A novel optimization design method for CFRP stranded wire composite anchor

Abstract

The invention discloses a novel CFRP stranded wire composite anchor optimization design method, which relates to the field of anchor design, and comprises the following steps: force analysis of a clip in an anchoring system, force analysis of an anchor cup in an anchoring system, force analysis of a bite between a clip thread and a CFRP stranded wire in an anchoring system, and simulation analysis. By combining theoretical analysis with simulation, design parameters such as the friction coefficient between the CFRP stranded wire and the clip, the friction coefficient between the anchor cup and the clip, the anchor cup cone angle, the anchor cup thickness, the anchor cup length, and the bite effect of the clip thread spacing are obtained, thereby effectively delaying the transverse incision effect of the CFRP stranded wire and improving the bearing capacity of the anchoring system.

Description

Technical Field

[0001] The invention relates to the field of anchor design, and in particular to a novel CFRP stranded wire composite anchor optimization design method. Background Art

[0002] At present, the steel cables of existing bridges have shortcomings such as heavy weight, low load-bearing efficiency, weak corrosion resistance and high subsequent maintenance costs, which seriously restrict the development of bridges towards lighter, larger spans and longer service life. Studies have shown that CFRP (Carbon Fiber Reinforced Polymers: carbon fiber reinforced composite materials) has the characteristics of light weight, high tensile strength and good durability. Therefore, CFRP cables are expected to replace steel cables and provide broad development prospects for lightweight, large span and long service life bridges.

[0003] CFRP strands are made by pre-impregnating multiple strands of small-diameter carbon fiber tendons with epoxy resin glue, and then twisting, heating and bonding. Their shape is similar to that of steel strands. Since CFRP materials have high axial tensile strength but low lateral strength, the existing anchors are prone to stress concentration at the anchoring port when anchoring CFRP strands, and even bite off the CFRP strands, making it unable to fully exert their excellent tensile properties. Therefore, according to the material characteristics of CFRP strands, it is urgent to develop suitable anchors. Therefore, it is necessary to provide a new CFRP strand composite anchor optimization design method to solve the above problems. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0005] A novel CFRP strand composite anchor optimization design method includes the following steps:

[0006] S1. Force analysis of clips in anchoring system;

[0007] S2. Anchor cup force analysis in anchoring system;

[0008] S3. Stress analysis of the bite between the clip thread and the CFRP strand in the anchoring system;

[0009] S4, simulation analysis;

[0010] The CFRP stranded wire composite anchor comprises a steel sleeve, a soft metal wrapping layer, a CFRP stranded wire, a nut, a clip and an anchor cup; the steel sleeve is a straight hollow cylinder and the CFRP stranded wire is passed through its axis, the inner wall of the steel sleeve is provided with a thread, a soft metal wrapping layer is arranged between the inner wall of the steel sleeve and the CFRP stranded wire, the outer wall of the steel sleeve is connected with an anchor cup, three structurally symmetrical clips are arranged between the steel sleeve and the anchor cup, the inclination angle of the clips is 2° to 3°, the outer wall of the steel sleeve is provided with a thread and is threadedly connected to a nut.

[0011] Preferably, the specific analysis of step S1 is as follows:

[0012] From the horizontal force balance of the clip, we can get:

[0013] P c-j +F j-m sinθ j =P j-m cosθ j (1)

[0014] From the vertical force balance of the clip, we can get:

[0015] P j-m sinθ j +F j-m cosθ j =F c-j (2)

[0016] At the same time: F j-m =μ j-m P j-m (3)

[0017] Where: c, j, m are CFRP strands, clips, and anchor cups respectively; P c-j is the normal pressure exerted by the clip on the CFRP strand; P j-m F is the normal pressure exerted by the clip on the anchor cup; c-j is the interface friction between the clip and the CFRP strand; F j-m is the interface friction between the clip and the anchor cup; θ j is the inclination angle of the clip; μ j-m is the interfacial friction coefficient between the clip and the anchor cup;

[0018] From the vertical force balance of CFRP strands, we can get: F c =2F c-j (4)

[0019] From equations (2), (3) and (4), we can get:

[0020]

[0021] Where: F c is the external load on the CFRP strand;

[0022] When the anchor is working under force, in order to ensure that the clip and the CFRP strands move together and avoid wire slippage, the following are required:

[0023] F c-j ≤μ c-j P c-j (6)

[0024] Where: μ c-j is the interfacial friction coefficient between the CFRP strand and the clip;

[0025] Substituting equations (1), (2), and (3) into equation (6), we can obtain:

[0026]

[0027] Where: μ j-m is the interfacial friction coefficient between the clip and the anchor cup;

[0028] When the anchor is working under force, in order to ensure that the clip and the CFRP strand are displaced together, the clip inclination angle must be less than or equal to the difference between the friction angle between the CFRP strand and the clip and the friction angle between the clip and the anchor cup, then:

[0029]

[0030] Where: is the friction angle between the CFRP strand and the clip; is the friction angle between the clip and the anchor cup.

[0031] Preferably, the specific analysis of step S2 is as follows:

[0032] The stress on the cross section of the anchor cup is evenly distributed, and the radial normal stress and shear stress applied by the clip to the anchor cup can be obtained:

[0033]

[0034] Where: j-m (x) is the radial normal stress function of the anchor cup; τ j-m (x) is the anchor cup shear stress function; l m is the contact length between the clip and the anchor cup; d m is the inner diameter of the tension end of the anchor cup;

[0035] The friction between the anchor cup and the clip causes axial stress in the cross section of the anchor cup, which can be obtained from the equilibrium equation:

[0036]

[0037] Where: h m is the thickness of the tension end of the anchor cup;

[0038] Substituting formula (9) into formula (10), we can obtain:

[0039]

[0040] The radial pressure between the anchor cup and the clip causes the anchor cup to produce annular normal stress. The total force of the radial pressure on the anchor cup is σj-m (x)d m dx, then from the equilibrium equation we can get:

[0041]

[0042] According to the stress state analysis of material mechanics, we know that: σ1=σ″(x), σ2=-σ j-m (x),σ3=-σ′(x); where the positive sign is tension and the negative sign is compression. According to the Von Mises yield criterion of material mechanics, we have:

[0043]

[0044] Where: s is the yield strength of the material.

[0045] Preferably, the specific analysis of step S3 is as follows:

[0046] Combining the horizontal and vertical force balance equations (1) and (2) of the clip with equation (5), the normal compressive stress between the clip and the CFRP strand can be obtained:

[0047]

[0048] Each clip has two contact points with the CFRP strand, and the corresponding normal pressure at each contact point is:

[0049] P c-j-0 =P c-j / 2n (15)

[0050] Where: P c-j-0 is the normal pressure at a single contact point between the clip and the CFRP strand; n is the number of threads.

[0051] Preferably, the specific analysis of step S4 is as follows:

[0052] A finite element model of the CFRP stranded wire composite anchor was established, and design parameters such as the friction coefficient between the CFRP stranded wire and the clip, the friction coefficient between the anchor cup and the clip, the anchor cup cone angle, the anchor cup thickness, the anchor cup length, and the bite effect of the clip thread spacing were further obtained to improve the design of the anchoring system.

[0053] Preferably, the CFRP strand is formed by twisting 7 strands of carbon fiber reinforcement.

[0054] Beneficial effects of the present invention:

[0055] 1. The present invention takes the clip as the analysis object, studies the friction coefficient between the CFRP strand and the clip, the friction coefficient between the clip and the anchor cup, and the clip angle when the anchor system meets the requirement of no wire slippage damage, and proposes a theoretical method for the coordinated work of the clip;

[0056] 2. The present invention takes the anchor cup as the analysis object, studies the parameters such as the anchor cup cone angle, anchor cup thickness, anchor cup length, etc. when the anchor system is working, and proposes a theoretical method for anchor cup design;

[0057] 3. The present invention takes the clip thread as the analysis object, studies the bite effect of the clip thread spacing on the CFRP strand when the anchor system is working, and proposes a theoretical method for the clip thread design;

[0058] 4. In the present invention, the inner wall of the steel sleeve is made into a threaded shape to match the surface of the CFRP strand, which can effectively improve the mechanical bite force of the contact surface between the two and thus improve the ultimate bearing capacity of the anchoring system;

[0059] 5. The soft metal coating on the surface of the CFRP stranded wire in the present invention can protect it from being bitten to a certain extent, and the clip assembly can provide a certain radial force to the anchor to further exert the tensile strength of the stranded wire;

[0060] 6. The novel composite anchor designed by the present invention can reduce the anchoring length of the CFRP strands, is easy to assemble and can avoid wet work, and the components can be reused. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a cross-sectional view of the CFRP stranded wire composite anchor structure;

[0062] Figure 2 This is the force analysis diagram of the CFRP stranded wire composite anchor clip;

[0063] Figure 3 This is the force analysis diagram of the anchor cup of the CFRP stranded wire composite anchor;

[0064] Figure 4 It is the aa section view of CFRP stranded wire composite anchor;

[0065] Figure 5 Schematic diagram of unit lay length and torsion angle of CFRP stranded wire;

[0066] Figure 6 This is a simulation diagram of the CFRP stranded wire composite anchor;

[0067] Figure 7 The force diagram for simulating the engagement between the CFRP strand and the anchor barrel thread;

[0068] Figure 8 Simulate the force diagram for the anchor cup;

[0069] Fig. 9 The force diagram for CFRP strands under radial compression simulation;

[0070] Fig.10The force diagram for CFRP strand simulation under axial tension.

[0071] In the figure: 1. anchor cylinder, 2. soft metal wrapping layer, 3. CFRP stranded wire, 4. nut, 5. clip, 6. anchor cup. DETAILED DESCRIPTION

[0072] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0073] like Figures 1 to 10 As shown, a novel CFRP strand composite anchor optimization design method includes the following steps:

[0074] S1. Force analysis of clip 5 in the anchoring system;

[0075] S2, force analysis of anchor cup 6 in anchoring system;

[0076] S3, Stress analysis of the bite between the thread of clip 5 and CFRP strand 3 in the anchoring system;

[0077] S4, simulation analysis;

[0078] The CFRP strand composite anchor comprises a steel sleeve 1, a soft metal wrapping layer 2, a CFRP strand 3, a nut 4, a clip 5 and an anchor cup 6; the steel sleeve 1 is a straight hollow cylinder and the CFRP strand 3 is passed through its axis, the inner wall of the steel sleeve 1 is provided with threads, a layer of soft metal wrapping layer 2 is arranged between the inner wall of the steel sleeve 1 and the CFRP strand 3, an anchor cup 6 is connected to the outer surface of the steel sleeve 1, three symmetrical clips 5 are arranged between the steel sleeve 1 and the anchor cup 6, the inclination angle of the clip 5 is 2° to 3°, the outer wall of the steel sleeve 1 is provided with threads and is threadedly connected with a nut 4, and the nut 4 locks the clip 5. Apply epoxy resin glue to the inner wall of the steel sleeve 1 and the soft metal wrapping layer 2, and wrap it around the outer side of the CFRP strand 3 for two weeks to make the connection between the CFRP strand 3 and the steel sleeve 1 tighter.

[0079] The specific analysis of step S1 is as follows:

[0080] From the horizontal force balance of the clip 5, we can get:

[0081] P c-j +F j-m sinθ j =P j-m cosθ j (1)

[0082] From the vertical force balance of the clip 5, we can get:

[0083] P j-m sinθj +F j-m cosθ j =F c-j (2)

[0084] At the same time: F j-m =μ j-m P j-m (3)

[0085] Where: c, j, m are CFRP strand 3, clip 5, anchor cup 6 respectively; P c-j P is the normal pressure applied by the clip 5 to the CFRP strand 3; j-m F is the normal pressure applied by the clip 5 to the anchor cup 6; c-j F is the interface friction force between the clip 5 and the CFRP strand 3; j-m is the interface friction between the clip 5 and the anchor cup 6; θ j is the inclination angle of the clip 5; μ j-m is the interface friction coefficient between the clip 5 and the anchor cup 6;

[0086] From the vertical force balance of CFRP strand 3, we can get: F c =2F c-j (4)

[0087] From equations (2), (3) and (4), we can get:

[0088]

[0089] Where: F c is the external load on the CFRP strand 3;

[0090] When the anchor is working under stress, in order to ensure that the clip 5 and the CFRP strand 3 are displaced together to avoid the slipping phenomenon, it is necessary to have:

[0091] F c-j ≤μ c-j P c-j (6)

[0092] Where: μ c-j is the interface friction coefficient between the CFRP strand 3 and the clip 5;

[0093] Substituting equations (1), (2), and (3) into equation (6), we can obtain:

[0094]

[0095] Where: μ j-m is the interface friction coefficient between the clip 5 and the anchor cup 6.

[0096] When the anchor is working under stress, in order to ensure that the clip 5 and the CFRP strand 3 are displaced together, the inclination angle of the clip 5 must be less than or equal to the difference between the friction angle between the CFRP strand 3 and the clip 5 and the friction angle between the clip 5 and the anchor cup 6, then:

[0097]

[0098] Where: is the friction angle between the CFRP strand 3 and the clip 5; is the friction angle between the clip 5 and the anchor cup 6; the above formula shows that in order to prevent the CFRP strand 3 from being damaged by wire slipping, the friction coefficient between the CFRP strand 3 and the clip 5 and the friction coefficient between the clip 5 and the anchor cup 6 must satisfy the above relationship.

[0099] The specific analysis of step S2 is as follows:

[0100] Practical engineering shows that the radial normal stress applied by the clip to the anchor cup 6 is linearly distributed along the contact surface between the anchor cup 6 and the clip 5, that is, the radial normal stress is the largest at the tension end of the anchor cup 6, and linearly decreases to the minimum value toward the free end of the anchor cup 6. When the inclination angle of the anchor cup 6 is small, the wall thickness of the anchor cup 6 is approximately equal, that is, the anchor cup 6 is regarded as a cylinder, and the stress on the cross section of the anchor cup 6 is uniformly distributed, then the radial normal stress and shear stress applied by the clip 5 to the anchor cup 6 can be obtained:

[0101]

[0102] Where: j-m (x) is the radial normal stress function of the anchor cup 6; τ j-m (x) is the shear stress function of the anchor cup 6; l m is the contact length between the clip 5 and the anchor cup 6; d m is the inner diameter of the tensioning end of anchor cup 6;

[0103] The friction between the anchor cup 6 and the clip 5 causes axial stress in the cross section of the anchor cup 6. From the equilibrium equation, we can get:

[0104]

[0105] Where: h m is the thickness of the tensioned end of anchor cup 6;

[0106] Substituting formula (9) into formula (10), we can obtain:

[0107]

[0108] The radial pressure between the anchor cup 6 and the clip 5 causes the anchor cup 6 to generate annular normal stress. The total force of the radial pressure on the annular direction of the anchor cup 6 is σ j-m (x)d mdx, then from the equilibrium equation we can get:

[0109]

[0110] According to the stress state analysis of material mechanics, we know that: σ1=σ″(x), σ2=-σ j-m (x),σ3=-σ′(x); where the positive sign is tension and the negative sign is compression. According to the Von Mises yield criterion of material mechanics, we have:

[0111]

[0112] Where: s is the yield strength of the material.

[0113] The specific analysis of step S3 is as follows:

[0114] Combining the horizontal and vertical force balance equations (1) and (2) of the clip 5 with equation (5), the normal compressive stress between the clip 5 and the CFRP strand 3 can be obtained:

[0115]

[0116] like Figure 4 As shown, each clip 5 has two contact points with the CFRP strand 3, and the corresponding normal pressure at each contact point is:

[0117] P c-j-0 =P c-j / 2n (15)

[0118] Where: P c-j-0 is the normal pressure at a single contact point between the clip 5 and the CFRP strand 3; n is the number of threads.

[0119] The specific analysis of step S4 is as follows:

[0120] The finite element model of the CFRP strand composite anchor was established; the friction coefficient between the CFRP strand 3 and the clip 5, the friction coefficient between the anchor cup 6 and the clip 5, the cone angle of the anchor cup 6, the thickness of the anchor cup 6, the length of the anchor cup 6, the bite effect of the thread spacing of the clip 5 and other design parameters were further obtained to improve the design of the anchoring system;

[0121] The simulation results show that the friction coefficient between the CFRP strand and the clip is 0.05-0.07, the friction coefficient between the anchor cup 6 and the clip 5 is 0.02-0.04, the cone angle of the anchor cup 6 is 7°-10°, the thickness of the anchor cup 6 is 25mm-40mm, the length of the anchor cup 6 is 100mm-150mm, and the thread pitch of the clip 5 is 2.5-3.5mm. The anchoring effect of the anchoring system is the best. According to the "Technical Code for Application of Anchors, Clamps and Connectors for Prestressed Reinforcement" JGJ85-2010, its anchoring efficiency coefficient reaches 99.5%.

[0122] The CFRP strand 3 is made of 7 strands of carbon fiber reinforcement, and the lay length is the straight line distance of the peripheral reinforcement rotating around the central reinforcement.

[0123] The outer surface of the steel sleeve 1 is processed with M60×4 external threads for connecting the nut 4;

[0124] The inner wall of the steel sleeve 1 is provided with an internal thread ( Figure 7 It can be seen that the distance of one rotation of the thread is equal to the lay length of the 7 strands of carbon fiber reinforcement, and the twisting direction and rotation angle are consistent, so the CFRP strand 3 can be twisted and inserted into the steel sleeve 1;

[0125] The soft metal wrapping layer 2 is arranged between the steel sleeve 1 and the carbon fiber strand 3. After the anchor is stressed, it deforms under the action of the circumferential extrusion force and can fit tightly with the steel sleeve 1 and the carbon fiber strand 3, so that the circumferential pressure tends to be uniform, thereby avoiding the internal thread from clamping the carbon fiber strand 3. The nut 4 is connected to the steel sleeve 1 through an external thread, which is convenient for fixing with the through-type jack during the static load test later, and can ensure that the position of the clip 5 will not move.

[0126] The clip 5 is a three-piece type, and its cone angle is smaller than that of the traditional clip-type anchor. The inclination angle of the clip 5 is 2° to 3°. Unlike the steel strand, a larger angle will damage the CFRP strand 3. During installation, ensure that the clip is aligned and evenly arranged to ensure that there is no relative slip between the steel sleeve 1. After the anchor is stressed, it can provide an inner cone effect to increase the radial force on the CFRP strand 3. The anchor cup 6 is made of Cr40 steel and fits tightly with the clip 5.

[0127] It is known from common technical knowledge that the present invention can be implemented by other embodiments that do not deviate from its spirit or essential features. Therefore, the above disclosed embodiments are only illustrative in all respects and are not exclusive. All changes within the scope of the present invention or within the scope equivalent to the present invention are included in the present invention.

Claims

1. A novel CFRP strand composite anchor optimization design method, characterized in that: The CFRP strand composite anchor comprises a steel sleeve, a soft metal wrapping layer, a CFRP strand, a nut, a clip and an anchor cup; the steel sleeve is a straight hollow cylinder and the CFRP strand is passed through its axis, the inner wall of the steel sleeve is provided with a thread, a soft metal wrapping layer is provided between the inner wall of the steel sleeve and the CFRP strand, an anchor cup is connected to the outer wall of the steel sleeve, three symmetrical clips are provided between the steel sleeve and the anchor cup, the inclination angle of the clip is 2° to 3°, the outer wall of the steel sleeve is provided with a thread and is threadedly connected to the nut; The optimization design method comprises the following steps: S1. Force analysis of clips in anchoring system; S2. Anchor cup force analysis in anchoring system; S3. Stress analysis of the bite between the clip thread and the CFRP strand in the anchoring system; S4, simulation analysis; The specific analysis of step S1 is as follows: From the horizontal force balance of the clip, we can get: P c-j +F j-m sinθ j =P j-m cosθ j (1) From the vertical force balance of the clip, we can get: P j-m sinθ j +F j-m cosθ j =F c-j (2) At the same time: F j-m =μ j-m P j-m (3) Where: c, j, m are CFRP strands, clips, and anchor cups respectively; P c-j is the normal pressure exerted by the clip on the CFRP strand; P j-m F is the normal pressure exerted by the clip on the anchor cup; c-j is the interface friction between the clip and the CFRP strand; F j-m is the interface friction between the clip and the anchor cup; θ j is the inclination angle of the clip; μ j-m is the interfacial friction coefficient between the clip and the anchor cup; From the vertical force balance of CFRP strands, we can get: F c =2F c-j (4) From equations (2), (3) and (4), we can get: Where: F c is the external load on the CFRP strand; When the anchor is working under force, in order to ensure that the clip and the CFRP strands move together and avoid wire slippage, the following are required: F c-j ≤μ c-j P c-j (6) Where: μ c-j is the interfacial friction coefficient between the CFRP strand and the clip; Substituting equations (1), (2), and (3) into equation (6), we can obtain: Where: μ j-m is the interfacial friction coefficient between the clip and the anchor cup; When the anchor is working under force, in order to ensure that the clip and the CFRP strand are displaced together, the clip inclination angle must be less than or equal to the difference between the friction angle between the CFRP strand and the clip and the friction angle between the clip and the anchor cup, then: Where: is the friction angle between the CFRP strand and the clip; is the friction angle between the clip and the anchor cup; The specific analysis of step S2 is as follows: The stress on the cross section of the anchor cup is evenly distributed, and the radial normal stress and shear stress applied by the clip to the anchor cup can be obtained: Where: j-m (x) is the radial normal stress function of the anchor cup; τ j-m (x) is the anchor cup shear stress function; l m is the contact length between the clip and the anchor cup; d m is the inner diameter of the tension end of the anchor cup; The friction between the anchor cup and the clip causes axial stress in the cross section of the anchor cup, which can be obtained from the equilibrium equation: Where: h m is the thickness of the tension end of the anchor cup; Substituting formula (9) into formula (10), we can obtain: The radial pressure between the anchor cup and the clip causes the anchor cup to produce annular normal stress. The total force of the radial pressure on the anchor cup is σ j-m (x)d m dx, then from the equilibrium equation we can get: According to the stress state analysis of material mechanics, we know that: σ1=σ″(x), σ2=-σ j-m (x),σ3=-σ′(x); where the positive sign is tension and the negative sign is compression. According to the Von Mises yield criterion of material mechanics, we have: Where: s is the yield strength of the material; The specific analysis of step S3 is as follows: Combining the horizontal and vertical force balance equations (1) and (2) of the clip with equation (5), the normal compressive stress between the clip and the CFRP strand can be obtained: Each clip has two contact points with the CFRP strand, and the corresponding normal pressure at each contact point is: P c-j-0 =P c-j / 2n (15) Where: P c-j-0 is the normal pressure at a single contact point between the clip and the CFRP strand; n is the number of threads; The specific analysis of step S4 is as follows: A finite element model of the CFRP stranded wire composite anchor was established, and the design parameters of the friction coefficient between the CFRP stranded wire and the clip, the friction coefficient between the anchor cup and the clip, the anchor cup cone angle, the anchor cup thickness, the anchor cup length, and the bite effect of the clip thread spacing were further obtained to improve the design of the anchoring system.

2. According to the novel CFRP strand composite anchor optimization design method described in claim 1, it is characterized by: The CFRP strand is formed by twisting 7 strands of carbon fiber reinforcement.

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