Design method of high-low arch bridge

Abstract

The invention relates to the field of bridge engineering, in particular to a method for designing a high-low arch bridge, which comprises the following steps of: initially planning the geometric dimension of the arch bridge according to topographic and geological information at an arch seat and the span of the arch bridge, and establishing a macroscopic finite element model of the arch bridge; calculating to obtain upper chord main pipe internal force and lower chord main pipe internal force of a high arch rib, upper chord main pipe internal force and lower chord main pipe internal force of a low arch rib, internal force of a cross brace, base internal force of a high arch rib side skewback and base internal force of a low arch rib side skewback, and then verifying whether the bearing capacity of the arch bridge meets the requirement to adjust the initial size. The influence of the slope terrain on the overall arrangement of the arch bridge is fully considered, the arch rib size is adjusted, the asymmetric high-low arch bridge is designed, it is not needed to arrange a high skewback on a side slope at the low ground elevation position, checking calculation of the corresponding bearing capacity is conducted after internal force is calculated, the size of the skewback is reduced, and meanwhile the construction cost is reduced. Complex load effects are separated and gradually considered, so that the bearing capacity of the arch bridge meets the requirements, the structure stress is safer, and the design is more reasonable.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering, and in particular to a design method for high and low arch bridges. Background Technology

[0002] As my country's highway construction extends into the western mountainous regions, and as arch bridges become increasingly longer and are more frequently used to cross mountain valleys, they have gained widespread application as a bridge type known for its economic efficiency, high load-bearing capacity, and strong spanning ability. However, in the southwestern mountainous areas, the construction of large-span arch bridges faces complex topographical and geological conditions. Bedding slopes and adverse geological phenomena often overlap at the bridge site, not only restricting the arch bridge's layout due to sloping terrain but also posing a significant risk of instability to the bedding slopes due to over-excavation. Conventional arch bridge design methods are no longer adequate to meet the construction needs.

[0003] Existing arch bridge designs all adopt a transversely symmetrical arrangement of the main arch and arch seat, that is, the same arch starting line elevation, the same arrangement of left and right side arch ribs and arch seat. This approach is a more suitable arch bridge scheme in plains and hilly areas, which can achieve complete force symmetry and good structural performance, but it is not suitable for sloping terrain.

[0004] Currently, existing technology has developed a high-low arch bridge, which includes a high arch rib, a low arch rib, cross bracing, side arch abutments of the high arch rib and the low arch rib, as well as the main beam, hangers, arch columns and junction piers of traditional bridges. The arch line of the high arch rib is higher and the arch line of the low arch rib is lower. The high arch rib is located at a higher elevation on the slope and the low arch rib is located at a lower elevation on the slope to adapt to the topographic and geological conditions of the bedding slope. Existing technology lacks design methods for high-low arch bridges with asymmetrical high arch ribs and low arch ribs, as well as side arch abutments of the high arch rib and the low arch rib. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing arch bridge designs that use symmetrical main arches and arch seats, which result in poor structural performance when applied to bedding slope terrain. This invention provides a design method for asymmetrical high and low arch ribs, as well as high arch rib side arch seats and low arch rib side arch seats.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution: A design method for a high-low arch bridge, comprising the following steps: S1. Based on the span of the arch bridge and the ground elevation at the side arch abutment of the high arch rib and the side arch abutment of the low arch rib, the geometric dimensions of the arch bridge are initially proposed, wherein the length and cross-sectional dimensions of the high arch rib and the low arch rib are the same. S2. Establish a macroscopic finite element model of the arch bridge and calculate the internal forces of the upper and lower chord main tubes of the high arch rib, the internal forces of the upper and lower chord main tubes of the low arch rib, the internal forces of the cross braces, the base internal forces of the arch abutments of the high arch rib and the base internal forces of the arch abutments of the low arch rib. S3. Verify whether the bearing capacity of the upper and lower chord main tubes of the high arch rib, the bearing capacity of the upper and lower chord main tubes of the low arch rib, the bearing capacity of the cross braces, the base stress of the side arch abutment of the high arch rib, the overturning stability and the sliding stability, and the base stress of the side arch abutment of the low arch rib, the overturning stability and the sliding stability meet the requirements. S4. If the requirements are not met, modify the geometry of the arch bridge and repeat steps S2 and S3 until the requirements are met.

[0007] The high arch rib is the arch rib of the arch bridge located on the side of the slope with a higher elevation, the low arch rib is the arch rib of the arch bridge located on the side of the slope with a lower elevation, the side arch seat of the high arch rib is the arch seat connected to the high arch rib, and the side arch seat of the low arch rib is the arch seat connected to the low arch rib.

[0008] In this field, the overturning stability and sliding stability of arch abutments are key performance indicators for measuring whether an arch abutment can maintain its own stability and not overturn or slide when subjected to external loads. The overturning stability of an arch abutment refers to its ability to resist rotation around a certain overturning point under the action of loads transmitted by the arch and its own weight. The sliding stability of an arch abutment refers to its ability to resist relative sliding along a sliding surface on the foundation surface or inside the foundation under the action of external forces such as horizontal thrust transmitted by the arch.

[0009] By fully considering the impact of sloping terrain on the overall layout of the arch bridge, an asymmetrical arch rib design was adopted, featuring high and low arch ribs, as well as corresponding high and low arch rib side abutments. This design eliminates the need for high abutments on slopes at lower elevations, reducing abutment dimensions, concrete and steel reinforcement usage, and overall construction costs, resulting in a more rational arch bridge design. Furthermore, it avoids over-excavation on slopes at higher elevations to near the lower elevation, minimizing excavation and ensuring slope stability. The asymmetrical use of high and low arch ribs in the upper and lower chord main sections, along with the high and low arch rib side abutments, improves structural performance and allows for dimensional design based on abutment requirements, leading to material and cost savings.

[0010] The initial geometric dimensions of the high and low arch bridge are determined based on the span of the arch bridge and the ground elevations at the arch abutments of the high and low arch ribs. This helps to make the initial geometric dimensions of the high and low arch bridge more reasonable. Furthermore, the initial dimensions of the high and low arch ribs are the same. By calculating the internal forces of the upper and lower chord main tubes of the high arch rib, the upper and lower chord main tubes of the low arch rib, the internal forces of the cross braces, and the base internal forces of the arch abutments of the high and low arch ribs, and by verifying the corresponding bearing capacity, the complex load effects are separated and considered step by step. The optimization direction can be quickly found during the design process before the dimensions of the high and low arch ribs are adjusted, which helps to improve the efficiency of the design and enhance the rationality of the design.

[0011] Preferably, in step S1, the preliminary geometric dimensions of the high and low arch bridge include the height h, width b, main pipe diameter d, arch axis L1, upper chord main pipe wall thickness ts1 and lower chord main pipe wall thickness tx1 of the high arch rib, the height h, width b, main pipe diameter d, arch axis L2, upper chord main pipe wall thickness ts2 and lower chord main pipe wall thickness tx2 of the low arch rib, the length l1, width b1 and height h1 of the side arch seat of the high arch rib, the length l2, width b2 and height h2 of the side arch seat of the low arch rib, and the main pipe diameter D of the cross brace; the height h1, width b1, main pipe diameter d1, arch axis L1, upper chord main pipe wall thickness ts1 and lower chord main pipe wall thickness tx1 of the high arch rib are equal to the height h2, width b2, main pipe diameter d2, arch axis L2, upper chord main pipe wall thickness ts2 and lower chord main pipe wall thickness tx2 of the low arch rib.

[0012] The geometric dimensions of the high and low arch supports were initially determined to provide initial data for the construction of the macroscopic finite element model.

[0013] More preferably, in step S1, the arching elevations of the two arch seats on both sides of the high arch rib are the same, the arching elevations of the two arch seats on both sides of the low arch rib are the same, and the vertical height difference between the arch axis L1 of the high arch rib and the arch axis L2 of the low arch rib is equal to the difference in arching elevation between the arch seats on the high arch rib and the arch seats on the low arch rib.

[0014] The values ​​of the arch axis L1 of the high arch rib and the arch axis L2 of the low arch rib are set according to the arch rise elevation at the side arch abutment of the high arch rib and the side arch abutment of the low arch rib.

[0015] Preferably, in step S3, if the bearing capacity of the upper chord main pipe or the lower chord main pipe of the high arch rib cannot meet the requirements, the wall thickness ts1 of the upper chord main pipe or the wall thickness tx1 of the lower chord main pipe of the high arch rib is modified; if the bearing capacity of the upper chord main pipe or the lower chord main pipe of the low arch rib cannot meet the requirements, the wall thickness ts2 of the upper chord main pipe or the wall thickness tx2 of the lower chord main pipe of the low arch rib is modified; if the bearing capacity of the cross brace cannot meet the requirements, the pipe diameter D of the cross brace is modified; if the base stress, overturning stability and slip resistance of the high arch rib side arch seat, the base stress, overturning stability and slip resistance of the low arch rib side arch seat cannot meet the requirements, the length l1 of the high arch rib side arch seat, the length l2 of the low arch rib side arch seat, the width b1 of the high arch rib side arch seat or the width b2 of the low arch rib side arch seat are modified.

[0016] Based on the results of the calculated bearing capacity requirements, overturning stability requirements, and sliding stability requirements, the following dimensions were modified simultaneously: height h, width b, main pipe diameter d, arch axis L1, upper chord main pipe wall thickness ts1 and lower chord main pipe wall thickness tx1; height h, width b, main pipe diameter d, arch axis L2, upper chord main pipe wall thickness ts2 and lower chord main pipe wall thickness tx2; length l1, width b1, and height h1 of the side arch abutment of the high arch rib; length l2, width b2, and height h2 of the side arch abutment of the low arch rib; and main pipe diameter D of the cross brace.

[0017] Further preferably, if adjusting the wall thickness ts1 of the upper chord main pipe of the high arch rib, the wall thickness tx1 of the lower chord main pipe of the high arch rib, the wall thickness ts2 of the upper chord main pipe of the low arch rib, and the wall thickness tx2 of the lower chord main pipe of the low arch rib cannot make the load-bearing capacity of the upper chord main pipe of the high arch rib and the lower chord main pipe meet the requirements, then the height of the arch axis L1 of the high arch rib and the arch axis L2 of the low arch rib can be adjusted.

[0018] Make the heights of the arch axis L1 of the high arch rib and the arch axis L2 of the low arch rib closer together, and adjust the height h1 of the high arch rib side arch seat, the height h2 of the low arch rib side arch seat, the height h of the high arch rib, the width b of the high arch rib, the height h of the low arch rib, and the width b of the low arch rib accordingly.

[0019] Preferably, in step S3, the formulas for calculating the bearing capacity of the upper and lower chord main tubes of the high arch rib and the upper and lower chord main tubes of the low arch rib are as follows:

[0020] Mode The value in the middle is the structural importance coefficient. For the main axial internal force, The slenderness ratio reduction factor for the main body. The reduction factor for the main bending moment. This represents the design value of the axial compressive strength of the concrete-filled steel tube. The cross-sectional area of ​​the main steel-concrete composite pipe is given. The initial stress reduction factor for the main steel pipe is given. This is the reduction factor for concrete voids.

[0021] Preferably, in step S3, the formula for calculating the main bearing capacity of the cross brace is as follows:

[0022] In the formula, This is the structural importance coefficient. For the axial force of the main cross brace, Let be the bending moment in the y-axis direction of the main cross brace. The bending moment in the z-axis direction of the main cross brace. Let be the cross-sectional area of ​​the main cross brace. Let be the area modulus of the main cross brace along the y-axis. Let be the area modulus of the main cross brace along the z-axis. This is the design strength value for the main cross brace.

[0023] Preferably, in step S3, the formula for calculating the bearing capacity of the foundation soil and rock is as follows:

[0024] In the formula, N is the base axial force, Let A be the bending moment along the y-axis of the base, and let A be the cross-sectional area of ​​the base. Let be the area modulus along the y-axis of the base. The maximum compressive stress of the base. This is the adjustment coefficient for the bearing capacity of the foundation. The characteristic value of the foundation bearing capacity is defined as the foundation base, which includes the foundation base of the high arch rib side arch abutment and the foundation base of the low arch rib side arch abutment.

[0025] Preferably, in step S3, Formula for calculating the overturning stability of an arch abutment:

[0026] In the formula, The values ​​of axial force N, shear force V, and vertical component of the projection of the arch abutment's self-weight G onto the base are given for the loads applied to the arch abutment other than its own weight. The values ​​of axial force N, shear force V, and centroidal lever arm of the arch abutment's self-weight G at the base section of the foundation are given for the loads applied to the arch abutment other than its own weight. The horizontal components of the axial force N and shear force V, excluding the self-weight, applied to the arch abutment, are projected onto the base. The lever arms of the axial force N and shear force V corresponding to the loads other than the self-weight applied to the arch abutment are located at the base section of the foundation. To ensure the overturning stability of the arch abutment, for The total value, the arch abutments include the high arch rib side abutments and the low arch rib side abutments. Preferably, in step S3, the formula for calculating the anti-slip stability of the arch abutment is as follows:

[0027] In the formula, The coefficient of friction of the substrate. for The total value, The sum of the anti-slip stabilizing horizontal forces, for The total value, To ensure the anti-slip stability of the arch abutment, the arch abutment includes the high arch rib side arch abutment and the low arch rib side arch abutment.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows: This design method fully considers the impact of sloping terrain on the overall layout of the arch bridge. It designs an asymmetrical arch rib design with high and low arch ribs, as well as corresponding side arch abutments for the high and low arch ribs. This eliminates the need for high abutments on slopes with lower ground elevations, reducing abutment size, concrete and steel reinforcement usage, and thus saving on construction costs. The resulting arch bridge design is more rational. Furthermore, it avoids over-excavation on slopes with higher ground elevations to near the lower elevation, minimizing excavation and ensuring slope stability. Based on the arch bridge span and the ground elevation at the side arch abutments of the high and low arch ribs... Using the ground elevation at the arch abutment to initially determine the geometric dimensions of the high and low arch bridge helps to make the initially proposed geometric dimensions more reasonable. Furthermore, the dimensions of the initially proposed high arch rib and low arch rib are the same. By calculating the internal forces of the upper and lower chord main tubes of the high arch rib, the upper and lower chord main tubes of the low arch rib, the internal forces of the cross braces, the base internal forces of the high arch rib side arch abutment, and the base internal forces of the low arch rib side arch abutment, and performing corresponding load-bearing capacity verification, the complex load effects are separated and considered step by step. The optimization direction can be quickly found during the design process before the dimensions of the high arch rib and low arch rib are adjusted, which helps to improve the efficiency of the design and enhance the rationality of the design. Attached Figure Description

[0029] Figure 1 A flowchart illustrating the design steps of a high-low arch bridge; Figure 2 A schematic diagram of the high and low arches and their abutments; Figure 3 A schematic diagram of the elevation of the low arch rib and its arch seat; Figure 4 This is a schematic diagram of the elevation of the high arch rib and its arch seat.

[0030] Markings in the diagram: 1-High arch rib, 2-Low arch rib, 3-Horizontal brace, 4-Side arch seat of high arch rib, 5-Side arch seat of low arch rib, 6-Main beam, 7-Hanging rod, 8-Column on the arch, 9-Boundary pier. Detailed Implementation

[0031] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0032] Unless otherwise specified, the terms "upper," "lower," "left," "right," "center," "inner," and "outer," etc., used in the description of specific embodiments of the present invention to indicate orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is usually placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, and for enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0033] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," "parallel," and "coaxial" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, parallel, or coaxial. Slight tilt or deviation is permissible, as long as it does not affect the normal function of the relevant component. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," not that the structure must be perfectly horizontal; a slight tilt is acceptable. "Coaxial" means that two components are arranged as coaxially as possible, allowing them to move coaxially or approximately coaxially when their relative positions change. Alternatively, it can be simplified to mean that the corresponding device / component / element, when arranged in "horizontal," "vertical," "suspended," "parallel," or "coaxial" directions, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. For example, the deviation in the "coaxial" direction is controlled within 0.2-1mm, preferably within 0.2-0.5mm. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the solution of the present invention.

[0034] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0035] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.

[0036] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to connection methods commonly used in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0037] Example 1 like Figure 1 As shown, a design method for a high-low arch bridge includes the following steps: S1. Based on the span of the arch bridge and the ground elevations at 4 points on the side arch abutments of the high arch rib and 5 points on the side arch abutments of the low arch rib, the geometric dimensions of the arch bridge are initially proposed, wherein the length and cross-sectional dimensions of the high arch rib 1 and the low arch rib 2 are the same. S2. Establish a macroscopic finite element model of the arch bridge and calculate the internal forces of the upper and lower chord main tubes of the high arch rib 1, the internal forces of the upper and lower chord main tubes of the low arch rib 2, the internal forces of the cross brace 3, the base internal forces of the high arch rib side arch seat 4, and the base internal forces of the low arch rib side arch seat 5. S3. Verify whether the bearing capacity of the upper chord main tube of the high arch rib 1, the bearing capacity of the upper chord main tube of the low arch rib 2, the bearing capacity of the cross brace 3, the base stress, overturning stability and sliding stability of the high arch rib side arch seat 4, and the base stress, overturning stability and sliding stability of the low arch rib side arch seat 5 meet the requirements. S4. If the requirements are not met, modify the geometry of the arch bridge and repeat steps S2 and S3 until the requirements are met.

[0038] This design method is applicable to both upper-bearing arch bridges and mid-bearing arch bridges.

[0039] Specifically, in step S1, characteristic values ​​of foundation bearing capacity are also obtained, including but not limited to. .

[0040] like Figure 2-4 As shown, specifically, in step S1, the preliminary geometric dimensions of the high and low arch bridge include the height h, width b, main pipe diameter d, arch axis L1, upper chord main pipe wall thickness ts1 and lower chord main pipe wall thickness tx1 of the high arch rib 1; the height h, width b, main pipe diameter d, arch axis L2, upper chord main pipe wall thickness ts2 and lower chord main pipe wall thickness tx2 of the low arch rib 2; the length l1, width b1 and height h1 of the high arch rib side arch seat 4; and the length l2, width b2 and height h2 of the low arch rib side arch seat 5. The main pipe diameter D of the cross brace 3; the height h1 of the high arch rib 1 is equal to the height h2 of the low arch rib 2; the width b1 of the high arch rib 1 is equal to the width b2 of the low arch rib 2; the main pipe diameter d1 of the high arch rib 1 is equal to the main pipe diameter d2 of the low arch rib 2; the arch axis L1 of the high arch rib 1 is equal to the arch axis L2 of the low arch rib 2; the upper chord main pipe wall thickness ts1 of the high arch rib 1 and the lower chord main pipe wall thickness tx1 of the high arch rib 1 are equal to the upper chord main pipe wall thickness ts2 of the low arch rib 2 and the lower chord main pipe wall thickness tx2 of the low arch rib 2.

[0041] In step S1, the initial dimensions of the high arch rib 1 and the low arch rib 2 are the same. Steps S2 and S3 modify the dimensions of the initially proposed high arch rib 1 and low arch rib 2. The main beam 6, suspenders 7, arch columns 8, and junction piers 9 of the high-low arch bridge are set to dimensions suitable for their own structural safety. The remaining components of the high-low arch bridge are also set to dimensions suitable for their own structural safety.

[0042] If the ground elevation inside the arch bridge is higher and the ground elevation outside the arch bridge is lower, then a high arch rib is set on the inside of the high-low arch bridge and a low arch rib is set on the outside. If the ground elevation inside the arch bridge is lower and the ground elevation outside the arch bridge is higher, then a high arch rib is set on the outside of the high-low arch bridge and a low arch rib is set on the inside. If the ground elevation on the upper slope side is higher and the ground elevation on the lower slope side is lower, then a high arch rib 1 and a high arch rib side arch seat 4 are set on the upper slope side, and a low arch rib 2 and a low arch rib side arch seat 5 are set on the lower slope side.

[0043] Specifically, the macroscopic finite element model of the arch bridge is a macroscopic finite element model of the arch bridge that includes asymmetric high and low arches and their arch abutments, namely, the macroscopic finite element model of the arch bridge including high arch rib 1, low arch rib 2, cross brace 3, high arch rib side arch abutment 4, low arch rib side arch abutment 5, main beam 6, hanger 7, arch column 8 and junction pier 9; the calculation is performed by inputting variable loads into the macroscopic finite element model of the arch bridge, and the input loads include variable loads such as vehicle load, crowd load, wind load and temperature load.

[0044] Specifically, in step S1, the arching elevations of the two arch seats on both sides of the high arch rib 1 are the same, and the arching elevations of the two arch seats on both sides of the low arch rib 2 are the same. The vertical height difference between the arch axis L1 of the high arch rib 1 and the arch axis L2 of the low arch rib 2 is equal to the difference in arching elevations at the arch seat 4 on the side of the high arch rib and the arch seat 5 on the side of the low arch rib.

[0045] Specifically, in step S3, if the bearing capacity of the upper chord main pipe or the lower chord main pipe of the high arch rib 1 cannot meet the requirements, modify the wall thickness ts1 of the upper chord main pipe or the wall thickness tx1 of the lower chord main pipe of the high arch rib 1; if the bearing capacity of the upper chord main pipe or the lower chord main pipe of the low arch rib 2 cannot meet the requirements, modify the wall thickness ts2 of the upper chord main pipe or the wall thickness tx2 of the lower chord main pipe of the low arch rib 2; if the bearing capacity of the cross brace 3 cannot meet the requirements, modify the main pipe diameter D of the cross brace 3; if the base stress, overturning stability and anti-slip stability of the high arch rib side arch seat 4, and the base stress, overturning stability and anti-slip stability of the low arch rib side arch seat 5 cannot meet the requirements, modify the length l1 of the high arch rib side arch seat 4, the length l2 of the low arch rib side arch seat 5, and the width b1 of the high arch rib side arch seat 4 or the width b2 of the low arch rib side arch seat 5.

[0046] Specifically, the bearing capacity of the upper and lower main chords of the high arch rib 1 and the low arch rib 2 is verified to be greater than the internal forces of the upper and lower main chords of the high arch rib 1 and the low arch rib 2, the bearing capacity of the cross brace 3 is greater than the internal forces of the cross brace 3, and the base stress, overturning stability and sliding stability of the high arch rib side arch seat 4 and the low arch rib side arch seat 5 are verified to meet the requirements.

[0047] Specifically, if adjusting the wall thickness ts1 of the upper chord main pipe of the high arch rib 1, the wall thickness tx1 of the lower chord main pipe of the high arch rib 1, the wall thickness ts2 of the upper chord main pipe of the low arch rib 2, and the wall thickness tx2 of the lower chord main pipe of the low arch rib 2 cannot meet the requirements for the bearing capacity of the upper chord main pipe of the high arch rib 1 and the lower chord main pipe of the low arch rib 2, then the height of the arch axis L1 of the high arch rib 1 and the arch axis L2 of the low arch rib 2 can be adjusted.

[0048] Make the heights of the arch axis L1 of the high arch rib 1 and the arch axis L2 of the low arch rib 2 closer together, and adjust the height h1 of the high arch rib side arch seat 4, the height h2 of the low arch rib side arch seat 5, the height h of the high arch rib 1, the width b of the high arch rib 1, the height h of the low arch rib 2, and the width b of the low arch rib 2 accordingly.

[0049] Specifically, in step S3, the formulas for calculating the bearing capacity of the upper and lower chord main tubes of the high arch rib 1 and the upper and lower chord main tubes of the low arch rib 2 are as follows:

[0050] Mode The value in the middle is the structural importance coefficient. For the main axial internal force, The slenderness ratio reduction factor for the main body. The reduction factor for the main bending moment. This represents the design value of the axial compressive strength of the concrete-filled steel tube. The cross-sectional area of ​​the main steel-concrete composite pipe is given. The initial stress reduction factor for the main steel pipe is given. The value is the concrete void reduction factor; the above values ​​are calculated based on the main pipe diameter d, the upper chord main pipe wall thickness ts1 of the high arch rib 1, the upper chord main pipe wall thickness ts2 of the low arch rib 2, the lower chord main pipe wall thickness tx1 of the high arch rib 1, the lower chord main pipe wall thickness tx2 of the low arch rib 2, the arch axis L1 of the high arch rib 1, and the L2 of the low arch rib 2.

[0051] Structural importance coefficient This is a key parameter used to reflect the importance of a structure in the overall project, and thus adjust its load-bearing capacity requirements. If the consequences of structural failure are particularly severe, then [the parameter is used]. A value greater than 1 implies a need for a higher safety margin, as shown on the left side of the formula. The load will increase, requiring a higher design value for the load-bearing capacity on the right side to satisfy the inequality and ensure structural safety. The specific structural importance coefficient... The value of is determined based on the possible consequences of structural failure.

[0052] Specifically, in step S3, the formula for calculating the main bearing capacity of the cross brace 3 is as follows:

[0053] In the formula, This is the structural importance coefficient. The axial force of the three main cross braces. Let be the bending moment in the y-axis direction of the main cross brace 3. The bending moment in the z-axis direction of the main cross brace 3. Let the cross-sectional area of ​​the main pipe of the cross brace 3 be _____. Let be the area modulus of the main cross brace 3 along the y-axis. Let be the area modulus of the main cross brace 3 along the z-axis. This is the design strength value for the main cross brace 3.

[0054] In the formula, the axial force of the main cross brace 3 is... The bending moment in the y-axis direction of the 3rd main cross brace The bending moment in the z-axis direction of the main cross brace 3 The strength design value of the main cross brace 3 was calculated based on the macroscopic finite element model. The strength design value is related to the grade and thickness of the steel. Common steels include, but are not limited to, Q235 and Q345. The strength design value is determined according to, but is not limited to, steel structure design standards and specifications.

[0055] Specifically, in step S3, the formula for calculating the bearing capacity of the foundation soil and rock is as follows:

[0056] In the formula, For the axial force of the base, Let A be the bending moment along the y-axis of the base, and let A be the cross-sectional area of ​​the base. Let be the area modulus along the y-axis of the base. The maximum compressive stress of the base. This is the adjustment coefficient for the bearing capacity of the foundation. The characteristic value of the foundation bearing capacity is the foundation base, which includes the foundation base of the high arch rib side arch seat 4 and the foundation base of the low arch rib side arch seat 5.

[0057] In the formula, the axial force of the base , Bending moment along the y-axis of the base The base cross-sectional area was calculated based on the macroscopic finite element model. , Area modulus of the base along the y-axis The length l1, width b1, and height h1 of the high arch rib side arch seat 4 and the length l2, width b2, and height h2 of the low arch rib side arch seat 5 are calculated.

[0058] Specifically, in step S3, Formula for calculating the overturning stability of an arch abutment:

[0059] In the formula, The values ​​of axial force N, shear force V, and vertical component of the projection of the arch abutment's self-weight G onto the base are given for the loads applied to the arch abutment other than its own weight. The values ​​of axial force N, shear force V, and centroidal lever arm of the arch abutment's self-weight G at the base section of the foundation are given for the loads applied to the arch abutment other than its own weight. The horizontal components of the axial force N and shear force V, excluding the self-weight, applied to the arch abutment, are projected onto the base. The lever arms of the axial force N and shear force V corresponding to the loads other than the self-weight applied to the arch abutment are located at the base section of the foundation. To ensure the overturning stability of the arch abutment, for The total value includes the arch seat 4 on the high arch rib side and the arch seat 5 on the low arch rib side.

[0060] Specifically, in step S3, the formula for calculating the anti-slip stability of the arch abutment is as follows:

[0061] In the formula, The coefficient of friction of the substrate. for The total value, The sum of the anti-slip stabilizing horizontal forces, for The total value, To ensure the anti-slip stability of the arch abutment, the arch abutment includes the high arch rib side arch abutment 4 and the low arch rib side arch abutment 5.

[0062] 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, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A design method for a high-low arch bridge, characterized in that, The design methodology includes the following steps: S1. Based on the span of the arch bridge and the ground elevation at the side arch seat (4) of the high arch rib and the ground elevation at the side arch seat (5) of the low arch rib, the geometric dimensions of the arch bridge are initially proposed, wherein the length and cross-sectional dimensions of the high arch rib (1) and the low arch rib (2) are the same. S2. Establish a macroscopic finite element model of the arch bridge and calculate the internal forces of the upper chord main tube and the lower chord main tube of the high arch rib (1), the internal forces of the upper chord main tube and the lower chord main tube of the low arch rib (2), the internal forces of the cross brace (3), the base internal forces of the side arch seat (4) of the high arch rib, and the base internal forces of the side arch seat (5) of the low arch rib. S3. Verify the bearing capacity of the upper chord main tube and the lower chord main tube of the high arch rib (1), the bearing capacity of the upper chord main tube and the lower chord main tube of the low arch rib (2), the bearing capacity of the cross brace (3), the base stress of the side arch seat (4) of the high arch rib, the overturning stability and the sliding stability, and the base stress of the side arch seat (5) of the low arch rib, the overturning stability and the sliding stability, and whether they meet the requirements. S4. If the requirements are not met, modify the geometry of the arch bridge and repeat steps S2 and S3 until the requirements are met.

2. The design method for a high-low arch bridge according to claim 1, characterized in that, In step S1, the preliminary geometric dimensions of the high and low arch bridge include the height h1, width b1, main pipe diameter d1, arch axis L1, upper chord main pipe wall thickness ts1 and lower chord main pipe wall thickness tx1 of the high arch rib (1), the height h2, width b2, main pipe diameter d2, arch axis L2, upper chord main pipe wall thickness ts2 and lower chord main pipe wall thickness tx2 of the low arch rib (2), the length l1, width b1 and height h1 of the high arch rib side arch seat (4), the length l2, width b2 and height h2 of the low arch rib side arch seat (5), and the main pipe diameter D of the cross brace (3); the height h1, width b1, main pipe diameter d1, arch axis L1, upper chord main pipe wall thickness ts1 and lower chord main pipe wall thickness tx1 of the high arch rib (1) are equal to the height h2, width b2, main pipe diameter d2, arch axis L2, upper chord main pipe wall thickness ts2 and lower chord main pipe wall thickness tx2 of the low arch rib (2).

3. The design method for a high-low arch bridge according to claim 2, characterized in that, In step S1, the arching elevations of the two arch seats on both sides of the high arch rib (1) are the same, and the arching elevations of the two arch seats on both sides of the low arch rib (2) are the same. The vertical height difference between the arch axis L1 of the high arch rib (1) and the arch axis L2 of the low arch rib (2) is equal to the difference in arching elevation between the arch seat (4) on the side of the high arch rib and the arch seat (5) on the side of the low arch rib.

4. A design method for a high-low arch bridge according to any one of claims 1-3, characterized in that, In step S3, if the bearing capacity of the upper chord main pipe or the lower chord main pipe of the high arch rib (1) does not meet the requirements, modify the wall thickness ts1 of the upper chord main pipe or the wall thickness tx1 of the lower chord main pipe of the high arch rib (1); if the bearing capacity of the upper chord main pipe or the lower chord main pipe of the low arch rib (2) does not meet the requirements, modify the wall thickness ts2 of the upper chord main pipe or the wall thickness tx2 of the lower chord main pipe of the low arch rib (2); if the cross brace (3) If the bearing capacity of the cross brace (3) cannot meet the requirements, modify the main pipe diameter D value of the cross brace (3); if the base stress, overturning stability and sliding stability of the high arch rib side arch seat (4), the base stress, overturning stability and sliding stability of the low arch rib side arch seat (5) cannot meet the requirements, modify the length l1 of the high arch rib side arch seat (4), the length l2 of the low arch rib side arch seat (5), the width b1 of the high arch rib side arch seat (4) or the width b2 of the low arch rib side arch seat (5).

5. The design method for a high-low arch bridge according to claim 4, characterized in that, If adjusting the wall thickness ts1 of the upper chord main pipe of the high arch rib (1), the wall thickness tx1 of the lower chord main pipe of the high arch rib (1), the wall thickness ts2 of the upper chord main pipe of the low arch rib (2), and the wall thickness tx2 of the lower chord main pipe of the low arch rib (2) cannot make the bearing capacity of the upper chord main pipe of the high arch rib (1) and the bearing capacity of the lower chord main pipe of the low arch rib (2) meet the requirements, then the height of the arch axis L1 of the high arch rib (1) and the arch axis L2 of the low arch rib (2) can be adjusted.

6. The design method for a high-low arch bridge according to claim 4, characterized in that, In step S3, the formulas for calculating the bearing capacity of the upper and lower chord main tubes of the high arch rib (1) and the upper and lower chord main tubes of the low arch rib (2) are as follows: Mode The value in the middle is the structural importance coefficient. For the main axial internal force, The slenderness ratio reduction factor for the main body. The reduction factor for the main bending moment. This represents the design value of the axial compressive strength of the concrete-filled steel tube. The cross-sectional area of ​​the main steel-concrete composite pipe is given. The initial stress reduction factor for the main steel pipe is given. This is the reduction factor for concrete voids.

7. The design method for a high-low arch bridge according to claim 4, characterized in that, In step S3, the formula for calculating the main bearing capacity of the cross brace (3) is as follows: In the formula, This is the structural importance coefficient. For the axial force of the main body of the cross brace (3), The bending moment in the y-axis direction of the main cross brace (3) is the bending moment of the main cross brace. The bending moment in the z-axis direction of the main cross brace (3), The cross-sectional area of ​​the main cross brace (3) is given. The area modulus of the main cross brace (3) in the y-axis direction is... The area modulus of the main cross brace (3) in the z-axis direction is the area modulus. The strength design value of the main body of the cross brace (3).

8. The design method for a high-low arch bridge according to claim 4, characterized in that, In step S3, the formula for calculating the bearing capacity of the foundation soil and rock is as follows: In the formula, N is the base axial force, Let A be the bending moment along the y-axis of the base, and let A be the cross-sectional area of ​​the base. Let be the area modulus along the y-axis of the base. The maximum compressive stress of the base. This is the adjustment coefficient for the bearing capacity of the foundation. The characteristic value of the bearing capacity of the foundation is the foundation of the high arch rib side arch seat (4) and the foundation of the low arch rib side arch seat (5).

9. The design method for a high-low arch bridge according to claim 4, characterized in that, In step S3, Formula for calculating the overturning stability of an arch abutment: In the formula, The values ​​of axial force N, shear force V, and vertical component of the projection of the arch abutment's self-weight G onto the base are given for the loads applied to the arch abutment other than its own weight. The values ​​of axial force N, shear force V, and centroidal lever arm of the arch abutment's self-weight G at the base section of the foundation are given for the loads applied to the arch abutment other than its own weight. The horizontal components of the axial force N and shear force V, excluding the self-weight, applied to the arch abutment, are projected onto the base. The lever arms of the axial force N and shear force V corresponding to the loads other than the self-weight applied to the arch abutment are located at the base section of the foundation. To ensure the overturning stability of the arch abutment, for The total value includes the arch seat, which includes the high arch rib side arch seat (4) and the low arch rib side arch seat (5).

10. The design method for a high-low arch bridge according to claim 4, characterized in that, In step S3, the formula for calculating the anti-slip stability of the arch abutment is as follows: In the formula, The coefficient of friction of the substrate. for The total value, The sum of the anti-slip stabilizing horizontal forces, for The total value, To ensure the anti-slip stability of the arch abutment, the arch abutment includes the high arch rib side arch abutment (4) and the low arch rib side arch abutment (5).

Images