Calculation method of shear bearing capacity of joints in precast segmental beam bridges based on steel shear keys

Abstract

The present invention discloses a method for calculating the shear bearing capacity of joints of prefabricated segmental beam bridges based on steel shear keys, and belongs to the technical field of prefabricated segmental beam bridges. Based on the local bearing pressure theory of concrete and the maximum shear stress failure criterion, the present invention corrects the local bearing pressure strength of concrete and establishes a calculation formula for the shear bearing capacity of a single steel shear key; constructs a theoretical force model of steel shear keys, and provides a calculation formula for the shear bearing capacity of joints of prefabricated segmental beam bridges based on steel shear keys under construction status, as well as a calculation formula for the shear bearing capacity of joints in the completed bridge status, thereby improving the refinement and efficiency of the design; assumes that the main compression area of ​​the steel shear key is the front #imgabs0# / 2 part, so that the shear bearing capacity of a single steel shear key can be calculated more safely; can accurately calculate the shear bearing capacity of prefabricated segmental beam bridges based on steel shear keys, and verifies the safety and reliability of the calculation method by comparison with experimental values.

Description

Technical Field

[0001] The present invention relates to the technical field of assembled prefabricated segmental beam bridges, and specifically to a method for calculating the shear bearing capacity of prefabricated segmental beam bridge joints based on steel shear keys. Background Art

[0002] The mechanical properties of joints are crucial in the design of precast segmental beam bridges. Previous studies have shown that joint failure significantly affects the mechanical properties and failure modes of segmental beams, and remains a key issue restricting structural safety and economic efficiency. Tests on Moustafa's 9-segment I-beam with a span of 28m and Takebayashi's 14-segment box girder with a span of 40.8m both indicate that structural failure is primarily concentrated near the joints. Currently, most precast segmental beam bridges utilize plain concrete shear keys for joints. To ensure uniform cross-sectional load distribution, numerous shear key teeth must be arranged. Improper placement can easily lead to direct shear failure, and this construction is also unsuitable for industrial production. In contrast, steel shear keys, due to their high load-bearing capacity and simplified joint configuration, have attracted widespread attention. The calculation and design of the shear resistance of joints, particularly those at the weakest link between precast segments, directly impact the overall stability of the bridge. Accurate calculation of shear resistance is crucial under complex loading conditions and long-term service.

[0003] However, how to accurately calculate the shear bearing capacity of prefabricated segmental beam bridge joints based on steel shear keys remains a technical challenge that needs to be solved urgently. The document "Shear Performance and Construction Method Design of Steel Tenon Key Joints in Prefabricated Segmental Bridges" (Zou Yu, Duanmu Xiangyong, Song Bingquan, et al., Shear Performance and Construction Method Design of Steel Tenon Key Joints in Prefabricated Segmental Bridges [J], China Civil Engineering Journal, 2022, 55(10):62-71) conducted direct shear tests on steel shear keys and conducted experimental research on the crack development, failure mode, shear displacement, ultimate bearing capacity, and residual bearing capacity of steel shear keys, but did not provide relevant calculation and design methods. To this end, the present invention proposes a method for calculating the shear bearing capacity of prefabricated segmental beam bridge joints based on steel shear keys. Summary of the Invention

[0004] The technical problem to be solved by the present invention is: how to solve the problem in the prior art that there is currently no reasonable and accurate method to quickly calculate the shear bearing capacity of the joints of prefabricated segmental beam bridges based on steel shear keys. A method for calculating the shear bearing capacity of the joints of prefabricated segmental beam bridges based on steel shear keys is provided, thereby achieving simplified structural design and improving connection reliability.

[0005] The present invention solves the above technical problems through the following technical solutions, which include the following steps:

[0006] Step S1: Based on the existence of vertical and rotational deformations of the steel shear key, a theoretical stress model of the steel shear key is constructed and relevant assumptions are made;

[0007] Step S2: Calculate the length of the stress distribution area of ​​the steel shear key based on the vertical force balance equation and the bending moment balance equation with the loading point as the centroid;

[0008] Step S3: Assuming that the main compression area of ​​the steel shear key is the first half of the stress distribution area and the secondary compression area is the second half of the stress distribution area, based on the concrete local bearing theory and the maximum shear stress failure criterion, and correcting the concrete local bearing strength, the shear bearing capacity of a single steel shear key is obtained. The calculation formula and calculation are performed;

[0009] Step S4: According to the shear bearing capacity of a single steel shear key The calculation formula is used to obtain the shear bearing capacity of the joints of prefabricated segmental beam bridges under construction. The calculation formula and calculation are performed;

[0010] Step S5: Based on the shear bearing capacity of the joints of the prefabricated segmental beam bridge under construction The calculation formula of the joint glue shear bearing capacity is superimposed to obtain the joint shear bearing capacity of the prefabricated segmental beam bridge in the completed state. The calculation formula is used to calculate the shear bearing capacity of the butt joint.

[0011] Furthermore, in step S1, the steel shear key includes a convex key and a concave key, which are respectively embedded in two adjacent prefabricated segment beam sections that need to be assembled. When the beam sections are assembled, the joints are assembled and connected by matching the concave key and the convex key under the action of longitudinal prestress.

[0012] Furthermore, in step S1, the relevant assumptions are as follows: it is assumed that the steel shear key will have a tendency to rotate downward and counterclockwise, and the surrounding concrete can ensure the balance of the steel shear key; it is assumed that the surrounding concrete provides elastic support for the steel shear key, and the compressive stress on the steel shear key changes linearly; it is assumed that the tensile stress between the concrete and the steel shear key is ignored.

[0013] Furthermore, in step S1, based on the assumption that the compressive stress on the steel shear key changes linearly, we have:

[0014] ;

[0015] in, is the maximum compressive stress at the lower end and the upper end of the steel shear key, is the length of the area where the steel shear key bears upward stress, that is, the length of the stress distribution area of ​​the steel shear key, and L is the buried depth of the steel shear key.

[0016] Furthermore, in step S2, the vertical force balance equation is:

[0017] ;

[0018] in, is the shear force design value of the steel shear key, The moment equilibrium equation with the loading point as the centroid is:

[0019] ;

[0020] Calculate the length of the stress distribution area of ​​the steel shear key by combining for;

[0021] .

[0022] Furthermore, in step S3, the shear bearing capacity of a single steel shear key is The calculation formula is as follows:

[0023] ;

[0024] in, is the design value of concrete compressive strength; B is the diameter of the steel shear key; A is the area of ​​the root of the steel shear key; is the design value of steel strength of steel shear key.

[0025] Furthermore, in step S4, the shear bearing capacity of the joints of the prefabricated segmental beam bridge under construction is The calculation formula is as follows:

[0026] ;

[0027] in, is the number of steel shear keys.

[0028] Furthermore, in step S5, the shear bearing capacity of the joints of the prefabricated segmental beam bridge in the completed state is The calculation formula is as follows:

[0029] ;

[0030] in, is the cross-sectional area of ​​the joint after removing the steel shear key area; is the average compressive stress in the joint section.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] 1. Based on the local bearing pressure theory of concrete and the maximum shear stress failure criterion, the present invention modifies the local bearing pressure strength of concrete and establishes a calculation formula for the shear bearing capacity of a single steel shear key.

[0033] 2. Based on the fact that steel shear keys have certain vertical and rotational deformations, the present invention constructs a theoretical force model of steel shear keys, provides a calculation formula for the shear bearing capacity of joints in the construction state of prefabricated segmental beam bridges based on steel shear keys, and provides a calculation formula for the shear bearing capacity of joints in the completed bridge state, thereby improving the refinement and efficiency of the design.

[0034] 3. The main compression area of ​​the steel shear key assumed in this invention is the front / 2 part, thus making it safer to calculate the shear capacity of a single steel shear key.

[0035] 4. The present invention can accurately calculate the shear bearing capacity of prefabricated segmental beam bridges based on steel shear keys. By comparing with experimental values, the calculation method is verified to be safe and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of a theoretical stress model of a steel shear key according to an embodiment of the present invention;

[0037] Figure 2 2 is a schematic structural diagram of a steel shear key according to an embodiment of the present invention;

[0038] Figure 3 It is a flow chart of the method for calculating the shear bearing capacity of the joints of prefabricated segmental beam bridges based on steel shear keys of the present invention. DETAILED DESCRIPTION

[0039] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process. However, the protection scope of the present invention is not limited to the following embodiment.

[0040] like Figure 3 As shown, the present invention solves the above technical problems through the following technical solutions, which include the following steps:

[0041] Step S1: Based on the existence of certain vertical and rotational deformations of the steel shear key, a theoretical stress model of the steel shear key is constructed and relevant assumptions are made;

[0042] Step S2: Based on the vertical force balance equation and the moment balance equation with the loading point as the centroid, the length of the stress distribution area of ​​the steel shear key is obtained. for;

[0043] ;

[0044] in, is the length of the area where the steel shear key is subjected to upward stress (both the concave key and the convex key are subjected to upward stress, and the steel shear key here includes the concave key and the convex key), and L is the embedded depth of the steel shear key.

[0045] Step S3: Assume that the main compression area of ​​the steel shear key is the front / 2 part, the secondary pressure area is the rear / 2, based on the principle of force interaction, the theory of local bearing of concrete and the maximum shear stress failure criterion, and the correction of the local bearing strength of concrete, the shear bearing capacity of a single steel shear key is obtained The calculation formula is:

[0046] ;

[0047] in, is the design value of concrete compressive strength; B is the diameter of the steel shear key; A is the area of ​​the root of the steel shear key; is the design value of steel strength of steel shear key.

[0048] Step S4: Obtaining the shear bearing capacity of the joints of the prefabricated segmental beam bridge under construction The calculation formula is:

[0049] ;

[0050] in, is the number of steel shear keys, It is the shear bearing capacity of the joints of prefabricated segmental beam bridges under construction.

[0051] Step S5: Superimpose the shear bearing capacity of the joint glue at the joint to obtain the shear bearing capacity of the joint of the prefabricated segmental beam bridge in the completed state The calculation formula is:

[0052] ;

[0053] in, is the shear bearing capacity of the joints of prefabricated segmental beam bridges in the completed state. is the cross-sectional area of ​​the joint after removing the steel shear key area; is the average compressive stress in the joint section.

[0054] In this embodiment, if Figure 2As shown, in step S1, the steel shear key includes a convex key and a concave key, wherein the convex key includes a convex key anchor head and a span tooth, and the concave key includes a concave key anchor head and a socket. The convex key and the concave key are respectively embedded in the prefabricated segment beam section 1 and the prefabricated segment beam section 2. When the segments are assembled, the joints are assembled and connected by matching the concave key and the convex key under the action of longitudinal prestress (internal beam or external beam).

[0055] In this embodiment, in step S1, the relevant assumptions are as follows: it is assumed that the steel shear key will have a tendency to rotate downward and counterclockwise, and the surrounding concrete can ensure the balance of the steel shear key; it is assumed that the surrounding concrete provides elastic support for the steel shear key, and the compressive stress on the steel shear key changes linearly; it is assumed that the tensile stress between the concrete and the steel shear key is ignored.

[0056] In this embodiment, in step S1, it is assumed that the compressive stress on the steel shear key changes linearly, so:

[0057]

[0058] in, is the maximum compressive stress at the lower end and the upper end of the steel shear key, see Figure 1 .

[0059] In this embodiment, in step S2, the vertical force balance equation is:

[0060] .

[0061] in, is the shear force design value of the steel shear key. In this embodiment, in step S2, the shear force design value The moment equilibrium equation with the loading point as the centroid is:

[0062] .

[0063] Calculate the length of the stress distribution area of ​​the steel shear key by combining for;

[0064] .

[0065] In this embodiment, in step S3, it is assumed that the main compression area of ​​the steel shear key is the front The / 2 part thus allows for a safer calculation of the shear capacity of a single steel shear key.

[0066] Based on the literature “Shear performance and construction method design of steel mortise and tenon joints in precast segmental bridges” (Zou Yu, Duanmu Xiangyong, Song Bingquan, et al., Shear performance and construction method design of steel mortise and tenon joints in precast segmental bridges [J], China Civil Engineering Journal, 2022, 55(10): 62-71), a direct shear test of steel shear keys was carried out and the calculated values ​​were compared with the measured values. The results are shown in Table 1.

[0067] Table 1 Comparison of bearing capacity of steel shear keys in direct shear test

[0068] As can be seen from Table 1, the experimental values ​​of the dry joint specimens after deducting the interface friction force were compared with the calculation results of the calculation formula for the shear bearing capacity of the joints of prefabricated segmental beam bridges in the construction state, that is, the calculation results of the steel shear key bearing capacity (construction state). The ratio of the calculated value to the experimental value was 0.77; the experimental values ​​of the adhesive joint specimens were compared with the calculation results of the calculation formula for the shear bearing capacity of the joints of prefabricated segmental beam bridges in the completed bridge state, that is, the calculation results of the adhesive joint bearing capacity (completed bridge state). The ratio of the calculated value to the experimental value was 0.94. The comparison experimental values ​​were basically consistent with the calculated values ​​of the present invention, verifying the accuracy of the formula.

[0069] To sum up, the method for calculating the shear bearing capacity of joints of prefabricated segmental beam bridges based on steel shear keys in the above-mentioned embodiment is based on the local bearing theory of concrete and the maximum shear stress failure criterion, and corrects the local bearing strength of concrete to establish a calculation formula for the shear bearing capacity of a single steel shear key; based on the existence of certain vertical and rotational deformations of steel shear keys, a theoretical force model of steel shear keys is constructed, and a calculation formula for the shear bearing capacity of joints of prefabricated segmental beam bridges based on steel shear keys under construction status and a calculation formula for the shear bearing capacity of joints of prefabricated segmental beam bridges under the completed bridge status are provided, thereby improving the refinement and design efficiency of the design; the present invention can accurately calculate the shear bearing capacity of prefabricated segmental beam bridges based on steel shear keys, and verifies the safety and reliability of the calculation method by comparison with experimental values.

[0070] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the shear bearing capacity of precast segmental beam bridge joints based on steel shear keys, characterized in that: The following steps are involved: Step S1: Based on the existence of vertical and rotational deformations of the steel shear key, a theoretical stress model of the steel shear key is constructed and relevant assumptions are made; Step S2: Based on the vertical force balance equation and the bending moment balance equation with the loading point as the centroid, the length of the area where the steel shear key bears the upward stress is obtained; Step S3: Assuming that the main compression area of ​​the steel shear key is the first half of the stress distribution area and the secondary compression area is the second half of the stress distribution area, based on the concrete local bearing theory and the maximum shear stress failure criterion, and correcting the concrete local bearing strength, the shear bearing capacity of a single steel shear key is obtained. The calculation formula and calculation are performed; In step S3, the shear bearing capacity of a single steel shear key is The calculation formula is as follows: ;in, is the design value of concrete compressive strength; B is the diameter of the steel shear key; A is the area of ​​the root of the steel shear key; is the design value of steel strength of steel shear key, is the length of the area where the steel shear key bears upward stress; Step S4: According to the shear bearing capacity of a single steel shear key The calculation formula is used to obtain the shear bearing capacity of the joints of prefabricated segmental beam bridges under construction. The calculation formula and calculation are performed; Step S5: Based on the shear bearing capacity of the joints of the prefabricated segmental beam bridge under construction The calculation formula of the joint glue shear bearing capacity is superimposed to obtain the joint shear bearing capacity of the prefabricated segmental beam bridge in the completed state. The calculation formula is used to calculate the shear bearing capacity of the butt joint.

2. The method for calculating the shear bearing capacity of precast segmental beam bridge joints based on steel shear keys according to claim 1 is characterized in that: In step S1, the steel shear key includes a convex key and a concave key, which are respectively embedded in two adjacent prefabricated segment beam sections that need to be assembled. When the beam sections are assembled, the concave key and the convex key are matched and aligned under the action of longitudinal prestress to achieve the assembly connection of the joints.

3. The method for calculating the shear bearing capacity of precast segmental beam bridge joints based on steel shear keys according to claim 1 is characterized in that: In step S1, the following assumptions are made: the steel shear key is assumed to have a tendency to rotate downward and counterclockwise, and the surrounding concrete is capable of ensuring the balance of the steel shear key; the surrounding concrete is assumed to provide elastic support for the steel shear key, and the compressive stress on the steel shear key changes linearly; and the tensile stress between the concrete and the steel shear key is assumed to be negligible.

4. The method for calculating the shear bearing capacity of precast segmental beam bridge joints based on steel shear keys according to claim 3 is characterized in that: In step S1, it is assumed that the compressive stress on the steel shear key changes linearly, so: ; in, is the maximum compressive stress at the lower end and the upper end of the steel shear key, is the length of the area where the steel shear key bears upward stress, and L is the embedding depth of the steel shear key.

5. The method for calculating the shear bearing capacity of precast segmental beam bridge joints based on steel shear keys according to claim 4 is characterized in that: In step S2, the vertical force balance equation is: ; in, is the shear force design value of the steel shear key, The moment equilibrium equation with the loading point as the centroid is: ; Combined calculation to obtain the length of the area where the steel shear key bears upward stress for: .

6. The method for calculating the shear bearing capacity of precast segmental beam bridge joints based on steel shear keys according to claim 1 is characterized in that: In step S4, the shear bearing capacity of the joints of the prefabricated segmental beam bridge under construction is The calculation formula is as follows: ;in, is the number of steel shear keys.

7. The method for calculating the shear bearing capacity of precast segmental beam bridge joints based on steel shear keys according to claim 6, characterized in that: In step S5, the shear bearing capacity of the joints of the prefabricated segmental beam bridge in the completed state is The calculation formula is as follows: ;in, is the cross-sectional area of ​​the joint after removing the steel shear key area; is the average compressive stress in the joint section.

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