A design method for high-fatigue-resistant suspender anchors that reduces peak stress in the anchor body

Abstract

This invention relates to a design method for high-fatigue-resistant cable anchors that reduces peak stress in the anchor body, belonging to the field of bridge engineering technology. Step 1: Establish a micro-unit compressive stress calculation model for the anchor cone; divide the anchor cone in the cable anchorage zone into n equidistant micro-units, and establish a compressive stress calculation model for the i-th micro-unit; Step 2: Determine the reliability constraints of the anchor cone angle; Step 3: Select and optimize the anchor structure to reduce the peak stress at the small end; based on the compressive stress calculation results in Step 1, if the peak compressive stress in the small end region exceeds the design allowable value, the following measures are adopted: Measure 1: Optimize the geometric parameters and friction coefficient of the anchor cone; Measure 2: Adopt a multi-cone segment structure; Measure 3: Adopt a combination structure of straight segments and conical segments. By optimizing the geometric parameters, friction coefficient, and structural form of the anchor cone, the peak compressive stress at the small end of the anchorage zone is reduced, improving the fatigue resistance of the cable.

Description

Technical Field

[0001] This invention relates to a design method for high fatigue-resistant cable anchors that reduce peak stress in the anchor body, belonging to the field of bridge engineering technology. Background Technology

[0002] Parallel wire rope (suspension) cables are made by twisting and extruding multiple high-strength steel wires to form a cable body, and then installing cold-cast upset head anchors at both ends of the cable body. In order to meet the requirements of anchorage reliability, the steel wire bundle in the anchorage zone of the rope (suspension) cable needs to be upset and filled with anchoring material to form an anchoring cone. In the above process, local stress concentration inevitably occurs in the steel wires in the anchorage zone, causing this part to fail prematurely under fatigue load, thus making the fatigue strength of the rope (suspension) cable lower than that of a single steel wire.

[0003] The strength of parallel wire slings depends on the anchoring performance of the corresponding anchorage. Under existing anchorages, the compressive stress on the surface of the parallel wire sling exhibits a non-linear distribution from the free end of the anchorage zone to the connection end with the cable (small end), increasing in magnitude. The compressive stress on the surface of the sling at the loaded end is relatively high, easily leading to stress concentration. Under cyclic fatigue loading, this causes premature breakage of the sling wire at the small end exit of the anchorage. To overcome the shortcomings of existing anchorages, a design method for a fatigue-resistant sling anchorage that reduces the peak stress of the anchor body is proposed. This method lowers the compressive stress level of the small end anchorage under ultimate conditions, resulting in a more uniform stress distribution in the anchorage zone and thus improving the fatigue resistance of the sling. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a design method for a high-fatigue-resistant sling anchor body that reduces the peak stress of the anchor body, thereby improving the fatigue resistance of the sling by optimizing the geometric parameters, friction coefficient and structural form of the anchor cone.

[0005] The technical solution adopted by this invention to solve the above problems is: a design method for a fatigue-resistant suspending cable anchor body that reduces peak stress in the anchor body, comprising the following steps: Step 1: Establish a micro-element extrusion stress calculation model for the anchoring cone; The anchoring cone of the cable anchorage zone is divided into n equidistant micro-elements along its axial direction. Based on the deformation compatibility condition and the theory of elasticity, a calculation model for the compressive stress of the i-th micro-element is established:

[0006] Where: σ(xi) is the micro-element extrusion stress; F is the tension in the sling; d1 is the diameter of the small end of the anchor body cone; L is the total length of the anchoring cone; α is the cone angle of the anchoring cone; μ is the coefficient of friction between the anchor cup and the anchor body; n is the number of micro-units; i is 1, 2, …, n; Step 2: Determine the reliability constraints of the anchor cone angle; Based on the principle of static equilibrium of the wedge, the relationship between the clamping force J and the cone angle α is established:

[0007] Where: J is the clamping force generated by the anchor cone wedge; F is the cable force acting on the anchoring cone; α is the angle of the anchoring cone; φ1 is the friction angle between the anchor cone wedge and the steel wire; φ2 is the friction angle between the anchor cone wedge and the inner wall of the anchor cup; Step 3: Select and optimize the anchor structure to reduce the peak stress at the small end; Based on the extrusion stress calculation results in step one, if the peak extrusion stress in the small end region exceeds the design allowable value, one or more of the following structural optimization measures shall be adopted: Measure 1: Adjust the diameter d1 of the small end and the diameter d2 of the large end of the anchor cone, increase the friction coefficient μ, and change the cone angle α. Then, verify the final anchor cavity size by using the force balance equation in step 2. Measure 2: Adopt a multi-conical segment structure: Divide the anchorage zone into K areas according to the tapered broken line, with each area bearing a cable force of F. K , Each region is treated as a single-cavity structure for compressive stress analysis. Each region is divided into micro-units, and the compressive stress of each micro-unit in each region is calculated according to the method in step one. Steps one to three are repeated until the maximum compressive stress in the entire length of the anchorage area is reduced to below the target value, thus completing the design. Measure 3: Adopt a combined structure of straight and conical sections, and calculate the compressive stress of the straight section using the following formula: ; In the above formula, d p The diameter of the straight section of the anchor body; μ is the coefficient of friction between the anchor cup and the anchor solid; F is the tension in the sling; L is the total length of the anchorage section; L p The length of the straight section for anchoring; Repeat steps one through three until the maximum compressive stress over the entire length of the anchorage zone drops below the target value, thus completing the design.

[0008] In step one, the value of n ranges from 10 to 30.

[0009] The friction coefficient μ ranges from 0.3 to 0.6.

[0010] The determination of the cone angle of the anchoring cone is related to the friction coefficient between the steel wire and the anchoring cone, and between the anchoring cone and the inner wall of the anchor; the cone angle α of the anchoring cone ranges from 5° to 8°.

[0011] Based on the anchoring reliability requirements, the clamping force J in step two is 1.1F~1.2F.

[0012] In step three, the length L of the straight section p The diameter D of the straight section shall not exceed half the total length L of the anchorage section. p It should not be less than the diameter of the small end of the cone segment.

[0013] Compared with existing technologies, the advantages of this invention are: a design method for a fatigue-resistant sling anchor body that reduces peak stress in the anchor body, effectively reducing the peak compressive stress at the small end of the anchorage zone and improving the fatigue resistance of the sling by optimizing the geometric parameters and structural form of the anchor cone. Based on static equilibrium and friction angle theory, it ensures that the anchor body does not slip or fail under ultimate load, improving anchorage reliability; and by using a combination of single cone, multi-cone segments, and straight segments with cone segments, it meets different structural size constraints. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the micro-unit division of the anchor body in a design method for a high-fatigue-resistant suspender anchor body to reduce peak stress in the anchor body according to an embodiment of the present invention; Figure 2 The diagram shows the stress analysis of the wedge in the anchorage zone. Figure 3 An energy balance diagram for the anchorage area; Figure 4 This is a schematic diagram of a multi-cone cavity anchoring structure; Figure 5 A schematic diagram of a single-cone cavity anchoring cone with continuous angles; Figure 6 This is a schematic diagram of a three-cone cavity anchoring cone; Figure 7 This is a schematic diagram of an anchoring cone that combines a straight section and a conical section (the diameter of the straight section is equal to the diameter of the small end of the conical section). Figure 8 This is a schematic diagram of an anchoring cone that combines a straight section and a conical section (the diameter of the straight section is larger than the diameter of the small end of the conical section). Detailed Implementation

[0015] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0016] This embodiment of a method for designing a fatigue-resistant suspender anchor body to reduce peak stress in the anchor body includes the following steps: Step 1: As Figure 1 As shown, the anchoring cone of the sling anchoring zone is divided into n micro-units along its axial direction, and a calculation model for the compressive stress of the micro-units of the anchoring cone is established. like Figure 2 As shown, when the sling is under stress, the inner wall of the anchor cup deforms, the anchor cone is compressed under radial pressure, and the sling is subjected to a large longitudinal tensile force, causing relative slippage between the anchor cone and the sling and the inner wall of the anchor cup. According to the deformation compatibility condition, the radial deformation of any micro-unit anchoring segment of the anchor cone is equal. Based on the theory of elasticity, when the sling is under load, the compressive stress on the outer surface of the micro-unit anchoring segment (perpendicular to the cone surface) and the frictional force between the anchoring segment and the anchor cup (parallel to the cone surface) in the x-axis direction are represented by F. i The sum of the tension forces on each micro-unit is equal to the total tension force of the sling.

[0017] Force balance equations for the micro-unit anchorage segment:

[0018] Wherein: F i The tensile force acting on the micro-unit; σ(x) represents the compressive stress of the micro-element; dxi is the diameter of the micro-unit anchor solid; The angle of the anchoring cone; μ is the coefficient of friction between the anchor cup and the anchor body.

[0019] Therefore, the compressive stress in the micro-unit anchorage section is:

[0020] Let the diameter of the small end of the anchoring cone be d1 and the diameter of the large end be d2. The anchoring cone is divided into n equal segments along the axis (the segments are x1, x2, ..., xn). n The number of segments ranges from 10 to 30, and the diameter increase for each segment is Δd. Starting from the smallest end, the formula for calculating the compressive stress of each micro-unit anchorage segment is:

[0021] in,

[0022]

[0023]

[0024] The formula for the compressive stress of the above micro-units can be simplified to the following:

[0025] In the above formula, d1 is the diameter of the small end of the anchor body cone; F is the tension in the sling; L is the total length of the anchoring cone.

[0026] Step 2: Determine the reliability constraints of the anchor cone angle; the determination of the anchor cone angle must ensure that the cone surface is wedge-clamped with the anchor and the steel wire to avoid the steel wire casting slipping out or the anchor cone sliding, which is related to the friction coefficient between the steel wire and the anchor cone, and between the anchor cone and the inner wall of the anchor.

[0027] Figure 3 As shown, F is the cable force acting on the anchor cone, J is the clamping force of the wedge on the workpiece, and F l F1 is the frictional resistance between the straight surface of the anchor cone wedge (i.e., the working surface where the steel wire is clamped) and the surface where the steel wire is clamped (equal to Jtanφ1). The resultant force of J and F1 is P. N is the reaction force of the inner cone surface of the anchor on the inclined surface of the anchor cone wedge, and its direction is perpendicular to the inclined surface. F2 is the frictional resistance between the inner cone surface of the anchor cup and the outer cone wedge of the anchor cone (equal to Ntanφ2). The resultant force of N and F2 is R. When the anchor cone wedge is clamped, these three forces F, P, and R should be in static equilibrium. The force equilibrium equation in the F direction is:

[0028]

[0029] Where: J is the clamping force generated by the anchor cone wedge; F is the cable force acting on the anchoring cone; α is the angle of the anchoring cone; φ1 is the friction angle between the anchor cone wedge and the steel wire; φ2 is the friction angle between the anchor cone wedge and the inner wall of the anchor cup; Based on the anchorage reliability requirement, i.e., the cable fails but the anchor cone does not fail, the clamping force J = 1.1F~1.2F; substituting this into the above force balance equation, we can see that... ; The anchoring material in this application is a zinc-aluminum-copper alloy, and the coefficient of friction between the zinc-aluminum-copper alloy and the inner wall of the anchor cup is approximately... ,Right now The coefficient of friction between steel wire and zinc-aluminum-copper alloy ,Right now According to the above calculation formula, the angle α of the anchoring cone is 5°~8°.

[0030] Step 3: Select and optimize the anchor structure to reduce the peak stress at the small end.

[0031] Based on the extrusion stress calculation results in step one, if the peak extrusion stress in the small end region exceeds the design allowable value, one or more of the following structural optimization measures shall be adopted: Measure 1: Adjust the diameter d1 of the small end and the diameter d2 of the large end of the anchor cone, increase the friction coefficient μ, and change the cone angle α. Then, verify the final anchor cavity size by using the force balance equation in step 2.

[0032] Measure 2: such as Figure 4 As shown, a multi-conical segment structure is adopted: the anchorage zone is divided into K regions according to the tapered broken line, and the cable force borne by each region is F. K , Each region is treated as a single-cavity structure for compressive stress analysis. Each region is divided into micro-units, and the compressive stress of each micro-unit in each region is calculated according to the method in step one. Steps one to three are repeated until the maximum compressive stress in the entire length of the anchorage area is reduced to below the target value, thus completing the design.

[0033] F K The cable force L borne by each region K L is the length of the area, F is the total length of the anchorage section, and F is the tension of the sling.

[0034] The principle for determining the wedge angle α of a multi-cone anchoring cone is consistent with the principle for determining the angle of a single-cone anchoring body with continuous cones. The anchoring material in this application is a zinc-aluminum-copper alloy, and the coefficient of friction between the zinc-aluminum-copper alloy and the inner wall of the anchor cup is approximately... ,Right now The coefficient of friction between steel wire and zinc-aluminum-copper alloy ,Right now According to the above calculation formula, the angle α of the anchoring cone is 5°~8°.

[0035] Measure 3: Adopt a combination structure of straight sections and conical sections, with the straight section length L p The diameter D of the straight section shall not exceed 50% of the total length L of the anchorage section. p The diameter must be no less than the small end diameter of the conical section, and must also meet the requirements for reducing the extrusion stress in the straight section. The formula for calculating the extrusion stress in the straight section is as follows: ; In the above formula, d p The diameter of the straight section of the anchor body; μ is the coefficient of friction between the anchor cup and the anchor solid; F is the tension in the sling; L is the total length of the anchorage section; Lp is the length of the straight section for anchoring.

[0036] Repeat steps one through three until the maximum compressive stress over the entire length of the anchorage zone drops below the target value, thus completing the design. Example

[0037] Taking the 7-91 specification single cone cavity sling as an example, Figure 5 The initially designed anchorage has a single cone with a continuous angle. The cable force F is 6204 KN, the diameter d2 of the large end of the anchorage cone is 148 mm, and the diameter d1 of the small end of the anchorage cone is 98 mm. The coefficient of friction between the anchor cup and the anchor body is 0.4. The angle α of the anchorage cone is 5.49°. The length L of the anchorage section is 260 mm, and n=20.

[0038] Starting from the small end, the anchorage zone is divided into 20 micro-unit anchorage segments. The local compressive stress within each micro-unit anchorage segment is calculated according to the formula in step one. The compressive stress values ​​are shown in Table 1. Table 1

[0039] Option 1 In Table 1, the local compressive stress of micro-units 1-4 is relatively large. Due to the limited dimensions of the anchorage, significant adjustments cannot be made. Therefore, measure two is adopted to optimize it. Figure 6 As shown, a three-cone cavity anchor structure is used to adjust the peak compressive stress. A three-segment method is used to divide each segment into n equidistant micro-units, and compressive stress analysis is performed within the micro-units.

[0040] The cable force F1 borne by segment 1 is 930.6 KN, the diameter d1 of the small end of the anchor cone of segment 1 is 108mm, the length L1 is 39mm, the friction coefficient between the anchor cup and the anchor body is 0.4, and the unit angle α of the anchor cone of segment 1 is 8.5°. Segment 1 is divided into 3 equidistant micro-units (n=3) along the axis, and the length L1 of each unit is 13mm.

[0041] The cable force F2 borne by segment 2 is 310.6 KN. The diameter of the anchor cone of segment 2 is d2, which is 148 mm and the length is L2, which is 13 mm. The friction coefficient between the anchor cup and the anchor body is 0.4. The angle α of the unit of the anchor cone of segment 2 is 0°. n=1.

[0042] The cable force F3 borne by segment 3 is 4963.2 KN. The diameter of the small end of the anchor cone of segment 3 is d3, which is 108 mm, and the length is L3, which is 13 mm. The coefficient of friction between the anchor cup and the anchor body is 0.4. The angle α of the unit of the anchor cone of segment 3 is 5.49°. n=16.

[0043] Starting from the small end of each of the three segmented areas, the local compressive stress within the micro-unit anchorage section of each segment is calculated using the formula in step one. The compressive stress values ​​are shown in Table 2.

[0044] Table 2

[0045] As shown in Tables 1 and 2 above, the maximum internal compressive stress decreased from 154.97 MPa to 127.12 MPa, a decrease of more than 18%.

[0046] Option 2 like Figure 7 As shown, measure three (straight section + conical section anchorage structure) was used to adjust the peak stress. A two-segment method was adopted, with the outer diameter of the anchor unchanged, the length of the anchor increased, and a straight section added. Each segment was divided into micro-units, and compressive stress analysis was performed within the micro-units.

[0047] The cable force F1 borne by segment 1 is 1778 kN, and the diameter of the small end of the anchor cone of segment 1 is d. p It is 98mm in diameter and has a length of L. p The unit diameter is 100mm, the coefficient of friction between the anchor cup and the anchor body is 0.4, the angle α of the anchor cone unit is 0°, and n=1.

[0048] The cable force F2 borne by segment 2 is 4623 KN. The small end diameter d1 of the anchor cone of segment 2 is 98mm, the large end diameter d2 is 148mm, the length L2 is 260mm, the friction coefficient between the anchor cup and the anchor body is 0.4, the unit angle α of the anchor cone is 5.49°, and n=20.

[0049] Starting from the small end of each of the two segmented areas, the local compressive stress within the micro-unit anchorage section of each segment is calculated using the formula in step one. The compressive stress values ​​are shown in Table 3.

[0050] Table 3

[0051] As shown in Tables 1 and 3, the maximum internal compressive stress decreased from 154.97 MPa to 144.38 MPa, indicating that the stress reduction was not significant.

[0052] Option 3 like Figure 8 As shown, measure three (large-diameter straight section + conical section anchorage structure) is used to adjust the stress peak. A two-segment method is adopted, with the outer diameter of the anchor unchanged, the length of the anchor is increased, a straight section is added, and the diameter of the anchor body in the straight section is increased. Each segment is divided into micro-units, and compressive stress analysis is performed within the micro-units.

[0053] The cable force F1 borne by segment 1 is 1778 kN, and the diameter of the anchoring cone of segment 1 is d. p It is 118mm long and has a length of L. p The unit diameter is 100mm, the coefficient of friction between the anchor cup and the anchor body is 0.4, the angle α of the anchor cone unit is 0°, and n=8.

[0054] The cable force F2 borne by segment 2 is 4623 KN. The small end diameter d1 of the anchor body cone of segment 2 is 98mm, the large end diameter d2 is 148mm, the length L2 is 260mm, the friction coefficient between the anchor cup and the anchor body is 0.4, the unit angle α of the anchor cone is 5.49°, and n=20.

[0055] Starting from the small end of the two segmented areas, the local compressive stress in the micro-unit anchorage section of each segment is calculated using the formula in step one. The compressive stress values ​​are shown in Table 4.

[0056] Table 4

[0057] As shown in Tables 1 and 4, the maximum internal compressive stress decreased from 154.97 MPa to 119.91 MPa, and the peak stress decreased by about 23%. By increasing the length of the anchor and the diameter of the straight section, the average compressive stress was also significantly reduced, demonstrating remarkable effectiveness.

[0058] This application effectively reduces the peak compressive stress at the small end of the anchorage zone and improves the fatigue resistance of the sling by optimizing the geometric parameters and structural form of the anchorage cone. Based on static equilibrium and friction angle theory, it ensures that the anchor body does not slip or fail under ultimate load, thus improving anchorage reliability. It is applicable to single cone, multi-cone, and combined straight and cone structures, meeting different structural size restrictions.

[0059] In addition to the above embodiments, the present invention also includes other embodiments. All technical solutions formed by equivalent transformation or equivalent substitution should fall within the protection scope of the claims of the present invention.

Claims

1. A method for designing a fatigue-resistant suspender anchor body with reduced peak stress in the anchor body, characterized in that: Includes the following steps: Step 1: Establish a micro-element extrusion stress calculation model for the anchoring cone; The anchoring cone of the cable anchorage zone is divided into n equidistant micro-elements along its axial direction. Based on the deformation compatibility condition and the theory of elasticity, a calculation model for the compressive stress of the i-th micro-element is established: ； Where: σ(xi) is the micro-element extrusion stress; F is the tension in the sling; d1 is the diameter of the small end of the anchor body cone; L is the total length of the anchoring cone; α is the cone angle of the anchoring cone; μ is the coefficient of friction between the anchor cup and the anchor body; n is the number of micro-units; i is 1, 2, …, n; Step 2: Determine the reliability constraints of the anchor cone angle; Based on the principle of static equilibrium of the wedge, the relationship between the clamping force J and the cone angle α is established: ； Where: J is the clamping force generated by the anchor cone wedge; F is the cable force acting on the anchoring cone; α is the angle of the anchoring cone; φ1 is the friction angle between the anchor cone wedge and the steel wire; φ2 is the friction angle between the anchor cone wedge and the inner wall of the anchor cup; Step 3: Select and optimize the anchor structure to reduce the peak stress at the small end; Based on the extrusion stress calculation results in step one, if the peak extrusion stress in the small end region exceeds the design allowable value, one or more of the following structural optimization measures shall be adopted: Measure 1: Adjust the diameter d1 of the small end and the diameter d2 of the large end of the anchor cone, increase the friction coefficient μ, and change the cone angle α. Then, verify the final anchor cavity size by using the force balance equation in step 2. Measure 2: Adopt a multi-conical segment structure: Divide the anchorage zone into K areas according to the tapered broken line, with each area bearing a cable force of F. K , Each region is treated as a single-cavity structure for compressive stress analysis. Each region is divided into micro-units, and the compressive stress of each micro-unit in each region is calculated according to the method in step one. Steps one to three are repeated until the maximum compressive stress in the entire length of the anchorage area is reduced to below the target value, thus completing the design. Measure 3: Adopt a combined structure of straight and conical sections, and calculate the compressive stress of the straight section using the following formula: ； In the above formula, d p The diameter of the straight section of the anchor body; μ is the coefficient of friction between the anchor cup and the anchor solid; F is the tension in the sling; L is the total length of the anchorage section; L p The length of the straight section for anchoring; Repeat steps one through three until the maximum compressive stress over the entire length of the anchorage zone drops below the target value, thus completing the design.

2. The method for designing a fatigue-resistant suspender anchor body with reduced peak stress in the anchor body according to claim 1, characterized in that: In step one, the value of n ranges from 10 to 30.

3. The method for designing a fatigue-resistant suspender anchor body with reduced peak stress in the anchor body according to claim 1, characterized in that: The friction coefficient μ ranges from 0.3 to 0.

6.

4. The method for designing a fatigue-resistant suspender anchor body with reduced peak stress in the anchor body according to claim 1, characterized in that: The determination of the cone angle of the anchoring cone is related to the friction coefficient between the steel wire and the anchoring cone, and between the anchoring cone and the inner wall of the anchor; the cone angle α of the anchoring cone ranges from 5° to 8°.

5. The method for designing a fatigue-resistant suspender anchor body with reduced peak stress in the anchor body according to claim 1, characterized in that: Based on the anchoring reliability requirements, the clamping force J in step two is 1.1F~1.2F.

6. The method for designing a fatigue-resistant suspender anchor body with reduced peak stress in the anchor body according to claim 1, characterized in that: In step three, the length L of the straight section p The diameter D of the straight section shall not exceed half the total length L of the anchorage section. p It should not be less than the diameter of the small end of the cone segment.

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