Method for calculating shear capacity of steel pipe and external concrete under freeze-thaw fatigue

Abstract

The present application relates to the technical field of steel pipe concrete structure design and safety evaluation, in particular to a kind of steel pipe and external concrete shear capacity calculation method under freeze-thaw fatigue. According to the load slip curve of the unanchored specimen, a three-segment constitutive model is established. According to the load slip curve and three-segment constitutive model of the unanchored specimen under N freeze-thaw cycles and n times fatigue load, a shear capacity formula of the unanchored specimen is established. According to the load slip curve of the anchored specimen in the target combined specimen under N freeze-thaw cycles and n times fatigue load, a shear capacity formula of the anchored specimen is obtained. A shear capacity calculation formula of the steel pipe and external concrete under freeze-thaw fatigue is established. The present application has the positive effect of realizing the safety evaluation and structure durability prediction of the combined structure of the external concrete wrapped steel pipe concrete under freeze-thaw cycles and fatigue load.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of steel tube concrete structure design and safety evaluation, in particular to a method for calculating the shear bearing capacity of steel tube and external concrete under freeze-thaw fatigue. BACKGROUND

[0002] In modern building structures, the combination structure of external concrete wrapping steel tube concrete as a kind of efficient structure form, the core advantage lies in the synergistic effect of steel-bolt-concrete, because of its high bearing capacity, good plasticity and ductility, superior seismic performance and other characteristics, it is widely used in high-rise buildings, subways, bridges and other engineering. The shear performance is the key to determine the overall performance of the structure, which directly affects the durability. However, the method for calculating the shear bearing capacity of steel tube and external concrete under freeze-thaw environment and fatigue load is not clear. The reasons include the following aspects: on the one hand, the internal steel tube concrete structure as a kind of smooth steel member, the shear performance of the combination structure formed after being wrapped by external concrete is different from ordinary reinforced concrete structure with or without bolt effect, and the traditional steel-concrete shear performance calculation formula cannot be used to effectively analyze and calculate the shear capacity of the steel tube and external concrete combination structure. On the other hand, the combination structure of external concrete wrapping steel tube concrete faces double challenges in cold regions: freeze-thaw cycle leads to microstructure damage of external concrete (volume expansion and shrinkage caused by water phase change), which weakens the bond strength of steel tube and external concrete and the shear capacity of bolt; and long-term fatigue load (vehicle, wind load, etc.) aggravates the cumulative damage of slip, further damaging the durability of the structure. In addition, the lack of evaluation ability of the shear performance of the combination structure of external concrete wrapping steel tube concrete is also not conducive to the prediction of the durability of the structure. SUMMARY

[0003] The purpose of the present application is to provide a method for calculating the shear bearing capacity of steel tube and external concrete under freeze-thaw fatigue, which solves the technical problem of calculating the shear bearing capacity of the combination structure of external concrete wrapping steel tube concrete under freeze-thaw cycle and fatigue load, so as to achieve the purpose of safety evaluation and structure durability prediction of the combination structure of external concrete wrapping steel tube concrete under freeze-thaw cycle and fatigue load.

[0004] The method for calculating the shear bearing capacity of steel tube and external concrete under freeze-thaw fatigue provided by the present application comprises the following steps:

[0005] Step 1, according to the number of freeze-thaw cycles and the number of fatigue load actions of the target combination test piece, determine the number of target combination test pieces after N times of freeze-thaw cycles and n times of fatigue load actions, wherein the target combination test piece is the combination structure of external concrete wrapping steel tube concrete with or without bolt, including bolted test piece and unbolted test piece;

[0006] Step 2, material experiments are performed on the target combination test pieces without studs and the target combination test pieces with studs;

[0007] Step 3, N times of freeze-thaw cycles and n times of fatigue load experiments are performed on the target combination test pieces without studs and the target combination test pieces with studs;

[0008] Step 4, push-out experiments under the action of freeze-thaw cycles and fatigue loads are performed on the target combination test pieces without studs and the target combination test pieces with studs, and load-sliding curves of the target combination test pieces without studs and the target combination test pieces with studs under N times of freeze-thaw cycles and n times of fatigue loads are obtained;

[0009] Step 5, a three-segment constitutive model is established according to the load-sliding curve of the target combination test piece without studs;

[0010] Step 6, a shear capacity formula of the target combination test piece without studs is established according to the load-sliding curve of the target combination test piece without studs and the three-segment constitutive model;

[0011] Step 7, a shear capacity formula of the studs of the target combination test piece with studs is obtained according to the load-sliding curve of the target combination test piece with studs under N times of freeze-thaw cycles and n times of fatigue loads;

[0012] Step 8, a shear bearing capacity calculation formula of the steel pipe and the external concrete under freeze-thaw fatigue is established according to the shear capacity formula of the target combination test piece without studs and the shear capacity formula of the studs of the target combination test piece with studs.

[0013] Further, in Step 1, the concrete selected is ordinary concrete; the hot-rolled smooth-welded ordinary carbon structural cylindrical steel pipe is selected as the component of the inner-steel-pipe concrete; the studs are ordinary studs, and the number of target combination test pieces required is determined according to the number of freeze-thaw cycles and the number of fatigue loads, wherein the target combination test pieces include test pieces with studs and test pieces without studs on the outer surface of the steel pipe.

[0014] Further, in Step 2, material experiments are performed on the materials constituting the target combination test pieces to determine the material properties of the materials constituting the target combination test pieces.

[0015] Further, in Step 3, n times of fatigue load experiments are performed on the target combination test pieces.

[0016] Further, in Step 4, push-out experiments under the action of freeze-thaw cycles and fatigue loads are performed on the target combination test pieces, and load-sliding curves of the target combination test pieces under N times of freeze-thaw cycles and n times of fatigue loads are obtained through a pressure control computer.

[0017] Further, for the non-studded specimen, the load obtained in the push-out test is converted into the bond strength of the target composite specimen according to the ratio of the load to the cross-sectional perimeter and the embedded length of the internal steel pipe concrete, and the calculation method is as follows,

[0018]

[0019] The load-slip curve of the non-studded specimen under N freeze-thaw cycles and n fatigue loads is drawn,

[0020] where τ is the bond strength; P is the load size; A is the total surface area of the steel pipe anchorage; C a is the cross-sectional perimeter of the internal steel pipe concrete; and L is the embedded length of the internal steel pipe concrete.

[0021] Further, for the studded specimen, the load-slip curve of the studded specimen under N freeze-thaw cycles and n fatigue loads is obtained by a pressure control computer.

[0022] Further, in step 5, the load-slip curve of the non-studded specimen is analyzed, and the bond-slip characteristic values are obtained by a pressure control computer, which are respectively denoted as the peak bond strength τ u , the residual bond strength τ r , the peak slip amount S u , and the residual slip amount S r , and a three-segment constitutive model is obtained; the three-segment constitutive model is described in segments according to the bond-slip characteristic values, and model functions of the ascending segment, the descending segment, and the residual segment are obtained;

[0023] The ascending segment is a power function, the descending segment is a linear function, and the residual segment is a constant with respect to τ, and the three-segment constitutive model is expressed as follows,

[0024]

[0025] In the formula, τ u is the peak bond strength, α, β, and γ are the ascending segment parameters affected by the number of freeze-thaw cycles and the number of fatigue loads, K is the descending segment parameter affected by the number of freeze-thaw cycles and the number of fatigue loads, δ is the residual segment parameter affected by the number of freeze-thaw cycles and the number of fatigue loads, S is the slip amount corresponding to the bond strength, S u , and S r are the slip amount corresponding to the peak bond strength and the residual slip amount, respectively.

[0026] Further, in step 5, the origin software is used to fit the three-segment constitutive model of the unstudded nail specimen, and the rising segment, the descending segment and the residual segment are obtained. The rising segment parameters, the descending segment parameters and the residual segment parameters are substituted into the three-segment constitutive model, and the three-segment constitutive model affected by the number of freeze-thaw cycles and the number of fatigue load actions is established as follows,

[0027] .

[0028] Further, in step 6, the relationship between the peak bond strength of the unstudded nail specimen in the target combined specimen and the number of freeze-thaw cycles N and the number of fatigue load actions n is obtained, and the shear capacity of the unstudded nail specimen is calculated. The calculation formula of the shear capacity of the unstudded nail specimen is as follows,

[0029]

[0030] Wherein, P u (N,n) is the shear capacity of the unstudded nail specimen, τ0 is the initial bond strength of the unstudded nail specimen in the target combined specimen under 0 freeze-thaw cycles and 0 fatigue load actions, α1 is the influence parameter of N freeze-thaw cycles on the unstudded nail specimen in the target combined specimen, that is, the freeze-thaw damage parameter, N is the number of freeze-thaw cycles applied to the target combined specimen, β1 is the influence parameter of n fatigue load on the unstudded nail specimen in the target combined specimen, that is, the fatigue gain parameter, n is the number of fatigue load actions applied to the target combined specimen, and A is the total surface area of the steel pipe anchorage.

[0031] Further, in step 6, the origin software is used to quantify the freeze-thaw damage parameter α1 and the fatigue gain parameter β1 of the unstudded nail specimen, and the shear capacity of the unstudded nail specimen is calculated. The calculation formula of the shear capacity of the unstudded nail specimen is,

[0032] .

[0033] Further, in step 7, the relationship between the peak load and the number of freeze-thaw cycles N and the number of fatigue load actions n in the load-slip curve of the studded nail specimen is obtained, and the shear capacity of the studded nail in the target combined specimen is obtained. The calculation formula is as follows,

[0034]

[0035] Wherein, P s (N,n) is the shear capacity of the studded nail specimen, P s0The bolt shear bearing capacity of the bolted specimen in the target combined specimen under 0 freeze-thaw cycles and 0 fatigue load is target combination specimen with bolted specimen bolt shear bearing capacity, gamma 1 is the influence parameter of N freeze-thaw cycles on the target combination specimen with bolted specimen, that is, the freeze-thaw contribution factor, and delta 1 is the influence parameter of n fatigue load on the target combination with bolted specimen, that is, the fatigue attenuation factor.

[0036] Further, in step 7, the freeze-thaw contribution factor gamma 1 and the fatigue attenuation factor delta 1 of the bolted specimen are quantified by the origin software, and the shear capacity calculation formula of the bolted specimen under the action of freeze-thaw cycles and fatigue load is obtained, which is expressed as,

[0037] .

[0038] Further, in step 8, the shear capacity calculation formula of the bolted specimen and the shear capacity calculation formula of the bolted specimen in the target combination specimen are used to establish the shear bearing capacity calculation formula of the steel pipe and the external concrete under freeze-thaw fatigue, which is expressed as,

[0039]

[0040] Wherein, P (N, n) is the shear bearing capacity of the steel pipe and the external concrete under freeze-thaw fatigue; the freeze-thaw damage parameter alpha 1 and the fatigue gain parameter beta 1， The freeze-thaw contribution factor gamma 1 and the fatigue attenuation factor delta 1 of the shear bearing capacity formula of the bolted specimen in the bolted specimen are obtained as follows,

[0041] .

[0042] The shear bearing capacity calculation method of the steel pipe and the external concrete under freeze-thaw fatigue provided by the application can obtain the shear bearing capacity of the target combination specimen through the action times of N freeze-thaw cycles and n fatigue loads when the target combination specimen is used subsequently, without the need for further experiments, thereby reducing the experimental process and saving costs. The application has the positive effect of realizing the safety evaluation and structure durability prediction of the combined structure of the external concrete wrapped steel pipe concrete under the action of freeze-thaw cycles and fatigue load. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 It is the working principle diagram of the application;

[0044] Figure 2 The target combination specimen cross section and longitudinal section size parameter diagram in the embodiment of the application;

[0045] Figure 3 The bolt design diagram in the embodiment of the application;

[0046] Figure 4The load-slip curve diagram of the non-staple nail test piece under the condition of 0 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0047] Figure 5 The load-slip curve diagram of the non-staple nail test piece under the condition of 90 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0048] Figure 6 The load-slip curve diagram of the non-staple nail test piece under the condition of 150 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0049] Figure 7 The load-slip curve diagram of the staple nail test piece under the condition of 0 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0050] Figure 8 The load-slip curve diagram of the staple nail test piece under the condition of 90 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0051] Figure 9 The load-slip curve diagram of the staple nail test piece under the condition of 150 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0052] Figure 10 It is a three-section constitutive model schematic diagram in the embodiment of the application;

[0053] Figure 11 It is a three-section constitutive model verification diagram under the condition of 0 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0054] Figure 12 It is a three-section constitutive model verification diagram under the condition of 90 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0055] Figure 13 It is a three-section constitutive model verification diagram under the condition of 150 freeze-thaw cycles and 0, 9000, and 15000 times of fatigue load action in the embodiment of the application;

[0056] Figure 14 It is a shear capacity formula verification diagram of the non-staple nail test piece in the embodiment of the application;

[0057] Figure 15 It is a shear bearing capacity calculation formula verification diagram of the steel pipe and the external concrete under freeze-thaw fatigue in the embodiment of the application. DETAILED DESCRIPTION

[0058] The method for calculating the shear bearing capacity of a steel pipe and external concrete under freeze-thaw fatigue provided by the application is described and explained further below through a specific embodiment of the application.

[0059] According to the number of freeze-thaw cycles and the number of fatigue load actions to which the target combination specimen is subjected, the number of target combination specimens under N freeze-thaw cycles and n fatigue load actions is determined. In this experiment, the number of freeze-thaw cycles is 0, 90 and 150, the number of fatigue load actions is 0, 9000 and 15000, the number of specimens and the naming method are shown in Table 1.

[0060] Table 1 Number of specimens and naming method

[0061]

[0062] A total of 18 target combination specimens are designed, including 9 combination structures of external concrete-wrapped steel pipe concrete without studs and 9 combination structures of external concrete-wrapped steel pipe concrete with studs. The target combination specimen is made, and the cross-sectional and longitudinal cross-sectional size parameter diagrams of the specimen are shown in Figure 2 and the stud design diagram is shown in Figure 3 Among them, the diameter of the steel pipe in the target combination specimen is 144 mm, the length of the steel pipe is 250 mm, the embedded length is 300 mm, the stud is 150 mm away from the bottom side of the steel pipe, the diameter of the stud is 10 mm, and the length of the stud is 40 mm.

[0063] Material experiments are performed on the target combination specimen without studs and the target combination specimen with studs. The concrete material table is shown in Table 2.

[0064] Table 2 Concrete material table

[0065]

[0066] The steel material table is shown in Table 3.

[0067] Table 3 Steel material table

[0068]

[0069] The target combination test piece without anchor and with anchor is subjected to N times of freeze-thaw cycle and n times of fatigue load experiment. The freeze-thaw experiment and fatigue experiment are respectively carried out according to the “Standard for Long-term and Durability Performance Test of Ordinary Concrete” (GB / T 50082-2009). The freeze-thaw experiment adopts slow freezing method (air freezing and water melting), and 0 times, 90 times and 150 times of freeze-thaw cycle test are designed. In the freezing stage, the air temperature of the freeze-thaw test box is maintained at-20℃ to-18℃, and in the melting stage, the concrete test piece is immersed in warm water at 18℃ to 20℃. DW-40 freeze-thaw machine is selected as the special equipment. The fatigue test is carried out on the target combination test piece by using electro-hydraulic servo dynamic and static test machine. The target combination test piece is first loaded to the preset maximum load Pmax, and then the sinusoidal wave fatigue load is applied at a frequency of 4Hz. When the predetermined cycle number or the free end slip reaches 30mm (the earlier one is used as the criterion), the test is stopped.

[0070] The push-out test is carried out on the above target combination test pieces which have completed freeze-thaw cycle experiment and fatigue load experiment. A 300KN universal servo test machine is used to obtain the load-slip curve, and the test results are brought into the following formula, The load obtained in the push-out test is converted into the bond strength of the target combination test piece,

[0071] Wherein, τ is the bond strength; P is the load size; A is the total surface area of the steel pipe anchorage; C a is the cross-sectional circumference of the internal steel pipe concrete; L is the embedded length of the internal steel pipe concrete.

[0072] After obtaining all the push-out test results of the above target combination test pieces, the load-slip curves of the target combination test pieces under N times of freeze-thaw cycle and n times of fatigue load are drawn, wherein the load-slip curves of A00, A01 and A02 in the target combination test piece are as shown in Figure 4 , the load-slip curves of A10, A11 and A12 in the target combination test piece are as shown in Figure 5 , the load-slip curves of A20, A21 and A22 in the target combination test piece are as shown in Figure 6 , the load-slip curves of B00, B01 and B02 in the target combination test piece are as shown in Figure 7 , the load-slip curves of B10, B11 and B12 in the target combination test piece are as shown in Figure 8 , and the load-slip curves of B20, B21 and B22 in the target combination test piece are as shown in Figure 9 .

[0073] The load-slip curve of the test piece without anchor is analyzed, and the bond slip characteristic values are obtained by the pressure control computer, which are respectively denoted as peak bond strength τ u , residual bond strength τ r , peak slip S u and residual slip Sr , and the three-segment constitutive model is obtained. As shown in Figure 10 , the three-segment constitutive model is described by segment according to the bond slip characteristic value, and the model functions of the ascending segment, the descending segment and the residual segment are obtained, wherein the ascending segment is a power function, the descending segment is a linear function, and the residual segment is a constant with respect to τ, and the three-segment constitutive model is expressed as follows,

[0074]

[0075] wherein τ u is the peak bond strength, α, β, γ are the ascending segment parameters affected by the number of freeze-thaw cycles and the number of fatigue load actions, K is the descending segment parameter affected by the number of freeze-thaw cycles and the number of fatigue load actions, δ is the residual segment parameter affected by the number of freeze-thaw cycles and the number of fatigue load actions, S is the slip amount corresponding to the bond strength, S u and S r are the slip amounts corresponding to the peak bond strength and the residual slip amount respectively.

[0076] The origin software is used to fit the ascending segment, the descending segment and the residual segment of the three-segment constitutive model of the non-staple nail specimen under 0 times, 90 times and 150 times of freeze-thaw cycles and 0 times, 9000 times and 15000 times of fatigue load actions, and the ascending segment parameters, the descending segment parameters and the residual segment parameters are obtained, and the parameter fitting values are shown in Table 4:

[0077] Table 4 Parameter fitting values

[0078]

[0079] Since the experimental curve of A20 is too different from those of other specimens, it is not considered in the calculation of the average value of the ascending segment. The three-segment constitutive model affected by the number of freeze-thaw cycles and the number of fatigue load actions is established by substituting the ascending segment parameters, the descending segment parameters and the residual segment parameters into the three-segment constitutive model, and the three-segment constitutive model is expressed as follows,

[0080] .

[0081] The obtained three-segment constitutive model is compared with the actual experimental data, and the comparison chart is shown in Figure 11 , Figure 12 , Figure 13 . The results show that the three-segment constitutive model has a high degree of agreement with the experimental data in the ascending stage, and the prediction accuracy of the descending segment is also relatively reliable, which verifies the feasibility of the model.

[0082] The shear capacity of the unanchored specimen is calculated by obtaining the relationship between the peak bond strength of the unanchored specimen under 0 times, 90 times, and 150 times of freeze-thaw cycles and 0 times, 9000 times, and 15000 times of fatigue load, and the number of times of freeze-thaw cycles and fatigue load, and the shear capacity of the unanchored specimen is calculated by the formula as follows,

[0083]

[0084] wherein, P u (N,n) is the shear capacity of the unanchored specimen, τ0 is the initial bond strength of the unanchored specimen in the target combination specimen under 0 times of freeze-thaw cycles and 0 times of fatigue load, α1 is the influence parameter of N times of freeze-thaw cycles on the unanchored specimen in the target combination specimen, i.e., the freeze-thaw damage parameter, N is the number of times of freeze-thaw cycles applied to the target combination specimen, β1 is the influence parameter of n times of fatigue load on the unanchored specimen in the target combination specimen, i.e., the fatigue gain parameter, n is the number of times of fatigue load applied to the target combination specimen, and A is the total surface area of the steel pipe anchoring.

[0085] The freeze-thaw damage parameter α1 and the fatigue gain parameter β1 of the unanchored specimen are quantified by the origin software, and the calculation formula of the shear capacity of the unanchored specimen is as follows,

[0086] .

[0087] For the calculation formula of the shear capacity of the unanchored specimen, its reliability is verified by its bond strength. As shown in Figure 14 , the formula calculation result has good consistency with the experimental data, the determination coefficient R²=0.98, the calculation error of the difference between the calculated value and the experimental value is obtained, the error analysis shows that the error value between the calculated value and the experimental value of the target combination specimen A01 is the minimum value of 0.2%, the error value between the calculated value and the experimental value of the target combination specimen A20 is the maximum value of 7.4%, and the overall average absolute error is 1.88%. The calculation result is relatively accurate, which shows that the obtained formula is feasible, which further verifies the reliability of the calculation formula of the shear capacity of the unanchored specimen.

[0088] The shear capacity of the anchor of the anchored specimen in the target combination specimen is obtained by the relationship between the peak load and the number of times of 0 times, 90 times, and 150 times of freeze-thaw cycles and the number of times of 0 times, 9000 times, and 15000 times of fatigue load in the load-slip curve of the anchored specimen, and the calculation formula is as follows:

[0089]

[0090] wherein, P s(N,n) is the shear capacity of the stud of the studed test piece, P s0 is the shear bearing capacity of the stud of the studed test piece in the target combined test piece under 0 freeze-thaw cycles and 0 fatigue load, γ1 is the influence parameter of N freeze-thaw cycles on the studed test piece in the target combined test piece, i.e., the freeze-thaw contribution factor, and δ1 is the influence parameter of n fatigue load on the studed test piece in the target combined test piece, i.e., the fatigue attenuation factor.

[0091] The freeze-thaw contribution factor γ1 and the fatigue attenuation factor δ1 of the studed test piece are quantified by the origin software, and the shear capacity calculation formula of the stud under the action of freeze-thaw cycles and fatigue load is obtained, which is expressed as,

[0092]

[0093] The shear bearing capacity calculation formula of the steel pipe and the external concrete under freeze-thaw fatigue is established by the shear capacity calculation formula of the non-studed test piece and the shear capacity calculation formula of the stud in the studed test piece, which is expressed as,

[0094]

[0095] The freeze-thaw damage parameter α1 and the fatigue gain parameter β1 in the shear capacity formula of the non-studed test piece, the freeze-thaw contribution factor γ1 and the fatigue attenuation factor δ1 in the shear bearing capacity formula of the stud in the studed test piece are brought in to obtain the following formula:

[0096] .

[0097] The verification of the shear bearing capacity calculation formula of the steel pipe and the external concrete under freeze-thaw fatigue is shown in Figure 15 The model calculation results and the test data have good consistency, the difference calculation error between the obtained calculation value and the actual value is obtained, the error between the actual value and the calculation value in B02 is the minimum value 3.9%, the error between the actual value and the calculation value in B20 is the maximum error 9.2%, and the average error is 5.37%. The calculation result is relatively accurate, which shows that the obtained formula is feasible, which further verifies the reliability of the shear bearing capacity calculation formula of the steel pipe and the external concrete under freeze-thaw fatigue of the present application.

Claims

1. A method for calculating the shear capacity of a steel pipe and external concrete under freeze-thaw fatigue, characterized by, The method comprises the following steps, Step 1, according to the number of freeze-thaw cycles and the number of fatigue load actions of the target combined test piece, the number of target combined test pieces after N freeze-thaw cycles and n fatigue load actions is determined, wherein the target combined test piece is a combined structure of external concrete and steel pipe concrete wrapped without a stud, including a stud test piece and a studless test piece; Step 2, materiality experiment is carried out on the target combination test piece without a stud test piece and a stud test piece; wherein, the load slip curve of the test piece without a stud is analyzed, the bond slip characteristic value is obtained through the pressure control computer, and is respectively recorded as the peak bond strength τ u , the residual bond strength τ r , the peak slip amount S u and the residual slip amount S r , and a three-segment constitutive model is obtained; the three-segment constitutive model is described in sections according to the bond slip characteristic value, and the model functions of the rising section, the falling section and the residual section are obtained; The ascending segment is a power function, the descending segment is a linear function, and the residual segment is a constant with respect to tau, and the three-segment constitutive model is represented as follows, where τ u is the peak bond strength, a, b, g are the ascending segment parameters affected by the number of freeze-thaw cycles and the number of fatigue load actions, K is the descending segment parameter affected by the number of freeze-thaw cycles and the number of fatigue load actions, d is the residual segment parameter affected by the number of freeze-thaw cycles and the number of fatigue load actions, S is the slip corresponding to the bond strength, S u , S r are the slip corresponding to the peak bond strength and the residual slip, respectively. The ascending segment, the descending segment and the residual segment of the three-segment constitutive model of the studless test piece are fitted by using the origin software, the ascending segment parameters, the descending segment parameters and the residual segment parameters are obtained, the ascending segment parameters, the descending segment parameters and the residual segment parameters are substituted into the three-segment constitutive model, and the three-segment constitutive model affected by the number of freeze-thaw cycles and the number of fatigue load actions is established as follows, ； Step 3, the studless test piece and the stud test piece in the target combined test piece are subjected to N freeze-thaw cycles and n fatigue load experiments; Step 4, the studless test piece and the stud test piece in the target combined test piece are subjected to the push-out experiment of freeze-thaw cycles and fatigue load actions, and the load-sliding curve of the studless test piece and the stud test piece under N freeze-thaw cycles and n fatigue load actions is obtained; Step 5, the three-segment constitutive model is established according to the load-sliding curve of the studless test piece; Step 6, the shear capacity formula of the studless test piece is established according to the load-sliding curve of the studless test piece and the three-segment constitutive model under N freeze-thaw cycles and n fatigue load actions; Step 7, the shear capacity formula of the stud of the stud test piece is obtained according to the load-sliding curve of the stud test piece in the target combined test piece under N freeze-thaw cycles and n fatigue load actions; Step 8, the shear bearing capacity calculation formula of the steel pipe and the external concrete under freeze-thaw fatigue is established according to the shear capacity formula of the studless test piece and the shear capacity formula of the stud in the stud test piece.

2. The method of calculating the shear capacity of a steel pipe subjected to freeze-thaw fatigue and an external concrete according to claim 1, characterized by, For the non-studded specimen, the load obtained in the push-out test is converted into the bond strength of the target composite specimen according to the ratio of the load to the cross-sectional perimeter and the embedded length of the internal steel pipe concrete in the push-out test, and the calculation method is as follows, , The load-sliding curve of the studless test piece under N freeze-thaw cycles and n fatigue load actions is drawn, Where τ is the bond strength; P is the load magnitude; A is the total surface area of the steel pipe anchorage; C a is the cross-sectional perimeter of the internal steel pipe concrete; and L is the embedded length of the internal steel pipe concrete.

3. The method of calculating the shear capacity of a steel pipe subjected to freeze-thaw fatigue and an external concrete according to claim 2, characterized by, The shear capacity of the studless test piece is calculated by obtaining the relationship between the peak bond strength of the studless test piece in the target combined test piece and the number of N freeze-thaw cycles and n fatigue load actions, and the shear capacity calculation formula of the studless test piece is as follows, wherein P u (N,n) is the shear capacity of the unanchored specimen, τ0 is the initial bond strength of the unanchored specimen in the target composite specimen under 0 freeze-thaw cycles and 0 fatigue load, α1 is the influence parameter of N freeze-thaw cycles on the unanchored specimen in the target composite specimen, i.e., the freeze-thaw damage parameter, N is the number of freeze-thaw cycles applied to the target composite specimen, β1 is the influence parameter of n fatigue loads on the unanchored specimen in the target composite specimen, i.e., the fatigue gain parameter, n is the number of fatigue load actions applied to the target composite specimen, and A is the total surface area of the steel pipe anchorage.

4. The method of calculating the shear capacity of a steel pipe subjected to freeze-thaw fatigue and an external concrete according to claim 3, characterized by, The freeze-thaw damage parameter alpha 1 and the fatigue gain parameter beta 1 of the studless test piece are quantified by using the origin software, the shear capacity of the studless test piece is calculated, and the shear capacity calculation formula of the studless test piece is as follows, 。 5. The method of calculating the shear capacity of a steel pipe subjected to freeze-thaw fatigue and an external concrete according to claim 4, characterized by, The shear capacity of the bolt of the bolted nail specimen in the target combined specimen is obtained through the relationship between the peak load and the number of N freeze-thaw cycles and the number of n fatigue load actions in the load-slip curve of the bolted nail specimen, and the calculation formula is as follows, Wherein, P s (N,n) is the shear capacity of the bolt of the bolted nail specimen, P s 0 is the shear bearing capacity of the bolt of the bolted nail specimen in the target combined specimen under 0 freeze-thaw cycles and 0 fatigue load actions, γ1 is the influence parameter of N freeze-thaw cycles on the bolted nail specimen in the target combined specimen, i.e. the freeze-thaw contribution factor, and δ1 is the influence parameter of n fatigue load on the bolted nail specimen in the target combined specimen, i.e. the fatigue attenuation factor.

6. The method of calculating the shear capacity of a steel pipe subjected to freeze-thaw fatigue and an external concrete according to claim 5, characterized by, The freeze-thaw contribution factor gamma 1 and the fatigue attenuation factor delta 1 of the stud test piece are quantified by using the origin software, the shear capacity calculation formula of the stud of the stud test piece under the action of freeze-thaw cycles and fatigue load is obtained, and is represented as follows, 。 7. The method of calculating the shear capacity of a steel pipe subjected to freeze-thaw fatigue and an external concrete according to claim 6, characterized by, The formula for calculating the shear capacity of the steel pipe and the external concrete under freeze-thaw fatigue is established by the formula for calculating the shear capacity of the test piece without studs and the formula for calculating the shear capacity of the studs in the test piece with studs, and is expressed as, Wherein, P(N, n) is the shear capacity of the steel pipe and the external concrete under freeze-thaw fatigue; the freeze-thaw damage parameter α1, the fatigue gain parameter β1, the freeze-thaw contribution factor γ1 and the fatigue attenuation factor δ1 of the formula for calculating the shear capacity of the studs in the test piece with studs are brought into the formula for calculating the shear capacity of the test piece without studs, and the formula is as follows, 。

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