A method for calculating shear stiffness of concrete-short stud connectors

Abstract

The present invention belongs to bridge engineering technology, specifically a method for calculating the shear stiffness of a concrete-short bolt connector, including S1) establishing and assembling a three-dimensional finite element model of a steel beam, a concrete slab, a loading steel plate and a short bolt, defining the material properties, interaction relationships, analysis steps, unit types of the model, dividing the grid, defining constraints, and loading on the top surface of the loading steel plate; S2) creating a displacement path for the nodes on the lower side of the short bolt to obtain a displacement distribution curve; S3) fitting the short bolt deflection curve equation according to the displacement distribution curve; S4) using the energy method to calculate the deformation energy of the short bolt and the deformation energy of the concrete slab respectively; S5) calculating the shear stiffness k of the short bolt. This calculation method takes into account the displacement of the nail rod and the nail cap at the same time, is suitable for short bolt connectors, and the calculation results are more accurate and reasonable. This method can provide technical guidance for the reinforcement design of old orthotropic steel bridge decks and improve structural safety and economy.

Description

Technical Field

[0001] The invention belongs to bridge engineering technology, and in particular is a method for calculating the shear stiffness of a concrete-short bolt connector. Background Art

[0002] In the existing calculation of shear stiffness of short stud connectors, the applicable condition for short studs is that the aspect ratio h s / d≥2.1, where h s is the length of the short stud rod, d is the diameter of the short stud, that is, it is considered that during the deformation of the short stud, only the rod part undergoes vertical deformation, and the deformation gradually decreases along the direction of the rod, and the nail cap does not participate in the deformation. This type of short stud has a large aspect ratio and is only suitable for newly built ultra-high performance concrete-orthotropic steel bridge deck composite beams. When ultra-high performance concrete is used to reinforce old orthotropic steel bridge decks, the welding spacing of the short studs should not be too dense to reduce the impact of welding residual stress on the old bridge deck. At the same time, the ultra-high performance concrete pavement layer should not be too thick to reduce the self-weight of the bridge. In order to meet the shear connection degree of the composite bridge deck, short studs with a small aspect ratio are required to connect the ultra-high performance concrete pavement layer and the orthotropic steel bridge deck. Their aspect ratio usually cannot meet h. s / d≥2.1, the existing shear stiffness calculation method cannot be used for analysis. Summary of the invention

[0003] In order to solve the above problems, the present invention provides a method for calculating the shear stiffness of a concrete-short stud connector. A method for calculating the shear stiffness of a concrete-short stud connector comprises the following steps: S1) Establish and assemble a three-dimensional finite element model of the steel beam, concrete slab, loading steel plate and short studs, define the material properties, interaction relationships, analysis steps, unit types of the model, divide the mesh, define constraints, and load on the top surface of the loading steel plate; S2) creating a displacement path for the nodes below the short studs to obtain a displacement distribution curve; S3) fitting the short stud deflection curve equation according to the displacement distribution curve; S4) The energy method is used to calculate the deformation energy of the short studs and the deformation energy of the concrete slab respectively; S5) Calculate the shear stiffness k of the short stud.

[0004] In the above step S1, the method of defining the constraint conditions is: applying symmetrical displacement constraints to the xy plane and yz plane of the model respectively, applying a fixed constraint to the bottom surface, and loading a displacement load of 0.2 mm on the top surface of the loading steel plate.

[0005] The deflection curve equation ω(x) in the above step S3 is linearly fitted, and the formula is: ; Where h is the total length of the bolt and δ is the relative slip value at the root of the bolt.

[0006] In the above step S4, the calculation formulas for the deformation energy Us of the stud and the deformation energy Uc of the concrete slab are respectively: ; Where: E s is the elastic modulus of the short stud; d is the diameter of the short stud rod; d1 is the diameter of the short stud cap; h s is the length of the short stud; h is the total length of the short stud; ε c1 and c1 are the strain and strain energy density of the concrete slab under the nail rod, respectively; ε c2 and c2 are the strain and strain energy density of the concrete slab under the nail cap, respectively; E c is the elastic modulus of the concrete slab; L is the compressive depth of the concrete slab under the nail rod, L=6d; L1 is the compressive depth of the concrete slab under the nail cap, L1=6d1.

[0007] In the above step S5, the calculation method of the short stud shear stiffness k is: .

[0008] In the above-mentioned method for calculating the shear stiffness of the concrete-short bolt connector, the compressive strength of the concrete slab 2 is not less than 100 MPa, and the elastic modulus is not less than 40 MPa; the ratio of the nail rod length to the nail rod diameter of the short bolt is not greater than 1.21.

[0009] The beneficial effects of the present invention are as follows: the calculation method takes into account the displacement of the nail rod and the nail cap at the same time, is suitable for short stud connectors, and the calculation results are more accurate and reasonable. The method can provide technical guidance for the reinforcement design of old orthotropic steel bridge decks and improve the structural safety and economy. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a schematic diagram of a finite element model of an embodiment of the present invention; Figure 2 A schematic diagram of a steel beam according to an embodiment of the present invention; Figure 3 A schematic diagram of a concrete slab according to an embodiment of the present invention; Figure 4 A vertical displacement cloud diagram and a displacement path schematic diagram of an embodiment of the present invention; Figure 5 is a displacement distribution curve diagram of the short stud below the embodiment of the present invention; Figure 6 This is a deformation energy calculation model diagram of an embodiment of the present invention.

[0011] In the figure: 1 is a steel beam, 2 is a concrete slab, 4 is a loading steel plate, 11 is a nail cap, 12 is a nail rod, and 21 is a channel. DETAILED DESCRIPTION

[0012] The technical solution of the present invention is explained in detail below in conjunction with the accompanying drawings. The following embodiments are all illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical terms used have the same meanings as those commonly understood by those skilled in the art to which the present application belongs. It should be noted that the terms used are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application.

[0013] A method for calculating the shear stiffness of a concrete-short stud connector comprises the following steps: S1) establishing and assembling a three-dimensional finite element model of a steel beam 1, a concrete slab 2, a loading steel plate 4 and short studs, defining material properties, interaction relationships, analysis steps, unit types of the model, dividing the mesh, defining constraint conditions, and performing loading on the top surface of the loading steel plate 4; S2) creating a displacement path for the nodes below the short studs to obtain a displacement distribution curve; S3) fitting the short stud deflection curve equation according to the displacement distribution curve; S4) using the energy method to calculate the deformation energy of the short studs and the deformation energy of the concrete slab 2 respectively; S5) Calculate the shear stiffness k of the short stud.

[0014] In the above step S1 , the method of defining the constraint conditions is: applying symmetrical displacement constraints to the xy plane and yz plane of the model respectively, applying a fixed constraint to the bottom surface, and loading a displacement load of 0.2 mm on the top surface of the loading steel plate 4 .

[0015] The deflection curve equation ω(x) in the above step S3 is linearly fitted, and the formula is: ; Wherein, h is the total length of the bolt; δ is the relative slip value at the root of the bolt rod 12.

[0016] In the above step S4, the calculation formulas for the deformation energy Us of the stud and the deformation energy Uc of the concrete slab are respectively: ; Where: E s is the elastic modulus of the short stud; d is the diameter of the short stud's nail rod 12; d1 is the diameter of the short stud's nail cap 11; h s is the length of the nail rod 12 of the short bolt; h is the total length of the short bolt; ε c1 and c1 are the strain and strain energy density of the concrete slab below the nail rod 12, respectively; εc2 and c2 are the strain and strain energy density of the concrete slab under the nail cap 11; E c is the elastic modulus of the concrete slab; L is the compression depth of the concrete slab below the nail rod 12, L=6d; L1 is the compression depth of the concrete slab below the nail cap 11, L1=6d1.

[0017] In the above step S5, the calculation method of the short stud shear stiffness k is: .

[0018] The compressive strength of the concrete slab 2 is not less than 100 MPa, and the elastic modulus is not less than 40 MPa. The ratio of the length of the nail rod 12 of the short bolt to the diameter of the nail rod 12 is not greater than 1.21.

[0019] In a specific embodiment, a three-dimensional finite element model of each component is established and assembled as follows: Figure 1 As shown, it includes a steel beam 1, a concrete slab 2, a steel mesh, and a loading steel plate 4, wherein the steel beam 1 is provided with short bolts, the concrete slab 2 is an ultra-high performance concrete slab, the concrete slab 2 is provided with a hole 21 for matching the short bolts, the loading steel plate 4 is arranged on the top surface of the steel beam 1, and the steel mesh is built into the concrete slab 2. In this embodiment, the compressive strength of the concrete slab 2 is 134MPa, the tensile strength is 9MPa, and the elastic modulus is 48.2MPa; the elastic modulus of the short bolt is 210GPa, the diameter of the nail rod 12 is d=19mm, and the length of the nail rod 12 is h s =23mm, the diameter of the nail cap 11 d1=32 mm, the total length of the short nail h=35mm, the aspect ratio h s / d=1.21.

[0020] A vertical displacement load is applied to the top surface of the loading steel plate 4, and the displacement value is 0.2 mm. The displacement calculation result is as follows: Figure 4 As shown in the figure, a displacement path is created for the nodes below the short studs, and the displacement distribution curve is obtained as shown in Figure 5 As shown, the nail rod 12 and the nail cap 11 of the short bolt are both displaced and deformed, and the displacement gradually decreases along the length direction of the short bolt, and is approximately linearly distributed, fitting the deflection curve equation ω(x) of the short bolt: .

[0021] The energy method is used to calculate the deformation energy of the short stud and the deformation energy of the concrete slab 2, and U s =276δ 2 kN·mm,U c =93δ 2 kN·mm, the specific calculation formula is as follows: .

[0022] According to the formula The shear stiffness of the short stud is obtained to be k=738kN / mm.

[0023] The above are only preferred implementations of the present application. It should be pointed out that for ordinary technicians in this technical field, several changes or improvements can be made without departing from the principles of the present application. These changes or improvements should also be regarded as the scope of protection of the present application.

Claims

1. A method for calculating the shear stiffness of a concrete-short stud connector, characterized in that: The following steps are involved: S1) establishing and assembling a three-dimensional finite element model of a steel beam (1), a concrete slab (2), a loading steel plate (4) and a short bolt, defining the material properties, interaction relationships, analysis steps, and unit types of the model, dividing the mesh, defining constraint conditions, and performing loading on the top surface of the loading steel plate (4); S2) creating a displacement path for the nodes below the short studs to obtain a displacement distribution curve; S3) fitting the short stud deflection curve equation according to the displacement distribution curve; S4) using the energy method to calculate the deformation energy of the short studs and the deformation energy of the concrete slab (2); S5) Calculate the shear stiffness k of the short stud.

2. The method for calculating the shear stiffness of a concrete-short stud connector according to claim 1, characterized in that: In the above step S1, the method of defining the constraint conditions is: applying symmetrical displacement constraints to the xy plane and yz plane of the model respectively, applying a fixed constraint to the bottom surface, and applying a displacement load of 0.2 mm on the top surface of the loading steel plate (4).

3. The method for calculating shear stiffness of a concrete-short stud connector according to claim 1, characterized in that: The deflection curve equation ω(x) in the above step S3 is linearly fitted, and the formula is: ； Where h is the total length of the bolt and δ is the relative slip value at the root of the bolt rod (12).

4. The method for calculating shear stiffness of a concrete-short stud connector according to claim 1, characterized in that: In the above step S4, the calculation formulas for the deformation energy Us of the stud and the deformation energy Uc of the concrete slab are respectively: ； Where: E s is the elastic modulus of the short bolt; d is the diameter of the bolt rod (12) of the short bolt; d1 is the diameter of the bolt cap (11) of the short bolt; h s is the length of the nail rod (12) of the short bolt; h is the total length of the short bolt; ε c1 and c1 are the strain and strain energy density of the concrete slab under the nail rod (12), respectively; ε c2 and c2 are the strain and strain energy density of the concrete slab under the nail cap (11); E c is the elastic modulus of the concrete slab; L is the compression depth of the concrete slab below the nail rod (12), L=6d; L1 is the compression depth of the concrete slab below the nail cap (11), L1=6d1.

5. The method for calculating shear stiffness of a concrete-short stud connector according to claim 1, characterized in that: In the above step S5, the calculation method of the short stud shear stiffness k is: .

6. The method for calculating shear stiffness of a concrete-short stud connector according to claim 1, characterized in that: The compressive strength of the concrete slab 2 is not less than 100 MPa, and the elastic modulus is not less than 40 MPa; the aspect ratio of the nail rod (12) of the short bolt is not greater than 1.21.

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