2 This is a schematic diagram of the micro-segment division of a prestressed friction loss calculation and analysis method according to the present invention; Figure 3 This is a flowchart of a single-stage recursive calculation of prestress loss in a prestress friction loss calculation and analysis method according to the present invention. Figure 4 This is a schematic diagram of the multi-stage stress redistribution iterative calculation of a prestressed friction loss calculation and analysis method according to the present invention. Detailed Implementation

[0019] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0020] like Figure 1 As shown, this invention provides a method for calculating and analyzing prestressed friction loss, comprising the following steps: S1. Obtain the preset coordinate data of the center line of the duct and perform spatial geometric modeling of the duct to obtain the geometric parameters of the duct; wherein, the duct is a pipe embedded in concrete for inserting prestressed tendons.

[0021] In one embodiment of the present invention, the duct is a metal corrugated pipe or a plastic corrugated pipe, and the prestressed tendon passes through the duct and is tensioned at the end of the component by a tensioning device.

[0022] like Figure 2 As shown, specifically, step S1 includes: Obtain preset coordinate data of the channel centerline, the coordinate data including the three-dimensional coordinates of each feature point on the channel centerline; A spatial geometric model of the channel is established based on the coordinate data, and the curvature and radius of curvature at various positions along the channel are calculated; the channel includes spatial curved channels and planar curved channels, wherein, For a spatial curve channel, the curvature is obtained by calculating the rate of change of the tangent vector of the channel centerline using differential geometry methods, and the deflection is obtained by calculating the rotation rate of the principal normal vector of the channel centerline. The deflection is used to characterize the three-dimensional torsional features of the channel. For planar curved channels, identify the boundaries between straight segments, circular curve segments, and other curved segments in the channel, and extract the radius of curvature of each curved segment.

[0023] Understandably, for planar curved channels, the vertical coordinates change parabolically or circularly along the length of the channel, while the horizontal coordinates remain constant or change linearly. For spatial curved channels, all three coordinate components change along the length of the channel, requiring the use of parametric equations to describe them.

[0024] S2. The channel is segmented to obtain multiple channel micro-segments and the geometric parameters of each channel micro-segment. Specifically, step S2 includes: The length of the micro-element segment is determined based on the total length of the duct and the required calculation accuracy. ; The center line of the channel is divided equally according to the length of the micro-segment to obtain multiple channel micro-segments, and each channel micro-segment is numbered. For the Extract the arc length coordinates of the starting point of each infinitesimal segment. , End point arc length coordinates And calculate the length of the infinitesimal segment. ; Calculate the curvature at the midpoint of each infinitesimal element. and radius of curvature The geometric parameters of the midpoint of the infinitesimal segment are used as the geometric parameters of the infinitesimal segment.

[0025] Understandably, the selection of the infinitesimal segment length ΔL requires a balance between computational accuracy and efficiency. A shorter infinitesimal segment offers higher accuracy but also increases computational complexity, while a longer segment offers higher efficiency but lower accuracy. The arc length coordinates of the midpoint of the infinitesimal segment are ( Query the curvature at that arc length position in the mathematical model of the centerline of the duct. and radius of curvature The geometric parameters of the midpoint of a infinitesimal segment represent the average geometric characteristics of that infinitesimal segment.

[0026] S3. Establish a dynamic friction coefficient model. The dynamic friction coefficient model determines the stress range in which the prestress is transferred based on the ratio of the current prestress value to the tension control stress. Different friction coefficient correction factors are used for different stress ranges. Specifically, step S3 includes: Define stress ratio Current prestress value With tension control stress The ratio:

[0027] According to stress ratio Dividing the prestress transmission process along the duct into three zones—low stress zone, normal stress zone, and high stress zone—the dynamic friction coefficient is then... for: ; in, For stress ratio The changing dynamic coefficient of friction, As the reference friction coefficient, It is a low-stress enhancement factor. As a high-stress adjustment factor, Stress ratio, Low stress threshold, For high stress threshold, This represents the maximum stress ratio threshold.

[0028] Understandable, the reference friction coefficient The value is typically between 0.15 and 0.25. The value is typically between 0.25 and 0.35, which marks the end of the low-stress zone. The value is typically between 0.75 and 0.85, which marks the boundary where the high-stress zone begins. The value is typically taken to be between 1.05 and 1.10, which is the saturation point for high stress adjustment. Typically, the value is between 1.2 and 1.5, which is a magnification factor for the coefficient of friction under extremely low stress. The value is typically between 0.85 and 0.95, which is the factor that reduces the coefficient of friction under extremely high stress.

[0029] The continuous change of the friction coefficient is simulated using a piecewise linear form: a linear increase in the low-stress segment corresponds to increased friction, a linear decrease in the high-stress segment corresponds to decreased friction, and a constant value in the normal segment ensures stability. All segments are continuous at the threshold, avoiding numerical problems caused by discontinuities.

[0030] This invention establishes a dynamic friction coefficient model to divide the prestress transmission process into three zones: a low-stress zone, a normal-stress zone, and a high-stress zone, based on the ratio of the prestress value to the tension control stress. Different friction coefficient correction factors are used for different zones, allowing the friction coefficient to be dynamically adjusted according to the prestress state. This avoids introducing unnecessary computational complexity under conventional working conditions, enabling the calculation results to more realistically reflect the actual friction characteristics change law during the prestress transmission process along the duct.

[0031] In one embodiment of the present invention, in the low-stress region, The value is 0.3, which is within the normal stress region. , High stress area It is 0.8.

[0032] S4. Starting from the tensioning end of the duct, perform recursive calculations on each duct micro-segment in sequence. Based on the starting prestress value of each duct as the far end, determine the dynamic friction coefficient of the micro-segment through the dynamic friction coefficient model. Calculate the prestress loss of the micro-segment based on the dynamic friction coefficient and the geometric parameters of the micro-segment, and transfer it to the next micro-segment. Recursively calculate to the end of the prestressing tendon duct to obtain the prestress distribution.

[0033] like Figure 3 and 4 As shown, specifically, step S4 includes: S41, Regarding the first Each micro-element segment, based on the prestress value at the starting point of the micro-element segment. and tension control stress Calculated stress ratio And based on the stress ratio The dynamic friction coefficient of the micro-segment is determined using a dynamic friction coefficient model. ; S42, Based on the dynamic friction coefficient Angular change of the infinitesimal segment Deviation coefficient per unit length of the duct and the length of the infinitesimal segment Calculate the prestress loss of the micro-element. The formula for calculating the prestress loss is: ; ; in, For the first The prestress value at the starting point of each micro-element segment, For the first The dynamic friction coefficient of each micro-element segment For the first The change in angle of each infinitesimal segment This is the deviation coefficient per unit length of the channel. For the first The length of each infinitesimal segment Let be the radius of curvature of this infinitesimal segment; S43. For single-stage tensioning, the prestress value... With prestress loss The difference is used as the final prestress value. And it is transferred to the next micro-element segment, from the tensioning end to the end of the duct, to obtain the prestress distribution; or, For multi-stage tensioning, during the first stage... During stage tensioning, read the first to the last... The prestress distribution of the prestressed duct in the first stage is taken as the initial state for the second stage. The prestress distribution of the newly tensioned duct is obtained through recursive calculation. Based on the prestress distribution of the newly tensioned duct, the resultant force and bending moment of the prestressing tendons in the new tensioned duct are calculated. The prestress distribution of the already tensioned duct is then obtained through iterative calculation based on the resultant force and bending moment. This process is repeated to obtain the prestress distribution after multiple stages of tensioning. It is a positive integer not less than 2.

[0034] Understandable. This is due to frictional losses caused by the bending of the channel. Frictional loss caused by accidental deviations in the duct. Deviation coefficient per unit length of the duct. It reflects the degree of deviation between the actual position of the duct and the designed position during construction. It is set according to the construction quality level, and this invention does not impose specific limitations on it.

[0035] For a single-end tensioned duct, the tensioning end is located at one end of the duct and the non-tensioning end is located at the other end of the duct. The prestress is transmitted unidirectionally from the tensioning end to the non-tensioning end. For a double-end tensioned duct, both ends are tensioned simultaneously, and the prestress is transmitted bidirectionally from both ends to the midpoint. It is necessary to perform recursive calculations for each half of the duct separately.

[0036] In one embodiment of the present invention, the calculation of the resultant force and bending moment of the prestressing tendons in the newly tensioned duct based on the prestress distribution specifically includes: For the For a newly tensioned duct, the average effective prestress of the duct is calculated based on the prestress distribution of each micro-element segment along the length of the duct. ; Based on the cross-sectional area of ​​the prestressing tendons and average effective prestress Calculate the resultant force of the prestressing tendons in this duct. and for the first The total resultant force of the prestressing tendons in the new tensioning ducts is obtained by summing the resultant forces of all newly tensioned ducts in each stage. : ; ; in For the first The collection of newly tensioned ducts in each stage, This represents the resultant force of the prestressing tendon in the j-th newly tensioned duct; For the For each newly tensioned duct in the stage, the bending moment generated by the prestressing tendons in the new tensioned duct is obtained by summing the results over all newly tensioned ducts: ; in, This represents the bending moment generated by the prestressing tendons in the newly tensioned duct. Indicates the index of the newly tensioned duct. Indicates the first The eccentricity of the centroid of the prestressing tendon in the new tensioning duct relative to the centroid of the component section.

[0037] Understandable, the cross-sectional area of ​​prestressing tendons The eccentricity can be found in the product manual based on the specifications and model of the prestressing tendons. It is calculated based on the position of the duct in the component cross-section and the geometric properties of the component cross-section.

[0038] Furthermore, the iterative calculation specifically includes: Based on the resultant force of the prestressed tendons in the newly tensioned duct The elastic modulus of concrete in structural members and concrete cross-sectional area Calculate the axial compressive strain of the component : ; in, Indicates the number of iterations. The elastic modulus of concrete. The concrete cross-sectional area of ​​the component; Based on the bending moment generated by the prestressing tendons in the newly tensioned duct and the moment of inertia of the concrete section of the component Calculate the change in curvature : ; in, The moment of inertia of the concrete section of the component; For the The prestressed duct is tensioned based on the eccentricity of its prestressing tendon centroid relative to the centroid of the member section. Axial compressive strain and changes in curvature Calculate the longitudinal strain increment at this location. : ; Based on the elastic modulus of prestressed tendons and longitudinal strain increment Calculate the stress variation of the prestressed tendons in this duct: ; in, The elastic modulus of the prestressing tendon; Update the prestress values ​​of the tensioned prestressed tendons. Calculate the maximum absolute value of the stress change in the tensioned prestressed tendons: ; ; ; ; in, Indicates the first During the nth iteration The axial stress of the prestressed tendons has been reduced. Indicates the first During the nth iteration The axial stress of the prestressed tendons has been reduced. This represents the elastic modulus of prestressed tendons. This represents the total axial force in the newly tensioned duct. It represents the equivalent axial stiffness of the component. This represents the total bending moment of the newly tensioned duct. Indicates the first The eccentricity of the centroid of the prestressed tendon relative to the centroid of the member section. It represents the equivalent bending stiffness of a component. Indicates the area of ​​the tensioned reinforcing bars; Determine the maximum absolute value Is it less than the convergence tolerance? : If so, output the current prestress distribution of each duct; If not, proceed to the next step. Repeat the iterations until the convergence condition is met.

[0039] Understandable, the elastic modulus of concrete The concrete cross-sectional area is calculated using empirical formulas. and moment of inertia of cross section The elastic modulus of prestressed tendons is calculated based on the cross-sectional dimensions and shape of the component. Find the information in the product manual based on the material type of the prestressing tendons.

[0040] For a complete multi-stage tensioning construction process, calculations are performed sequentially from the first stage to the Nth stage. The first stage only performs single-stage recursive calculations and does not involve multi-stage analysis. Starting from the second stage, each stage first reads the state of the tensioned prestressed tendons from the previous stage, then performs the recursive calculation of this stage using the dynamic friction coefficient, and then updates the final stress state of all prestressed tendons through an iterative algorithm. This state is recorded as the calculation result of this stage and used as the input for the next stage, thus realizing dynamic simulation and cumulative effect analysis of the entire construction process.

[0041] This invention uses an iterative algorithm to simulate the interaction process between prestressed tendons and structural members. By calculating the strain increment at the location of the tensioned prestressed tendons through changes in axial compressive strain and bending curvature, the passive stress loss of the prestressed tendons is obtained. This ensures the calculation accuracy and convergence of the multi-stage interaction analysis, accurately assesses the cumulative stress loss during batch tensioning construction, and provides a more reliable technical basis for ensuring the safety and durability of the structure during long-term use.

[0042] In one embodiment of the present invention, convergence tolerance The convergence tolerance should be selected to balance calculation accuracy and iteration efficiency, with the tolerance set at one-thousandth of the tension control stress. Too small a convergence tolerance will lead to an increase in the number of iterations and a longer calculation time, while too large a convergence tolerance will lead to insufficient calculation accuracy.

[0043] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating and analyzing prestressed friction loss, characterized in that: Includes the following steps: S1. Obtain the preset coordinate data of the center line of the duct and perform spatial geometric modeling of the duct to obtain the geometric parameters of the duct; wherein, the duct is a pipe embedded in concrete for inserting prestressed tendons. S2. The channel is segmented to obtain multiple channel micro-segments and the geometric parameters of each channel micro-segment. S3. Establish a dynamic friction coefficient model. The dynamic friction coefficient model determines the stress range in which the prestress is transferred based on the ratio of the current prestress value to the tension control stress. Different friction coefficient correction factors are used for different stress ranges. S4. Starting from the tensioning end of the duct, perform recursive calculations on each duct micro-segment in sequence. Based on the starting prestress value of each duct as the far end, determine the dynamic friction coefficient of the micro-segment through the dynamic friction coefficient model. Calculate the prestress loss of the micro-segment based on the dynamic friction coefficient and the geometric parameters of the micro-segment, and transfer it to the next micro-segment. Recursively calculate to the end of the prestressing tendon duct to obtain the prestress distribution.

2. The method for calculating and analyzing prestressed friction loss as described in claim 1, characterized in that: Step S3 specifically includes: Define stress ratio Current prestress value With tension control stress The ratio; According to stress ratio Dividing the prestress transmission process along the duct into three zones—low stress zone, normal stress zone, and high stress zone—the dynamic friction coefficient is then... for: ； in, For stress ratio The changing dynamic coefficient of friction, As the reference friction coefficient, It is a low-stress enhancement factor. As a high-stress adjustment factor, Stress ratio, Low stress threshold, For high stress threshold, This represents the maximum stress ratio threshold.

3. The method for calculating and analyzing prestressed friction loss as described in claim 1, characterized in that: Step S4 specifically includes: S41, Regarding the first Each micro-element segment, based on the prestress value at the starting point of the micro-element segment. and tension control stress Calculated stress ratio And based on the stress ratio The dynamic friction coefficient of the micro-segment is determined using a dynamic friction coefficient model. ; S42, Based on the dynamic friction coefficient Angular change of the infinitesimal segment Deviation coefficient per unit length of the duct and the length of the infinitesimal segment Calculate the prestress loss of the micro-element. ; S43. For single-stage tensioning, the prestress value... With prestress loss The difference is used as the final prestress value. And it is transferred to the next micro-element segment, from the tensioning end to the end of the duct, to obtain the prestress distribution; or, For multi-stage tensioning, during the first stage... During stage tensioning, read the first to the last... The prestress distribution of the prestressed duct in the first stage is taken as the initial state for the second stage. The prestress distribution of the newly tensioned duct is obtained through recursive calculation. Based on the prestress distribution of the newly tensioned duct, the resultant force and bending moment of the prestressing tendons in the new tensioned duct are calculated. The prestress distribution of the already tensioned duct is then obtained through iterative calculation based on the resultant force and bending moment. This process is repeated to obtain the prestress distribution after multiple stages of tensioning. It is a positive integer not less than 2.

4. The method for calculating and analyzing prestressed friction loss as described in claim 3, characterized in that: The formula for calculating the prestress loss is: ； ； in, For the first The prestress value at the starting point of each micro-element segment, For the first The dynamic friction coefficient of each micro-element segment For the first The change in angle of each infinitesimal segment This is the deviation coefficient per unit length of the channel. For the first The length of each infinitesimal segment Let be the radius of curvature of this infinitesimal segment.

5. The method for calculating and analyzing prestressed friction loss as described in claim 3, characterized in that: The calculation of the resultant force and bending moment of the prestressing tendons in the newly tensioned duct based on the prestress distribution specifically includes: For the For a newly tensioned duct, the average effective prestress of the duct is calculated based on the prestress distribution of each micro-element segment along the length of the duct. ; Based on the cross-sectional area of ​​the prestressing tendons and average effective prestress Calculate the resultant force of the prestressing tendons in this duct. and for the first The total resultant force of the prestressing tendons in the new tensioning ducts is obtained by summing the resultant forces of all newly tensioned ducts in each stage. : ； ； in For the first The collection of newly tensioned ducts in each stage, This represents the resultant force of the prestressing tendon in the j-th newly tensioned duct; For the For each newly tensioned duct in the stage, the bending moment generated by the prestressing tendons in the new tensioned duct is obtained by summing the results over all newly tensioned ducts: ； in, This represents the bending moment generated by the prestressing tendons in the newly tensioned duct. Indicates the index of the newly tensioned duct. Indicates the first The eccentricity of the centroid of the prestressing tendon in the new tensioning duct relative to the centroid of the component section.

6. The method for calculating and analyzing prestressed friction loss as described in claim 5, characterized in that: The iterative calculation specifically includes: Based on the resultant force of the prestressed tendons in the newly tensioned duct The elastic modulus of concrete in structural members and concrete cross-sectional area Calculate the axial compressive strain of the component : ； in, Indicates the number of iterations. The elastic modulus of concrete. The concrete cross-sectional area of ​​the component; Based on the bending moment generated by the prestressing tendons in the newly tensioned duct and the moment of inertia of the concrete section of the component Calculate the change in curvature : ； in, The moment of inertia of the concrete section of the component; For the The prestressed duct is tensioned based on the eccentricity of its prestressing tendon centroid relative to the centroid of the member section. Axial compressive strain and changes in curvature Calculate the longitudinal strain increment at this location. : ； Based on the elastic modulus of prestressed tendons and longitudinal strain increment Calculate the stress variation of the prestressed tendons in this duct: ； in, The elastic modulus of the prestressing tendon; Update the prestress values ​​of the tensioned prestressed tendons. Calculate the maximum absolute value of the stress change in the tensioned prestressed tendons: ； ； ； ； in, Indicates the first During the nth iteration The axial stress of the prestressed tendons has been reduced. Indicates the first During the nth iteration The axial stress of the prestressed tendons has been reduced. This represents the elastic modulus of prestressed tendons. This represents the total axial force in the newly tensioned duct. It represents the equivalent axial stiffness of the component. This represents the total bending moment of the newly tensioned duct. Indicates the first The eccentricity of the centroid of the prestressed tendon relative to the centroid of the member section. It represents the equivalent bending stiffness of a component. Indicates the area of ​​the tensioned reinforcing bars; Determine the maximum absolute value Is it less than the convergence tolerance? : If so, output the current prestress distribution of each duct; If not, proceed to the next step. Repeat the iterations until the convergence condition is met.

7. The method for calculating and analyzing prestressed friction loss as described in claim 1, characterized in that: Step S1 specifically includes: Obtain preset coordinate data of the channel centerline, the coordinate data including the three-dimensional coordinates of each feature point on the channel centerline; Based on the coordinate data, a spatial geometric model of the channel is established, and the curvature and radius of curvature at each position along the channel are calculated.

8. The method for calculating and analyzing prestressed friction loss as described in claim 7, characterized in that: The channels include spatial curved channels and planar curved channels, wherein... For a spatial curve channel, the curvature is obtained by calculating the rate of change of the tangent vector of the channel centerline using differential geometry methods, and the deflection is obtained by calculating the rotation rate of the principal normal vector of the channel centerline. The deflection is used to characterize the three-dimensional torsional features of the channel. For planar curved channels, identify the boundaries between straight segments, circular curve segments, and other curved segments in the channel, and extract the radius of curvature of each curved segment.

9. The method for calculating and analyzing prestressed friction loss as described in claim 8, characterized in that: Step S2 specifically includes: The length of the micro-element segment is determined based on the total length of the duct and the required calculation accuracy. ; The center line of the channel is divided equally according to the length of the micro-segment to obtain multiple channel micro-segments, and each channel micro-segment is numbered. For the Extract the arc length coordinates of the starting point of each infinitesimal segment. , End point arc length coordinates And calculate the length of the infinitesimal segment. ; Calculate the curvature at the midpoint of each infinitesimal segment. and radius of curvature The geometric parameters of the midpoint of the infinitesimal segment are used as the geometric parameters of the infinitesimal segment.

10. A prestressed friction loss calculation and analysis system, characterized in that: The method for calculating and analyzing prestressed friction loss as described in any one of claims 1-9 includes: The parameter acquisition module is used to acquire the preset coordinate data of the center line of the duct and to perform spatial geometric modeling of the duct to obtain the geometric parameters of the duct; wherein, the duct is a pipe embedded in concrete for inserting prestressed tendons. The channel segmentation module is used to segment the channel to obtain multiple channel micro-segments and the geometric parameters of each channel micro-segment; The model building module is used to establish a dynamic friction coefficient model. The dynamic friction coefficient model determines the stress range in which the prestress is transferred based on the ratio of the current prestress value to the tension control stress. Different friction coefficient correction factors are used for different stress ranges. The calculation and analysis module is used to perform recursive calculations on each micro-segment of the duct starting from the tensioning end. Based on the starting prestress value of each duct as the far end, the dynamic friction coefficient of the micro-segment is determined by the dynamic friction coefficient model. Based on the dynamic friction coefficient and the geometric parameters of the micro-segment, the prestress loss of the micro-segment is calculated and transferred to the next micro-segment, and the process is repeated until the end of the prestressing tendon duct to obtain the prestress distribution.

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