Laminated beam hanging basket structure stress checking calculation method based on multi-working-condition load combination

Abstract

The invention discloses a superposed beam hanging basket structure stress checking calculation method based on multi-working-condition load combination, and belongs to the technical field of bridge construction safety monitoring. According to the method, a beam element finite element model based on the actual geometric dimension and the connection relation is established, and the boundary conditions of hinge constraint or spring unit constraint and lateral displacement limitation are set; load parameters including dead load, live load and wind load are defined, a multi-working-condition load combination is set according to building structure load specifications, and the structural safety is judged by comparing strength and deflection after calculation. The method is mainly used for solving the problem of inaccurate stress evaluation caused by single load working condition and simplified boundary condition in the traditional hanging basket checking calculation, and provides more reliable safety guarantee for the construction of the hanging basket of the composite beam bridge.

Description

Technical Field

[0001] This invention relates to the field of bridge construction safety monitoring technology. More specifically, this invention relates to a method for stress verification of composite beam hanging basket structures based on multi-condition load combinations. Background Technology

[0002] The composite beam formwork is a temporary load-bearing frame structure used for painting and welding operations at the bottom of composite beam bridges. Its main body consists of vertical, horizontal, and longitudinal members. The top of the vertical members has a top horizontal bar for overlapping with the composite beam. The components are mostly made of steel materials such as #8 channel steel and equal-sided angle steel, and are fixed to the composite beam using clamps or overlapping methods to form a construction operation platform. As a temporary load-bearing structure, the safety of the composite beam formwork directly affects the success or failure of the overall project and the safety of personnel. Currently, stress verification of composite beam formwork typically uses simplified calculation methods or basic finite element analysis. These methods have some shortcomings. First, in load considerations, they often focus on dead loads and construction live loads, while wind loads, especially transverse wind loads that significantly affect structural stability, are often ignored or simplified, failing to fully reflect the stress state of the structure in actual complex environments. Secondly, in boundary condition simulation, the complex clamp connection between the formwork and the main beam is often simply assumed to be an ideal hinged or rigid connection. This simplification fails to accurately reflect the semi-rigid characteristics and potential slight slippage of the connection node under actual stress, leading to deviations between the calculated results and the actual stress. Furthermore, conventional verification methods often employ static analysis, making it difficult to simulate the dynamic load effects caused by the movement of construction personnel and equipment. These factors collectively mean that existing verification methods may fail to promptly identify structural safety hazards under certain unfavorable working conditions, thus introducing potential risks. Therefore, there is an urgent need in this field for a stress verification method that can more accurately and comprehensively reflect the actual working state of the formwork structure. Summary of the Invention

[0003] This invention provides a stress verification method for composite beam hanging basket structures based on multi-condition load combinations. By integrating multiple types of loads, refined boundary simulation, and multi-condition combination analysis, it achieves a more comprehensive and accurate assessment of the safety of composite beam hanging basket structures.

[0004] To achieve these objectives and other advantages according to the present invention, a stress calculation method for a composite beam hanging basket structure based on multi-load combination is provided. The composite beam hanging basket structure includes a hanging basket body composed of vertical rods, horizontal rods, and longitudinal rods, and a top horizontal rod disposed at the top of the vertical rods for overlapping with the composite beam. The method includes the following steps: A finite element model of the composite beam hanging basket structure is established. The finite element model uses beam elements to simulate the vertical bars, horizontal bars and longitudinal bars. Each beam element is constructed based on the actual geometric dimensions and connection relationships of the composite beam hanging basket structure. Boundary conditions are set in the finite element model. The boundary conditions include using hinge constraints or spring element constraints at the overlap of the top horizontal bar and the composite beam, and setting lateral displacement restrictions at the contact position of the top horizontal bar and the composite beam. Define load parameters, which include dead load, live load and wind load. The dead load is the self-weight of the composite beam hanging basket structure multiplied by an amplification factor based on the weight of the unmodeled components. The live load is the load of construction personnel and equipment. The wind load is calculated based on the basic wind pressure, the wind pressure height variation coefficient, the wind load shape coefficient and the wind vibration coefficient. A multi-load combination is set, which includes a strength verification load case and a stiffness verification load case. The load combination of the strength verification load case is determined according to the combination rules of permanent load and variable load in the building structure load code, and the design values ​​of dead load, live load and wind load are taken into account at the same time. The load combination of the stiffness verification load case adopts the standard values ​​of dead load and live load. The finite element model was used to calculate the strength verification condition and the stiffness verification condition respectively, and the maximum combined stress and maximum deflection of the composite beam hanging basket structure were obtained. The maximum combined stress is compared with the design value of the bending strength of the steel actually used in the composite beam hanging basket structure, and the maximum deflection is compared with the allowable deflection value determined based on the structural calculation span and the preset deflection control standard. If the maximum combined stress ≤ the design value of bending strength and the maximum deflection ≤ the allowable deflection value, then the stress verification of the composite beam hanging basket structure is deemed to have passed.

[0005] Preferably, the application of the wind load needs to consider two directions: the first direction is along the length of the composite beam, and the standard value of the wind load is calculated according to the formula. W k = β z × m z × m s × W 0. Calculation; the second direction is perpendicular to the length of the composite beam, and the standard value of wind load is based on the standard value of wind load along the bridge direction. W k Determined by multiplying by an amplification factor; where β z For wind vibration coefficient, m z This is the coefficient of wind pressure height variation. m s This is the wind load shape coefficient. W 0 represents the basic wind pressure value, with an amplification factor ranging from 1.1 to 1.3. For strength verification, the maximum combined stress after combining the two wind load directions with the dead load and live load should be calculated separately, and the larger of the two values ​​should be taken as the final maximum combined stress for judgment.

[0006] Preferably, when setting boundary conditions in the finite element model, the constraint at the overlap between the top horizontal bar and the composite beam is simulated using spring elements; The axial stiffness, shear stiffness, and bending stiffness of the spring unit are determined based on the bolt preload of the clamping device connected thereto and the coefficient of friction of the contact surface.

[0007] Preferably, the bolt preload of the clamp is applied by a torque wrench and its value is determined by a calibrated torque-preload relationship curve.

[0008] Preferably, the shear stiffness of the spring unit is... K s Through formula K s = ( n × m × F p ) / d The calculation determines that, n The number of contact surfaces between the clamp and the composite beam. m The coefficient of sliding friction between the channel steel and the concrete surface is 0.4-0.5. F p The preload force of a single bolt is determined based on the torque-preload relationship curve. d This is a preset allowable small amount of interface slippage, ranging from 0.8 to 1.2 mm.

[0009] Preferably, it also includes strength verification of lateral displacement limitation: Based on the lateral force borne by the spring unit under the strength verification condition, calculate the maximum compressive stress of the limiting block that simulates lateral displacement restriction; The maximum compressive stress is compared with the design value of the compressive strength of the steel actually used in the composite beam hanging basket structure. If the maximum compressive stress exceeds the design value of the compressive strength, the equivalent contact area of ​​the limiting block is increased, and the shear stiffness and maximum compressive stress of the spring unit are recalculated until the strength requirements are met.

[0010] Preferably, when defining the live load, at least one dynamic load case is included; This dynamic load case is simulated by transforming the loads of construction personnel and equipment into a concentrated mass block moving along the critical path of the hanging basket structure, and transient dynamic analysis is performed to obtain the maximum combined stress and maximum deflection under this condition.

[0011] Preferably, the critical path is the longitudinal centerline of the hanging basket structure, and the movement range of the concentrated mass block starts from the connection between the vertical bar and the top horizontal bar and ends at the cantilever end of the longitudinal bar.

[0012] Preferably, after determining that the stress calculation of the composite beam hanging basket structure has passed, the following steps are also included: After the composite beam hanging basket structure is installed on site, stress sensors are placed on its key members, and the measured stress values ​​of the key members are measured when a known static load test load is applied. The measured stress value is compared with the calculated stress value calculated by the finite element model under the same test load. When the deviation between the two exceeds a preset threshold of 5-15%, the boundary conditions or material parameters of the finite element model are adjusted in reverse until the calculation result matches the measured data. The boundary conditions of the finite element model are adjusted in reverse, specifically by adjusting the shear stiffness value of the spring element simulating the overlap between the top horizontal bar and the composite beam with a preset step size of 5%.

[0013] Preferably, after model calibration, the following steps are also included: In the validated finite element model, the system adjusts the design values ​​of live load and wind load to generate parameter combinations covering different load levels. Finite element calculations are performed on each load combination to extract the Mises stress and the overall maximum deflection of all components in the entire hanging basket structure. From the calculation results, the component whose Mises stress first exceeds the material strength design value is selected, marked as the most unfavorable stress component, and its stress peak value is recorded. At the same time, the corresponding maximum deflection value is also recorded. The generated combination of multiple load parameters is used as the input feature vector, and the peak value of the Mises stress of the corresponding most unfavorable stress member and the maximum deflection of the structure are used as the output targets. The supervised learning training dataset is constructed together, a multilayer perceptron neural network is constructed and trained, and the error between the predicted stress and predicted deflection output by the network and the true value is reduced to a preset accuracy threshold through iterative optimization, so as to obtain a fast prediction model for the safety performance of the hanging basket structure. During the subsequent construction of the composite beam hanging basket structure, the live load and wind load values ​​obtained from real-time on-site monitoring or evaluation will be input into the rapid prediction model for the safety performance of the hanging basket structure, and the predicted most unfavorable stress value and predicted maximum deflection value under the current load conditions will be output.

[0014] The present invention has at least the following beneficial effects: First, this invention systematically and comprehensively verifies the stress and stiffness of the composite beam hanging basket structure. The finite element model is constructed based on the actual geometric dimensions and connection relationships, and the boundary conditions are set to fit the actual connection characteristics. The load parameters are clearly defined and cover the main stress types. The load combination follows the specifications, ensuring the scientific and rational nature of the verification process. The maximum combined stress and maximum deflection obtained through calculation can accurately reflect the actual stress state and deformation capacity of the hanging basket structure. Based on the judgment results of the steel bending strength design value and allowable deflection value, it can reliably determine whether the hanging basket structure meets the construction safety requirements, effectively avoiding construction safety accidents caused by insufficient structural strength or excessive deformation.

[0015] Secondly, by distinguishing between wind load application methods along the length of the composite beam and those perpendicular to the length of the composite beam, this invention specifically considers the characteristics of the transverse bridge hanging basket structure having a larger wind-receiving area and more significant vibration response. By reasonably increasing the standard value of the transverse bridge wind load through a factor, the simulation of wind load is made more consistent with actual engineering scenarios. At the same time, by taking the maximum combined stress after the combination of the two directions as the judgment criterion, it comprehensively covers the most unfavorable stress state that wind load may cause, further improving the safety and accuracy of the verification results.

[0016] Third, by introducing dynamic load conditions, this invention transforms the loads of construction personnel and equipment into moving concentrated mass blocks and performs transient dynamic analysis, which makes up for the shortcomings of traditional static load simulation in capturing dynamic effects. It can accurately reflect the instantaneous stress peak and deflection changes of the hanging basket structure during the movement of personnel and equipment, avoids the calculation results that are too optimistic due to ignoring dynamic effects, and further improves the level of safety assurance for the construction of the hanging basket structure.

[0017] Fourth, this invention calibrates the finite element model through actual measurement, trains a multilayer perceptron neural network with multidimensional input and output, and deploys the trained hanging basket structure safety performance rapid prediction model on a mobile terminal. After real-time load parameters are input at the construction site, the most unfavorable stress value, maximum deflection, and location of dangerous components are output in milliseconds, which significantly improves the efficiency and response speed of safety monitoring and provides safety assurance for composite beam hanging basket construction.

[0018] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the finite element model of a composite beam hanging basket structure according to a technical solution of the present invention; Figure 2 This is a comparison diagram of structural stress based on the bidirectional wind load calculation effect of a technical solution of the present invention; Figure 3 This is a comparison diagram of structural displacements based on the bidirectional wind load verification effect of one technical solution of the present invention. Detailed Implementation

[0020] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0021] It should be understood that terms such as “having,” “comprising,” and “including” as used herein do not exclude the presence or addition of one or more other elements or combinations thereof.

[0022] It should be noted that, unless otherwise specified, the experimental methods described in the following embodiments are conventional methods, and the reagents and materials mentioned are commercially available. In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "setting" should be interpreted broadly. For example, they can refer to fixed connection or setting, detachable connection or setting, or integral connection or setting. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances. The terms "lateral," "longitudinal," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention and simplifying the description. They do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0023] This invention provides a stress verification method for a composite beam hanging basket structure based on multi-load combination. The composite beam hanging basket structure includes a main body consisting of vertical rods, horizontal rods, and longitudinal rods, and a top horizontal rod installed at the top of the vertical rods for overlapping with the composite beam. The vertical rods mainly bear vertical loads, the horizontal and longitudinal rods are used to maintain the overall stability of the structure, and the top horizontal rod is used to connect the hanging basket to the composite beam. The method includes the following steps: Step 1: Establish the finite element model of the composite beam hanging basket structure: Based on the design drawings of the composite beam hanging basket structure, the actual geometric dimensions of all major load-bearing members, such as vertical, horizontal, and longitudinal members, are obtained, including cross-sectional dimensions, lengths, and connection positions and methods between members. A finite element model of the composite beam hanging basket structure is then established. This finite element model uses beam elements to simulate the vertical, horizontal, and longitudinal members. Each beam element is constructed based on the actual geometric dimensions and connection relationships of the composite beam hanging basket structure. During the modeling process, the node connections of each beam element are constructed strictly according to the connection relationships in the design drawings to ensure that the model can accurately reflect the overall geometric shape and force transmission path of the hanging basket structure. Figure 1 The image shown is a schematic diagram of the completed finite element model of the composite beam hanging basket structure. Step 2: Set the boundary conditions for the finite element model: Boundary conditions are set in the finite element model. The boundary conditions include using hinge constraints or spring element constraints at the overlap of the top horizontal bar and the composite beam. If the connection stiffness at the overlap is large and the deformation is small, hinge constraints can be used to limit the vertical and horizontal displacement of the top horizontal bar at the overlap, allowing only rotation around the overlap point. If there is a certain deformation capacity at the overlap, such as through a clamp, spring element constraints can be used. Lateral displacement constraints are set at the contact position between the top horizontal bar and the composite beam. This is achieved by adding lateral constraint elements to the model to limit the displacement of the top horizontal bar along the length of the composite beam. Step 3: Define load parameters: The load parameters are defined, including dead load, live load, and wind load. The dead load is the self-weight of the composite beam hanging basket structure multiplied by an amplification factor based on the weight of unmodeled components. When calculating the dead load, the self-weight of the hanging basket structure is first calculated based on the geometric dimensions and material density of each member, and then the weight of unmodeled components such as planks and connectors is considered and multiplied by an amplification factor. The amplification factor is determined based on the actual weight ratio of the unmodeled components and is usually in the range of 1.03-1.07. The live load is the load of construction personnel and equipment, which can be in the form of uniformly distributed load or concentrated load. The uniformly distributed load is determined based on the density of construction personnel and the density of material stacking, while the concentrated load is determined based on the maximum weight of a single piece of equipment. The wind load is calculated based on the basic wind pressure, the wind pressure height variation coefficient (determined based on the installation height of the hanging basket structure), the wind load shape coefficient (determined based on the shape of the hanging basket structure), and the wind vibration coefficient (determined based on the dynamic characteristics of the structure). Step 4: Set up multi-load combinations: A multi-load combination is set, which includes a strength verification load case and a stiffness verification load case. The load combination of the strength verification load case is determined according to the combination rules of permanent load and variable load in the "Code for Design of Building Structures" (GB 50009-2012), and the design values ​​of dead load, live load and wind load are also taken into account. That is, according to the degree of adverse effect of the load on the structure, the dead load, live load and wind load are multiplied by the corresponding partial factors and then superimposed. The partial factor of permanent load is determined according to whether the load effect is favorable, and the partial factor of variable load is taken according to the code. When there are multiple variable loads, the combination value coefficient needs to be considered. The load combination of the stiffness verification load case adopts the standard values ​​of dead load and live load, without considering the amplification of the partial factors, and only calculates the structural deformation under the actual load. Step 5: Use the established finite element model to calculate the strength and stiffness verification conditions respectively: The finite element model is used to calculate the strength and stiffness verification conditions respectively. The defined load parameters and load combination schemes are input into the finite element software, and the corresponding solution parameters are set. Based on the mechanical properties, boundary conditions and load combinations of each beam element, the stress and displacement of each node of the hanging basket structure are solved, and the maximum combined stress and maximum deflection of the composite beam hanging basket structure are obtained. Step Six: Determining the Verification Results: Obtain the actual steel type used in the composite beam hanging basket structure, consult relevant specifications to determine its bending strength design value, and determine the allowable deflection value of each member based on the calculated span of each member in the composite beam hanging basket structure and the preset deflection control standard. Compare the maximum combined stress with the bending strength design value of the actual steel used in the composite beam hanging basket structure, and compare the maximum deflection with the allowable deflection value determined based on the structural calculated span and the preset deflection control standard. If the maximum combined stress ≤ the bending strength design value and the maximum deflection ≤ the allowable deflection value, the stress verification of the composite beam hanging basket structure is deemed to have passed; otherwise, the composite beam hanging basket structure needs to be optimized and adjusted before recalculation.

[0024] In the above technical solution, the stress and stiffness of the composite beam hanging basket structure are comprehensively verified. The finite element model is constructed based on the actual geometric dimensions and connection relationships. The boundary conditions are set to fit the actual connection characteristics. The load parameters are clearly defined and cover the main stress types. The load combination follows the specifications, ensuring the scientific and rational nature of the verification process. The maximum combined stress and maximum deflection obtained through calculation can accurately reflect the actual stress state and deformation capacity of the hanging basket structure. Based on the judgment results of the steel bending strength design value and allowable deflection value, it can reliably determine whether the hanging basket structure meets the construction safety requirements, effectively avoiding construction safety accidents caused by insufficient structural strength or excessive deformation.

[0025] Taking the composite beam formwork of Yanglintang Bridge as an example, the specific information is as follows: Structural composition: 4 vertical bars, 6 horizontal bars, 4 longitudinal bars made of No. 8 channel steel, and 4 top horizontal bars made of No. 8 channel steel; Component geometry: All members (4 vertical members, 4 top horizontal members, 6 horizontal members, and 4 longitudinal members) are made of No. 8 channel steel with a cross-sectional dimension of 80mm × 43mm × 5mm. Vertical pole arrangement: 4 vertical poles with a horizontal spacing of 2.0m × 2.0m (forming a 4.0m span). 2 (Operating platform) Component lengths: Vertical poles 2.8m (working height of the hanging basket); Top horizontal poles 1.8m (each corresponding to one vertical pole); Horizontal poles: 2.0m (6 in total, 3 on each of the upper and lower layers, connecting to 4 vertical poles); Vertical poles: 1.948m; Materials: Q235 steel is used throughout, with a design bending strength of 215 MPa, a design compressive strength of 215 MPa, and an elastic modulus of 2.06 × 10⁻⁶. 5 MPa; Construction scenario: basic wind pressure 0.25kPa, hanging basket installation height 12m, construction live load is considered as a uniformly distributed load of 2.5kPa.

[0026] Step 1: The ANSYS finite element analysis software was used, and beam elements (BEAM188 elements) were employed to simulate the vertical, horizontal, and longitudinal members: The node configuration includes 16 physical nodes; Node connections: The top horizontal bar is welded to the vertical bar (rigid connection), and the horizontal and vertical bars are bolted to the vertical bar (simulated as hinged connection using finite element method).

[0027] Step Two: At the joint between the top horizontal bar and the composite beam: it is an overlapping joint, with hinged constraints to limit vertical and horizontal displacement, but allow rotation around the joint point; Lateral displacement restriction: Lateral constraints (simulated limit blocks) are set at the contact position between the top horizontal bar and the composite beam.

[0028] Step 3: Dead load: First calculate the self-weight of the hanging basket structure. The unit length weight of the 8# channel steel is 8.04kg / m, and the total self-weight of the entire structure is 161kg (approximately 1.61kN). Considering unmodeled components such as scaffolding and connectors, take an amplification factor of 1.05, and the final dead load G1 = 1.61 × 1.05 ≈ 1.69kN. Live load: The load of construction personnel and equipment is calculated as a uniformly distributed load of 2.5 kPa, and the area of ​​the hanging basket working platform is 4m². 2 The total live load is 2.5 × 4 = 10 kN; Wind load: basic wind pressure W 0 = 0.25 kPa, wind pressure height variation coefficient m z =1.1 (Class B site at a height of 12m), wind load shape coefficient m s =1.0, wind vibration coefficient β z =1.0, Standard value of wind load W k =1.0×1.1×1.0×0.25=0.275kPa, the total wind load is 0.275×4=1.1kN.

[0029] Step Four: Strength verification load case: According to Article 3.2.4 of the "Code for Design of Building Structures" GB50009-2012, the combined load is "1.2×dead load + 1.4×live load + 1.4×0.6×wind load" (live load is the dominant load). The total design load after combination is 1.2×1.69+1.4×10+1.4×0.6×1.1=1.512+14+0.924≈16.95kN; Stiffness verification load case: using "1.0 × dead load + 1.0 × live load", the standard value of the total load after combination = 1.69 + 10 = 11.69 kN; Step 5: Input the above parameters into the finite element model and set the solution convergence criterion (displacement convergence accuracy 1×10⁻⁶). -6 m), start the calculation: Strength verification condition: The maximum combined stress of the hanging basket structure was calculated to be 166MPa (at the end of the longitudinal cantilever, in the stress concentration area). Stiffness verification condition: The maximum deflection of the hanging basket structure is calculated to be 5.5 mm (at the same location).

[0030] Step Six: Strength assessment: The design value of the bending strength of Q235 steel is 215MPa, and the maximum combined stress is 166MPa≤215MPa, so the strength meets the requirements. Stiffness determination: The span of the cantilever section of the longitudinal bar is 1948mm, and the allowable deflection is 1948÷125≈15.58mm. Since 5.5mm≤15.58mm, the requirements are met. Final determination: The stress calculation of the composite beam hanging basket structure has passed and it can be put into construction and use.

[0031] Existing verification methods only apply wind loads in one direction and do not consider the wind sensitivity in the direction perpendicular to the length of the composite beam. This results in an incomplete verification of the impact of wind loads on the hanging basket structure and cannot cover the complex scenario of multiple wind directions in actual construction.

[0032] In another technical solution, the application of wind load needs to consider two directions: the first direction is along the length of the composite beam, i.e., the longitudinal direction of the bridge. In this direction, the wind-receiving area of ​​the hanging basket structure is relatively small, and the lateral force on the structure is weak. The standard value of wind load is calculated according to the formula. W k = β z × m z × m s × W0. Calculation; The second direction is perpendicular to the length of the composite beam, i.e., the transverse direction. In this direction, the exposed wind area of ​​the hanging basket structure is larger, and the vibration response of the structure is more significant. It is a sensitive direction for wind loads because the hanging basket, as a temporary frame structure at the bottom of the composite beam, has a much larger exposed wind area in the transverse direction than in the longitudinal direction. Furthermore, the presence of the cantilever section exacerbates the transverse vibration response, making it a wind-load sensitive direction. Calculations based solely on the longitudinal direction cannot reflect the most unfavorable stress. The standard wind load value is based on the standard wind load value in the longitudinal direction. W k Multiply by an amplification factor to determine the stress characteristics of the transverse bridge as a wind-sensitive direction; where β z This is the wind vibration coefficient (considering the vibration effect of wind load on the structure), with a value of 1.0. m z This is the wind pressure height variation coefficient (reflecting the variation of wind pressure with altitude), with a value of 1.1. m s This is the wind load shape coefficient (considering the influence of structural shape on wind load), with a value of 1.0. W 0 represents the basic wind pressure value (the maximum wind pressure value that may occur at the project site within a specified period), determined based on meteorological data of the project site. Considering that the transverse direction of the bridge is the wind-sensitive direction of the formwork, it is used to amplify the standard value of the longitudinal wind load and reflect the wind effect in the transverse direction. Therefore, an amplification factor of 1.1-1.3 is set. If the transverse wind-receiving area of ​​the formwork structure is large and the structural stability is relatively weak, a value of 1.3 can be used; if the structural stiffness is large and the wind influence is relatively small, a value of 1.1 can be used. In the strength verification case, the wind loads in both directions are combined with the dead load and live load respectively. The dead load, live load and wind load are multiplied by the corresponding partial factors. The strength verification case needs to calculate the maximum combined stress after combining the two wind load directions with the dead load and live load respectively. The longitudinal wind load mainly acts on the surface of the longitudinal members of the hanging basket structure, and the transverse wind load mainly acts on the surface of the transverse members of the hanging basket structure. The larger of the two values ​​is taken as the final maximum combined stress for judgment.

[0033] Based on the aforementioned fundamental parameters of the composite beam formwork for the Yanglintang Bridge, the effectiveness of the bidirectional wind load calculation is further verified. Considering that a partially distributed load (half-distributed live load) is more unfavorable than a fully distributed load during construction, and that traditional calculations only consider wind load in one direction, which has potential drawbacks, this analysis selects a half-distributed 2.5kPa live load plus bidirectional wind load conditions. The fundamental parameters are as follows: Combination factors: Wind load combination value factor 0.6 (as required by standard GB50009-2012), partial factors 1.2 (dead load), 1.4 (live load / wind load); β z =1.0, mz =1.1, m s =1.0, W 0 = 0.25 kPa (meteorological parameters at the project site), magnification factor = 1.2; Dead load effect: Bending compressive stress -20MPa (longitudinal bar / transverse bar); Live load effect: Bending tensile stress 30MPa (work platform load); Wind load along the bridge: shear stress +40MPa (top rod lap joint). Transverse wind load on the bridge: bending tensile stress +55MPa (cantilever end of longitudinal member). Design value for bending strength of steel: 215MPa.

[0034] Step 1: Calculate the standard value and design value of wind load: Along the bridge: Standard value = 1.0 × 1.1 × 1.0 × 0.25 = 0.275 kPa; Design value = 0.275 × 1.4 = 0.385 kPa; Cross-bridge direction: Standard value = 0.275 × 1.2 = 0.33 kPa; Design value = 0.33 × 1.4 = 0.462 kPa; Step 2: Calculate the wind loads in both directions: Wind load along the bridge: Condition A (Wind load along the bridge direction): 1.2 × Dead load + 1.4 × Live load + 1.4 × 0.6 × Wind load along the bridge direction = 51.6 MPa Wind load on the transverse bridge: Load case B (cross-bracing wind load): = 1.2 × dead load + 1.4 × live load + 1.4 × 0.6 × cross-bracing wind load = 64.2 MPa Step 3: Determine the maximum combined stress From the calculation results of working condition A, the maximum combined stress in working condition A is 51.6 MPa (overlap joint of top horizontal bar). The calculation results for working condition B show that the maximum combined stress in working condition B is 64.2 MPa (cantilever end of longitudinal bar). Final determination: 64.2MPa≤215MPa (design value of bending strength of Q235 steel), the structural strength meets the requirements.

[0035] Taking the composite beam formwork of Yanglintang Bridge as an example, its verification results under the semi-distributed 2.5kPa construction live load condition are as follows: Figure 2 , Figure 3 As shown.

[0036] like Figure 2As shown in the figure, under the same working condition of 2.5kPa construction live load, the composite beam formwork of Yanglintang Bridge is subjected to wind load only along the length direction of the composite beam (longitudinal direction). The extreme values ​​of the combined stress of the section are marked as -24~+43MPa (local surface stress). However, there is a hidden over-limit at the cantilever end of the longitudinal member. Because the wind load is sensitive in the transverse direction, the exposed wind area of ​​the formwork is larger and the vibration response is more significant. The calculation method does not cover the wind load in this direction, resulting in the stress actually borne by the longitudinal wind load + live load + unincluded transverse wind load at the cantilever end of the longitudinal member exceeding the design value of 215MPa bending strength of Q235 steel.

[0037] The figure below shows the application of wind loads in two directions (longitudinal and transverse) using the above method. The design value of the longitudinal wind load is calculated to be 0.385 kPa, and the design value of the transverse wind load is calculated to be 0.462 kPa. The combined stress is calculated by superimposing 1.2 × dead load (self-weight of hanging basket 1.69 kN) + 1.4 × half-distribution live load (5 kN) + 1.4 × 0.6 × design value of wind loads in both directions. The extreme values ​​of the combined stress of the section are marked as -87 to +122 MPa. The stress in all parts is <215 MPa, and the combined stress in the transverse direction reaches 122 MPa. This shows that the combined design value of wind loads in both directions and the strength verification in each direction can effectively control the stress from exceeding the limit and achieve the strength standard.

[0038] like Figure 3 As shown in the figure, under the same working condition of 2.5 kPa construction live load, the composite beam formwork of Yanglintang Bridge is subjected to wind load only along the length direction of the composite beam (longitudinal bridge direction). The deflection of the longitudinal connecting beam is marked as 3.788 mm. Although it is less than the allowable value of 8 mm, there is a hidden stiffness risk. Because the transverse wind load is sensitive, the exposed wind-receiving area of ​​the formwork is larger and the vibration response is more significant. The calculation method does not include the standard value of wind load in this direction in the stiffness combination, which can easily cause additional lateral displacement. As a result, if the transverse wind load is superimposed in actual construction, the total displacement of the longitudinal connecting beam will be close to or even exceed the allowable value of 8 mm.

[0039] The figure below shows the application of wind loads in two directions (longitudinal and transverse) using the above method. The standard value of wind load in the longitudinal direction is calculated to be 0.275 kPa, and the standard value of wind load in the transverse direction is calculated to be 0.33 kPa. The superposition of 1.0 × dead load (self-weight of hanging basket 1.69 kN) + 1.0 × semi-distributed live load (5 kN) + 1.0 × standard value of wind load in both directions results in a longitudinal connecting beam deflection of 3.0 mm, which is much less than the allowable value of 8 mm. The stiffness margin reaches 5 mm, indicating that the coverage of the standard value of wind load in both directions and the use of the standard value of load for stiffness verification can effectively avoid the risk of stiffness exceeding the limit caused by wind load in the transverse direction and achieve the stiffness standard.

[0040] In the above technical solution, by distinguishing between the wind load application methods along the length of the composite beam and those perpendicular to the length of the composite beam, and specifically considering the characteristics of the transverse bridge hanging basket structure having a larger wind-receiving area and more significant vibration response, the standard value of the transverse bridge wind load is amplified by a reasonable increase factor, making the simulation of wind load more in line with the actual engineering scenario. At the same time, by taking the maximum combined stress after the combination of the two directions as the judgment criterion, the most unfavorable stress state that may be caused by wind load is fully covered, further improving the safety and accuracy of the verification results.

[0041] In existing calculations, the constraints at the overlap between the top horizontal bar and the composite beam fail to accurately reflect the stiffness characteristics of the clamp connection, leading to discrepancies between the finite element model boundary conditions and reality, and resulting in low calculation accuracy. In another technical solution, when setting boundary conditions in the finite element model, spring elements are used to simulate the constraints at the overlap between the top horizontal bar and the composite beam. The placement of the spring elements is determined based on the connection form between the top horizontal bar and the composite beam. One end of the spring element is connected to a node of the top horizontal bar, and the other end is connected to the corresponding node of the composite beam, ensuring that the spring element can accurately transmit the force between the two. By setting parameters such as axial stiffness, shear stiffness, and bending stiffness, the elastic deformation characteristics of the connection are accurately reflected.

[0042] The axial stiffness, shear stiffness, and bending stiffness of the spring unit are determined based on the bolt preload of the clamp at the connection point and the coefficient of friction of the contact surface. The structural form and number of bolts of the clamp are clearly defined. Typically, the clamp is made of #8 channel steel, and high-strength bolts are used. Material information of the contact surfaces between the clamp and the composite beam is collected to determine the coefficient of friction. For the contact between channel steel and the concrete surface, the coefficient of friction is typically taken as 0.4-0.5. When calculating the axial stiffness of the spring unit, the axial constraint effect generated by the bolt preload is mainly considered. The axial stiffness value is comprehensively determined based on the stiffness characteristics of the bolts, the deformation characteristics of the clamp, and the degree of compression of the contact surface. When calculating the shear stiffness, the anti-slip capability generated by the contact surface friction coefficient and the bolt preload is mainly considered. The greater the bolt preload and the higher the coefficient of friction, the greater the shear stiffness. When calculating the bending stiffness, the bending stiffness of the clamp and the constraint effect of the bolts are mainly considered. The bending stiffness value is comprehensively determined based on the cross-sectional dimensions and material properties of the clamp, as well as the bolt spacing. In finite element software, the calculated axial stiffness, shear stiffness, and bending stiffness parameters are input into the property settings of the spring element to complete the definition of the spring element.

[0043] In the above technical solution, spring units are used to simulate the constraint at the joint between the top horizontal bar and the composite beam, breaking through the limitations of traditional simplified hinged or fixed joints. By combining the bolt preload of the clamp and the friction coefficient of the contact surface, the stiffness parameters of the spring units are determined, so that the simulation of boundary conditions can truly reflect the mechanical characteristics of the actual connection. This method effectively improves the accuracy of the finite element model, reduces the calculation deviation caused by boundary simplification, and makes the stress and deflection calculation results of the hanging basket structure closer to the actual stress situation.

[0044] Furthermore, to improve the accuracy of boundary condition simulation, in another technical solution, the bolt preload of the clamp is applied using a torque wrench, and its value is determined by a calibrated torque-preload relationship curve. Specifically, a test device similar to the actual connection condition is constructed. The bolt is passed through the clamp simulation component and the test plate, a nut is installed and initially tightened, a strain gauge is attached to one end of the bolt, and the strain value of the bolt is measured using a strain gauge. Then, the bolt preload is calculated based on the bolt's elastic modulus. Simultaneously, the torque is gradually applied using a torque wrench. After each application of a certain increment of torque, the torque is stabilized for a period of time, and the torque value displayed by the torque wrench and the strain value measured by the strain gauge are recorded. The corresponding preload is then calculated. The above steps are repeated to apply different magnitudes of torque, obtaining multiple sets of torque-preload corresponding data to ensure that the data covers the torque range that may be used in actual construction. The obtained multiple sets of data are organized, and a torque-preload relationship curve is plotted with the torque value on the x-axis and the preload on the y-axis. The value of the torque-preload relationship curve was determined by calibrating it, which avoided the subjectivity and arbitrariness of bolt preload values, ensured the reliability and consistency of spring unit stiffness parameters, and further guaranteed the accuracy of boundary condition simulation.

[0045] Furthermore, by limiting key parameters such as the coefficient of friction and allowing for minute interface slippage, the reliability of the calculation is ensured. In another technical solution, in friction-type connections (such as bolted joints where friction resists shear), the shear friction force of a single contact surface = coefficient of friction × preload = m × F p The maximum static friction force generated at the contact surface is related to the preload of a single bolt, the number of contact surfaces, and the coefficient of friction. n One contact surface (or n (Several bolts) share the load, and the total shear friction force is: Total shear friction force = n × m × F p Furthermore, under normal stress conditions, a small relative slippage distance is allowed between the clamping fixture and the composite beam contact interface, when the total shear friction causes the spring unit to undergo shear deformation. d At that time, the shear stiffness of the spring unitK s Through formula K s =( n × m × F p ) / d Calculations have determined that this formula is used to calculate the spring element when the nodes primarily resist shear through friction (rather than the bolts being directly sheared). K s It can accurately reflect the ability of a spring unit to resist deformation in the shear direction, among which... n The number of contact surfaces between the clamp and the composite beam. m The coefficient of sliding friction between the channel steel and the concrete surface is 0.4-0.5. F p The preload force of a single bolt is determined based on the torque-preload relationship curve. d The preset allowable minute slip at the interface is 0.8-1.2 mm. In subsequent structural stress calculations, the spring element will respond to the shear force according to this shear stiffness parameter, generating corresponding shear deformation, which in turn affects the stress and displacement distribution of the entire hanging basket structure. By clarifying the specific value ranges of the friction coefficient and the allowable minute slip at the interface in the shear stiffness calculation, a unified standard for shear stiffness calculation is achieved, avoiding ambiguity and uncertainty in parameter values. This value range is determined based on engineering practice experience of channel steel contacting concrete, ensuring both the operability of the calculation and reflecting the mechanical characteristics under actual working conditions. This makes the calculation results of the spring element shear stiffness more reasonable and valuable, further improving the accuracy of boundary condition simulation.

[0046] Existing calculations only focus on the strength of the main structure of the hanging basket, without verifying the strength of the limiting blocks that restrict lateral displacement. This could lead to the limiting blocks failing due to insufficient strength, thereby affecting the lateral restraint effect and causing safety risks to the hanging basket structure.

[0047] Another technical solution also includes strength verification of lateral displacement limitation: Based on the lateral force borne by the spring unit under the strength verification condition, the maximum compressive stress of the limiting block simulating lateral displacement restriction is calculated. First, the lateral force value borne by the spring unit under the strength verification condition is obtained. This value can be extracted from the calculation results of the finite element model. The force data of the spring unit in the lateral direction is extracted in the finite element software and used as the lateral force input value for the strength calculation of the limiting block, ensuring that the lateral force value is consistent with the actual force condition. Then, the structural parameters of the limiting block simulating lateral displacement restriction are determined, including the shape, size, and connection method with the contact component of the limiting block, based on the hanging basket structure. Based on the installation space and lateral constraint requirements, the initial dimensions of the limiting block are initially determined. Typically, the limiting block adopts a cuboid structure, and its contact area is calculated based on the initial design dimensions. The geometric parameters and material performance parameters of the limiting block (consistent with the steel used in the main structure of the hanging basket) are input into the finite element model or the compressive stress calculation method in mechanics of materials is used to calculate the maximum compressive stress of the limiting block under the aforementioned lateral force. During the calculation process, the point of application and distribution of the lateral force must be considered to ensure the accuracy of the compressive stress calculation. If the point of application of the lateral force is not at the center of the limiting block, the influence of eccentric compression must be considered. The maximum compressive stress is compared with the design compressive strength of the steel actually used in the composite beam hanging basket structure. If the maximum compressive stress exceeds the design compressive strength, the equivalent contact area of ​​the limiting block is increased, and the shear stiffness and maximum compressive stress of the spring unit are recalculated until the strength requirements are met. The optimization adjustment method is to increase the equivalent contact area of ​​the limiting block, which can be achieved by increasing the contact surface size of the limiting block, such as increasing the length or width of the contact between the limiting block and the composite beam. The increase ratio of the contact area is determined according to the extent of the compressive stress exceeding the standard. The greater the compressive stress exceeds the standard, the larger the contact area needs to be increased. After increasing the contact area, the maximum compressive stress of the limiting block is recalculated. At the same time, the shear stiffness of the spring unit also needs to be recalculated because the increase in the contact area of ​​the limiting block may affect the friction characteristics and stiffness of the contact surface. The above calculation and comparison steps are repeated until the maximum compressive stress of the limiting block is less than or equal to the design compressive strength of the steel, ensuring that the limiting block has sufficient strength to withstand lateral forces.

[0048] In the above technical solution, by adding a strength verification step for the limiting block to restrict lateral displacement, the shortcomings of existing calculations that only focus on the main structure of the hanging basket and ignore the safety of the constraint structure itself are overcome. This step calculates the maximum compressive stress of the limiting block and compares it with the design value of the compressive strength of the steel to ensure that the limiting block has sufficient strength to withstand lateral forces, thus avoiding the loss of lateral displacement restriction function due to the failure of the limiting block, which could lead to instability of the hanging basket structure.

[0049] In existing calculations, live loads are simulated only as static loads, ignoring the dynamic effects caused by the movement of construction personnel and equipment. This results in the inability to capture the instantaneous maximum stress and deflection of the hanging basket structure under dynamic loads, and the calculation results cannot fully reflect the actual stress state.

[0050] In another technical solution, when defining the live load, at least one dynamic load condition is included. In the construction of composite beam hanging basket, the main manifestations are the loads generated by the walking of construction personnel and the movement of construction equipment. This dynamic load case is simulated by transforming the loads of construction personnel and equipment into a concentrated mass block moving along the critical path of the hanging basket structure. A concentrated mass block corresponding to the total mass is created in the finite element model. This concentrated mass block uses a virtual mass point to simulate the dynamic load, and its mass is equal to the total mass of the construction personnel and equipment. The concentrated mass block is associated with the critical path nodes of the hanging basket structure to ensure that it can move along the critical path. The determination of the critical path needs to consider the geometric characteristics of the hanging basket structure and the actual construction movement. Typically, the longitudinal centerline of the hanging basket structure is selected, as this path covers the main stress area of ​​the hanging basket and can effectively reflect the most unfavorable effects of the dynamic load. The movement trajectory of the concentrated mass block is defined in the model, specifying the starting point, ending point, and path shape to ensure that the movement trajectory is consistent with the actual construction movement. Transient dynamic analysis is then performed. The Newmark-β method in the direct integration method is used to capture the stress, displacement, and velocity parameters of the structure at different times. The time step of the analysis is set, and the size of the time step needs to be determined according to the moving speed of the concentrated mass block and the natural frequency of the structure. It is set to 0.01-0.05s to ensure accurate capture of the instantaneous response of the structure. Dynamic loads are applied to the finite element model, and the gravity of the concentrated mass block is used as the dynamic load. The position of the load changes with the movement of the concentrated mass block. At the same time, the dead load and wind load in the strength verification case are superimposed to ensure that the load combination of the dynamic case is consistent with the actual stress. Transient dynamic analysis is started, and the finite element software calculates the stress, displacement and other response data of the hanging basket structure at each time step. The maximum combined stress and maximum deflection during the movement of the concentrated mass block are captured to obtain the maximum combined stress and maximum deflection under the condition.

[0051] In the above technical solution, by introducing dynamic load conditions, the loads of construction personnel and equipment are transformed into moving concentrated mass blocks and transient dynamic analysis is performed. This makes up for the shortcomings of traditional static load simulation in capturing dynamic effects. It can accurately reflect the instantaneous stress peak and deflection changes of the hanging basket structure during the movement of personnel and equipment, avoid the calculation results that are too optimistic due to ignoring dynamic effects, and further improve the safety guarantee level of the hanging basket structure construction.

[0052] Furthermore, by clearly defining the movement path and range of the concentrated mass block, the dynamic effects of key stress areas can be accurately captured. In another technical solution, the critical path is the longitudinal centerline of the hanging basket structure, and the movement range of the concentrated mass block starts from the connection between the vertical rod and the top horizontal rod and ends at the cantilever end of the longitudinal rod. The connection between the vertical rod and the top horizontal rod is a key node connecting the hanging basket structure and the composite beam. The movement of the concentrated mass block from this point can simulate the movement of construction personnel from the composite beam into the hanging basket structure. The cantilever end of the longitudinal rod is a sensitive area for deformation and stress. When the concentrated mass block moves to this point, it can reflect the dynamic response of the structure in the most unfavorable position, enabling the dynamic analysis to be targeted. Focusing on the main stress-bearing areas of the hanging basket structure, the movement path is divided into several straight or curved segments based on the structural geometry between the starting and ending points. The moving speed of the concentrated mass block is kept constant along each segment, conforming to the normal walking speed of construction workers. During transient dynamic analysis, finite element software calculates the load effect at each location in real time, capturing stress and deflection changes in the structure at different movement stages. During movement, it is crucial to ensure accurate mechanical transfer between the concentrated mass block and the hanging basket structure, ensuring that the gravity of the concentrated mass block is fully transferred to the corresponding structural nodes. This path and range setting, based on the geometric characteristics of the hanging basket structure and the actual construction movement, effectively captures the dynamic response of key areas, avoiding the blindness of dynamic simulation and making the calculation of maximum combined stress and deflection under dynamic loads more targeted and accurate.

[0053] Existing verification methods rely solely on theoretical calculations using finite element models, which leads to the inability to correct discrepancies between theoretical calculations and actual stress conditions, resulting in insufficient reliability of the verification results. In another technical solution, after determining that the stress verification of the composite beam hanging basket structure has passed, the following steps are also included: After the composite beam hanging basket structure is installed on site, the key members of the hanging basket structure are identified based on the calculation results of the finite element model. These members have high stress under load and are critical parts for structural safety. Stress sensors are installed on these key members. The magnitude of the test load is determined based on the live load design value of the hanging basket structure, usually 1.0 times the live load design value, to ensure that the test load can reflect the actual load level during construction. When a known static load test load is applied, the measured stress value of the key members is measured. After the load is applied, the structure is left to stand for a period of time until the deformation stabilizes. The measured stress value of each stress sensor is read through a data acquisition instrument, the measurement data of each sensor is recorded, and the average stress value of each key member is calculated as the measured stress result of that member. At the same time, a static load test load of the same magnitude and distribution is applied in the finite element model for calculation and analysis to obtain the calculated stress value of each key member. The measured stress value is compared with the calculated stress value calculated by the finite element model under the same test load. When the deviation exceeds a preset threshold of 5-15%, the boundary conditions or material parameters of the finite element model are adjusted in reverse. The cause of the deviation is analyzed, and the boundary condition parameters (such as spring element stiffness) or material parameters (such as elastic modulus) of the finite element model are adjusted. After the adjustment, the stress values ​​of each key member are recalculated and compared with the measured data again until the calculation results match the measured data, ensuring that the stress characteristics of the finite element model are consistent with those of the actual structure. Specifically, the boundary conditions of the finite element model are adjusted in reverse. In the finite element model, the shear stiffness of the spring element directly affects the stress transmission and deformation characteristics of the connection part, and has the most significant impact on the stress distribution of the entire hanging basket structure. Therefore, it is the priority adjustment object. Specifically, with a preset step size of 5% (too large a step size may lead to over-adjustment, and too small a step size will reduce the adjustment efficiency), the shear stiffness value of the spring element simulating the overlap between the top horizontal bar and the composite beam is adjusted first. When making the reverse adjustment, the initial shear stiffness of the current spring element is first obtained. Initially, based on the stress deviation, determine the adjustment direction. If the calculated stress value is greater than the measured stress value, it indicates that the shear stiffness of the model is too large, and the constraint at the connection is too strong, requiring a reduction in shear stiffness. If the calculated stress value is less than the measured stress value, it indicates that the shear stiffness of the model is too small, and the constraint at the connection is too weak, requiring an increase in shear stiffness. Adjust the shear stiffness value of the spring element according to a preset step size of 5%, update the spring element parameters in the finite element model, and recalculate the stress under the known static load test condition to obtain the new calculated stress values ​​for each key member. The calculated stress value is compared with the measured stress value again, and the deviation percentage is calculated. If the deviation percentage still exceeds the preset threshold of 5-15%, the shear stiffness value is adjusted according to the above step size and direction, and the calculation and comparison steps are repeated. If the deviation increases due to incorrect adjustment direction, the step size direction is adjusted in the opposite direction. If the deviation percentage still cannot meet the requirements after multiple adjustments, the axial stiffness of the spring unit or other parameters such as the elastic modulus of the material can be appropriately adjusted on the basis of adjusting the shear stiffness until the stress deviation percentage of all key members is less than or equal to the preset threshold.

[0054] In the above technical solution, the on-site deployment of stress sensors and the application of known static load test loads can accurately obtain the actual stress data of the hanging basket structure. Through deviation comparison and reverse adjustment, the calculation results of the finite element model are made consistent with the measured data. This reverse adjustment method can quickly reduce the deviation between theoretical calculation and measured data, improve the efficiency and effect of model correction, make the entire verification method more practical, and significantly improve the reliability and accuracy of the model.

[0055] To enable real-time assessment and immediate response to load exceedances at the composite beam formwork construction site, another technical solution, after model calibration, also includes: In the validated finite element model, the system adjusts the design values ​​of live load and wind load to generate parameter combinations covering different load levels. Specifically, the design value of construction live load is set between 1-5 kN / m. 2 Within the range of 0.5 kN / m 2 Values ​​are taken at intervals. Simultaneously, the design values ​​of wind loads (longitudinal and transverse) within the range of 0.1-1.5 kPa are taken at 0.1 kPa intervals. Through permutation and combination, dozens or even hundreds of different load cases are generated. When the sample is generated, a unique number is assigned to each component. An automated script controls the finite element solver to perform finite element calculations for each load combination. The Mises stress and the overall maximum deflection of the structure of all components in the entire hanging basket structure are extracted. All components are scanned, and the component with the first (i.e. the first) Mises stress exceeding the material strength design value is selected from the calculation results. These are usually weak parts such as the cantilever end of the longitudinal bar and the connection between the horizontal bar and the vertical bar. These are marked as the most unfavorable stress components. The number of the most unfavorable component under each load combination is recorded, as well as its stress peak value and the corresponding maximum deflection value. Multiple sets of generated load parameters are combined as input feature vectors, and the peak Mises stress of the corresponding most unfavorable stress member and the maximum deflection of the structure are used as output targets to jointly construct a supervised learning training dataset. 80% is used as the training set and 20% as the test set. The input features of the training set are two-dimensional data, namely the live load design value and the wind load design value (longitudinal and transverse directions). The output targets are also two-dimensional data, namely the most unfavorable stress value and the maximum deflection value. A multilayer perceptron neural network is constructed and trained, specifically including an input layer with three neurons to receive load input; two hidden layers, each containing sixty-four neurons, using a linear rectified function as the activation function to learn the complex nonlinear mapping relationship between load and response; and an output layer with two neurons to output the predicted stress and deflection values ​​respectively, without using an activation function. The training process uses an adaptive moment estimation optimizer, with the loss function defined as mean square error. The training cycle is set to one thousand rounds. Through iterative optimization, the error between the predicted stress and predicted deflection output by the network and the true value is made lower than a preset accuracy threshold (5%), resulting in a trained fast prediction model for the safety performance of the hanging basket structure. During the subsequent construction of the composite beam hanging basket structure, on-site engineers do not need to perform any complex finite element modeling and analysis. They only need to input the live load and wind load values ​​obtained from real-time monitoring or evaluation on-site into an application deployed on a mobile terminal or industrial control computer. The trained hanging basket structure safety performance rapid prediction model outputs the predicted most unfavorable stress value and predicted maximum deflection value under the current load conditions within milliseconds, and locates the number / location of the most unfavorable component. Based on this, construction personnel can quickly judge and decide on the safety status. If the predicted stress value is much lower than the material strength design value, the current state can be determined to be safe; if the predicted value is close to or exceeds the allowable value, an alarm must be issued immediately, and load limiting, evacuation, or reinforcement measures must be taken.

[0056] The above technical solution successfully solves the problem that the traditional stress calculation of composite beam hanging baskets is not suitable for real-time on-site applications, and realizes accurate and efficient assessment of safety performance, which greatly improves the efficiency and response speed of on-site safety monitoring.

[0057] The number of devices and processing scale described herein are for the purpose of simplifying the description of the invention. Applications, modifications, and variations of the invention will be readily apparent to those skilled in the art.

[0058] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A stress calculation method for a composite beam hanging basket structure based on multi-load combination, wherein the composite beam hanging basket structure includes a hanging basket body composed of vertical rods, horizontal rods, and longitudinal rods, and a top horizontal rod set at the top of the vertical rods for overlapping with the composite beam, characterized in that, The method includes the following steps: A finite element model of the composite beam hanging basket structure is established. The finite element model uses beam elements to simulate the vertical bars, horizontal bars and longitudinal bars. Each beam element is constructed based on the actual geometric dimensions and connection relationships of the composite beam hanging basket structure. Boundary conditions are set in the finite element model. The boundary conditions include using hinge constraints or spring element constraints at the overlap of the top horizontal bar and the composite beam, and setting lateral displacement restrictions at the contact position of the top horizontal bar and the composite beam. Define load parameters, which include dead load, live load and wind load. The dead load is the self-weight of the composite beam hanging basket structure multiplied by an amplification factor based on the weight of the unmodeled components. The live load is the load of construction personnel and equipment. The wind load is calculated based on the basic wind pressure, the wind pressure height variation coefficient, the wind load shape coefficient and the wind vibration coefficient. A multi-load combination is set, which includes a strength verification load case and a stiffness verification load case. The load combination of the strength verification load case is determined according to the combination rules of permanent load and variable load in the building structure load code, and the design values ​​of dead load, live load and wind load are taken into account at the same time. The load combination of the stiffness verification load case adopts the standard values ​​of dead load and live load. The finite element model was used to calculate the strength verification condition and the stiffness verification condition respectively, and the maximum combined stress and maximum deflection of the composite beam hanging basket structure were obtained. The maximum combined stress is compared with the design value of the bending strength of the steel actually used in the composite beam hanging basket structure, and the maximum deflection is compared with the allowable deflection value determined based on the structural calculation span and the preset deflection control standard. If the maximum combined stress ≤ the design value of bending strength and the maximum deflection ≤ the allowable deflection value, then the stress verification of the composite beam hanging basket structure is deemed to have passed.

2. The stress verification method for composite beam hanging basket structure based on multi-load combination according to claim 1, characterized in that, The application of wind load needs to consider two directions: the first direction is along the length of the composite beam, and the standard value of wind load is calculated according to the formula. W k = β z × μ z × μ s × W 0. Calculation; the second direction is perpendicular to the length of the composite beam, and the standard value of wind load is based on the standard value of wind load along the bridge direction. W k Determined by multiplying by an amplification factor; where β z For wind vibration coefficient, μ z This is the coefficient of wind pressure height variation. μ s This is the wind load shape coefficient. W 0 represents the basic wind pressure value, with an amplification factor ranging from 1.1 to 1.

3. For strength verification, the maximum combined stress after combining the two wind load directions with the dead load and live load should be calculated separately, and the larger of the two values ​​should be taken as the final maximum combined stress for judgment.

3. The stress verification method for composite beam hanging basket structure based on multi-load combination according to claim 1, characterized in that, When setting boundary conditions in the finite element model, the constraint at the overlap between the top horizontal bar and the composite beam is simulated using spring elements. The axial stiffness, shear stiffness, and bending stiffness of the spring unit are determined based on the bolt preload of the clamping device connected thereto and the coefficient of friction of the contact surface.

4. The stress verification method for composite beam hanging basket structure based on multi-load combination according to claim 3, characterized in that, The bolt preload of the clamp is applied by a torque wrench and its value is determined by a calibrated torque-preload relationship curve.

5. The stress verification method for composite beam hanging basket structure based on multi-condition load combination according to claim 4, characterized in that, The shear stiffness of the spring unit K s Through formula K s = ( n × μ × F p ) / δ The calculation determines that, n The number of contact surfaces between the clamp and the composite beam. μ The coefficient of sliding friction between the channel steel and the concrete surface is 0.4-0.

5. F p The preload force of a single bolt is determined based on the torque-preload relationship curve. δ This is a preset allowable small amount of interface slippage, ranging from 0.8 to 1.2 mm.

6. The stress verification method for composite beam hanging basket structure based on multi-load combination according to claim 3, characterized in that, This also includes strength verification of lateral displacement constraints: Based on the lateral force borne by the spring unit under the strength verification condition, calculate the maximum compressive stress of the limiting block that simulates lateral displacement restriction; The maximum compressive stress is compared with the design value of the compressive strength of the steel actually used in the composite beam hanging basket structure. If the maximum compressive stress exceeds the design value of the compressive strength, the equivalent contact area of ​​the limiting block is increased, and the shear stiffness and maximum compressive stress of the spring unit are recalculated until the strength requirements are met.

7. The stress verification method for composite beam hanging basket structure based on multi-condition load combination according to claim 1, characterized in that, When defining the live load, at least one dynamic load case must be included; This dynamic load case is simulated by transforming the loads of construction personnel and equipment into a concentrated mass block moving along the critical path of the hanging basket structure, and transient dynamic analysis is performed to obtain the maximum combined stress and maximum deflection under this condition.

8. The stress verification method for composite beam hanging basket structure based on multi-load combination according to claim 7, characterized in that, The critical path is the longitudinal centerline of the hanging basket structure, and the movement range of the concentrated mass block starts from the connection between the vertical bar and the top horizontal bar and ends at the cantilever end of the longitudinal bar.

9. The stress verification method for composite beam hanging basket structure based on multi-load combination according to claim 1, characterized in that, After determining that the stress calculation of the composite beam hanging basket structure has passed, the following steps are also included: After the composite beam hanging basket structure is installed on site, stress sensors are placed on its key members, and the measured stress values ​​of the key members are measured when a known static load test load is applied. The measured stress value is compared with the calculated stress value calculated by the finite element model under the same test load. When the deviation between the two exceeds a preset threshold of 5-15%, the boundary conditions or material parameters of the finite element model are adjusted in reverse until the calculation result matches the measured data. The boundary conditions of the finite element model are adjusted in reverse, specifically by adjusting the shear stiffness value of the spring element simulating the overlap between the top horizontal bar and the composite beam with a preset step size of 5%.

10. The stress verification method for composite beam hanging basket structure based on multi-condition load combination according to claim 9, characterized in that, Following model calibration, the following is also included: In the validated finite element model, the system adjusts the design values ​​of live load and wind load to generate parameter combinations covering different load levels. Finite element calculations are performed on each load combination to extract the Mises stress and the overall maximum deflection of all components in the entire hanging basket structure. From the calculation results, the component whose Mises stress first exceeds the material strength design value is selected, marked as the most unfavorable stress component, and its stress peak value is recorded. At the same time, the corresponding maximum deflection value is also recorded. The generated combination of multiple load parameters is used as the input feature vector, and the peak value of the Mises stress of the corresponding most unfavorable stress member and the maximum deflection of the structure are used as the output targets. The supervised learning training dataset is constructed together, a multilayer perceptron neural network is constructed and trained, and the error between the predicted stress and predicted deflection output by the network and the true value is reduced to a preset accuracy threshold through iterative optimization, so as to obtain a fast prediction model for the safety performance of the hanging basket structure. During the subsequent construction of the composite beam hanging basket structure, the live load and wind load values ​​obtained from real-time on-site monitoring or evaluation will be input into the fast prediction model for the safety performance of the hanging basket structure, and the predicted most unfavorable stress value and predicted maximum deflection value under the current load conditions will be output.

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