A method for determining the failure mode of three-point bending of physically asymmetric double steel plate-concrete composite beams

Abstract

The present application specifically relates to a method for determining the three-point bending failure mode of a physically asymmetric double steel plate-concrete composite beam. The method first calculates the position of the neutral plane by obtaining the geometric and physical parameters of the composite beam to determine the interval of the subsequent failure load, then calculates the expression of the critical failure load of the composite beam and establishes a failure mode determination diagram based on the minimum value of the critical failure load, and finally determines its failure mode based on the geometric parameters of the composite beam to be determined. The present application makes up for the deficiency of the prior art in the determination of the failure mode of physically asymmetric double steel plate composite beams. The present application can determine the failure modes of composite beams of different sizes with different yield strengths of the upper and lower steel plates.

Description

Technical Field

[0001] The present application belongs to the field of computer material science, and specifically relates to a method for determining a three-point bending failure mode of a physically asymmetric double steel plate-concrete composite beam. Background Art

[0002] There are two structures in the disclosed failure mode determination method of double steel plate-concrete composite beam. One is a symmetrical double steel plate-concrete composite beam, that is, the thickness and material properties of the upper and lower steel plates are the same; the other is an asymmetric double steel plate-concrete composite beam, that is, the thickness of the upper and lower steel plates is different, but the material properties are the same. The determination of the failure mode of the upper and lower steel plates with different or same thickness is carried out at the geometric level. In practical applications, the thickness of the steel plate can be subjectively designed according to engineering requirements. When the thickness of the steel plate is insufficient, the steel plate can be replaced or thickened. Considering factors such as the dead weight of the component, the fixing method, and the matching size, the steel plate cannot be thickened blindly. Therefore, the design only at the geometric level cannot adapt to all working conditions, and it is impossible to comprehensively determine whether the composite beam meets the design requirements. In addition, the yield strength of the steel plate has multiple standards. It cannot design the required yield strength by itself like the thickness, but giving a yield strength limit to determine whether the actual steel plate meets the requirements is a feasible way. For the above problems, the prior art does not provide a method for determining the failure mode of the composite beam from the material level. Summary of the invention

[0003] To solve the above problems, the present invention provides a method for determining the three-point bending failure mode of a physically asymmetric double steel plate-concrete composite beam, and provides a method for determining the three-point bending failure mode of a double steel plate-concrete composite beam with different yield strengths from a material level.

[0004] The technical solution of the present invention is as follows:

[0005] A method for determining a three-point bending failure mode of a physically asymmetric double steel plate-concrete composite beam comprises the following steps:

[0006] Step 1: Obtain the geometric parameters and physical parameters of the double steel plate-concrete composite beam;

[0007] The geometric parameters include: the beam span extension length H , distance from the fulcrum to the center line of the core L , steel plate thickness h , core material height c , deflection at the loading position W , core material width b ;

[0008] After non-dimensionalizing the geometric parameters, we get: relative thickness , height-to-length ratio , relative extension length ;

[0009] in: , , ;

[0010] The physical parameters include: yield strength of the upper steel plate , yield strength of lower steel plate , concrete compressive strength , concrete tensile strength , concrete shear strength ;

[0011] After non-dimensionalizing the physical parameters, we get: tensile and compressive strength ratio , relative compressive strength , shear ratio , yield strength factor ;

[0012] in: , , , .

[0013] Step 2: Determine the position of the neutral plane;

[0014] The physical neutral plane of a physically asymmetric double-plate composite beam will change when the geometric dimensions and material properties of the material change. For ease of calculation and understanding, the vertical coordinate of the physical neutral plane is defined as z p , it can be obtained from the cross-sectional equilibrium condition z p Relationship with material parameters.

[0015] The section equilibrium condition is:

[0016] ;

[0017] z p for:

[0018] ;

[0019] For ease of presentation and understanding, z p The expression is converted into the yield strength factor express:

[0020] ;

[0021] From the above formula, we can know that:

[0022] when When , the neutral plane is located inside the upper steel plate;

[0023] when When , the neutral plane is located inside the lower steel plate;

[0024] when When , the neutral plane is located in the concrete above the horizontal mid-section of the concrete;

[0025] when When the neutral plane is located in the concrete below the horizontal mid-section of the concrete.

[0026] Step 3: Calculate the critical failure load .

[0027] Critical failure load include , , .

[0028] in, represents the critical load for bending failure, represents the critical load for partial shear failure; It represents the critical load of shear failure of the whole section;

[0029] in, It is defined as the failure load when the bending moment of the double steel plate-concrete composite beam reaches the plastic limit bending moment. It is defined as the failure load corresponding to the shear crack extending throughout the concrete core and generating plastic hinges only at the loading position; It is defined as the corresponding failure load when plastic hinge is generated at the loading position and support of the steel plate;

[0030] After determining the position of the neutral plane, the failure load when the double steel plate-concrete composite beam reaches the plastic limit bending moment is determined according to the functional relationship, that is, .

[0031] ;

[0032] in, represents the fully plastic bending moment, and its expression is represents the critical load before bending failure which is dimensionless.

[0033] ;

[0034] According to the dimensionless formula of load, it can be obtained:

[0035] ;

[0036] The dimensionless formula is:

[0037] ;

[0038] in, P represents the critical load before becoming dimensionless; represents the dimensionless critical load.

[0039] Similarly, according to the energy conservation formula:

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] Can be obtained separately and The expression is:

[0045] ;

[0046] .

[0047] Step 4: is the horizontal axis, is the vertical coordinate, drawn in the same coordinate system , , about and curve, and take the minimum value of the three curves to form the failure mode determination diagram.

[0048] Generally speaking, and , The area formed is small, so it can be omitted in practical applications , directly draw . Things that need to be explained, and The formula is the same over the entire interval, and Different expressions need to be used in different intervals.

[0049] Step 5: Calculate the height-to-length ratio and relative thickness of the concrete composite beam and compose the coordinates, and judge the failure mode according to the position in the failure mode determination diagram according to the composed coordinates.

[0050] It should be noted that the yield strength factor of the failure mode determination diagram in step 4 is The yield strength factor of the concrete composite beam to be determined is the same but the geometric dimensions are different. Because the yield strength of the steel plate is of a universal grade, it is more meaningful to establish a failure mode determination diagram in advance, which is also in line with the logic of component design.

[0051] Furthermore, the core material of the double steel plate-concrete composite beam is ordinary concrete, high performance concrete or ultra-high performance concrete.

[0052] Due to the adoption of the above technical solution, the beneficial effects of the present invention are as follows:

[0053] 1. Since the yield strength of steel has a universal grade, the present application can calculate the yield strength of the steel plates commonly used in the project in advance, thereby providing a failure mode determination diagram in advance, and then determine its failure mode specifically according to the actual component size of the project. This determination method is scalable, forward-looking and highly efficient.

[0054] 2. This application can be passed through multiple groups The value can be used to judge the changing trend of failure modes and provide guidance for practical engineering.

[0055] 3. This application is approved by a group The failure mode of components of different sizes can be determined by the value, which is convenient and quick. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0057] Figure 1 A schematic diagram of three-point bending loading of a physically asymmetric double steel plate-concrete composite beam in this application;

[0058] Figure 2 This is a failure mode determination diagram of Example 1 in this application;

[0059] Figure 3 This is the damage cloud map of Example 2 in this application;

[0060] Figure 4 This is the damage cloud map of Example 3 in this application. DETAILED DESCRIPTION

[0061] Embodiment 1:

[0062] The engineering laboratory uses a double steel plate-concrete composite beam with the same upper and lower thickness but different yield strength. The geometric parameters of the composite beam are H= 500mm, L= 2500mm, h= 15mm, c=1500mm;

[0063] Physical parameters include: 375Mp a， 545MPa, 143.2Mpa, 8.1Mpa, 8.1Mpa;

[0064] After dimensionless transformation, we get: 0.01, 0.6, 0.6; β =0.688;

[0065] Will be removed and Substitute the geometric and physical parameters into the following formula to calculate the critical load of bending failure , Partial shear failure critical load , Full-section shear failure critical load ;

[0066] ;

[0067] ;

[0068] ;

[0069] make , , The formula is as follows:

[0070] :

[0071] ;

[0072] :

[0073] ;

[0074] :

[0075] ;

[0076] As attached Figure 2 As shown, the failure mode determination diagram of this embodiment is the minimum value after the three curves are superimposed. The area is small, and this embodiment only and In this embodiment, according to 0.01, 0.6, can be found in the attached Figure 2 It is concluded that the failure mode of the composite beam is bending failure.

[0077] Embodiment 2:

[0078] The engineering laboratory uses a double steel plate-concrete composite beam with the same upper and lower thickness but different yield strength. The geometric parameters of the composite beam include: H= 500mm, L= 500mm, h= 15mm, c= 150mm;

[0079] Physical parameters include: 375Mpa, 545MPa, 143.2Mpa, 8.1Mpa, 8.1Mpa;

[0080] After dimensionless, we get: 0.1, 0.3, 0.2, β =0.688;

[0081] In this embodiment, the failure mode determination diagram may not be established to directly calculate the failure load. When determining, the neutral axis position selection needs to be calculated. The expression of =0.00616 =0.0068 =0.0062. From the failure load results, it can be seen that and The calculation results are similar to those of , indicating that the failure mode of the composite beam is in the transition stage between bending failure and full-section shear failure. The composite beam was numerically simulated using finite element software, and the simulation results are shown in the attached figure. Figure 3 As shown, from Figure 3 It can be seen that the damaged part of the composite beam is transitioning to the core material part, which is consistent with the judgment result of the failure mode.

[0082] Example 3: The engineering laboratory uses a double steel plate-concrete composite beam with the same upper and lower thicknesses but different yield strengths. The geometric parameters of the composite beam include: H= 60mm, L= 300mm, h= 15mm, c= 60mm;

[0083] Physical parameters include: 375Mpa, 545MPa, 143.2Mpa, 8.1Mpa, 8.1Mpa;

[0084] After dimensionless, we get: 0.25, 0.2, 0.2, β =1.58;

[0085] Direct calculation =0.011 =0.0061 =0.0056, the composite beam was simulated using finite element software, and the simulation results are shown in the attached Figure 4 As shown by Figure 4 It can be seen that the core material completely failed in shear, which is consistent with expectations.

[0086] Anything not described in this application can be achieved by adopting or drawing on existing technologies.

[0087] The above is only an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims

1. A method for determining the three-point bending failure mode of a physically asymmetric double steel plate-concrete composite beam, characterized in that: The following steps are involved: Step 1: Obtain the geometric parameters and physical parameters of the double steel plate-concrete composite beam; The geometric parameters include: the beam span extension length H , distance from the fulcrum to the center line of the core L , steel plate thickness h , core material height c , deflection at the loading position W , core material width b ; After non-dimensionalizing the geometric parameters, we get: relative thickness , height-to-length ratio , relative extension length ; in: , , ; The physical parameters include: yield strength of the upper steel plate , yield strength of lower steel plate , concrete compressive strength , concrete tensile strength , concrete shear strength ; After non-dimensionalizing the physical parameters, we get: tensile and compressive strength ratio , relative compressive strength , shear ratio , yield strength factor ; in: , , , ; Step 2: Determine the neutral plane position; when When , the neutral plane is located inside the upper steel plate; when When , the neutral plane is located inside the lower steel plate; when When , the neutral plane is located in the concrete above the horizontal mid-section of the concrete; when When , the neutral plane is located in the concrete below the horizontal mid-section of the concrete; Step 3: Calculate the critical failure load ; Critical failure load include , , ; in, represents the critical load for bending failure, represents the critical load for partial shear failure; It represents the critical load of shear failure of the whole section; and: ； ； ； Step 4: is the horizontal axis, is the vertical coordinate, drawn in the same coordinate system , , about and Curve, and take the minimum value of the three curves to form the failure mode determination diagram; Step 5: Calculate the height-to-length ratio and relative thickness of the concrete composite beam and compose the coordinates, and judge the failure mode according to the position in the failure mode determination diagram according to the composed coordinates.

2. The method for determining the three-point bending failure mode of a physically asymmetric double steel plate-concrete composite beam according to claim 1 is characterized in that: The core material of the double steel plate-concrete composite beam is ordinary concrete, high performance concrete or ultra-high performance concrete.

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