A practical calculation method for shear stress of composite beam bridge with variable cross-section corrugated steel webs caused by external prestressing

Abstract

The present invention discloses a practical calculation method for the shear stress of a composite beam bridge with a variable cross-section corrugated steel web caused by external prestressing. This method is based on the equivalent load method, which equates the external prestressing force to a pair of self-balancing force systems, calculates the effective shear force, axial force and bending moment on the corrugated steel web caused by the external prestressing force, and then based on the accordion effect of the corrugated steel web PC composite beam bridge, equates the bending moment to a pair of couples acting on the centroid of the top and bottom plates, and equates the axial force to a parallel force system acting on the centroid of the top and bottom plates. According to the characteristic of uniform distribution of shear stress on the corrugated steel web, the shear stress on the corrugated steel web is obtained. The method of the present invention is simple and accurate, avoiding the calculation error caused by the traditional calculation method based on the assumption that the corrugated steel web bears the shear force of all sections. At the same time, it is applicable to the case where the external prestressed tendons are straight lines, and also to the case where the external prestressed tendons are broken lines. Compared with the complicated analytical formula for the shear stress of prestressed variable cross-section beams, this method is more convenient for engineering designers to use.

Description

Technical Field

[0001] The present invention relates to the field of structural engineering, and in particular to a practical calculation method for shear stress of a composite beam bridge with variable-section corrugated steel webs caused by external prestressing. Background Art

[0002] In existing specifications, when calculating the shear resistance of prestressed composite beam bridges with corrugated steel webs, the shear force is assumed to be caused by the vertical component of the prestress. The shear force on the cross section is divided by the effective shear area of the corrugated steel web to obtain the average shear stress borne by the corrugated steel web. This traditional calculation assumption generally assumes that the shear force on the cross section is entirely borne by the corrugated steel web, while ignoring the shear bearing capacity of the concrete top and bottom slabs. However, the shear performance of composite beams with corrugated steel webs of uniform cross section and those with variable cross section differ significantly. For composite beams with variable cross section, this calculation assumption can lead to large calculation errors, and the existing standard calculation theory is no longer applicable to structures with variable cross section. Under prestressing, due to the variable cross section of the beam and the wrinkling effect of the corrugated steel web, the inclined concrete bottom slab shares part of the shear force on the beam cross section, thereby changing the effective shear force borne by the corrugated steel web. This phenomenon is called the Resal effect.

[0003] However, further research on the Resal effect of composite beams with variable cross-section corrugated steel webs has not yet been conducted, nor has a simplified calculation method for shear stress under prestressing been proposed. While the analytical formula for calculating shear stress in composite beams with variable cross-section corrugated steel webs caused by prestressing is highly accurate, if the shear bearing of the horizontal concrete top slab, the corrugated steel web, and the inclined concrete bottom slab are considered simultaneously, the calculation requires additional shear stress caused by the prestressing moment and axial force, and involves differential formulas for numerous variable cross-section geometric parameters. This makes the calculation process complex and inconvenient for practical engineering applications. Summary of the Invention

[0004] In response to the above technical problems, in view of the limitations of traditional calculation assumptions and the complexity of shear stress analytical formulas, the main purpose of the present invention is to provide a shear stress calculation method for composite beam bridges with variable cross-section corrugated steel webs under external prestressing, taking into account the Resal effect.

[0005] The calculation method provided by the present invention ignores the shear bearing capacity of the horizontal concrete top plate and only considers the shear bearing capacity of the corrugated steel web and the inclined concrete bottom plate. Compared with the precise analytical method of the composite beam with variable cross-section corrugated steel web, the shear stress calculation model of the corrugated steel web is simplified to a certain extent. Therefore, the calculation method can be greatly simplified while meeting the engineering accuracy.

[0006] The purpose of the present invention is achieved by the following technical solutions:

[0007] A method for calculating shear stress of a composite beam with a variable cross-section and corrugated steel webs comprises the following steps:

[0008] (1) The external prestress is equivalent to a pair of self-balancing forces P acting on the anchor end and the turning point. P can be further decomposed into a horizontal force Pcosθ and a vertical force Psinθ, where θ is the angle between the prestressed tendons and the horizontal direction. A micro-segment dx is taken along the horizontal direction of the beam, and the right section of the micro-end of the beam is taken as the analysis object. At this time, under the action of prestress, the vertical section of the micro-end of the beam is subjected to the horizontal component Pcosθ and vertical component Psinθ of the prestress and the prestress bending moment M.

[0009] (2) Due to the accordion effect of the corrugated steel web, the web does not bear the bending moment. The bending moment M acting on the beam section can be equivalent to a pair of couples {T, T'} acting at the centroid of the concrete top and bottom plates. The calculation formula is as follows:

[0010]

[0011] Where: concentrated forces T and T' are equivalent to bending moment M and act at the centroid of the concrete top and bottom plates; N1 is the axial pressure borne by the inclined concrete bottom plate; α is the inclination angle between the concrete bottom plate and the horizontal line; h x It is the distance between the centroids of the concrete top and bottom slabs.

[0012] (3) The horizontal force Pcosθ is translated to the centroid of the section, and an additional eccentric bending moment ePcosθ is generated on the section. The horizontal component of the prestress Pcosθ is equivalent to a pair of horizontal components 1 / 2Pcosθ acting at the centroids of the top and bottom plates respectively. The same as step (2), the eccentric bending moment ePcosθ can be equivalent to a pair of couples acting at the centroids of the concrete top and bottom plates. At this time, under the action of the horizontal component of the prestress Pcosθ, the forces on the concrete top and bottom plates are respectively:

[0013]

[0014]

[0015] Where: T1 is the horizontal force on the concrete top plate, T2 is the horizontal force on the concrete bottom plate, e is the distance between the horizontal force Pcosθ and the centroid of the cross section; N2 is the axial pressure on the concrete bottom plate; θ is the angle between the prestressed tendon and the horizontal line; h x —The distance between the centroids of the concrete top and bottom slabs.

[0016] (4) The concentrated force N1 on the concrete bottom plate of the beam is actually the resultant force of the horizontal force T and the vertical shear force Q1. Similarly, N2 is actually the resultant force of the horizontal force T2 and the vertical shear force Q2. So the shear force Q B and shear stress τB for:

[0017]

[0018]

[0019] Where A B is the vertical cross-sectional area of the concrete base plate at the micro-segment section of the beam;

[0020] (5) According to the equilibrium equation, the corrugated steel web will produce additional shear forces Q1' and Q2' that are equal in magnitude and opposite in direction to Q1 and Q2 on the bottom plate. Then the effective shear force Q1' and Q2' actually borne by the corrugated steel web at the micro-segment section of the beam is w and its shear stress τ w The calculation formula is as follows:

[0021]

[0022]

[0023] Where Q0 is the vertical component of the external prestress, which is equal to Psinθ, A w —The vertical cross-sectional area of the corrugated steel web at the micro-segment section of the beam.

[0024] Furthermore, the calculation method assumes that the beam structure is in an elastic working state and the material stress thereof obeys Hooke's law.

[0025] Furthermore, the concrete top plate, bottom plate and corrugated steel web can work together in the elastic stage, and no shear slip occurs at the connection interface between the two.

[0026] Furthermore, the axial stiffness of the corrugated steel web in steps (2) and (3) is neglected due to the accordion effect, and therefore it is assumed that the section bending moment and axial force are borne jointly by the concrete top and bottom plates.

[0027] Furthermore, in step (5), when calculating the shear force borne by the corrugated steel web, it is assumed that the shear force borne by the horizontal concrete top plate is very small and can be ignored.

[0028] Furthermore, in steps (4) and (5), when calculating the shear stress of the concrete base plate and the corrugated steel web, it is assumed that the shear stress on the corrugated steel web is uniformly distributed along its height direction.

[0029] The beneficial effects of the present invention are:

[0030] The present invention provides a method for calculating shear stress under external prestressing for a composite beam bridge with a variable cross-section and corrugated steel web, taking into account the Resal effect. Compared with traditional calculation methods, this shear stress calculation method considering the Resal effect not only considers the shear stress caused by the vertical component of the prestress, but also the additional shear stress generated by the prestress bending moment and axial force, thereby reducing calculation errors and more accurately calculating the shear stress experienced by each component of the composite beam bridge with a variable cross-section. Compared with the analytical calculation formula for shear stress of composite beams with variable cross-section, the shear stress formula in the present invention is more convenient for application in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The figure is a schematic diagram of the theoretical model for the practical calculation method of shear stress of composite beam bridges with variable cross-section corrugated steel webs under external prestressing.

[0032] The meaning of the marks in the figure: 1-horizontal concrete top plate, 2-corrugated steel web, 3-inclined concrete bottom plate, 4-external prestressed tendons, 5-bridge support. DETAILED DESCRIPTION

[0033] The features of the present invention and other related features are further described in detail below with reference to the accompanying drawings and examples to facilitate understanding by those skilled in the art.

[0034] Example

[0035] like Figure 1 As shown, taking the simply supported beam with variable cross-section corrugated steel web as an example, the internal forces borne by the beam and the calculation model considering the Resal effect are shown as follows: Figure 1 shown.

[0036] The practical calculation method for shear stress of composite beam bridges with variable cross-section corrugated steel webs under external prestressing includes the following steps:

[0037] (1) The external prestress is equivalent to a pair of self-balancing forces P acting on the anchor end and the turning point. P can be further decomposed into a horizontal force Pcosθ and a vertical force Psinθ, where θ is the angle between the prestressed tendons and the horizontal direction. A micro-segment dx is taken along the horizontal direction of the beam, and the right section of the micro-end of the beam is taken as the analysis object. At this time, under the action of prestress, the vertical section of the micro-end of the beam is subjected to the horizontal component Pcosθ and vertical component Psinθ of the prestress and the prestress bending moment M.

[0038] (2) Due to the accordion effect of the corrugated steel web, the web does not bear the bending moment. The bending moment M acting on the beam section can be equivalent to a pair of couples {T, T'} acting at the centroid of the concrete top and bottom plates. The calculation formula is as follows:

[0039]

[0040] Where: concentrated forces T and T' are equivalent to bending moment M and act at the centroid of the concrete top and bottom plates; N1 is the axial pressure borne by the inclined concrete bottom plate; α is the inclination angle between the concrete bottom plate and the horizontal line; h x It is the distance between the centroids of the concrete top and bottom slabs.

[0041] (3) The horizontal force Pcosθ is translated to the centroid of the section, and an additional eccentric bending moment ePcosθ is generated on the section. The horizontal component of the prestress Pcosθ is equivalent to a pair of horizontal components 1 / 2Pcosθ acting at the centroids of the top and bottom plates respectively. The same as step (2), the eccentric bending moment ePcosθ can be equivalent to a pair of couples acting at the centroids of the concrete top and bottom plates. At this time, under the action of the horizontal component of the prestress Pcosθ, the forces on the concrete top and bottom plates are respectively:

[0042]

[0043]

[0044] Where: T1 is the horizontal force on the concrete top plate, T2 is the horizontal force on the concrete bottom plate, e is the distance between the horizontal force Pcosθ and the centroid of the cross section; N2 is the axial pressure on the concrete bottom plate; θ is the angle between the prestressed tendon and the horizontal line; h x —The distance between the centroids of the concrete top and bottom slabs.

[0045] (4) The concentrated force N1 on the concrete bottom plate of the beam is actually the resultant force of the horizontal force T and the vertical shear force Q1. Similarly, N2 is actually the resultant force of the horizontal force T2 and the vertical shear force Q2. Therefore, the shear force Q B and shear stress τ B for:

[0046]

[0047]

[0048] Where A B is the vertical cross-sectional area of the concrete base plate at the micro-segment section of the beam;

[0049] (5) According to the equilibrium equation, the corrugated steel web will produce additional shear forces Q1' and Q2' that are equal in magnitude and opposite in direction to Q1 and Q2 on the bottom plate. Therefore, the effective shear force Q w and its shear stress τ w The calculation formula is as follows:

[0050]

[0051]

[0052] Where Q0 is the vertical component of the external prestress, which is equal to Psinθ, A w —The vertical cross-sectional area of the corrugated steel web at the micro-segment section of the beam.

[0053] In this embodiment, the following calculation assumptions should be met when calculating the shear stress of a composite beam bridge with variable-section corrugated steel webs under external prestressing:

[0054] 1) The structure is in an elastic working state, and the force law of its material follows Hooke's law.

[0055] 2) Due to the accordion effect of the corrugated steel web 2, its axial stiffness can be ignored. Therefore, the bending moment on the section is entirely borne by the concrete top plate 1 and bottom plate 3.

[0056] 3) In the elastic stage, the concrete top plate 1, bottom plate 3 and corrugated steel web 2 can work together, and the deformation of the two is coordinated, and no shear slip occurs at the connection interface.

[0057] 4) The shear stress borne by the corrugated steel web 2 is evenly distributed along the height direction.

[0058] 5) The shear ratio of the horizontal concrete top plate 1 is very small and can be ignored.

[0059] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent replacements and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention should be included in the scope of protection of the invention.

Claims

1. A practical calculation method for shear stress of composite beam bridge with variable cross-section corrugated steel web caused by external prestressing, characterized by: The following steps are involved: (1) The external prestress is equivalent to a pair of self-balancing forces P acting on the anchor end and the turning point. P can be further decomposed into a horizontal force Pcosθ and a vertical force Psinθ, where θ is the angle between the prestressed tendon and the horizontal direction. A micro-segment dx is taken along the horizontal direction of the beam, and the right section of the micro-end of the beam is taken as the analysis object. At this time, under the action of prestress, the vertical section of the micro-end of the beam is subjected to the horizontal component Pcosθ and vertical component Psinθ of the prestress and the prestress bending moment M. (2) The bending moment M acting on the beam section is equivalent to a pair of couples {T, T'} acting at the centroids of the concrete top and bottom plates. The calculation formula is as follows: Where: concentrated forces T and T' are equivalent to bending moment M and act at the centroid of the concrete top and bottom plates; N1 is the axial pressure borne by the inclined concrete bottom plate; α is the inclination angle between the concrete bottom plate and the horizontal line; h x is the distance between the centroids of the concrete top and bottom slabs; (3) The horizontal force Pcosθ is translated to the centroid of the section, and an additional eccentric bending moment ePcosθ is generated on the section. The horizontal component of the prestress Pcosθ is equivalent to a pair of horizontal components 1 / 2Pcosθ acting at the centroids of the top and bottom plates respectively. The same as step (2), the eccentric bending moment ePcosθ can be equivalent to a pair of couples acting at the centroids of the concrete top and bottom plates; under the action of the horizontal component of the prestress Pcosθ, the forces on the concrete top and bottom plates are respectively: Where: T1 is the horizontal force on the concrete top plate, T2 is the horizontal force on the concrete bottom plate, e is the distance between the horizontal force Pcosθ and the centroid of the cross section; N2 is the axial pressure on the concrete bottom plate; θ is the angle between the prestressed tendon and the horizontal line; h x is the distance between the centroids of the concrete top and bottom slabs; (4) The concentrated force N1 on the concrete bottom plate of the beam is actually the resultant force of the horizontal force T and the vertical shear force Q1. Similarly, N2 is actually the resultant force of the horizontal force T2 and the vertical shear force Q2. So the shear force Q B and shear stress τ B for: Where A B is the vertical cross-sectional area of the concrete base plate at the micro-segment section of the beam; (5) According to the equilibrium equation, the corrugated steel web will produce additional shear forces Q1' and Q2' that are equal in magnitude and opposite in direction to Q1 and Q2 on the bottom plate. Then the effective shear force Q1' and Q2' actually borne by the corrugated steel web at the micro-segment section of the beam is w and its shear stress τ w The calculation formula is as follows: Where Q0 is the vertical component of the external prestress, which is equal to Psinθ, A w —The vertical cross-sectional area of the corrugated steel web at the micro-segment section of the beam.

2. The method according to claim 1, wherein: The calculation method assumes that the beam structure is in an elastic working state and the material forces obey Hooke's law.

3. The method according to claim 1, wherein: Under the action of prestressing, the concrete top and bottom plates and the corrugated steel web work together in the elastic stage, and no shear slip occurs at the connection interface between the two.

4. The method according to claim 1, wherein: The corrugated steel web in steps (2) and (3) is based on the accordion effect and its axial stiffness is ignored, and it is assumed that the section bending moment is borne jointly by the concrete top plate and bottom plate.

5. The method according to claim 1, wherein: In step (5), when calculating the shear force borne by the corrugated steel web, it is assumed that the shear force borne by the horizontal concrete top plate is very small and is therefore negligible in the calculation.

6. The method according to claim 1, wherein: When calculating the shear stress of the corrugated steel web in step (5), it is assumed that the shear stress on the corrugated steel web is uniformly distributed along its height direction.

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