Deflection calculation method for steel-bamboo composite beam with perforated web

Abstract

The invention relates to the field of building structure engineering, and discloses a deflection calculation method of a web perforated steel-bamboo composite beam, which comprises the following steps of: determining geometric parameters, material parameters and perforated sizes of the steel-bamboo composite beam; mechanical property parameters of the steel and the bamboo plywood are measured, and the overall flexural rigidity of the composite beam is calculated; according to the loading conditions, calculating the overall deflection without tapping and the local deflection under the influence of tapping; superposing the non-tapping deflection and the tapping deflection to obtain the overall deflection distribution of the composite beam; and determining the maximum deflection value and the position of the composite beam. According to the method, the superposition model of the deflection of the non-perforated area and the deflection of the perforated area is established, the transverse isotropic characteristic of the bamboo, the rigidity of the steel and the secondary bending moment distribution of the perforated area are comprehensively considered, the influence of tapping on the overall deflection can be accurately calculated, the tapping arrangement design is optimized, and a theoretical basis is provided for structural design and checking of the steel-bamboo composite beam.

Description

Technical Field

[0001] The invention relates to the technical field of building structure engineering, in particular to a method for calculating the deflection of a steel-bamboo composite beam with a web opening. Background Art

[0002] With the increasing requirements of space utilization and functionality in construction projects, the design of beams with web openings has gradually become an important method to optimize the performance of building structures. In modern buildings, in order to arrange pipeline equipment (such as HVAC, water supply and drainage systems, etc.), it is often necessary to set openings on the web of the beam to reduce the equipment's occupation of the building's net height. However, the introduction of openings will inevitably lead to a weakening of the local stiffness of the beam, further affecting the overall bending performance. Especially in composite beams, the secondary bending moment and stress distribution in the opening area will change significantly, making traditional design and analysis methods difficult to apply.

[0003] As a new type of green building structure, steel-bamboo composite beams have attracted extensive attention in structural engineering due to the advantages of bamboo's light weight, high strength and renewability and steel's high stiffness and shear resistance. However, due to the heterogeneity of the material properties of steel-bamboo composite beams, the deflection distribution characteristics after openings are more complicated. Existing research mainly focuses on the overall mechanical performance analysis of steel-bamboo composite beams without openings. There are few studies on the local stiffness changes and maximum deflection deviation laws caused by openings. Existing deflection calculation methods are mostly based on the assumption of homogeneous material beams without openings, which makes it difficult to effectively describe the actual deformation behavior of steel-bamboo composite beams.

[0004] The main technical problems caused by openings are the asymmetry of the deflection distribution and the offset of the maximum deflection position. The traditional deflection analysis method fails to fully consider the impact of the weakening of the stiffness in the opening area on the overall deflection distribution, which easily leads to large deviations in the calculation results. In addition, the existing design fails to provide an efficient and accurate calculation model to analyze the deflection characteristics of steel-bamboo composite beams after openings, especially the prediction of the maximum deflection value and its position under different opening positions, sizes and loading conditions. Therefore, a calculation method that can accurately analyze the deflection characteristics of steel-bamboo composite beams with web openings is needed to solve the problem of the impact of openings on the overall stiffness and deflection distribution of composite beams, and provide reliable theoretical support for optimization design. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a method for calculating the deflection of a steel-bamboo composite beam with web openings, which solves the problem that it is difficult to accurately analyze the local stiffness weakening and maximum deflection offset caused by the web openings in the existing steel-bamboo composite beam deflection calculation.

[0006] To achieve the above purpose, the present invention is implemented by the following technical scheme: A method for calculating the deflection of a steel-bamboo composite beam with web openings, comprising the following steps:

[0007] Determine the structural parameters of the steel-bamboo composite beam, including beam length, opening size, location, and loading point location;

[0008] Determine the mechanical properties of steel and bamboo plywood, and calculate the overall bending stiffness of the composite beam;

[0009] According to the loading conditions of the composite beam, the overall deflection without openings and the local deflection under the influence of openings are calculated respectively;

[0010] The deflection without openings is superimposed with the deflection with openings to obtain the overall deflection distribution of the composite beam;

[0011] Determine the maximum deflection of the composite beam and its location.

[0012] Preferably, the structural parameters include the cross-sectional inertia moment of the steel, the thickness and width of the bamboo plywood, the diameter and height of the opening, and the position of the opening area;

[0013] The overall bending stiffness of the composite beam is the superposition value of the bending stiffness of the steel material and the bending stiffness of the bamboo plywood.

[0014] Preferably, the overall deflection when no hole is opened is calculated by the following formula:

[0015]

[0016] Among them, F is the concentrated load, EI is the overall bending stiffness, L is the span of the beam, and x is the horizontal distance from the starting point of one end support of the beam to the specified position along the length direction of the beam.

[0017] Preferably, the local deflection under the influence of the opening is calculated according to the following formula:

[0018]

[0019] Among them, δ1 and δ2 are the local deflections at the left and right ends of the opening area, δ is the total deflection of the opening area, l1 and l2 are the distances between the two ends of the opening, a0 is the opening diameter, F is the applied load, L is the total length of the beam, and i is the linear stiffness of the opening area.

[0020] Preferably, the linear stiffness i of the opening area is calculated according to the following formula:

[0021]

[0022] Among them, EI h is the bending stiffness of the opening area, and a0 is the opening diameter.

[0023] Preferably, the local deflection distribution under the influence of the opening is expressed by the secondary moment equilibrium equation:

[0024] EIh y″=M1-Fx

[0025] Where y″ is the second-order derivative of the deflection curve, M1 is the secondary bending moment at the opening, F is the applied load, x is the horizontal distance from the left edge of the opening to the specified position along the length of the beam, and EI h is the bending stiffness of the opening area.

[0026] Preferably, the deflection function of the local deflection distribution under the influence of the opening is expressed by the following formula:

[0027]

[0028] Where y is the deflection, M1 is the secondary bending moment at the opening, F is the applied load, x is the horizontal distance from the left edge of the opening to the specified position along the length of the beam, and A and B are integration constants determined by boundary conditions.

[0029] Preferably, when the deflection without opening is superimposed with the deflection with opening, a correction coefficient λ is introduced to characterize the influence of the slip at the steel-bamboo interface and the weakening of the opening stiffness, and the correction formula is:

[0030]

[0031] Among them, λ is the reduction factor, which is 0.96, a0 is the opening diameter, F is the applied load, L is the total length of the beam, i is the linear stiffness of the opening area, EI is the overall bending stiffness, and x is the horizontal distance from the starting point of the support at one end of the beam to the specified position along the length direction of the beam.

[0032] The present invention also provides a device for calculating the deflection of a steel-bamboo composite beam with web openings, the device comprising:

[0033] Data input module, used to input geometric parameters, material parameters and opening dimensions of steel-bamboo composite beams;

[0034] A deflection calculation module is used to calculate the overall deflection of the unperforated area and the local deflection of the perforated area based on input data;

[0035] The superposition module is used to determine the deflection distribution of the entire beam according to the superposition principle;

[0036] Display module, used to output the whole beam deflection curve and the maximum deflection position.

[0037] Preferably, the deflection calculation module includes:

[0038] The first calculation module is used to calculate the overall deflection without openings;

[0039] The second calculation module is used to calculate the secondary bending moment and local deflection of the opening area;

[0040] Correction module to correct the deflection results for bamboo anisotropy and steel-bamboo interface slip effects.

[0041] The present invention provides a method for calculating the deflection of a steel-bamboo composite beam with web openings. It has the following beneficial effects:

[0042] 1. The present invention establishes a superposition model of the overall deflection without openings and the local deflection in the opening area, and comprehensively considers the influence of the local stiffness weakening and secondary bending moment distribution caused by the openings. Compared with the traditional non-opening assumption model, this method can accurately describe the deflection distribution under actual working conditions, especially when the maximum deflection position is offset, which greatly improves the accuracy of deflection calculation and provides more reliable reference data for engineering design.

[0043] 2. Based on the parametric input of the opening size, position and beam span length, the present invention can flexibly adjust the deflection calculation model to adapt to the design of composite beams with different opening arrangements. Regardless of whether the opening is in the middle of the span or close to the support, this method can accurately analyze the impact of the opening on the overall deflection distribution, and has strong applicability and universality.

[0044] 3. By accurately determining the maximum deflection value and position of the composite beam, the present invention can effectively check whether the design scheme meets the deflection allowable value requirements and provide a theoretical basis for adjusting the opening position, size or reinforcement measures. This method greatly reduces the need for repeated test verification and improves the design efficiency of steel-bamboo composite beams.

[0045] 4. The present invention combines the elastic modulus of steel and bamboo plywood and the secondary bending moment distribution characteristics of the opening area to propose a simple and easy-to-use deflection calculation method, while taking into account the accuracy of the theoretical model and the simplicity of the calculation process, which is convenient for promotion and application in engineering and helps to improve the design reliability and structural performance of open-hole steel-bamboo composite beams.

[0046] 5. By calculating the maximum deflection and the deflection distribution curve, the present invention can intuitively show the influence of the opening on the overall stiffness of the steel-bamboo composite beam, providing a scientific basis for optimizing the opening arrangement and size design. In practical applications, this method can also be combined with different loading conditions and reinforcement measures to further guide the structural optimization and efficient resource utilization of the composite beam. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0048] Figure 2 The calculation diagram of the composite beam with web openings in the embodiment of the present invention is shown in FIG. 1 , wherein (a) is the actual deflection curve, (b) does not consider the influence of the openings, and (c) only considers the influence of the openings;

[0049] Figure 3The opening area of ​​the embodiment of the present invention is intended to;

[0050] Figure 4 It is a schematic diagram of the structure of the device of the present invention;

[0051] Figure 5 It is a schematic diagram of the structure of the deflection calculation module of the present invention.

[0052] Among them, 10, data input module; 20, deflection calculation module; 21, first calculation module; 22, second calculation module; 23, correction module; 30, superposition module; 40, display module. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the specification of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] Please see attached Figure 1 The present invention provides a method for calculating the deflection of a steel-bamboo composite beam with a web opening. By combining a simplified mechanical model and introducing a correction coefficient, the influence of the opening of the steel-bamboo composite beam is accurately modeled and calculated, and the deflection distribution and the maximum deflection position of the composite beam can be effectively predicted. The various steps of the method of the present invention are described in detail below.

[0055] S1. Determine the structural parameters of steel-bamboo composite beams

[0056] First, it is necessary to determine the structural parameters of the steel-bamboo composite beam, which are the basis for deflection calculation and directly affect the accuracy of the calculation results and the applicability of the model. Specifically, by measuring and recording the geometric characteristics, material properties and geometric parameters of the openings of the composite beam, the necessary input data is provided for the subsequent deflection calculation. In some embodiments, combined with the actual engineering application requirements, some parameters can also be adjusted according to specific design conditions to optimize the impact of the opening design on the deflection performance.

[0057] In this embodiment, the structural parameters of the steel-bamboo composite beam mainly include the overall length of the beam, the cross-sectional dimensions, the opening dimensions, the opening position and the loading point position.

[0058] In general, the full length L of a steel-bamboo composite beam refers to the distance between the two ends of the beam, which can be directly obtained through design drawings or actual measurements. As an option, in structures with larger spans, the full length of the beam can also include a certain support extension length so that the influence of boundary effects can be considered during calculation.

[0059] Specifically, the cross-sectional dimensions of the composite beam include the width b of the steel section. s and height h s , and the width b of the bamboo section b and height h b In a possible implementation, the steel section is usually cold-bent thin-walled steel, and its width and height can be obtained by consulting the standard section size table or on-site measurement; the width and height of the bamboo plywood section can be determined by the processing dimensions of the standard material sample.

[0060] In some embodiments, the size of the opening includes the diameter a0 and height h0 of the opening. Generally, the diameter a0 of the opening is the dimension that runs through the web of the beam in the horizontal direction, and the height h0 of the opening is usually the sum of the thickness of the bamboo plywood and the steel web. As an option, when the height of the opening is small, its effect on the deflection calculation can be ignored, and only the width a0 is retained as the calculation parameter.

[0061] The position of the opening refers to the distance from the center of the opening to the left support of the beam, represented by l1. The lengths of the remaining beam segments on both sides of the opening are l1 and l2, respectively, satisfying the following geometric relationship:

[0062] l1+a0+l2=L

[0063] In some embodiments, the position of the openings can be adjusted according to actual engineering requirements to optimize the degree to which the openings weaken the overall stiffness of the beam. Generally, the openings should be arranged in areas with low bending-shear ratios to reduce their impact on the maximum deflection offset.

[0064] The loading point position refers to the specific position where the concentrated load F acts, and is represented by the distance x from the left support. As a possible implementation method, the loading point is usually arranged at the mid-span to calculate the deflection at the maximum bending moment position. In some special cases, the loading point can be deviated from the mid-span to analyze the contribution of the eccentric load to the deflection of the opening influence area.

[0065] In one possible implementation, the measurement and calculation of parameters can be further refined. For example, the cross-sectional dimensions can be used to calculate the moment of inertia I of steel and bamboo. s and I b :

[0066]

[0067] Among them, b s ,h s is the cross-sectional width and height of the steel, b b ,h b It is the cross-sectional width and height of the bamboo plywood.

[0068] In addition, when determining the parameters, it is also necessary to record the moment of inertia I of the opening area of ​​the steel-bamboo composite beam.h In general, I h It can be determined experimentally or calculated using the superposition principle:

[0069] I h =I s +I b

[0070] As an option, the opening area can be treated as a simplified cross-section and the effect of the opening on the stiffness reduction can be simulated by adjusting the moment of inertia.

[0071] In some embodiments, the geometric parameters and loading conditions of the beam can also be checked in combination with finite element modeling to more accurately determine the calculation input parameters. As an extension, the geometric parameters and loading point positions obtained in this embodiment can be further used for deflection distribution analysis to provide guidance for subsequent optimization design.

[0072] S2. Determine the mechanical properties of steel and bamboo plywood, and calculate the overall bending stiffness of the composite beam

[0073] To ensure the accuracy of the deflection calculation of the steel-bamboo composite beam with web openings, the present invention requires accurate determination of the mechanical property parameters of the steel and bamboo plywood, and the overall bending stiffness of the composite beam is calculated based on the geometric dimensions and material parameters of the beam. This process is the basis for subsequent deflection calculation and distribution analysis. In general, the material performance parameters and cross-sectional bending stiffness can be quickly and accurately obtained by combining standard test methods with theoretical calculations. In some embodiments, the calculation of the moment of inertia can also be verified by experimental measurement to optimize the accuracy of the bending stiffness calculation.

[0074] In this embodiment, the elastic modulus E of the steel material s and elastic modulus E of bamboo plywood b It is obtained through experimental measurement. Specifically, the elastic modulus can be obtained by conducting a tensile test on a steel specimen in accordance with "Tensile Test of Metallic Materials Part 1: Room Temperature Test Method" (GB / T 228.1-2021). As a transversely isotropic material, the elastic modulus of bamboo plywood needs to be measured separately in the direction parallel to the grain and perpendicular to the grain, and then the average value is taken as the approximate equivalent elastic modulus. The test of the elastic modulus of bamboo plywood can be carried out in accordance with the "Test Method for Physical and Mechanical Properties of Defect-free Small Specimens of Wood".

[0075] In a possible implementation, the yield strength parameters of the bamboo plywood can be further determined, including the yield strength X, Y, Z in the principal stress direction and the shear strength S ij These parameters have a great influence on the subsequent calculation of the local stiffness of the opening area and are generally obtained through uniaxial tension tests and shear tests.

[0076] In general, the elastic modulus of steel and bamboo plywood can be directly used to calculate their respective bending stiffness EI s and EI b As an option, the steel bending stiffness EI s And bamboo plywood bending stiffness EI b The calculation formula is as follows:

[0077] EI s =E s I s ,EI b =EI b I b

[0078] Among them, I s and I b are the moments of inertia of the steel and bamboo plywood cross sections, respectively.

[0079] In some embodiments, the overall bending stiffness EI of the composite beam can be calculated by the superposition principle. Specifically, the overall bending stiffness is determined by the sum of the bending stiffness of the steel and the bamboo plywood, and the calculation formula is:

[0080] EI=EI s +EI b

[0081] As a possible implementation method, for areas with openings, the moment of inertia needs to take into account the stiffness reduction caused by the openings. In general, the combined moment of inertia of the opening area I h It can be expressed as:

[0082] I h =I s +I b

[0083] However, in actual calculation, it is necessary to adjust the i according to the size and position of the opening. h Corrections are made to reflect the reduction in bending stiffness caused by the openings.

[0084] Specifically, in certain embodiments, the linear stiffness i of the open hole area is calculated by the following formula:

[0085]

[0086] Where a0 is the opening width, EI h is the combined inertia moment of the opening area. The introduction of linear stiffness can more accurately describe the effect of the opening on the local deflection.

[0087] S3. According to the loading conditions, calculate the overall deflection without opening and the local deflection under the influence of opening.

[0088] In order to accurately describe the overall deformation of the steel-bamboo composite beam with web openings, it is necessary to calculate the overall deflection in the unperforated state and the local deflection under the influence of the openings based on the loading conditions. These two parts are the core components of the calculation of the deflection of the whole beam. In general, the deflection of the unperforated beam can be calculated by the classical mechanics formula, and the influence of the opening on the local deflection can be analyzed by combining the secondary bending moment and local stiffness changes in the perforated area. In some embodiments, the two parts of the deflection can also be integrated through the superposition principle to construct a more complete deflection distribution model.

[0089] In this embodiment, the calculation of the overall deflection without openings is based on the full length and overall stiffness of the composite beam. In general, the deflection of the steel-bamboo composite beam without openings under the action of concentrated load F can be expressed as:

[0090]

[0091] Among them, EI is the overall bending stiffness of the composite beam, L is the total length of the beam, and x is the distance from the load application point to the left support.

[0092] As an option, if the load position changes, for example, not in the middle of the span but towards one end, the deflection formula needs to be adjusted accordingly, still based on the classical beam deflection formula in elastic mechanics.

[0093] Specifically, the effect of the opening on the local deflection is mainly reflected in the distribution of the secondary bending moment and the weakening of the local stiffness. In a possible implementation, the secondary bending moment balance relationship in the opening area can be expressed as:

[0094] M1+M2=a0·F

[0095] Among them, M1 and M2 are the bending moments on both sides of the opening, a0 is the diameter of the opening, and F is the applied load.

[0096] The local deflections on both sides of the opening can be expressed as:

[0097]

[0098] Among them, l1 and l2 are the lengths of the beam segments on the left and right sides of the opening area, respectively, L is the length of the entire beam, and i is the linear stiffness of the opening area.

[0099] In some embodiments, the sum of the local deflections can represent the overall deflection contribution of the open area, and the specific formula is:

[0100]

[0101] In this formula, l1+l2 is the total length of both ends of the opening area, and i is the line stiffness.

[0102] In a possible implementation, for a larger opening, the deflection distribution may present nonlinear characteristics. In this case, the above formula needs to be corrected by numerical methods to improve the adaptability of the model.

[0103] Specifically, in order to reflect the weakening of the overall stiffness caused by the opening, a correction model is further proposed in this embodiment, which adjusts the calculation result of the deflection without opening by introducing a reduction coefficient λ to make it more consistent with the experimental data. The corrected overall deflection expression is:

[0104]

[0105] Where λ is the stiffness reduction factor, which is usually taken as 0.96.

[0106] In some embodiments, the calculation of the secondary bending moment and local deflection can be further refined according to the specific position and shape of the opening area. For example, when the opening is close to the support point, the contribution of the local deflection to the overall deflection will be significantly reduced, and the effect of the opening on the mid-span deflection can be appropriately ignored.

[0107] S4. Superimpose the deflection of the unopened hole and the deflection of the opened hole

[0108] In order to accurately describe the overall deformation behavior of the steel-bamboo composite beam with web openings under loading conditions, the present invention is based on the deflection superposition principle, and comprehensively calculates the overall deflection under the condition of no openings and the local deflection caused by the openings, so as to obtain a complete deflection distribution curve. In general, by superimposing the deflections without openings and the deflections affected by openings, the overall stiffness characteristics of the steel-bamboo composite beam and the local effects of the opening area can be fully reflected. In a possible implementation, the superposition process simultaneously considers the comprehensive influence of the opening position and the distribution of the secondary bending moment on the deflection distribution.

[0109] In this embodiment, the calculation of the whole beam deflection follows the superposition principle, that is, the overall deflection f(Δ) of the composite beam can be expressed as the superposition of the deflection f(Δ1) of the unopened area and the deflection f(Δ2) of the opened area. The formula is as follows:

[0110] f(Δ)=f(Δ1)+f(Δ2)

[0111] In the superposition process, in order to ensure the accuracy of the overall deflection calculation, it is necessary to distinguish and check the contribution areas of the unperforated deflection and the perforated deflection. This implementation adopts a segmented analysis method to describe the unperforated and perforated areas separately.

[0112] In general, the deflection f(Δ1) without openings is determined by the bending stiffness EI of the whole beam and the load position, which has been clearly described in the previous steps. For the deflection f(Δ2) with openings, the present invention further refines the distribution law of the deflection. Specifically, the deflection effect of the opening area is mainly concentrated near the opening position, and the local deformation caused by the bending moment will cause the deflection distribution of the whole beam to shift toward the opening area.

[0113] As a possible implementation method, a correction factor λ needs to be introduced in the superposition process to reflect the nonlinear effects of interface slip and opening stiffness reduction under actual working conditions. The correction factor can be calibrated by test data and is usually around 0.96.

[0114] In the superposition calculation, the mutual influence between the local stiffness of the opening area and the stiffness of the whole beam needs to be considered. In one embodiment, a piecewise function is constructed to express the deflection distribution law of the non-opening area and the opening area.

[0115] In some embodiments, the focus of the superposition calculation is also on the offset position of the maximum deflection. Generally, the maximum deflection of the entire beam no longer occurs in the mid-span, but is biased to one side of the opening area. During the superposition process, the maximum deflection position can be effectively determined by comparing the deflection values ​​of different areas.

[0116] In one possible implementation, the deflection distribution curve of the whole beam can be plotted to intuitively display the comprehensive deformation characteristics of the beam without holes and holes. For example, the curve is still close to the classic bending shape near the mid-span position, but there will be obvious asymmetric offset in the hole area. This offset characteristic has important guiding significance for optimizing the design of the hole position and reducing the deflection deformation.

[0117] Through the above-mentioned superposition calculation, the present invention can comprehensively reflect the comprehensive influence of the deflection of the open hole and the open hole on the overall deflection distribution, providing a reliable basis for the subsequent maximum deflection analysis, and laying a theoretical foundation for the optimal design and practical engineering application of open hole steel-bamboo composite beams.

[0118] S5. Determine the maximum deflection of the composite beam and its position

[0119] The present invention further determines the maximum deflection value and its occurrence position of the steel-bamboo composite beam with web openings by calculating the deflection distribution. In general, the maximum deflection position of the steel-bamboo composite beam without openings usually occurs at the mid-span position, and the influence of the openings causes the deflection distribution curve to shift, and the maximum deflection position may deviate from the mid-span. As a possible implementation method, the present invention combines the aforementioned superimposed deflection distribution model and uses an analytical method or a numerical iteration method to accurately obtain the maximum deflection value and its corresponding position, providing key data support for the design and verification of the composite beam.

[0120] In this embodiment, the maximum deflection of the composite beam is calculated based on the overall deflection distribution model. max The derivative of the overall deflection function satisfies the condition of zero, that is:

[0121]

[0122] Specifically, the deflection function f(Δ) has different expressions in the unperforated area and the perforated area, so it is necessary to calculate the maximum deflection position in sections. In the unperforated area, the deflection distribution curve is mainly controlled by the classical bending formula, and its maximum value usually appears at the mid-span position. In the opening area, the distribution curve of the deflection is affected by the weakening of the local stiffness, and its maximum value may be biased toward the opening area. To this end, the present invention introduces the following steps to determine the maximum deflection position of the opening area:

[0123] As a possible implementation method, the deflection distribution of the opening area is affected by the opening width a0, the secondary bending moments M1, M2 and the line stiffness i. By deriving the deflection distribution of the opening area through a piecewise function and combining the equilibrium relationship of the secondary bending moment M1+M2=a0·F, the maximum deflection position after offset can be further determined.

[0124] In some embodiments, the maximum deflection value f(Δ max ) can be obtained by substituting the maximum deflection position into the overall deflection function. The specific formula is:

[0125] f(Δ max )=f(Δ1)+f(Δ2)

[0126] Among them, f(Δ1) is the deflection part without opening, and f(Δ2) is the deflection part with opening.

[0127] As an extension, if the maximum deflection position is offset to the vicinity of the opening area, the calculation of the maximum deflection needs to be further corrected. After introducing the correction coefficient λ, the correction formula is as follows:

[0128]

[0129] Among them, x max is the maximum deflection position, EI is the overall stiffness, and i is the opening line stiffness.

[0130] In one possible implementation, if the opening area is close to the support or far away from the mid-span, the position of the maximum deflection may be affected by the support constraint or the weakening of the secondary bending moment. In this case, the deflection distribution can be iteratively solved by numerical analysis, and the offset range can be corrected in combination with experimental data.

[0131] In general, the calculated maximum deflection value f(Δ max) should be checked against the design standard to ensure that it meets the allowable deflection requirements. For example, when the allowable deflection specified in the design standard is The following conditions should be met:

[0132]

[0133] Specifically, if the calculated maximum deflection value exceeds the allowable deflection range, it is necessary to reduce the maximum deflection value by optimizing the opening position, reducing the opening size, or adding reinforcement measures (such as longitudinal stiffening ribs or criss-cross stiffening ribs).

[0134] Through the above process, the present invention can accurately determine the maximum deflection value and position of the composite beam, providing a key theoretical basis for optimizing the design of the composite beam, while ensuring its safety and reliability in practical engineering applications.

[0135] The present invention introduces a superposition model of the overall deflection of the unperforated area and the local deflection of the perforated area, combined with the analysis of the position, size and material properties of the perforated area, to accurately calculate the overall deflection distribution and the maximum deflection position of the composite beam. The method comprehensively considers the elastic properties of the steel-bamboo composite material, the weakening of the rigidity in the perforated area and the influence of the secondary bending moment distribution, and proposes a calculation model of the correction coefficient and piecewise function, which can effectively solve the deflection offset problem caused by the perforation, and provides a theoretical basis and calculation method for optimizing the perforation arrangement and improving the performance of the beam structure in engineering design. At the same time, the present invention has the characteristics of strong versatility and high calculation accuracy, and can be widely used in the design and verification of perforated steel-bamboo composite beams.

[0136] In order to better understand the present invention, the above method is described in detail below in conjunction with specific embodiments.

[0137] Example:

[0138] Please see attached Figure 2 -Attached Figure 3 This embodiment proposes a deflection calculation method for the change in the overall stress performance of the steel-bamboo composite beam with web openings after the openings. Generally, web openings will change the stiffness distribution characteristics of the composite beam, resulting in the maximum deflection value of the entire beam under the normal service limit state being affected by the opening parameters, deviating from the regular distribution of the mid-span position of the traditional non-hole composite beam. The existing non-hole steel-bamboo composite beam deflection calculation formula cannot accurately reflect the impact of the openings on the deflection distribution and the maximum deflection position.

[0139] This embodiment combines test data and structural damage phenomena to establish a deflection calculation model that comprehensively considers the influence of openings and the mechanical properties of bamboo, which is used to calculate the specific location of the maximum deflection value of the entire beam and the deflection deformation of the entire beam. Specifically, based on the superposition principle, the overall deflection is decomposed into two parts: one part is the deflection f(Δ1) of the entire beam when the influence of openings is not considered, and the other part is the deflection f(Δ2) of the entire beam when only the influence of openings is considered. Figure 2 As shown in Fig. 2b and Fig. 2c, the flexural deformation of the composite beam under load is obtained by superimposing the calculation results of f(Δ1) and f(Δ2) to obtain the complete deflection distribution curve.

[0140] In order to simplify the calculation process of the deflection of steel-bamboo composite beams with web openings and ensure that the calculation model can effectively reflect the deformation characteristics under actual loading conditions, the following basic assumptions are proposed based on experimental phenomena and data.

[0141] Generally speaking, when the steel-bamboo composite beam with web openings reaches the limit state of normal use, the whole is still in the elastic working stage. Specifically, in order to simplify the analysis process, this embodiment assumes that the materials are in an elastic state, that is, the nonlinear effect of the material stiffness changing with stress and the effect of plastic deformation on the deflection distribution are not considered. In addition, the interface bonding quality between steel and bamboo plywood is good, and the local instability of the beam body and the relative slip that may occur at the steel-bamboo interface are ignored in the calculation, thereby ensuring the applicability and stability of the model.

[0142] In the calculation of the deflection f(Δ2) of the opening area, this embodiment further makes an assumption that only the direct effect of the opening on the beam deflection is considered, and the beam sections on both sides of the opening are treated as rigid bodies, thereby simplifying the transfer calculation of the secondary bending moment. In addition, in order to facilitate the calculation of the secondary bending moment effect caused by the shear force, it is assumed that the inflection point of the opening area is located at the center of the opening. This assumption can better reflect the bending stiffness distribution of the opening area.

[0143] In terms of material mechanical properties, the bamboo plywood is approximately regarded as a transversely isotropic material in this embodiment, that is, it exhibits similar elastic properties in the radial and chord directions of the bamboo plywood. This assumption fully considers the orthogonal anisotropy characteristics of bamboo and simplifies the description of the performance of the bamboo plywood under complex stress states in the calculation.

[0144] Equation derivation:

[0145] The deflection equation of the composite beam can be written as:

[0146] f(Δ)=f(Δ1)+f(Δ2) (1)

[0147] Among them, f(Δ1) is the calculation formula for the overall deflection of the beam without holes in the web under load, which is written as:

[0148]

[0149] Where:

[0150] L—calculated span of the whole beam;

[0151] EI—is the bending stiffness of the composite beam section (EI=EI s +EI b ).

[0152] During the loading process, bamboo is basically in a complex stress state. The uniaxial stress performance measured by the test cannot be simply applied to the von-Mises classical strength theory to define the bamboo yield criterion. This embodiment refers to the Hill yield criterion and sets different coefficients before each principal stress to consider the contribution of each principal stress to the equivalent stress of the material. At the same time, considering that bamboo is a transversely isotropic material, the yield strength of bamboo under a complex stress state can be calculated as shown in formula (2.1).

[0153]

[0154] Where:

[0155] X, Y, Z—yield strength of bamboo in the 1st, 2nd, 3rd principal stress directions;

[0156] S ij —Shear strength of bamboo in the ij plane.

[0157] The stress condition of the opening area in f(Δ2) is as follows Figure 3 As shown, the equilibrium relationship of the opening section is written as:

[0158] M1+M2=a0×f (3)

[0159] The relationship between the deformation of the opening and the secondary bending moment generated by the shear force satisfies the following equation:

[0160]

[0161]

[0162] Where:

[0163] i—Linear stiffness of opening area

[0164] I h —Moment of inertia of steel-bamboo composite beams

[0165] Substituting equations (4) and (5) into equation (3), we can obtain

[0166]

[0167] Since the inflection point of the secondary bending moment in the opening area is in the middle of the opening, it can be obtained that

[0168]

[0169] Substituting equations (4) and (5) into equation (7), we can obtain

[0170]

[0171] The deflection relationship of the opening area conforms to

[0172] δ1+δ2=δ (9) Combining equations (6), (8), and (9) we can obtain δ1, δ2, and δ

[0173]

[0174] In the opening area, the differential equation can be established

[0175]

[0176] Substitute the boundary conditions and solve for the integral constants A and B

[0177]

[0178] Because when calculating f(Δ1), the stiffness of the section without weakening is used to replace the stiffness of the section with the web opening and the relative slip of the adhesive joint is not considered, when substituting the integral constant back into formula (11), the reduction factor λ = 0.96 is introduced to solve the deflection differential function of the composite beam with opening;

[0179]

[0180] The deflection calculation device of the steel-bamboo composite beam with web openings described below and the deflection calculation method of the steel-bamboo composite beam with web openings described above can be referred to each other.

[0181] Please see attached Figure 4 -Attached Figure 5 The present invention also provides a device for calculating the deflection of a steel-bamboo composite beam with web openings, comprising:

[0182] A data input module 10 is used to input geometric parameters, material parameters and opening dimensions of the steel-bamboo composite beam;

[0183] The deflection calculation module 20 is used to calculate the overall deflection of the unperforated area and the local deflection of the perforated area based on the input data;

[0184] A superposition module 30, for determining the deflection distribution of the entire beam according to the superposition principle;

[0185] The display module 40 is used to output the whole beam deflection curve and the maximum deflection position.

[0186] Wherein, the deflection calculation module 20 includes:

[0187] The first calculation module 21 is used to calculate the overall deflection without openings;

[0188] The second calculation module 22 is used to calculate the secondary bending moment and local deflection of the opening area;

[0189] The correction module 23 is used to correct the deflection result according to the anisotropy of bamboo and the influence of the steel-bamboo interface slip.

[0190] The device of this embodiment can be used to execute the above method embodiment, and its principles and technical effects are similar, which will not be repeated here.

[0191] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the deflection of a steel-bamboo composite beam with web openings, characterized in that: The following steps are involved: Determine the structural parameters of the steel-bamboo composite beam, including beam length, opening size, location, and loading point location; Determine the mechanical properties of steel and bamboo plywood, and calculate the overall bending stiffness of the composite beam; According to the loading conditions of the composite beam, the overall deflection without openings and the local deflection under the influence of openings are calculated respectively; The deflection without openings is superimposed with the deflection with openings to obtain the overall deflection distribution of the composite beam; Determine the maximum deflection of the composite beam and its location; When the deflection without opening is superimposed with the deflection with opening, the correction coefficient λ is introduced to characterize the influence of the slip of the steel-bamboo interface and the weakening of the opening stiffness. The correction formula is: Among them, λ is the reduction factor, which is 0.96, a0 is the opening diameter, F is the applied load, L is the total length of the beam, i is the linear stiffness of the opening area, EI is the overall bending stiffness, and x is the horizontal distance from the starting point of the support at one end of the beam to the specified position along the length direction of the beam.

2. The method for calculating the deflection of a steel-bamboo composite beam with web openings according to claim 1 is characterized in that: The structural parameters include the section inertia moment of the steel, the thickness and width of the bamboo plywood, the diameter and height of the opening, and the position of the opening area; The overall bending stiffness of the composite beam is the superposition value of the bending stiffness of the steel material and the bending stiffness of the bamboo plywood.

3. The method for calculating the deflection of a steel-bamboo composite beam with web openings according to claim 1, characterized in that: The overall deflection when no hole is opened is calculated by the following formula: Among them, F is the concentrated load, EI is the overall bending stiffness, L is the span of the beam, and x is the horizontal distance from the starting point of one end support of the beam to the specified position along the length direction of the beam.

4. The method for calculating the deflection of a steel-bamboo composite beam with web openings according to claim 1, characterized in that: The local deflection under the influence of the opening is calculated according to the following formula: Among them, δ1 and δ2 are the local deflections at the left and right ends of the opening area, δ is the total deflection of the opening area, l1 and l2 are the distances between the two ends of the opening, a0 is the opening diameter, F is the applied load, L is the total length of the beam, and i is the linear stiffness of the opening area.

5. The method for calculating the deflection of a steel-bamboo composite beam with web openings according to claim 4 is characterized in that: The linear stiffness i of the opening area is calculated according to the following formula: Among them, EI h is the bending stiffness of the opening area, and a0 is the opening diameter.

6. The method for calculating the deflection of a steel-bamboo composite beam with web openings according to claim 4, characterized in that: The local deflection distribution under the influence of the opening is expressed by the secondary moment equilibrium equation: HE h y″=M1-Fx Where y″ is the second-order derivative of the deflection curve, M1 is the secondary bending moment at the opening, F is the applied load, x is the horizontal distance from the left edge of the opening to the specified position along the length of the beam, and EI h is the bending stiffness of the opening area.

7. The method for calculating the deflection of a steel-bamboo composite beam with web openings according to claim 4, characterized in that: The deflection function of the local deflection distribution under the influence of the opening is expressed by the following formula: Where y is the deflection, M1 is the secondary bending moment at the opening, F is the applied load, x is the horizontal distance from the left edge of the opening to the specified position along the length of the beam, and A and B are integration constants determined by boundary conditions.

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