Steel shear key-based prefabricated segment beam bridge joint shear capacity calculation method

Abstract

The invention discloses a method for calculating the shear capacity of a joint of a prefabricated segmental girder bridge based on a steel shear key, and belongs to the technical field of fabricated prefabricated segmental girder bridges. On the basis of a concrete local pressure bearing theory and a maximum shear stress failure criterion, the concrete local pressure bearing strength is corrected, and a shear bearing capacity calculation formula of a single steel shear key is established; according to the method, a theoretical stress model of the steel shear keys is constructed, a joint shear bearing capacity calculation formula based on the steel shear keys under the construction state of the fabricated prefabricated segmental girder bridge and a joint shear bearing capacity calculation formula under the bridge forming state are provided, and design refinement and design efficiency are improved; assuming that the main compression area of the steel shear key is the front # imgabs0 # / 2 part, so that the shear bearing capacity of the single steel shear key can be calculated more safely; the shear bearing capacity of the fabricated prefabricated segmental girder bridge based on the steel shear keys can be accurately calculated, and through comparison with an experimental value, it is verified that the calculation method is safe and reliable.

Description

Technical Field

[0001] The present invention relates to the technical field of precast segmental girder bridges, and particularly to a calculation method for the shear bearing capacity of joints of precast segmental girder bridges based on steel shear keys. Background Art

[0002] When designing precast segmental girder bridges, the mechanical properties at the joints are crucial. Existing research has shown that the failure at the joints has a significant impact on the mechanical characteristics and failure modes of segmental girders, and it has always been a key issue restricting the structural safety and economy. The test results of 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 show that the structural failure mainly concentrates near the joints. Currently, most joints of precast segmental girder bridges use plain concrete shear keys. In order to ensure uniform cross-section force, a large number of shear key teeth need to be arranged. If the arrangement is improper, it is easy to cause direct shear failure, and this structure is also not conducive to industrial production. In contrast, steel shear keys are favored due to their high bearing capacity and the advantage of simplifying the joint form, and have received extensive attention. In particular, the calculation and design of the shear bearing capacity at the joints, as a weak link between precast segments, its mechanical properties directly affect the overall stability of the bridge. Under complex loads and long-term service conditions, the accurate calculation of the shear bearing capacity is crucial.

[0003] However, how to accurately calculate the shear bearing capacity of joints of precast segmental girder bridges based on steel shear keys is still a technical problem to be solved urgently. The literature "Shear Performance and Construction Method Design of Steel Tenon Joints in Precast Segment Bridges" (Zou Yu, Duanmu Xiangyong, Song Bingquan, etc., Shear Performance and Construction Method Design of Steel Tenon Joints in Precast Segment Bridges [J], China Civil Engineering Journal, 2022, 55(10): 62-71) conducted direct shear tests on steel shear keys, and experimentally studied the crack development, failure mode, shear displacement, ultimate bearing capacity, residual bearing capacity, etc. of steel shear keys, but did not give relevant calculation and design methods. Therefore, the present invention proposes a calculation method for the shear bearing capacity of joints of precast segmental girder bridges 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 that there is currently no reasonable and accurate method to quickly calculate the shear bearing capacity at the joints of precast segmental girder bridges based on steel shear keys in the prior art, and provide a calculation method for the shear bearing capacity of joints of precast segmental girder bridges based on steel shear keys, so as to realize the simplified design of the structure and improve the connection reliability.

[0005] The present invention solves the above technical problem through the following technical solutions. The present invention includes the following steps:

[0006] Step S1: Based on the vertical and rotational deformations of the steel shear key, construct a theoretical stress model of the steel shear key and make relevant assumptions;

[0007] Step S2: According to the vertical force balance equation and the moment balance equation with the loading point as the centroid, solve the length of the stress distribution region of the steel shear key by simultaneous equations;

[0008] Step S3: Assume that the main compression region of the steel shear key is the first half of the stress distribution region, and the secondary compression region is the second half of the stress distribution region. Based on the local bearing theory of concrete and the maximum shear stress failure criterion, and correct the local bearing strength of concrete to obtain the shear bearing capacity of a single steel shear key and calculate it using the calculation formula;

[0009] Step S4: According to the calculation formula of the shear bearing capacity of a single steel shear key, obtain the calculation formula of the shear bearing capacity of the joint of the precast segmental girder bridge under the construction state and calculate it;

[0010] Step S5: According to the calculation formula of the shear bearing capacity of the joint of the precast segmental girder bridge under the construction state, superimpose the shear bearing capacity of the joint sealant at the joint to obtain the calculation formula of the shear bearing capacity of the joint of the precast segmental girder bridge in the completed bridge state and calculate it to realize the calculation of the shear bearing capacity of the joint.

[0011] Furthermore, in the step S1, the steel shear key includes a male key and a female key, which are respectively embedded in two adjacent precast girder segments to be assembled. When the girder segments are assembled, the joints are assembled and connected through the matching and alignment of the female key and the male key under the action of longitudinal prestress.

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

[0013] Furthermore, in the step S1, according to the assumption, the compressive stress borne by the steel shear key changes linearly, then:

[0014] ;

[0015] wherein, are the maximum compressive stress at the lower end and the maximum compressive stress at the upper end of the steel shear key, is the length of the region where the steel shear key bears upward stress, that is, the length of the stress distribution region of the steel shear key, and L is the embedding depth of the steel shear key.

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

[0017] ;

[0018] Among them, is the shear design value of the steel shear key. Taking the shear design value as the centroid, the moment balance equation of the loading point is:

[0019] ;

[0020] By solving the equations simultaneously, the length of the stress distribution region of the steel shear key is obtained as:

[0021] .

[0022] Further, in the step S3, the shear bearing capacity of a single steel shear key is calculated as follows:

[0023] ;

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

[0025] Further, in the step S4, the shear bearing capacity of the joint of the precast segmental girder bridge in the construction state is calculated as follows:

[0026] ;

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

[0028] Further, in the step S5, the shear bearing capacity of the joint of the precast segmental girder bridge in the completed bridge state is calculated as follows:

[0029] ;

[0030] Among them, is the joint cross-sectional area excluding the area of the steel shear key; is the average compressive stress of the joint cross-section.

[0031] The present invention has the following advantages compared with the prior art:

[0032] 1. 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.

[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 the present 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 the prefabricated segmental beam bridge based on steel shear keys. By comparing with the experimental values, it is verified that the calculation method is safe and reliable. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0037] Figure 2 is a schematic diagram of the structure of a steel shear key in an embodiment of the present invention;

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

[0039] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given, but 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, and the present invention comprises the following steps:

[0041] Step S1: Based on the existence of certain vertical and rotational deformations of the steel shear key, a theoretical force 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 by simultaneous calculation: for;

[0043] ;

[0044] Among them, is the length of the upward stress-bearing area of the steel shear key (both the concave key and the convex key bear upward stress, and here the steel shear key 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 first / 2 part, and the secondary compression area is the latter / 2 part. Based on the principle of interaction of forces, the local bearing theory of concrete and the maximum shear stress failure criterion, and by correcting the local bearing strength of concrete, the shear bearing capacity of a single steel shear key is obtained, and the calculation formula is:

[0046] ;

[0047] Among them, is the design value of the concrete compressive strength; B is the diameter of the steel shear key; A is the area at the root of the convex key of the steel shear key; is the design value of the steel strength of the steel shear key.

[0048] Step S4: Obtain the calculation formula for the shear bearing capacity of the joint of the precast segmental girder bridge under the construction state:

[0049] ;

[0050] Among them, is the number of steel shear keys, is the shear bearing capacity of the joint of the precast segmental girder bridge under the construction state.

[0051] Step S5: Superimpose the shear bearing capacity of the joint sealant at the joint to obtain the calculation formula for the shear bearing capacity of the joint of the precast segmental girder bridge in the completed bridge state:

[0052] ;

[0053] Among them, is the shear bearing capacity of the joint of the precast segmental girder bridge in the completed bridge state, is the cross-sectional area of the joint excluding the area of the steel shear key; is the average compressive stress of the joint cross-section.

[0054] In this embodiment, as Figure 2As shown in the figure, in step S1, the steel shear key includes a convex key and a concave key. The convex key includes a convex key anchor head and a cross-seam tooth, and the concave key includes a concave key anchor head and a bearing slot. The convex key and the concave key are respectively embedded in the precast segment beam 1 and the precast segment beam 2. During segment assembly, under the action of longitudinal prestress (internal tendon or external tendon), the joints are assembled and connected through the matching and alignment of the concave key and the convex key.

[0055] In this embodiment, in step S1, the following assumptions are made: It is assumed that the steel shear key will tend to move downward and rotate 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 borne by the steel shear key varies 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, according to the assumption that the compressive stress borne by the steel shear key varies linearly, there is:

[0057]

[0058] Among them, are the maximum compressive stress at the lower end and the maximum compressive stress at the upper end of the steel shear key, as shown in Figure 1 .

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

[0060] .

[0061] Among them, is the shear design value of the steel shear key. In this embodiment, in step S2, taking the shear design value as the centroid of the loading point, the moment balance equation is:

[0062] .

[0063] By solving the equations simultaneously, the length of the stress distribution area of the steel shear key is obtained as;

[0064] .

[0065] In this embodiment, in step S3, it is assumed that the main compression area of the steel shear key is the first / 2 part, so as to calculate the shear bearing capacity of a single steel shear key more safely.

[0066] Based on the literature "Shear Performance and Construction Method Design of Steel Tenon Joints in Prefabricated Segment Bridges" (Zou Yu, Duanmu Xiangyong, Song Bingquan, etc., Shear Performance and Construction Method Design of Steel Tenon Joints in Prefabricated Segment 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 test values. The results are shown in Table 1.

[0067] Table 1 Comparison of Bearing Capacities in the Direct Shear Test of Steel Shear Keys

[0068] As can be seen from Table 1, the experimental values of the dry joint specimens after deducting the interface friction are compared with the calculation results of the shear resistance bearing capacity formula of the joints of assembled precast segment bridges under the construction state, that is, the calculation results of the bearing capacity of steel shear keys (under the construction state) are compared. The ratio of the calculated value to the experimental value is 0.77; the experimental values of the glued joint specimens are compared with the calculation results of the shear resistance bearing capacity formula of the joints of assembled precast segment bridges under the completed bridge state, that is, the calculation results of the bearing capacity of the glued joints (under the completed bridge state) are compared. The ratio of the calculated value to the experimental value is 0.94. The comparison between the experimental values and the calculated values of the present invention is basically consistent, verifying the accuracy of the formula.

[0069] In summary, the calculation method for the shear resistance bearing capacity of the joints of assembled precast segment bridges based on steel shear keys in the above embodiments is based on the concrete local bearing theory and the maximum shear stress failure criterion, and the concrete local bearing strength is corrected to establish a calculation formula for the shear resistance bearing capacity of a single steel shear key; based on the fact that there are certain vertical and rotational deformations in the steel shear keys, a theoretical stress model of the steel shear keys is constructed, providing a calculation formula for the shear resistance bearing capacity of the joints of assembled precast segment bridges under the construction state based on steel shear keys, and a calculation formula for the shear resistance bearing capacity of the joints of assembled precast segment bridges under the completed bridge state, improving the refinement and design efficiency of the design; the present invention can accurately calculate the shear resistance bearing capacity of assembled precast segment bridges based on steel shear keys, and through comparison with the experimental values, the safety and reliability of the calculation method are verified.

[0070] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

Claims

1. A calculation method for the shear resistance of the joint of a precast segmental beam bridge based on steel shear keys, characterized in that It includes the following steps: Step S1: Based on the vertical and rotational deformations of the steel shear key, construct a theoretical stress model of the steel shear key and make relevant assumptions; Step S2: According to the vertical force balance equation and the moment balance equation with the loading point as the centroid, solve the length of the stress distribution area of the steel shear key by simultaneous equations; Step S3: Assume 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 and the calculation formula is calculated; Step S4: Obtain the calculation formula for the shear resistance bearing capacity of the joint of the prefabricated segmental girder bridge under the construction state according to the calculation formula for the shear resistance bearing capacity of a single steel shear key and perform the calculation; ​ Step S5: According to the calculation formula of the shear resistance capacity of the joints of the precast segmental girder bridge under the construction state superimpose the shear resistance capacity of the joint sealant at the joint to obtain the calculation formula of the shear resistance capacity of the joints of the precast segmental girder bridge in the completed bridge state and perform the calculation to realize the calculation of the shear resistance capacity of the joints.

2. The shear resistance calculation method for the joint of precast segmental girder bridges based on steel shear keys according to claim 1, characterized in that, In the step S1, the steel shear key includes a convex key and a concave key, which are respectively embedded in two adjacent precast segment beams to be assembled. When the beam segments are assembled, the assembly connection of the joint is realized through the matching of the concave key and the convex key under the action of longitudinal prestress.

3. The shear resistance calculation method for the joint of precast segmental girder bridges based on steel shear keys according to claim 1, characterized in that, In the step S1, the relevant assumptions are as follows: it is assumed that the steel shear key has a tendency to move downward and rotate 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 borne by the steel shear key changes linearly; it is assumed that the tensile stress between the concrete and the steel shear key is ignored.

4. The shear resistance calculation method for the joint of a precast segmental beam bridge based on steel shear keys according to claim 3, characterized in that, In the step S1, according to the assumption that the compressive stress borne by the steel shear key changes linearly, there is: ； Among them, are the maximum compressive stress at the lower end and the maximum compressive stress at 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 embedded depth of the steel shear key.

5. The shear resistance calculation method for the joint of a precast segmental beam bridge based on steel shear keys according to claim 4, characterized in that, In the step S2, the vertical force balance equation is: ； Among them, is the shear design value of the steel shear key. Taking the shear design value The moment equilibrium equation with the loading point as the centroid is: ； The length of the stress distribution region of the steel shear key is obtained by simultaneous solution as; 。 6. The shear resistance calculation method for the joint of a precast segmental girder bridge based on steel shear keys according to claim 5, wherein In the step S3, the shear bearing capacity of a single steel shear key is calculated as follows: ； Among them, is the design value of the concrete compressive strength; B is the diameter of the steel shear key; A is the area at the root of the convex key of the steel shear key; is the design value of the steel strength of the steel shear key.

7. The shear resistance calculation method for the joint of precast segmental girder bridges based on steel shear keys according to claim 6, characterized in that, In the step S4, the shear resistance capacity of the joints of the prefabricated segmental girder bridge under construction is calculated as follows: ； Among them, is the number of steel shear keys.

8. The shear resistance calculation method for the joint of precast segmental girder bridges based on steel shear keys according to claim 7, characterized in that, In the step S5, the shear resistance capacity of the joints of the assembled precast segmental beam bridge in the completed bridge state is calculated by the following formula: ； Among them, is the joint cross-sectional area after removing the area of the steel shear key; is the average compressive stress of the joint cross-section.

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