Calculation method and storage medium of stiffness in negative moment zone of steel-concrete composite beams under random fatigue load

Abstract

The present invention relates to the field of stiffness calculation of negative moment zone of steel-concrete composite beams, and specifically discloses a stiffness calculation method and storage medium for the negative moment zone of steel-concrete composite beams under random fatigue loads, including the following steps: calculating the stiffness degradation law of concrete under random fatigue loads; calculating the stiffness degradation law of studs under random fatigue loads; calculating the deflection of the extended end considering concrete cracking when loading at different times; calculating the additional deflection caused by interface slippage considering the stiffness degradation of studs when loading at different times; calculating the variation law of the total deflection in the negative moment zone of the composite beam; and calculating the stiffness degradation law in the negative moment zone of the composite beam. The present invention starts with the stiffness degradation law of concrete and studs, and through the force analysis of the negative moment zone of the composite beam, obtains a theoretical calculation method for the stiffness degradation law of the negative moment zone of the steel-concrete composite beam based on the degradation of material properties, thereby avoiding tedious random fatigue load tests. Compared with the test results, the calculation results of the present invention have higher accuracy.

Description

Technical Field

[0001] The invention relates to the technical field of calculation of stiffness in a negative moment zone of a steel-concrete composite beam, and in particular to a calculation method and a storage medium for stiffness in a negative moment zone of a steel-concrete composite beam under random fatigue load. Background Art

[0002] The mechanical properties of steel-concrete composite bridges are constantly degraded under long-term vehicle loads, especially for the negative bending moment zone of continuous composite beams, the degradation of its stiffness is one of the main factors affecting driving comfort and driving safety. At present, the research objects of the stiffness degradation law of the negative bending moment zone of composite beams are all the stiffness degradation laws under constant amplitude fatigue loads, and the research methods adopt experimental research methods. In fact, the vehicle loads on bridges are random loads, and there are problems such as high difficulty, long test time, and unstable test results in experimental research. Therefore, exploring the calculation method of the stiffness degradation law of the negative bending moment zone of steel-concrete composite beams under random fatigue loads is a problem that needs to be solved urgently. The steel-concrete composite beam is a structure composed of materials such as steel and concrete. The present invention starts with the stiffness degradation law of concrete and studs, and obtains the theoretical calculation method of the stiffness degradation law of the negative bending moment zone of the steel-concrete composite beam based on the material performance degradation through the force analysis of the negative bending moment zone of the composite beam, thereby avoiding cumbersome random fatigue load tests. The calculation results of the present invention are compared with the test results, which proves that the present invention has a high accuracy. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the present invention provides a method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load and a storage medium, which solves the problems mentioned in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solution: a method for calculating the stiffness of a steel-concrete composite beam in a negative moment zone under a random fatigue load, comprising the following steps:

[0005] S1. Calculate the stiffness degradation law of concrete under random fatigue load;

[0006] S2. Calculate the stiffness degradation law of the stud under random fatigue load;

[0007] S3, calculation of the deflection of the extended end considering the degradation of concrete stiffness at different loading times;

[0008] S4, calculation of additional deflection caused by interface slip considering stud stiffness degradation at different loading times;

[0009] S5. Calculate the variation law of total deflection in negative moment zone of composite beam under different loading times;

[0010] S6. Calculate the stiffness degradation law of the negative moment zone of the composite beam under different loading times.

[0011] Preferably, in step S1, the degradation of concrete stiffness is represented by the degradation of concrete elastic modulus, and the random fatigue load with N loading times is regarded as a multi-level fatigue load S k (k=1,2…N), in multi-level fatigue load, a group of adjacent cyclic loads with the same peak value and amplitude are taken as one level; valley value-peak value-valley value is taken as one loading. After experiencing k-level fatigue load, the calculation formula of the residual stiffness of concrete is expressed as follows:

[0012]

[0013] In the formula, E is the elastic modulus of concrete after applying k-level random fatigue load; c (0) is the initial elastic modulus of concrete before fatigue load is applied; n i is the number of loadings corresponding to each level of fatigue load before the kth level;

[0014] N fci is the fatigue life of concrete under each level of fatigue load before level k, and the calculation formula is expressed as follows:

[0015]

[0016] Δσ i is the stress range of the steel bars in the concrete corresponding to the fatigue load of this level, that is, the difference between the peak stress value and the valley stress value. The peak stress value and the valley stress value are determined by the peak moment M of the reinforced concrete slab. max,i and the bending moment valley value M min , calculated according to the material mechanics formula;

[0017] K ck is the concrete fatigue failure coefficient corresponding to the kth level fatigue load, which is calculated based on the concrete fatigue test results and the applied load peak value, amplitude and ultimate bearing capacity. The formula is expressed as follows:

[0018]

[0019] M max,k is the peak value of the kth level fatigue load; ΔM k is the amplitude of the kth level fatigue load, that is, the difference between the peak value and the valley value of the load; M u It is the ultimate static load bearing capacity of reinforced concrete beams, which is determined by experiments or according to the design principles of concrete structures, based on the reinforcement ratio of reinforced concrete beams, steel strength, concrete strength, and member dimensions.

[0020] Preferably, in step S2, the multi-level fatigue shear force experienced by the bolt is assumed to be S i, after experiencing k-level fatigue load, the calculation formula of the residual stiffness of the stud is expressed as follows:

[0021]

[0022] In the formula, K is the shear stiffness of the stud after applying k-level random fatigue load, s (0) is the initial shear stiffness of the stud before fatigue load is applied; n i N is the number of loadings corresponding to each level of fatigue load before the kth level; fsi is the fatigue life of the stud under each level of fatigue load before the kth level, and the calculation formula is expressed as follows:

[0023]

[0024] P s0 is the initial shear strength of the stud, P max,i is the peak shear force of the stud under the i-th level random fatigue load, P m,i is the mean shear force of the stud under the i-th level random fatigue load;

[0025] K sk is the shear fatigue failure coefficient of the stud corresponding to the kth fatigue load, which is obtained by numerical fitting method based on the stud fatigue test results and the applied load peak value, amplitude and ultimate bearing capacity, and is expressed as:

[0026]

[0027] P max,k is the peak shear force of the stud under the kth fatigue load, ΔP k is the shear amplitude of the stud under the kth level fatigue load, and the formula is expressed as;

[0028]

[0029] α1, α2, β1, β2 are calculation parameters, expressed as:

[0030]

[0031] λ is the relative stiffness coefficient, expressed as:

[0032]

[0033] F max,k is the peak value of the kth random fatigue load on the extended end; ΔF k is the amplitude of the kth random fatigue load on the extended end, that is, the difference between the peak value and the valley value of the load; p is the spacing between two rows of bolts; Ec (0) and E s are the elastic moduli of concrete and steel beam respectively; A c and A s are the cross-sectional areas of concrete and steel beams respectively; I c and I s are the section inertia moments of the concrete slab and steel beam respectively; d cs is the distance between the center of gravity of the steel beam and the center of gravity of the concrete slab; K is the initial shear stiffness of a row of bolts in the transverse direction of the beam, K = nK s (0), n is the number of studs in a transverse row of the beam.

[0034] Preferably, in step S3, the deflection of the outrigger considering the degradation of concrete stiffness is calculated at different loading times, and the deflection variation law of the outrigger beam after random fatigue load loading level k is expressed as:

[0035]

[0036] f k (x) is the deflection value of the cantilever beam under the static load F after applying the k-level random fatigue load considering the degradation of concrete stiffness, F is the static load applied to the cantilever end after the k-level random fatigue load is applied to the cantilever end, x is the coordinate of the deflection calculation point, I0 is the converted section inertia moment after the steel is equivalent to concrete according to the elastic modulus ratio, is the elastic modulus of concrete after loading k-level random fatigue load. Considering the continuous decrease of the elastic modulus of concrete during cyclic loading, the elastic modulus degradation law under random fatigue load is calculated according to step S1. a represents the cantilever length of the cantilever beam, and b represents the distance between the two supports of the cantilever beam.

[0037] Preferably, in step S4, the additional deflection caused by the interface slippage of the stud stiffness degradation is calculated when different loading times are considered, and the calculation process is as follows:

[0038] S41. Establish a finite element model of the composite beam, specify the initial stiffness for the studs, and specify the initial elastic modulus for the concrete;

[0039] S42, applying a concentrated load F to the outrigger end, and calculating the initial deflection f0(x) of the outrigger beam, where x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam;

[0040] S43, establish a cyclic process, apply cyclic loads to the finite element model in sequence, and perform time history analysis on the model;

[0041] S44. After each cycle, extract the peak shear force P of each stud under the kth fatigue load according to the finite element time history analysis results. max,k , shear force valley value P min,k , mean shear force P m,k, shear force amplitude ΔP k , calculate the shear fatigue failure coefficient K of the stud corresponding to the kth level fatigue load sk ;

[0042] S45, using the shear peak value P under each fatigue load before the kth level (i = 1, 2, 3 ... k) max,i and the mean shear force P m,i , calculate the fatigue life N of each stud of the composite beam under each fatigue load before the kth level fsi ;

[0043] S46. Calculate the shear stiffness of each stud after k cycles Assign this stiffness to each stud;

[0044] S47. After applying k-level random fatigue load, a concentrated load F is applied to the extended end of the finite element model and a static analysis is performed to obtain the deflection f of the extended composite beam. k (x), x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam;

[0045] S48. Calculate the additional deflection Δf of the cantilever beam under static load F after applying random fatigue load of level k, considering the degradation of stud stiffness k (x) = f k (x)-f0(x).

[0046] Preferably, in step S5, the variation law of the total deflection in the negative moment zone of the composite beam at different loading times is calculated. The total deflection in the negative moment zone of the composite beam is the sum of the calculated deflection considering the degradation of concrete stiffness and the additional deflection caused by the interface slip considering the degradation of stud stiffness. The formula is expressed as follows:

[0047] f tk (x) = f k (x)+Δf k (x);

[0048] f k (x) is the deflection value of the cantilever beam under static load F after applying k-level random fatigue load considering the degradation of concrete stiffness; Δf k (x) is the additional deflection of the cantilever beam under static load F after applying random fatigue load of level k considering the degradation of stud stiffness; f tk (x) is the total deflection of the composite beam in the negative moment zone.

[0049] Preferably, in step S6, the stiffness degradation law of the composite beam in the negative moment zone is calculated at different loading times, and the stiffness calculation formula of the composite beam in the negative moment zone is expressed as:

[0050]

[0051] In the formula, Bk (x) is the bending stiffness of the cantilever beam at coordinate x, f tk (x) is the total deflection of the composite beam in the negative moment zone, calculated according to step S5.

[0052] On the other hand, to achieve the above-mentioned purpose, the present invention also provides the following technical solution: a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load.

[0053] The beneficial effects of the present invention are as follows: starting from the stiffness degradation law of concrete and studs, the present invention obtains a theoretical calculation method for the stiffness degradation law of the negative moment zone of a steel-concrete composite beam based on material performance degradation through a stress analysis of the negative moment zone of the composite beam, thereby avoiding tedious random fatigue load tests. The calculation results of the present invention are compared with the test results, which proves that the present invention has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of an outrigger beam in an embodiment of the present invention;

[0055] Figure 2 A schematic diagram of the dimensions of the cantilever beam in an embodiment of the present invention;

[0056] Figure 3 Schematic diagram of random fatigue load applied to the extended end in an embodiment of the present invention;

[0057] Figure 4 Schematic diagram of the degradation law of concrete stiffness in an embodiment of the present invention;

[0058] Figure 5 Schematic diagram of the stiffness degradation law of the protruding end bolt in the embodiment of the present invention;

[0059] Figure 6 It is a schematic diagram of calculating the deflection of the extended end of a composite beam under random fatigue in an embodiment of the present invention;

[0060] Figure 7 A schematic diagram showing a comparison between theoretical and experimental values ​​of composite beam stiffness under random fatigue considering material performance degradation in an embodiment of the present invention;

[0061] Figure 8 Schematic diagram of the finite element model component of the composite beam in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0063] Combined cantilever beam Figure 1 As shown, Figure 1 The cantilever beam shown in the figure is subjected to random fatigue load at the cantilever end, and the stiffness degradation law of the negative bending moment zone of the composite beam under random fatigue load is calculated by using the method proposed in the present invention using the MATLAB program. Figure 2 shown.

[0064] The values ​​of relevant calculation parameters are shown in Table 1.

[0065] Table 1 Related calculation parameters

[0066] Serial number parameter Value 1 <![CDATA[E c (0)]]> <![CDATA[41130N / mm 2 ]]> 2 <![CDATA[M u ]]> 24kN.m 3 <![CDATA[P s0 ]]> 38600N 4 p 140mm 5 n 2 6 <![CDATA[E s ]]> <![CDATA[2×10 5 N / mm 2 ]]> 7 K 34000N / mm 8 <![CDATA[d cs ]]> 121.78mm

[0067] The loading frequency of the random fatigue load applied to the extension end is 3 Hz. In order to clearly show the load, the 20 s random fatigue load is intercepted, as shown in Figure 3 shown.

[0068] The technical solution proposed by the present invention is a method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load. The calculation process is as follows:

[0069] (1) Calculation of the degradation law of concrete stiffness (elastic modulus)

[0070] like Figure 4 As shown in the figure, the degradation of concrete stiffness is represented by the degradation of concrete elastic modulus, and the random fatigue load with N loading times is regarded as a multi-level fatigue load S k (k=1,2…N), in multi-level fatigue load, a group of adjacent cyclic loads with the same peak value and amplitude is regarded as one level. The calculation method of the residual stiffness of concrete after experiencing k-level fatigue load is:

[0071]

[0072] In formula (1), E is the elastic modulus of concrete after applying k-level random fatigue load; c (0) is the initial elastic modulus of concrete before fatigue load is applied; n i N is the number of loadings corresponding to each level of fatigue load before the kth level; fciis the fatigue life of concrete under each fatigue load before the kth level, calculated using formula (2):

[0073]

[0074] In formula (2), Δσ i is the stress range of the steel bars in the concrete corresponding to the fatigue load of this level, that is, the difference between the peak stress value and the valley stress value. The peak stress value and the valley stress value are determined by the peak moment M of the reinforced concrete slab. max,i and the bending moment valley value M min , calculated according to the material mechanics formula.

[0075] In formula (1), K ck is the concrete fatigue failure coefficient corresponding to the kth level fatigue load, which is calculated based on the concrete fatigue test results and the applied load peak value, amplitude and ultimate bearing capacity, and is expressed as

[0076]

[0077] In formula (3), M max,k is the peak value of the kth level fatigue load; ΔM k is the amplitude of the kth level fatigue load (i.e. the difference between the peak value and the valley value of the load); M u It is the ultimate static load bearing capacity of reinforced concrete beams, which can be determined by experiments or by calculation based on the design principles of concrete structures, according to the reinforcement ratio of reinforced concrete beams, steel strength, concrete strength, and component dimensions.

[0078] (2) Calculation of the stiffness degradation law of the stud

[0079] like Figure 5 As shown in Figure 2, the multi-level fatigue shear force experienced by the stud is S i , the number of loadings corresponding to each level of shear force is n i ;for Figure 1 For the composite cantilever beam shown in the figure, after experiencing k-level fatigue load, the residual stiffness of the studs is expressed as:

[0080]

[0081] In formula (4), K is the stiffness of the stud after random fatigue load of level k is applied, s (0) is the initial shear stiffness of the stud before fatigue load is applied; n i N is the number of loadings corresponding to each level of fatigue load before the kth level; fsi is the fatigue life of the stud under each level of fatigue load before the kth level, calculated using the following formula:

[0082]

[0083] In formula (5), P s0 is the initial shear strength of the stud, P max,i is the peak shear force of the stud under the i-th level random fatigue load, P m,i is the mean shear force of the stud under the fatigue load under the i-th level random fatigue load.

[0084] In formula (4), K sk is the shear fatigue failure coefficient of the stud corresponding to the kth fatigue load, which is obtained by numerical fitting method based on the stud fatigue test results and the applied load peak value, amplitude and ultimate bearing capacity, and is expressed as

[0085]

[0086] Where P s0 is the initial shear strength of the stud, P max,k is the peak shear force of the stud under the kth fatigue load, ΔP k is the shear amplitude of the stud under the kth level fatigue load, and the formula is expressed as;

[0087]

[0088] α1, α2, β1, β2 are calculation parameters, expressed as:

[0089]

[0090] λ is the relative stiffness coefficient, expressed as:

[0091]

[0092] F max,k is the peak value of the kth random fatigue load on the extended end; ΔF k is the amplitude of the kth random fatigue load on the extended end, that is, the difference between the peak value and the valley value of the load; p is the spacing between two rows of bolts; E c (0) and E s are the elastic moduli of concrete and steel beam respectively; A c and A s are the cross-sectional areas of concrete and steel beams respectively; I c and I s are the section inertia moments of the concrete slab and steel beam respectively; d cs is the distance between the center of gravity of the steel beam and the center of gravity of the concrete slab; K is the initial shear stiffness of a row of bolts in the transverse direction of the beam, K = nK s (0), n is the number of studs in a transverse row of the beam.

[0093] (3) Calculate the deflection of the extended end considering concrete cracking and the additional deflection caused by interface slip considering the degradation of stud stiffness at different loading times, such as Figure 6 shown.

[0094] (3.1) Calculation of the deflection of the extended end considering the degradation of concrete stiffness at different loading times

[0095] The variation law of the deflection of the cantilever beam after random fatigue load k can be expressed as

[0096]

[0097] In the formula, f k (x) is the deflection value of the cantilever beam under the static load F after applying the k-level random fatigue load considering the degradation of concrete stiffness, F is the static load applied to the cantilever end after the k-level random fatigue load is applied to the cantilever end, x is the coordinate of the deflection calculation point, I0 is the converted section inertia moment after the steel is equivalent to concrete according to the elastic modulus ratio, is the elastic modulus of concrete after loading k-level random fatigue load. Considering the continuous decrease of the elastic modulus of concrete during cyclic loading, the elastic modulus degradation law under random fatigue load can be calculated according to formula (1), where a represents the cantilever length of the cantilever beam and b represents the distance between the two supports of the cantilever beam.

[0098] (3.2) The additional deflection caused by the interface slip considering the degradation of the stud stiffness is calculated at different loading times. The calculation process is as follows:

[0099] ① Establish a finite element model of the composite beam, specify the initial stiffness for the studs and the initial elastic modulus for the concrete;

[0100] The steel beam is simulated by shell element shell181, the steel bar is simulated by beam element beam188, the concrete is simulated by solid element solid65, and the stud is simulated by spring element combin14. The contact elements conta175 and targe170 are set on the contact surface between the concrete slab and the steel beam. The component decomposition of the finite element model is as follows: Figure 8 shown.

[0101] ② Apply concentrated load F at the extended end and calculate the initial deflection f0(x) of the extended beam, where x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam.

[0102] Calculation shows that when F=50kN, the deflection of the extended end is 9.828mm.

[0103] ③ Establish a cyclic process, apply cyclic loads to the finite element model in sequence, and perform time history analysis on the model;

[0104] ④ After each cycle, the peak shear force P of each stud under the fatigue load of this level (kth level) is extracted according to the results of finite element time history analysis. max,k , shear force valley value P min,k , mean shear force P m,k , shear force amplitude ΔP k According to formula (6), the shear fatigue failure coefficient K of the stud corresponding to the k-th fatigue load is calculated: sk .

[0105] ⑤ According to formula (5), use the shear force peak value P under each fatigue load before the kth level (i = 1, 2, 3...k) max,i and the mean shear force P m,i , calculate the fatigue life N of each stud of the composite beam under each fatigue load before the kth level fsi ;

[0106] ⑥ According to formula (4), calculate the shear stiffness of each stud after k-level cycles: Assign this stiffness to each stud;

[0107] ⑦ After applying k-level random fatigue load, a concentrated load F is applied to the extended end of the finite element model and a static analysis is performed to obtain the deflection f of the extended composite beam. k (x), x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam;

[0108] ⑧ Calculate the additional deflection Δf of the cantilever beam under static load F after applying k-level random fatigue load considering the degradation of stud stiffness k (x) = f k (x)-f0(x).

[0109] (4) The total deflection is obtained by adding the deflection of the extension end considering the degradation of concrete stiffness and the additional deflection caused by the interface slip considering the degradation of stud stiffness. The deflection value of the extension end when the static load F = 50 kN is calculated as follows: Figure 6 shown.

[0110] The total deflection of the composite beam in the negative moment zone is the sum of the calculated deflection considering the degradation of concrete stiffness and the additional deflection caused by interface slip considering the degradation of stud stiffness, which can be expressed as

[0111] f tk (x) = f k (x)+Δf k (x) (12)

[0112] In formula (12), f k (x) is the deflection of the cantilever beam under static load F after applying k-level random fatigue load considering the degradation of concrete stiffness, Δf k(x) is the additional deflection of the cantilever beam under static load F after applying random fatigue load of level k, taking into account the degradation of stud stiffness, calculated according to step (3); f tk (x) is the total deflection of the composite beam in the negative moment zone.

[0113] (5) Calculation of stiffness degradation law of composite beam in negative moment zone under different loading times

[0114] The bending stiffness is calculated according to the following formula:

[0115]

[0116] In the formula, B k (x) is the bending stiffness of the cantilever beam at coordinate x, f tk (x) is the total deflection of the composite beam in the negative moment zone, calculated according to step S5.

[0117] Finally, the stiffness during loading is calculated, and the residual stiffness of the test beam is obtained by back-calculating the deflection of the extended end, such as Figure 7 shown.

[0118] The calculated results are compared with the experimental results, as shown in Table 2.

[0119] Table 2 Calculated and tested values ​​of composite beam stiffness considering material performance degradation under random fatigue

[0120]

[0121] It can be seen from Table 2 that when the number of loadings is 500,000 times, the difference between the calculated value and the test value is the largest, which is 5.388%. When the loading is 2 million times, the calculated residual stiffness is 0.832, and the test residual stiffness is 0.811, and the difference is 2.589%. By comparison, it is proved that the method proposed in the present invention can more accurately calculate the stiffness degradation law of the negative moment zone of the composite beam under random fatigue load.

[0122] Based on the same inventive concept as the above method embodiment, an embodiment of the present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the above method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load is implemented.

[0123] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the stiffness of a steel-concrete composite beam in the negative moment zone under random fatigue load, characterized in that: The steps include: S1. Calculate the stiffness degradation law of concrete under random fatigue load; S2. Calculate the stiffness degradation law of the stud under random fatigue load; S3, calculation of the deflection of the extended end considering the degradation of concrete stiffness at different loading times; S4, calculation of additional deflection caused by interface slip considering stud stiffness degradation at different loading times; S5. Calculate the variation law of total deflection in negative moment zone of composite beam under different loading times. The total deflection in negative moment zone of composite beam is the sum of calculated deflection considering concrete stiffness degradation and additional deflection caused by interface slip considering stud stiffness degradation. The formula is: f tk (x)=f k (x)+Δf k (x); f k (x) is the deflection value of the cantilever beam under static load F after applying k-level random fatigue load considering the degradation of concrete stiffness; Δf k (x) is the additional deflection of the cantilever beam under static load F after applying random fatigue load of level k considering the degradation of stud stiffness; f tk (x) is the total deflection of the composite beam in the negative moment zone; S6. Calculate the stiffness degradation law of the negative moment zone of the composite beam under different loading times. The calculation formula of the stiffness of the negative moment zone of the composite beam is expressed as: In the formula, B k (x) is the bending stiffness of the cantilever beam at coordinate x, f tk (x) is the total deflection of the composite beam in the negative moment zone, F is the static load applied to the outrigger end after the k-level random fatigue load is applied to the outrigger end, x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam, a represents the cantilever length of the outrigger beam, and b represents the distance between the two supports of the outrigger beam.

2. The method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load according to claim 1 is characterized in that: In step S1, the degradation of concrete stiffness is represented by the degradation of concrete elastic modulus, and the random fatigue load with N loading times is regarded as a multi-level fatigue load S k , k = 1, 2, ..., N, in multi-level fatigue loads, a group of adjacent cyclic loads with the same peak value and amplitude are taken as one level; valley value-peak value-valley value is taken as one loading. After experiencing k-level fatigue load, the calculation formula of the residual stiffness of concrete is expressed as follows: In the formula, E is the elastic modulus of concrete after applying k-level random fatigue load; c (0) is the initial elastic modulus of concrete before fatigue load is applied; n i is the number of loadings corresponding to each level of fatigue load before the kth level; N fci is the fatigue life of concrete under each level of fatigue load before level k, and the calculation formula is expressed as follows: Δσ i is the stress range of the steel bars in the concrete corresponding to the fatigue load of this level, that is, the difference between the peak stress value and the valley stress value. The peak stress value and the valley stress value are determined by the peak moment M of the reinforced concrete slab. max,i and the bending moment valley value M min , calculated according to the material mechanics formula; K ck is the concrete fatigue failure coefficient corresponding to the kth level fatigue load, which is calculated based on the concrete fatigue test results and the applied load peak value, amplitude and ultimate bearing capacity. The formula is expressed as follows: M max,k is the peak value of the kth level fatigue load; ΔM k is the amplitude of the kth level fatigue load, that is, the difference between the peak value and the valley value of the load; M u It is the ultimate static load bearing capacity of reinforced concrete beams, which is determined by experiments or according to the design principles of concrete structures, based on the reinforcement ratio of reinforced concrete beams, steel strength, concrete strength and member dimensions.

3. The method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load according to claim 1 is characterized in that: In step S2, the multi-level fatigue shear force experienced by the bolt is assumed to be S i , after experiencing k-level fatigue load, the calculation formula of the residual stiffness of the stud is expressed as follows: In the formula, K is the shear stiffness of the stud after applying k-level random fatigue load, s (0) is the initial shear stiffness before fatigue load is applied; n i N is the number of loadings corresponding to each level of fatigue load before the kth level; fsi is the fatigue life of the stud under each level of fatigue load before the kth level, and the calculation formula is expressed as follows: P s0 is the initial shear strength of the stud, P max,i is the peak shear force of the stud under the i-th level random fatigue load, P m,i is the mean shear force of the stud under the i-th level random fatigue load; K sk is the shear fatigue failure coefficient of the stud corresponding to the kth fatigue load, which is obtained by numerical fitting method based on the stud fatigue test results and the applied load peak value, amplitude and ultimate bearing capacity, and is expressed as: P max,k is the peak shear force of the stud under the kth fatigue load, ΔP k is the shear amplitude of the stud under the kth level fatigue load, and the formula is expressed as; a represents the cantilever length of the cantilever beam, α1, α2, β1, β2 are calculation parameters, expressed as: λ is the relative stiffness coefficient, expressed as: F max,k is the peak value of the kth random fatigue load on the extended end; ΔF k is the amplitude of the kth random fatigue load on the extension end, that is, the difference between the peak value and the valley value of the load; p is the spacing between two rows of bolts; E c (0) and E s are the elastic moduli of concrete and steel beam respectively; A c and A s are the cross-sectional areas of concrete and steel beams respectively; I c and I s are the section inertia moments of the concrete slab and steel beam respectively; d cs is the distance between the center of gravity of the steel beam and the center of gravity of the concrete slab; K is the initial shear stiffness of a row of bolts in the transverse direction of the beam, K = nK s (0), n is the number of studs in a transverse row of the beam.

4. The method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load according to claim 1 is characterized in that: In step S3, the deflection of the outrigger considering the degradation of concrete stiffness is calculated for different loading times. The deflection variation law of the outrigger beam after random fatigue load loading level k is expressed as: f k (x) is the deflection value of the cantilever beam under the static load F after applying the k-level random fatigue load considering the degradation of concrete stiffness, F is the static load applied to the cantilever end after the k-level random fatigue load is applied to the cantilever end, x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam, n i is the number of loadings corresponding to each level of fatigue load before the kth level, I0 is the converted section inertia moment after the steel is equivalent to concrete according to the elastic modulus ratio, is the elastic modulus of concrete after loading k-level random fatigue load. Considering the continuous decrease of the elastic modulus of concrete during cyclic loading, the elastic modulus degradation law under random fatigue load is calculated according to step S1. a represents the cantilever length of the cantilever beam, and b represents the distance between the two supports of the cantilever beam.

5. The method for calculating the stiffness of the negative moment zone of a steel-concrete composite beam under random fatigue load according to claim 1 is characterized in that: In step S4, the additional deflection caused by the interface slip considering the degradation of the stud stiffness is calculated at different loading times. The calculation process is as follows: S41. Establish a finite element model of the composite beam, specify the initial stiffness for the studs, and specify the initial elastic modulus for the concrete; S42, apply a static load F to the outrigger end, and calculate the initial deflection f0(x) of the outrigger beam, where x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam; S43, establish a cyclic process, apply cyclic loads to the finite element model in sequence, and perform time history analysis on the model; S44. After each cycle, extract the peak shear force P of each stud under the kth fatigue load according to the finite element time history analysis results. max,k , shear force valley value P min,k , mean shear force P m,k , shear force amplitude ΔP k , calculate the shear fatigue failure coefficient K of the stud corresponding to the kth level fatigue load sk ; S45. Using the shear peak and shear mean values ​​under each fatigue load before the kth level, calculate the fatigue life N of each stud of the composite beam under each fatigue load before the kth level. fsi ; S46. Calculate the shear stiffness of each stud after k cycles Assign this stiffness to each stud; S47. After applying k-level random fatigue load, a static load F is applied to the extended end of the finite element model and a static analysis is performed to obtain the deflection f of the extended composite beam. k (x), x is the coordinate of the deflection calculation point along the longitudinal direction of the composite beam; S48. Calculate the additional deflection Δf of the cantilever beam under static load F after applying random fatigue load of level k, considering the degradation of stud stiffness k (x) = f k (x)-f0(x).

6. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor, the method for calculating the stiffness of a steel-concrete composite beam in a negative moment zone under random fatigue load as described in any one of claims 1 to 5 is implemented.

Images