A method for calculating deflection and external tendon stress of externally prestressed steel-concrete composite beam

Abstract

This invention discloses a method for calculating the deflection and stress of externally prestressed steel-concrete composite beams, comprising: constructing a stiffness reduction coefficient calculation model for the composite beam and calculating the stiffness reduction coefficient; inputting the stiffness reduction coefficient into a pre-established effective bending stiffness calculation model considering interface slip effects in the positive and negative bending moment zones of the composite beam to obtain the effective bending stiffness in the positive and negative bending moment zones of the composite beam; calculating the total mid-span deflection of the composite beam under the serviceability limit state based on the obtained effective bending stiffness in the positive and negative bending moment zones of the composite beam; and calculating the stress of the externally prestressed tendons under the serviceability limit state based on the obtained total mid-span deflection and in conjunction with the overall deformation compatibility conditions between the externally prestressed tendons and the composite beam. This invention can balance the accuracy and efficiency of calculating the mid-span deflection and stress of the externally prestressed tendons of the composite beam.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, specifically to a method for calculating the deflection and stress of external prestressed steel-concrete composite beams. Background Technology

[0002] External prestressing technology can significantly improve the flexural stiffness and load-bearing capacity of steel-concrete composite beams (hereinafter referred to as composite beams, or steel-concrete composite beams), making them a suitable structural form for long-span bridges and building projects. These composite beams typically consist of an upper concrete slab (bridge deck) and a lower steel beam connected by shear-resistant connectors (such as studs), and prestressing tendons may be arranged inside the concrete slab or outside the steel beam. The external prestressing system mainly includes prestressing tendons arranged outside the beam body, as well as anchorage ends and steering blocks that provide anchorage and steering. Under normal serviceability limits, the deflection of the composite beam and the stress control of the external prestressing tendons are core indicators for structural safety design.

[0003] Existing technologies have the following drawbacks: The steel-concrete interface exhibits a slip effect; neglecting the additional deflection caused by slip leads to an overestimation of the composite beam's flexural stiffness, resulting in an underestimation of the deflection value. Unlike internal prestressed tendons, external prestressed tendons only connect to the beam at the anchorage and turning blocks; their stress depends on the overall deformation coordination between the external prestressed tendons and the beam, making accurate stress calculation complex. After cracking in the negative moment zone of a continuous beam, there is a coupling effect between tensile stiffening and interface slip; existing flexural stiffness models fail to effectively reflect this coupling mechanism, resulting in insufficient deflection calculation accuracy and difficulty in meeting engineering design requirements. Current design codes or guidelines do not provide methods for calculating the deflection and stress of externally prestressed steel-concrete composite beams. While existing nonlinear finite element methods can yield accurate results, they are computationally cumbersome, hindering rapid engineering design and lacking simplified analytical methods for design.

[0004] Based on the above problems, it is urgent to propose a unified calculation method that considers the interface slip effect, the tensile stiffening effect of concrete, and the overall deformation coordination of external prestressing tendons, so as to achieve accurate prediction of the deflection of external prestressed steel-concrete composite beams and the stress of external prestressing tendons. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for calculating the deflection and stress of external prestressed steel-concrete composite beams that can take into account both the mid-span deflection and the stress of external prestressed tendons, in view of the above-mentioned problems of the prior art.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam includes the following steps: S1. By analyzing the ratio of the additional deflection of the composite beam caused by the interface slip between the steel beam and the concrete slab to the elastic deflection when the interface slip is not considered, a stiffness reduction coefficient calculation model for the composite beam is constructed. The size parameters, material parameters, and arrangement parameters of the shear connectors of the composite beam are input into the stiffness reduction coefficient calculation model to obtain the stiffness reduction coefficient of the composite beam. The coefficient is used to characterize the interface slip effect between the steel beam and the concrete slab. S2. Input the stiffness reduction factor into a pre-established calculation model for the effective bending stiffness of the composite beam in the positive bending moment region, considering the interface slip effect, to obtain the effective bending stiffness of the composite beam in the positive bending moment region; if the composite beam is a continuous beam, then further input the stiffness reduction factor into a pre-established calculation model for the effective bending stiffness of the composite beam in the negative bending moment region, considering the interface slip effect, to obtain the effective bending stiffness of the composite beam in the negative bending moment region; S3. Based on the effective bending stiffness of the positive and negative bending moment zones of the composite beam obtained in S2, calculate the total mid-span deflection of the composite beam under the normal serviceability limit state. S4. Based on the total mid-span deflection obtained in S3, and in conjunction with the overall deformation coordination conditions of the external prestressing tendons and the composite beam, calculate the stress of the external prestressing tendons under the normal serviceability limit state.

[0007] Optionally, in step S1, when constructing the calculation model for the stiffness reduction coefficient of the composite beam, it is assumed that the shear force-slip relationship at the steel-concrete interface of the composite beam is linear elastic, and it is also assumed that the slip strain is linearly distributed along the beam length.

[0008] Optionally, the stiffness reduction factor calculation model is as follows: , In the above formula, This is the stiffness reduction factor; Let be the area moment of the equivalent section of the concrete bridge deck about the neutral axis of the equivalent composite section; This refers to the height of the composite beam section. Calculate the span for the composite beam; The elastic modulus of steel; The number of shear connectors within each shear span; This refers to the shear stiffness of a single shear connector.

[0009] Optionally, in step S2, the calculation model for the effective bending stiffness of the composite beam in the positive bending moment zone considering the interface slip effect is as follows: , In the above formula, This represents the effective bending stiffness of the composite beam in the positive bending moment region. The elastic modulus of steel; This is the stiffness reduction factor; .

[0010] Optionally, in step S2, the calculation model for the effective flexural stiffness of the composite beam in the negative moment zone considering the interface slip effect is as follows: , In the above formula, The effective bending stiffness of the composite beam in the negative bending moment zone; The effective moment of inertia of the cracked section; For cracking moment; The calculated bending moment is under the normal serviceability limit state. The elastic modulus of steel; Effective moment of inertia; Effective moment of inertia of cracked section Calculated using the following formula: , Cracking moment Calculated using the following formula: , in, The moment of inertia of the cracked section; This refers to the tensile strength of concrete. This is the distance from the top of the concrete bridge deck to the elastic neutral axis of the composite beam; This is the ratio of the elastic modulus of steel to that of concrete. This is the stiffness reduction factor; Let be the equivalent moment of inertia of the composite beam.

[0011] Optionally, in step S3, the total mid-span deflection of the composite beam under the serviceability limit state. Calculated using the following formula: , In the above formula, Calculate the span for the composite beam; For composite beams in The actual load bending moment at the cross section; For composite beams in Bending moment per unit virtual load at the cross section; For composite beams in Effective bending stiffness at the section, when When the section is in the positive bending moment region The value is taken as the effective bending stiffness in the positive bending moment zone of the composite beam. ,when When the section is in the negative bending moment region The value is taken as the effective flexural stiffness in the negative moment zone of the composite beam. .

[0012] Optionally, when the composite beam is a simply supported beam, its entire span is considered as the positive bending moment zone; when the composite beam is a continuous beam, the range of 0.15 times the beam span on both sides of the intermediate support is defined as the negative bending moment zone, and the remaining area is the positive bending moment zone.

[0013] Optionally, in step S4, the stress of the external prestressing tendon under normal serviceability limit state is... Calculated using the following formula: , In the above formula, This represents the stress increment of externally prestressed tendons under normal serviceability limit conditions. For effective prestress; Stress increment of external prestressed tendons under normal service limit state It is obtained through the following calculation formula: , In the above formula, The elastic modulus of external prestressing tendons; This is the total length of the external prestressing tendons within the span; The total number of sections divided by the external prestressing tendons according to their anchorage points and the corresponding turning blocks; For the first The angle between the external prestressing tendons of the segment and the horizontal direction; and The first Vertical deflection of the composite beam sections where the right and left ends of the external prestressing tendons are located; , The first The eccentricity of the centroid of the prestressing tendon to the converted neutral axis of the composite beam section where the right and left ends of the external prestressing tendon are located. and The first The section rotation angle of the composite beam section where the right and left ends of the external prestressing tendons are located.

[0014] Optionally, when a steering block is arranged at mid-span, the stress increment of the external prestressing tendons under the normal serviceability limit state is... It is obtained through the following calculation formula: , When two steering blocks are symmetrically arranged at mid-span, the stress increment of the external prestressing tendons under the serviceability limit state is... It is obtained through the following calculation formula: , in, The total length between the two anchorage ends of the continuous external prestressed tendon; To and The sum of the relevant load span lengths determined by the most unfavorable arrangement diagram of live loads; The horizontal projection length of the prestressed tendon between the anchoring end and the first turning block.

[0015] Furthermore, the present invention also provides a device for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam, comprising a microprocessor and a memory interconnected thereto, wherein the microprocessor is programmed or configured to execute the above-described method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam.

[0016] Compared with the prior art, the present invention has the following main advantages: Step S1 calculates the stiffness reduction factor characterizing the interface slip effect between the steel beam and the concrete slab. Then, in step S2, this stiffness reduction factor is input into a pre-built calculation model for calculation, thus incorporating the interface slip effect into the effective flexural stiffness of the composite beam in both positive and negative bending moment zones. Therefore, the mid-span total deflection calculation result of the composite beam under the normal serviceability limit state obtained in step S3 more accurately reflects the actual deformation, overcoming the shortcomings of existing methods that overestimate stiffness due to neglecting the slip effect, resulting in a lower calculated deflection value, and improving the accuracy of the mid-span total deflection calculation. Step S4, based on the mid-span total deflection obtained in step S3, calculates the stress of the external prestressing tendons based on the overall deformation coordination conditions between the external prestressing tendons and the composite beam, thereby accurately obtaining the external prestressing stress. This invention fills the gap in the calculation methods for composite beam deflection and external prestressing tendon stress. Compared with the nonlinear finite element method, its calculation is simpler and more efficient, making it suitable for rapid engineering design. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the execution flow of the method in an embodiment of the present invention.

[0018] Figure 2 This is a schematic diagram of the flexural stiffness distribution when the externally prestressed steel-concrete composite beam is a continuous beam.

[0019] Figure 3 This is a schematic diagram of an externally prestressed steel-concrete composite beam with one turning block arranged in the middle of the span.

[0020] Figure 4 This is a schematic diagram of an externally prestressed steel-concrete composite beam with two symmetrically arranged turning blocks at mid-span.

[0021] Figure 5 The predicted and experimental values ​​of deflection of externally prestressed steel-concrete composite beams as simply supported beams, using the American ANSI / AISC 360 method. ) Results comparison chart.

[0022] Figure 6 The predicted and experimental values ​​of deflection of externally prestressed steel-concrete composite beams as simply supported beams, using the method in Chinese GB 50017. ) Results comparison chart.

[0023] Figure 7 The deflection prediction and experimental values ​​of the externally prestressed steel-concrete composite beam as a simply supported beam are obtained using the European Eurocode 4 method. ) Results comparison chart.

[0024] Figure 8 This refers to the predicted and experimental deflection values ​​of the externally prestressed steel-concrete composite beam when it is a simply supported beam, using the method described in this embodiment. ) Results comparison chart.

[0025] Figure 9 The predicted and experimental values ​​of deflection for externally prestressed steel-concrete composite beams when the beams are simply supported, using the method of neglecting slippage. ) Results comparison chart.

[0026] Figure 10 The predicted and experimental values ​​of deflection of the externally prestressed steel-concrete composite beam as a continuous beam are ( ) Results comparison chart.

[0027] Figure 11 The predicted and experimental values ​​of external prestressed tendon stress in simply supported steel-concrete composite beams are ( ). / Comparison chart. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and specific preferred embodiments, but this does not limit the scope of protection of the present invention.

[0029] As disclosed in this invention, unless the context clearly indicates otherwise, words such as "a," "an," "an," and / or "the" do not specifically refer to the singular and may also include the plural. The terms "first," "second," and similar terms used in this invention disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Similarly, words such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connected" or "linked" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect.

[0030] To facilitate understanding, the relevant technical terms that may be involved in this application will be introduced first.

[0031] The technical solution of the present invention will now be described in further detail with reference to the accompanying drawings.

[0032] like Figure 1 As shown, the method for calculating the deflection and external reinforcement stress of the externally prestressed steel-concrete composite beam in this embodiment specifically includes the following steps: S1. By analyzing the ratio of the additional deflection of the composite beam caused by the interface slip between the steel beam and the concrete slab to the elastic deflection when the interface slip is not considered, a stiffness reduction coefficient calculation model for the composite beam is constructed. The size parameters, material parameters and arrangement parameters of the shear connection of the composite beam are input into the stiffness reduction coefficient calculation model to obtain the stiffness reduction coefficient of the composite beam. The coefficient is used to characterize the interface slip effect between the steel beam and the concrete slab. S2. Input the stiffness reduction factor into the pre-established calculation model of the effective bending stiffness of the composite beam in the positive bending moment zone considering the interface slip effect to calculate the effective bending stiffness of the composite beam in the positive bending moment zone; if the composite beam is a continuous beam, then further input the stiffness reduction factor into the pre-established calculation model of the effective bending stiffness of the composite beam in the negative bending moment zone considering the interface slip effect to calculate the effective bending stiffness of the composite beam in the negative bending moment zone. S3. Based on the effective bending stiffness of the positive and negative bending moment zones of the composite beam obtained in S2, calculate the total mid-span deflection of the composite beam under the normal serviceability limit state. S4. Based on the total mid-span deflection obtained in S3, and in conjunction with the overall deformation coordination conditions of the external prestressing tendons and the composite beam, calculate the stress of the external prestressing tendons under the normal serviceability limit state.

[0033] The method for calculating the deflection and stress of externally prestressed steel-concrete composite beams in this embodiment calculates the stiffness reduction factor, which characterizes the interface slip effect between the steel beam and the concrete slab, in step S1. Then, in step S2, this stiffness reduction factor is input into a pre-constructed calculation model for calculation, thus incorporating the interface slip effect into the effective flexural stiffness of the composite beam in both positive and negative bending moment zones. Therefore, the mid-span total deflection calculation result of the composite beam under the normal serviceability limit state obtained in step S3 more accurately reflects the actual deformation, overcoming the shortcomings of existing methods that overestimate stiffness due to neglecting the slip effect, resulting in a lower calculated deflection value, and improving the accuracy of the mid-span total deflection calculation. In step S4, based on the mid-span total deflection obtained in step S3 and the overall deformation coordination condition between the externally prestressed tendons and the composite beam, the stress of the externally prestressed tendons is calculated, thereby accurately obtaining the externally prestressed stress. This invention fills the gap in the calculation method for composite beam deflection and externally prestressed tendon stress. Compared with the nonlinear finite element method, its calculation is simpler and more efficient, making it suitable for rapid engineering design.

[0034] Furthermore, in this embodiment, the calculation model for the stiffness reduction factor is as follows:

[0035] In the above formula, This is the stiffness reduction factor; Let be the area moment of the equivalent section of the concrete bridge deck about the neutral axis of the equivalent composite section; This refers to the height of the composite beam section. Calculate the span for the composite beam; The elastic modulus of steel; The number of shear connectors within each shear span; This refers to the shear stiffness of a single shear connector.

[0036] The process of constructing the stiffness reduction factor calculation model is as follows: Assuming the shear-slip relationship at the steel-concrete interface is linearly elastic, with slip strain linearly distributed along the beam length; the strain at the composite beam section is linearly distributed, and the deflection and curvature of the steel beam and concrete slab are the same at the same section; shear deformation is neglected; the beam is in a linearly elastic working state. For common four-point symmetrically loaded members, the additional curvature caused by interface slip... It can be calculated using the following formula: (2) In the above formula, a For the span length; The maximum slip strain typically occurs at the point of load application.

[0037] slip strain This can be expressed as the average slip strain along the beam length multiplied by a magnification factor. : (3) In the above formula, This represents the average slip along the beam span.

[0038] Substituting equation (3) into equation (2), the curvature caused by slip can be expressed as: (4) The deflection caused by slip can be obtained by integrating the corresponding curvature along the span: (5) Substituting equation (4) into equation (5), equation (5) can be rewritten as: (6) In the above formula, The slip amplification factor is set to a constant value of 4.0.

[0039] When shear connectors are uniformly and continuously arranged along the beam, the interface slip can be estimated using the following formula: (7) In the above formula, p Spacing between shear connectors; This refers to the number of shear connectors per row. This refers to the shear-slip stiffness of a single shear connector.

[0040] In the elastic stage, the horizontal shear force per unit length at the contact surface between the steel beam and the concrete slab can be expressed as: (8) In the above formula, To calculate the shear force at the cross section; The static moment of the converted area of ​​the concrete slab about the neutral axis of the composite.

[0041] For a simply supported externally prestressed composite beam with symmetrical four-point bending, substituting equations (7) and (8) into equation (6), the additional deflection due to slippage can be calculated using the following formula: (9) Therefore, the stiffness reduction factor calculation model can be expressed as: (10) In the above formula, This represents the shear stiffness of all shear connections between the section with maximum bending moment and the section with zero bending moment.

[0042] Furthermore, in this embodiment, in step S2, the calculation model for the effective bending stiffness of the composite beam in the positive bending moment zone considering the interface slip effect is as follows:

[0043] In the above formula, This represents the effective bending stiffness of the composite beam in the positive bending moment region. The elastic modulus of steel; This is the stiffness reduction factor; .

[0044] Furthermore, in this embodiment, in step S2, the calculation model for the effective bending stiffness of the composite beam in the negative bending moment region considering the interface slip effect is as follows:

[0045] In the above formula, The effective bending stiffness of the composite beam in the negative bending moment zone; The effective moment of inertia of the cracked section; For cracking moment; The calculated bending moment is under the normal serviceability limit state. The elastic modulus of steel; Effective moment of inertia; Effective moment of inertia of cracked section Calculated using the following formula:

[0046] Cracking moment Calculated using the following formula:

[0047] in, The moment of inertia of the cracked section; This refers to the tensile strength of concrete. This is the distance from the top of the concrete bridge deck to the elastic neutral axis of the composite beam; This is the ratio of the elastic modulus of steel to that of concrete. This is the stiffness reduction factor; Let be the equivalent moment of inertia of the composite beam.

[0048] From the calculation formula of the effective flexural stiffness calculation model of the composite beam in the negative bending moment zone considering the interface slip effect and the concrete stiffening effect, it can be seen that by introducing the cracking moment into the numerator of formula (3), This design cleverly utilizes the cracking moment. Calculated bending moment under normal serviceability limit state The relative relationship makes the effective bending stiffness It can automatically adjust as stress increases. When the cross-sectional stress approaches or exceeds the cracking moment, the model can accurately reflect the contribution of concrete's participation in tensile work (rigidification effect) to the overall stiffness, solving the problem that existing flexural stiffness models cannot reflect the coupling mechanism between tensile rigidification effect and interface slip effect. This is beneficial for providing accurate calculations of the total mid-span deflection of composite beams under the serviceability limit state and the stress of external prestressing tendons under the serviceability limit state.

[0049] Furthermore, in this embodiment, in step S3, the total mid-span deflection of the composite beam under normal serviceability limit state is... Calculated using the following formula:

[0050] In the above formula, Calculate the span for the composite beam; For composite beams in The actual load bending moment at the cross section; For composite beams in Bending moment per unit virtual load at the cross section; For composite beams in Effective bending stiffness at the section, when When the section is in the positive bending moment region The value is taken as the effective bending stiffness in the positive bending moment zone of the composite beam. ,when When the section is in the negative bending moment region The value is taken as the effective flexural stiffness in the negative moment zone of the composite beam. .

[0051] Furthermore, in this embodiment, when the composite beam is a simply supported beam, its entire span is considered as the positive bending moment zone; when the composite beam is a continuous beam, the area 0.15 times the beam span from both sides of the intermediate support is defined as the negative bending moment zone (e.g., ...). Figure 2 As shown, the left span length is The right span length is Therefore, the negative bending moment zone is located at a distance of 100 km from the left side of the intermediate support. right side The area within which the bending moment occurs is the positive bending moment zone, while the remaining area is the positive bending moment zone.

[0052] Furthermore, in this embodiment, in step S4, the stress of the external prestressing tendon under normal serviceability limit state... Calculated using the following formula:

[0053] In the above formula, This represents the stress increment of externally prestressed tendons under normal serviceability limit conditions. For effective prestress; Stress increment of external prestressed tendons under normal service limit state It is obtained through the following calculation formula:

[0054] In the above formula, The elastic modulus of external prestressing tendons; This is the total length of the external prestressing tendons within the span; The total number of sections divided by the external prestressing tendons according to their anchorage points and the corresponding turning blocks; For the first The angle between the external prestressing tendons of the segment and the horizontal direction; and The first Vertical deflection of the composite beam sections where the right and left ends of the external prestressing tendons are located (e.g.) Figure 3 As shown, since there is only one steering block, the external prestressing tendon is divided into two sections. The vertical deflection at the left end of the first section of the external prestressing tendon is 0, while the deflection at the right end is the total mid-span deflection under the normal serviceability limit state. The vertical deflection at the left end of the second external prestressed tendon is the total mid-span deflection under the normal serviceability limit state. (and the right end is 0). , The first The eccentricity of the centroid of the prestressing tendon to the converted neutral axis of the composite beam section where the right and left ends of the external prestressing tendon are located. and The first The section rotation angle of the composite beam section where the right and left ends of the external prestressing tendons are located.

[0055] In particular, when a steering block is placed in the middle of the span (e.g. Figure 3 As shown), the stress increment of external prestressed tendons under normal serviceability limit state. It is obtained through the following calculation formula:

[0056] When two steering blocks are symmetrically arranged at the mid-span (e.g.) Figure 4 As shown), the stress increment of external prestressed tendons under normal serviceability limit state. It is obtained through the following calculation formula:

[0057] in, The total length between the two anchorage ends of the continuous external prestressed tendon; To and The sum of the relevant load span lengths determined by the most unfavorable arrangement diagram of live loads; The horizontal projection length of the prestressed tendon between the anchoring end and the first turning block.

[0058] To verify the accuracy of the calculation method in this embodiment, experimental data of externally prestressed steel-concrete composite beams from published literature were selected for comparative analysis (see data in Tables 1 and 2). The shear span ratio, span, and connector stiffness parameters of the composite beams in the published literature all cover common engineering ranges. The calculation methods for the total mid-span deflection of composite beams under the serviceability limit state, as described in American standard ANSI / AISC-360, Chinese standard GB50017, and European standard Eurocode 4, were selected, along with methods that neglect slippage (i.e., when using the method of this embodiment for calculation...). A simplified method for calculating the total mid-span deflection of a composite beam under normal serviceability limit state (taking a value of 0) is used to obtain a predicted deflection value, which serves as a benchmark for comparison in this embodiment. The ratio of the predicted deflection value obtained by different methods to the experimental value is compared. This demonstrates the superiority of the method in this embodiment for calculating the total mid-span deflection of the composite beam under normal serviceability limit state.

[0059]

[0060] In the above table, Ac The cross-sectional area of ​​the concrete bridge deck; As The cross-sectional area of ​​the steel beam; Ap The cross-sectional area of ​​the external prestressing tendons; H This represents the total height of the composite beam section; L Calculate the span for the composite beam; p The longitudinal spacing of the shear connectors; β For shear connection degree, Pu This represents the ultimate bearing capacity of the specimen.

[0061]

[0062] In the above table, For the span length; p (Sagging) is the spacing of shear connection members in the positive bending moment zone; p (Hogging) represents the spacing of shear connection members in the negative bending moment zone; Ps A load of 0.5 is applied to the test under normal operating conditions. Pu .

[0063] Document 1 is Ayyub BM, Sohn YG, Saadatmanesh H. Prestressed compositegirders under positive moment[J]. Journal of Structural Engineering, 1990,116(11): 2931-2951; Document 2 is Chen S, Gu P. Load carrying capacity of compositebeams prestressed with external tendons under positive moment[J]. Journal of Constructional Steel Research, 2005, 61(4): 515-530; Document 3 is Lorenc W, KubicaE. Behavior of composite beams prestressed with external tendons: Experimental study[J]. Journal of Constructional Steel Research, 2006, 62:1353-1366; Document 4 is Saadatmanesh H, Albrecht P, Ayyub B M. Experimental study of prestressed composite beams[J]. Journal of Structural Engineering, Reference 5 is Yang Tao, Xue Weichen. Stress performance of externally prestressed steel-concrete composite beams under monotonic load [J]. Journal of Jiangsu University (Natural Science Edition), 2012, 33(02): 233-238; Reference 6 is Zhang Yunlong. Experimental study on structural behavior of externally prestressed steel-concrete composite beams [D]. Jilin University, 2005; Reference 7 is Zhang N, Fu C C. Experimental and theoretical studies on composite steel-concrete box beams with external tendons [J]. Engineering Structures, 2009, 31(2): 275-283; Reference 8 is Peng F, Xue WC, Bai L.Flexural behavior of externally prestressedcontinuous steel-concrete composite beams[J]. Journal of Constructional SteelResearch, 2024, 212: 108282; Reference 9 is Chen S, Wang X, Jia Y. A comparative study of continuous steel-concrete composite beams prestressed with externaltendons: Experimental investigation[J]. Journal of Constructional SteelResearch, 2009, 65: 1480-1489; Document 10 is Nie JG, Tao M, Cai CS, et al. Deformation analysis of prestressed continuous steel-concrete composite beams[J]. Journal of Structural Engineering, 2009, 135(11): Reference 11 is [1] Zong Zhouhong, Zheng Zequn, Fang Zhenzheng, et al. Experimental study on externally prestressed steel-concrete composite continuous beams [J]. Journal of China Highway and Transport, 2002, (01): 47-52; Reference 12 is Sun Q, Yang Y, Fan J, et al. Effect of longitudinal reinforcement and prestressing on stiffness of composite beams under hogging moments [J]. Journal of Constructional Steel Research, 2014, 100: 1-11. For the simply supported beam condition (using the specimens in Table 1), when applying 0.3 times the ultimate load (0.3... Pu ), 0.5 times the ultimate load (0.5) Pu ) and 0.65 times the ultimate load (0.65) Pu Under level 3 load conditions, the ratio (Δ) of predicted deflection values ​​to experimental values ​​using different methods pre / Δ exp The statistical results are shown in Table 3 and Figures 5 to 9 As shown.

[0064]

[0065] From Table 3 and Figures 5 to 9 It can be seen from this that: the American standard ANSI / AISC 360 method The mean values ​​range from 1.219 to 1.280, generally high and with large dispersion; Chinese standard GB 50017 method The mean value ranges from 1.095 to 1.155, which is generally conservative and the accuracy is average; it conforms to the Eurocode 4 method. The mean values ​​range from 0.945 to 0.988, generally underestimating the deflection; the slip method is ignored. The mean value ranges from 0.823 to 0.886, showing the most significant underestimation of deflection; the value obtained using the method of this invention... The mean range is 1.015~1.085, with the smallest standard deviation and the narrowest 95% confidence interval. The method of this invention exhibits optimal accuracy and stability across the entire load range.

[0066] For continuous beam load cases (using specimens in Table 2), the ratio of predicted deflection values ​​to experimental values ​​using different methods (Δ) pre / Δ exp The statistical results are shown in Table 4 and Figure 10 As shown.

[0067]

[0068] From Table 4 and Figure 10 This shows that the American standard ANSI / AISC 360 method... The mean is 1.163, with the largest dispersion; Chinese standard GB 50017 method. The mean is 1.087, indicating moderate accuracy; Eurocode 4 method. The mean value is 0.965, which is relatively low overall; ignoring the slip method. The mean value is only 0.797, which significantly underestimates the deflection; the value obtained by the method of this invention The mean is 1.035, the standard deviation is 0.122, and the confidence interval is optimal. This method can accurately reflect the true deformation of composite continuous beams.

[0069] To verify the accuracy of the method of this invention in predicting the stress of externally prestressed tendons, the calculation results under different load levels were compared in the case of simply supported beams. See Table 5 and... Figure 11 As shown, at 0.3 times the ultimate load (0.3... Pu ), 0.5 times the ultimate load (0.5) Pu) and 0.65 times the ultimate load (0.65) Pu Under level 3 load, the ratio of the predicted stress value of the external prestressed tendon calculated using the method of this invention to the experimental value ( / The statistical results are as follows:

[0070] From Table 5 and Figure 11 It can be seen from this that the ratio of the predicted stress value of the external prestressed tendon obtained by the method of this invention to the experimental value is ( / The mean range of the values ​​is 1.011 to 1.023, and the standard deviation is less than 0.2. The overall accuracy is high and the dispersion is small.

[0071] Furthermore, this embodiment also provides a device for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam, including a microprocessor and a memory interconnected thereto. The microprocessor is programmed or configured to execute the above-described method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam.

[0072] Those skilled in the art will understand that the technical solutions provided by the embodiments of this application may be in the form of a method, system, or computer program product. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create an implementation for the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0073] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam, characterized in that, Specifically, the following steps are included: S1. By analyzing the ratio of the additional deflection of the composite beam caused by the interface slip between the steel beam and the concrete slab to the elastic deflection when the interface slip is not considered, a stiffness reduction coefficient calculation model for the composite beam is constructed. The size parameters, material parameters, and arrangement parameters of the shear connectors of the composite beam are input into the stiffness reduction coefficient calculation model to obtain the stiffness reduction coefficient of the composite beam. The coefficient is used to characterize the interface slip effect between the steel beam and the concrete slab. S2. Input the stiffness reduction factor into a pre-established calculation model for the effective bending stiffness of the composite beam in the positive bending moment region, considering the interface slip effect, to obtain the effective bending stiffness of the composite beam in the positive bending moment region; if the composite beam is a continuous beam, then further input the stiffness reduction factor into a pre-established calculation model for the effective bending stiffness of the composite beam in the negative bending moment region, considering the interface slip effect, to obtain the effective bending stiffness of the composite beam in the negative bending moment region; S3. Based on the effective bending stiffness of the positive and negative bending moment zones of the composite beam obtained in S2, calculate the total mid-span deflection of the composite beam under the normal serviceability limit state. S4. Based on the total mid-span deflection obtained in S3, and in conjunction with the overall deformation coordination conditions of the external prestressing tendons and the composite beam, calculate the stress of the external prestressing tendons under the normal serviceability limit state.

2. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to claim 1, characterized in that, In step S1, when constructing the calculation model for the stiffness reduction factor of the composite beam, it is assumed that the shear force-slip relationship at the steel-concrete interface of the composite beam is linear elastic, and it is also assumed that the slip strain is linearly distributed along the beam length.

3. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to claim 2, characterized in that, The calculation model for the stiffness reduction factor is as follows: In the above formula, This is the stiffness reduction factor; Let be the area moment of the equivalent section of the concrete bridge deck about the neutral axis of the equivalent composite section; This refers to the height of the composite beam section. Calculate the span for the composite beam; The elastic modulus of steel; The number of shear connectors within each shear span; This refers to the shear stiffness of a single shear connector.

4. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to claim 1, characterized in that, In step S2, the calculation model for the effective bending stiffness of the composite beam in the positive bending moment zone considering the interface slip effect is as follows: In the above formula, This represents the effective bending stiffness of the composite beam in the positive bending moment region. The elastic modulus of steel; This is the stiffness reduction factor; .

5. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to claim 1, characterized in that, In step S2, the calculation model for the effective flexural stiffness of the composite beam in the negative moment zone considering the interface slip effect is as follows: In the above formula, The effective bending stiffness of the composite beam in the negative bending moment zone; The effective moment of inertia of the cracked section; For cracking moment; The calculated bending moment is under the normal serviceability limit state. The elastic modulus of steel; Effective moment of inertia; Effective moment of inertia of cracked section Calculated using the following formula: Cracking moment Calculated using the following formula: in, The moment of inertia of the cracked section; This refers to the tensile strength of concrete. This is the distance from the top of the concrete bridge deck to the elastic neutral axis of the composite beam; This is the ratio of the elastic modulus of steel to that of concrete. This is the stiffness reduction factor; Let be the equivalent moment of inertia of the composite beam.

6. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to claim 1, characterized in that, In step S3, the total mid-span deflection of the composite beam under the normal serviceability limit state is... Calculated using the following formula: In the above formula, Calculate the span for the composite beam; For composite beams in The actual load bending moment at the cross section; For composite beams in Bending moment per unit virtual load at the cross section; For composite beams in Effective bending stiffness at the section, when When the section is in the positive bending moment region The value is taken as the effective bending stiffness in the positive bending moment zone of the composite beam. ,when When the section is in the negative bending moment region The value is taken as the effective flexural stiffness in the negative moment zone of the composite beam. .

7. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to any one of claims 1 to 6, characterized in that, When the composite beam is a simply supported beam, its entire span is considered as the positive bending moment zone; when the composite beam is a continuous beam, the area 0.15 times the beam span on both sides of the intermediate support is defined as the negative bending moment zone, and the remaining area is the positive bending moment zone.

8. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to claim 1, characterized in that, In step S4, the stress of the external prestressing tendon under normal serviceability limit state. Calculated using the following formula: In the above formula, This represents the stress increment of externally prestressed tendons under normal serviceability limit conditions. For effective prestress; Stress increment of external prestressed tendons under normal service limit state It is obtained through the following calculation formula: In the above formula, The elastic modulus of external prestressing tendons; This is the total length of the external prestressing tendons within the span; The total number of sections divided by the external prestressing tendons according to their anchorage points and the corresponding turning blocks; For the first The angle between the external prestressing tendons of the segment and the horizontal direction; and The first Vertical deflection of the composite beam sections where the right and left ends of the external prestressing tendons are located; , The first The eccentricity of the centroid of the prestressing tendon to the converted neutral axis of the composite beam section where the right and left ends of the external prestressing tendon are located. and The first The section rotation angle of the composite beam section where the right and left ends of the external prestressing tendons are located.

9. The method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam according to claim 8, characterized in that, When a steering block is placed at mid-span, the stress increment of the external prestressing tendons under the serviceability limit state is... It is obtained through the following calculation formula: When two steering blocks are symmetrically arranged at mid-span, the stress increment of the external prestressing tendons under the serviceability limit state is... It is obtained through the following calculation formula: in, The total length between the two anchorage ends of the continuous external prestressed tendon; To and The sum of the relevant load span lengths determined by the most unfavorable arrangement diagram of live loads; The horizontal projection length of the prestressed tendon between the anchoring end and the first turning block.

10. A device for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam, comprising a microprocessor and a memory interconnected, characterized in that, The microprocessor is programmed or configured to execute the method for calculating the deflection and external reinforcement stress of an externally prestressed steel-concrete composite beam as described in any one of claims 1 to 9.

Images