Method for estimating static wind uplift resistance of light steel roof photovoltaic structure

Abstract

The application provides a kind of light steel roof photovoltaic structure wind lifting resistance static strength estimation method, it is related to light steel roof photovoltaic structure strength estimation technical field, the application specifically includes the finite element model considering that roof panel is to purlin lateral restraint is constructed;Roof is divided into wind pressure area, calculates the area component of photovoltaic array in each area projection, according to this, wind load is converted into the concentrated force acting on fixed point;Carry out statics solution, obtain purlin stress and fixed point roof normal displacement;According to purlin yield strength and maximum bending stress, the safety of purlin is evaluated, according to the displacement of roof, additional bending moment of fixed point is calculated, and it is combined to obtain total load with concentrated force, and the overall safety is evaluated by comparing the design uplift bearing capacity of fixed point;Finally, the minimum value of all safety factors is taken as the static strength margin of structure, compared with the preset threshold to determine the overall safety, and the weak link is automatically positioned to give reinforcement suggestion.

Description

Technical Field

[0001] This invention relates to the field of strength estimation technology for light steel roof photovoltaic structures, specifically a method for estimating the static strength of light steel roof photovoltaic structures against wind uplift. Background Technology

[0002] With the advancement of "dual carbon" goals, installing photovoltaic power generation systems on the lightweight steel roofs of existing large buildings such as industrial plants, logistics warehouses, and commercial centers has become a widely adopted practice. These buildings typically use lightweight, relatively low-stiffness thin-walled C- or Z-shaped steel purlins paired with profiled steel sheets as their roofing system, resulting in structural characteristics that are drastically different from traditional reinforced concrete roofs. It is precisely in this specific application scenario that the installation of photovoltaic systems presents new structural challenges.

[0003] In existing technologies, there are generally two mainstream methods for assessing the wind resistance of rooftop photovoltaic systems. One method is overly simplistic, treating the photovoltaic structure merely as an additional static load and calculating its impact on the main structure, while completely ignoring the upward force of wind suction on the roof and the resulting critical issues such as purlin buckling and local deformation of the roof panels. The other method involves complex overall finite element simulation, which, although theoretically more accurate, is cumbersome in modeling, computationally expensive, and requires highly specialized engineers, making it difficult to apply quickly and widely in the early planning and design stages of projects.

[0004] The shortcomings of existing technologies lie primarily in their failure to specifically address the interaction between lightweight steel roofs and photovoltaic systems. Specifically, under strong wind suction, the lightweight roof base (purlins and roof panels) undergoes significant deformation. This deformation, in turn, generates additional bending moments and pull-out forces on the fixing points of the photovoltaic supports, creating an unstable feedback loop. Traditional assessment methods neglect this crucial mechanism, leading to significant discrepancies between calculated results and actual conditions, and failing to accurately predict the risk of components being overturned or localized roof damage due to loosening or failure of fixing points.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide an optimized configuration method and apparatus for a magnetic reactive dynamic voltage restorer to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift, comprising the following steps: Step 1: Construct a finite element model of the photovoltaic structure of the light steel roof, where the fixed points of the photovoltaic structure are taken as local rigid support points, and the roof is equivalent to a constraint boundary that provides continuous lateral support to the purlins, so as to simulate the constraint effect of the roof on the stability of the purlins; Step 2: Divide the roof into several wind pressure zones. For each photovoltaic array, determine its projected area component in each wind pressure zone based on the overlap between its projected area and each wind pressure zone. Calculate the total wind suction force of the photovoltaic array based on the standard value of wind suction force and the corresponding projected area component of each wind pressure zone. Distribute this total wind suction force evenly to all fixed points below the photovoltaic array, thereby converting the wind load into a concentrated force acting on the fixed points in the finite element simulation model. Step 3: After applying a concentrated force to the finite element model, perform static solution to calculate its deformation response and stress response; and determine the roof normal displacement at the fixed point based on the deformation response, and determine the maximum bending normal stress of each purlin based on the stress response; Step 4: Determine the strength safety factor for each purlin based on its design yield strength and maximum bending normal stress; analyze the roof normal displacement at each fixed point to determine the additional bending moment generated at each fixed point; combine the additional bending moment with the concentrated force caused by wind suction to obtain the total load at each fixed point; compare the design tensile bearing capacity at the fixed point with the total load to determine the strength safety factor at each fixed point. Step 5: Determine the minimum strength safety factor among all purlins and fixing points as the static strength margin of the roof photovoltaic structure; compare it with the preset minimum safety threshold to assess whether the light steel roof photovoltaic structure is safe.

[0008] Furthermore, the finite element model of the aforementioned light steel roof photovoltaic structure specifically includes: Based on the actual construction of the roof photovoltaic structure, its finite element model is established; the constraint boundary is achieved by setting a set of linear spring supports at the upper flange node of the purlin in the finite element model. The constraint direction of the spring is perpendicular to the purlin axis and located in the plane of the roof panel, in order to simulate the constraint effect of the roof panel on the lateral displacement and torsion of the purlin. The equivalent stiffness of the linear spring characterizes the lateral restraint provided by the roof panel as a continuous support to a single purlin. Its determination logic is as follows: Based on the bending stiffness of the roof panel itself, the inherent bending stiffness, jointly determined by the roof panel material and its cross-sectional thickness, is represented by the product of the cube of the roof panel's substrate thickness and the elastic modulus of the roof panel material. A constant 1 is subtracted from the square of the roof panel material's Poisson's ratio to correct the effect of lateral strain caused by the Poisson effect on the equivalent stiffness. The total supporting effect of the roof panel is distributed according to the purlin spacing; therefore, the purlin spacing is multiplied by the correction term as the denominator, and the inherent bending stiffness as the numerator. This ratio characterizes the theoretical equivalent lateral support stiffness provided by the roof panel. Finally, a preset stiffness correction coefficient is multiplied by the theoretical equivalent lateral support stiffness to obtain the actual equivalent stiffness provided by the roof panel to a single purlin. In the finite element model, the fixed points of the photovoltaic structure are modeled as a set of coupled nodes that are rigidly connected to the upper flange nodes of the purlin; the concentrated force acts on this set of coupled nodes, thereby directly transferring the load of the photovoltaic structure to the purlin; The photovoltaic structure includes at least one photovoltaic array, which is a basic power generation unit composed of multiple photovoltaic structures.

[0009] Furthermore, determining the standard values ​​for wind suction in each wind pressure zone specifically includes: Based on the roof structure, the roof is divided into three wind pressure zones: edge zone, corner zone, and middle zone. According to the building load code, the wind load shape coefficient corresponding to each wind pressure zone is obtained. The standard value of wind suction for each wind pressure zone is calculated. The specific logic is as follows: determine the gust coefficient, wind pressure height variation coefficient, and basic wind pressure of the location of the photovoltaic structure on the roof for each wind pressure zone; multiply the wind load shape coefficient, gust coefficient, wind pressure height variation coefficient, and basic wind pressure for each wind pressure zone to obtain the standard value of wind suction for the corresponding wind pressure zone, where z represents the average height from the outer surface of the roof to the outdoor ground level in the wind pressure zone.

[0010] Furthermore, determining the concentrated force acting on the fixed point specifically includes: For any photovoltaic array, identify all wind pressure areas covered by its projection area; for each wind pressure area it covers, calculate the area of ​​the photovoltaic array projection within that wind pressure area, which is the projection area component of the photovoltaic array in that wind pressure area. The arrangement of photovoltaic arrays is divided into two cases, specifically including: If a photovoltaic array spans different wind pressure zones, the array is virtually divided into several sub-arrays according to the wind pressure zone of the roof below it. For each sub-array, the standard value of wind suction is calculated using the wind load shape coefficient of its respective wind pressure zone. The product of the projected area of ​​each sub-array on the roof and its corresponding standard value of wind suction is defined as the total wind suction of the sub-array. The total wind suction of all sub-arrays is summed to obtain the total wind suction of the photovoltaic array. The number of fixed points below the photovoltaic array is counted, and the total wind suction is divided by the number of fixed points to obtain the concentrated force at each fixed point. When the photovoltaic array is located entirely within the same wind pressure zone, the total wind suction force of the photovoltaic array is obtained by multiplying the standard value of the wind suction force of the wind pressure zone where the photovoltaic array is located by the projected area of ​​the photovoltaic array on the roof. Then, based on the number of fixed points below the photovoltaic array, the total wind suction force is divided by the number of fixed points to obtain the concentrated force at each fixed point.

[0011] Furthermore, calculating the deformation response and stress response specifically includes: In the finite element model, each purlin is discretized into multiple beam elements, and the connection points of these beam elements and the connection points of the roof panel springs are defined as purlin nodes; the fixing points are photovoltaic fixing points, and the photovoltaic fixing points are bound to the nearest purlin node to which they are located; From the static solution, the displacement vector at the purlin node of each fixed point is extracted, and the component in the direction perpendicular to the normal direction of the initial plane of the roof is defined as the roof normal displacement at that fixed point. After solving the statics problem, for each purlin, we traverse all beam elements, extract the maximum bending normal stress of each beam element, and determine the maximum bending normal stress of the purlin based on the maximum value among them. While extracting the maximum bending normal stress, the vertical deflection of each purlin node at the mid-span position under wind suction is also extracted. The maximum value of the vertical deflection at the mid-span position of all purlins is determined as the maximum mid-span deflection, so as to verify whether the stiffness of the purlin meets the preset deflection limit based on the maximum mid-span deflection.

[0012] Further determination of the additional bending moment specifically includes: The strength safety is characterized by a strength safety factor; The strength safety of a purlin is characterized by its strength safety factor, which is the ratio of the design yield strength to the maximum bending normal stress. The specific logic for calculating the additional bending moment generated by the normal displacement of the roof at each fixed point is as follows: For each fixed point, the product of the elastic modulus of the photovoltaic support steel frame material and the moment of inertia of the cross section of the photovoltaic support steel frame about its bending neutral axis is defined as the cross section bending stiffness of the photovoltaic support steel frame. This cross section bending stiffness characterizes the ability of the photovoltaic support steel frame to resist bending deformation. The preset constant coefficients are multiplied by the section bending stiffness and the roof normal displacement at the corresponding fixed point, and the product is used to characterize the generalized force that generates forced deformation. The extreme sensitivity of the support frame length to the additional bending moment is characterized by the cube of the length of the free segment of the photovoltaic support steel frame extending out of the roof. Using the generalized force as the numerator and the cube of the free segment length as the denominator, this ratio represents the additional bending moment generated by the normal displacement of the roof at the fixed point.

[0013] Furthermore, the specific calculation logic for the total load is as follows: The product of the preset load effect combination coefficient and the concentrated force at the fixed point is used as the first load coefficient, and the product of the distance from the fixed point to the inflection point of the photovoltaic support steel frame and the additional bending moment at the fixed point is used as the second load coefficient. The square root of the sum of the squares of the first and second load factors is the total load at that fixed point. The strength safety of a fixed point is characterized by its strength safety factor, which is defined as the ratio of the design pull-out bearing capacity of the fixed point to the total load.

[0014] Furthermore, assessing the safety of the aforementioned light steel roof photovoltaic structure specifically includes: The preset minimum security threshold is not less than 1; The strength safety factors of all purlins and all fixed points are collected into the same set for comparison. All strength safety factor values ​​in the set are traversed, and the strength safety factor with the smallest value is taken as the static strength margin of the roof photovoltaic structure. The component corresponding to the static strength margin is determined as the weakest component. The component is a specific purlin or a specific fixed point. The specific logic of the assessment is as follows: if the static strength margin is not less than the minimum safety threshold, the assessment conclusion is safe; if the static strength margin is less than the minimum safety threshold, the assessment conclusion is unsafe. When the assessment concludes that the system is unsafe, it automatically identifies the weak points and provides a conclusion, specifically: If the weakest component is a certain purlin, then output the conclusion that the purlin is not strong enough and suggest reinforcement measures; If the weakest component is a fixed point, the conclusion that the tensile strength of that fixed point is insufficient and a suggested reinforcement measure will be output.

[0015] The technical effects and advantages provided by the present invention in the above technical solution are as follows: The core benefit of this method lies in its successful solution to the challenge of evaluating the interaction between light steel roofs and photovoltaic systems under wind suction. By establishing a refined finite element model that considers the constraint effect of the roof panel on the purlins and quantifying roof deformation as an additional load on the fixed points, this method achieves accurate simulation of the coupled system of purlin-roof panel-photovoltaic support. This not only more realistically reveals the wind uplift failure mechanisms unique to light steel roofs, such as purlin buckling and fixed point failure, thus significantly improving the accuracy and reliability of the evaluation results, but also simplifies the complex structural analysis process through parametric modeling and explicit mathematical formulas while ensuring accuracy. This allows designers to quickly complete safety checks and scheme optimization in the early stages of a project, effectively overcoming the shortcomings of traditional simplification methods, such as crudeness and inefficiency in overall simulation. This provides crucial technical support for the safe and efficient promotion of photovoltaic systems in a wide range of light steel roof scenarios. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a schematic diagram illustrating the relationship between purlin spacing and key mechanical response in this invention; Figure 3 This is a schematic diagram showing the relationship between the purlin spacing and the normal displacement of the roof according to the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figures 1 to 3 The present invention provides a technical solution: A method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift, comprising the following steps: Step 1: Construct a finite element model of the photovoltaic structure of the light steel roof, where the fixed points of the photovoltaic structure are taken as local rigid support points, and the roof is equivalent to a constraint boundary that provides continuous lateral support to the purlins, in order to simulate the constraint effect of the roof on the stability of the purlins.

[0020] In this embodiment, constructing the finite element model of the light steel roof photovoltaic structure specifically includes: Based on the actual construction of the rooftop photovoltaic structure, a finite element model of it is established. The light steel rooftop photovoltaic structure includes, but is not limited to, the following components: Purlins: Typically C-shaped or Z-shaped cold-formed thin-walled steel components, serving as load-bearing components of the roofing system; Roof panels: Typically profiled steel sheets, covering the purlins to form the roof covering layer; Photovoltaic array: Consists of several photovoltaic modules fixed to the roof by a supporting steel frame; Anchoring points: Anchoring points used to connect the photovoltaic supporting steel frame to the purlins or roof panels.

[0021] During the modeling process, a corresponding finite element model needs to be established based on parameters such as the actual structure's geometric dimensions, material properties, and connection methods. Specifically, purlins are discretized using beam elements (such as Beam188 or similar elements), roof panels can be simulated using shell elements (such as Shell181) or an equivalent spring system, and photovoltaic support structures can be simplified to beam elements or rigid connections based on their stiffness characteristics.

[0022] The constraint boundary is achieved by setting a set of linear spring supports at the upper flange nodes of the purlins. The constraint direction of the springs is perpendicular to the purlin axis and lies within the plane of the roof panel, simulating the constraint effect of the roof panel on the lateral displacement and torsion of the purlins. A spring unit is set at the node where the upper flange of each purlin contacts the roof panel. The spring stiffness direction is along the plane of the roof panel and perpendicular to the longitudinal axis of the purlin, simulating the lateral support of the roof panel on the purlins. Linear springs are used, and their stiffness values ​​are calculated and determined using the following equivalent stiffness formula.

[0023] The equivalent stiffness of the linear spring characterizes the lateral restraint provided by the roof panel as a continuous support to a single purlin, and its determination logic is as follows: The restraining effect of the roof panel on the purlins mainly comes from its own bending stiffness. According to plate and shell theory, the roof panel can be regarded as a continuous elastic foundation, and its supporting stiffness on the purlins is closely related to the material properties, geometric dimensions, and purlin spacing of the roof panel.

[0024] Based on the inherent bending stiffness of the roof panel itself, the product of the cube of the base thickness of the roof panel and the elastic modulus of the roof panel material is used to characterize the inherent bending stiffness determined by the roof panel material and the cross-sectional thickness. A constant 1 is subtracted from the square of the Poisson's ratio of the roof panel material as a correction term for the influence of the lateral strain of the roof panel material under stress due to the Poisson effect on the equivalent stiffness. The total supporting effect of the roof panel is distributed according to the purlin spacing, so the purlin spacing is multiplied by the correction term as the denominator, and the inherent bending stiffness is used as the numerator. This ratio is used to characterize the theoretical equivalent lateral support stiffness that the roof panel can provide. By multiplying a preset stiffness correction coefficient by the theoretical equivalent lateral support stiffness, the actual equivalent stiffness provided by the roof panel to a single purlin is obtained. Expressed as a formula: in, This represents the equivalent stiffness per unit length provided by the roof panel to a single purlin, expressed in units of [unit missing]. k is a dimensionless stiffness correction coefficient related to the profiled steel sheet type; this coefficient is used to correct the theoretical stiffness based on the actual structural features of the roof panel, such as wave height, wave pitch, and connection method. This is the elastic modulus of the roof panel material, expressed in Pa. This parameter is determined by the physical properties of the roof panel material (such as galvanized steel sheet, aluminum-magnesium-manganese sheet, etc.) and can be obtained from the technical data or relevant standards provided by the material supplier. This refers to the thickness of the substrate of the roof panel, in meters (m). It is important to distinguish between substrate thickness and coating thickness; the nominal thickness of the substrate is usually the standard. This is the purlin spacing, in meters. This parameter is a design input value, usually determined based on factors such as roof load and span, and its range is generally [1m, 2.5m]. Poisson's ratio is the dimensionless ratio of the roofing panel material; it is usually taken as 0.3 for steel and 0.33 for aluminum alloy. Specific values ​​can be found in material standards or determined by testing.

[0025] The stiffness correction factor k can be determined in one of the following ways: Experimental determination method: Through on-site or laboratory loading tests, the lateral displacement of the roof panel under a unit load is measured, and its equivalent support stiffness is calculated and compared with the theoretical value. For example, a lateral load can be applied to the actual roof slab, the lateral displacement of the purlins can be measured, and the load-displacement relationship can be used to infer the displacement. And then calculate value.

[0026] Manufacturer-provided: Roofing panel manufacturers typically provide corresponding stiffness coefficients based on their product panel type, connection method, etc. For example, for common types 760 and 820 profiled steel sheets, The value may be in the range of [0.8, 1.2].

[0027] Empirical approach: In the absence of test or manufacturer data, recommended values ​​can be referenced in industry standards or design manuals. For example, for common standing seam roofing panel systems, 1.0 is acceptable; for lap-joint panels, 0.9 is acceptable.

[0028] The rationale for the stiffness correction coefficient lies in its comprehensive reflection of the difference between the actual structure of the roof panel and the ideal flat panel model, thus ensuring the accuracy of the equivalent stiffness.

[0029] In the finite element model, the fixed points of the photovoltaic structure are modeled as a set of coupled nodes rigidly connected to the upper flange nodes of the purlins. The specific implementation is as follows: Coupled Node Set: Establishes a rigid connection between each fixed point and the upper flange node of the purlin it belongs to (e.g., using the MPC184 rigid beam node or node coupling command), so that there is no relative displacement between the fixed point and the purlin.

[0030] Load transfer path: External forces such as wind loads are applied to the coupling node in the form of concentrated forces and are directly transferred to the purlins through rigid connections, simulating the mechanical behavior of loads being transferred to the purlins through supports in actual structures.

[0031] The photovoltaic structure includes at least one photovoltaic array, which is a basic power generation unit composed of multiple photovoltaic structures. During modeling, the photovoltaic array can be simplified as a uniformly distributed mass or a rigid mass block, depending on the actual situation. Its stiffness contribution can be ignored, and only its load effect is considered.

[0032] Before constructing the finite element model, the following input data needs to be preprocessed: Geometric data: including purlin span, spacing, cross-sectional dimensions, roof panel thickness, waveform, photovoltaic array dimensions, and arrangement; Material parameters, including elastic modulus, Poisson's ratio, yield strength, etc., should be ensured to be consistent with the International System of Units (SI) (e.g., Pa, m). Boundary conditions include wind load, snow load, and self-weight, among which wind load needs to be allocated according to the wind pressure zone division in subsequent steps.

[0033] The preprocessing operations include, but are not limited to: Unit conversion is crucial; finite element analysis requires that the units of all physical quantities be unified within a consistent system. In practice, original design data may come from different national standards or manufacturers, resulting in inconsistent unit systems (e.g., mixing millimeters and meters for length, and MPa and Pa for stress). Therefore, a strict unit conversion must be performed before modeling.

[0034] For example, in the design drawings, the purlin spacing is specified as 1500mm, the roof panel substrate thickness is specified as 0.8mm, the elastic modulus of the purlin material is 205GPa, and the basic wind pressure is 0.45. All physical quantities were converted to the International System of Units (SI), specifically as follows: purlin spacing of 1500mm was converted to 1.5m; roof panel substrate thickness of 0.8mm was converted to 0.0008m; and elastic modulus of 205GPa was converted to... Pa; Basic wind pressure 0.45 Converted to 450 Pa. By standardizing units, problems such as model errors, distorted calculation results, and even numerical calculation failures caused by mismatched units are avoided.

[0035] Data validity verification: The reasonableness of the input data directly affects the reliability of the model. It is necessary to verify the numerical range of key parameters and identify and remove obviously unreasonable outliers.

[0036] For example, when inputting the thickness of the roof panel substrate, the operator might mistakenly input 8mm (the reasonable range is usually between 0.4mm and 1.5mm). Comparing this parameter with the preset reasonable range will show that the value is unreasonable. The correct value can be determined by re-measuring or reviewing relevant records. Specific data preprocessing involves setting parameter reasonableness verification rules in the data input interface or preprocessing script. For example, verifying whether the roof panel thickness is within the range of [0.0004m, 0.0015m]; verifying whether the purlin spacing is within the range of [0.5m, 3m]; verifying whether the elastic modulus is within the range of […]. Pascal, Within the Pascal range. When the input value exceeds the preset range, the system automatically triggers a warning and prompts the user, "The input data exceeds the normal empirical range; please verify the accuracy of the data source." This data preprocessing step effectively prevents serious deviations in model stiffness calculations due to human input errors, improving the reliability of the analysis.

[0037] Model geometry cleanup: Geometric models imported from CAD drawings may contain quality issues that do not affect manufacturing but may affect finite element mesh generation, and need to be cleaned up. At the same time, it is necessary to ensure that the connection relationships between all components in the model are correct.

[0038] For example, exporting roof geometry from a Building Information Model (BIM) may result in minor gaps or overlaps, leading to duplicate, closely spaced nodes at the purlin-to-roof spring connections. Preprocessing operations include merging coincident nodes and checking and repairing discontinuous topology. Merging coincident nodes involves setting a tolerance (e.g., 0.001m), searching the model for all node pairs with distances less than this tolerance, and merging them into a single node. This ensures that the purlin upper flange nodes and roof spring support points are completely contiguous, thus accurately simulating their mechanical connections. Checking and repairing discontinuous topology specifically involves checking the continuity of all purlin beam elements and identifying any isolated nodes. For discontinuous segments, they are connected or re-meshed. This preprocessing avoids meshing failures, abnormal stress concentrations, or interrupted force transmission paths caused by geometric defects, ensuring the numerical stability and accuracy of the finite element calculations.

[0039] Step 2: Divide the roof into several wind pressure zones. For each photovoltaic array, determine its projected area component in each wind pressure zone based on the overlap between its projected area and each wind pressure zone. Calculate the total wind suction force of the photovoltaic array based on the standard value of wind suction force and the corresponding projected area component of each wind pressure zone. Distribute the total wind suction force evenly to all fixed points below the photovoltaic array, thereby converting the wind load into a concentrated force acting on the fixed point location in the finite element simulation model.

[0040] In this embodiment, determining the standard value of wind suction in each wind pressure zone specifically includes: Based on the roof structure, the roof is divided into three wind pressure zones: edge zone, corner zone, and central zone. This division method is directly derived from relevant building structure load codes. These codes clearly stipulate that for low-rise buildings, under wind loads, the edge and corner areas of the roof will generate significantly greater wind suction than the central zone due to airflow separation and reattachment. The edge zone is typically a strip of a certain width extending inward from the windward and lateral edges of the roof; the corner zone is the area formed by the intersection of two adjacent edge zones; and the remaining portion constitutes the central zone. The width of each zone (e.g., 10% of the minimum horizontal dimension of the roof or a specific value such as 1.5 meters) must strictly adhere to the applicable load codes. During modeling, the boundaries of these wind pressure zones need to be automatically or manually generated based on the roof's geometric contour using programming or CAD tools. Subsequently, each zone is assigned a unique index for identification and retrieval of its corresponding wind load shape coefficient in subsequent calculations.

[0041] According to the building load code, the wind load shape coefficient corresponding to each wind pressure area is obtained; the standard value of wind suction in each wind pressure area is calculated. The specific logic is as follows: determine the gust coefficient, wind pressure height variation coefficient and basic wind pressure of the location of the roof photovoltaic structure in each wind pressure area at height z; multiply the wind load shape coefficient, gust coefficient at height z, wind pressure height variation coefficient and basic wind pressure of each wind pressure area to obtain the standard value of wind suction in the corresponding wind pressure area, where z represents the average height from the outer surface of the roof to the outdoor ground level in the wind pressure area.

[0042] Expressed as a formula: in, Let be the standard value of wind suction in the i-th wind pressure region. Let z be the gust coefficient at height z. Let be the wind load shape coefficient corresponding to the i-th wind pressure region. This is the wind pressure height variation coefficient. The basic wind pressure at the location of the rooftop photovoltaic structure, in units of , where i is the index of the wind pressure region.

[0043] Basic wind pressure is a location-specific parameter, determined entirely by referring to the national basic wind pressure distribution map and accompanying tables in the building structure load code. For example, the basic wind pressure for a certain urban area with a 50-year return period can be taken as 0.55. Meanwhile, a certain coastal island might reach 0.9. When inputting data, ensure that the units are consistent with the system (e.g., ...). The corresponding return period (e.g., 50 years) should be specified, and this return period should match the project design life.

[0044] The wind pressure height variation coefficient reflects the phenomenon that wind speed increases with increasing height above the ground. Its value depends on the ground roughness category and the calculation height. The standard classifies ground roughness into categories such as A (near sea surface), B (fields, rural areas), C (urban suburbs), and D (city centers), and provides corresponding coefficient tables or calculation formulas. The height is taken as the average height of the outdoor ground level above the roof surface in the wind pressure zone. For example, for a factory building located in an urban suburb (Category C), with a ridge height of 15 meters, the wind pressure height variation coefficient, according to the standard table, is approximately 0.74.

[0045] The gust coefficient is used to account for the instantaneous fluctuations in wind speed. It relies on the same parameters as the wind pressure height variation coefficient: ground roughness category and height, and is determined by referring to the corresponding tables or formulas in the specifications.

[0046] The wind load shape coefficient is a key parameter for distinguishing different wind pressure zones. Standards specify different wind load shape coefficients for different areas of the roof (such as the central zone, edge zone, and corner zone), and these are usually negative values, representing wind suction. For example, the wind load shape coefficient for the central zone of a gable roof might be -1, while the edge zone and corner zone might reach -1.4 and -2, respectively.

[0047] In the program, a mapping relationship needs to be established to associate the index of each wind pressure zone with its corresponding wind load shape coefficient value.

[0048] In this embodiment, determining the concentrated force acting on the fixed point specifically includes: For any photovoltaic array, identify all wind pressure areas covered by its projection area; for each wind pressure area it covers, calculate the area of ​​the photovoltaic array projection within that wind pressure area, which is the projection area component of the photovoltaic array in that wind pressure area. The arrangement of photovoltaic arrays is divided into two cases, specifically including: If a photovoltaic array spans different wind pressure zones, the array is virtually divided into several sub-arrays according to the wind pressure zone of the roof below it. For each sub-array, the wind suction standard value of the sub-array is calculated using the wind load shape coefficient of its respective wind pressure zone. The product of the projected area of ​​each sub-array on the roof and its corresponding wind suction standard value is defined as the total wind suction of the sub-array. The total wind suction of all sub-arrays is summed to obtain the total wind suction of the photovoltaic array. The number of fixed points below the photovoltaic array is counted, and the total wind suction is divided by the number of fixed points to obtain the concentrated force at each fixed point.

[0049] For example, a projected area of ​​24 The rectangular photovoltaic array has half of its projection located in the central zone and the other half in the edge zone. The standard wind suction value for the central zone is -0.8. The standard value for edge-mounted air suction is -1.2. The array has 10 fixed points at the bottom. The array is virtually divided into two 12-bit subarrays. The subarray has a suction force of -9.6kN in the middle strip subarray and -14.4kN in the edge strip subarray, with a total suction force of -24kN. Therefore, the concentrated force at each fixed point is -2.4kN.

[0050] This method accurately reflects the increased total load effect caused by the array crossing different wind pressure zones (in this case, it is 50% greater than when the array is entirely in the middle zone). If the entire array were simply misjudged as being in the middle zone, the total load would be only -19.2 kN, which would severely underestimate the risk of wind uplift.

[0051] When the photovoltaic array is located entirely within the same wind pressure zone, the total wind suction force of the photovoltaic array is obtained by multiplying the standard value of the wind suction force of the wind pressure zone where the photovoltaic array is located by the projected area of ​​the photovoltaic array on the roof. Then, based on the number of fixed points below the photovoltaic array, the total wind suction force is divided by the number of fixed points to obtain the concentrated force at each fixed point.

[0052] For example, a projected area of ​​20 The photovoltaic array is entirely located in the middle zone, where the standard wind suction value is -0.8. There are 8 fixed points below it, so the total wind suction force is -16kN and the concentrated force at each fixed point is -2kN.

[0053] In this step, key data preprocessing includes: ensuring accurate division of the wind pressure zone geometry, consistent with standard definitions; establishing a standardized parameter database and correlating it with the region and height information in the model; and accurately calculating the projected area components of the photovoltaic array within each wind pressure zone through geometric calculations. This typically requires using a computational geometry library in the program. Additionally, ensuring unit consistency is crucial for direct use in finite element software.

[0054] Step 3: After applying a concentrated force to the finite element model, perform static solution to calculate its deformation response and stress response; and determine the roof normal displacement at the fixed point based on the deformation response, and determine the maximum bending normal stress of each purlin based on the stress response.

[0055] In this embodiment, calculating the deformation response and stress response specifically includes: In the finite element model, each purlin is discretized into multiple beam elements, and the connection points of these beam elements and the connection points of the roof panel springs are defined as purlin joints.

[0056] Purlins must be divided into a sufficient number of beam elements (e.g., each segment no longer than 0.5 meters) to ensure accurate capture of their bending deformation and stress distribution under wind suction, especially the peak bending moment. Overly sparse meshes will lead to inaccurate calculations.

[0057] Purlin nodes include the two end nodes (natural connection points) of the beam element and the middle node connecting to the roof panel spring element. These nodes are the main output locations of the structural response (displacement, reaction force).

[0058] The fixed point is a photovoltaic fixed point, which is bound to the nearest purlin node. This means that during modeling, the degree of freedom of the fixed point is associated with the purlin node below it through rigid connection or node coupling (e.g., using the CERIG or CP command), so that there is no relative displacement between the fixed point and the purlin node, and the load can be directly transferred.

[0059] The specific settings for statics solutions include: Analysis type: Select linear statics analysis; Boundary conditions: In addition to the roof panel spring constraints defined in step 1, the correct constraints must also be applied to the support nodes at both ends of the purlin. These are usually simulated as hinged (releasing the rotational constraints around the purlin axis) or fixed, which needs to be determined according to the actual support structure.

[0060] Load application: Apply the concentrated points calculated in step 2 to the corresponding fixed point coupling node set in the form of a force load in the negative Z direction (assuming the Z axis is vertically upward).

[0061] Solver: Use a sparse matrix direct solver (such as a Sparse Direct Solver) or an iterative solver to ensure numerical stability.

[0062] From the static solution, the displacement vector at each purlin node of the fixed point is extracted, and the component in the direction perpendicular to the normal to the initial plane of the roof is defined as the roof normal displacement at that fixed point.

[0063] After solving, iterate through all fixed points and read the displacement results of their bound purlin nodes. The roof normal is crucial for component projection. For sloping roofs, this direction is not absolutely vertical (Z-axis). Vector projection calculation is required. First, perform preprocessing to define the initial plane of the roof. This can be done by selecting three non-collinear points around the fixed points to determine a plane, or by directly using the roof design slope angle (e.g., 5%). Then, calculate the unit normal vector of this plane. Finally, project the total displacement vector of the nodes onto this normal vector to obtain the normal displacement.

[0064] For each purlin, iterate through all the beam elements it contains, extract the maximum bending normal stress of each beam element, and use the maximum value among them to determine the maximum bending normal stress of that purlin.

[0065] For each purlin beam element, finite element software typically outputs stress components at multiple integration points or nodes. The bending normal stress caused by the bending moment needs to be specifically extracted (usually labeled SBEND or AxialStress in the beam element results).

[0066] For each beam element, compare the normal stress values ​​at all output locations, and take the one with the largest absolute value as the maximum bending normal stress of that element. Record this value along with the element and location it belongs to.

[0067] The maximum bending normal stress identifies the point in all purlins where the wind suction causes the most severe bending stress on each purlin, and is a decisive indicator for assessing whether the purlin structural strength meets the requirements.

[0068] Identify the mid-span node of each purlin (usually defined during modeling) and directly read its displacement in the Z-direction of the global coordinate system from the solution results. Compare the displacements of all purlins in the Z-direction of the global coordinate system and find the one with the largest absolute value, which is recorded as the maximum mid-span deflection. Compare the maximum mid-span deflection with a preset deflection limit. The deflection limit is set according to structural design codes (such as the "Steel Structure Design Standard" GB50017). For roof purlins, the deflection limit is usually a fraction of their span. For example, for purlins that only bear roof loads, the limit can be the ratio of the span to 150; for purlins that also bear photovoltaic loads, given their greater sensitivity to deformation, the limit may be tightened to the ratio of the span to 200 or the ratio of the span to 250. The specific value depends on the design code followed by the project. If the maximum deflection at mid-span does not exceed the deflection limit, the purlin stiffness meets the requirements; otherwise, the stiffness is considered insufficient and needs to be strengthened in the design.

[0069] For example, a purlin has a span of 6m, and the standard specifies a deflection limit of 30mm. The calculated maximum deflection at mid-span is 25mm. Since 25mm < 30mm, the purlin stiffness meets the standard requirements.

[0070] Step 4: Determine the strength safety factor for each purlin based on its design yield strength and maximum bending normal stress; analyze the roof normal displacement at each fixed point to determine the additional bending moment generated at each fixed point; combine the additional bending moment with the concentrated force caused by wind suction to obtain the total load at each fixed point; compare the design pull-out bearing capacity at the fixed point with the total load to determine the strength safety factor at each fixed point.

[0071] In this embodiment, determining the additional bending moment specifically includes: The strength safety of a purlin is characterized by its strength safety factor, which is the ratio of the purlin's design yield strength to its maximum bending normal stress. Expressed as a formula: in, The strength safety factor for the purlin, This is the design yield strength of the purlin material, expressed in MPa. This value is determined by structural design specifications based on the purlin steel grade. This represents the maximum bending normal stress of all purlins, expressed in MPa.

[0072] The design value of the yield strength of purlin material is not the actual measured yield strength of the material, but rather a reduced design value based on structural design specifications (such as the "Technical Specification for Cold-Formed Thin-Walled Steel Structures" GB 50018). Its value primarily depends on the grade of the purlin steel (e.g., Q235 steel, Q355 steel). Taking Q355 steel as an example, its standard yield strength is 355 MPa, but according to the specification, considering factors such as material partial factors and thickness effects, its bending strength design value may be 305 MPa. Designers must determine the accurate bending strength design value by consulting tables or calculations based on the specific steel grade used and the relevant specification clauses.

[0073] The maximum bending normal stress parameter of all purlins is derived from the static solution in step 3. It is necessary to ensure that its unit is consistent with the design value of bending strength, which is usually MPa.

[0074] like This indicates that the maximum stress of the purlin did not exceed its design strength, and the strength meets the requirements; if This indicates that the purlin has exceeded its elastic working state, is at risk of yielding, and is insufficient in strength. It's not just a Boolean judgment; its numerical value directly reflects the degree of purlin strength reserve. For example, This means that the purlin strength has a margin of 80%.

[0075] The specific logic for calculating the additional bending moment generated by the normal displacement of the roof at each fixed point is as follows: For each fixed point, the product of the elastic modulus of the photovoltaic support steel frame material and the moment of inertia of the cross section of the photovoltaic support steel frame about its bending neutral axis is defined as the cross section bending stiffness of the photovoltaic support steel frame. This cross section bending stiffness characterizes the ability of the photovoltaic support steel frame to resist bending deformation. The preset constant coefficients are multiplied by the section bending stiffness and the roof normal displacement at the corresponding fixed point, and the product is used to characterize the generalized force that generates forced deformation. The extreme sensitivity of the support frame length to the additional bending moment is characterized by the cube of the length of the free segment of the photovoltaic support steel frame extending out of the roof. Using the generalized force as the numerator and the cube of the free segment length as the denominator, this ratio represents the additional bending moment generated by the normal displacement of the roof at the fixed point.

[0076] Expressed as a formula: in, This represents the additional bending moment generated at the root of the photovoltaic support steel frame due to the normal displacement of the roof at the j-th fixed point, in units of... ; This refers to the elastic modulus of the photovoltaic support steel frame material, expressed in Pa. The moment of inertia of the cross-section of the photovoltaic support steel frame about its bending neutral axis is expressed in units of 1000 m / s. ; The normal displacement of the roof at the j-th fixed point is expressed in meters (m). This refers to the length of the free section of the photovoltaic support steel frame extending out of the roof, expressed in meters (m).

[0077] The modulus of elasticity of the photovoltaic support steel frame material is determined by the material of the support frame. It is typically carbon steel (…). ) or aluminum alloy ( This value should be obtained from the support frame manufacturer's technical documentation.

[0078] The moment of inertia of the photovoltaic support steel frame cross-section about its bending neutral axis is a geometric parameter that depends on the cross-sectional shape and dimensions of the support steel frame. For example, the moment of inertia of a C-shaped steel section: if the support frame is a C80×40×2 C-shaped steel, the moment of inertia about its strong axis (80mm direction) can be calculated using formulas from mechanics of materials or found in a steel profile table, and is approximately... The free section length of the photovoltaic support steel frame extending above the roof is a design input value, referring to the vertical height from the roof surface to the photovoltaic module mounting surface. This parameter is extremely sensitive to additional bending moments and must be accurately measured or determined according to the design scheme. Furthermore, the free section length should be minimized as much as possible during the design phase to significantly reduce additional bending moments.

[0079] In this embodiment, to verify the effectiveness of the static strength estimation method for wind uplift resistance of the light steel roof photovoltaic structure and to quantify the impact of key design parameters, 33 sets of data on maximum bending normal stress, roof normal displacement, and additional bending moment under different purlin spacings were collected, and the changes in these three sets of data were observed. During the data collection, the specific values ​​of the fixed parameters were as follows: roof panel thickness was 0.8 mm, and the roof panel elastic modulus was... Poisson's ratio is 0.3, stiffness correction factor is 1, free section length of support frame is 0.3m, and moment of inertia of support frame section is... The elastic modulus of the support frame is The specific data is shown in the table below: Table 1: Schematic diagram of purlin spacing and key mechanical response data Based on Table 1 above, Figure 2 and Figure 3 , Figure 2The left vertical axis corresponds to the maximum bending normal stress of the purlin, which is the result of the static solution in step 3, directly reflecting the stress level of the purlin as the main load-bearing component. The right vertical axis corresponds to the additional bending moment, characterizing the secondary bending moment effect generated at the root of the photovoltaic support steel frame due to the roof normal displacement. The two monotonically increasing curves in the figure clearly show that as the purlin spacing increases (and the roof normal displacement also increases), both the maximum bending normal stress of the purlin and the additional bending moment at the fixed point increase significantly.

[0080] This further verifies the technical problem this invention aims to solve: the interaction mechanism between the light steel roof and the photovoltaic system under wind suction. Specifically, the increased purlin spacing leads to a decrease in the lateral constraint stiffness of the roof panel on the purlins (this can also be verified by the equivalent stiffness formula in step 1 of the specification). The direct consequence is that the bending stress of the purlins under wind load intensifies (left longitudinal axis response). More importantly, the overall deformation (normal displacement) of the roof system is amplified accordingly, and through the leverage effect of the photovoltaic support steel frame (its sensitivity is determined by the cube of the free segment length), it ultimately acts violently on the fixed point in the form of an additional bending moment (right longitudinal axis response). This indicates that the failure risk of the fixed point is not solely caused by direct wind suction, but is dominated by the combined load of wind suction and roof deformation. Therefore, the evaluation method of this invention, by simultaneously considering purlin stress and the additional bending moment at the fixed point, achieves accurate simulation of the coupled system of purlin-roof panel-photovoltaic support, overcoming the evaluation bias caused by neglecting the interaction between the systems in traditional methods, and providing a more reliable guarantee for structural safety.

[0081] And through observation, it can be found that Figure 2 The difference in the shape of the two curves corresponding to the two key mechanical parameters (i.e., maximum bending normal stress and additional bending moment) profoundly reflects the different sensitivities of the two physical phenomena of purlin stress and roof deformation to the increase of purlin spacing.

[0082] In this embodiment, the wind load acting on the purlin has been simplified to a concentrated force acting at a fixed point. For a single purlin, when its span, cross-section, and load distribution pattern are fixed, its maximum bending moment is proportional to the load. Increasing the purlin spacing leads to an increase in the roof projection area shared by each purlin, meaning the total wind load it bears is approximately proportional to the purlin spacing. Therefore, the maximum bending normal stress of the purlin exhibits a quasi-linear response, i.e., a linear growth relationship. This also reflects the mechanical behavior of the purlin as an independent bending member.

[0083] And the bending moment of the attachment The generation of this is a two-stage coupling process. Its calculation follows... The normal displacement of the roof This is crucial. The roof's normal displacement is not linearly related to the purlin spacing. As described in step 1, the roof panel is considered equivalent to an elastic foundation providing continuous support to the purlins, and its equivalent stiffness is proportional to the reciprocal of the purlin spacing. This means that as the purlin spacing increases, the overall support stiffness of the roof panel decreases hyperbolically. A roof system with rapidly decreasing stiffness, when subjected to a nearly linearly increasing load, will have its roof's normal displacement approximately proportional to the square of the purlin spacing (e.g., ...). Figure 3 (As shown). Substituting this relationship into the additional bending moment formula, we get... This indicates that its growth rate itself is accelerating, therefore in Figure 2 It is represented by a concave upward curve (characteristic of a quadratic curve).

[0084] In this embodiment, the specific calculation logic for the total load is as follows: The product of the preset load effect combination coefficient and the concentrated force at the fixed point is used as the first load coefficient, and the product of the distance from the fixed point to the inflection point of the photovoltaic support steel frame and the additional bending moment at the fixed point is used as the second load coefficient. The square root of the sum of the squares of the first load coefficient and the second load coefficient is the total load at the fixed point.

[0085] This calculation logic originates from mechanical principles, combining the axial pull-out force and bending moment at the fixed point into an equivalent generalized load. The load effect combination coefficient is a preset value, determined according to the adopted structural design code. For example, in the "Code for Design of Building Structures" GB 50009, for wind-dominated load cases, this coefficient is usually taken as 1.4 or 1.5. Its purpose is to consider possible overload and uncertainty of the load, and it is an important component of structural reliability design. The distance from the fixed point to the inflection point of the photovoltaic support steel frame is a simplification. For typical cantilever support frames, the location of the inflection point is difficult to determine precisely. In engineering practice, a conservative estimate is usually made, taking the length of the free section of the photovoltaic support steel frame extending beyond the roof as equal to the distance from the fixed point to the inflection point of the photovoltaic support steel frame, i.e., assuming the inflection point is at the root of the support. This approach is on the safe side, so the actual inflection point may be higher, making the distance from the fixed point to the inflection point of the photovoltaic support steel frame less than the length of the free section of the photovoltaic support steel frame extending beyond the roof, thus resulting in a larger calculated total load.

[0086] The strength safety of a fixed point is characterized by its strength safety factor, which is defined as the ratio of the design pull-out bearing capacity of the fixed point to the total load. The design pull-out bearing capacity is the core parameter and must be determined using one of the following two methods, taking the smaller value: The first type: technical data provided by the fastener manufacturer; manufacturers typically provide the design pull-out bearing capacity of a single fastener in different substrates (such as profiled steel sheets, concrete) based on tests. This is the most direct and commonly used basis.

[0087] The second factor is the roof system's load-bearing capacity; failure at the anchor point could also be due to the roof panel itself being torn. Therefore, the design pull-out load-bearing capacity must not exceed the design tear resistance of the roof panel at the anchor point, and this value should be provided by the roof panel system supplier.

[0088] For example, a certain brand of self-tapping screws has a design pull-out strength of 3.5kN for 0.8mm thick profiled sheet, while the roof panel system supplier provides a tear resistance of 4kN. Therefore, the design pull-out strength should be 3.5kN.

[0089] Step 5: Determine the minimum strength safety factor among all purlins and fixing points as the static strength margin of the roof photovoltaic structure; compare it with the preset minimum safety threshold to assess whether the light steel roof photovoltaic structure is safe.

[0090] In this embodiment, assessing the safety of the light steel roof photovoltaic structure specifically includes: The strength safety factors of all purlins and all fixed points are collected into the same set for comparison. All strength safety factor values ​​in the set are traversed, and the strength safety factor with the smallest value is taken as the static strength margin of the roof photovoltaic structure.

[0091] First, data is collected by creating a dataset containing all purlin strength safety factors and all fixed-point strength safety factors calculated in step 4. Second, the minimum value is found by iterating through the dataset.

[0092] According to the "barrel theory," the overall safety level of a structural system is determined by its weakest link. The minimum value found here is the static strength margin of the system, which quantifies the overall safety reserve of the entire rooftop photovoltaic structure under wind suction. The component corresponding to the static strength margin is identified as the weakest component. This component could be any purlin or any fixed point. In the program implementation, while searching for the static strength margin (i.e., the minimum value), it is necessary to record the component type, unique identifier (such as purlin number or fixed point number), and its position coordinates within the structure corresponding to this safety factor.

[0093] The preset minimum security threshold is not less than 1.

[0094] The theoretical lower limit of the minimum safety threshold is, theoretically, the point at which the safety factor equals 1, represents the critical point between safety and failure. At this point, the load effect is exactly equal to the design resistance of the component.

[0095] In engineering practice, considering factors such as the uncertainty of calculation models, the dispersion of material properties, and construction errors, the minimum safety threshold usually needs to be set to an allowable value greater than 1. The specific value must be determined comprehensively based on the structural design codes, safety requirements, and engineering experience followed by the project. For example, for general industrial and civil buildings, the minimum safety threshold is usually 1 or 1.2. For important or high-risk projects, such as important buildings or areas with high wind disaster risk, the minimum safety threshold may be increased to 1.3 or 1.4 to provide a higher safety margin. Some codes may indirectly specify this value, for example, requiring that the effect under a load combination not exceed 1 / 1.1 of the resistance design value, which is equivalent to a minimum safety threshold of 1.1.

[0096] The specific logic of the assessment is as follows: if the static strength margin is not less than the minimum safety threshold, the assessment conclusion is safe. This indicates that even the weakest component has a safety reserve that meets or exceeds the preset minimum requirements, and the entire structural system is considered reliable. If the static strength margin is less than the minimum safety threshold, the assessment conclusion is unsafe. This indicates that there is at least one weak link in the structure with insufficient safety reserve, posing a risk of failure under design wind loads, and requiring reinforcement.

[0097] When the assessment concludes that the system is unsafe, it automatically locates weaknesses and provides a conclusion. For example, automatic system insecurity diagnosis and recommendations: An evaluation was conducted on the photovoltaic subsystem on the light steel roof of a logistics warehouse. The preset minimum safety threshold was 1.1. The system iterates through the safety factors of all components and determines the static strength margin to be 0.92. Since 0.92 < 1.1, the system determines that the structure is unsafe. The system retrieves the construction information associated with the static strength margin and finds that it corresponds to purlin numbered B-5.

[0098] Automatic output conclusion: The assessment conclusion is unsafe, and the weakest link is purlin numbered B-5. The strength safety factor of this purlin is 0.92, which is lower than the minimum safety threshold of 1.1. Under the design wind load, the maximum bending stress of this purlin has exceeded its material yield strength design value, posing a risk of plastic deformation or even failure.

[0099] Recommended reinforcement measures: Increase the purlin cross-section; it is suggested to replace the original C160×60×20×2 purlins with a larger or thicker model, such as C200×70×20×2.5. The new interface has a larger section modulus, which can effectively reduce bending stress. Alternatively, reduce the purlin spacing: add two purlins of the same specification at 0.75 meters on each side of purlin B-5 (assuming the original spacing is 1.5 meters). This will distribute the load originally acting on purlin B-5, reducing the load it bears by approximately 50%.

[0100] Scenario 1: If the weakest component is a purlin, the output conclusion is: the structure is unsafe. The weakest link is the purlin numbered [e.g., B-5], whose strength safety factor is insufficient, and the recommended reinforcement measures include increasing the purlin cross-section or decreasing the purlin spacing. If the weakest component is a fixed point, the conclusion that the fixed point has insufficient pull-out bearing capacity is output, along with recommended reinforcement measures, including increasing the number of fixed points or using higher-specification fasteners.

[0101] For example, automatic diagnosis and suggestions for unsafe fixed points: An evaluation was conducted on a photovoltaic array on the roof of an industrial plant. The preset minimum safety threshold was 1.05. After calculation, the system determined the static strength margin to be 0.85. Since 0.85 < 1.05, the system determined the structure to be unsafe. The system retrieved component information associated with the static strength margin and found that it corresponded to a fixed point A-7 located at coordinates (X=12.5m, Y=45.2m).

[0102] Automatic output conclusion: The assessment conclusion is unsafe. The weakest link is located at fixed point A-7 at coordinates (X=12.5m, Y=45.2m). The pull-out safety factor of this fixed point is 0.85, which is lower than the minimum safety threshold of 1.05. The total load at this point (including direct wind suction and additional bending moment effects) has exceeded its design pull-out bearing capacity, and there is a risk of it being pulled out.

[0103] Reinforcement measures include: increasing the number of fixing points; adding one fixing point of the same specification on each side of the photovoltaic support steel frame main beam to which point A-7 belongs, within a range of 0.5 meters. By adding two fixing points to share the load, the stress on point A-7 can be significantly reduced. Alternatively, higher-specification fasteners can be used; replacing the self-tapping screws with a design pull-out bearing capacity of 3.5kN currently used at point A-7 with high-strength self-tapping screws or through-bolts with a design pull-out bearing capacity of 5kN.

[0104] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0105] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0106] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0107] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for estimating the static strength of wind uplift resistance of a light steel roof photovoltaic structure, characterized in that, The specific steps include: Step 1: Construct a finite element model of the photovoltaic structure of the light steel roof, where the fixed points of the photovoltaic structure are taken as local rigid support points, and the roof is equivalent to a constraint boundary that provides continuous lateral support to the purlins, so as to simulate the constraint effect of the roof on the stability of the purlins; Step 2: Divide the roof into several wind pressure zones. For each photovoltaic array, determine its projected area component in each wind pressure zone based on the overlap between its projected area and each wind pressure zone. Calculate the total wind suction force of the photovoltaic array based on the standard value of wind suction force and the corresponding projected area component of each wind pressure zone. Distribute this total wind suction force evenly to all fixed points below the photovoltaic array, thereby converting the wind load into a concentrated force acting on the fixed points in the finite element simulation model. Step 3: After applying a concentrated force to the finite element model, perform static solution to calculate its deformation response and stress response; and determine the roof normal displacement at the fixed point based on the deformation response, and determine the maximum bending normal stress of each purlin based on the stress response; Step 4: Determine the strength safety factor for each purlin based on its design yield strength and maximum bending normal stress; analyze the roof normal displacement at each fixed point to determine the additional bending moment generated at each fixed point; combine the additional bending moment with the concentrated force caused by wind suction to obtain the total load at each fixed point; compare the design tensile bearing capacity at the fixed point with the total load to determine the strength safety factor at each fixed point. Step 5: Determine the minimum strength safety factor among all purlins and fixing points as the static strength margin of the roof photovoltaic structure; compare it with the preset minimum safety threshold to assess whether the light steel roof photovoltaic structure is safe.

2. The method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift according to claim 1, characterized in that, The finite element model of the aforementioned light steel roof photovoltaic structure specifically includes: Based on the actual construction of the roof photovoltaic structure, its finite element model is established; the constraint boundary is achieved by setting a set of linear spring supports at the upper flange node of the purlin in the finite element model. The constraint direction of the spring is perpendicular to the purlin axis and located in the plane of the roof panel, in order to simulate the constraint effect of the roof panel on the lateral displacement and torsion of the purlin. The equivalent stiffness of the linear spring characterizes the lateral restraint provided by the roof panel as a continuous support to a single purlin. Its determination logic is as follows: Based on the bending stiffness of the roof panel itself, the inherent bending stiffness, jointly determined by the roof panel material and its cross-sectional thickness, is represented by the product of the cube of the roof panel's substrate thickness and the elastic modulus of the roof panel material. A constant 1 is subtracted from the square of the roof panel material's Poisson's ratio to correct the effect of lateral strain caused by the Poisson effect on the equivalent stiffness. The total supporting effect of the roof panel is distributed according to the purlin spacing; therefore, the purlin spacing is multiplied by the correction term as the denominator, and the inherent bending stiffness as the numerator. This ratio characterizes the theoretical equivalent lateral support stiffness provided by the roof panel. Finally, a preset stiffness correction coefficient is multiplied by the theoretical equivalent lateral support stiffness to obtain the actual equivalent stiffness provided by the roof panel to a single purlin. In the finite element model, the fixed points of the photovoltaic structure are modeled as a set of coupled nodes that are rigidly connected to the upper flange nodes of the purlin; the concentrated force acts on this set of coupled nodes, thereby directly transferring the load of the photovoltaic structure to the purlin; The photovoltaic structure includes at least one photovoltaic array, which is a basic power generation unit composed of multiple photovoltaic structures.

3. The method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift according to claim 2, characterized in that, Determining the standard values ​​of wind suction for each wind pressure zone specifically includes: Based on the roof structure, the roof is divided into three wind pressure zones: edge zone, corner zone, and middle zone. According to the building load code, the wind load shape coefficient corresponding to each wind pressure zone is obtained. The standard value of wind suction for each wind pressure zone is calculated. The specific logic is as follows: determine the gust coefficient, wind pressure height variation coefficient, and basic wind pressure of the location of the photovoltaic structure on the roof for each wind pressure zone; multiply the wind load shape coefficient, gust coefficient, wind pressure height variation coefficient, and basic wind pressure for each wind pressure zone to obtain the standard value of wind suction for the corresponding wind pressure zone, where z represents the average height from the outer surface of the roof to the outdoor ground level in the wind pressure zone.

4. The method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift according to claim 3, characterized in that, The concentrated force acting on the fixed point specifically includes: For any photovoltaic array, identify all wind pressure areas covered by its projection area; for each wind pressure area it covers, calculate the area of ​​the photovoltaic array projection within that wind pressure area, which is the projection area component of the photovoltaic array in that wind pressure area. The arrangement of photovoltaic arrays is divided into two cases, specifically including: If a photovoltaic array spans different wind pressure zones, the array is virtually divided into several sub-arrays according to the wind pressure zone of the roof below it. For each sub-array, the standard value of wind suction is calculated using the wind load shape coefficient of its respective wind pressure zone. The product of the projected area of ​​each sub-array on the roof and its corresponding standard value of wind suction is defined as the total wind suction of the sub-array. The total wind suction of all sub-arrays is summed to obtain the total wind suction of the photovoltaic array. The number of fixed points below the photovoltaic array is counted, and the total wind suction is divided by the number of fixed points to obtain the concentrated force at each fixed point. When the photovoltaic array is located entirely within the same wind pressure zone, the total wind suction force of the photovoltaic array is obtained by multiplying the standard value of the wind suction force of the wind pressure zone where the photovoltaic array is located by the projected area of ​​the photovoltaic array on the roof. Then, based on the number of fixed points below the photovoltaic array, the total wind suction force is divided by the number of fixed points to obtain the concentrated force at each fixed point.

5. The method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift according to claim 1, characterized in that, The calculation of the deformation response and stress response specifically includes: In the finite element model, each purlin is discretized into multiple beam elements, and the connection points of these beam elements and the connection points of the roof panel springs are defined as purlin nodes; the fixing points are photovoltaic fixing points, and the photovoltaic fixing points are bound to the nearest purlin node to which they are located; From the static solution, the displacement vector at the purlin node of each fixed point is extracted, and the component in the direction perpendicular to the normal direction of the initial plane of the roof is defined as the roof normal displacement at that fixed point. After solving the statics problem, for each purlin, we traverse all the beam elements it contains, extract the maximum bending normal stress of each beam element, and determine the maximum bending normal stress of the purlin by taking the maximum value among them. While extracting the maximum bending normal stress, the vertical deflection of each purlin node at the mid-span position under wind suction is also extracted. The maximum value of the vertical deflection at the mid-span position of all purlins is determined as the maximum mid-span deflection, so as to verify whether the stiffness of the purlin meets the preset deflection limit based on the maximum mid-span deflection.

6. The method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift according to claim 3, characterized in that, Determining the additional bending moment specifically includes: The strength safety is characterized by a strength safety factor; The strength safety of a purlin is characterized by its strength safety factor, which is the ratio of the design yield strength to the maximum bending normal stress. The specific logic for calculating the additional bending moment generated by the normal displacement of the roof at each fixed point is as follows: For each fixed point, the product of the elastic modulus of the photovoltaic support steel frame material and the moment of inertia of the cross section of the photovoltaic support steel frame about its bending neutral axis is defined as the cross section bending stiffness of the photovoltaic support steel frame. This cross section bending stiffness characterizes the ability of the photovoltaic support steel frame to resist bending deformation. The preset constant coefficients are multiplied by the section bending stiffness and the roof normal displacement at the corresponding fixed point, and the product is used to characterize the generalized force that generates forced deformation. The extreme sensitivity of the support frame length to the additional bending moment is characterized by the cube of the length of the free segment of the photovoltaic support steel frame extending out of the roof. Using the generalized force as the numerator and the cube of the free segment length as the denominator, this ratio represents the additional bending moment generated by the normal displacement of the roof at the fixed point.

7. The method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift according to claim 6, characterized in that, The specific calculation logic for the total load is as follows: The product of the preset load effect combination coefficient and the concentrated force at the fixed point is used as the first load coefficient, and the product of the distance from the fixed point to the inflection point of the photovoltaic support steel frame and the additional bending moment at the fixed point is used as the second load coefficient. The square root of the sum of the squares of the first and second load factors is the total load at that fixed point. The strength safety of a fixed point is characterized by its strength safety factor, which is defined as the ratio of the design pull-out bearing capacity of the fixed point to the total load.

8. The method for estimating the static strength of a light steel roof photovoltaic structure against wind uplift according to claim 1, characterized in that, The assessment of the safety of the aforementioned light steel roof photovoltaic structure specifically includes: The preset minimum security threshold is not less than 1; The strength safety factors of all purlins and all fixed points are collected into the same set for comparison. All strength safety factor values ​​in the set are traversed, and the strength safety factor with the smallest value is taken as the static strength margin of the roof photovoltaic structure. The component corresponding to the static strength margin is determined as the weakest component. The component is a specific purlin or a specific fixed point. The specific logic of the assessment is as follows: if the static strength margin is not less than the minimum safety threshold, the assessment conclusion is safe; if the static strength margin is less than the minimum safety threshold, the assessment conclusion is unsafe. When the assessment concludes that the system is unsafe, it automatically identifies the weak points and provides a conclusion, specifically: If the weakest component is a certain purlin, then output the conclusion that the purlin is not strong enough and suggest reinforcement measures; If the weakest component is a fixed point, the conclusion that the tensile strength of that fixed point is insufficient and a suggested reinforcement measure will be output.

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