Prestressing Arrangement Method and Tooth Block Anchoring System for Rigid Frame Bridges with Adaptable Short-Side Span Variable Width

Abstract

The present invention relates to a prestress layout method and a tooth block anchoring system for a variable-width rigid-frame bridge with a short-side span, belonging to the technical field of electronic digital data processing, and includes the following steps: Step S1: In the short-side span area of the variable-width rigid-frame bridge, arrange the main prestressed tendons along the longitudinal direction of the bridge to adapt to the change in the bridge deck width; Step S2: Set up reinforcing prestressed tendons in the area at the top of the bridge pier to enhance the shear and torsion resistance of the variable-width section; Step S3: Set up auxiliary prestressed tendons in the transition area of the variable-width rigid-frame bridge to balance the local stress concentration of the bridge; Step S4: The main prestressed tendons, the reinforcing prestressed tendons and the auxiliary prestressed tendons are respectively anchored in the embedded structures on the bridge and at the top of the bridge pier through the anchoring devices to form a spatial cooperative stress system; The beneficial effect of the present invention: By arranging the main prestressed tendons, the reinforcing prestressed tendons and the auxiliary prestressed tendons, the prestress of the variable-width rigid-frame bridge with a short-side span is reasonably arranged.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric digital data processing, and particularly relates to a prestress layout method and a tooth block anchoring system suitable for a short-side variable-width rigid-frame bridge. Background Art

[0002] Due to the short length of the short-side rigid-frame bridge, the moment and shear force distributions under load are different from those of conventional spans. If the prestressed tendons are still arranged in the conventional shape, it may cause excessive stress concentration in the end anchorage area of the short side span, while the prestress in the mid-span part is insufficient, resulting in cracking or excessive deformation of the rigid-frame bridge.

[0003] For a variable-width bridge deck, in the width change area, if the layout of the transverse prestressed tendons fails to fully consider the stress changes caused by the change in the bridge deck width, it may lead to uneven transverse stress distribution on the bridge deck and transverse cracks.

[0004] The layout of prestress should match the stress state of the rigid-frame bridge. In a short-side variable-width rigid-frame bridge, it is necessary to reasonably adjust the quantity, tensile force and layout mode of the prestressed tendons according to the stress characteristics of different parts, so that the prestress can effectively offset the adverse internal forces generated by the load and improve the bearing capacity and crack resistance of the rigid-frame bridge. Summary of the Invention

[0005] The present invention provides a prestress layout method and a tooth block anchoring system suitable for a short-side variable-width rigid-frame bridge, which are used to solve the technical problem of how to realize the reasonable layout of prestress in a short-side variable-width rigid-frame bridge. In the short-side span area of the variable-width rigid-frame bridge, main prestressed tendons are arranged along the longitudinal direction of the bridge to adapt to the change in the bridge deck width. Reinforcing prestressed tendons are set in the area at the top of the bridge pier to enhance the shear and torsion resistance of the variable-width section. Auxiliary prestressed tendons are set in the transition area of the variable-width rigid-frame bridge to balance the local stress concentration of the bridge, so as to realize the reasonable layout of prestress in the short-side variable-width rigid-frame bridge.

[0006] To achieve the above purpose, the present invention is realized through the following technical solutions:

[0007] A prestress layout method suitable for a short-side variable-width rigid-frame bridge includes the following steps:

[0008] Step S1: In the short-side span area of the variable-width rigid-frame bridge, main prestressed tendons are arranged along the longitudinal direction of the bridge, and the main prestressed tendons are arranged in a bifurcated manner in the variable-width section to adapt to the change in the bridge deck width;

[0009] Step S2: Reinforcing prestressed tendons are set in the area at the top of the bridge pier, and the reinforcing prestressed tendons are distributed in a fan shape to enhance the shear and torsion resistance of the variable-width section;

[0010] Step S3: Set auxiliary prestressed tendons in the transition area of the variable-width rigid-frame bridge. The auxiliary prestressed tendons are arranged with a gradually changing spacing in the transverse direction of the bridge to balance the local stress concentration of the bridge.

[0011] Step S4: The main prestressed tendons, the strengthening prestressed tendons and the auxiliary prestressed tendons are respectively anchored in the embedded structures on the bridge and at the top of the bridge pier through the anchoring devices to form a spatial cooperative stress system.

[0012] Optionally, in Step S1, for the calculation of the tensile force of the prestressed tendons arranged in the longitudinal direction of the bridge in the main prestressed tendons: ;

[0013] Wherein, is the tensile control stress, is the total prestress loss; Given the effective prestress and the area of the prestressed tendon , then the tensile force of the prestressed tendon is: .

[0014] Optionally, in Step S1, for the elongation of the prestressed tendons arranged in the longitudinal direction of the bridge in the main prestressed tendons: The elongation of the prestressed tendon during the tensioning process is calculated according to the following formula:

[0015] ;

[0016] Wherein, is the average tensile force of the prestressed tendon. For a curved prestressed tendon, is calculated according to the following formula: , is the tensile force at the tensioning end of the prestressed tendon, is the influence coefficient of the local deviation per meter of the duct on friction, is the length of the duct from the tensioning end to the calculated section, is the friction coefficient between the prestressing tendon and the duct wall, is the sum of the angles between the tangents of the curved duct part from the tensioning end to the calculated section (calculated in radians); is the length of the prestressed tendon, is the cross-sectional area of the prestressed tendon, is the elastic modulus of the prestressing tendon.

[0017] Optionally, in Step S1, for the spacing of the positioning bars in the main prestressed tendons arranged in the longitudinal direction of the bridge:

[0018] In the straight section, the spacing of the positioning bars, formula: In the formula, is the empirical coefficient of the straight line segment, taking a value of 0.8 - 1.0, is the outer diameter of the prestressed duct, is the lateral pressure exerted on the duct during concrete vibration, refers to the distance between two adjacent positioning bars on the straight line segment of the prestressed duct; takes a value of 0.8 - 1.0, and is used to consider the influence of factors such as concrete vibration force and duct fixing method under different engineering conditions on the spacing of the positioning bars, is an important factor affecting the spacing of the positioning bars; the lateral pressure exerted on the duct during concrete vibration;

[0019] In the curve segment, the spacing of the positioning bars should be appropriately reduced, and the formula is: , where, is the empirical coefficient of the curve segment, taking a value of 0.5 - 0.6, is the radius of curvature of the curve segment.

[0020] Optionally, in step S1, the main prestressed tendon is arranged in a bifurcated manner in the variable-width section:

[0021] Calculation of the length of the prestressed tendon: The length of the parabolic prestressed tendon The calculation formula is:

[0022] ;

[0023] Among them, represents the infinitesimal length of the curve, and by integrating it over the length of the gradual change section, the length of the entire parabolic prestressed tendon can be obtained;

[0024] is the quadratic parabola equation. Assuming the quadratic parabola equation is , the coefficients , , , are determined according to the boundary conditions of the gradual change section is the first derivative of

[0025] Calculation of the prestressed tendon tension:

[0026] Determine the standard value of the prestressed tendon tension according to the structural design requirements, considering the prestress loss , then the prestressed tendon tension

[0027] should satisfy:

[0028] Calculation of the layout angle of prestressed tendons:

[0029] In the variable-width section, the layout angle of the prestressed tendons changes. At the starting point of the transition section, the angle between the prestressed tendon and the beam axis is , and at the ending point, the angle is ; For the prestressed tendons arranged in a parabolic shape, at any position , the tangent angle can be obtained by differentiating the parabolic equation to get the slope , , the slope is equal to the tangent value of the angle between the positive direction at the position of and , .

[0030] Optionally, in step S2, for setting the enhanced prestressed tendons in the pier top area:

[0031] Calculation of the length of prestressed tendons:

[0032] For the parabola , the curve length in the interval is calculated by the formula:

[0033] ;

[0034] Among them, , substituting it into the above formula, we get: ;

[0035] The enhanced prestressed tendons are distributed in a fan shape: The parabolic equation is used to describe the curve shape of the fan-shaped prestressed tendons. Taking the center of the pier top as the origin, the horizontal direction as the axis, and the vertical direction as the axis, the parabolic equation can be expressed as ; Among them, is the parameter of the parabola, which determines the opening size and shape of the parabola, The value of is determined according to the specific layout requirements of the prestressed tendons, the dimensions of the pier top, and the factors of the prestressing effect.

[0036] Optionally, in step S3, the gradually changing spacing of the auxiliary prestressed tendons arranged along the transverse direction of the bridge is:

[0037] Assume the length of the transition zone is , the starting spacing is , the ending spacing is , and the linear gradient formula is used to calculate the tendon spacing at a distance from the starting point of the transition zone: ;

[0038] Among them, the value range of is

[0039] Optionally, in step S4, the steps for forming the spatial cooperative force system are as follows:

[0040] Step A: Define the prestressed tendon element: Simulate all prestressed tendons with the selected element type;

[0041] Step B: Set the prestressed tendon application method: Set the corresponding loading method in the model according to the actual prestress application method during the construction process;

[0042] Step C: Calculate the prestress loss of the prestressed tendon: Consider the prestress loss of the prestressed tendon during its use in the model.

[0043] The tooth block anchoring system adapted to the prestress layout of the short-side span variable-width rigid-frame bridge includes:

[0044] A data receiving module for receiving model data;

[0045] A data processing module for processing model data;

[0046] A data output module for outputting model data;

[0047] The data receiving module is connected to the data processing module, and the data processing module is connected to the data output module.

[0048] Advantages of the present invention:

[0049] In the present invention, by arranging the main prestressed tendons along the longitudinal direction of the bridge in the short-side span area of the variable-width rigid-frame bridge to adapt to the change of the bridge deck width, strengthening prestressed tendons are arranged in the pier top area to enhance the shear and torsion resistance performance of the variable-width section, and auxiliary prestressed tendons are arranged in the transition area of the variable-width rigid-frame bridge to balance the local stress concentration of the bridge, the reasonable layout of the prestress of the short-side span variable-width rigid-frame bridge is solved. The main prestressed tendons, strengthening prestressed tendons and auxiliary prestressed tendons are respectively anchored to the embedded structures on the bridge and at the pier top through the anchoring devices to form a spatial cooperative force system. Brief description of the drawings

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0051] Figure 1Schematic diagram of the system structure of the present invention;

[0052] Figure 2 Schematic diagram of the working process of the present invention. Specific implementation manners

[0053] The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0054] Embodiment 1:

[0055] As Figure 1 shown, this embodiment provides a tooth block anchoring system adapted to the prestress layout of a short-side span variable-width rigid frame bridge, including:

[0056] A data receiving module, configured to receive model data;

[0057] A data processing module, configured to process model data;

[0058] A data output module, configured to output model data;

[0059] The data receiving module is connected to the data processing module, and the data processing module is connected to the data output module.

[0060] Specifically, the data receiving module receives the 3D model data of the short-side span variable-width rigid frame bridge. There is a BIM model in the data processing module. The data processing module arranges the main prestressed tendons along the longitudinal direction of the bridge in the short-side span area of the variable-width rigid frame bridge through the BIM model, sets the strengthening prestressed tendons in the pier top area, sets the auxiliary prestressed tendons in the transition area of the variable-width rigid frame bridge, and forms a spatial cooperative stress system through the main prestressed tendons, strengthening prestressed tendons and auxiliary prestressed tendons. The data output module outputs the spatial cooperative stress system.

[0061] The anchoring tooth block is one of the common structures in post-tensioned prestressed components, mainly used for anchoring prestressed steel bars or steel bundles, aiming to provide a stable anchoring point in the prestressed concrete bridge structure to ensure that the prestressed steel bars or steel bundles can effectively transfer the tensile force, thereby ensuring the stability and durability of the structure.

[0062] Anchoring prestressed steel bars or steel bundles: Through the anchoring effect of the tooth block, ensure that the prestressed steel bars or steel bundles can be firmly fixed in the concrete, thereby effectively transferring the tensile force and enhancing the bearing capacity of the structure.

[0063] Resisting local tensile action: When designing the anchoring tooth block, various local tensile actions need to be considered, such as: the splitting force under the anchor, the tensile stress concentration in the concave corner area at the end face root, and the pulling force behind the anchor, to ensure the stability and safety of the structure when stressed.

[0064] Embodiment 2:

[0065] The prestress layout of a rigid-frame bridge with variable width in the short-side span is usually carried out in a BIM model. BIM (Building Information Modeling) technology can achieve targeted analysis of the upper and lower structures of the bridge, especially the parameter analysis of different components. Through BIM technology, a three-dimensional model can be constructed for comprehensive analysis, grasping the actual terrain conditions of the construction site, determining the specific alignment of the line, and obtaining information related to all components. The application of BIM technology in the prestress layout of rigid-frame bridges is as follows:

[0066] Three-dimensional modeling: BIM technology can construct a three-dimensional model of the bridge and conduct targeted analysis through parametric expression forms to ensure the accuracy and effectiveness of information;

[0067] Collision check: Traditional two-dimensional drawings cannot predict whether there are collision phenomena in the bridge, while BIM technology can predict collision phenomena by establishing a three-dimensional model and take timely measures to solve problems;

[0068] Engineering quantity statistics: BIM technology can accurately calculate the engineering quantity, reduce human errors, and improve efficiency;

[0069] Information model construction and application: BIM technology can construct a comprehensive information model to support decision-making in complex design stages.

[0070] Specifically, as Figure 2 shown, this embodiment provides a prestress layout method suitable for a rigid-frame bridge with variable width in the short-side span, including the following steps:

[0071] Step S1: In the short-side span area of the variable-width rigid-frame bridge, arrange the main prestress tendons along the longitudinal direction of the bridge. The main prestress tendons are arranged in a bifurcated manner in the variable-width section to adapt to the change in the deck width;

[0072] For the calculation of the tendon tension of the main prestress tendons arranged along the longitudinal direction of the bridge:

[0073] According to the design principle of prestressed concrete structures, the tendon tension of the prestress tendons needs to be determined according to the force requirements of the structure and the prestress loss factors.

[0074] For a post-tensioned prestressed concrete beam, the effective prestress , is calculated by the following formula:

[0075] ;

[0076] Wherein, is the tension control stress, is the total prestress loss, and the total prestress loss includes: the friction loss between the prestressing tendon and the duct wall, the prestress loss caused by the deformation of the anchor and the shrinkage of the steel bar The prestress loss caused by the temperature difference between the tensioned steel bars during the heat curing of concrete and the equipment bearing the tension The prestress loss caused by the stress relaxation of steel bars The prestress loss caused by the shrinkage and creep of concrete , that is ;

[0077] Given the effective prestress and the area of the prestressing tendon , then the tension of the prestressing tendon is: .

[0078] represents the effective prestress, which is the actual prestress value existing in the concrete structure after the prestressing tendon has undergone various prestress losses. It is a key index for measuring the performance of prestressed concrete structures and directly affects the crack resistance, stiffness, and durability of the structure

[0079] represents the tension control stress, which is the stress value set during the tensioning of the prestressing tendon. It is usually determined according to the type, strength grade of the prestressing tendon, and the service requirements of the structure in accordance with relevant specifications and is the target stress value for prestress application

[0080] represents the total prestress loss, which is the sum of the prestress losses caused by various factors such as the friction between the prestressing tendon and the pipe wall, the deformation of the anchor and the shrinkage of the steel bar, the temperature difference, the stress relaxation of the steel bar, the shrinkage of the concrete, and the creep. These factors will inevitably occur during the construction and use of prestressed concrete structures, so accurate calculation is required to determine the final effective prestress

[0081] is the tension of the prestressing tendon, which is the external force applied to the prestressing tendon to cause elastic deformation of the prestressing tendon, thereby establishing prestress in the concrete structure

[0082] is the area of the prestressing tendon, which is determined according to the specifications and quantity of the prestressing tendon and reflects the ability of the prestressing tendon to bear tension. It is closely related to the tension and the effective prestress. Given the effective prestress and the area of the prestressing tendon, the required applied tension can be calculated

[0083] For the calculation of the elongation of the prestressing tendon in the main prestressing tendon arranged along the longitudinal direction of the bridge:

[0084] The elongation of the prestressing tendon during the tensioning process is calculated according to the following formula:

[0085] ;

[0086] Among them, is the average tensile force of the prestressed tendon. For a curved prestressed tendon, is calculated according to the following formula: , is the tensile force at the tensioning end of the prestressed tendon, is the influence coefficient of local deviation per meter of the duct on friction, is the length of the duct from the tensioning end to the calculated section, is the friction coefficient between the prestressing tendon and the duct wall, is the sum of the angles of the tangents of the curved duct section from the tensioning end to the calculated section (calculated in radians); is the length of the prestressed tendon, is the cross-sectional area of the prestressed tendon, is the elastic modulus of the prestressing tendon.

[0087] is the elongation of the prestressed tendon during the tensioning process, which is an important index to measure the deformation degree of the prestressed tendon. By measuring and controlling the elongation, the effect of prestress application is verified to ensure that the prestressed tendon reaches the stress state required by the design.

[0088] is the average tensile force of the prestressed tendon. For a curved prestressed tendon, since the tensile force varies along the length of the tendon, it is necessary to calculate the average tensile force to accurately calculate the elongation. Through the calculation formula takes into account the influence coefficient of local deviation per meter of the duct on friction , the length of the duct from the tensioning end to the calculated section , the friction coefficient between the prestressing tendon and the duct wall and the sum of the angles of the tangents of the curved duct section from the tensioning end to the calculated section factors. These factors jointly affect the distribution of forces on the curved prestressed tendon, thus affecting the calculation of the average tensile force.

[0089] is in the form of an exponential function and is used to describe the tensile force loss of the prestressed tendon due to friction. represents the friction loss caused by local deviation of the duct, represents the friction loss between the prestressing tendon in the curved section and the duct wall. As (the length of the duct from the tensioning end to the calculated section) and (the sum of the angles of the tangents of the curved duct section from the tensioning end to the calculated section) increase, and (the influence coefficient of local deviation per meter of the duct on friction) and (the friction coefficient between the prestressing tendon and the duct wall) increase, The value of will gradually decrease, which means the loss of tension force is greater.

[0090] It is the remaining proportion of tension after taking into account the friction loss. Subtract the part lost due to friction from 1. , the tensile force on the prestressed tendon after friction loss is relative to the initial tensile force of the remaining proportion.

[0091] From the overall perspective, the molecules represents the actual remaining amount of prestressing force after considering friction loss, but due to It reflects the comprehensive influence of friction loss, so the numerator is divided by , we get the average tension force after considering the friction loss over the entire channel length .

[0092] It is the length of the prestressed tendon, which is the actual length from the tensioning end to the anchoring end, including the length of the straight segment and the curve segment. It is an important parameter for calculating the elongation. The longer the length, the greater the elongation under the same tensioning force.

[0093] It is the area of the prestressed tendon in the calculation of the tension of the prestressed tendon, and is inversely proportional to the elongation, that is, the larger the area, the smaller the elongation under the same tension and length.

[0094] It is the elastic modulus of the prestressed tendon, which reflects the elastic deformation characteristics of the prestressed tendon when subjected to stress. Different types of prestressed tendons have different elastic moduli. It is an inherent property of the material, which is determined through experiments or reference to relevant data. The larger the elastic modulus, the smaller the elongation under the same tension, area and length conditions.

[0095] For the calculation of the spacing of the locating bars in the main prestressing tendons arranged along the longitudinal direction of the bridge:

[0096] The spacing of the locating bars needs to be determined based on the diameter of the prestressed pipe and the vibration force factor during concrete pouring to ensure that the pipe does not undergo excessive displacement during the concrete pouring process.

[0097] In straight line segments, the spacing between positioning ribs , refer to the following empirical formula: , where is the empirical coefficient of the straight line segment, generally taken as 0.8-1.0, is the outer diameter of the prestressed pipe, It is the lateral pressure exerted on the pipe when concrete is vibrated (can be determined through tests or experience).

[0098] It refers to the distance between two adjacent positioning bars on the straight section of the prestressed duct. A reasonable spacing setting can ensure that the prestressed duct maintains the correct position during the concrete pouring process and avoid excessive displacement.

[0099] Generally, it is taken as 0.8 - 1.0, which is obtained based on a large number of engineering practices and experimental studies, and is used to consider the influence of factors such as the concrete vibration force and the duct fixing method on the positioning bar spacing under different engineering conditions.

[0100] It is an important factor affecting the positioning bar spacing. The larger the outer diameter of the duct, the larger the spacing required to ensure the stability of the duct. However, the concrete vibration effect and the integrity of the structure also need to be considered.

[0101] The pressure is related to factors such as the slump of the concrete, the vibration method, and the power of the vibrator. It can be determined through experiments or by referring to the experience of similar projects. The greater the lateral pressure, the smaller the positioning bar spacing should be to prevent the duct from displacing during vibration.

[0102] In the curve section, the positioning bar spacing should be appropriately reduced and can be calculated according to the following formula: , where is the empirical coefficient for the curve section, generally taken as 0.5 - 0.6, is the radius of curvature of the curve section.

[0103] is the spacing of the positioning bars in the curve section. Since the lateral force on the prestressed duct in the curve section during concrete pouring is more complex and there is an influence of the radius of curvature, the positioning bar spacing in the curve section is usually smaller than that in the straight section.

[0104] is smaller than the empirical coefficient for the straight section because the stability requirements for the duct in the curve section are higher and denser positioning bars are needed to fix it.

[0105] , have the same meanings as those in the formula for the straight section, and are the outer diameter of the prestressed duct and the lateral pressure on the duct during concrete vibration, respectively.

[0106] reflects the degree of curvature of the curve. The smaller the radius of curvature, the more curved the curve, and the more likely the duct is to displace during concrete pouring. Therefore, a smaller positioning bar spacing is required. The in the formula reflects the influence of the radius of curvature on the positioning bar spacing. As the radius of curvature decreases and the ratio decreases, the positioning bar spacing decreases.

[0107] For the main prestressed tendons, a bifurcated layout is adopted in the variable-width section:

[0108] Calculation of the length of the prestressed tendons:

[0109] For the length of the prestressed tendons in the straight section , it is determined according to the actually measured distance between the starting and ending points. If the variable-width section gradually changes from a width to , the length of the transition section is , and the prestressed tendons are arranged along a curve in the transition section, which can be approximated as a quadratic parabola.

[0110] For the length of the prestressed tendons in the straight section , in actual engineering, the accurate value is obtained by measuring the distance between the anchorage points of the prestressed tendons in the straight section. For example: in the layout of the prestressed tendons in the straight section of a box girder bridge, the distance between the two end anchorages is directly measured, which is the length of the prestressed tendons in the straight section.

[0111] For the length of the prestressed tendons in the shape of a parabola The calculation formula is:

[0112] ;

[0113] Among them, represents the infinitesimal length of the curve. Integrating it over the length of the transition section can obtain the length of the entire parabolic prestressed tendon;

[0114] is the quadratic parabola equation. Assuming the quadratic parabola equation is , the coefficients , , are determined according to the boundary conditions of the transition section. is the first derivative of with respect to

[0115] The quadratic parabola equation is , and the coefficients , and are determined according to the boundary conditions of the transition section. For example, given the starting point coordinates and the ending point coordinates of the transition section, as well as the slopes and of the prestressed tendons at the starting and ending points, the coefficients can be solved through the following system of equations:

[0116] ;

[0117] For the integration over the length of the transition section In actual calculations, numerical integration methods are usually adopted, such as Simpson's rule. Simpson's rule divides the integration interval into several small intervals, approximates the integrand with a quadratic parabola on each small interval, and then approximately calculates the integral value by summation. The specific calculation formula is: ; where is the length of the small interval, is the number of small intervals, which is obtained by evenly dividing the length of the transition section into small intervals, When calculating the differential element length at a certain specific point , first find , and then substitute it into to calculate , and this value is the approximate value of the curve differential element length at this specific point;

[0118] By increasing the number of small intervals , the calculation accuracy can be improved. represents the endpoint coordinates of the small interval, which are obtained by starting from the lower integration limit 0 and incrementing successively with the length of the small interval as the step size, that is , , , and so on until . is used to determine at which points to calculate the value of the integrand . In Simpson's rule, it is necessary to calculate the values of at these points and perform weighted summation according to the formula to obtain the approximate value of the integral. For example, when calculating the value of at , substitute into to get , and this value will be used in the summation calculation of Simpson's rule.

[0119] Calculation of the prestressing tendon tension:

[0120] Determine the standard value of the prestressing tendon tension according to the structural design requirements , considering the prestress losses , including the friction loss between the prestressing tendon and the pipe wall , the prestress loss caused by the deformation of the anchor and the shrinkage of the steel bar , the prestress loss caused by the temperature difference between the steel bar under tension and the equipment bearing the tension during the hot curing of the concrete 、 Prestress losses caused by steel bar stress relaxation 、 Prestress losses caused by concrete shrinkage and creep ;

[0121] Then the tension of the prestressed tendon should satisfy:

[0122] ;

[0123] By dividing the initial tension control stress by the coefficient after deducting various prestress losses , the actual tension control stress considering all these losses is obtained to ensure that the prestressed tendon can still provide sufficient effective prestress during the service stage of the structure and meet the force-bearing performance requirements of the structure.

[0124] Calculation of the layout angle of the prestressed tendon:

[0125] In the variable-width section, the layout angle of the prestressed tendon is variable. Assume that the angle between the prestressed tendon and the beam axis at the starting point of the gradual change section is , and the angle at the ending point is .

[0126] For the prestressed tendon arranged in a parabolic shape, the tangent angle at any position can be obtained by differentiating the parabolic equation to get the slope , and then .

[0127] The slope is equal to the tangent value of the positive direction angle at the position (tangent angle), that is .

[0128] Therefore, after obtaining the slope at the starting point of the gradual change section by differentiating the parabolic equation, the angle between the tangent at the position and the positive direction can be obtained, and thus the tangent angle of the prestressed tendon at the position is obtained.

[0129] By differentiating the parabolic equation to obtain the slope, the tangent angle of the prestressed tendon at any position can be determined, which is of great significance for analyzing the mechanical action of the prestressed tendon in the structure and the direction of force transmission.

[0130] Step S2: Set strengthening prestressed tendons in the top area of the pier. The strengthening prestressed tendons are distributed in a fan shape to enhance the shear and torsion resistance of the variable-width section;

[0131] For setting the strengthening prestressed tendons in the top area of the pier:

[0132] Calculation of the length of the prestressed tendon:

[0133] The length is calculated by integrating the curve (meeting the conditions of the prestressed tendons with fan-shaped distribution). For the above parabola , in the interval The curve length The calculation formula is: ;

[0134] Among them, , substituting it into the above formula, we can get: ;

[0135] This is in the form of an elliptic integral. Generally, it needs to be solved by numerical methods or special functions. In actual engineering, approximate methods can also be used for calculation. For example: divide the curve into several small segments, approximate the curve segment with a straight line segment, and then sum to obtain the approximate length.

[0136] Calculation of prestress loss:

[0137] Prestress loss will occur during the use of the prestressed tendon, including: friction loss, anchorage loss, and concrete shrinkage and creep loss.

[0138] The calculation formula for friction loss is , among which, is the control stress of the prestressed tendon, is the friction coefficient between the prestressed tendon and the duct wall, is the sum of the angles (rad) of the tangent of the curve duct part from the tensioning end to the calculation section, is the influence coefficient of the local deviation per meter of the duct on friction, is the duct length (m) from the tensioning end to the calculation section.

[0139] The exponent as a whole determines the degree of prestress friction loss. When The value of is larger, The value of is smaller, The value of is larger, and thus the prestress friction loss is also larger. On the contrary, when The value of is smaller, the prestress friction loss is smaller. Through this exponential part, the influence of various factors on the prestress friction loss can be quantitatively analyzed, so as to take corresponding measures in design and construction to control the prestress loss and ensure the performance and safety of the prestressed structure.

[0140] The calculation formula for anchorage loss is , where is the value of the deformation of the anchorage end anchor, the retraction of the steel bar, and the compression of the joint (mm), is the elastic modulus of the prestressed tendon (MPa), is the distance between the tensioning end and the anchorage end (m).

[0141] Stress analysis under prestress:

[0142] Under prestress, compressive stress will be generated in the concrete at the top of the pier. According to the principle of mechanics of materials, for an eccentric tension (compression) member, the cross-sectional stress calculation formula is: , where is the axial force generated by the prestress, is the cross-sectional area of the top of the pier, is the bending moment generated by the prestress, is the distance from the calculation point to the centroid axis of the cross-section, used to determine the position of the calculation point on the cross-section, is the moment of inertia of the cross-section.

[0143] The strengthening prestressed tendons are distributed in a fan shape: Usually, a parabola equation is used to describe the curve shape of the fan-shaped prestressed tendons. Taking the center of the top of the pier as the origin, the horizontal direction is axis, and the vertical direction is axis, and the parabola equation can be expressed as ; where is the parameter of the parabola, which determines the opening size and shape of the parabola, The value of

[0144] Step S3: Set auxiliary prestressed tendons in the transition area of the variable-width rigid-frame bridge. The auxiliary prestressed tendons are arranged with a gradually changing spacing along the transverse direction of the bridge to balance the local stress concentration of the bridge;

[0145] For the gradually changing spacing of the auxiliary prestressed tendons arranged along the transverse direction of the bridge:

[0146] Assume that the length of the transition area is , the starting spacing is , and the ending spacing is . Use a linear gradient formula to calculate the spacing of the prestressed tendon at a distance from the starting point of the transition area: ;

[0147] where The value range of .

[0148] If more complex variation rules are considered, quadratic functions or other curve functions can also be used to describe the gradual change of the spacing. For example:

[0149] ;

[0150] In the formula, 、 and are undetermined coefficients, which are determined according to the starting spacing, the ending spacing and some special point conditions in the transition zone.

[0151] In actual engineering, it is necessary to conduct simulation analysis and optimization design through structural calculation software based on the detailed design parameters and mechanical analysis of the specific bridge, so as to determine the most reasonable layout of the auxiliary prestressed tendons and the way of gradual change of the spacing, and ensure the safety and performance of the bridge structure.

[0152] When setting the auxiliary prestressed tendons in the transition zone of a variable-width rigid-frame bridge, the formula for determining the lateral gradual change spacing needs to comprehensively consider various factors of the bridge. The following is a more specific formula example based on a cubic function:

[0153] ;

[0154] In the formula: is the tendon spacing at a distance from the starting point of the transition zone; is an undetermined coefficient. Specifically, it can be determined through the following boundary conditions and constraint conditions:

[0155] Given the spacing at the starting point of the transition zone, then ; Given the spacing at the ending point of the transition zone and substituting it into the formula, we can get: ;

[0156] To ensure the smoothness of the spacing change, the first derivative at the starting point can be set to 0. By differentiating the formula, we get , so ;

[0157] At the same time, to make the spacing change more reasonable throughout the transition zone, a condition regarding the second derivative can be given according to the actual situation. For example: at the midpoint of the transition zone, let ( is a constant determined according to engineering experience or structural analysis), then .

[0158] By solving the above equations simultaneously, we can obtain and , so as to determine the complete spacing.

[0159] In practical applications, it is also necessary to consider the minimum spacing requirements of the prestressed tendons, the non-uniformity of the transverse force distribution of the bridge, and the factors of prestress loss, and make appropriate adjustments and optimizations to the formula. In addition, different bridge designs may adopt different functional forms and boundary conditions to determine the spacing formula, and specific analysis and design should be carried out according to the actual engineering situation.

[0160] The above formula can accurately describe the spacing of the prestressed tendons at different positions in the transition zone by determining the undetermined coefficients , and at the , compared with the simple linear change, the cubic function form can more flexibly and accurately adapt to the complex bridge structure and force requirements, making the layout of the prestressed tendons more in line with the actual engineering needs.

[0161] For the balance bridge, local stress concentration is to ensure uniform structural stress. In the transition zone of the variable-width rigid-frame bridge, the width of the bridge changes, and the structural stress situation is relatively complex. A reasonable layout of the prestressed tendon spacing is crucial for evenly distributing the prestress and improving the structural stress state. This formula can make the prestress more evenly distributed in the transition zone by controlling the gradual change of the spacing, effectively reducing the stress concentration phenomenon, and improving the overall performance and safety of the bridge structure.

[0162] Step S4: The main prestressed tendons, the strengthening prestressed tendons and the auxiliary prestressed tendons are respectively anchored in the embedded structures on the bridge and at the top of the bridge pier through the anchoring devices to form a spatial cooperative stress system.

[0163] Main prestressed tendons: They are the prestressed tendons that bear the main load in the bridge structure and are usually arranged in the key stress-bearing parts of the bridge, such as the bottom or web of the main girder. Their function is to offset part or all of the tensile stress through the pre-applied prestress when the bridge bears the self-weight and vehicle load external forces, thereby improving the bearing capacity and crack resistance of the bridge.

[0164] Strengthening prestressed tendons: They are mainly used to strengthen certain key parts of the bridge structure or areas that bear large local loads. For example, near the supports of the bridge, at the mid-span where the bending moment is large, or at the parts with special load effects, setting strengthening prestressed tendons can further improve the bearing capacity and anti-deformation ability of these parts to meet the safety and service requirements of the structure.

[0165] Auxiliary prestressed tendons: Generally, they are set to assist the main prestressed tendons and the strengthening prestressed tendons to act together, or to meet the stress requirements of the bridge structure under specific working conditions. For example, in some complex bridge structures, auxiliary prestressed tendons are set to adjust the internal force distribution of the structure, improve the dynamic performance of the structure, or enhance the durability of the structure.

[0166] Specifically, the steps for forming the spatial cooperative force system are as follows:

[0167] Step A: Define the prestressed tendon element: Simulate all prestressed tendons using the selected element type (e.g., bar element or cable element), endow the prestressed tendons with corresponding material properties and cross-sectional characteristics, accurately draw the spatial path of the prestressed tendons in the model according to the actual shape and layout of the prestressed tendons, and determine the starting point, ending point of the prestressed tendons and their anchorage positions in the structure.

[0168] Step B: Set the prestressed tendon application method: Set the corresponding loading method in the model according to the actual prestress application method during the construction process. Commonly, the application of prestress is simulated through initial strain or initial stress. If the prestressed tendons are tensioned in batches, it is also necessary to perform loading simulation step by step according to the actual tensioning sequence and the magnitude of the tensile force.

[0169] Step C: Calculate the prestress loss of the prestressed tendons: Consider the prestress loss of the prestressed tendons during use in the model, such as relaxation of steel, shrinkage and creep of concrete, and friction loss. Correct it in the model by introducing corresponding coefficients or calculating the prestress loss.

[0170] Anchored to the bridge: The prestressed tendons are anchored at different parts of the bridge, enabling the bridge structure to bear the action of prestress as a whole. By reasonably arranging the anchorage points of the prestressed tendons, the internal stress distribution of the bridge can be made more uniform when the bridge bears the load, reducing the stress concentration phenomenon, thereby improving the overall load-bearing capacity and stability of the bridge. For example, anchoring the main prestressed tendons at the ends and mid-span of the main girder can effectively control the deformation and cracking of the main girder under the action of the load.

[0171] Anchored in the embedded structure at the top of the pier: The top of the pier is the part of the bridge structure that bears relatively large pressure and bending moment. Anchoring the prestressed tendons in the embedded structure at the top of the pier can apply prestress to the pier, improving the compressive and flexural capacities of the pier. At the same time, through the action of the prestressed tendons, the connection between the pier and the upper structure of the bridge can be made closer, and the cooperative working performance is better, thus forming an overall spatial cooperative force system.

[0172] Formation of the spatial cooperative force system: The main prestressed tendons, strengthening prestressed tendons and auxiliary prestressed tendons are respectively anchored to the bridge and the embedded structure at the top of the pier through the anchorage device. They cooperate with each other and interact with each other to jointly form a spatial cooperative force system. In this system, different types of prestressed tendons play roles at different positions and in different directions. Through the connection of the concrete structure and the anchorage device, the forces at each part are organically combined together, enabling the bridge structure to form an overall force system in space.

[0173] Significance of the spatial cooperative force-bearing system: The spatial cooperative force-bearing system can give full play to the load-bearing capacity of each part of the bridge structure and improve the overall performance of the structure. It can effectively resist various load actions, including vertical loads, horizontal loads, and torques, enabling the bridge to maintain a good working state under complex force conditions. At the same time, this system can also reduce the structural deformation and crack width, improving the durability and service life of the bridge.

[0174] Specifically, the spatial cooperative force-bearing system is as shown in Table 1 below:

[0175] Table 1 Spatial Cooperative Force-Bearing System Table

[0176]

[0177] As described above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope recorded in the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claimed rights.

Claims

1. Prestressing layout method for adapting to variable-width rigid-frame bridges with short-side spans, characterized in that It includes the following steps: Step S1: In the short side span area of the variable-width rigid-frame bridge, arrange the main prestressed tendons along the longitudinal direction of the bridge. The main prestressed tendons are arranged in a bifurcated manner in the variable-width section to adapt to the change in the bridge deck width; Step S2: Set up strengthening prestressed tendons in the pier top area. The strengthening prestressed tendons are distributed in a fan shape to enhance the shear and torsion resistance of the variable-width section; Step S3: Set up auxiliary prestressed tendons in the transition area of the variable-width rigid-frame bridge. The auxiliary prestressed tendons are arranged with a gradually changing spacing along the transverse direction of the bridge to balance the local stress concentration of the bridge; Step S4: The main prestressed tendons, strengthening prestressed tendons and auxiliary prestressed tendons are respectively anchored in the embedded structures on the bridge and at the pier top through anchoring devices to form a spatial cooperative stress system.

2. The prestress layout method for a rigid frame bridge with variable width adapting to short-side span as claimed in claim 1, wherein In the step S1, the calculation of the prestressing tendon tensile force for the prestressing tendons arranged along the longitudinal direction of the bridge is as follows: ; Among them, is the tensile control stress, is the total loss of prestress; Given the effective prestress and the area of the prestressing tendon, then the tensile force of the prestressing tendon is: .

3. The prestress layout method for adapting to short-side cross-variable-width rigid frame bridges according to claim 1, characterized in that, In the step S1, the elongation of the prestressed tendon in the main prestressed tendon arranged along the longitudinal direction of the bridge is: the elongation of the prestressed tendon during the tensioning process , which is calculated according to the following formula: ； Among them, is the average tensile force of the prestressed tendon. For a curved prestressed tendon, it is calculated according to the following formula: , is the tensile force at the tensioning end of the prestressing tendon, is the influence coefficient of local deviation per meter of the duct on friction, is the length of the duct from the tensioning end to the calculated section, is the friction coefficient between the prestressing tendon and the duct wall, is the sum of the angles of the tangents of the curved duct section from the tensioning end to the calculated section (calculated in radians); is the length of the prestressing tendon, is the cross-sectional area of the prestressing tendon, is the elastic modulus of the prestressing tendon.

4. The prestress layout method for adapting to the short-side cross-variable-width rigid frame bridge according to claim 1, characterized in that In the said Step S1, for the spacing of the positioning bars in arranging the main prestressed tendons along the longitudinal direction of the bridge: In the straight-line section, the spacing of the positioning bars , formula: , where is the empirical coefficient for the straight-line section, taking 0.8 - 1.0, is the outer diameter of the prestressed duct, is the lateral pressure exerted on the duct during concrete vibration, refers to the distance between two adjacent positioning bars on the straight-line section of the prestressed duct; Taking 0.8 - 1.0 is used to consider the influence of factors such as concrete vibration force and duct fixing method under different engineering conditions on the spacing of the positioning bars, is an important factor affecting the spacing of the positioning bars; The lateral pressure exerted on the duct during concrete vibration; In the curve section, the spacing of the positioning bars should be appropriately reduced. The formula is: , where is the empirical coefficient of the curve section, taking 0.5 - 0.6, is the radius of curvature of the curve section.

5. The prestress layout method for adapting to short-side cross-variable-width rigid-frame bridges according to claim 1, characterized in that In the said Step S1, the main prestressed tendons are arranged in a bifurcated manner in the variable-width section: Calculation of the length of the prestressed tendon: The length of the prestressed tendon in a parabolic shape The calculation formula is as follows: ； Among them, represents the differential length of the curve, and integrating it over the length of the gradual change section can obtain the length of the entire parabolic prestressed tendon; It is a quadratic parabola equation. Assume the quadratic parabola equation is , and determine the coefficients , , according to the boundary conditions of the transition section. is the first derivative of . Calculation of the tendon tension of the prestressed tendon: Determine the standard value of the tension of the prestressed tendon according to the structural design requirements , considering the prestress loss , then the tension of the prestressed tendon shall satisfy: ； Calculation of the arrangement angle of the prestressed tendon: In the variable-width section, the layout angle of the prestressed tendon changes. At the starting point of the transition section, the included angle between the prestressed tendon and the beam axis is , and at the end point, the included angle is ; for the prestressed tendon arranged in a parabolic shape, at any position , the tangent angle can be obtained by differentiating the parabolic equation to get the slope , , the slope and the positive direction at the position The included angle has the same tangent value, .

6. The prestress arrangement method for a rigid frame bridge with variable width adapting to short-side span change according to claim 1, wherein In the said Step S2, for the setting up of the strengthening prestressed tendons in the pier top area: Calculation of the tendon length of the prestressed tendon: Parabola , the curve length on the interval is calculated by the formula: ； Among them, , substituting it into the above formula, we can get: ; The reinforcing prestressed tendons are distributed in a fan shape: The parabolic equation is used to describe the curve shape of the fan-shaped prestressed tendons. Taking the center of the pier top as the origin, the horizontal direction is axis, and the vertical direction is axis. The parabolic equation can be expressed as ; where is the parameter of the parabola, which determines the opening size and shape of the parabola. The value of is determined according to the specific layout requirements of the prestressed tendons, the dimensions of the pier top, and the factors of the prestress application effect.

7. The prestress layout method for adapting to the short-side cross-variable-width rigid-frame bridge according to claim 1, characterized in that In the said Step S3, the gradually changing spacing of the auxiliary prestressed tendons arranged along the transverse direction of the bridge is: Assume that the length of the transition zone is , the starting spacing is , the ending spacing is , and a linear gradient formula is used to calculate the prestressed tendon spacing at a distance from the starting point of the transition zone : ; Among them, The value range of .

8. The prestress layout method for adapting to short-side cross-variable-width rigid-frame bridges according to claim 1, characterized in that In the said Step S4, the steps for forming the spatial cooperative stress system are as follows: Step A: Define the prestressed tendon element: Simulate all the prestressed tendons with the selected element type; Step B: Set the prestressed tendon application method: Set the corresponding loading method in the model according to the actual prestressed application method during the construction process; Step C: Calculate the prestress loss of the prestressed tendon: Consider the prestress loss of the prestressed tendon during its service in the model.

9. A tooth block anchoring system adapted to the prestress layout of a rigid frame bridge with variable width in the short side span, for implementing the method for prestress layout of a rigid frame bridge with variable width in the short side span according to any one of claims 1-8, characterized in that, It includes: A data receiving module for receiving model data; A data processing module for processing model data; A data output module for outputting model data; The data receiving module is connected to the data processing module, and the data processing module is connected to the data output module.

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