Method for calculating rigidity of composite beam connected by high-strength bolts

Abstract

The invention relates to the technical field of bridge construction, and discloses a method for calculating the rigidity of a composite beam connected by high-strength bolts, which comprises the following steps of: considering the most unfavorable load possibly occurring in a normal use stage and a construction stage during calculation, calculating a standard value of the most unfavorable load combination on the composite beam, and setting a mid-span displacement judgment value at the same time. The method analyzes the stress state of the steel-concrete interface under the action of various loads, can accurately capture the critical point of interface shear stress and friction failure, can accurately simulate the nonlinear change rule of the equivalent stiffness of the composite beam along with the loads by adopting different stiffness calculation formulas, and meanwhile, the design method systematically considers multiple influence factors, and the design method is simple and convenient. According to the method, the nonlinear mechanism of a bolt connection area is simulated, a relatively accurate displacement value can be given, economic evaluation is considered, and the method is a relatively comprehensive composite beam design analysis method.

Description

Technical Field

[0001] The invention relates to the field of bridge construction, and more particularly to a method for calculating the stiffness of a composite beam connected by high-strength bolts. Background Art

[0002] In the context of sustainable industrial development, bridge construction is gradually moving towards assembly and industrialization. The construction of the concrete deck of the composite bridge has always been cast in situ, with large on-site wet operations, long construction period, and inability to achieve complete assembly, which is a bottleneck in achieving assembly construction. The development of composite beams connected by high-strength bolts can not only realize on-site assembly and disassembly of concrete, but also avoid welding defects caused by stud welding.

[0003] The current specifications for composite structure design are all for cast-in-place composite beams connected by studs, and no clear provisions have been made for precast composite beams connected by bolts;

[0004] Deflection control is of great significance to the design and construction of bolted composite beams in bridges. It is determined by the size of the steel beam, the diameter of the bolts, the number of bolts and the pre-tension. The connection method and force transmission mechanism of bolted composite beams and stud composite beams are very different. If the friction of the pre-tensioned bolts is overcome and the bolt rod has not yet contacted the bolt hole wall, the bolt will temporarily stop working and the composite beam will degenerate into a variable stiffness beam. The range of the low stiffness section will change with the load. At this time, the composite beam still has a large bearing capacity, but the influence of friction overcoming and interface slip on the bending stiffness cannot be ignored. Summary of the invention

[0005] The invention provides a method for calculating the stiffness of a composite beam connected by high-strength bolts, which solves the technical problem in the related art that the deflection of a composite beam with variable stiffness cannot be calculated.

[0006] The present invention provides a method for calculating the stiffness of a composite beam connected by high-strength bolts, comprising the following steps:

[0007] S100: The most unfavorable loads occurring during the use and construction phases are calculated, and the standard value of the most unfavorable load combination on the composite beam is calculated, and the mid-span displacement judgment value [ω] is set at the same time;

[0008] S200: Determine the geometric parameters of the steel beam population C i , bolt shear connector parameter population D j , assign multiple common values ​​to each parameter in each population, and C i , D j Sort by economic parameters; assign multiple common values ​​to each variable, then the first group of variables C i And the second set of variables D j There are multiple combination schemes between them, and then the economic parameters E of each scheme are output C，iand E D，j ;

[0009] S300: Given a parameter population, calculate the yield judgment condition M of the composite beam under the parameter population y ;

[0010] If M y <M s , return to S300, set i=i+1;

[0011] If M y >M s , enter S400;

[0012] Among them, M s is the standard value of bending moment;

[0013] S400: Calculate the longitudinal shear force V(x) of the composite beam connected by studs when it degenerates from a beam of equal stiffness to a beam of variable stiffness;

[0014] S500: Calculation of external load q when a composite beam connected by studs degenerates from a beam of constant stiffness to a beam of variable stiffness f ;

[0015] S600: Use the reduced equivalent stiffness of the composite beam to calculate the mid-span deflection ω under the standard load value in sections;

[0016] S610: Determine interface status:

[0017] If q s <q f , the composite beam is in the state of a beam with equal stiffness throughout the entire process under the action of load;

[0018] If q s >q f , the composite beam degenerates from a beam of equal stiffness to a beam of variable stiffness under load;

[0019] S620: Determine based on the deflection criterion:

[0020] If the mid-span deflection is greater than the mid-span displacement judgment value, ω>[ω], then return to S200 and set j=j+1;

[0021] The mid-span deflection is less than the mid-span displacement judgment value, ω<[ω], and the design is completed.

[0022] Furthermore, the load combination standard values ​​and bending moment standard values ​​are as follows:

[0023] q s =(h·W+D+S G +S Q );

[0024]

[0025] Among them, q s is the standard value of load combination, M s is the standard value of bending moment, h is the thickness of concrete slab, W is the concrete density, D is the additional permanent load, S G is the additional dead load, S Q To use live load, l is the span length of the beam;

[0026] In step S100, the following steps are included:

[0027] S110: Load identification, first of all, it is necessary to identify various permanent loads and possible temporary loads acting on the composite beam structure, including structural deadweight, additional permanent loads, live loads, wind loads, and temperature loads;

[0028] S120: Load combination. According to different load conditions and load combination specifications, the identified permanent loads and temporary loads are combined to form a series of different load condition combinations. The load combinations are:

[0029] ∑(γ i , Q i );

[0030] Among them, Q i represents the standard value of the i-th load, γ i is the corresponding combination coefficient, and the combination coefficient of different load types is determined according to the specifications;

[0031] S130: Load internal force calculation, for each load condition combination, calculate the corresponding internal force effects, including bending moment, shear force, and axial force;

[0032] S140: Limit state check, compare the calculated internal force effect with the bearing capacity of the structure to check whether the requirements of the relevant limit states are met, including the bearing capacity limit state and the serviceability limit state;

[0033] S150: Identification of unfavorable load combinations: for different design requirements, identify the corresponding most unfavorable load combinations;

[0034] S160: Setting of mid-span displacement judgment value: according to the specification requirements or actual project needs, set the allowable mid-span displacement judgment value [ω] of the composite beam under normal use conditions.

[0035] Furthermore, according to E C，i and E D，j Sort the values ​​of , and assign values ​​to i and j respectively;

[0036] i=(h s b-(h s -2t)(b-t1))f y ;

[0037] E D，j =1.8d2n s ;

[0038] Where i=1, 2, 3, ..., j=1, 2, 3, ...

[0039] Furthermore, in step S200, the span L of the composite beam and the thickness h of the concrete slab are set according to the engineering conditions. c is a fixed value;

[0040] The cross-sectional height h of the H-beam s , width b, steel web thickness t1, steel flange thickness t and steel yield strength f y Composed of the first set of variables C i :

[0041] C i ={h s ,b,t1,t,f y};

[0042] The number of shear keys of friction-type high-strength bolts in the shear span is n s , the diameter of the friction type high-strength bolt in the shear span is d, and the bolt preload is P, which constitutes the second group of variables Dj:

[0043] D j ={n s , d, P};

[0044] It is also necessary to calculate the geometric parameter C i The corresponding economic cost E C，i Calculate the connection parameter D j The corresponding economic cost E D，j , and according to all C i and D j List the combinations of the above, and calculate the total economic cost E for each combination, including the following:

[0045] 1) Calculate the geometric parameters C i The corresponding economic cost E C，i ;

[0046] E C，i It is related to the amount of concrete and steel used and the difficulty of construction, and is estimated using the following empirical formula:

[0047] E C，i =αcV c +αsW S +βcL c +βsL S ;

[0048] Among them, Vc and Ws are the amounts of concrete and steel, respectively. c and K S are the construction difficulty coefficients of concrete and steel structures, respectively, αc, αs, βc, βs are the corresponding unit cost coefficients;

[0049] 2) Calculate the connection parameter D j The corresponding economic cost E D，j ;

[0050] E D，j It is related to the number and type of high-strength bolt connections and is estimated using the following formula:

[0051] E D，j =γ*n s *Cs(d);

[0052] Among them, n s is the number of high-strength bolts, Cs(d) is the cost of a single high-strength bolt with diameter d, and γ is the additional cost coefficient for installation;

[0053] 3) All C i and D j List the combinations of , and calculate the total economic cost E for each combination:

[0054] E=E C，i +E D，j ;

[0055] According to the size of E, all combination plans are sorted and numbered, with plans with lower economic costs being ranked first and having relatively smaller numbers.

[0056] Further, in step S300, the combined population C is set i and D j The initial value of the material, the stiffness reduction calculation method, conforms to Hooke's law, sets the yield judgment condition, and determines that all materials have not yet reached the yield stress;

[0057] 1) Calculate the yield moment M of the cross section y :

[0058]

[0059] where f y is the yield strength of steel, (EI) ∞ is the equivalent stiffness, h0 is the geometric centroid distance between the steel beam and the concrete slab;

[0060] 2) Calculate the equivalent stiffness (EI) of the hybrid section ∞ and axial stiffness (EA) ∞ :

[0061] (EI) ∞ =h0 2 E2A2+E1I1;

[0062] E1I1=E s I s +E c I c ;

[0063] (EA) ∞ =E c A c +E s A s ;

[0064]

[0065] Among them, M y is the yield moment of the cross section under boundary conditions, f y is the yield strength of steel, (EI) ∞ is the equivalent stiffness, (EA) ∞ is the axial stiffness, E1I1 is the equivalent stiffness of the mixed section, E s is the elastic modulus of steel, I s is the moment of inertia of steel, E c is the elastic modulus of concrete, I c is the moment of inertia of the concrete slab, E2A2 is the equivalent axial stiffness of the hybrid section, A c is the cross-sectional area of ​​the concrete slab, A s is the cross-sectional area of ​​the steel;

[0066] In step S300, the combined population C i and D j The initial value of is:

[0067] C i =C1;

[0068] D j =D1.

[0069] Further, in step S400, when the friction force at the steel-concrete interface is sufficient to overcome the longitudinal shear force, when all bolts are in the friction stage, the shear stiffness of each bolt is constant at k, which is determined by the push-out test, and the composite beam is a beam of equal stiffness;

[0070] If the load continues to increase and the friction force is insufficient to overcome the shear force, the bolts overcome the friction from the support end to the mid-span in sequence, and the shear stiffness of the bolts degenerates to zero, and the composite beam degenerates to the state of a variable stiffness beam. The variable stiffness beam has a zero-stiffness area of ​​length x1 at the support end.

[0071] The implementation steps are as follows:

[0072] S410: When the friction force at the steel-concrete interface is large enough, all connecting bolts are in the friction stage, that is, they only bear shear force but not bending moment;

[0073] At this time, the shear stiffness k of each bolt is a constant, and its value needs to be determined through a push-out test;

[0074] The composite beam is considered as a beam of equal stiffness in this case;

[0075] S420: As the load continues to increase, when the interface friction is insufficient to bear the shear force, the bolts will overcome the friction one by one from the support end to the mid-span;

[0076] For bolts that have overcome friction, their shear stiffness will degenerate to 0;

[0077] The composite beam is considered as a variable stiffness beam in this case;

[0078] S430: Within a certain length range near the support, the variable stiffness beam is equivalent to a non-stiffness area because the bolts no longer provide shear stiffness, and the length is recorded as x1;

[0079] S440: When there is a shear force V(x) at the interface, the longitudinal shear force on the steel-concrete interface to overcome friction is:

[0080]

[0081] Among them, n s is the number of shear keys of the friction type high-strength bolts in the shear span, d is the diameter of the friction type high-strength bolts in the shear span, k is the shear stiffness of each bolt, α and β are both intermediate parameters used to calculate the longitudinal shear force distribution on the steel-concrete interface in the shear connection hybrid member, α is a combined parameter related to the member stiffness and the connection stiffness parameters, reflecting the rate of change of the shear force distribution along the axial direction of the member, β is another combined parameter related to the member stiffness and the connection parameters, reflecting the overall size of the shear force in the member, q is the uniformly distributed load intensity, x1 is the distance from the support to the considered section, L is the shear span length, and e is a natural constant.

[0082] Further, in step S500, according to the load form, the load qf required for the first bolt at the end of the support to overcome the friction is calculated:

[0083]

[0084] Where μ is the friction coefficient and T is the interface shear stress;

[0085] If q s <q f , where q≤q s, according to the principle of minimum potential energy, the stiffness reduction coefficient of the composite beam considering the interface slip effect is taken as ξ1;

[0086]

[0087] If q s >q f , where q>q s According to the principle of minimum potential energy, the stiffness reduction coefficient of the composite beam considering the interface slip and friction overcoming effect is taken as ξ2;

[0088]

[0089] The calculation steps are as follows:

[0090] S510: List the geometric parameters and material parameters of the composite beam: L is the shear span length, d is the diameter of the friction-type high-strength bolts in the shear span, n s is the number of shear keys of the friction-type high-strength bolts in the shear span, k is the shear stiffness of each bolt, E1I1 is the equivalent stiffness of the hybrid section, E2A2 is the equivalent axial stiffness of the hybrid section, h0 is the geometric centroid distance between the steel beam and the concrete slab, μ is the friction coefficient, and T is the interface shear stress;

[0091] S520: Calculate auxiliary parameters α and β:

[0092]

[0093] S530: Based on the limit state when the first bolt at the support end overcomes friction, write the expression for the interface shear stress T:

[0094]

[0095] S540: Substitute T into q f The expression of q f :

[0096]

[0097] S550: Simplify and sort out the information about q f The equation is:

[0098]

[0099] S560: Solve the equation to obtain the critical uniformly distributed load q for the first bolt at the support end to overcome friction f , by calculating the critical load q f :

[0100] When s <q f When , the equal stiffness beam model can be used;

[0101] When s >q f It is necessary to convert to a variable stiffness beam model and consider the influence of bolt failure.

[0102] Further, in step S600, the implementation process in this step is as follows:

[0103] 1) Determine the interface status

[0104] According to the results of the interface state analysis, it is determined whether the interface is in the full friction stage or partial / complete failure state;

[0105]

[0106] Among them, ξ1 is the stiffness reduction factor of the first composite beam, B F1 is the shear retention coefficient of the beam with uniform stiffness;

[0107]

[0108] Among them, ξ2 is the stiffness reduction factor of the second composite beam, B F2 Shear retention coefficient of variable stiffness beam;

[0109] 2) Calculate basic parameters

[0110] In the complete friction stage, the calculation is equivalent to:

[0111] EI=E c I c +E s I s ;

[0112] Where E c ,I c are the elastic modulus and moment of inertia of concrete, E s ,I s are the elastic modulus and moment of inertia of the steel beam respectively;

[0113] Partial / complete failure requires determining the number of failed bolts nb and calculating the interface shear deformation angle γ;

[0114] 3) Calculate equivalent stiffness in sections

[0115] In the full friction stage, the equivalent stiffness is EIeq;

[0116] In the partial failure stage, the equivalent stiffness EIeq′ is calculated according to the following formula:

[0117]

[0118] Where ψ is the correction factor, k is the shear shape factor, G is the shear modulus of the steel beam material, A is the cross-sectional area, b is the clear distance between the steel and concrete interface, and n b is the number of failed bolts, n is the total number of bolts, and L is the span length;

[0119] At the complete failure stage, the equivalent stiffness EIeq″ is calculated according to the following formula:

[0120]

[0121] The above formulas describe the effects of bolt failure and interface shear slip on the overall stiffness of the composite beam. By calculating and reducing the equivalent stiffness in sections, the deformation performance of the composite beam at each load stage is simulated.

[0122] 4) Obtain equivalent stiffness

[0123] According to the results of the segmented calculation of equivalent stiffness, the equivalent stiffness EIeq, EIeq′ or EIeq″ corresponding to the current load stage is obtained;

[0124] 5) Establish deflection calculation model

[0125] The composite beam is equivalent to a simply supported beam, and the basic formula in material mechanics is used:

[0126] During the full friction phase:

[0127]

[0128] During the partial failure phase:

[0129]

[0130] During the complete failure phase:

[0131]

[0132] Where q is the external uniformly distributed load, and L is the span length of the beam;

[0133] 6) Correction calculation

[0134] For practical engineering problems, the correction coefficient is introduced, and the beam end constraint conditions and load distribution form are considered:

[0135] ω′=β*ω;

[0136] Where β is the correction factor, which depends on the constraints and load distribution;

[0137] Among them, EIeq, EIeq′, and EIeq″ are the current equivalent stiffness provided by the above steps, and EIeq corresponds to B F1 , EIeq′ or EIeq″ corresponds to B F2.

[0138] The present invention also provides a method for calculating the stiffness of a composite beam connected by high-strength bolts, which is used in the steps of the above-mentioned method for calculating the stiffness of a composite beam connected by high-strength bolts, including:

[0139] Load calculation module: This module is used to calculate the most unfavorable load combination in the normal use stage and the construction stage, and set the mid-span displacement judgment value [ω];

[0140] Geometric parameter input module: This module is used to input the geometric parameters of the composite beam, including span L, concrete slab thickness h c 、H-beam section height h s , width b, steel web thickness t1, steel flange thickness t and steel yield strength f y , these parameters constitute the first set of variables C i ;

[0141] Connection parameter input module: This module is used to input the parameters of high-strength bolt connections, including the number of friction-type high-strength bolts in the shear span n s , diameter d and preload force P, these parameters constitute the second set of variables D j ;

[0142] Economic evaluation module: According to C i and D j Different combinations of the economic parameters E of various schemes are calculated C，i and E D，j , and sort and number the combination schemes according to the size of these two parameters;

[0143] Material constitutive module: This module sets the constitutive model of the material, the material complies with Hooke's law, and determines the yield criterion;

[0144] Interface state analysis module: According to the load size, analyze whether the friction force of the steel-concrete interface is sufficient to overcome the longitudinal shear force, and judge whether each bolt is in the friction stage or failure state, corresponding to the situation of equal stiffness beam or variable stiffness beam;

[0145] Critical load calculation module: Calculates the critical load q required for the first bolt at the support end to overcome friction f ;

[0146] Stiffness reduction module: According to the interface state, the equivalent stiffness of the composite beam is calculated and reduced in sections;

[0147] Displacement calculation module: Use the reduced equivalent stiffness to calculate the mid-span deflection ω of the composite beam under load.

[0148] The present invention provides a storage medium storing non-transitory computer-readable instructions for executing one or more steps in the above-mentioned method for calculating the stiffness of a composite beam connected by high-strength bolts.

[0149] The beneficial effects of the present invention are:

[0150] The present invention analyzes the stress state of the steel-concrete interface under various loads, can accurately capture the critical point of failure of interface shear stress and friction, and uses different stiffness calculation formulas to accurately simulate the nonlinear change law of the equivalent stiffness of the composite beam with the load. At the same time, this design method systematically considers various influencing factors, simulates the nonlinear mechanism of the bolt connection area, can give relatively accurate displacement values, and takes into account economic evaluation. It is a more comprehensive composite beam design and analysis method. BRIEF DESCRIPTION OF THE DRAWINGS

[0151] Figure 1 It is a flow chart of a method for calculating the stiffness of a composite beam connected by high-strength bolts proposed by the present invention;

[0152] Figure 2 It is a structural schematic diagram of the vertical section of the cast-in-place composite beam proposed in the present invention;

[0153] Figure 3 It is a structural schematic diagram of the cast-in-place composite beam proposed in the present invention as a beam of equal stiffness;

[0154] Figure 4 It is a structural schematic diagram of the cast-in-place composite beam proposed in the present invention degenerating into a variable stiffness beam. DETAILED DESCRIPTION

[0155] The subject matter described herein will now be discussed with reference to example embodiments. It should be understood that the discussion of these embodiments is only to enable those skilled in the art to better understand and implement the subject matter described herein, and the functions and arrangements of the elements discussed may be changed without departing from the scope of protection of the contents of this specification. Each example may omit, replace or add various processes or components as needed. In addition, the features described relative to some examples may also be combined in other examples.

[0156] See also Figure 1-Figure 4 As shown, a method for calculating the stiffness of a composite beam connected by high-strength bolts comprises the following steps:

[0157] S100: The most unfavorable loads that may occur during normal use and construction should be considered during calculation, the standard value of the most unfavorable load combination on the composite beam should be calculated, and the mid-span displacement judgment value [ω] should be set at the same time;

[0158] q s =(h·W+D+S G +SQ );

[0159]

[0160] Where: q s is the standard value of load combination, M s is the standard value of bending moment, h is the thickness of concrete slab, W is the concrete density, D is the additional permanent load, S G is the additional dead load, S Q To use live load, l is the span length of the beam;

[0161] In step S100, the following steps are also included:

[0162] S110: Load identification: First, it is necessary to identify various permanent loads and possible temporary loads acting on the composite beam structure, including but not limited to the self-weight of the structure, additional permanent loads (such as pavement loads), live loads (such as vehicle loads), wind loads, temperature loads, etc.

[0163] S120: Load combination: According to different load conditions and load combination specifications, the identified permanent loads and temporary loads are combined to form a series of different load condition combinations. The mathematical expression of the load combination is generally in the form of:

[0164] ∑(γ i , Q i );

[0165] Among them, Q i represents the standard value of the i-th load, γ i is the corresponding combination coefficient, and the combination coefficient of different load types is determined according to the specifications;

[0166] S130: Load internal force calculation: For each load condition combination, calculate the corresponding internal force effects, including bending moment, shear force, axial force, etc.;

[0167] S140: Limit state check: Compare the calculated internal force effect with the bearing capacity of the structure to check whether it meets the requirements of the relevant limit state, such as the bearing capacity limit state, the serviceability limit state, etc.

[0168] S150: Identification of unfavorable load combinations: For different design requirements (such as bearing capacity design, deformation control under normal use, etc.), identify the corresponding most unfavorable load combination;

[0169] S160: Setting the mid-span displacement judgment value: according to the specification requirements or actual project needs, set the allowable mid-span displacement judgment value [ω] of the composite beam under normal use conditions;

[0170] In addition to the above steps, it is also necessary to determine the standard values ​​or characteristic values ​​of various loads. For example, for live loads, it may be necessary to obtain the characteristic value through statistical fitting methods. The mathematical expression is as follows:

[0171] Q k =Q m (1+αV);

[0172] Among them, Q k is the characteristic value of the live load, Q m is the mean, V is the coefficient of variation, and α is the confidence level coefficient.

[0173] S200: Determine the geometric parameters of the steel beam population C i , bolt shear connector parameter population D j , assign multiple common values ​​to each parameter in each population, and C i , D j Sort by economic parameters;

[0174] According to the engineering conditions, set the composite beam span L and the concrete slab thickness h c is a fixed value;

[0175] H-beam cross-section height h s , width b, steel web thickness t1, steel flange thickness t and steel yield strength f y The first set of variables C i :

[0176] C i ={h s ,b,t1,t,f y};

[0177] The number of shear keys of friction type high-strength bolts in a shear span n s , diameter d, bolt preload P is the second set of variables D j :

[0178] D j ={n s ,d,P};

[0179] Assign multiple common values ​​to each variable, then combine C i And combination D j There are multiple combination plans;

[0180] Then output the economic parameters E of each plan C，i and E D，j ;

[0181] According to E C，i and E D，jSort the values ​​of , and assign values ​​to i and j respectively, i = 1, 2, 3, ..., j = 1, 2, 3, ...;

[0182] i=(h s b-(h s -2t)(b-t1))f y ;

[0183] E D，j =1.8d 2 n s ;

[0184] In step S200, the user is required to input the following parameters:

[0185] Span L: calculated span of composite beam;

[0186] Concrete slab thickness h c : The thickness of the upper concrete slab of the composite beam;

[0187] H-beam cross-section height h s : The cross-sectional height of the steel beam part of the composite beam;

[0188] Steel beam flange width b: the width of the steel beam flange of the composite beam;

[0189] Steel web thickness t1: thickness of the steel web of the composite beam;

[0190] Steel flange plate thickness t: thickness of the steel flange plate of the composite beam;

[0191] Steel yield strength f y : Yield strength of composite beam steel;

[0192] These parameters can be input through the user interface or parameter file and form the first set of variables C i ,Right now:

[0193] C i = {L, h c ,h s ,b,t1,t,f y};

[0194] During the implementation process, a reasonable value range and increment can be set for each parameter to facilitate subsequent parameter combination and optimization calculation;

[0195] At the same time, the validity of the input parameters needs to be checked to ensure that they meet the requirements of relevant design specifications and engineering practices;

[0196] For example, for the flange width b and web thickness t1, the following mathematical expressions can be given as inspection conditions based on the requirements of the overall stability of the section:

[0197] b / t1≤(b / t1)lim;

[0198] Among them, (b / t1)lim is the limit value given by the specification or experience;

[0199] By inputting the parameters in this step, precise geometric parameter input can be provided for subsequent structural analysis and optimization design, thus ensuring the accuracy and reliability of the calculation results.

[0200] In step S200, the main function is to obtain the relevant parameters of the high-strength bolt connectors in the steel-concrete connection area of ​​the composite beam, which will directly affect the overall performance of the entire structure;

[0201] It also includes the following parameters that require the user to input: the number of friction-type high-strength bolts in the shear span n s : refers to the total number of high-strength bolts used in a shear span (i.e. the area between two adjacent supports); high-strength bolt diameter d: the nominal diameter of the high-strength bolt; high-strength bolt preload P: the preload tension applied to the high-strength bolt; these parameters are combined into the second group of variables D j ,Right now:

[0202] D j ={n s , d, P};

[0203] When implementing this module, it is necessary to set a reasonable value range and increment for the above parameters to meet engineering requirements and facilitate subsequent optimization calculations. At the same time, it is also necessary to check the validity of the input parameters to ensure that they meet the requirements of relevant specifications and engineering practices.

[0204] For example, for the preload force P of high-strength bolts, the following mathematical inspection conditions can be given according to the requirements of the bolt tensile strength:

[0205] P≤0.7f u A s ;

[0206] Among them, f u is the tensile strength of the bolt material, A s is the cross-sectional area of ​​the bolt.

[0207] In addition, the module also needs to consider the impact of the number and arrangement of high-strength bolts in different shear spans to ensure sufficient shear transmission capacity and deformation coordination.

[0208] Through the implementation of this module, accurate connector parameter input can be provided for subsequent structural analysis and optimization design, which is crucial to ensuring the overall performance of the composite beam.

[0209] In step S200, the following steps may also be included:

[0210] Calculate the geometric parameters C i The corresponding economic cost E C，i :

[0211] E C，i It is usually related to factors such as the amount of concrete and steel used, construction difficulty, etc. The following empirical formula can be used for estimation:

[0212] E c，i =αcV c +αsW S +βcL c +βsL S ;

[0213] Among them, V c and W S are the amounts of concrete and steel respectively; L c and L S are the construction difficulty coefficients of concrete and steel structures respectively; αc, αs, βc, βs are the corresponding unit cost coefficients.

[0214] Calculate the connection parameter D j The corresponding economic cost E D，j :

[0215] E D，j It is mainly related to the number and type of high-strength bolt connectors and can be estimated using the following formula:

[0216] E D，j =γ*n s *Cs(d);

[0217] Among them, n s is the number of high-strength bolts, Cs(d) is the cost of a single high-strength bolt with diameter d, and γ is the additional cost coefficient such as installation.

[0218] All C i and D j List the combinations of , and calculate the total economic cost E for each combination:

[0219] E=E C，i +E D，j ;

[0220] According to the size of E, all combination plans are sorted and numbered, with plans with lower economic costs being ranked first and having relatively smaller numbers.

[0221] Through the above steps, the economic feasibility of various composite beam solutions can be systematically evaluated, providing valuable information for subsequent optimization;

[0222] It should be noted that the calculation of economic costs in actual projects is usually more complicated and may require the introduction of more influencing factors. The above formula is only a simplified example.

[0223] S300: Given a parameter population, calculate the yield judgment condition M of the composite beam under this condition y ;

[0224] Specifically, in the example, the combined population C i and D j The initial value is C i =C1,D j =D1;

[0225] The stiffness reduction calculation method assumes that the material is linearly elastic and conforms to Hooke's law, so the yield judgment condition must be set to ensure that all materials have not reached the yield stress;

[0226] If M y <M s , return to S300, set i=i+1;

[0227] If M y >M s , enter S400;

[0228] Specifically, step S300 is a step at the beginning of a cycle, which is used for stiffness reduction calculation. In this step, the values ​​of some parameters, such as population size and number of iterations, are initialized.

[0229] Before entering the loop, some important assumptions are made:

[0230] The material follows linear elasticity and conforms to Hooke's law; the yield criterion needs to be set to ensure that all materials do not reach the yield stress;

[0231] The main calculation steps in the cycle are:

[0232] 1. Calculate the yield moment M of the cross section y :

[0233]

[0234] where f y is the yield strength of steel, (EI) ∞ is the equivalent stiffness, h0 is the geometric centroid distance between the steel beam and the concrete slab;

[0235] 2. Calculate the equivalent stiffness (EI) of the hybrid section ∞ and axial stiffness (EA) ∞ :

[0236] (EI) ∞ =h0 2E2A2+E1I1;

[0237] E1I1=E s I s +E c I c ;

[0238] (EA) ∞ =E c A c +E s A s ;

[0239]

[0240] Among them, E s 、E c are the elastic moduli of steel and concrete, I s ,I c are the moments of inertia of steel and concrete, A s , A c are the areas of steel bars and concrete respectively;

[0241] Specifically, M. y is the yield moment of the cross section under boundary conditions, f y is the yield strength of steel, (EI) ∞ is the equivalent stiffness, h0 is the geometric centroid distance between the steel beam and the concrete slab, E1I1 is the equivalent stiffness of the mixed section, E s is the elastic modulus of steel, I s is the moment of inertia of steel, E c is the elastic modulus of concrete, I c is the moment of inertia of the concrete slab, E2A2 is the equivalent axial stiffness of the hybrid section, A c is the cross-sectional area of ​​the concrete slab, A s is the cross-sectional area of ​​the steel;

[0242] The calculated M y Compared with the standard value M s For comparison:

[0243] If M y <M s , indicating that the material has not yielded yet, return to S300, increase the number of iterations i=i+1, and perform the next iterative calculation;

[0244] If M y >M s , indicating that yield occurs, the program enters S400 and performs corresponding processing, such as margin adjustment, etc.;

[0245] Through continuous iterative calculation until the convergence condition is met, the final M is obtained. sand M y , thereby completing the stiffness reduction calculation.

[0246] S400: Calculate the longitudinal shear force V(x) of the composite beam connected by studs when it degenerates from a beam of equal stiffness to a beam of variable stiffness;

[0247] When the friction force at the steel-concrete interface is sufficient to overcome the longitudinal shear force, and all bolts are in the friction stage, the shear stiffness of each bolt is constant at k, which is determined by the push-out test. The composite beam is an equal stiffness beam. Figure 3 ;

[0248] If the load continues to increase and the friction force is insufficient to overcome the shear force, the bolts will overcome the friction from the support end to the mid-span, and the shear stiffness of the bolts will degenerate to zero, and the composite beam will degenerate into a variable stiffness beam. Figure 4 ;

[0249] The variable stiffness beam has a stiffness-free region of length x1 at the support end;

[0250] The longitudinal shear force on the steel-concrete interface when overcoming friction is:

[0251]

[0252] Among them, n s is the number of shear keys of the friction type high-strength bolts in the shear span, d is the diameter of the friction type high-strength bolts in the shear span, k is the shear stiffness of each bolt, α and β are both intermediate parameters used to calculate the longitudinal shear force distribution on the steel-concrete interface in the shear connection hybrid member, α is a combined parameter related to the member stiffness, connector stiffness and other parameters, reflecting the rate of change of the shear force distribution along the axial direction of the member, β is another combined parameter related to the member stiffness and connector parameters, reflecting the overall size of the shear force in the member, q is the uniform load intensity, x1 is the distance from the support to the considered section, L is the shear span length, and e is a natural constant;

[0253] In step S400, the specific implementation steps are as follows:

[0254] S410: When the friction force at the steel-concrete interface is large enough, all connecting bolts are in the friction stage, that is, they only bear shear force but not bending moment;

[0255] At this time, the shear stiffness k of each bolt is a constant, and its value needs to be determined through a push-out test;

[0256] The composite beam is considered as a beam of equal stiffness in this case;

[0257] S420: As the load continues to increase, when the interface friction is insufficient to bear the shear force, the bolts will overcome the friction one by one from the support end to the mid-span;

[0258] For bolts that have overcome friction, their shear stiffness will degenerate to 0;

[0259] The composite beam is considered as a variable stiffness beam in this case;

[0260] S430: Within a certain length range near the support, the variable stiffness beam is equivalent to a non-stiffness area because the bolts no longer provide shear stiffness, and the length is recorded as x1;

[0261] S440: When there is shear force V(x) at the interface, its distribution can be calculated as follows:

[0262]

[0263] Among them, n s is the number of shear keys of the friction type high-strength bolts in the shear span, d is the diameter of the friction type high-strength bolts in the shear span, k is the shear stiffness of each bolt, α and β are both intermediate parameters used to calculate the longitudinal shear force distribution on the steel-concrete interface in the shear connection hybrid member, α is a combined parameter related to the member stiffness, connector stiffness and other parameters, reflecting the rate of change of shear force distribution along the axial direction of the member, β is another combined parameter related to the member stiffness and connector parameters, reflecting the overall size of the shear force in the member, q is the uniformly distributed load intensity, x1 is the distance from the support to the considered section, L is the shear span length, and e is a natural constant.

[0264] S500: Calculation of external load q when a composite beam connected by studs degenerates from a beam of constant stiffness to a beam of variable stiffness f ;

[0265] Specifically, according to the load form, calculate the load q when the first bolt at the end of the support overcomes the friction f :

[0266]

[0267] Where μ is the friction coefficient and T is the interface shear stress;

[0268] This example takes uniformly distributed load as an example:

[0269] If q s <q f According to the principle of minimum potential energy, the stiffness reduction factor of the composite beam considering the interface slip effect is ξ1, where q≤q s ;

[0270]

[0271] If q s >q fAccording to the principle of minimum potential energy, the composite beam stiffness reduction factor considering both interface slip and friction overcoming effects is ξ2, where q>q s ;

[0272]

[0273] Specifically, the calculation steps are as follows:

[0274] 1. List the geometric parameters and material parameters of the composite beam: L is the shear span length, d is the diameter of the friction type high-strength bolt in the shear span, n s is the number of shear keys of the friction-type high-strength bolts in the shear span, k is the shear stiffness of each bolt, E1I1 is the equivalent stiffness of the hybrid section, E2A2 is the equivalent axial stiffness of the hybrid section, h0 is the geometric centroid distance between the steel beam and the concrete slab, μ is the friction coefficient, and T is the interface shear stress;

[0275] 2. Calculate auxiliary parameters α and β:

[0276]

[0277] 3. Based on the limit state when the first bolt at the support end overcomes friction, write the expression of the interface shear stress T:

[0278]

[0279] 4. Substitute T into q f The expression of q f :

[0280]

[0281] 5. Simplify and organize to get the following about q f The equation is:

[0282]

[0283] 6. Solve the equation to obtain the critical uniformly distributed load q for the first bolt at the support end to overcome friction f , by calculating the critical load q f ,This model provides an important basis for the overall structural analysis;

[0284] When s <q f When , the equal stiffness beam model can be used;

[0285] When s <q f When , it is necessary to convert to a variable stiffness beam model and consider the influence of bolt failure;

[0286] This segmented modeling approach can simulate the stress-strain behavior of actual structures more accurately;

[0287] S600: Use the reduced equivalent stiffness of the composite beam to calculate the mid-span deflection ω under the standard load value in sections;

[0288] S610: Determine the interface status;

[0289] S611: If q s <q f , the composite beam is in the state of a beam with equal stiffness throughout the entire process under the action of load;

[0290]

[0291] Among them, ξ1 is the stiffness reduction factor of the first composite beam, B F1 is the shear retention coefficient of the beam with uniform stiffness;

[0292] S612: If q s <q f , the composite beam degenerates from a beam of equal stiffness to a beam of variable stiffness under load;

[0293]

[0294] Among them, ξ2 is the stiffness reduction factor of the second composite beam, B F2 Shear retention coefficient of variable stiffness beam;

[0295] S620: Determine according to the deflection criterion;

[0296] S621: If the mid-span deflection is greater than the mid-span displacement judgment value, ω>[ω], then return to S200 and set j=j+1;

[0297] S622: The mid-span deflection is less than the mid-span displacement judgment value, ω<[ω], and the design is completed.

[0298] In step S600, the implementation process in this step is as follows:

[0299] 1. Determine the interface status

[0300] Based on the results of the interface state analysis, it is determined whether the interface is in a complete friction stage or a partial / complete failure state.

[0301] 2. Calculate basic parameters

[0302] In the complete friction stage, the calculation is equivalent to:

[0303] EI=E c I c +E s I s ;

[0304] Where E c ,Ic are the elastic modulus and moment of inertia of concrete, E s ,I s are the elastic modulus and moment of inertia of the steel beam respectively;

[0305] Partial / complete failure, the number of failed bolts n needs to be determined b , and calculate the interface shear deformation angle γ;

[0306] 3. Calculate equivalent stiffness in sections

[0307] In the full friction stage, the equivalent stiffness is EIeq;

[0308] In the partial failure stage, the equivalent stiffness EIeq′ is calculated according to the following formula:

[0309]

[0310] Where ψ is the correction factor, k is the shear shape factor, G is the shear modulus of the steel beam material, A is the cross-sectional area, b is the clear distance between the steel and concrete interface, and n b is the number of failed bolts, n is the total number of bolts, and L is the span length;

[0311] At the complete failure stage, the equivalent stiffness EIeq″ is calculated according to the following formula:

[0312]

[0313] The above formula reflects the influence of bolt failure and interface shear slip on the overall stiffness of the composite beam;

[0314] By calculating and reducing the equivalent stiffness in sections, this module can accurately simulate the deformation performance of composite beams at various load stages, laying the foundation for subsequent structural analysis.

[0315] 4. Obtain equivalent stiffness

[0316] According to the above, obtain the equivalent stiffness EIeq, EIeq′ or EIeq″ corresponding to the current load stage;

[0317] 5. Establish deflection calculation model

[0318] The composite beam is equivalent to a simply supported beam, and the basic formula in material mechanics is used:

[0319] During the full friction phase:

[0320]

[0321] During the partial failure phase:

[0322]

[0323] During the complete failure phase:

[0324]

[0325] Where q is the external uniformly distributed load, and L is the span length of the beam;

[0326] 6. Correction calculation

[0327] For practical engineering problems, it may be necessary to introduce correction factors to consider the effects of beam end constraints, load distribution, etc.:

[0328] ω′=β*ω;

[0329] Where β is the correction factor, which depends on the constraints and load distribution;

[0330] The key parameters in this step include:

[0331] Among them, EIeq, EIeq′, and EIeq″ are the current equivalent stiffness provided by the above steps, EIeq corresponds to BF1, and EIeq′ or EIeq″ corresponds to B F2 ;

[0332] By making reasonable use of equivalent stiffness and material mechanics formulas, this module can calculate the actual deflection value of the composite beam at each load stage, providing a basis for structural design and safety assessment. This module is closely dependent on the calculation results of the first two modules.

[0333] According to the above method for calculating the stiffness of a composite beam connected by high-strength bolts, a method for calculating the stiffness of a composite beam connected by high-strength bolts is also proposed, including:

[0334] Load calculation module: This module is used to calculate the most unfavorable load combination in the normal use stage and the construction stage, and set the mid-span displacement judgment value [ω];

[0335] Geometric parameter input module: This module is used to input the geometric parameters of the composite beam, including span L, concrete slab thickness h c 、H-beam section height h s , width b, steel web thickness t1, steel flange thickness t and steel yield strength f y , these parameters constitute the first set of variables C i ;

[0336] Connection parameter input module: This module is used to input the parameters of high-strength bolt connections, including the number of friction-type high-strength bolts in the shear span n s , diameter d and preload force P, these parameters constitute the second set of variables D j ;

[0337] Economic evaluation module: According to Ci and D j Different combinations of the economic parameters E of various schemes are calculated C，i and E D，j , and sort and number the combination schemes according to the size of these two parameters;

[0338] Material constitutive module: This module sets the material constitutive model, assumes that the material is linear elastic, conforms to Hooke's law, and determines the yield criterion;

[0339] Interface state analysis module: According to the load size, analyze whether the friction force of the steel-concrete interface is sufficient to overcome the longitudinal shear force, and judge whether each bolt is in the friction stage or failure state, corresponding to the situation of equal stiffness beam or variable stiffness beam;

[0340] Critical load calculation module: Calculates the critical load q required for the first bolt at the support end to overcome friction f ;

[0341] Stiffness reduction module: According to the interface state, the equivalent stiffness of the composite beam is calculated and reduced in sections;

[0342] Displacement calculation module: Use the reduced equivalent stiffness to calculate the mid-span deflection ω of the composite beam under load.

[0343] At least one embodiment of the present disclosure provides a storage medium storing non-transitory computer-readable instructions for executing one or more steps in the aforementioned method for calculating the stiffness of a composite beam connected by high-strength bolts.

[0344] The computer program may be stored / distributed on a suitable medium, such as an optical storage medium or a solid-state medium supplied together with or as part of other hardware, but may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunication systems. Any reference signs in the claims should not be construed as limiting the scope.

[0345] The above describes an embodiment of the present embodiment, but the present embodiment is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present embodiment, ordinary technicians in this field can also make many forms, all of which are protected by the present embodiment.

Claims

1. A method for calculating the stiffness of a composite beam connected by high-strength bolts, characterized in that: The following steps are involved: S100: The most unfavorable loads occurring during the use and construction phases are calculated, and the standard value of the most unfavorable load combination on the composite beam is calculated, and the mid-span displacement judgment value [ω] is set at the same time; S200: Determine the geometric parameters of the steel beam population C i , bolt shear connector parameter population D j , assign multiple common values ​​to each parameter in each population, and C i , D j Sort by economic parameters; Assign multiple common values ​​to each variable, then the first group of variables C i And the second set of variables D j There are multiple combination schemes between them, and then the economic parameters E of each scheme are output C，i and E D，j ; S300: given a parameter population, calculating the yield judgment condition of the composite beam under the parameter population; If M y <M s , return to S300, set i=i+1; If M y >M s , enter S400; Among them, M s is the standard value of bending moment, M y is the yield moment produced by the cross section; S400: Calculate the longitudinal shear force V(x) of the composite beam connected by studs when it degenerates from a beam of equal stiffness to a beam of variable stiffness; S500: Calculation of external load q when a composite beam connected by studs degenerates from a beam of constant stiffness to a beam of variable stiffness f ; S600: Use the reduced equivalent stiffness of the composite beam to calculate the mid-span deflection ω under the standard load value in sections; S610: Determine interface status: If q s <q f , the composite beam is in the state of a beam with equal stiffness throughout the entire process under the action of load; If q s >q f , the composite beam degenerates from a beam of equal stiffness to a beam of variable stiffness under load; where q s is the standard value of load combination; S620: Determine based on the deflection criterion: If the mid-span deflection is greater than the mid-span displacement judgment value, ω>[ω], then return to S200 and set j=j+1; The mid-span deflection is less than the mid-span displacement judgment value, ω<[ω], and the design is completed.

2. The method for calculating the stiffness of a composite beam connected by high-strength bolts according to claim 1, characterized in that: The standard values ​​of load combinations and bending moments are as follows: q s =(h·W+D+S G +S Q ); Among them, q s is the standard value of load combination, M s is the standard value of bending moment, h is the thickness of concrete slab, W is the concrete density, D is the additional permanent load, S G is the additional dead load, S Q To use live load, l is the span length of the beam; In step S100, the following steps are included: S110: Load identification, first of all, it is necessary to identify various permanent loads and possible temporary loads acting on the composite beam structure, including structural deadweight, additional permanent loads, live loads, wind loads, and temperature loads; S120: Load combination. According to different load conditions and load combination specifications, the identified permanent loads and temporary loads are combined to form a series of different load condition combinations. The load combinations are: ∑(γ i ,Q i ); Among them, Q i represents the standard value of the i-th load, γ i The corresponding combination coefficients are determined according to the specifications for different load types; S130: Load internal force calculation, for each load condition combination, calculate the corresponding internal force effects, including bending moment, shear force, and axial force; S140: Limit state check, compare the calculated internal force effect with the bearing capacity of the structure to check whether the requirements of the relevant limit states are met, including the bearing capacity limit state and the serviceability limit state; S150: Identification of unfavorable load combinations: for different design requirements, identify the corresponding most unfavorable load combinations; S160: Setting of mid-span displacement judgment value: according to the specification requirements or actual project needs, set the allowable mid-span displacement judgment value [ω] of the composite beam under normal use conditions.

3. The method for calculating the stiffness of a composite beam connected by high-strength bolts according to claim 2, characterized in that: According to E C，i and E D，j Sort the values ​​of , and assign values ​​to i and j respectively; i=(h s b-(h s -2t)(b-t1))f y ; Yes D，j =1.8d 2 n s ; Where i = 1, 2, 3, ..., j = 1, 2, 3, ...; where h s and b are the height and width of the H-beam section, t1 is the thickness of the steel web, t is the thickness of the steel flange, and f y is the yield strength of steel; where n s is the number of shear keys of the friction type high-strength bolts in the shear span, and d is the diameter of the friction type high-strength bolts in the shear span.

4. The method for calculating the stiffness of a composite beam connected by high-strength bolts according to claim 3, characterized in that: In step S200, the span L of the composite beam and the thickness h of the concrete slab are set according to the engineering conditions. c is a fixed value; The cross-sectional height h of the H-beam s , width b, steel web thickness t1, steel flange thickness t and steel yield strength f y Composed of the first set of variables C i : C i ={h s ,b,t1,t,f y }; The number of shear keys of friction-type high-strength bolts in the shear span is n s , the diameter of the friction type high-strength bolt in the shear span is d, and the bolt preload is P, which constitutes the second group of variables Dj: D j ={n s ,d,P}; It is also necessary to calculate the geometric parameter C i The corresponding economic cost E C，i Calculate the connection parameter D j The corresponding economic cost E D，j , and according to all C i and D j List the combinations of the above, and calculate the total economic cost E for each combination, including the following: 1) Calculate the geometric parameters C i The corresponding economic cost E C，i ; E C，i It is related to the amount of concrete and steel used and the difficulty of construction, and is estimated using the following empirical formula: E C，i =αcV c +αsW S +βcL c +βsL S ; Among them, V c and Ws are the amounts of concrete and steel, respectively. c and L S are the construction difficulty coefficients of concrete and steel structures, respectively, αc, αs, βc, βs are the corresponding unit cost coefficients; 2) Calculate the connection parameter D j The corresponding economic cost E D，j ; E D，j It is related to the number and type of high-strength bolt connections and is estimated using the following formula: E D，j =γ*n s *Cs(d); Among them, n s is the number of high-strength bolts, Cs(d) is the cost of a single high-strength bolt with diameter d, and γ is the additional cost coefficient for installation; 3) All C i and D j List the combinations of , and calculate the total economic cost E for each combination: E=E C，i +E D，j ; According to the size of E, all combination plans are sorted and numbered, with plans with lower economic costs being ranked first and having relatively smaller numbers.

5. The method for calculating the stiffness of a composite beam connected by high-strength bolts according to claim 4, characterized in that: In step S300, set the combined population C i and D j The initial value of the material, the stiffness reduction calculation method, conforms to Hooke's law, sets the yield judgment condition, and determines that all materials have not yet reached the yield stress; 1) Calculate the yield moment M of the cross section y : where f y is the yield strength of steel, (EI) ∞ is the equivalent stiffness, h0 is the geometric centroid distance between the steel beam and the concrete slab; 2) Calculate the equivalent stiffness (EI) of the hybrid section ∞ and axial stiffness (EA) ∞ : (NO) ∞ =h0 2 E2A2+E1I1; E1I1=E s THE s +E c THE c ; (EA) ∞ =Yes c A c +Yes s A s ; Among them, M y is the yield moment of the cross section under boundary conditions, f y is the yield strength of steel, (EI) ∞ is the equivalent stiffness, (EA) ∞ is the axial stiffness, E1I1 is the equivalent stiffness of the mixed section, E s is the elastic modulus of steel, I s is the moment of inertia of steel, E c is the elastic modulus of concrete, I c is the moment of inertia of the concrete slab, E2A2 is the equivalent axial stiffness of the hybrid section, A c is the cross-sectional area of ​​the concrete slab, A s is the cross-sectional area of ​​the steel; In step S300, the combined population C i and D j The initial value of is: C i =C1; D j =D1。 6. The method for calculating the stiffness of a composite beam connected by high-strength bolts according to claim 5, characterized in that: In step S400, when the friction force at the steel-concrete interface is sufficient to overcome the longitudinal shear force, and all bolts are in the friction stage, the shear stiffness of each bolt is constant at k, which is determined by the push-out test, and the composite beam is a beam of equal stiffness; If the load continues to increase and the friction force is insufficient to overcome the shear force, the bolts overcome the friction from the support end to the mid-span in sequence, and the shear stiffness of the bolts degenerates to zero, and the composite beam degenerates to the state of a variable stiffness beam. The variable stiffness beam has a zero-stiffness area of ​​length x1 at the support end. The implementation steps are as follows: S410: When the friction force at the steel-concrete interface is large enough, all connecting bolts are in the friction stage, that is, they only bear shear force but not bending moment; At this time, the shear stiffness k of each bolt is a constant, and its value needs to be determined through a push-out test; The composite beam is considered as a beam of equal stiffness in this case; S420: As the load continues to increase, when the interface friction is insufficient to bear the shear force, the bolts will overcome the friction one by one from the support end to the mid-span; For bolts that have overcome friction, their shear stiffness will degenerate to 0; The composite beam is considered as a variable stiffness beam in this case; S430: Within a certain length range near the support, the variable stiffness beam is equivalent to a non-stiffness area because the bolts no longer provide shear stiffness, and the length is recorded as x1; S440: When there is a shear force V(x) at the interface, the longitudinal shear force on the steel-concrete interface to overcome friction is: Among them, n s is the number of shear keys of the friction type high-strength bolts in the shear span, d is the diameter of the friction type high-strength bolts in the shear span, k is the shear stiffness of each bolt, α and β are both intermediate parameters used to calculate the longitudinal shear force distribution on the steel-concrete interface in the shear connection hybrid member, α is a combined parameter related to the member stiffness and the connection stiffness parameters, reflecting the rate of change of the shear force distribution along the axial direction of the member, β is another combined parameter related to the member stiffness and the connection parameters, reflecting the overall size of the shear force in the member, q is the uniformly distributed load intensity, x1 is the distance from the support to the considered section, L is the shear span length, and e is a natural constant.

7. The method for calculating the stiffness of a composite beam connected by high-strength bolts according to claim 6, characterized in that: In step S500, the load q required for the first bolt at the end of the support to overcome friction is calculated according to the load form. f : Where μ is the friction coefficient and T is the interface shear stress; If q s <q f , where q≤q s , according to the principle of minimum potential energy, the stiffness reduction coefficient of the composite beam considering the interface slip effect is taken as ξ1; If q s >q f , where q>q s According to the principle of minimum potential energy, the composite beam stiffness reduction coefficient considering the interface slip and friction overcoming effects is ξ2; The calculation steps are as follows: S510: List the geometric parameters and material parameters of the composite beam: L is the shear span length, d is the diameter of the friction-type high-strength bolts in the shear span, n s is the number of shear keys of the friction-type high-strength bolts in the shear span, k is the shear stiffness of each bolt, E1I1 is the equivalent stiffness of the hybrid section, E2A2 is the equivalent axial stiffness of the hybrid section, h0 is the geometric centroid distance between the steel beam and the concrete slab, μ is the friction coefficient, and T is the interface shear stress; S520: Calculate auxiliary parameters α and β: S530: Based on the limit state when the first bolt at the support end overcomes friction, write the expression for the interface shear stress T: S540: Substitute T into q f The expression of q f : S550: Simplify and sort out the information about q f The equation is: S560: Solve the equation to obtain the critical uniformly distributed load q for the first bolt at the support end to overcome friction f , by calculating the critical load q f : When s <q f When , the equal stiffness beam model can be used; When s >q f It is necessary to convert to a variable stiffness beam model and consider the influence of bolt failure.

8. The method for calculating the stiffness of a composite beam connected by high-strength bolts according to claim 7, characterized in that: In step S600, the implementation process in this step is as follows: 1) Determine the interface status According to the results of the interface state analysis, it is determined whether the interface is in the full friction stage or partial / complete failure state; Among them, ξ1 is the stiffness reduction factor of the first composite beam, B F1 is the shear retention coefficient of the beam with uniform stiffness; Among them, ξ2 is the stiffness reduction factor of the second composite beam, B F2 Shear retention coefficient of variable stiffness beam; 2) Calculate basic parameters In the complete friction stage, the calculation is equivalent to: EI=E c ESSENTIAL c +E s ESSENTIAL s ; Where E c ,I c are the elastic modulus and moment of inertia of concrete, E s ,I s are the elastic modulus and moment of inertia of the steel beam respectively; Partial / complete failure, the number of failed bolts n needs to be determined b , and calculate the interface shear deformation angle γ; 3) Calculate equivalent stiffness in sections In the full friction stage, the equivalent stiffness is EIeq; In the partial failure stage, the equivalent stiffness EIeg′ is calculated according to the following formula: Where ψ is the correction factor, κ is the shear shape factor, G is the shear modulus of the steel beam material, A is the cross-sectional area, b is the clear distance between the steel and concrete interface, and n b is the number of failed bolts, n is the total number of bolts, and L is the span length; At the complete failure stage, the equivalent stiffness EIeq″ is calculated according to the following formula: The above formula describes the effect of bolt failure and interface shear slip on the overall stiffness of the composite beam. By calculating and reducing the equivalent stiffness in sections, the deformation performance of the composite beam at each load stage is simulated. 4) Obtain equivalent stiffness According to the results of the segmented calculation of equivalent stiffness, the equivalent stiffness EIeq, EIeq′, and EIeq″ corresponding to the current load stage are obtained; 5) Establish deflection calculation model The composite beam is equivalent to a simply supported beam, and the basic formula in material mechanics is used: During the full friction phase: During the partial failure phase: During the complete failure phase: Where q is the external uniformly distributed load, and L is the span length of the beam; 6) Correction calculation For practical engineering problems, the correction coefficient is introduced, and the beam end constraint conditions and load distribution form are considered: ω′=β*ω; Where β is the correction factor, which depends on the constraints and load distribution; Among them, EIeq, EIeq′, and EIeq″ are the current equivalent stiffness provided by the above steps, and EIeq corresponds to B F1 , EIeq′ or EIeq″ corresponds to B F2 .

9. A method for calculating the stiffness of a composite beam connected by high-strength bolts, used to perform the steps in the method for calculating the stiffness of a composite beam connected by high-strength bolts as claimed in any one of claims 1 to 8, characterized in that: include: Load calculation module: This module is used to calculate the most unfavorable load combination in the normal use stage and the construction stage, and set the mid-span displacement judgment value [ω]; Geometric parameter input module: This module is used to input the geometric parameters of the composite beam, including span L, concrete slab thickness h c 、H-beam section height h s , width b, steel web thickness t1, steel flange thickness t and steel yield strength f y , these parameters constitute the first set of variables C i ; Connection parameter input module: This module is used to input the parameters of high-strength bolt connections, including the number of friction-type high-strength bolts in the shear span n s , diameter d and preload force P, these parameters constitute the second set of variables D j ; Economic evaluation module: According to C i and D j Different combinations of the economic parameters E of various schemes are calculated C，i and E D,j , and sort and number the combination schemes according to the size of these two parameters; Material constitutive module: This module sets the constitutive model of the material, the material complies with Hooke's law, and determines the yield criterion; Interface state analysis module: According to the load size, analyze whether the friction force of the steel-concrete interface is sufficient to overcome the longitudinal shear force, and judge whether each bolt is in the friction stage or failure state, corresponding to the situation of equal stiffness beam or variable stiffness beam; Critical load calculation module: Calculates the critical load q required for the first bolt at the support end to overcome friction f ; Stiffness reduction module: According to the interface state, the equivalent stiffness of the composite beam is calculated and reduced in sections; Displacement calculation module: Use the reduced equivalent stiffness to calculate the mid-span deflection ω of the composite beam under load.

10. A storage medium, characterized in that: Non-transitory computer-readable instructions are stored, which are used to execute the steps in the method for calculating the stiffness of a composite beam with high-strength bolt connection as claimed in any one of claims 1 to 8.

Images