A method and structure for reinforcing the span of an overhead pipeline support

Abstract

The application discloses a kind of overhead pipeline support hanger span's reinforcing design method and structure, belong to pipeline engineering design technical field.The method uses finite element modeling analysis to extract the bending moment distribution data of pipeline along axial direction, the high stress area of support top and midspan bottom is determined by bending moment extreme value search algorithm, upper reinforcing plate is set in support top, lower reinforcing plate is set in midspan bottom, reinforcing plate and pipeline are constructed as integral combination section and equivalent section inertia moment is calculated based on plane section assumption and parallel axis theorem, new allowable span is recalculated based on equivalent section inertia moment and compared with actual span, when new allowable span is less than actual span, reinforcing plate size is iteratively adjusted until requirements are met.The application further discloses a kind of overhead pipeline support hanger span's reinforcing design structure.The application realizes the technical effect of increasing span without changing the overall specifications of pipeline, with the advantages of low cost, simple construction, remarkable effect.

Description

Technical Field

[0001] This invention relates to the field of pipeline engineering design technology, specifically to a method and structure for strengthening the span of overhead pipeline supports and hangers. Background Technology

[0002] In industrial pipeline design, the span design of supports and hangers for overhead pipelines is a crucial technical issue. Pipe supports and hangers are used to support overhead pipelines, and their span design directly affects the safety and economy of the pipeline system. A reasonable span design needs to minimize the number of supports and hangers while meeting the pipeline's strength and stiffness requirements, thereby reducing engineering costs and increasing the flexibility of pipeline layout.

[0003] In existing technologies, when the pipe span exceeds the allowable value, the following three solutions are usually adopted: First, increase the number of supports and hangers to shorten the span to meet the requirement of L≤L0; second, increase the overall pipe diameter to increase the moment of inertia I and section modulus W of the entire pipe section; third, use external steel structures such as trusses or suspension cables for auxiliary support.

[0004] However, the above solutions have the following drawbacks: increasing the number of supports and hangers limits the flexibility of pipeline layout and increases construction costs; increasing the overall pipe diameter significantly increases material costs and may affect the matching of standard parts such as valves and flanges; and using external steel structures such as trusses or suspension cables for auxiliary support is complex to construct and has an unsightly appearance. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention discloses a method for strengthening the span of overhead pipeline supports and hangers, the technical solution of which is as follows: A method for strengthening the span of overhead pipeline supports and hangers includes the following steps: Step 1: Obtain the basic parameters of the pipeline design, establish a beam element numerical model of the pipeline structure using the finite element modeling and analysis method, apply the pipeline's self-weight load and internal pressure load to the beam element numerical model, and extract the internal force distribution data of the pipeline section through static solution calculation. The internal force distribution data includes bending moment value, shear force value and axial force value. Calculate the moment of inertia and section modulus of the pipeline section based on the internal force distribution data. Step 2: Based on the moment of inertia and section modulus of the pipe section, calculate the allowable span for strength at the section with maximum bending moment using strength theory, and calculate the allowable span for stiffness at the section with maximum deflection using deflection theory. Take the smaller of the allowable span for strength and the allowable span for stiffness as the initial allowable span for the pipe. Obtain the actual span required for the actual layout of the pipe. Compare the actual span with the initial allowable span for the pipe. When the actual span is greater than the initial allowable span for the pipe, trigger the execution of the reinforcement design process. Step 3: Based on the bending moment distribution calculation results of the beam element numerical model, extract the bending moment values ​​at each section along the axial direction of the pipeline, and determine the high stress region with the largest absolute value of the bending moment. The high stress region includes the negative bending moment peak region at the top of the support and the positive bending moment peak region at the bottom of the mid-span. An upper reinforcing plate is arranged at the top of the pipeline along the circumference of the negative bending moment peak region at the top of the support, and a lower reinforcing plate is arranged at the bottom of the pipeline along the circumference of the positive bending moment peak region at the bottom of the mid-span. Both the upper and lower reinforcing plates extend along the axial direction of the pipeline to cover the high stress region. Step 4: Construct the upper reinforcing plate and the lower reinforcing plate together with the outer wall of the pipe to form an integral composite section. Calculate the equivalent section moment of inertia of the composite section using the equivalent section method. The equivalent section method is based on the plane section assumption and strain compatibility conditions, and adds the contribution of the moment of inertia of the reinforcing plate section relative to the centroidal axis of the composite section to the moment of inertia of the original pipe section. Step 5: Based on the equivalent cross-sectional moment of inertia, the maximum tensile stress theory is used to calculate the allowable span of the reinforced pipeline at the critical section for strength, and the elastic deflection curve differential equation is used to calculate the allowable span of the reinforced pipeline at the critical section for stiffness. The smaller value between the allowable span of the reinforced pipeline for strength and the allowable span of the reinforced pipeline for stiffness is taken as the new allowable span. Step Six: Compare the new allowable span with the actual span. If the new allowable span is greater than or equal to the actual span, the current reinforcement design is deemed to meet the requirements. If the new allowable span is less than the actual span, increase the thickness or width parameter of the upper or lower reinforcement plate and return to Step Four to recalculate until the requirements are met.

[0006] This invention also discloses a reinforced design structure for the span of an overhead pipeline support, comprising: a pipeline body, which is a hollow cylindrical structure, with both ends of the pipeline body supported on supports, the pipeline body bearing a uniformly distributed load and generating a negative bending moment in the top region of the supports and a positive bending moment in the bottom region of the mid-span; and an upper reinforcing plate, which is attached and fixed to the top of the outer wall of the pipeline body and located in the top region of the supports, the upper reinforcing plate covering at least one-eighth of the actual span length on both sides of the center line of the supports along the pipeline axis, and the upper reinforcing plate covering a circumference of 120 to 180 degrees around the top of the outer wall of the pipeline along the pipeline circumference. Scope; lower reinforcing plate, which is attached and fixed to the bottom of the outer wall of the pipe body and located in the bottom area of ​​the mid-span, the lower reinforcing plate covers at least one-eighth of the actual span length on both sides of the mid-span section along the pipe axis, and the lower reinforcing plate covers a circumferential range of 120 to 180 degrees from the bottom of the outer wall of the pipe along the pipe circumference; the centroid of the cross section of the upper reinforcing plate and the centroid of the cross section of the lower reinforcing plate are both offset from the centroid of the cross section of the pipe body, the upper reinforcing plate and the lower reinforcing plate are fixedly connected to the pipe body to form an integral composite cross section, and the equivalent cross section moment of inertia of the integral composite cross section is greater than the moment of inertia of the individual cross section of the pipe body.

[0007] Beneficial effects 1. A numerical model of the pipeline structure is established using the finite element modeling and analysis method. The self-weight load and internal pressure load of the pipeline are applied to the numerical model of the beam element, and the internal force distribution data such as bending moment, shear force and axial force of the pipeline section are extracted. This can accurately locate the stress distribution state of each section of the pipeline along the axial direction, overcome the technical defect of traditional simplified calculation methods that cannot accurately identify the location of high stress areas, and provide a reliable data basis for the accurate arrangement of the stiffening plate.

[0008] 2. The fourth strength theory is used to calculate the allowable span of the pipeline at the section with the maximum bending moment, and the Euler-Bernoulli beam theory is used to calculate the allowable span of the pipeline at the section with the maximum deflection. The smaller value between the allowable span of strength and the allowable span of stiffness is taken as the initial allowable span of the pipeline. This combines the dual constraints of strength and stiffness conditions. Compared with the existing method of estimating the span based solely on empirical formulas, the allowable span calculation results of this invention are more accurate and reliable.

[0009] 3. A bending moment extreme value search algorithm is adopted to extract the sets of negative bending moment values ​​and positive bending moment values ​​from the bending moment values ​​of each node in the numerical model of the beam element. The node position with the largest absolute value in the set of negative bending moment values ​​is determined as the peak position of negative bending moment at the top of the support, and the node position with the largest absolute value in the set of positive bending moment values ​​is determined as the peak position of positive bending moment at the bottom of the mid-span. This achieves automated and accurate identification of high-stress areas and avoids the deviation caused by human experience judgment.

[0010] 4. Upper and lower reinforcing plates are installed in the negative bending moment peak area at the top of the support and the positive bending moment peak area at the bottom of the mid-span, respectively. The upper and lower reinforcing plates cover the area of ​​one-eighth of the actual span on both sides of the support centerline or the mid-span section along the pipe axis, and cover the circumferential range of 120 to 180 degrees of the top or bottom of the outer wall of the pipe along the pipe circumference. This achieves directional and precise reinforcement of the high-stress area of ​​the pipe. Compared with the existing technology of increasing the pipe diameter as a whole, the material consumption is greatly reduced and the construction workload is significantly reduced.

[0011] 5. By constructing the upper and lower reinforcing plates with the outer wall of the pipe as an integral composite section, based on the plane section assumption and strain compatibility conditions, the equivalent section moment of inertia of the composite section is calculated using the parallel axis theorem. The contribution of the moment of inertia of the reinforcing plate section relative to the centroidal axis of the composite section is superimposed on the moment of inertia of the original pipe section, so that the equivalent section moment of inertia of the reinforced pipe is effectively improved, thereby increasing the span without changing the overall pipe specifications.

[0012] 6. Based on the equivalent cross-sectional moment of inertia, the maximum tensile stress theory is used to recalculate the allowable span of the reinforced pipeline at the critical section. The elastic deflection curve differential equation is used and the fourth-order Runge-Kutta method is used for numerical integration to recalculate the allowable span of the stiffness of the reinforced pipeline at the critical section. Compared with the existing technology that relies solely on experience to estimate the effect of span increase, this invention can quantitatively evaluate the improvement in the bearing capacity of the reinforced pipeline, and the design results are verifiable and repeatable.

[0013] 7. By comparing the new allowable span with the actual span, an iterative judgment is made. When the new allowable span is less than the actual span, the thickness or width of the reinforcing plate is increased by an incremental step and recalculated. The thickness increment step is 10% of the pipe wall thickness and the width increment step is 5% of the pipe outer diameter, forming a closed-loop optimization design process. This can meet the span design requirements with the least amount of reinforcing material and avoid material waste caused by over-reinforcement.

[0014] 8. In the reinforced design structure, both the upper and lower reinforcing plates are arc-shaped plates with the inner wall curvature consistent with the outer wall curvature of the pipe. The inner wall of the reinforcing plate is provided with multiple stress relief grooves distributed at intervals along the pipe axis, which can effectively release the welding residual stress generated during the welding process, reduce the impact of welding deformation on the fit between the reinforcing plate and the pipe, and ensure the overall working performance of the composite section.

[0015] 9. The reinforcing plate is fixed to the outer wall of the pipe body by continuous fillet welds. The reinforcing plate is provided with sloping welding grooves at both ends of the axial direction. The pipe body and the reinforcing plate are made of the same material with a linear expansion coefficient difference of no more than 5%. This can effectively reduce the additional stress caused by the thermal expansion difference between the reinforcing plate and the pipe body under the action of temperature difference load, and ensure the long-term reliable operation of the reinforced structure under temperature change conditions. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the pipe bending moment distribution; Figure 3 A schematic diagram showing the arrangement of the reinforcing plates; Figure 4 This is a schematic diagram of the cross-sectional structure of the upper reinforcing plate; Figure 5 This is a schematic diagram of the cross-sectional structure of the lower reinforcing plate; Figure 6 This is a schematic diagram for calculating the equivalent cross section; Among them, the pipe body (1), upper reinforcing plate (2), lower reinforcing plate (3), support (4), pipe cross-section centroid (O), upper reinforcing plate cross-section centroid (O upper), lower reinforcing plate cross-section centroid (O lower), composite cross-section neutral axis (CC), support top negative bending moment peak position (A), mid-span bottom positive bending moment peak position (B). Detailed Implementation

[0017] Example 1: Design of reinforced span for support and hanger of DN300 steam pipe This embodiment takes a DN300 steam pipeline laid overhead in a chemical plant area as an example to provide a detailed description of the design method and structure for strengthening the span of overhead pipeline supports provided by the present invention.

[0018] The DN300 steam pipeline transports saturated steam at an operating temperature of 250 degrees Celsius and a design pressure of 1.6 MPa. The pipeline needs to cross the main road within the plant area. Due to existing structures on both sides of the road, it is not possible to install intermediate supports in the middle of the road. Therefore, the pipeline span needs to be increased from the conventional design value to 12 meters.

[0019] Step 1: Obtain the basic parameters of the pipeline design, establish a beam element numerical model of the pipeline structure using the finite element modeling and analysis method, apply the pipeline's self-weight load and internal pressure load to the beam element numerical model, extract the internal force distribution data of the pipeline section through static solution calculation, and calculate the pipeline section moment of inertia and pipeline section modulus based on the internal force distribution data.

[0020] As is well known in the art, traditional pipeline span design methods typically employ simplified mechanical models and analytical calculation formulas, treating the pipeline as a homogeneous continuous beam and directly calculating the allowable span based on analytical expressions for maximum bending moment and maximum deflection. However, this method can only calculate the extreme values ​​of bending moment and deflection at the most critical single cross-section of the pipeline, failing to obtain the bending moment distribution along the entire pipeline length. When the pipeline span needs to be increased due to site constraints, traditional methods can only provide a qualitative conclusion that "reinforcement is needed," but cannot quantitatively determine which specific locations along the pipeline axis are high-stress areas, where the reinforcing plates should be placed, and what coverage area is most economical and effective. For example, for continuous multi-span pipelines, the stress levels at the top of the supports and the bottom of the mid-span are significantly higher than at other locations, but traditional analytical methods cannot output stress distribution data for each cross-section along the pipeline. This leads to engineering practice relying solely on experience to place reinforcing plates near the supports or mid-span, resulting in either insufficient coverage or over-reinforcement.

[0021] To address the aforementioned technical issues, this step employs the finite element method (FEM) to establish a numerical model of the pipeline structure using beam elements. A three-dimensional beam element is used to simulate the main structure of the pipeline. Each node of this three-dimensional beam element has six degrees of freedom, including three translational and three rotational degrees of freedom. Compared to traditional analytical methods that can only obtain a single extreme value, this numerical model can discretize the entire pipeline length into several elements, and each node can output cross-sectional internal force data, thus obtaining complete distribution curves of bending moment, shear force, and axial force values ​​at various cross-sections along the pipeline's axial direction. (Pipe outer diameter) The pipe wall thickness is 325 mm. The inner diameter of the pipe is eight millimeters. According to the formula Calculate the elastic modulus of the pipe material, which is No. 20 steel, at an operating temperature of 250 degrees Celsius. The allowable stress is 2.1 times 10 to the power of 5 megapascals. It is 130 MPa. Weight per unit length of pipe. This includes the weight of the pipe itself, the weight of the insulation layer, and the weight of the medium. Allowable pipe deflection. According to industrial pipeline design specifications, it is taken as one three-hundredth of the span. Bending moment reduction factor. The value is determined based on the number of consecutive spans of the pipeline and the combined load conditions.

[0022] In the numerical model of the beam element, simply supported boundary conditions are applied at the nodes at both ends of the pipe. These simply supported boundary conditions constrain the vertical translational degrees of freedom of the nodes at both ends of the pipe while releasing the axial translational and rotational degrees of freedom. This simulates the working state where the pipe is supported on supports at both ends and allows for free axial expansion and contraction. The selection of this boundary condition is based on the fact that overhead pipe supports typically only provide vertical support to the pipe and do not constrain its axial displacement or cross-sectional rotation. Therefore, the simply supported boundary condition closely matches the actual stress state of the pipe. If a fixed-support boundary condition is incorrectly used, the constraint stiffness at the pipe ends will be artificially increased, resulting in underestimation of the calculated bending moment and deflection values, leading to a false increase in the allowable span and potentially causing engineering safety hazards. The weight per unit length of the pipe is considered. The uniformly distributed load is applied to each node of the beam element, converting the internal pressure load of the pipe into equivalent nodal forces applied to the inner wall of the pipe. The global stiffness equation is then solved using a finite element statics solver. Solve the problem to obtain the displacement vectors of each node. ,in For the overall stiffness matrix, This is the equivalent nodal load vector. Based on the nodal displacement vector, the internal forces at each element section are calculated, yielding the bending moment, shear force, and axial force values ​​at each section along the axial direction of the pipe.

[0023] The moment of inertia and section modulus of the pipe section are calculated based on the internal force distribution data. The moment of inertia of the pipe section... According to the formula for the section of a circular ring

[0024] Calculate the cross-sectional modulus of the pipe. According to the formula for the section of a circular ring

[0025] Calculation. Among them... The outer diameter of the pipe. The inner diameter of the pipe. , This refers to the pipe wall thickness.

[0026] Step 2: Based on the moment of inertia and section modulus of the pipe section, calculate the allowable span for strength at the section with maximum bending moment using strength theory, and calculate the allowable span for stiffness at the section with maximum deflection using deflection theory. Take the smaller of the allowable span for strength and the allowable span for stiffness as the initial allowable span for the pipe, obtain the actual span required for the actual layout of the pipe, and compare the actual span with the initial allowable span for the pipe. When the actual span is greater than the initial allowable span for the pipe, trigger the execution of the reinforcement design process.

[0027] As is well known in the art, the design of allowable pipeline spans is subject to both strength and stiffness constraints. The strength constraint requires that the bending stress at the maximum bending moment section of the pipeline does not exceed the allowable stress of the material. If this condition is not met, the pipeline will undergo excessive plastic deformation or even fracture. The stiffness constraint requires that the elastic deflection at the maximum deflection section of the pipeline does not exceed the allowable deflection. If this condition is not met, the pipeline will undergo excessive vertical deformation, leading to obstructed medium flow, insulation layer cracking, or excessive additional stress at the interface between the pipeline and adjacent equipment. In traditional designs, designers often select the smaller of the strength and stiffness allowable spans based solely on experience, without clearly identifying which condition is controlling, resulting in a lack of targeted reinforcement design. For example, when the stiffness condition is controlling, increasing the moment of inertia of the pipeline section is the most effective reinforcement method; while when the strength condition is controlling, increasing the section modulus of the pipeline is more direct and effective. Failure to identify the dominant controlling condition may lead to the adoption of incorrect reinforcement strategies, resulting in wasted effort.

[0028] To address the aforementioned technical issues, this step employs the fourth strength theory to calculate the allowable span for strength and the Euler-Bernoulli beam theory to calculate the allowable span for stiffness. The smaller of the two values ​​is used as the initial allowable span, and the controlling condition is recorded to provide a theoretical basis for selecting subsequent strengthening design strategies.

[0029] According to the fourth strength theory, the maximum bending stress of the pipeline at the section with the maximum bending moment does not exceed the allowable stress of the pipeline material. The allowable span for strength is thus calculated. The allowable span for strength is determined according to the formula...

[0030] Calculation. The mechanical principle behind this formula is: for a simply supported beam subjected to a uniformly distributed load, the maximum bending moment occurs at the mid-span section, and its value is... The maximum bending stress is ,make Inverse solution This yields the above formula for the allowable span for strength. The allowable stress of the pipe material, For the section modulus of the pipe, This is the moment reduction factor. This represents the weight per unit length of the pipe. A bending moment reduction factor is introduced. The reason is that for continuous multi-span pipelines, the absolute value of the negative bending moment at the top of the support is usually less than the theoretical value of the positive bending moment at the mid-span of a simply supported beam. After considering the effect of plastic internal force redistribution, the actual maximum bending moment value can be appropriately reduced. This coefficient is determined by structural mechanics analysis based on the number of pipeline spans and support constraints.

[0031] The deflection theory is the Euler-Bernoulli beam theory. According to this theory, the elastic deflection of the pipeline at the section with maximum deflection does not exceed the allowable deflection of the pipeline. From this, the allowable stiffness span can be calculated. The allowable stiffness span is calculated according to the formula...

[0032] Calculation. The derivation of this formula is as follows: The formula for calculating the maximum deflection of a simply supported beam under uniformly distributed load is: .make ,Right now Canceling both sides of the equation ,get Inverse solution This yields the above formula for allowable stiffness span in the form of a cubic square root. The elastic modulus of the pipe material. Let the moment of inertia of the pipe cross section be... This refers to the weight per unit length of the pipe. The coefficient 1500 is derived from the conversion factor when the allowable deflection is taken as one three-hundredth of the span. The dimensional analysis of this formula is as follows: The dimensions are The cube root of the equation is: The dimensions are correctly closed. If the fourth square root form is used, which may be incorrectly used by those skilled in the art, the dimensions are not closed, and the error can be determined from the perspective of dimensional analysis.

[0033] The initial allowable span of the pipeline is taken as follows

[0034] That is, the initial allowable span is the smaller value between the strength allowable span and the stiffness allowable span. In this embodiment, the strength allowable span is calculated by substituting specific parameters. The span is 15.8 meters, and the allowable stiffness span is... The initial allowable span is 9.7 meters. The span is taken as 9.7 meters. The calculation results show that, under the dual constraints of strength and stiffness, the stiffness condition plays a controlling role in the DN300 steam pipeline; that is, the allowable span of the pipeline is determined by the stiffness condition, not the strength condition. This determination has important guiding significance for the selection of subsequent reinforcement design strategies: since the stiffness condition plays a controlling role, the reinforcement design should focus on increasing the moment of inertia of the pipeline section. The core objective is to increase the equivalent moment of inertia of the composite section by adding reinforcing plates. This directly increases the allowable span for stiffness.

[0035] Obtain the actual span required for the actual pipeline layout Compare the actual span With respect to the initial allowable span of the pipeline The actual span in this embodiment It is twelve meters, because If the actual span is greater than the initial allowable span of the pipeline, it is determined that the maximum deflection of the pipeline at the actual span will exceed the allowable deflection, requiring pipeline reinforcement design. In this case, a trigger signal is generated containing the deviation value between the actual span and the initial allowable span of the pipeline. This trigger signal is used to initiate the reinforcement design process. The magnitude of this deviation value directly reflects the target range of the allowable span for increasing stiffness, providing a quantitative basis for the subsequent selection of reinforcement plate size parameters.

[0036] Step 3: Based on the bending moment distribution calculation results of the numerical model of the beam element, extract the bending moment values ​​at each section along the axial direction of the pipeline, and determine the high stress region with the largest absolute value of the bending moment. The high stress region includes the negative bending moment peak region at the top of the support and the positive bending moment peak region at the bottom of the mid-span. An upper reinforcing plate is arranged at the top of the pipeline along the circumference of the negative bending moment peak region at the top of the support, and a lower reinforcing plate is arranged at the bottom of the pipeline along the circumference of the positive bending moment peak region at the bottom of the mid-span. Both the upper and lower reinforcing plates extend along the axial direction of the pipeline to cover the high stress region.

[0037] As is well known in the art, for continuous multi-span pipelines subjected to uniformly distributed loads, the bending moment is periodically distributed along the pipeline axis. At the support locations, the pipeline experiences a negative bending moment, with the top fibers under tension and the bottom fibers under compression, and the maximum tensile stress occurring on the outer wall of the top of the pipeline. At the mid-span locations, the pipeline experiences a positive bending moment, with the bottom fibers under tension and the top fibers under compression, and the maximum tensile stress occurring on the outer wall of the bottom of the pipeline. The stress levels in these high-stress areas are much higher than in other parts of the pipeline, making them critical sections that determine the pipeline's load-bearing capacity. However, existing methods of increasing the overall pipe diameter distribute the strengthening effect evenly across all sections along the entire length of the pipeline, including many low-stress areas, resulting in low material utilization. For example, for a pipeline with an actual span of twelve meters, increasing the overall pipe diameter only increases the moment of inertia of the cross-section within a range of approximately 7.5 meters outside the supports and mid-span, without substantially contributing to increasing the allowable span, resulting in significant waste of material costs.

[0038] To address the aforementioned technical issues, this step employs a bending moment extremum search algorithm to determine the high-stress region. The bending moment extremum search algorithm includes: extracting a set of negative bending moment values ​​and a set of positive bending moment values ​​from the bending moment values ​​of each node in the beam element numerical model; determining the node position with the largest absolute value in the negative bending moment value set as the peak position of the negative bending moment at the top of the support; and determining the node position with the largest absolute value in the positive bending moment value set as the peak position of the positive bending moment at the bottom of the mid-span. This algorithm can automatically search and determine the locations of all bending moment extremum points along the pipe axis using the bending moment data of each node output from the finite element calculation in step one, achieving quantitative and automated identification of high-stress regions and avoiding the arbitrariness and uncertainty of manual experience-based judgment.

[0039] The negative bending moment peak region at the top of the support is located within the axial range of one-eighth of the actual span on each side of the support centerline, that is, on each side of the support centerline. The range, with a total coverage length of The peak positive bending moment region at the bottom of the mid-span is located within the axial range of one-eighth of the actual span on each side of the mid-span section, i.e., on each side of the mid-span section. The range, with a total coverage length of .choose The basis for defining the coverage area is that, for a continuous beam subjected to a uniformly distributed load, its bending moment approximately follows a parabolic distribution near the supports and mid-span, and decreases further away from the supports or mid-span. At that location, the bending moment has decreased to approximately 75% to 80% of its peak value. Beyond this range, the marginal contribution of the stiffening plate to increasing the equivalent section moment of inertia decreases sharply. If the coverage area is smaller than... If the high-stress area is not completely covered, the reinforcement effect is insufficient; if the coverage area is significantly larger than... This increases the material usage of the reinforcing plate but limits the improvement effect, thus reducing economic efficiency. In this embodiment, the actual span... If the span is 12 meters, then the coverage area of ​​the reinforcing plate at the top of the support and the bottom of the mid-span is 1.5 meters on each side of the support centerline or the mid-span section, with a total coverage length of 3 meters.

[0040] Before arranging the upper reinforcing plate, the high-stress area at the top of the pipe's outer wall is first subjected to surface rust removal and roughening treatment to achieve a preset surface roughness level. Before arranging the lower reinforcing plate, the high-stress area at the bottom of the pipe's outer wall is first subjected to surface rust removal and roughening treatment. In this embodiment, sandblasting is used to remove oxide scale and rust products from the pipe's outer wall surface, achieving a preset surface roughness level of Sa2.5. The key role of surface roughening treatment is twofold: firstly, removing surface contaminants and oxide layers prevents the formation of welding defects such as porosity and slag inclusions during welding; secondly, appropriate surface roughness enhances the mechanical bonding and chemical adhesion of the structural adhesive layer, ensuring a reliable pre-fixed connection between the reinforcing plate and the pipe's outer wall before welding, preventing slippage and misalignment of the reinforcing plate during welding.

[0041] The upper reinforcing plate is a strip-shaped plate extending along the pipe's axial direction, made of the same material as the pipe to ensure that the linear expansion coefficients of the pipe body and the reinforcing plate are consistent. The technical basis for this material selection is that if the linear expansion coefficients of the reinforcing plate and the pipe differ, they will generate different amounts of thermal deformation under temperature changes, creating additional thermal stress at the connection interface. When this additional thermal stress exceeds the connection strength, it may lead to weld cracking or peeling of the structural adhesive layer, causing the reinforcing structure to fail. Especially for operating conditions with frequent temperature changes, such as steam pipelines, thermal expansion matching is a key factor in ensuring the long-term reliable operation of the reinforcing structure. The thickness of the upper reinforcing plate is one to one and a half times the pipe wall thickness. When the thickness is less than one times the pipe wall thickness, the stiffness contribution of the reinforcing plate itself is insufficient, and the increase in the equivalent section moment of inertia is limited. When the thickness is greater than one and a half times the pipe wall thickness, although the equivalent section moment of inertia continues to increase, the weight of the reinforcing plate itself increases significantly, and the pipe body may experience welding deformation due to excessive welding heat input. The upper reinforcing plate extends circumferentially along the pipe, and its width is less than or equal to the pipe's outer diameter. The upper reinforcing plate is arranged on the upper semicircle of the pipe cross-section, with a coverage angle ranging from 120 to 180 degrees above the top of the pipe circumference. The reason for a coverage angle greater than 120 degrees is that when the pipe is subjected to a negative bending moment, the bending stress in the top region is distributed circumferentially. If only a small area at the top is covered, the peak stress area at the top may not be completely covered. When the coverage angle exceeds 180 degrees, the reinforcing plate will extend to the area below the neutral axis on both sides of the pipe. The stress level in this area has been significantly reduced, and the increase in the moment of inertia contribution of the reinforcing plate is limited, but the amount of material used increases significantly.

[0042] The lower reinforcing plate is a strip-shaped plate extending along the axial direction of the pipe, made of the same material as the pipe. The thickness of the lower reinforcing plate is one to one and a half times the pipe wall thickness. The width of the lower reinforcing plate extends circumferentially along the pipe, and its width is less than or equal to the pipe's outer diameter. The lower reinforcing plate is arranged on the lower semicircle of the pipe cross-section, covering an angle range of 120 to 180 degrees from the bottom of the pipe circumference. The lower reinforcing plate covers at least one-eighth of the actual span on both sides of the mid-span section along the pipe axial direction.

[0043] The upper and lower reinforcing plates are coated with structural adhesive layers between themselves and the outer wall of the pipe. The thickness of the structural adhesive layer is 0.5 mm to 2 mm. In this embodiment, an epoxy resin-based structural adhesive is used, with a thickness of 1 mm. The function of this structural adhesive layer is pre-fixation and stress transfer. During the welding process, before the weld is formed between the reinforcing plate and the pipe, the structural adhesive layer can firmly adhere the reinforcing plate to the outer wall of the pipe, preventing relative displacement caused by welding thermal stress. The upper and lower reinforcing plates are pre-fixed to the outer wall of the pipe through the structural adhesive layer before being welded together. The welded connection uses continuous fillet welds along the circumferential and axial edges of the upper and lower reinforcing plates. The technical basis for using continuous fillet welds instead of intermittent welds is that the mechanical premise for the reinforcing plate and the pipe to work together is that sufficient shear force can be transferred between them. Only continuous welds can ensure the continuity of shear force transfer at all cross-sections along the entire length of the reinforcing plate, ensuring that the plane section assumption holds. If intermittent welds are used, shear force cannot be effectively transferred between the reinforcing plate and the pipe in the weldless section, and the two cannot form an integral composite section. Therefore, the assumption for calculating the equivalent section moment of inertia will no longer hold. The weld leg height of the continuous fillet weld is 0.6 to 0.8 times the thickness of the upper or lower reinforcing plate. Both ends of the upper and lower reinforcing plates are provided with sloping weld bevels. The bevel angle of the sloping weld bevel is 45 to 60 degrees, and the root gap of the sloping weld bevel is 2 to 4 millimeters. The purpose of the weld bevel is to ensure sufficient penetration at the weld root, improve the weld's connection strength and fatigue performance, and avoid stress concentration at the ends of the reinforcing plates.

[0044] The inner walls of the upper and lower reinforcing plates are provided with multiple stress relief grooves spaced apart along the pipe axial direction. Each stress relief groove is an arc-shaped groove, and each groove extends circumferentially through the inner wall of the upper or lower reinforcing plate. The spacing between adjacent stress relief grooves is 50 to 100 millimeters. The technical basis for setting the stress relief grooves is as follows: During the welding process between the reinforcing plate and the outer wall of the pipe, the welding thermal cycle causes the surface metal of the reinforcing plate and the pipe to expand and contract, generating high residual stress in the weld and heat-affected zone. Without stress relief grooves, the residual welding stress will cause the contact surface between the inner wall of the reinforcing plate and the outer wall of the pipe to tend to separate, forming a gap between them, destroying the integrity of the combined section, and thus reducing the actual equivalent section moment of inertia. With stress relief grooves, the residual stress generated during welding is concentrated and released at the bottom of the groove, reducing the separation deformation of the contact surface and ensuring close contact between the reinforcing plate and the outer wall of the pipe along the entire contact surface.

[0045] Step 4: Construct the upper reinforcing plate and the lower reinforcing plate together with the outer wall of the pipe to form an integral composite section. Calculate the equivalent section moment of inertia of the composite section using the equivalent section method. The equivalent section method is based on the plane section assumption and strain compatibility conditions, and adds the contribution of the moment of inertia of the reinforcing plate section relative to the centroidal axis of the composite section to the moment of inertia of the original pipe section.

[0046] As is well known in this art, the mechanical property analysis of composite sections is based on the plane section assumption, which states that a section perpendicular to the beam axis before deformation remains planar and perpendicular to the beam axis after deformation. This assumption is a fundamental premise of beam theory in mechanics of materials, and its validity depends on the sufficiently large ratio of the beam's span to its section height. For overhead pipelines, the span is typically tens of times greater than the section height, fully satisfying the applicability conditions of the plane section assumption. Under the plane section assumption, the strain at each point on the composite section is linearly distributed along the section height, and the stress and strain satisfy Hooke's law. Therefore, the contributions of the moments of inertia of each sub-section about the neutral axis of the composite section can be linearly superimposed.

[0047] To address the low material utilization rate of the overall pipe diameter enlargement scheme, this step constructs the upper and lower reinforcing plates and the pipe body into an integral composite section. The equivalent moment of inertia of the composite section includes not only the moment of inertia of the original pipe section but also the contribution of the moment of inertia of each reinforcing plate section relative to the neutral axis of the composite section. This contribution consists of two parts: firstly, the moment of inertia of the reinforcing plate about its own centroidal axis. Secondly, the area of ​​the reinforcing plate. Multiply by the distance from the centroid to the neutral axis The square of the first term is the sum of the squared values ​​of the first and the second term. The second term typically contributes far more than the first, which is the core mechanical principle behind placing the reinforcing plate far from the neutral axis. The farther the reinforcing plate is from the neutral axis, the more significant the increase in the equivalent section moment of inertia. Therefore, placing the upper reinforcing plate at the top of the pipe and the lower reinforcing plate at the bottom, as far away from the neutral axis as possible, achieves the maximum increase in the equivalent section moment of inertia with minimal material usage. Placing the reinforcing plate on the pipe sidewall near the neutral axis, while still increasing the cross-sectional area, contributes very little to improving the bending stiffness of the section, constituting a waste of material.

[0048] In this embodiment, before calculating the equivalent cross-sectional moment of inertia, the position of the neutral axis of the combined cross-section is first determined. The method for determining the position of the neutral axis includes: establishing a rectangular coordinate system with the center of the pipe cross-section as the origin; discretizing the pipe cross-section into several infinitesimal elements; calculating the area moment for each infinitesimal element; and iteratively solving for the coordinate value of the neutral axis in the rectangular coordinate system based on the condition that the area moment is zero. When the upper and lower reinforcing plates are symmetrically arranged on the upper and lower sides of the pipe cross-section, the neutral axis of the combined cross-section basically coincides with the centroidal axis of the pipe cross-section, and the neutral axis is located at the center of the pipe cross-section. However, when the upper and lower reinforcing plates are asymmetrically arranged, the neutral axis will shift towards the side with the larger reinforcing plate area, requiring precise calculation using the area moment balance condition.

[0049] The equivalent cross-sectional moment of inertia is calculated according to the formula.

[0050] Calculation. Among them... Let be the moment of inertia of the original pipe cross-section about its own centroidal axis. The total number of reinforcing plates, For the first The moment of inertia of the cross section of the reinforcing plate about its own centroidal axis. For the first The area of ​​the cross-section of the reinforcing plate. For the first The distance from the centroid of the reinforcing plate to the neutral axis of the composite section. The position of the neutral axis of the composite section is determined according to the equilibrium condition of the area moment of the cross section.

[0051] Confirmed, among which This represents the total number of sub-sections in the composite section. For the first The area of ​​each sub-section For the first The distance from the centroid of each sub-section to the neutral axis of the combined section.

[0052] For a single reinforcing plate, the moment of inertia of its cross section about its own centroidal axis follows the formula for a rectangular cross section. Calculation, where For the first The width of the reinforcing plate, For the first The thickness of the reinforcing plates. The cross-sectional area of ​​each reinforcing plate is calculated according to... Calculate the distance from the centroid of each reinforcing plate to the neutral axis of the composite section. The location of the reinforcing plates in the circumferential direction of the pipe is determined. For the upper reinforcing plate located at the top of the pipe, the distance from its centroid to the neutral axis of the composite section is the outer radius of the pipe plus half the thickness of the upper reinforcing plate. For the lower reinforcing plate located at the bottom of the pipe, the distance from its centroid to the neutral axis of the composite section is the outer radius of the pipe plus half the thickness of the lower reinforcing plate.

[0053] Step 5: Based on the equivalent cross-sectional moment of inertia, calculate the allowable span of the reinforced pipeline at the critical section using the maximum tensile stress theory, and calculate the allowable span of the reinforced pipeline at the critical section using the elastic deflection curve differential equation. Take the smaller value between the reinforced strength allowable span and the reinforced stiffness allowable span as the new allowable span.

[0054] As is well known in the art, after pipe reinforcement, the equivalent moment of inertia and equivalent section modulus of the composite section change, necessitating a re-verification of whether the strength and stiffness of the reinforced pipe meet the requirements. Relying solely on experience or simplified estimations may lead to erroneous conclusions. For example, some technicians might assume that simply adding a reinforcing plate will significantly improve the pipe's load-bearing capacity, thus neglecting precise quantitative verification of the allowable span after reinforcement. However, the effect of increasing the equivalent moment of inertia varies by orders of magnitude depending on the location and dimensional parameters of the reinforcing plate. If the reinforcing plate is placed outside the high-stress area or its dimensions are improperly selected, the new allowable span after reinforcement may still fail to meet the actual span requirements, necessitating verification through iterative calculations.

[0055] The reinforced strength allowable span is calculated according to the formula.

[0056] Calculation. Among them... The equivalent section modulus of the composite section is calculated according to the formula.

[0057] calculate, This is the distance from the farthest fiber in the composite section to the neutral axis of the composite section, i.e., the distance from the outer surface of the reinforcing plate to the neutral axis. ,in The thickness of the reinforcing plate is used. The mechanical principle of this formula is the same as the formula for calculating the allowable span of strength in step two, the only difference being the use of the equivalent section modulus of the composite section. Replaced the original pipe section modulus .

[0058] The allowable span for the enhanced stiffness is calculated according to the formula.

[0059] Calculation. The mechanical principle of this formula is the same as the formula for calculating the allowable span of stiffness in step two, the only difference being that it uses the equivalent moment of inertia of the composite section. Replaced the original pipe section moment of inertia The new allowed span is...

[0060] The differential equation of the elastic deflection curve is:

[0061] in For pipe deflection, These are the position coordinates along the axial direction of the pipeline. For position The bending moment at the section is given. This differential equation is the core governing equation of the Euler-Bernoulli beam theory, and its physical meaning is: the curvature of the beam axis. With section bending moment Proportional to the bending stiffness of the cross section Inversely proportional. The enhanced equivalent cross-sectional moment of inertia... Substituting into the equation, the deflection value of each point along the axial direction of the reinforced pipe can be calculated.

[0062] The differential equation of the elastic deflection curve is solved using a numerical integration method. The pipeline is divided into several integration intervals along its axial direction. Within each interval, a fourth-order Runge-Kutta method is used for step-by-step integration to obtain the deflection and rotation values ​​at various positions along the axial direction of the pipeline. The maximum deflection value is then extracted from the deflection values ​​at each position. The technical basis for using the fourth-order Runge-Kutta method is that for a continuous multi-span pipeline subjected to a uniformly distributed load, its bending moment distribution... The deflection is a piecewise continuous function along the axial direction, but it abruptly changes at the supports, making it difficult to obtain an analytical deflection expression. The fourth-order Runge-Kutta method, a classic numerical integration method, offers fourth-order accuracy and maintains good numerical stability while ensuring computational accuracy, making it suitable for the engineering calculation scenarios described in this invention. In the maximum tensile stress theory, the critical section of the pipe is the section where the farthest fiber of the composite section is located. The maximum tensile stress at the farthest fiber is calculated, and the pipe span corresponding to when the maximum tensile stress equals the allowable stress of the pipe material is determined as the strength-allowable span. The physical meaning of this theory is that the stress level is highest at the farthest fiber of the composite section, and it is the first position in the entire section to reach the allowable stress of the material; this position determines the strength bearing capacity of the section.

[0063] In this embodiment, the equivalent cross-sectional moment of inertia is calculated using the method described above. It is 3.905 x 10⁸ cubic millimeters. Equivalent section modulus according to Calculate the distance from the farthest fiber in the composite section to the neutral axis. Add a reinforcing plate to the outer radius of the pipe. The increased strength allows for a certain span. It is 20.7 meters. The allowable span for stiffness enhancement is... It is 12.8 meters. The new permissible span... Take 12.8 meters.

[0064] Step Six: Compare the new allowable span with the actual span. If the new allowable span is greater than or equal to the actual span, the current reinforcement design is deemed to meet the requirements. If the new allowable span is less than the actual span, increase the thickness or width parameter of the upper or lower reinforcement plate and return to Step Four to recalculate until the requirements are met.

[0065] It is well known in this field that there is an optimal solution problem in reinforcement design. If the reinforcement is insufficient, the new allowable span will still be smaller than the actual span, and the reinforcement design will fail; if the reinforcement is excessive, the amount of material used will be too large, and the economy will deteriorate. Therefore, an iterative optimization mechanism is needed to achieve the span design goal with the minimum amount of reinforcement material used.

[0066] In this step, if the new allowable span after the first iteration is less than the actual span, the thickness or width parameter of the upper or lower reinforcing plate is increased. This is adjusted iteratively according to an incremental step size. The incremental step size for the thickness parameter is 10% of the pipe wall thickness, and the incremental step size for the width parameter is 5% of the pipe outer diameter. Steps four and five are re-executed after each iteration until the desired result is met. The criteria for determining the thickness increment are as follows: If the increment is too large, it may skip the minimum reinforcement size combination that meets the requirements, resulting in material waste; if the increment is too small, the number of iterations increases, reducing computational efficiency. A thickness increment of 10% of the pipe wall thickness and a width increment of 5% of the pipe outer diameter are reasonable values ​​that strike a balance between computational efficiency and material utilization. When the thickness of both the upper and lower reinforcement plates increases to 1.5 times the pipe wall thickness and still does not meet the criteria, the width parameters of the upper and lower reinforcement plates are increased, and iterative calculations continue. The technical basis for setting the upper limit of thickness to 1.5 times the pipe wall thickness is as follows: When the reinforcement plate thickness exceeds this ratio, the weld heat input is too large, which may cause unacceptable welding deformation in the pipe body, and the weight of the reinforcement plate itself increases significantly, causing a sharp decrease in the efficiency of increasing the equivalent section moment of inertia with further increases in thickness.

[0067] In this embodiment, the new allowed span The actual span is 12.8 meters. It is twelve meters. Comparing the two, If the new allowable span is greater than the actual span, the current reinforcement design is deemed to meet the requirements. At this point, the actual maximum deflection of the reinforced pipeline is less than the allowable deflection of the pipeline, and the actual maximum bending stress of the reinforced pipeline is less than the allowable stress of the pipeline material. The strength and stiffness of the pipeline at the actual span of twelve meters both meet the design requirements.

[0068] This embodiment uses upper and lower reinforcing plates in the high-stress areas at the top of the support and the bottom of the mid-span, respectively. Utilizing the parallel axis theorem, the equivalent moment of inertia of the combined section is calculated, increasing it from 1.86 x 10^8 cubic millimeters before reinforcement to 3.905 x 10^8 cubic millimeters. The allowable span for stiffness increases from 9.7 meters before reinforcement to 12.8 meters after reinforcement, meeting the design requirement of a 12-meter span. The material usage of the reinforcing plates is only 3.8% of the original pipe material, far lower than the material cost increase of the overall pipe diameter enlargement scheme. Furthermore, in this embodiment, the reinforcing plates are precisely positioned to correspond to the high-stress areas of the pipe's bending moment distribution, resulting in high material utilization, simplified construction, and no need to modify the external support structure.

[0069] Example 2: Reinforced span design structure for DN300 steam pipe supports and hangers This embodiment uses the same DN300 steam pipeline as in Embodiment 1 as an example to describe in detail the reinforced design structure for the span of the overhead pipeline support provided by this invention. The DN300 steam pipeline transports saturated steam at an operating temperature of 250 degrees Celsius and a design pressure of 1.6 MPa. The pipeline is laid overhead along the main road of the plant area, with an actual span of twelve meters. See also... Figure 1 The flowchart shown illustrates the method. The reinforced design structure in this embodiment is the specific product structure prepared according to the methods described in steps one through six. (See also...) Figure 2 The diagram showing the pipe bending moment distribution illustrates that when the pipe is subjected to a uniformly distributed load, the bending moment is periodically distributed along the axial direction. The top of the support bears a negative bending moment, while the bottom of the mid-span bears a positive bending moment. These two locations are the high-stress areas with the largest absolute values ​​of bending moment. (See also...) Figure 3 The diagram shows the arrangement of the reinforcing plates. In this embodiment, the reinforcing design structure includes a pipe body, an upper reinforcing plate, and a lower reinforcing plate. The upper reinforcing plate is located at the top of the support, and the lower reinforcing plate is located at the bottom of the mid-span. (See also...) Figure 4 The schematic diagram of the upper reinforcing plate cross-section structure shown is as follows: Figure 5 The schematic diagram of the lower reinforcing plate cross-section shows that both the upper and lower reinforcing plates are arc-shaped plates, respectively attached to the top and bottom of the pipe's outer wall. (See also...) Figure 6The equivalent cross-section calculation diagram shown depicts the upper and lower reinforcing plates, which together with the pipe body form a composite cross-section. The centroid of each reinforcing plate's cross-section deviates from the neutral axis of the composite cross-section. The structural composition and working principle of this embodiment will be described in detail below with reference to the aforementioned figures.

[0070] I. Pipeline Body Structure See Figure 2 and Figure 3 As shown, the pipe body is a hollow cylindrical structure, made of No. 20 steel, with an outer diameter of... The pipe wall thickness is 325 mm. The diameter is eight millimeters. The two ends of the pipe body are supported on supports. At the supports, the pipe is only constrained by vertical supports and can freely expand and contract axially to simulate simply supported boundary conditions. In service, the pipe body bears a uniformly distributed load including the pipe's own weight, the weight of the insulation layer, and the weight of the steam medium. The uniformly distributed load is evenly distributed along the entire length of the pipe.

[0071] See Figure 2 The bending moment distribution diagram shown illustrates that for a continuous multi-span pipeline subjected to a uniformly distributed load, the bending moment exhibits a periodic distribution along the axial direction. At support location A, due to the constraint of the deflection deformation of the adjacent two spans at the support, the pipeline section bears a negative bending moment. This means that the fibers at the top of the pipe are under tension, and the fibers at the bottom are under compression. The maximum tensile stress occurs at the top generatrix of the outer wall of the pipe, which is the core location of the high-stress area at the top of the support. At the mid-span section B, between two adjacent supports, the pipe section experiences a positive bending moment because the deflection at this section reaches its maximum value. This means that the bottom fibers of the pipe are under tension, while the top fibers are under compression. The maximum tensile stress occurs at the bottom generatrix of the outer wall of the pipe, which is the core location of the high-stress region at the bottom of the mid-span. The stress levels at the top of the support and the bottom of the mid-span are much higher than at other locations on the pipe, making them key cross-sectional locations that determine the pipe's load-bearing capacity.

[0072] II. Upper Reinforcing Plate Structure See Figure 3 and Figure 4 As shown, the upper reinforcing plate is located at the top of the support area of ​​the pipe body. The upper reinforcing plate is an arc-shaped plate made of the same No. 20 steel as the pipe body to ensure that their coefficients of linear expansion are consistent, thus avoiding additional thermal stress caused by differences in thermal expansion under temperature loads. See also... Figure 4 The schematic diagram of the upper reinforcing plate cross-section shows that the inner wall curvature of the arc-shaped plate is consistent with the outer wall curvature of the pipe body; that is, the radius of curvature of the inner arc surface of the arc-shaped plate is the same as the radius of curvature of the outer wall of the pipe body. This ensures that the inner wall of the arc-shaped plate can form a tight, gapless fit with the top of the outer wall of the pipe, thus guaranteeing the overall performance of the composite section.

[0073] See Figure 4 As shown, the inner wall of the upper reinforcing plate is provided with multiple stress relief grooves spaced apart along the pipe axis. Each stress relief groove is an arc-shaped groove, extending circumferentially through the inner wall of the upper reinforcing plate, with a spacing of 60 mm between adjacent grooves. The cross-sectional shape of the stress relief groove is an arc-shaped groove, with a depth of 1-2 mm and a width of 3-5 mm. While the stress relief groove extends circumferentially through the pipe, it does not sever the structural continuity of the reinforcing plate; the bottom of the groove retains sufficient wall thickness to ensure the structural strength of the reinforcing plate itself. The working principle of the stress relief groove is as follows: During welding, the welding thermal cycle causes non-uniform expansion and contraction of the reinforcing plate and the surface metal of the pipe, resulting in high residual stress in the weld and heat-affected zone. Without stress relief grooves, the residual stress would cause separation deformation at the contact surface between the inner wall of the reinforcing plate and the outer wall of the pipe, forming a local gap between them, compromising the overall working performance of the combined section, and thus reducing the actual achieved equivalent moment of inertia. After the stress relief groove is set, the residual stress generated during the welding process is concentrated and released at the bottom of the groove, which reduces the separation deformation of the mating surface and ensures that the reinforcing plate and the outer wall of the pipe maintain close contact along the entire mating surface, so that the plane section assumption can be established.

[0074] See Figure 3 and Figure 4 As shown, the upper reinforcing plate extends circumferentially along the pipe. It is positioned on the upper semicircle of the pipe's cross-section, covering an angle of 120 degrees from the top of the pipe's circumference, i.e., extending 60 degrees to the left and right from the pipe's top centerline. The width of the upper reinforcing plate is less than the pipe's outer diameter. Specifically, the width of the upper reinforcing plate is 300 mm, and the central angle corresponding to its arc length is approximately 128 degrees. The structural basis for choosing this width value is as follows: when the pipe is subjected to a negative bending moment, the bending stress in the top region of the cross-section gradually decreases circumferentially from the top generatrix to both sides. When the coverage angle is approximately 120 degrees, the peak stress region at the top is completely covered. At the same time, the reinforcing plate does not extend to the area near the neutral axis on both sides of the pipe, where the stress level has been significantly reduced. Further increasing the coverage angle would lead to an increase in material usage while the increase in moment of inertia would be limited.

[0075] The thickness of the upper reinforcing plate extends radially along the pipe. The thickness of the upper reinforcing plate is one to one and a half times the pipe wall thickness; in this embodiment, it is 12 millimeters, which is 1.5 times the pipe wall thickness. The thickness of the upper reinforcing plate is determined based on the following: when the thickness is less than one times the pipe wall thickness, the reinforcing plate itself does not contribute enough to the bending stiffness, and the increase in the equivalent section moment of inertia of the composite section is limited; when the thickness is greater than one and a half times the pipe wall thickness, although the equivalent section moment of inertia continues to increase, the self-weight of the reinforcing plate increases significantly, and excessive heat input during welding can easily cause welding deformation of the pipe body, affecting the roundness and dimensional accuracy of the pipe.

[0076] See Figure 3 As shown, the upper reinforcing plate extends along the pipe axial direction. The upper reinforcing plate covers at least one-eighth of the actual span on each side of the support centerline along the pipe axial direction. In this embodiment, the actual span... If the length is twelve meters, then the total coverage length of the upper reinforcing plate is three meters, with 1.5 meters on each side of the support centerline. The structural basis for setting this coverage length is: for a continuous beam subjected to a uniformly distributed load, the negative bending moment near the support is parabolic along the axial direction. At the cross-section, the negative bending moment has decreased to approximately 75% of the peak bending moment at the support. Beyond this range, the stress level of the pipe cross-section has significantly decreased, and the marginal contribution of continuing to install reinforcing plates to increase the equivalent cross-sectional moment of inertia rapidly diminishes, leading to a decrease in material utilization efficiency. Therefore, The coverage range is an optimized structural value that balances ensuring complete coverage of high-stress areas with saving material usage.

[0077] A structural adhesive layer is applied between the upper reinforcing plate and the outer wall of the pipe body. This structural adhesive layer, made of epoxy resin, is one millimeter thick. Its function is to pre-fix the upper reinforcing plate to the top of the pipe's outer wall using chemical adhesion and mechanical interlocking forces before welding, preventing slippage or misalignment under welding thermal stress and ensuring the reinforcing plate maintains its designed position throughout the welding process. Simultaneously, the structural adhesive layer possesses a certain shear strength after curing, which helps to transfer shear forces between the reinforcing plate and the pipe.

[0078] See Figure 4As shown, the upper reinforcing plate is fixed to the outer wall of the pipe body by continuous fillet welds. The continuous fillet welds run along the circumferential and axial edges of the upper reinforcing plate, meaning continuous fillet welds are present on the left, right, front, and rear edges. The structural basis for using continuous fillet welds instead of intermittent welds is that the mechanical premise of the reinforcing plate and pipe sharing the load is that sufficient longitudinal shear force can be transferred between their interfaces. Only continuous welds can guarantee the continuity of shear force transfer at all sections along the entire length of the reinforcing plate, thus ensuring that the plane section assumption holds true and the calculated result of the equivalent section moment of inertia of the combined section matches the actual value. If intermittent welds are used, shear force cannot be effectively transferred between the reinforcing plate and the pipe in the unwelded sections, and the two cannot form an integral combined section; the equivalent section moment of inertia will be much lower than the calculated value. The weld leg height of the continuous fillet weld is 0.7 times the thickness of the upper reinforcing plate, i.e., 8.4 mm.

[0079] See Figure 4 As shown, both ends of the upper reinforcing plate are provided with sloping weld bevels. The bevel angle of the sloping weld bevel is 45 degrees, and the root gap of the sloping weld bevel is 3 millimeters. The function of the weld bevel is to ensure that the weld root can be fully penetrated during the welding process, so that the weld metal and the base metal can be completely fused together, avoiding the formation of incomplete fusion defects and stress concentration at the ends of the reinforcing plate, thereby improving the connection strength and fatigue resistance of the weld. See also Figure 3 As shown, the upper reinforcing plate is set above each support, that is, an independent upper reinforcing plate is set in the top area of ​​each support.

[0080] III. Lower Reinforcing Plate Structure See Figure 3 and Figure 5 As shown, the lower reinforcing plate is located at the bottom mid-span of the pipe body. The lower reinforcing plate is an arc-shaped plate made of the same No. 20 steel as the pipe body. See also... Figure 5 The schematic diagram of the cross-sectional structure of the lower reinforcing plate shown shows that the inner wall curvature of the arc-shaped plate is consistent with the outer wall curvature of the pipe body. That is, the radius of curvature of the inner arc surface of the arc-shaped plate is the same as the radius of curvature of the outer wall of the pipe body, so that the inner wall surface of the arc-shaped plate can form a tight fit with the bottom of the outer wall of the pipe without gaps.

[0081] See Figure 5 As shown, the inner wall of the lower reinforcing plate is also provided with multiple stress relief grooves spaced apart along the pipe axis. Each stress relief groove is an arc-shaped groove, extending circumferentially through the inner wall of the lower reinforcing plate, with a spacing of sixty millimeters between adjacent grooves. The cross-sectional shape, dimensions, and working principle of the stress relief grooves are the same as those of the upper reinforcing plate, used to release residual welding stress and ensure tight contact between the lower reinforcing plate and the bottom of the outer wall of the pipe along the mating surface.

[0082] See Figure 3 and Figure 5 As shown, the lower reinforcing plate extends circumferentially along the pipe. It is positioned on the lower semicircle of the pipe's cross-section, covering an angle of 120 degrees from the bottom of the pipe's circumference, specifically 60 degrees to the left and right from the pipe's bottom centerline. The width of the lower reinforcing plate is 300 millimeters. The structural basis for selecting this width is the same as for the upper reinforcing plate: when the pipe is subjected to a positive bending moment, the bending stress in the bottom region of the cross-section gradually decreases circumferentially from the bottom generatrix towards both sides. This width completely covers the peak stress region at the bottom while avoiding material waste.

[0083] See Figure 3 As shown, the thickness of the lower reinforcing plate extends radially along the pipe. The thickness of the lower reinforcing plate is one to one and a half times the pipe wall thickness; in this embodiment, it is twelve millimeters, which is 1.5 times the pipe wall thickness.

[0084] See Figure 3 As shown, the lower reinforcing plate extends along the pipe axial direction. The lower reinforcing plate covers at least one-eighth of the actual span on each side of the mid-span section along the pipe axial direction. In this embodiment, the actual span... If the span is 12 meters, then the span is 1.5 meters on each side of the mid-span section, meaning the total coverage length of the lower reinforcing plate is 3 meters.

[0085] A structural adhesive layer is applied between the lower reinforcing plate and the outer wall of the pipe body. This structural adhesive layer uses an epoxy resin-based adhesive and is one millimeter thick. The lower reinforcing plate is pre-fixed to the bottom of the pipe's outer wall using this structural adhesive layer before being welded together.

[0086] See Figure 5 As shown, the lower reinforcing plate is fixed to the outer wall of the pipe body by continuous fillet welds. The continuous fillet welds are set along the circumferential and axial edges of the lower reinforcing plate, and the weld leg height of the continuous fillet welds is 0.7 times the thickness of the lower reinforcing plate, i.e., 8.4 mm.

[0087] See Figure 5 As shown, both ends of the lower reinforcing plate have sloping weld bevels. The bevel angle of the sloping weld bevel is 45 degrees, and the root gap of the sloping weld bevel is 3 millimeters. See also Figure 3 As shown, the lower reinforcing plate is set below each mid-span, that is, an independent lower reinforcing plate is set in the bottom area of ​​each mid-span.

[0088] IV. Composite Section Structure and Its Working Principle See Figure 6The diagram showing the equivalent cross-section calculation illustrates that after the upper and lower reinforcing plates are fixedly connected to the pipe body, the three together form an integral composite cross-section. In this composite cross-section, the centroids of both the upper and lower reinforcing plates deviate from the centroid of the pipe body. Specifically, the centroid of the upper reinforcing plate... Located at the centroid of the pipe cross section Directly above, at a distance equal to the outer radius of the pipe plus half the thickness of the upper reinforcing plate, i.e. Millimeters; Centroid of the lower reinforcing plate section Located at the centroid of the pipe cross section Directly below, at a distance equal to the outer radius of the pipe plus half the thickness of the upper and lower reinforcing plates, i.e. Millimeters. See also Figure 6 As shown, since the upper and lower reinforcing plates are symmetrically arranged on the upper and lower sides of the pipe section, the neutral axis of the combined section... The centroidal axis of the cross section basically coincides with that of the pipe body, and the neutral axis is located at the center of the pipe cross section.

[0089] See Figure 6 As shown, in this composite section, the upper and lower reinforcing plates are positioned relative to the neutral axis. With a large distance and According to the parallel axis theorem, the contribution of each stiffening plate to the moment of inertia of the composite section about the neutral axis is equal to the moment of inertia of the stiffening plate about its own centroidal axis. Plus the area of ​​the reinforcing plate Multiply by the distance from the centroid to the neutral axis The square of, that is Due to the squared term of the distance Despite occupying only a small portion of the original pipe cross-sectional area, the upper and lower reinforcing plates, which make a dominant contribution, provide a significant increase in the moment of inertia. Specifically, the cross-sectional area of ​​the upper reinforcing plate... The square millimeter contributes its moment of inertia about the neutral axis of the composite section as follows: cubic millimeters. The lower reinforcing plate provides the same moment of inertia contribution. The total contribution of the two reinforcing plates is approximately... cubic millimeters. Combined with the original pipe cross-section moment of inertia. cubic millimeters, equivalent moment of inertia of composite section The cubic millimeter represents an increase of approximately 110% in the moment of inertia compared to the original pipe cross-section, which is completely consistent with the calculation data in Example 1.

[0090] The working principle of this composite section is as follows: When the pipeline is subjected to lateral loads and undergoes bending deformation, according to the plane section assumption, the longitudinal strain at each point on the composite section is linearly distributed along the section height. Since the upper reinforcing plate is located at the top of the section and the lower reinforcing plate is located at the bottom, both are in high-strain regions far from the neutral axis. According to Hooke's law, stress is proportional to strain; therefore, the upper and lower reinforcing plates bear a higher stress level when the pipeline bends, effectively improving the bending capacity and bending stiffness of the composite section. This structural design utilizes the positional advantage of the reinforcing plates in the composite section to achieve a significant increase in the section moment of inertia with minimal material increment.

[0091] The pipe body, upper reinforcing plate, and lower reinforcing plate are all made of No. 20 steel, with the same coefficient of linear expansion and a difference of zero, not exceeding the design requirement of 5%. The technical basis for this material consistency design is that under temperature variations, the pipe body and reinforcing plate will experience the same amount of thermal deformation, preventing additional thermal stress at the connection interface. This ensures the long-term reliable operation of the reinforced structure within a working temperature range of 150°C to 250°C, avoiding weld cracking or adhesive layer peeling failure caused by temperature difference loads.

[0092] See Figure 3 As shown, in this embodiment, the upper reinforcing plate is positioned above each support, and the lower reinforcing plate is positioned below each mid-span. For continuous pipeline systems with multiple spans, reinforcing plates are installed at the top of the supports and the bottom of the mid-span in the same manner for each span, ensuring uniform reinforcement throughout the pipeline. This reinforcement design structure achieves an increase in pipeline span from 9.7 meters to 12 meters with only a material increase of approximately 3.8% of the original pipeline material by setting local reinforcing plates in high-stress areas, while maintaining a clean appearance of the pipeline's outer wall. No additional external support structure is required, making construction and installation convenient and quick.

[0093] In summary, the overhead pipeline support span reinforcement design method and structure provided by this invention establishes a numerical model of the pipeline beam element through finite element modeling analysis, accurately obtains the bending moment distribution data of each section along the axial direction of the pipeline, and automatically identifies high-stress areas at the top of the support and the bottom of the mid-span using a bending moment extremum search algorithm, overcoming the technical deficiency of traditional analytical methods that cannot quantitatively locate high-stress areas. By setting the upper and lower reinforcing plates at the top of the support and the bottom of the mid-span respectively in the high-stress areas, the equivalent section moment of inertia of the combined section is calculated based on the plane section assumption and the parallel axis theorem, so that the contribution of the reinforcing plate's moment of inertia is maximized by multiplying the area by the square of the distance from the centroid to the neutral axis, achieving a significant improvement in the section bending stiffness with minimal material usage. By iteratively adjusting the reinforcing plate size and recalculating the new allowable span, a closed-loop optimization design process is formed, ensuring the economy and reliability of the reinforcement design. This invention effectively solves the contradiction between increasing the span and controlling costs in the prior art. It achieves the technical effect of increasing the span by 20% to 50% without changing the overall specifications of the pipeline and the external support structure. At the same time, the increase in material costs is only 3% to 5%, which has significant economic benefits and engineering application value.

[0094] Many specific details have been set forth in the foregoing description to provide a thorough understanding of the present invention. However, the above description is merely a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed above. Furthermore, any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, using the methods and techniques disclosed above, without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for reinforcing the span of overhead pipeline supports, characterized in that, Includes the following steps: Step 1: Obtain the basic parameters of the pipeline design, establish a beam element numerical model of the pipeline structure using the finite element modeling and analysis method, apply the pipeline's self-weight load and internal pressure load to the beam element numerical model, and extract the internal force distribution data of the pipeline section through static solution calculation. The internal force distribution data includes bending moment value, shear force value and axial force value. Calculate the moment of inertia and section modulus of the pipeline section based on the internal force distribution data. Step 2: Based on the moment of inertia and section modulus of the pipe section, calculate the allowable span for strength at the section with maximum bending moment using strength theory, and calculate the allowable span for stiffness at the section with maximum deflection using deflection theory. Take the smaller of the allowable span for strength and the allowable span for stiffness as the initial allowable span for the pipe. Obtain the actual span required for the actual layout of the pipe. Compare the actual span with the initial allowable span for the pipe. When the actual span is greater than the initial allowable span for the pipe, trigger the execution of the reinforcement design process. Step 3: Based on the bending moment distribution calculation results of the beam element numerical model, extract the bending moment values ​​at each section along the axial direction of the pipeline, and determine the high stress region with the largest absolute value of the bending moment. The high stress region includes the negative bending moment peak region at the top of the support and the positive bending moment peak region at the bottom of the mid-span. An upper reinforcing plate is arranged at the top of the pipeline along the circumference of the negative bending moment peak region at the top of the support, and a lower reinforcing plate is arranged at the bottom of the pipeline along the circumference of the positive bending moment peak region at the bottom of the mid-span. Both the upper and lower reinforcing plates extend along the axial direction of the pipeline to cover the high stress region. Step 4: Construct the upper reinforcing plate and the lower reinforcing plate together with the outer wall of the pipe to form an integral composite section. Calculate the equivalent section moment of inertia of the composite section using the equivalent section method. The equivalent section method is based on the plane section assumption and strain compatibility conditions, and adds the contribution of the moment of inertia of the reinforcing plate section relative to the centroidal axis of the composite section to the moment of inertia of the original pipe section. Step 5: Based on the equivalent cross-sectional moment of inertia, the maximum tensile stress theory is used to calculate the allowable span of the reinforced pipeline at the critical section for strength, and the elastic deflection curve differential equation is used to calculate the allowable span of the reinforced pipeline at the critical section for stiffness. The smaller value between the allowable span of the reinforced pipeline for strength and the allowable span of the reinforced pipeline for stiffness is taken as the new allowable span. Step Six: Compare the new allowable span with the actual span. If the new allowable span is greater than or equal to the actual span, the current reinforcement design is deemed to meet the requirements. If the new allowable span is less than the actual span, increase the thickness or width parameter of the upper or lower reinforcement plate and return to Step Four to recalculate until the requirements are met.

2. The reinforced design method according to claim 1, characterized in that, In step one, the finite element modeling and analysis method includes: simulating the main structure of the pipeline using three-dimensional beam elements, each node of which has six degrees of freedom, including three translational degrees of freedom and three rotational degrees of freedom; applying simply supported boundary conditions at the nodes at both ends of the pipeline, constraining the vertical translational degrees of freedom and releasing the axial translational and rotational degrees of freedom; applying the weight per unit length of the pipeline as a uniformly distributed load to each node of the beam element, converting the internal pressure load of the pipeline into equivalent nodal forces applied to the inner wall of the pipeline; and using a finite element static solver to solve the overall stiffness equation. Solve the problem to obtain the displacement vectors of each node. ,in For the overall stiffness matrix, The equivalent nodal load vector is used; the internal forces of each element section are calculated based on the nodal displacement vector; the moment of inertia of the pipe section is calculated according to the formula for the annular section. The cross-sectional modulus of the pipe is calculated according to the formula for annular cross-sections: Calculation, where The outer diameter of the pipe. The inner diameter of the pipe. , This refers to the pipe wall thickness.

3. The reinforced design method according to claim 1, characterized in that, In step two, the strength theory is the fourth strength theory. According to this fourth strength theory, the maximum bending stress of the pipeline at the maximum bending moment section does not exceed the allowable stress of the pipeline material. The strength allows for a certain span. According to the formula: Calculation; the deflection theory is the Euler-Bernoulli beam theory. According to this theory, the elastic deflection of the pipe at the maximum deflection section does not exceed the allowable deflection of the pipe, and the allowable stiffness span... According to the formula: Calculation, where The elastic modulus of the pipe material. Let the moment of inertia of the pipe cross section be... The weight per unit length of the pipe, with a coefficient of 1500 derived from a conversion factor when the allowable deflection is taken as one-three-hundredth of the span; the initial allowable span of the pipe. Pick and The smaller value in, i.e. ,in The allowable stress of the pipe material, For the section modulus of the pipe, This is the moment reduction factor; when the actual span is greater than the initial allowable span of the pipeline. At that time, a trigger signal is generated containing the deviation value between the actual span and the initial allowable span of the pipeline, and the trigger signal is used to initiate the reinforcement design process.

4. The reinforced design method according to claim 1, characterized in that, In step three, a bending moment extreme value search algorithm is used to determine the high-stress region. The bending moment extreme value search algorithm includes: extracting a set of negative bending moment values ​​and a set of positive bending moment values ​​from the bending moment values ​​of each node in the numerical model of the beam element; determining the node position with the largest absolute value in the set of negative bending moment values ​​as the peak position of negative bending moment at the top of the support; determining the node position with the largest absolute value in the set of positive bending moment values ​​as the peak position of positive bending moment at the bottom of the mid-span; the peak region of negative bending moment at the top of the support is located within the axial range of one-eighth of the actual span on both sides of the centerline of the support; the peak region of positive bending moment at the bottom of the mid-span is located within the axial range of one-eighth of the actual span on both sides of the mid-span section; the upper reinforcing plate is arranged on the upper semicircle of the pipe cross-section and covers an angle range of 120 to 180 degrees from the top of the pipe circumference; the lower reinforcing plate is arranged on the lower semicircle of the pipe cross-section and covers an angle range of 120 to 180 degrees from the bottom of the pipe circumference; the thickness of the upper and lower reinforcing plates is one to one and a half times the pipe wall thickness.

5. The reinforced design method according to claim 1, characterized in that, In step three, before arranging the upper reinforcing plate, the high-stress area at the top of the pipe's outer wall is first subjected to surface rust removal and roughening treatment to ensure that the surface roughness of the pipe's outer wall reaches a preset level; before arranging the lower reinforcing plate, the high-stress area at the bottom of the pipe's outer wall is first subjected to surface rust removal and roughening treatment; a structural adhesive layer is coated between the upper reinforcing plate and the lower reinforcing plate and the pipe's outer wall, with the thickness of the structural adhesive layer being 0.5 mm to 2 mm; the upper reinforcing plate and the lower reinforcing plate are pre-fixed to the pipe's outer wall through the structural adhesive layer and then welded together.

6. The reinforced design method according to claim 1, characterized in that, In step four, before calculating the equivalent cross-sectional moment of inertia, the position of the neutral axis of the composite cross-section is first determined. The method for determining the position of the neutral axis includes: establishing a rectangular coordinate system with the center of the pipe cross-section as the origin; discretizing the pipe cross-section into several infinitesimal elements; calculating the area moment for each infinitesimal element; and iteratively solving for the coordinate value of the neutral axis in the rectangular coordinate system based on the condition that the area moment is zero. The equivalent cross-sectional moment of inertia is calculated according to the formula: in Let be the moment of inertia of the original pipe cross-section about its own centroidal axis. The total number of reinforcing plates, For the first The moment of inertia of the cross section of the reinforcing plate about its own centroidal axis. For the first The area of ​​the cross-section of the reinforcing plate. For the first The distance from the centroid of the reinforcing plate to the neutral axis of the composite section; the position of the neutral axis of the composite section according to the equilibrium condition of the area moment of the cross section. Confirmed, among which This represents the total number of sub-sections in the composite section. For the first The area of ​​each sub-section For the first The distance from the centroid of each sub-section to the neutral axis of the combined section.

7. The reinforced design method according to claim 1, characterized in that, In step five, the reinforced strength allows for a certain span. According to the formula Calculate the allowable span of the stiffness after reinforcement. According to the formula Calculation, where The elastic modulus of the pipe material. For the equivalent cross-sectional moment of inertia, Weight per unit length of pipe; new allowable span Pick and The smaller value in, i.e. ,in The allowable stress of the pipe material, The equivalent section modulus of the composite section. The moment reduction factor; equivalent section modulus According to the formula Calculation, where The distance from the farthest fiber in the composite section to the neutral axis of the composite section is; the differential equation of the elastic deflection curve is: in For pipe deflection, These are the position coordinates along the pipeline axis. For position The bending moment value at the section is obtained; the differential equation of the elastic deflection curve is solved by numerical integration. The pipeline is divided into several integration intervals along the axial direction. The fourth-order Runge-Kutta method is used to integrate step by step in each integration interval to obtain the deflection value and rotation angle value at each position along the axial direction of the pipeline. The maximum deflection value is extracted from the deflection value at each position.

8. The reinforced design method according to claim 1, characterized in that, In step six, when increasing the thickness or width parameter of the upper or lower reinforcing plate, it is adjusted iteratively according to the increment step size. The increment step size for the thickness parameter is 10% of the pipe wall thickness, and the increment step size for the width parameter is 5% of the pipe outer diameter. After each iteration, steps four and five are re-executed until the desired result is achieved. The determination criteria, among which The actual span is given. If the thickness of both the upper and lower reinforcing plates is increased to 1.5 times the pipe wall thickness and the judgment condition is still not met, the width parameters of the upper and lower reinforcing plates are increased and the iterative calculation continues.

9. A reinforced design structure for the span of overhead pipeline supports, characterized in that, include: The pipe body is a hollow cylindrical structure, with both ends supported on supports. The pipe body bears a uniformly distributed load and generates a negative bending moment at the top of the supports and a positive bending moment at the bottom of the mid-span. An upper reinforcing plate is attached and fixed to the top of the outer wall of the pipe body and located at the top of the supports. The upper reinforcing plate covers at least one-eighth of the actual span length on both sides of the support centerline along the pipe axis, and covers a circumferential range of 120 to 180 degrees around the top of the outer wall of the pipe. A lower reinforcing plate is attached and fixed to... The bottom of the outer wall of the pipe body is located in the mid-span bottom region. The lower reinforcing plate covers at least one-eighth of the actual span length on both sides of the mid-span section along the pipe axis. The lower reinforcing plate covers a circumferential range of 120 to 180 degrees around the bottom of the outer wall of the pipe along the pipe circumference. The centroids of the cross sections of the upper and lower reinforcing plates are both offset from the centroid of the cross section of the pipe body. The upper and lower reinforcing plates are fixedly connected to the pipe body to form an integral composite cross section. The equivalent moment of inertia of the integral composite cross section is greater than the moment of inertia of the individual cross section of the pipe body.

10. The reinforced design structure according to claim 9, characterized in that, Both the upper and lower reinforcing plates are arc-shaped plates. The inner wall curvature of the arc-shaped plate is consistent with the outer wall curvature of the pipe body. The width of the arc-shaped plate extends circumferentially along the pipe and its width is less than or equal to the pipe's outer diameter. The thickness of the arc-shaped plate extends radially along the pipe and its thickness is one to one and a half times the pipe wall thickness. The length of the arc-shaped plate extends axially along the pipe and its length is not less than one-quarter of the actual span. The inner walls of the upper and lower reinforcing plates are provided with multiple stress-relieving grooves spaced apart along the pipe's axial direction. Each stress-relieving groove is an arc-shaped groove. The upper or lower reinforcing plate extends through its inner wall surface; the upper and lower reinforcing plates are welded to the outer wall of the pipe body via continuous fillet welds, which run along the circumferential and axial edges of the upper and lower reinforcing plates; the upper and lower reinforcing plates are respectively provided with sloping weld bevels at both axial ends, with bevel angles ranging from 45 to 60 degrees; the difference in linear expansion coefficients between the pipe body, the upper reinforcing plate, and the lower reinforcing plate does not exceed 5%; the upper reinforcing plate is positioned above each support, and the lower reinforcing plate is positioned below each mid-span.

Images