A method for predicting the bending resistance of a large-span multi-rib concrete composite slab

Abstract

The application relates to a method for predicting the bending performance of a large-span multi-rib concrete composite slab, which comprises the following steps: S1: constructing a space rectangular coordinate system of the large-span multi-rib concrete composite slab, and restraining the physical properties of the large-span multi-rib concrete composite slab; S2: constructing a shear lag effect displacement function of the large-span multi-rib concrete composite slab according to a shear lag control equation derived based on the minimum potential energy principle; S3: deriving a bending balance equation based on the shear lag effect displacement function and the minimum potential energy principle, and constructing a bending performance prediction model of the large-span multi-rib concrete composite slab considering the shear lag effect based on the bending balance equation. The bending moment of the large-span multi-rib concrete composite slab can be predicted through the bending performance prediction model, so that the deflection and stress state of the composite slab under the service load can be more accurately evaluated.

Description

Technical Field

[0001] This application relates to the field of flexural performance prediction technology for concrete composite slabs, and in particular to a method for predicting the flexural performance of large-span multi-ribbed concrete composite slabs. Background Technology

[0002] Traditional methods for predicting flexural performance typically assume a uniform longitudinal stress distribution across the cross-section, based on the plane section assumption. However, in composite slabs with longitudinal ribs (complex structures), the uneven shear force transfer between the ribs and the base plate leads to a shear lag effect, causing the stress to be non-uniformly distributed along the width of the cross-section. Traditional methods fail to consider this effect and often simplify composite slabs into homogeneous beams for calculation, neglecting factors such as material stiffness differences, rib locations, and inter-story shear force transfer. This affects the accuracy of load-bearing capacity and deflection predictions. Summary of the Invention

[0003] Therefore, it is necessary to provide a method for predicting the flexural performance of large-span multi-ribbed concrete composite slabs, including: S1: Construct a spatial rectangular coordinate system for a large-span multi-ribbed concrete composite slab and constrain the physical properties of the large-span multi-ribbed concrete composite slab. S2: Based on the shear hysteresis control equation derived from the principle of minimum potential energy, construct the shear hysteresis displacement function of a large-span multi-ribbed concrete composite slab. S3: Based on the displacement function of shear hysteresis effect and the principle of minimum potential energy, the bending equilibrium equation is derived, and a bending performance prediction model of large-span multi-ribbed concrete composite slab considering shear hysteresis effect is constructed based on the bending equilibrium equation.

[0004] Preferably, the spatial rectangular coordinate system for constructing the large-span multi-ribbed concrete composite slab includes: Taking any one end of the long-span multi-ribbed concrete composite slab as the origin, the major axis originating from the end is taken as the Z-axis, the minor axis originating from the end is taken as the X-axis, and the vertical axis originating from the end is taken as the Y-axis.

[0005] Preferably, the physical properties of the constrained large-span multi-ribbed concrete composite slab include: The arrangement of external loads eliminates torsion, distortion and lateral bending of the cross section of the large-span multi-ribbed concrete composite slab, and the cross section is symmetrical along the YZ plane. The effect of transverse ribs in the ceramsite concrete layer of the multi-ribbed concrete composite slab is ignored. Multi-ribbed concrete composite slabs possess symmetry; In multi-ribbed concrete composite slabs, both the steel reinforcement and concrete are constrained to be linearly elastic and ideally bonded together. In the multi-ribbed concrete composite slab, both the ordinary concrete layer and the ceramsite concrete layer are constrained to be linearly elastic and the interlayer bonding is ideal.

[0006] Preferably, S2 includes: Step 1: By superimposing warping coordinates on the Z-axis displacement of the large-span multi-rib concrete composite slab to model the shear hysteresis effect, the shear hysteresis effect of the longitudinal ribs at different positions in the large-span multi-rib concrete composite slab is analyzed. Step 2: Differentiate the warped coordinates along the Z and Y axes to obtain the shear strain and the normal strain of the concrete and steel reinforcement; Step 3: Calculate the axial stress of concrete and steel reinforcement based on the normal strain and Young's modulus of concrete and steel reinforcement respectively, and calculate the shear stress of concrete based on shear strain and shear modulus of concrete. Step 4: Calculate the strain energy of concrete based on its axial stress, normal strain, shear strain, and shear stress; calculate the strain energy of steel reinforcement based on its normal strain and axial stress. Step 5: Calculate the total potential energy of the large-span multi-ribbed concrete composite slab based on the strain energy of the concrete and steel reinforcement and the potential energy caused by the external load. Step 6: Based on the total potential energy and according to the principle of minimum potential energy, perform variational analysis on the shear lag displacement, construct the shear lag control equation, solve the general solution of the shear lag displacement in the shear lag control equation, and construct the shear lag effect displacement function of the large-span multi-ribbed concrete composite slab.

[0007] Preferably, the expression for the shear hysteresis displacement function is: ; ; ; in, This represents the shear force hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab. The first warping characteristic of the longitudinal ribs at the edge or center of the composite slab. Represents the hyperbolic cosine function. The second warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. Represents the hyperbolic sine function. The third warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. This represents the attenuation rate of the displacement due to shear hysteresis. Let Q(z) represent the total stiffness of the composite slab after cracking, and let Q(z) represent the shear force of the composite slab. The strength representing the displacement due to shear hysteresis. The fourth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. This represents the equivalent moment of inertia of a large-span multi-ribbed concrete composite slab. The fifth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate.

[0008] Preferably, S3 includes: The bending equilibrium equation is derived based on the principle of minimum potential energy. The expression for the bending equilibrium equation is: ; Where, represents the second derivative, The z-axis represents the total stiffness of the composite slab after cracking. The fifth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. The first derivative of the shear hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab is given by q, which represents the uniformly distributed load applied to the large-span multi-ribbed concrete composite slab. Based on the bending equilibrium equation, the total stiffness of the composite slab, and the shear hysteresis displacement function, the vertical displacement of the large-span multi-ribbed concrete composite slab considering the shear hysteresis effect is solved. The formula for calculating the vertical displacement is: ; in, Let Q(z) represent the vertical displacement, and Q(z) represent the shear force of the composite plate. This represents the shear force hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab. Denotes the first constant. Represents the second constant. Represents the third constant. Represents the fourth constant; Based on the second-order derivatives of the total stiffness and vertical displacement of the composite slab after cracking, a bending performance prediction model for large-span multi-ribbed concrete composite slabs considering shear hysteresis is constructed. The expression for the bending performance prediction model is as follows: ; in, This represents the bending moment of the composite slab considering the shear hysteresis effect. The second derivative represents the vertical displacement.

[0009] Preferably, the process of solving for the vertical displacement further includes: iteratively solving the formula for calculating the vertical displacement until the vertical displacement converges, thus obtaining the converged vertical displacement; the convergence condition for the vertical displacement is: ; in, This represents the vertical displacement obtained in the (k+1)th iteration step. This represents the vertical displacement obtained in the k-th iteration step. This represents the L2 norm.

[0010] Preferred options also include: Substituting the formula for calculating the normal strain of concrete into the formula for calculating the axial stress of concrete, we obtain the normal stress distribution, which is expressed as follows: ; in, express The distribution of normal stress at the location, The value represents the bending moment of a long-span, multi-ribbed concrete composite slab, and y represents the Y-axis coordinate. This represents the equivalent moment of inertia of a large-span multi-ribbed concrete composite slab. Let d represent the elastic modulus of a long-span, multi-ribbed concrete composite slab, where d denotes differentiation and z represents the Z-axis coordinate. This represents the shear force hysteresis displacement of the longitudinal ribs at the edge of the composite slab. This represents the shear force hysteresis displacement of the longitudinal rib at the center of the composite slab. The warping coordinates represent the longitudinal ribs at the edge of the composite slab. The warping coordinates of the longitudinal rib at the center of the composite slab; The shear hysteresis coefficient of a large-span multi-ribbed concrete composite slab is calculated based on the normal stress distribution. The formula is as follows: ; in, Indicates the shear hysteresis coefficient. B represents the effective width of the large-span multi-ribbed concrete composite slab, and B represents the actual width of the large-span multi-ribbed concrete composite slab. This indicates the maximum stress in the reinforcing steel of a large-span multi-ribbed concrete composite slab. when At that time, the flexural performance of the large-span multi-ribbed concrete composite slab is relatively weak. when At that time, the flexural performance of the large-span multi-ribbed concrete composite slab was of medium type. when At that time, the flexural resistance of the large-span multi-ribbed concrete composite slab was relatively strong.

[0011] Beneficial effects: This method predicts the bending moment of large-span multi-ribbed concrete composite slabs by constructing a bending performance prediction model, thereby enabling a more accurate assessment of the deflection and stress state of the composite slab under service loads. It can also provide a theoretical basis for subsequent component section optimization, rib arrangement design and connection structure, thereby improving the design rationality and economy of prefabricated composite slab structures. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart of the method for predicting the flexural performance of large-span multi-ribbed concrete composite slabs in the embodiments of this application.

[0014] Figure 2 This is a schematic diagram of the spatial rectangular coordinate system of the large-span multi-ribbed concrete composite slab in the embodiments of this application.

[0015] Figure 3 This is a schematic diagram of the cross section and the transverse force in an embodiment of this application.

[0016] Figure 4a This is a schematic diagram of the warping function of the longitudinal ribs at the edge in an embodiment of this application.

[0017] Figure 4b This is a schematic diagram of the warping function of the central longitudinal rib in an embodiment of this application.

[0018] Figure 5a This is a schematic diagram of the structural design of the N4C4R20 sample in the embodiments of this application.

[0019] Figure 5b This is a schematic diagram of the structural design of the N5C3R20 sample in the embodiments of this application.

[0020] Figure 5c This is a schematic diagram of the structural design of the N5C3R0 sample in the embodiments of this application.

[0021] Figure 6a This is a comparison chart of prediction errors for the N4C4R20 sample in the embodiments of this application.

[0022] Figure 6b This is a comparison chart of the prediction errors of the N5C3R20 sample in the embodiments of this application.

[0023] Figure 6c This is a comparison chart of the prediction errors of the N5C3R0 sample in the embodiments of this application. Detailed Implementation

[0024] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0025] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0026] like Figure 1 As shown in the figure, this embodiment provides a method for predicting the flexural performance of a large-span multi-ribbed concrete composite slab, including: S1: Construct a spatial rectangular coordinate system for large-span multi-ribbed concrete composite slabs and constrain the physical properties of the large-span multi-ribbed concrete composite slabs.

[0027] Specifically, the construction of the spatial rectangular coordinate system for the large-span multi-ribbed concrete composite slab includes: Taking any one end of the long-span multi-ribbed concrete composite slab as the origin, the major axis emanating from that end is taken as the Z-axis, the minor axis emanating from that end is taken as the X-axis, and the vertical axis emanating from that end is taken as the Y-axis, as follows: Figure 2 As shown.

[0028] Furthermore, the physical properties of the constrained large-span multi-ribbed concrete composite slab include: The arrangement of external loads eliminates torsion, distortion and lateral bending of the cross section of the large-span multi-ribbed concrete composite slab, and the cross section is symmetrical along the YZ plane. The effect of transverse ribs in the ceramsite concrete layer of the multi-ribbed concrete composite slab is ignored. Multi-ribbed concrete composite slabs possess symmetry; In multi-ribbed concrete composite slabs, both the steel reinforcement and concrete are constrained to be linearly elastic and ideally bonded together. In the multi-ribbed concrete composite slab, both the ordinary concrete layer and the ceramsite concrete layer are constrained to be linearly elastic and the interlayer bonding is ideal.

[0029] S2: Based on the shear lag control equation derived from the principle of minimum potential energy, construct the shear lag effect displacement function of a large-span multi-ribbed concrete composite slab.

[0030] Specifically, the steps include: Step 1: By superimposing warping coordinates on the Z-axis displacement of the large-span multi-rib concrete composite slab to model the shear hysteresis effect, the shear hysteresis effect of the longitudinal ribs at different positions in the large-span multi-rib concrete composite slab is analyzed. Figure 3 The multi-ribbed half-plate shown is subjected to a load that generates a longitudinal bending moment M(z) and a shear force Q(z). The expression for the shear hysteresis effect is: ; in, express The warping displacement at point v'(z) represents the first derivative of the vertical displacement. The warping coordinates of the longitudinal ribs at the edge or center of the composite slab. The shear hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab is represented by i=1,2, which correspond to the longitudinal ribs at the edge or center of the composite slab, respectively.

[0031] Warped coordinates via warp function f i ( x )(like Figure 4a , Figure 4b (As shown) Definition: ; ; ; in, f i ( x ) represents the warping function of the longitudinal ribs at the edge or center. f 1( x ) represents the warping function of the longitudinal ribs at the edge. f 2( x () represents the warping function of the central longitudinal rib, and B represents the actual width of the large-span multi-ribbed concrete composite slab. x Represents the coordinates along the X-axis.

[0032] Step 2: Differentiate the warped coordinates along the Z and Y axes to obtain the shear strain and the normal strain of the concrete and reinforcement; the calculation formulas are as follows: ; ; ; in, Represents the normal strain of concrete. Indicates the normal strain of the reinforcing steel. Represents shear strain. Let denote the partial derivative, and u denote the warping displacement. This represents the coordinates of the reinforcing bar in the XY plane of a spatial rectangular coordinate system.

[0033] Step 3: Calculate the axial stress of concrete and reinforcing steel based on their normal strain and Young's modulus, respectively; calculate the shear stress of concrete based on its shear strain and shear modulus. The calculation formulas are as follows: ; ; ; in, This represents the axial stress in concrete. Indicates the axial stress of the reinforcing steel. Indicates shear stress. This represents the Young's modulus of concrete. This indicates the Young's modulus of the reinforcing steel. This indicates the shear modulus of concrete.

[0034] Step 4: Calculate the strain energy of concrete based on its axial stress, normal strain, shear strain, and shear stress; calculate the strain energy of reinforcing steel based on its normal strain and axial stress; the calculation formulas are as follows: ; ; in, This represents the strain energy of concrete. Let V represent the strain energy of the reinforcing steel, V represent the volume of half a large-span multi-ribbed concrete composite slab, L represent the span of the large-span multi-ribbed concrete composite slab, and n represent the number of reinforcing steel bars. This indicates the cross-sectional area of ​​a single steel bar.

[0035] Step 5: Calculate the total potential energy of the large-span multi-ribbed concrete composite slab based on the strain energy of the concrete and reinforcing steel, as well as the potential energy caused by external loads; the calculation formula is: ; ; ; ; in, Represents the total potential energy. Represents internal potential energy. Let Q(z) represent the external potential energy, and let Q(z) represent the shear force of the composite plate.

[0036] Step 6: Based on the total potential energy and according to the principle of minimum potential energy, perform variational analysis on the shear lag displacement, construct the shear lag control equation, solve the general solution of the shear lag displacement in the shear lag control equation, and construct the shear lag effect displacement function of the large-span multi-ribbed concrete composite slab.

[0037] The specific process of step 6 is as follows: Using the principle of minimum potential energy and the relationship between bending moment and curvature, the generalized displacement v'(z) and shear hysteresis displacement U are analyzed. i (z) A variational analysis was performed. The shear hysteresis displacement U was obtained through the derived system of differential equations. i (z): (1) in, E c I eff This represents the equivalent bending stiffness of the reinforced concrete section after transformation. , , , These represent four possible values ​​for the warping characteristic parameters of the first cross-section. , , , These represent four possible values ​​for the warping characteristic parameters of the second cross section. , These represent two possible values ​​for the warping characteristic parameters of the third section.

[0038] Boundary position z = z l The boundary conditions at the point can be expressed as: (2) The bending characteristics of a cross section are determined by its bending coordinates. (3) (4) (5) in, This represents the warping characteristic parameters of the first cross section. This indicates the warping characteristic parameters of the second cross section. The third section represents the warping characteristic parameter, and A represents the cross-sectional area of ​​the specimen, which is the total cross-sectional area after converting the area of ​​the reinforcing steel into the equivalent concrete area using the equivalent section method, taking into account the difference in elastic modulus between the reinforcing steel and the two types of concrete. α E It represents the ratio of the Young's modulus of the steel reinforcement to the Young's modulus of the concrete.

[0039] Based on the above formulas (1) to (5), the shear hysteresis displacement function is derived, and the expression of the shear hysteresis displacement function is: ; ; ; in, This represents the shear force hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab. The first warping characteristic of the longitudinal ribs at the edge or center of the composite slab. Represents the hyperbolic cosine function. The second warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. Represents the hyperbolic sine function. The third warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. This represents the attenuation rate of the displacement due to shear hysteresis. Let Q(z) represent the total stiffness of the composite slab after cracking, and let Q(z) represent the shear force of the composite slab. The strength representing the displacement due to shear hysteresis. The fourth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. This represents the equivalent moment of inertia of a large-span multi-ribbed concrete composite slab. The fifth warping characteristic of the longitudinal ribs at the edge or center of the composite slab; parameter , According to boundary conditions U i (0) = 0 and U i ( l It is determined by )=0.

[0040] S3: Based on the displacement function of shear hysteresis effect and the principle of minimum potential energy, the bending equilibrium equation is derived, and a bending performance prediction model of large-span multi-ribbed concrete composite slab considering shear hysteresis effect is constructed based on the bending equilibrium equation.

[0041] Specifically, the steps include: The bending equilibrium equation is derived based on the principle of minimum potential energy. The expression for the bending equilibrium equation is: ; Where, represents the second derivative, The z-axis represents the total stiffness of the composite slab after cracking. The fifth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. The first derivative of the shear hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab is given by q, which represents the uniformly distributed load applied to the large-span multi-ribbed concrete composite slab. Based on the bending equilibrium equation, the total stiffness of the composite slab, and the shear hysteresis displacement function, the vertical displacement of the large-span multi-ribbed concrete composite slab considering the shear hysteresis effect is solved. The formula for calculating the vertical displacement is: ; in, Let Q(z) represent the vertical displacement, and Q(z) represent the shear force of the composite plate. This represents the shear force hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab. Denotes the first constant. Represents the second constant. Represents the third constant. Represents the fourth constant; Based on the second-order derivatives of the total stiffness and vertical displacement of the composite slab after cracking, a bending performance prediction model for large-span multi-ribbed concrete composite slabs considering shear hysteresis is constructed. The expression for the bending performance prediction model is as follows: ; in, This represents the bending moment of the composite slab considering the shear hysteresis effect. The second derivative represents the vertical displacement.

[0042] A schematic diagram of the analysis of the total bending stiffness of the specimen is shown below. Figure 2 As shown. Total flexural stiffness of the cross section of the complete concrete composite slab. E I0 The sum of the total stiffness of the NC layer (the lower concrete layer in the diagram) and the CC layer (the upper concrete layer in the diagram) about the centroidal axis of the composite is expressed as: ; in, E nc This represents the elastic modulus of a typical concrete layer. E cc This indicates the elastic modulus of the expanded clay concrete layer. h 1 and t 1 represents the thickness of the weathering steel layer and its centroid offset relative to the center of the composite, respectively; h 2 and t 2 are equivalent to the thickness of the carbon fiber composite layer and its centroid offset, respectively; while d s This represents the distance between the centroid of the reinforcing bar and the neutral axis; it is determined by the total bending stiffness of the cross section. E I0 Calculate the total stiffness of the composite slab after cracking The calculation formula is: ; in, β This represents the elastic-plastic shrinkage coefficient, which is usually taken as 0.2.

[0043] Furthermore, the process of solving for the vertical displacement also includes: iteratively solving the formula for calculating the vertical displacement until the vertical displacement converges, thus obtaining the converged vertical displacement; the convergence condition for the vertical displacement is: ; in, This represents the vertical displacement obtained in the (k+1)th iteration step. This represents the vertical displacement obtained in the k-th iteration step. This represents the L2 norm.

[0044] In this embodiment, it also includes: Substituting the formula for calculating the normal strain of concrete into the formula for calculating the axial stress of concrete, we obtain the normal stress distribution, which is expressed as follows: ; in, express The distribution of normal stress at the location, The value represents the bending moment of a long-span, multi-ribbed concrete composite slab, and y represents the Y-axis coordinate. This represents the equivalent moment of inertia of a large-span multi-ribbed concrete composite slab. Let d represent the elastic modulus of a long-span, multi-ribbed concrete composite slab, where d denotes differentiation and z represents the Z-axis coordinate. This represents the shear force hysteresis displacement of the longitudinal ribs at the edge of the composite slab. This represents the shear force hysteresis displacement of the longitudinal rib at the center of the composite slab. The warping coordinates represent the longitudinal ribs at the edge of the composite slab. The warping coordinates of the longitudinal rib at the center of the composite slab; The shear hysteresis coefficient of a large-span multi-ribbed concrete composite slab is calculated based on the normal stress distribution. The formula is as follows: ; in, Indicates the shear hysteresis coefficient. B represents the effective width of the large-span multi-ribbed concrete composite slab, and B represents the actual width of the large-span multi-ribbed concrete composite slab. This indicates the maximum stress in the reinforcing steel of a large-span multi-ribbed concrete composite slab. when At that time, the flexural performance of the large-span multi-ribbed concrete composite slab is relatively weak. when At that time, the flexural performance of the large-span multi-ribbed concrete composite slab was of medium type. when At that time, the flexural resistance of the large-span multi-ribbed concrete composite slab was relatively strong.

[0045] This embodiment provides a specific example of flexural performance prediction to better illustrate the accuracy and feasibility of the solution.

[0046] Large-span multi-ribbed concrete composite slabs were constructed using C30 ordinary concrete and LC30 lightweight aggregate concrete. Each specimen measures 3600mm × 1100mm × 80mm. Specific details of each specimen are as follows: Figures 5a-5c As shown. The sample name consists of the character combination NX-CY-RZ, where "NX" represents the thickness of ordinary concrete (X cm), "CY" represents the thickness of expanded clay concrete (Y cm), and "RZ" represents the height of the raised rib (Z mm). When Z equals 0 mm, it indicates that there is no raised rib.

[0047] The flexural performance prediction method of this invention was used to predict the flexural performance of each sample, and the results are as follows: Figures 6a-6c And as shown in Table 1; Table 1 Comparison of measured and predicted deflection values

[0048] Depend on Figures 6a-6c As shown in Table 1, a comparison of the calculated deflection response and the experimental deflection response using the theoretical model reveals that they are essentially consistent. Table 1 quantifies the deflection prediction errors for all specimens within 3% under yield load and within 18% under ultimate load. The increase in error under ultimate load stems from the gradual degradation of effective stiffness throughout the loading process. These results demonstrate that the proposed model reliably reproduces the deflection response under different concrete layer thickness ratios and rib geometry parameters.

[0049] The method for predicting the flexural performance of large-span multi-ribbed concrete composite slabs provided in this embodiment has the following beneficial effects: This method establishes a displacement function and mechanical control equations that consider the effect of shear lag, introduces a shear lag coefficient to quantify the strength of the effect, and constructs a bending performance prediction model that reflects the actual stress distribution and deformation characteristics by combining the principle of minimum potential energy. By introducing the shear lag displacement function and shear lag coefficient, it is clarified that longitudinal ribs are the key factor causing the shear lag effect. Through a shear lag-considered analysis model, the influence of the position and height of longitudinal ribs on bending performance is evaluated, and the non-uniform stress distribution phenomenon caused by longitudinal ribs is quantified, thus providing a more realistic feedback on the actual stress state of the section. This method can more reasonably predict the bending performance of multi-ribbed concrete composite slabs. This model can not only more accurately assess the deflection and stress state of composite slabs under service loads, but also provide a theoretical basis for component section optimization, rib arrangement design, and connection construction, thereby improving the design rationality and economy of prefabricated composite slab structures.

[0050] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0051] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for predicting the flexural performance of a large-span multi-ribbed concrete composite slab, characterized in that, include: S1: Construct a spatial rectangular coordinate system for a large-span multi-ribbed concrete composite slab and constrain the physical properties of the large-span multi-ribbed concrete composite slab. S2: Based on the shear hysteresis control equation derived from the principle of minimum potential energy, construct the shear hysteresis displacement function of a large-span multi-ribbed concrete composite slab. S3: Based on the displacement function of shear hysteresis effect and the principle of minimum potential energy, the bending equilibrium equation is derived, and a bending performance prediction model of large-span multi-ribbed concrete composite slab considering shear hysteresis effect is constructed based on the bending equilibrium equation.

2. The method for predicting the flexural performance of a large-span multi-ribbed concrete composite slab according to claim 1, characterized in that, The spatial rectangular coordinate system for constructing the large-span multi-ribbed concrete composite slab includes: Taking any one end of the long-span multi-ribbed concrete composite slab as the origin, the major axis originating from the end is taken as the Z-axis, the minor axis originating from the end is taken as the X-axis, and the vertical axis originating from the end is taken as the Y-axis.

3. The method for predicting the flexural performance of a large-span multi-ribbed concrete composite slab according to claim 2, characterized in that, The physical properties of the constrained large-span multi-ribbed concrete composite slab include: The arrangement of external loads eliminates torsion, distortion and lateral bending of the cross section of the large-span multi-ribbed concrete composite slab, and the cross section is symmetrical along the YZ plane. The effect of transverse ribs in the ceramsite concrete layer of the multi-ribbed concrete composite slab is ignored. Multi-ribbed concrete composite slabs possess symmetry; In multi-ribbed concrete composite slabs, both the steel reinforcement and concrete are constrained to be linearly elastic and ideally bonded together. In the multi-ribbed concrete composite slab, both the ordinary concrete layer and the ceramsite concrete layer are constrained to be linearly elastic and the interlayer bonding is ideal.

4. The method for predicting the flexural performance of large-span multi-ribbed concrete composite slabs according to claim 2, characterized in that, S2 include: Step 1: By superimposing warping coordinates on the Z-axis displacement of the large-span multi-rib concrete composite slab to model the shear hysteresis effect, the shear hysteresis effect of the longitudinal ribs at different positions in the large-span multi-rib concrete composite slab is analyzed. Step 2: Differentiate the warped coordinates along the Z and Y axes to obtain the shear strain and the normal strain of the concrete and steel reinforcement; Step 3: Calculate the axial stress of concrete and steel reinforcement based on the normal strain and Young's modulus of concrete and steel reinforcement respectively, and calculate the shear stress of concrete based on shear strain and shear modulus of concrete. Step 4: Calculate the strain energy of concrete based on its axial stress, normal strain, shear strain, and shear stress; calculate the strain energy of steel reinforcement based on its normal strain and axial stress. Step 5: Calculate the total potential energy of the large-span multi-ribbed concrete composite slab based on the strain energy of the concrete and steel reinforcement and the potential energy caused by the external load. Step 6: Based on the total potential energy and according to the principle of minimum potential energy, perform variational analysis on the shear lag displacement, construct the shear lag control equation, solve the general solution of the shear lag displacement in the shear lag control equation, and construct the shear lag effect displacement function of the large-span multi-ribbed concrete composite slab.

5. The method for predicting the flexural performance of a large-span multi-ribbed concrete composite slab according to claim 4, characterized in that, The expression for the shear hysteresis displacement function is: ； ； ； in, This represents the shear force hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab. The first warping characteristic of the longitudinal ribs at the edge or center of the composite slab. Represents the hyperbolic cosine function. The second warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. Represents the hyperbolic sine function. The third warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. This represents the attenuation rate of the displacement due to shear hysteresis. Let Q(z) represent the total stiffness of the composite slab after cracking, and let Q(z) represent the shear force of the composite slab. The strength representing the displacement due to shear hysteresis. The fourth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. This represents the equivalent moment of inertia of a large-span multi-ribbed concrete composite slab. The fifth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate.

6. The method for predicting the flexural performance of large-span multi-ribbed concrete composite slabs according to claim 1, characterized in that, S3 include: The bending equilibrium equation is derived based on the principle of minimum potential energy. The expression for the bending equilibrium equation is: ； Where, represents the second derivative, The z-axis represents the total stiffness of the composite slab after cracking. The fifth warping characteristic indicates the longitudinal ribs at the edge or center of the composite plate. The first derivative of the shear hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab is given by q, which represents the uniformly distributed load applied to the large-span multi-ribbed concrete composite slab. Based on the bending equilibrium equation, the total stiffness of the composite slab, and the shear hysteresis displacement function, the vertical displacement of the large-span multi-ribbed concrete composite slab considering the shear hysteresis effect is solved. The formula for calculating the vertical displacement is: ； in, Let Q(z) represent the vertical displacement, and Q(z) represent the shear force of the composite plate. This represents the shear force hysteresis displacement of the longitudinal ribs at the edge or center of the composite slab. Denotes the first constant. Represents the second constant. Represents the third constant. Represents the fourth constant; Based on the second-order derivatives of the total stiffness and vertical displacement of the composite slab after cracking, a bending performance prediction model for large-span multi-ribbed concrete composite slabs considering shear hysteresis is constructed. The expression for the bending performance prediction model is as follows: ； in, This represents the bending moment of the composite slab considering the shear hysteresis effect. The second derivative represents the vertical displacement.

7. The method for predicting the flexural performance of a large-span multi-ribbed concrete composite slab according to claim 6, characterized in that, The process of solving for the vertical displacement also includes: iteratively solving the formula for calculating the vertical displacement until the vertical displacement converges, thus obtaining the converged vertical displacement; the convergence condition for the vertical displacement is: ； in, This represents the vertical displacement obtained in the (k+1)th iteration step. This represents the vertical displacement obtained in the k-th iteration step. This represents the L2 norm.

8. The method for predicting the flexural performance of a large-span multi-ribbed concrete composite slab according to claim 4, characterized in that, Also includes: Substituting the formula for calculating the normal strain of concrete into the formula for calculating the axial stress of concrete, we obtain the normal stress distribution, which is expressed as follows: ； in, express The distribution of normal stress at the location, The value represents the bending moment of a long-span, multi-ribbed concrete composite slab, and y represents the Y-axis coordinate. This represents the equivalent moment of inertia of a large-span multi-ribbed concrete composite slab. Let d represent the elastic modulus of a long-span, multi-ribbed concrete composite slab, where d denotes differentiation and z represents the Z-axis coordinate. This represents the shear force hysteresis displacement of the longitudinal ribs at the edge of the composite slab. This represents the shear force hysteresis displacement of the longitudinal rib at the center of the composite slab. The warping coordinates represent the longitudinal ribs at the edge of the composite slab. The warping coordinates of the longitudinal rib at the center of the composite slab; The shear hysteresis coefficient of a large-span multi-ribbed concrete composite slab is calculated based on the normal stress distribution. The formula is as follows: ； in, Indicates the shear hysteresis coefficient. B represents the effective width of the large-span multi-ribbed concrete composite slab, and B represents the actual width of the large-span multi-ribbed concrete composite slab. This indicates the maximum stress in the reinforcing steel of a large-span multi-ribbed concrete composite slab; when At that time, the flexural performance of the large-span multi-ribbed concrete composite slab is relatively weak. when At that time, the flexural performance of the large-span multi-ribbed concrete composite slab was of medium type. when At that time, the flexural resistance of the large-span multi-ribbed concrete composite slab is relatively strong.

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