A method for calculating deflection of a web-opening steel-bamboo composite beam

Abstract

The application relates to the field of building structure engineering and discloses a deflection calculation method for a web-opening steel-timber composite beam, which comprises the following steps: determining the geometric parameters, material parameters and opening size of the steel-timber composite beam; measuring the mechanical property parameters of steel and bamboo plywood, and calculating the overall bending stiffness of the composite beam; respectively calculating the overall deflection without openings and the local deflection under the influence of openings according to loading conditions; superimposing the deflection without openings and the deflection with openings to obtain the overall deflection distribution of the composite beam; and determining the maximum deflection value and the position of the composite beam. Through the establishment of the superposition model of the deflection of the non-opening and opening areas, the transverse isotropic characteristics of the bamboo, the steel stiffness and the secondary bending moment distribution of the opening area are comprehensively considered, the influence of the openings on the overall deflection can be accurately calculated, the opening arrangement design is optimized, and a theoretical basis is provided for the structure design and checking of the steel-timber composite beam.

Description

Technical Field

[0001] This invention relates to the field of building structure engineering technology, specifically to a method for calculating the deflection of a steel-bamboo composite beam with perforated web. Background Technology

[0002] With the increasing demands for space utilization and functionality in building construction, the design of beams with open webs has gradually become an important method for optimizing building structural performance. In modern buildings, openings are often required in the beam webs to accommodate pipeline equipment (such as HVAC and water supply systems), thereby reducing the equipment's impact on the building's height. However, the introduction of openings inevitably weakens the local stiffness of the beam, further affecting its overall bending performance. Especially in composite beams, the secondary bending moments and stress distribution in the open area are significantly altered, making traditional design and analysis methods difficult to apply.

[0003] Steel-bamboo composite beams, as a novel green building structure, have garnered widespread attention in structural engineering due to the lightweight, high strength, and renewable advantages of bamboo, combined with the high stiffness and shear resistance of steel. However, the heterogeneity of the material properties of steel-bamboo composite beams leads to more complex deflection distribution characteristics after perforation. Existing research mainly focuses on the overall mechanical performance analysis of steel-bamboo composite beams without perforations, with limited research on the local stiffness changes and maximum deflection shifts caused by perforations. Furthermore, existing deflection calculation methods are largely based on the assumption of homogeneous beams without perforations, which fails to effectively describe the actual deformation behavior of steel-bamboo composite beams.

[0004] The main technical challenges posed by openings lie in the asymmetry of deflection distribution and the shift in the location of maximum deflection. Traditional deflection analysis methods fail to adequately consider the impact of stiffness reduction in the opening area on the overall deflection distribution, easily leading to significant deviations in calculation results. Furthermore, existing designs lack an efficient and accurate computational model to analyze the deflection characteristics of steel-bamboo composite beams after openings, particularly for predicting the maximum deflection value and its location under different opening positions, sizes, and loading conditions. Therefore, a computational method capable of accurately analyzing the deflection characteristics of steel-bamboo composite beams with web openings is needed to address the impact of openings on the overall stiffness and deflection distribution of the composite beam, providing reliable theoretical support for optimized design. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a deflection calculation method for steel-bamboo composite beams with web openings, solving the problem of difficulty in accurately analyzing the local stiffness reduction and maximum deflection offset caused by web openings in existing steel-bamboo composite beam deflection calculations.

[0006] To achieve the above objectives, the present invention provides the following technical solution: 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] The mechanical properties of steel and bamboo plywood were determined, and the overall bending stiffness of the composite beam was calculated.

[0009] Based on 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 overall deflection distribution of the composite beam is obtained by superimposing the deflection without holes and the deflection with holes.

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

[0012] Preferably, the structural parameters include the moment of inertia of the steel section, the thickness and width of the bamboo plywood, the diameter and height of the opening, and the location of the opening area;

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

[0014] Preferably, the overall deflection without openings is calculated using the following formula:

[0015]

[0016] Where 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 along the length of the beam to the specified position.

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

[0018]

[0019] Where 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 diameter of the opening, 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 region is calculated according to the following formula:

[0021]

[0022] Among them, EI h denoted as , where is the bending stiffness of the opening region, and a0 is the diameter of the opening.

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

[0024] EIh y″=M1-Fx

[0025] Where y″ is the second 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 along the beam length to the specified position, and EI h This represents the bending stiffness of the perforated 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 along the beam length to the specified position, and A and B are integral constants determined by the boundary conditions.

[0029] Preferably, when superimposing the unperforated deflection with the perforated deflection, a correction coefficient λ is introduced to characterize the effects of steel-bamboo interface slippage and weakened perforated stiffness. The correction formula is as follows:

[0030]

[0031] Where 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 one end support of the beam along the length of the beam to the specified position.

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

[0033] The data input module is used to input the geometric parameters, material parameters, and opening dimensions of the steel-bamboo composite beam;

[0034] The deflection calculation module is used to calculate the overall deflection of the un-drilled area and the local deflection of the drilled area based on the input data.

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

[0036] The display module is used to output the deflection curve of the entire beam and the location of the maximum deflection.

[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 in the opening area;

[0040] The correction module is used to correct the deflection results based on the anisotropy of bamboo and the slippage effect at the steel-bamboo interface.

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

[0042] 1. This invention establishes a superposition model of the overall deflection without openings and the local deflection in the opening area, comprehensively considering the effects of local stiffness reduction and secondary bending moment distribution caused by openings. Compared with the traditional model assuming no openings, this method can accurately describe the deflection distribution under actual working conditions, especially when the maximum deflection position is offset, significantly improving the accuracy of deflection calculation and providing more reliable reference data for engineering design.

[0043] 2. Based on parametric input of opening size, location, and beam span length, this invention allows for flexible adjustment of the deflection calculation model, adapting to composite beam designs with different opening arrangements. Whether the opening is located at mid-span or near the support, this method can accurately analyze the impact of the opening on the overall deflection distribution, demonstrating strong applicability and universality.

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

[0045] 4. This invention combines the elastic modulus of steel and bamboo plywood with the secondary bending moment distribution characteristics of the perforated area to propose a simple and easy-to-use deflection calculation method. It takes into account both the accuracy of the theoretical model and the simplicity of the calculation process, making it easy to promote and apply in engineering and helping to improve the design reliability and structural performance of perforated steel-bamboo composite beams.

[0046] 5. By calculating the maximum deflection and deflection distribution curve, this invention can intuitively demonstrate the impact of openings on the overall stiffness of steel-bamboo composite beams, providing a scientific basis for optimizing opening arrangement and dimensional 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 composite beams. Attached Figure Description

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

[0048] Figure 2 The following is a simplified calculation diagram of the web-perforated composite beam according to an embodiment of the present invention; wherein, (a) is the actual deflection curve, (b) without considering the effect of the perforation, and (c) only considering the effect of the perforation;

[0049] Figure 3Force diagram within the opening area according to an embodiment of the present invention;

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

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

[0052] Among them, 10 is the data input module; 20 is the deflection calculation module; 21 is the first calculation module; 22 is the second calculation module; 23 is the correction module; 30 is the superposition module; and 40 is the display module. Detailed Implementation

[0053] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Please see the appendix Figure 1 This invention provides a method for calculating the deflection of a steel-bamboo composite beam with web openings. By simplifying the mechanical model and introducing correction coefficients, the method accurately models and calculates the influence of the openings in the steel-bamboo composite beam, effectively predicting the deflection distribution and the location of the maximum deflection. The steps of this invention are described in detail below.

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

[0056] First, the structural parameters of the steel-bamboo composite beam need to be determined. These parameters form the basis for deflection calculations 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 in the composite beam, necessary input data is provided for subsequent deflection calculations. In some implementations, depending on the actual engineering application requirements, some parameters can be adjusted according to specific design conditions to optimize the impact of the opening design on deflection performance.

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

[0058] Generally, the total length L of a steel-bamboo composite beam refers to the distance between the supports at both ends of the beam, which can be obtained directly from design drawings or actual measurements. Alternatively, in structures with large spans, the total length of the beam can also include a certain length of support extension to account for boundary effects in calculations.

[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 cross section b and height h b In one possible implementation, the steel section is typically made of cold-formed thin-walled steel, the width and height of which can be obtained by consulting a standard profile size table or by on-site measurement; the width and height of the bamboo plywood section can be determined by the processing dimensions of standard material samples.

[0060] In some implementations, the opening dimensions include the diameter a0 and the height h0. Generally, the diameter a0 is the dimension that extends transversely through the beam web, while the height h0 is typically the sum of the thicknesses of the bamboo plywood and the steel web. Alternatively, when the opening height is small, its impact on deflection calculation can be ignored, and only the width a0 is retained as a calculation parameter.

[0061] The location of the opening refers to the distance from the center of the opening to the left end support of the beam, denoted 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 implementations, the location of the opening can be adjusted according to actual engineering needs to optimize the degree to which the opening weakens the overall stiffness of the beam. Generally, the opening should be placed in the low bending-shear ratio region to reduce its impact on the maximum deflection offset.

[0064] The loading point location refers to the specific location where the concentrated load F is applied, denoted by the distance x from the left support. As one possible implementation, the loading point is typically placed at mid-span to calculate the deflection at the location of maximum bending moment. In certain special cases, the loading point can be offset from mid-span to analyze the contribution of eccentric loading to the deflection in the area affected by the opening.

[0065] In one possible implementation, the measurement and calculation of parameters can be further refined. For example, 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 b represents the cross-sectional width and height of the steel. b ,h b This refers to 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 open area of ​​the steel-bamboo composite beam.h Generally speaking, I h It can be determined experimentally or calculated using the superposition principle:

[0069] I h =I s +I b

[0070] Alternatively, the perforated area can be treated as a simplified section, and the effect of the perforation on stiffness reduction can be simulated by adjusting the moment of inertia.

[0071] In some implementations, the beam's geometric parameters and loading conditions can also be verified using finite element modeling, thereby more accurately determining the calculation input parameters. As an extension, the geometric parameters and loading point locations obtained in this implementation can be further used for deflection distribution analysis, providing guidance for subsequent optimization design.

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

[0073] To ensure the accuracy of deflection calculations for perforated steel-bamboo composite beams, this invention requires precise measurement of the mechanical properties of the steel and bamboo plywood, and simultaneous calculation of the overall bending stiffness of the composite beam based on its geometric dimensions and material parameters. This process forms the basis for subsequent deflection calculations and distribution analysis. Generally, material property parameters and section bending stiffness can be obtained quickly and accurately through a combination of standard testing methods and theoretical calculations. In some embodiments, experimental measurements can be used to verify the moment of inertia calculation, thereby optimizing the accuracy of the bending stiffness calculation.

[0074] In this embodiment, the elastic modulus E of the steel s The elastic modulus E of bamboo plywood b The elastic modulus is obtained through experimental determination. Specifically, it can be determined by conducting tensile tests on steel specimens according to the standard "Metallic Materials - Tensile Testing - Part 1: Tests at Room Temperature" (GB / T 228.1-2021). As a transversely isotropic material, the elastic modulus of bamboo plywood needs to be measured separately along both the grain direction and perpendicular to the grain direction, and then the average value is taken as an approximate equivalent elastic modulus. The elastic modulus of bamboo plywood can be tested according to the standard "Test Methods for Physical and Mechanical Properties of Defect-Free Small Samples of Wood".

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

[0076] Generally, the modulus of elasticity of steel and bamboo plywood can be directly used to calculate their respective bending stiffness EI. s and EI b As an alternative, the bending stiffness EI of steel... s And the bending stiffness EI of bamboo plywood 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 These are the moments of inertia of the steel and bamboo plywood sections, respectively.

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

[0080] EI = EI s +EI b

[0081] As one possible implementation, for regions with openings, the moment of inertia needs to consider the stiffness reduction caused by the openings. Generally, the combined moment of inertia I for regions with openings... h It can be represented as:

[0082] I h =I s +I b

[0083] However, in actual calculations, i needs to be adjusted based on the opening size and location. h The corrections are made to reflect the reduction in bending stiffness caused by the opening.

[0084] Specifically, in some implementations, the linear stiffness i of the opening region is calculated by the following formula:

[0085]

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

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

[0088] To accurately describe the overall deformation of a steel-bamboo composite beam with web openings, it is necessary to calculate the overall deflection in the unopened 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 overall beam deflection calculation. Generally, the deflection of the unopened beam can be calculated using classical mechanics formulas, while the influence of the openings on the local deflection can be analyzed by combining the secondary bending moment and local stiffness changes in the open area. In some implementations, the two deflection components can be integrated using the superposition principle to construct a more complete deflection distribution model.

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

[0090]

[0091] Where 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 alternative, if the load location changes, for example, instead of being at the mid-span but biased towards one end, the deflection formula needs to be adjusted accordingly, still based on the classical beam deflection formula in elasticity mechanics.

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

[0094] M1 + M2 = a0·F

[0095] Where 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 follows:

[0097]

[0098] Where 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 implementations, the sum of local deflections can characterize the overall deflection contribution of the opening region, as shown in the following formula:

[0100]

[0101] In this formula, l1+l2 is the total length of the two ends of the opening region, and i is the linear stiffness.

[0102] In one possible implementation, the deflection distribution may exhibit nonlinear characteristics when the opening is large. In this case, numerical methods are needed to modify the above formula to improve the model's adaptability.

[0103] Specifically, to reflect the reduction in overall stiffness caused by the opening, this embodiment further proposes a modified model. This model introduces a reduction coefficient λ to adjust the calculated deflection without the opening, making it more consistent with experimental data. The modified overall deflection expression is:

[0104]

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

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

[0107] S4. Superimpose the deflection without openings with the deflection with openings.

[0108] To accurately describe the overall deformation behavior of a steel-bamboo composite beam with web openings under loading conditions, this invention, based on the principle of deflection superposition, comprehensively calculates the overall deflection under the unopened condition and the local deflection caused by the opening effect, thereby obtaining a complete deflection distribution curve. Generally, by superimposing the deflections under the unopened and opened conditions, the overall stiffness characteristics of the steel-bamboo composite beam and the local effects of the open area can be fully reflected. In one possible implementation, this superposition process simultaneously considers the combined influence of the opening location and the distribution of secondary bending moments on the deflection distribution.

[0109] In this embodiment, the deflection calculation of the entire beam follows the superposition principle, that is, the overall deflection f(Δ) of the composite beam can be expressed as the superposition of the deflection without openings f(Δ1) and the deflection of the opening area f(Δ2). The formula is as follows:

[0110] f(Δ)=f(Δ1)+f(Δ2)

[0111] During the superposition process, to ensure the accuracy of the overall deflection calculation, it is necessary to distinguish and verify the contribution areas of the un-drilled deflection and the drilled deflection. This implementation method adopts a segmented analysis approach, describing the un-drilled and drilled areas separately.

[0112] Generally, the deflection f(Δ1) without openings is determined by the bending stiffness EI of the entire beam and the load location, as clearly described in the preceding steps. For the deflection f(Δ2) with openings, this invention further refines the distribution law of deflection. Specifically, the deflection influence in the opening area is mainly concentrated near the opening location, and secondly, the local deformation caused by the bending moment will cause the deflection distribution of the entire beam to shift towards the opening area.

[0113] As one possible approach, a correction coefficient λ needs to be introduced during the superposition process to reflect the nonlinear effects of interface slippage and reduced opening stiffness under actual working conditions. The correction coefficient can be calibrated using experimental data and is typically taken to be around 0.96.

[0114] In the superposition calculation, the interaction between the local stiffness of the perforated region and the overall beam stiffness must also be considered. In one implementation, a piecewise function is constructed to express the deflection distribution patterns of the perforated and non-perforated regions.

[0115] In some implementations, the focus of the superposition calculation is also on the offset location of the maximum deflection. Generally, the maximum deflection of the entire beam no longer occurs at the mid-span, but rather towards the opening area. During the superposition process, the location of the maximum deflection can be effectively determined by comparing the deflection values ​​of different regions.

[0116] In one possible implementation, the combined deformation characteristics of the beam with and without openings can be visually displayed by plotting the deflection distribution curve of the entire beam. For example, the curve remains close to the classic bending shape near the mid-span, while a significant asymmetric offset occurs in the opening area. This offset characteristic is of great guiding significance for optimizing the design of opening positions and reducing deflection deformation.

[0117] Through the above superposition calculations, the present invention can comprehensively reflect the combined influence of unperforated and perforated deflections on the overall deflection distribution, providing a reliable basis for subsequent maximum deflection analysis, and laying a theoretical foundation for the optimized design and practical engineering application of perforated steel-bamboo composite beams.

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

[0119] This invention, through the calculation of deflection distribution, further determines the maximum deflection value and its location in steel-bamboo composite beams with web openings. Generally, the maximum deflection of an un-opened steel-bamboo composite beam typically occurs at the mid-span, while the opening causes a shift in the deflection distribution curve, potentially causing the maximum deflection location to deviate from the mid-span. As one possible implementation, this invention combines the aforementioned superimposed deflection distribution model with analytical methods or numerical iteration methods to accurately determine the maximum deflection value and its corresponding location, providing crucial data support for the design and verification of composite beams.

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

[0121]

[0122] Specifically, the expression for the deflection function f(Δ) differs between the unperforated and perforated regions, thus requiring piecewise calculation of the location of maximum deflection. In the unperforated region, the deflection distribution curve is primarily controlled by the classical bending formula, with its maximum value typically occurring at the mid-span. In the opening region, the deflection distribution curve is affected by the local stiffness reduction, and its maximum value may be biased towards the opening region. Therefore, this invention introduces the following steps to determine the location of the maximum deflection in the opening region:

[0123] As one possible implementation, the deflection distribution in the opening region is influenced by the opening width a0, secondary bending moments M1 and M2, and linear stiffness i. By differentiating the deflection distribution in the opening region using a piecewise function and combining it with the equilibrium relationship of secondary bending moments M1 + M2 = a0·F, the location of the maximum deflection after offset can be further determined.

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

[0125] f(Δ max f(Δ1) + f(Δ2)

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

[0127] As an extension, if the location of the maximum deflection shifts to the vicinity of the opening area, the calculation of the maximum deflection needs further correction. Introducing a correction factor λ, the corrected formula is as follows:

[0128]

[0129] Where, x max The position of maximum deflection is EI, the overall stiffness is EI, and the stiffness of the opening line is i.

[0130] In one possible implementation, if the opening area is close to the support or far from the mid-span, the location of the maximum deflection may be affected by support constraints or the reduction of secondary bending moments. In this case, the deflection distribution can be iteratively solved using numerical analysis, and the offset range can be corrected by combining experimental data.

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

[0132]

[0133] Specifically, if the calculated maximum deflection value exceeds the allowable deflection range, the maximum deflection value needs to be reduced by optimizing the opening position, reducing the opening size, or adding reinforcement measures (such as longitudinal stiffeners or grid-shaped stiffeners).

[0134] Through the above process, the present invention can accurately determine the maximum deflection value and location 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] This invention introduces a superposition model of the overall deflection without openings and the local deflection in the opening area. Combined with the analysis of the opening location, size, and material properties, it accurately calculates the overall deflection distribution and the location of maximum deflection in composite beams. This method comprehensively considers the elastic properties of the steel-bamboo composite material, the weakening of stiffness in the opening area, and the influence of secondary bending moment distribution. It proposes a calculation model with correction coefficients and piecewise functions, effectively solving the deflection offset problem caused by openings. This provides a theoretical basis and calculation method for optimizing the opening arrangement and improving beam structural performance in engineering design. Furthermore, this invention is highly versatile and has high calculation accuracy, making it widely applicable in the design and verification of perforated steel-bamboo composite beams.

[0136] To better understand the present invention, the above method will be described in detail below with reference to specific embodiments.

[0137] Example:

[0138] Please see the appendix Figure 2 - Appendix Figure 3 This embodiment proposes a deflection calculation method to address the change in the overall stress performance of a steel-bamboo composite beam after opening a hole in its web. Generally, opening a hole in the web alters the stiffness distribution characteristics of the composite beam, causing the maximum deflection value of the entire beam under normal serviceability limit conditions to deviate from the regular distribution at the mid-span position of traditional non-perforated composite beams due to the influence of the opening parameters. Existing deflection calculation formulas for non-perforated steel-bamboo composite beams cannot accurately reflect the impact of the opening on the deflection distribution and the location of the maximum deflection.

[0139] This embodiment, combining experimental data and structural failure phenomena, establishes a deflection calculation model that comprehensively considers the influence of openings and the mechanical properties of bamboo. This model 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 beam deflection f(Δ1) without considering the influence of openings, and the other part is the beam deflection f(Δ2) considering only the influence of openings. For example... Figure 2 As shown in b and 2c, the deflection 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] To simplify the calculation process of the deflection of the steel-bamboo composite beam with web openings and to 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, steel-bamboo composite beams with web openings remain in an elastic working state when they reach their serviceability limit. Specifically, to simplify the analysis, this embodiment assumes that all materials are in an elastic state, i.e., the nonlinear effects of material stiffness with stress and the influence of plastic deformation on deflection distribution are not considered. Furthermore, the bonding quality between the steel and bamboo plywood is good, and local instability of the beam and possible relative slippage at the steel-bamboo interface are ignored in the calculation, thus ensuring the applicability and stability of the model.

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

[0143] Regarding the mechanical properties of the materials, this embodiment approximates bamboo plywood as a transversely isotropic material, meaning that it exhibits similar elastic properties in both the radial and tangential directions. This assumption fully considers the orthotropic characteristics of bamboo and simplifies the description of bamboo plywood performance under complex stress states in the calculations.

[0144] Equation derivation:

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

[0146] f(Δ)=f(Δ1)+f(Δ2) (1)

[0147] Where f(Δ1) is the formula for calculating the overall deflection of the unperforated beam in the web under load, written as:

[0148]

[0149] In the formula:

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

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

[0152] During loading, bamboo is generally under complex stress, and the yield criterion for bamboo cannot be simply defined by applying the classical von Mises strength theory to the uniaxial stress performance measured in experiments. This embodiment refers to the Hill yield criterion, setting different coefficients before each principal stress to consider the contribution of each principal stress to the equivalent stress of the material. Considering that bamboo is a transversely isotropic material, the yield strength of bamboo under complex stress can be calculated in a more comprehensive manner, as shown in equation (2.1).

[0153]

[0154] In the formula:

[0155] X, Y, Z—Yield strength of bamboo in the directions of principal stress 1, 2, and 3;

[0156] S ij —In-plane shear strength of bamboo.

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

[0158] M1+M2=a0×f (3)

[0159] The relationship between the opening deformation and the secondary bending moment generated by the shear force at the left and right ends of the opening region due to torsion and relative displacement satisfies:

[0160]

[0161]

[0162] In the formula:

[0163] i—Linear stiffness of the opening area

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

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

[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 concluded that...

[0168]

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

[0170]

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

[0172] δ1+δ2=δ (9) By combining equations (6), (8), and (9), we can find δ1, δ2, and δ.

[0173]

[0174] Differential equations can be established in the open area.

[0175]

[0176] Substituting the boundary conditions, we can solve for the integral constants A and B.

[0177]

[0178] When calculating f(Δ1), the stiffness of the web opening section without weakening is used instead of the relative slip of the adhesive surface. When the integral constant is substituted back into equation (11), the reduction coefficient λ = 0.96 is introduced to obtain the deflection differential function of the composite beam with opening.

[0179]

[0180] The deflection calculation device for steel-bamboo composite beams with web openings described below can be used in conjunction with the deflection calculation method for steel-bamboo composite beams with web openings described above.

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

[0182] Data input module 10 is used to input the 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 un-drilled area and the local deflection of the drilled area based on the input data;

[0184] The superposition module 30 is used to determine the deflection distribution of the entire beam based on the superposition principle;

[0185] Display module 40 is used to output the deflection curve of the entire beam and the location of the maximum deflection.

[0186] 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 in the opening area;

[0189] Correction module 23 is used to correct the deflection results based on the anisotropy of bamboo and the slippage effect of the steel-bamboo interface.

[0190] The device in this embodiment can be used to execute the above method embodiments, and its principle and technical effects are similar, so they will not be described again here.

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

Claims

1. A method for calculating the deflection of a steel-bamboo composite beam with perforated web, characterized in that, Includes the following steps: Determine the structural parameters of the steel-bamboo composite beam, including beam length, opening size, location, and loading point location; The mechanical properties of steel and bamboo plywood were determined, and the overall bending stiffness of the composite beam was calculated. Based on 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 overall deflection distribution of the composite beam is obtained by superimposing the deflection without holes and the deflection with holes. Determine the maximum deflection of the composite beam and its location; When superimposing the unperforated deflection with the perforated deflection, a correction coefficient λ is introduced to characterize the effects of steel-bamboo interface slippage and weakened perforated stiffness. The correction formula is as follows: Where 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 one end support of the beam along the length of the beam to the specified position.

2. The deflection calculation method for the steel-bamboo composite beam with web openings according to claim 1, characterized in that, The structural parameters include the moment of inertia of the steel section, the thickness and width of the bamboo plywood, the diameter and height of the opening, and the location of the opening area. The overall bending stiffness of the composite beam is the sum of the bending stiffness of the steel and the bending stiffness of the bamboo plywood.

3. The deflection calculation method for the steel-bamboo composite beam with web openings according to claim 1, characterized in that, The overall deflection without openings is calculated using the following formula: Where 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 along the length of the beam to the specified position.

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

6. The deflection calculation method for the 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 represented by the secondary bending moment equilibrium equation: HE h y″=M1-Fx Where y″ is the second 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 along the beam length to the specified position, and EI h This represents the bending stiffness of the perforated area.

7. The deflection calculation method for the 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 along the beam length to the specified position, and A and B are integral constants determined by the boundary conditions.

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