Method for calculating safe bearing capacity of gate-type operating platform for construction

Abstract

The invention discloses a method for calculating the safety bearing capacity of a gate-type operation platform for construction, belongs to the technical field of safety calculation of building construction structures, and solves the problems that in the prior art, the safety bearing capacity of the gate-type operation platform under complex load and environmental conditions is not accurately calculated, and the system stability is difficult to comprehensively evaluate. According to the method, a parameterization calculation model is established based on a finite element theory, wherein a portal vertical rod is modeled by adopting a beam unit, a cross rod is modeled by adopting a beam unit, a wall connecting piece is modeled by adopting a rod unit, and a foundation is simulated by adopting a spring unit; the method comprises the steps of calculating dead load and live load axial force standard values, wind load standard values and bending moments thereof, solving an axial force design value, a bending moment design value, a wall connecting piece internal force design value and a basic reaction force design value through iteration, checking portal stability, wall connecting piece strength and foundation bearing capacity, and generating a safety evaluation report based on results. The method is used for safety design and bearing capacity evaluation of the gate-type operation platform in construction, and it is ensured that the construction process is safe and reliable.

Description

Technical Field

[0001] This invention relates to the field of structural safety calculation technology in building construction. More specifically, this invention relates to a method for calculating the safe load-bearing capacity of a gantry crane used in construction. Background Technology

[0002] Gantry cranes are widely used in construction, providing temporary working surfaces and material storage space for high-altitude operations. The safety of these structures is crucial for the construction process, and accurate calculation of their load-bearing capacity is a prerequisite for ensuring safety. Currently, the design and calculation of such temporary structures typically reference standards for permanent building structures, supplemented by some empirical simplification methods.

[0003] Existing calculation methods often treat the portal frame structure, wall ties, and foundation as relatively independent components for separate calculations. For example, when calculating the stability of the portal frame uprights, the calculated length coefficient method is often used to estimate their stable bearing capacity, while the wall ties are simplified as ideal supports, and the foundation's bearing capacity is checked based on average pressure. This separate calculation method fails to accurately reflect the collaborative performance between the portal frame, wall ties, and foundation. The actual working state of the portal frame is a spatial whole; the wall ties provide lateral constraints, but their constraint stiffness is not infinite; the foundation soil also experiences certain compressive deformation. The interaction between these factors has a significant impact on the overall stability of the structural system, which existing methods fail to adequately consider.

[0004] Regarding loads, the distribution of construction live loads is uncertain, and various unfavorable arrangement conditions may exist. Meanwhile, wind loads, as the main horizontal load, require calculation according to load codes; however, for temporary structures during construction, there are still some ambiguities regarding the values ​​of wind pressure height variations, shape coefficients, and wind-induced vibration effects. Furthermore, as a steel structure, the initial geometric imperfections of the portal frame structure (such as initial bending of the uprights) can reduce its stable bearing capacity; how to reasonably consider this factor in calculations is also a challenge.

[0005] Another source of complexity stems from the variability of foundation conditions. The soil at the construction site may be non-uniform, and its stiffness and bearing capacity are not constant but rather vary within a range. Changes in foundation stiffness directly alter the boundary constraints at the base of the uprights, thereby affecting the internal force distribution and stability of the entire gantry structure. Existing calculation methods typically assume a uniform and sufficiently rigid foundation, which differs from reality and may introduce calculation errors.

[0006] Therefore, in engineering practice, several major difficulties have been encountered when calculating the safe bearing capacity of gantry cranes: first, how to establish a mechanical model that can reasonably reflect the coordinated force distribution among the gantry, wall ties, and foundation; second, how to systematically consider the coupling effects of multiple factors such as unfavorable construction load distribution, wind load, and initial structural defects; and third, how to quantify and address the significant impact of actual variability in parameters such as foundation stiffness on the calculation results. These factors make accurately assessing the overall stability and safe bearing capacity of gantry cranes complex, necessitating a more systematic and refined calculation and analysis method. Summary of the Invention

[0007] One object of the present invention is to solve at least the above-mentioned problems and to provide at least the advantages that will be described later.

[0008] Another objective of this invention is to provide a method for calculating the safe bearing capacity of a gantry crane for construction, which solves the problems in existing gantry crane calculation methods that separate the gantry, wall ties and foundation for verification without considering their collaborative work, and make it difficult to systematically consider unfavorable load distribution, initial defects and foundation variability.

[0009] To achieve these objectives and other advantages of the present invention, a method for calculating the safe bearing capacity of a gantry crane for construction is provided, comprising the following steps: Step 1: Based on the input gantry basic parameters, load parameters, and environmental parameters, establish a parametric calculation model of the gantry operation platform. The parametric calculation model is constructed based on finite element theory, and its core components include gantry uprights (modeled using beam elements), crossbars (modeled using beam elements), wall ties (modeled using pole elements), and foundation (simulated using spring elements). The modeling parameters must meet the requirements for the mechanical performance of components in the current "Steel Structure Design Standard". Step 2: Preset the initial bending defect value, unfavorable load distribution conditions and foundation stiffness variation range in the parametric calculation model, and obtain the sensitivity analysis results through parameter analysis, which at least includes identifying the sensitive parameters that have the greatest impact on the stability of the gantry-wall tie-foundation system. Step 3: Calculate the standard value N of the axial force generated by the dead load based on the parametric calculation model. Gk and the standard value of axial force N generated by construction live load Qk Simultaneously calculate the standard value of wind load ω k and the standard value M of the bending moment generated in the gantry uprights wk Standard value of wind load ω k The calculation is performed in accordance with the provisions on wind load calculation for temporary construction structures in the "Code for Design of Building Structures"; Step 4: N Gk N Qk M wkand wind load standard value ω k The parameterized calculation model is input, load effects are combined according to the load code, and initial bending defect values ​​are introduced. A coordinated stress analysis of the gantry-wall tie-foundation system is performed, and the design value N of the axial force acting on the gantry uprights is obtained through iterative calculation. d With bending moment design value M d Design value of internal force R of wall tie d and the design value of the reaction force F of the pole foundation d ; Step 5: Design axial force N d and bending moment design value M d The stability bearing capacity of the gantry is verified by using the design value R of the internal force of the wall ties. d As input for verifying the strength of wall ties and their connections, the design value of the foundation reaction force F of the uprights is used. d As input for verifying the foundation bearing capacity; Step 6: Based on the results of various verifications and sensitivity analysis, generate a safety bearing capacity assessment report. This report should include at least the safety factor for each verification, the primary failure modes of the gantry-wall tie-foundation system, and control recommendations for the sensitivity parameters.

[0010] Preferably, in the method for calculating the safe bearing capacity of the construction gantry crane, step two, obtaining the preset initial bending defect value specifically includes: S2.1 Perform linear buckling analysis on the parametric calculation model and extract its first N buckling mode vectors {φ1, φ2, ..., φ N} and the corresponding eigenvalues ​​λ1, λ2, ..., λ N Where N takes values ​​from 3 to 5; S2.2 Based on the first N buckling modes, the Monte Carlo simulation method is used to generate M sets of random geometric defect samples that conform to the Gaussian random field distribution; M takes a value of not less than 100 sets to ensure the statistical representativeness of the samples; S2.3 Construct an optimization model with the linear combination of the Nth order buckling mode vectors as variables. The objective function of the optimization model is to find the defect distribution pattern that minimizes the second-order elastic stability coefficient of the gantry upright under the unfavorable load distribution condition in step two among M groups of random defect samples. S2.4. The optimization model is solved by using a sequential quadratic programming algorithm. The solution corresponding to the most unfavorable initial bending defect distribution pattern is selected as the optimal solution, which is the preset initial bending defect value.

[0011] Preferably, in the method for calculating the safe bearing capacity of the construction gantry crane, step four, the iterative calculation specifically includes: S4.1 Within each load increment step, based on the determinant sign of the current tangent stiffness matrix and the rate of change of the residual norm of the current iteration step, dynamically select either the spherical arc length method or the cylindrical arc length method to control the iteration path; use the spherical arc length method when the determinant sign changes, and use the cylindrical arc length method in other cases. S4.2 In each iteration step, the tangent stiffness matrix is ​​updated using the Broyden–Fletcher–Goldfarb–Shanno (BFGS, a quasi-Newton method for approximating the stiffness matrix) formula in the quasi-Newton method, so as to reduce the computational cost of directly forming the accurate tangent stiffness matrix. S4.3. An error indicator based on the energy norm is introduced to monitor the convergence of the iterative process. When the indicator falls below a first tolerance limit, the incremental step is considered convergent. The first tolerance limit is set to 1 × 10⁻⁶. -5 The calculation accuracy is determined according to the finite element calculation accuracy standard. When the number of iterations exceeds the preset value (20 times) and fails to converge, and the error indicator shows an oscillation or divergence trend, the load step size reduction algorithm is automatically triggered to halve the current load increment step size and recalculate from the starting point of the increment step.

[0012] Preferably, in the method for calculating the safe bearing capacity of the construction gantry crane, the construction live load distribution condition of the load parameters in step one is dynamically determined in the following way: S1.1 Based on image recognition or sensor network, the location and weight information of building materials, equipment and personnel stacked on the operating platform are obtained in real time; among which, the image recognition adopts the YOLOv8 deep learning algorithm, and the cameras need to be symmetrically arranged around the platform and the top, with a positioning accuracy of not less than ±5cm; the sensor network consists of weight sensors (measurement error ≤2%) and UWB positioning sensors (positioning error ≤10cm). The weight sensors are deployed at the top nodes of the platform uprights, and the positioning sensors are deployed on the workers and large equipment; S1.2. Grid the platform working surface, with the grid size set to 0.5m × 0.5m; using position and weight information as prior knowledge, use the Markov Chain Monte Carlo (MCMC) method to simulate and generate multiple possible future load distribution states, with no less than 50 simulations. S1.3. Multiple load distribution states are used as candidate working conditions and input into the parametric calculation model for parallel calculation. The working condition that maximizes the combined effect of bending moment and axial force of the gantry upright is selected as the unfavorable load distribution working condition in step two.

[0013] Preferably, in the method for calculating the safe bearing capacity of the gantry crane for construction, the method for determining the range of foundation stiffness variation in step two is as follows: Pressure sensors and displacement sensors are installed at the bottom of the pole foundation. When a known load increment ΔF is applied (ΔF is 10% of the standard value of the gantry dead load), the foundation settlement increment ΔS is measured. The sensor measurement accuracy must meet the requirements of pressure error ≤1% and displacement error ≤0.1mm. Calculate the foundation reaction coefficient K based on the measured data. 实测 =ΔF / (A×ΔS), where A is the area of ​​the pole pad; K based on multiple field measurements 实测 The data distribution type is determined by a normality test (using the Shapiro-Wilk test). If the data conforms to a normal distribution, its mean μ is calculated. K and standard deviation σ K And set the range of foundation stiffness variation to [μ K -2σ K ,μ K +2σ K If the distribution does not conform to a normal distribution, then the quantile method is used to determine the range of variation as [P]. 10 ,P 90 ](P 10 P is the 10th percentile. 90 (The 90th percentile) is used for parameter sensitivity analysis in step two.

[0014] Preferably, in the method for calculating the safe bearing capacity of the construction gantry crane, the method for generating random geometric defect samples in step S2.2 includes: S2.2.1. The Latin Hypercube Sampling (LHS) method is used to generate M sets of high-dimensional sample points in the amplitude space of the first N buckling modes. The dimension in "high-dimensional" corresponds to the order N of the buckling mode, that is, each sample point contains N amplitude parameters, which correspond to the amplitudes of the first N buckling modes respectively. S2.2.2 Assign a weight to each group of sample points based on the Mahalanobis distance between the sample point and the mean point; S2.2.3 In the optimization model of step S2.3, the weights are used as weighting coefficients to construct a weighted objective function.

[0015] Preferably, in the method for calculating the safe bearing capacity of the construction gantry crane, step four of the iterative calculation further includes: S4.4 When using the arc length method for iteration, simultaneously monitor the ratio U / V of the lateral displacement U at the top of the gantry to the vertical displacement V. S4.5 When the rate of change of the U / V ratio in three consecutive iterations is less than the second tolerance limit (the second tolerance limit is 5 × 10⁻⁶), -4 Furthermore, the change in the total potential energy of the system is less than 1 × 10⁻⁶ of the initial total potential energy in all three consecutive iterations. -5 When the change in the total potential energy of the system tends to be stable, the incremental step is determined to converge in advance, and the next load step is entered.

[0016] Preferably, in the method for calculating the safe bearing capacity of the construction gantry crane, step five involves verifying the stability bearing capacity of the gantry as follows: S5.1 Extract the design value of the internal force (N) of the most dangerous section of the upright from the convergence result of the iterative calculation. d M d The most dangerous section is defined as the section where the combined effect of axial force and bending moment is greatest. S5.2 Plot the MN correlation curve for this cross section. This curve is generated by the fiber model method that considers material nonlinearity and geometric defects. The steel fiber adopts a bilinear kinematic strengthening constitutive model. S5.3, Design internal force value (N) d M d The point is plotted on the MN correlation curve, and the distance from the point to the curve is calculated as the reliability index β1. Stability is judged by whether the value of β1 is greater than the target reliability index β2. The target reliability index β2 is determined according to the "Unified Standard for Reliability Design of Building Structures", and is taken as 2.3 for temporary construction platforms.

[0017] Preferably, the safety bearing capacity calculation method for the construction gantry crane platform, in step six, further includes the safety bearing capacity assessment report generated as follows: S6.1 Based on the sensitivity analysis results, the Sobol index method was used to identify the three most sensitive parameters that have the greatest impact on system performance; S6.2 For each sensitive parameter, automatically generate its monitoring and measurement plan during the construction process, including the following: measurement point layout suggestions (specifying the specific location and number of measurement points), measurement frequency (set to every 2 hours or daily according to the construction stage), and alarm threshold (determined by back-calculation based on the target reliability index β2). S6.3 Output the monitoring and measurement scheme and evaluation report together.

[0018] The present invention has at least the following beneficial effects: 1. This invention analyzes the portal frame, wall ties, and foundation as a cohesive system through a parametric model, overcoming the limitations of traditional separate calculations and enabling a more realistic simulation of the actual stress state of the structure. Through systematic sensitivity analysis, load combinations, and iterative calculations, it can accurately identify the maximum internal forces and weakest points of the structure, thereby significantly improving the accuracy and reliability of safety bearing capacity assessment and providing a solid technical guarantee for construction safety.

[0019] 2. This invention obtains the structural instability modes through linear buckling analysis and uses an optimization algorithm to automatically search for the most unfavorable defect distribution pattern among a large number of random defect samples, thereby scientifically determining the initial bending defect value. This avoids the arbitrariness of human assumptions, ensuring that the introduction of defect values ​​not only conforms to the actual instability modes that the structure may experience, but also accurately leads to the lowest stable bearing capacity, thus ensuring the accuracy and safety of the stability verification results.

[0020] 3. The iterative method of this invention greatly enhances the robustness and computational efficiency of the nonlinear analysis process by dynamically selecting the arc length method type, updating the stiffness matrix using the BFGS formula, and introducing intelligent step size control and convergence criteria. It can effectively handle complex situations such as instability at extreme points and crossing bifurcation points, avoid computational divergence, and ensure that the equilibrium path and final internal forces of the system can be stably and efficiently obtained under various complex loads and boundary conditions, with reliable calculation results.

[0021] 4. This invention integrates IoT sensing technology with probabilistic simulation algorithms to achieve real-time perception of construction live loads and intelligent prediction of future working conditions. It can automatically filter out the most unfavorable working conditions for the structure from numerous possible load arrangements, providing precise and stringent input conditions for the calculation model. This solves the drawback of relying on empirical estimation for load values, making safety verification more reflective of extreme dangerous situations during construction and improving the foresight and practicality of the assessment.

[0022] 5. This invention inverts the foundation stiffness through on-site measurements and determines its reasonable range of variation based on statistical methods. It transforms the foundation parameters from fixed empirical values ​​into probability distributions that conform to actual on-site conditions, making parameter sensitivity analysis more meaningful for engineering purposes. It can assess the impact of uncertainties in foundation characteristics on the overall structural safety, thereby guiding the design and taking targeted measures to effectively reduce the safety risks caused by variations in foundation conditions.

[0023] 6. Latin hypercube sampling ensures the uniformity and representativeness of the high-dimensional space samples, avoiding the blindness of simple random sampling. By introducing weights based on Mahalanobis distance, the optimization search is focused on sample regions with higher probability of occurrence or more significant impact on stability. This significantly improves the computational efficiency of searching for the most unfavorable defect value while ensuring statistical significance, achieving a balance between accuracy and efficiency.

[0024] 7. By introducing displacement ratio and total system potential energy as additional convergence criteria, this invention can more sensitively capture the changing trend of the system tending to equilibrium. This allows the program to identify and determine convergence in advance before the traditional force or displacement convergence criteria are met, effectively reducing the number of unnecessary iterations within each load increment step, thereby further saving computational resources and improving the efficiency of large-scale nonlinear analysis.

[0025] 8. This invention employs a fiber model method that considers material nonlinearity and geometric nonlinearity to accurately plot the MN correlation curve of the component, which can truly reflect the complex stress performance of the compression-bending component. By calculating reliability indices and verifying target reliability, a stable bearing capacity assessment based on probability theory is achieved, with an accuracy far exceeding that of the traditional length coefficient method, resulting in more scientific and reliable evaluation results.

[0026] 9. This invention not only provides static verification results, but more importantly, it outputs a dynamic construction monitoring scheme, directly transforming the calculation and analysis conclusions into specific technical parameters (measuring points, frequencies, thresholds) to guide on-site construction monitoring, forming a closed-loop management system from design calculations to construction monitoring. This greatly enhances the practical value of the evaluation report and provides core decision support for achieving dynamic, information-based, and intelligent safety management of the construction process.

[0027] 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. Detailed Implementation

[0028] The present invention will be further described in detail below with reference to embodiments, so that those skilled in the art can implement it based on the description.

[0029] 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.

[0030] It should be noted that, unless otherwise specified, the experimental methods described in the following implementation plan are all conventional methods, and the reagents and materials described are all commercially available unless otherwise specified.

[0031] In one embodiment of the present invention, a method for calculating the safe bearing capacity of a gantry crane for construction is provided, comprising the following steps: Step 1: Based on the input gantry basic parameters, load parameters, and environmental parameters, establish a parametric calculation model of the gantry operation platform. The parametric calculation model is constructed based on finite element theory, and its core components include gantry uprights (modeled using beam elements), crossbars (modeled using beam elements), wall ties (modeled using pole elements), and foundation (simulated using spring elements). The modeling parameters must meet the requirements for the mechanical performance of components in the current "Steel Structure Design Standard". Step 2: Preset the initial bending defect value, unfavorable load distribution conditions and foundation stiffness variation range in the parametric calculation model, and obtain the sensitivity analysis results through parameter analysis, which at least includes identifying the sensitive parameters that have the greatest impact on the stability of the gantry-wall tie-foundation system. Step 3: Calculate the standard value N of the axial force generated by the dead load based on the parametric calculation model. Gk and the standard value of axial force N generated by construction live load Qk Simultaneously calculate the standard value of wind load ω k and the standard value M of the bending moment generated in the gantry uprights wk Standard value of wind load ω k The calculation is performed in accordance with the provisions on wind load calculation for temporary construction structures in the "Code for Design of Building Structures"; Step 4: N Gk N Qk M wk and wind load standard value ω k The parameterized calculation model is input, load effects are combined according to the load code, and initial bending defect values ​​are introduced. A coordinated stress analysis of the gantry-wall tie-foundation system is performed, and the design value N of the axial force acting on the gantry uprights is obtained through iterative calculation. d With bending moment design value M d Design value of internal force R of wall tie d and the design value of the reaction force F of the pole foundation d ; Step 5: Design axial force N d and bending moment design value M d The stability bearing capacity of the gantry is verified by using the design value R of the internal force of the wall ties. d As input for verifying the strength of wall ties and their connections, the design value of the foundation reaction force F of the uprights is used. d As input for verifying the foundation bearing capacity; Step 6: Based on the results of various verifications and sensitivity analysis, generate a safety bearing capacity assessment report. This report should include at least the safety factor for each verification, the primary failure modes of the gantry-wall tie-foundation system, and control recommendations for the sensitivity parameters.

[0032] This embodiment relates to a method for calculating the safe bearing capacity of a gantry crane for construction, aiming to solve several key technical problems existing in the prior art. Traditional calculation methods typically treat the gantry structure, wall ties, and foundation as independent components for separate calculations, failing to fully consider the synergistic effects among them. Furthermore, existing methods tend to be simplistic or empirical in their consideration of unfavorable construction load distribution conditions, initial structural geometric defects, and variability in foundation conditions, leading to discrepancies between the calculation results and actual conditions, making it difficult to accurately assess the overall stability and safe bearing capacity of the platform.

[0033] To address the aforementioned technical challenges, this embodiment provides a systematic solution, including a parametric calculation model. This model is a digital model constructed based on finite element theory. In this model, the gantry uprights and crossbars are simulated using beam elements to represent their bending and compressive characteristics, the wall ties are simulated using rod elements to represent their axial stress behavior, and the foundation is characterized by spring elements to represent its elastic support function. Unfavorable load distribution conditions refer to the construction live load arrangement determined through analysis that would cause the structural internal forces to reach the most unfavorable state. Initial bending defect values ​​refer to the structural geometric deviations introduced into the calculation model to account for manufacturing and installation errors. Sensitivity parameters are the calculation input parameters that have the most significant impact on the stability of the gantry-wall tie-foundation system.

[0034] This implementation method first requires collecting the basic parameters, load parameters, and environmental parameters of the gantry, and then establishing a parametric calculation model based on these parameters. The modeling process must adhere to the requirements of current steel structure design standards regarding the mechanical performance of components. Subsequently, initial bending defect values, unfavorable load distribution conditions, and the range of foundation stiffness variations are preset in the model. Through parameter analysis, the most sensitive parameters affecting system stability are identified. Next, the standard values ​​of axial forces generated by dead loads and construction live loads are calculated, and the standard values ​​of wind loads and their resulting bending moments are calculated according to load specifications. After inputting these load values ​​into the model, load combinations are performed according to specifications, and initial defect values ​​are introduced. A collaborative stress analysis is conducted on the gantry-wall tie-foundation system, and the design values ​​of axial force and bending moment of the gantry uprights, internal force of the wall ties, and foundation reaction force of the uprights are solved through iterative calculations. Finally, based on the above design values, the stability bearing capacity of the gantry, the strength of the wall ties and their connections, and the bearing capacity of the foundation are verified. A safety bearing capacity assessment report is generated based on the verification results and sensitivity analysis results.

[0035] Compared to the closest existing technology, this implementation method, by establishing an overall parametric model and performing collaborative stress analysis, can more realistically reflect the actual working condition of the gantry, wall ties, and foundation working together. It overcomes the limitations of traditional separate verification methods. Employing a systematic parametric analysis method, it can scientifically identify the most critical influencing factors, providing clear direction for design and management. By considering multiple factors such as unfavorable load distribution, initial defects, and foundation variability, the calculation results are closer to the actual engineering situation. Verification based on the internal force design values ​​obtained through precise iterative calculations significantly improves the reliability of the safety assessment. The final safety bearing capacity assessment report not only includes conventional verification results but also provides the system's primary failure modes and control recommendations for sensitive parameters, possessing significant engineering guidance value.

[0036] In another embodiment of the present invention, the method for calculating the safe bearing capacity of the construction gantry crane, in step two, specifically includes obtaining the preset initial bending defect value: S2.1 Perform linear buckling analysis on the parametric calculation model and extract its first N buckling mode vectors {φ1, φ2, ..., φ N} and the corresponding eigenvalues ​​λ1, λ2, ..., λ N Where N takes values ​​from 3 to 5; S2.2 Based on the first N buckling modes, the Monte Carlo simulation method is used to generate M sets of random geometric defect samples that conform to the Gaussian random field distribution; M takes a value of not less than 100 sets to ensure the statistical representativeness of the samples; S2.3 Construct an optimization model with the linear combination of the Nth order buckling mode vectors as variables. The objective function of the optimization model is to find the defect distribution pattern that minimizes the second-order elastic stability coefficient of the gantry upright under the unfavorable load distribution condition in step two among M groups of random defect samples. S2.4. The optimization model is solved by using a sequential quadratic programming algorithm. The solution corresponding to the most unfavorable initial bending defect distribution pattern is selected as the optimal solution, which is the preset initial bending defect value.

[0037] This embodiment relates to the determination of the initial bending defect value in the calculation method of the safe bearing capacity of a gantry crane for construction. In structural stability analysis, the initial geometric defect is a key factor affecting the bearing capacity, but its size and distribution pattern have significant uncertainties. Traditional methods usually use simple assumptions, such as using a fixed initial bending value or the first buckling mode as the defect pattern. This method may not accurately capture the true worst-case state of the structure, resulting in calculation results that are either too conservative or biased towards danger, and cannot scientifically assess the actual stability performance of the structure under the influence of defects.

[0038] To address this technical challenge, this embodiment provides a method for determining the initial bending defect value based on structural buckling modes and optimization theory. Linear buckling analysis is a theoretical method for calculating the instability load and corresponding instability modes of an ideal elastic structure. The buckling mode vector describes the deformation morphology when the structure experiences instability at a specific order. Monte Carlo simulation is a numerical method that simulates uncertainty through random sampling. Sequential quadratic programming is an efficient numerical algorithm for solving nonlinear optimization problems with constraints.

[0039] In this embodiment, firstly, linear buckling analysis is performed on the established parameterized gantry calculation model to extract its first three to five buckling modes and their corresponding eigenvalues. These modes represent several basic instability forms that the structure may experience. Next, based on these buckling modes, a sufficient number of random geometric defect samples are generated using the Monte Carlo simulation method. These samples simulate various initial defect morphologies that may exist in reality through random combinations of different order modes. Then, an optimization model is constructed with the amplitude combination of these modes as variables. The goal of this model is to find the specific defect distribution morphology that minimizes the second-order elastic stability coefficient of the gantry uprights under a specified load condition among all these random defect samples. Finally, a sequential quadratic programming algorithm is used to solve this optimization model, and the optimal solution obtained, i.e., the defect morphology that leads to the worst structural stability, is determined as the preset initial bending defect value used in the subsequent co-stress analysis.

[0040] Compared with the closest existing technology, which usually subjectively assumes a defect value or only uses the first-order mode, this implementation objectively identifies and determines the initial defect mode that is most unfavorable to structural stability through systematic buckling mode analysis, a large number of random scenario simulations and rigorous mathematical optimization. This greatly reduces the arbitrariness of human assumptions and makes the introduction of defects more consistent with the potential real instability mechanism of the structure. As a result, the subsequent nonlinear stability analysis results are more accurate and reliable, providing a more scientific and rigorous theoretical basis for evaluating the safety bearing capacity of the gantry crane.

[0041] In another embodiment of the present invention, the method for calculating the safe bearing capacity of the construction gantry crane, in step four, specifically includes the iterative calculation: S4.1 Within each load increment step, based on the determinant sign of the current tangent stiffness matrix and the rate of change of the residual norm of the current iteration step, dynamically select either the spherical arc length method or the cylindrical arc length method to control the iteration path; use the spherical arc length method when the determinant sign changes, and use the cylindrical arc length method in other cases. S4.2 In each iteration step, the tangent stiffness matrix is ​​updated using the Broyden–Fletcher–Goldfarb–Shanno (BFGS, a quasi-Newton method for approximating the stiffness matrix) formula in the quasi-Newton method, so as to reduce the computational cost of directly forming the accurate tangent stiffness matrix. S4.3. An error indicator based on the energy norm is introduced to monitor the convergence of the iterative process. When the indicator falls below a first tolerance limit, the incremental step is considered convergent. The first tolerance limit is set to 1 × 10⁻⁶. -5 The calculation accuracy is determined according to the finite element calculation accuracy standard. When the number of iterations exceeds the preset value (20 times) and fails to converge, and the error indicator shows an oscillation or divergence trend, the load step size reduction algorithm is automatically triggered to halve the current load increment step size and recalculate from the starting point of the increment step.

[0042] This embodiment relates to the nonlinear numerical solution problem in calculating the safety bearing capacity of a gantry crane for construction. The mechanical response of the gantry-wall tie-foundation system under load exhibits high geometric and material nonlinearity. Traditional incremental iterative methods often face difficulties in convergence and low efficiency when analyzing such complex systems. Especially when approaching the ultimate bearing capacity of the structure, the stiffness matrix may become singular, and the equilibrium path may experience sharp turns or bifurcations. Using fixed iterative strategies and step-size control methods easily leads to calculation failures, making it impossible to accurately track the complete stress process of the structure and obtain reliable internal force design values.

[0043] To address this technical challenge, this implementation provides a highly adaptive and stable iterative calculation method. The arc-length method is a numerical approach that effectively tracks the nonlinear equilibrium path of a structure. It controls the iteration process by simultaneously treating the load factor and displacement increment as unknowns. The spherical arc-length method and the cylindrical arc-length method are two common variants of this method, each suitable for different equilibrium path configurations. Quasi-Newton methods are optimization algorithms that avoid reconstructing the exact tangent stiffness matrix in each iteration by approximating the Hessian matrix or its inverse. The BFGS formula is widely recognized as one of the algorithms that best preserves matrix positive definiteness and update accuracy. Convergence monitoring is a crucial step in determining whether the iterative process tends towards equilibrium.

[0044] In this implementation, the iterative process involves dynamic decision-making within each load increment step. The system continuously monitors the determinant sign of the current tangent stiffness matrix and the rate of change of the iterative residuals, intelligently selecting between the spherical arc length method and the cylindrical arc length method to guide the iteration direction, adapting to potential complex changes in the equilibrium path. Within each iteration step, the stiffness matrix is ​​updated using the BFGS formula, significantly reducing the enormous computational overhead caused by repeatedly calculating the full stiffness matrix precisely. Simultaneously, an error indicator based on system energy changes is introduced to rigorously monitor the convergence process. Once this indicator falls below a set strict tolerance limit, the load step is considered to have successfully converged. If the number of iterations exceeds a preset upper limit and the error indicator shows signs of oscillation or divergence, the system automatically activates a step size reduction mechanism, halving the current load increment and reverting to the previous convergence point to restart the calculation, effectively preventing computational crashes.

[0045] Compared to the closest existing technology, this implementation significantly improves the robustness and solution efficiency of nonlinear analysis. Traditional methods typically employ a single iterative algorithm and a fixed step size, which struggles to handle drastic changes in the equilibrium path in complex nonlinear problems, leading to frequent calculation failures. This implementation, through dynamically selecting iterative control methods, intelligently updating the stiffness matrix, and introducing a rigorous convergence monitoring and adaptive step size adjustment mechanism, can stably and efficiently traverse challenging points such as extreme points and bifurcation points, reliably obtaining the internal force response of the system under various load combinations. This provides a solid and accurate data foundation for subsequent bearing capacity verification, ensuring the effective completion of the entire safety assessment process.

[0046] In another embodiment of the present invention, the method for calculating the safe bearing capacity of the gantry crane for construction, wherein the construction live load distribution condition of the load parameters in step one is dynamically determined in the following manner: S1.1 Based on image recognition or sensor network, the location and weight information of building materials, equipment and personnel stacked on the operating platform are obtained in real time; among which, the image recognition adopts the YOLOv8 deep learning algorithm, and the cameras need to be symmetrically arranged around the platform and the top, with a positioning accuracy of not less than ±5cm; the sensor network consists of weight sensors (measurement error ≤2%) and UWB positioning sensors (positioning error ≤10cm). The weight sensors are deployed at the top nodes of the platform uprights, and the positioning sensors are deployed on the workers and large equipment; S1.2. Grid the platform working surface, with the grid size set to 0.5m × 0.5m; using position and weight information as prior knowledge, use the Markov Chain Monte Carlo (MCMC) method to simulate and generate multiple possible future load distribution states, with no less than 50 simulations. S1.3. Multiple load distribution states are used as candidate working conditions and input into the parametric calculation model for parallel calculation. The working condition that maximizes the combined effect of bending moment and axial force of the gantry upright is selected as the unfavorable load distribution working condition in step two.

[0047] This implementation addresses the problem of determining live load conditions in the safety calculation of gantry cranes used in construction. During construction, the distribution of personnel, materials, and equipment on the platform is dynamic and random. Traditional methods typically rely on engineers' experience to assume several fixed load arrangements for calculation. This approach struggles to comprehensively capture all the adverse situations that may arise during actual construction, especially those specific load distributions that pose the greatest threat to the local or overall stability of the structure. This results in blind spots in safety assessments, failing to ensure that the calculated load conditions truly represent the most dangerous states.

[0048] To address this technical challenge, this implementation provides a method for determining dynamic load conditions based on real-time data perception and probabilistic prediction. Image recognition is a technology that automatically identifies specific objects and their locations in images using computer algorithms; sensor networks are systems where spatially distributed autonomous devices collaborate to monitor physical or environmental conditions; YOLOv8 is an advanced high-speed, high-precision target detection algorithm; and the Markov chain Monte Carlo method is a statistical calculation method that simulates complex probability distributions through sampling.

[0049] This implementation first utilizes a camera array deployed around and on top of the platform to identify and locate workers, equipment, and building materials on the platform in real time using deep learning algorithms. Simultaneously, weight sensors pre-installed at key nodes and positioning tags worn on mobile units accurately acquire their weight and location information. Then, the entire platform operating area is divided into regular grid cells. Using the aforementioned real-time data as the basic input, a large number of possible future load spatial distribution states are simulated using probabilistic statistical methods. Finally, these simulated load conditions are input one by one into the gantry's structural calculation model and rapidly calculated. By comparing and analyzing all calculation results, the most significant and unfavorable load distribution condition leading to the most pronounced combined effect of internal forces in the gantry uprights is automatically selected and formally determined as the load input condition for subsequent structural safety analysis.

[0050] Compared to the closest existing technology, this implementation method fundamentally changes the way load conditions are determined. The traditional method of relying on manual experience to pre-set static load conditions is replaced by dynamic intelligent screening based on real-time data and probabilistic simulation. It can proactively detect and quantify the uncertainty of construction loads, accurately locate the load arrangement most unfavorable to structural safety from a massive number of possible load conditions, and make safety verification no longer a passive check based on conservative assumptions, but an active assessment based on real risk scenarios. This greatly improves the pertinence and reliability of safety bearing capacity evaluation and provides forward-looking protection for construction safety.

[0051] In another embodiment of the present invention, the method for determining the range of foundation stiffness variation in step two of the method for calculating the safe bearing capacity of the construction gantry crane is as follows: Pressure sensors and displacement sensors are installed at the bottom of the pole foundation. When a known load increment ΔF is applied (ΔF is 10% of the standard value of the gantry dead load), the foundation settlement increment ΔS is measured. The sensor measurement accuracy must meet the requirements of pressure error ≤1% and displacement error ≤0.1mm. Calculate the foundation reaction coefficient K based on the measured data. 实测 =ΔF / (A×ΔS), where A is the area of ​​the pole pad; K based on multiple field measurements 实测 The data distribution type is determined by a normality test (using the Shapiro-Wilk test). If the data conforms to a normal distribution, its mean μ is calculated. K and standard deviation σ K And set the range of foundation stiffness variation to [μ K -2σ K μ K +2σ K If the distribution does not conform to a normal distribution, then the quantile method is used to determine the range of variation as [P]. 10 P 90 ](P 10 P is the 10th percentile. 90 (The 90th percentile) is used for parameter sensitivity analysis in step two.

[0052] This implementation addresses the determination of foundation parameters in the safety calculation of gantry cranes used in construction. In temporary structure design, foundation stiffness is a crucial but difficult-to-determine parameter. Traditional methods typically rely on geological survey reports or empirical tables to select a fixed value for calculation. However, the actual stiffness and uniformity of the foundation soil at the construction site may differ significantly from design assumptions due to backfilling, compaction, dewatering, or disturbance. This uncertainty prevents calculation models based on fixed values ​​from accurately reflecting the interaction between the foundation and the superstructure, thus affecting the accuracy of the overall stability assessment.

[0053] To address this technical challenge, this embodiment provides a method for determining the range of foundation stiffness variation based on field measurements and statistical analysis. A pressure sensor is a measuring device that converts pressure signals into electrical signals, while a displacement sensor is used to accurately measure minute changes in vertical settlement. The foundation reaction coefficient is an important parameter characterizing the ability of foundation soil to resist deformation; its value is the pressure required to produce a unit settlement per unit area of ​​foundation soil. The normality test is a statistical method used to determine whether a set of data conforms to a normal distribution, while the quantile rule is a statistical method independent of the specific distribution type of the data, used to determine a specific percentage range of the data.

[0054] This implementation first installs high-precision pressure and displacement sensors on the foundation plate of the gantry uprights. Then, a known, controllable load increment is applied to the gantry; this increment is a small proportion of the gantry's own dead load standard value to ensure the test process does not damage the foundation and structure. Simultaneously, the pressure changes and settlement changes of the foundation are collected. Based on these measured data, the actual reaction coefficient of the foundation soil at the measuring point can be calculated. By conducting multiple such field tests at different locations and times, a set of data samples representing the actual variation in foundation stiffness can be obtained. Finally, statistical analysis methods are used to process this data. If the data conforms to a normal distribution, the mean plus or minus two standard deviations is used to determine its representative variation range; if it does not conform to a normal distribution, the range between the decimal and ninetieths is used as the input range for foundation stiffness in subsequent parameter sensitivity analysis.

[0055] Compared to the closest existing technology, this embodiment transforms the determination of foundation stiffness from a fixed empirical estimate to a statistical inference based on field measurement data. Traditional methods cannot account for the variability of conditions at specific engineering sites, while this invention obtains first-hand data through direct field testing and scientifically defines its possible range of variation using statistical principles. This makes the input of foundation parameters closer to actual engineering conditions, significantly improving the simulation accuracy of the calculation model for real foundation conditions and providing a reliable data foundation for accurately assessing the impact of foundation stiffness uncertainty on the safety of the superstructure.

[0056] In another embodiment of the present invention, the method for calculating the safe bearing capacity of the construction gantry crane platform, wherein step S2.2, the method for generating random geometric defect samples includes: S2.2.1. The Latin Hypercube Sampling (LHS) method is used to generate M sets of high-dimensional sample points in the amplitude space of the first N buckling modes. The dimension in "high-dimensional" corresponds to the order N of the buckling mode, that is, each sample point contains N amplitude parameters, which correspond to the amplitudes of the first N buckling modes respectively. S2.2.2 Assign a weight to each group of sample points based on the Mahalanobis distance between the sample point and the mean point; S2.2.3 In the optimization model of step S2.3, the weights are used as weighting coefficients to construct a weighted objective function.

[0057] This implementation addresses the efficiency and representativeness issues of initial defect simulation in the safety calculation of gantry cranes used in construction. Traditional simple random sampling methods have significant limitations in generating a large number of random defect samples based on buckling modes to find the most unfavorable scenario. Since the amplitude combination of defect modes is a sampling problem in a high-dimensional space, simple random sampling may lead to uneven distribution of sample points, with sparse samples in some key areas and oversampling in others. This not only reduces the efficiency of searching for the most unfavorable defect morphology but may also affect the statistical reliability and engineering significance of the final results.

[0058] To address this technical challenge, this implementation provides an improved method for generating and optimizing random geometric defect samples. Latin hypercube sampling is a stratified random sampling technique that ensures all values ​​of each input variable are uniformly covered, thus representing the entire probability space better with fewer sample points. Mahalanobis distance is a metric that measures the distance between a point and a distribution; it considers the correlation between variables and reflects the statistically significant anomalies of sample points better than ordinary Euclidean distance.

[0059] This implementation first employs Latin hypercube sampling to systematically generate a sufficient number of uniformly distributed sample points in a high-dimensional parameter space composed of the amplitudes of the first N buckling modes. Each sample point represents a possible initial defect morphology composed of different buckling modes with specific amplitude combinations. Subsequently, the Mahalanobis distance between each generated sample point and the mean point of the high-dimensional space is calculated, and each sample point is assigned a corresponding weight based on this distance. The weight of sample points that are farther away or more anomalous is adjusted accordingly. Finally, in the subsequent optimization model, instead of treating all sample points equally, this weight is used as a weighting coefficient to construct the optimization objective function. This allows the optimization search process to more specifically focus on defect sample regions with a higher probability of occurrence or a more significant impact on structural stability, thereby guiding the optimization algorithm to find the most unfavorable initial bending defect value more quickly and accurately.

[0060] Compared to the closest existing technology, this implementation significantly improves the efficiency of defect simulation and the targeting of the search process. Traditional simple random sampling is inefficient and lacks representativeness in high-dimensional space, while Latin hypercube sampling achieves more comprehensive and uniform coverage of the parameter space with a smaller sample size. The introduction of a Mahalanobis distance-based weighting mechanism guides the optimization process away from blind searching and towards regions that are statistically more likely to occur or have a greater impact on stability. This greatly improves the computational efficiency of searching for the most unfavorable defect value, making the entire analysis process more intelligent and efficient while ensuring the statistical significance of the results.

[0061] In another embodiment of the present invention, the method for calculating the safe bearing capacity of the construction gantry crane platform, step four of the iterative calculation further includes: S4.4 When using the arc length method for iteration, simultaneously monitor the ratio U / V of the lateral displacement U at the top of the gantry to the vertical displacement V. S4.5 When the rate of change of the U / V ratio in three consecutive iterations is less than the second tolerance limit (the second tolerance limit is 5 × 10⁻⁶), -4 Furthermore, the change in the total potential energy of the system is less than 1 × 10⁻⁶ of the initial total potential energy in all three consecutive iterations. -5 When the change in the total potential energy of the system tends to be stable, the incremental step is determined to converge in advance, and the next load step is entered.

[0062] This implementation addresses the computational efficiency issue of nonlinear iterative processes in the safety calculation of gantry cranes used in construction. When using the arc-length method for structural nonlinear analysis, traditional convergence criteria typically rely solely on whether the norm of the residual force or displacement is less than a certain tolerance limit. However, while the system response may have stabilized near equilibrium, strict norm tolerance standards may still require several iterations to meet. Especially in large-scale complex model calculations, these additional iterative steps significantly increase computation time, causing unnecessary consumption of computational resources and impacting overall analysis efficiency.

[0063] To address this technical challenge, this implementation provides an additional intelligent early convergence determination mechanism. The ratio of the lateral displacement to the vertical displacement at the top of the gantry is a dimensionless parameter that can sensitively reflect the stability and trend of the structural deformation mode. The total potential energy of the system is the sum of the strain energy and the potential energy of the external forces within the system, and its change directly reflects the energy process by which the system approaches equilibrium. When the system approaches equilibrium infinitely, the change in its total potential energy will tend to be infinitesimal.

[0064] In addition to the original force or displacement convergence monitoring, this implementation method simultaneously monitors two additional physical quantities during the iterative process using the arc-length method. The first is the ratio of the lateral to vertical displacement at the top of the gantry, and the second is the change in the total potential energy of the entire system. The program continuously tracks the changes of these two quantities in consecutive iteration steps. When the rate of change of the lateral to vertical displacement ratio over three consecutive iteration steps becomes negligible, and the change in the total potential energy of the system remains below a very small threshold over three consecutive iteration steps, the program can intelligently determine that the system state has sufficiently stabilized, even if the traditional force or displacement residuals have not yet fully met their tolerance requirements. This allows the program to predict in advance that the current load increment step has converged and automatically proceed to the next load step for further calculation.

[0065] Compared to the closest existing technology, this implementation method effectively improves the computational efficiency of nonlinear iterative analysis. Traditional methods rigidly rely on a single convergence criterion, often requiring redundant iterations. This implementation method introduces displacement ratio and total system potential energy—two physical quantities that can predict the equilibrium state earlier—as additional criteria. This allows for the more sensitive detection of the system response trending towards stability, thus enabling earlier exit from the iterative loop. While maintaining the accuracy of the calculation results, this significantly reduces the number of iterations within each load step. Especially for multi-step analysis of large and complex models, this saves considerable computation time and improves the efficiency of the entire safety bearing capacity assessment process.

[0066] In another embodiment of the present invention, the method for calculating the safe bearing capacity of the gantry crane in step five of the method for calculating the gantry crane's stable bearing capacity is as follows: S5.1 Extract the design value of the internal force (N) of the most dangerous section of the upright from the convergence result of the iterative calculation. d M d The most dangerous section is defined as the section where the combined effect of axial force and bending moment is greatest. S5.2 Plot the MN correlation curve for this cross section. This curve is accurately generated by the fiber model method that takes into account material nonlinearity and geometric defects. The steel fiber adopts a bilinear kinematic strengthening constitutive model. S5.3, Design internal force value (N) d M d The point is plotted on the MN correlation curve, and the distance from the point to the curve is calculated as the reliability index β1. Stability is judged by whether the value of β1 is greater than the target reliability index β2. The target reliability index β2 is determined according to the "Unified Standard for Reliability Design of Building Structures", and is taken as 2.3 for temporary construction platforms.

[0067] This implementation addresses the problem of accurately assessing the stability and bearing capacity of gantry cranes used in construction. Traditional methods typically employ simplified approaches such as the calculated length coefficient method to verify the stability of the gantry uprights. These methods are based on elastic stability theory and a large number of parametric analysis results, calculating the equivalent slenderness ratio and determining the stability coefficient by referring to tables. However, for compression-bending members subjected to large bending moments, these methods struggle to accurately account for the coupled effects of material nonlinearity, residual stress, and geometric defects. The calculation results are often coarse and fail to accurately reflect the true ultimate bearing capacity of the member under combined compression and bending stress, potentially leading to overly conservative designs or potential safety risks.

[0068] To address this technical challenge, this embodiment provides a method for verifying the stable bearing capacity based on a precise cross-section analysis model. The MN correlation curve represents the ultimate bearing capacity combination of a structural member's cross-section under the combined action of axial pressure and bending moment; each point on this curve represents a specific ultimate state of internal force combination. The fiber model method is a precise numerical analysis method that discretizes the structural member's cross-section into numerous tiny fiber elements and considers material and geometric nonlinearities through integral calculations. The reliability index is a numerical indicator used to measure the reliability of a structural member, representing the probability level of the member being in a safe state.

[0069] This implementation first searches for and extracts the most unfavorable section location and corresponding internal force design value of the portal frame uprights from the converged results of the overall structural nonlinear iterative calculation. Then, for this most critical section, a refined section analysis is performed using the fiber model method. In this process, the steel fibers employ a bilinear kinematic hardening model that reflects the Bauschinger effect, and the complete MN correlation curve for this section is accurately plotted through integral calculations. This curve represents the true bearing capacity envelope of the section after considering material nonlinearity and geometric imperfections. Finally, the obtained internal force design value points are plotted on this MN correlation curve, and the distance from the coordinates of this point to the bearing capacity envelope curve is calculated. This distance is then converted into a reliability index quantification value. By judging whether this reliability index is higher than the target reliability index set by the code for temporary structures, a scientific assessment of the stability of the portal frame uprights is made.

[0070] Compared to the closest existing technology, the technical advantage of this embodiment lies in elevating the stability bearing capacity verification from approximate calculations based on empirical coefficients to a reliability evaluation based on precise cross-sectional analysis. Traditional length coefficient methods cannot adequately account for material nonlinearity, defects, and complex stress states, while the fiber model method employed in this embodiment can accurately simulate the true response of the cross-section under compressive and bending loads, drawing an accurate bearing capacity envelope. By calculating reliability indices and comparing them with target values, stability assessment is no longer a simple Boolean judgment of a safety factor greater than one, but a quantitative measurement and graded evaluation based on probabilistic meaning. This significantly improves the accuracy, scientific rigor, and reliability of the stability bearing capacity verification results, providing a more precise guarantee for structural safety.

[0071] In another embodiment of the present invention, the safety bearing capacity calculation method for the construction gantry crane platform, the safety bearing capacity assessment report generated in step six further includes: S6.1 Based on the sensitivity analysis results, the Sobol index method was used to identify the three most sensitive parameters that have the greatest impact on system performance; S6.2 For each sensitive parameter, automatically generate its monitoring and measurement plan during the construction process, including the following: measurement point layout suggestions (specifying the specific location and number of measurement points), measurement frequency (set to every 2 hours or daily according to the construction stage), and alarm threshold (determined by back-calculation based on the target reliability index β2). S6.3 Output the monitoring and measurement scheme and evaluation report together.

[0072] This implementation method addresses the practicality and guidance of safety assessment results for gantry cranes used in construction. Traditional safety load-bearing capacity assessment reports typically only provide the final calculation results and a conclusion on whether the specifications are met. While these reports provide safety factors, they fail to clearly reveal the most critical factors affecting system safety and lack the ability to translate these analytical conclusions into specific, actionable construction monitoring guidelines. This creates a disconnect between the calculation results and actual on-site safety management, making it difficult for on-site personnel to take targeted preventative and control measures based on the report's content, thus limiting the report's practical application value.

[0073] To address this technical challenge, this implementation provides a method for generating a safety bearing capacity assessment report that can directly guide construction monitoring. The Sobol index method is a global sensitivity analysis method based on variance decomposition, which can quantify the contribution of individual input parameters or their interactions to the uncertainty of the output results, thereby accurately identifying the most critical influencing factors. The monitoring and measurement scheme is a set of specific operational guidelines that clearly defines the parameters to be monitored, the specific locations and number of monitoring points, the monitoring time frequency, and the threshold values ​​for triggering early warnings.

[0074] After completing all structural calculations and parameter sensitivity analyses, this implementation method first uses the Sobol index method to process all input parameters, quantitatively identifying the top three critical parameters with the greatest impact on the overall performance or stability of the gantry system. Subsequently, for each identified critical sensitivity parameter, the system automatically generates a detailed, customized construction process monitoring plan. This plan clearly specifies the exact locations and number of measuring points to be placed on-site to monitor the parameter, sets corresponding measurement frequencies based on different construction stages (such as peak loading periods or normal operation periods), for example, once every two hours or once daily, and derives the safety alarm threshold for the parameter during construction through back-calculation based on the target reliability index used in previous calculations. Finally, this concrete and directly executable monitoring and measurement plan will be an important component of the safety bearing capacity assessment report, output along with traditional calculation results, safety factors, and failure mode analyses, forming a complete deliverable.

[0075] Compared to the closest existing technology, this implementation method achieves a leap from static safety assessment to dynamic risk management. Traditional reports only provide post-event verification conclusions, while the reports generated by this implementation method go forward, transforming in-depth analysis results into forward-looking action guidelines. Through scientific sensitivity analysis, it accurately identifies the "critical few" parameters and automatically generates monitoring plans containing specific measurement points, frequencies, and thresholds. This transforms the report from mere numbers on paper into a direct technical basis for guiding on-site construction personnel to conduct key monitoring and achieve refined safety management, greatly enhancing the practical value of safety assessments and the ability to ensure construction safety.

[0076] Example 1: Calculation of the safe bearing capacity of a gantry crane used in the construction of a high-rise building I. Project Background and Implementation Overview A high-rise building project in a certain city uses a gantry crane as a temporary support structure for high-altitude operations. The platform is 15m high and has a span of 6m. To assess its safety, the method of this invention is used for calculation. The implementation process is summarized as follows: Input parameters: Collect gantry geometry, material properties (Q235 steel), dead load (platform self-weight), and live load distribution information acquired in real time through a field sensor network. Determine wind load according to the "Code for Design of Building Structures".

[0077] Model and Analysis: A parametric finite element model considering the coordinated operation of the gantry, wall ties, and foundation was established. Through sensitivity analysis, foundation stiffness, wind load, and live load amplitude were identified as key influencing parameters.

[0078] Calculation and Verification: Based on the model, nonlinear iterative calculations were performed to obtain the design values ​​of internal forces (axial force and bending moment) at the most dangerous section of the upright, the internal forces of the wall ties, and the foundation reaction force. Subsequently, the stability bearing capacity of the gantry, the strength of the wall ties, and the bearing capacity of the foundation were verified respectively.

[0079] Report generation: The system automatically generates a safety assessment report, which, in addition to verifying the calculation results, identifies the primary failure modes and generates specific construction monitoring plans for key parameters.

[0080] II. Effect Verification To verify the effectiveness and advancement of the method of this invention, the calculation results are compared with field measurement data and calculation results of traditional methods: Compared with traditional methods, the design value of the control bending moment of the gantry upright calculated by the method of this invention is 68.3 kN·m. Under the same load conditions, the traditional separate verification method calculates the upright bending moment as 52.1 kN·m. The comparison shows that the traditional method, due to its insufficient consideration of system coordination and nonlinear effects, yields an unsafe calculation result, underestimating the actual internal force by approximately 31%.

[0081] Comparison with on-site measurements: During construction, the maximum bending moment of the upright was measured to be 66.8 kN·m using strain gauges. The relative error between the calculated value (68.3 kN·m) and the measured value using the method of this invention is only 2.2%, proving that the model of this invention has extremely high accuracy. The relative error between the calculated value and the measured value of the traditional method is as high as 28%, further highlighting the accuracy advantage of this invention.

[0082] System reliability verification: Monte Carlo simulation was used to analyze the system's reliability, and the calculated reliability index β was 2.6. This value is higher than the target reliability index of 2.0 set for temporary structures in the "Unified Standard for Reliability Design of Building Structures," which, from a probabilistic perspective, proves that the platform safety assessed using the method of this invention meets the standard requirements.

[0083] This embodiment demonstrates that the method of the present invention overcomes the limitations of traditional calculation methods, and can more realistically and accurately reflect the stress state of the gantry crane platform. The calculation results are in high agreement with the measured data, providing reliable technical assurance for construction safety. Furthermore, the output monitoring scheme can be directly used to guide on-site safety management. This embodiment confirms that the method of the present invention can effectively improve the accuracy and practicality of safety assessment in complex construction environments, providing a reliable basis for dynamic construction monitoring.

[0084] 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.

[0085] Although the 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.

Claims

1. A method for calculating the safe bearing capacity of a gantry crane for construction, characterized in that, Includes the following steps: Step 1: Based on the input gantry basic parameters, load parameters, and environmental parameters, establish a parametric calculation model for the gantry operation platform; Step 2: Preset the initial bending defect value, unfavorable load distribution conditions and foundation stiffness variation range in the parametric calculation model, and obtain the sensitivity analysis results through parameter analysis, which at least includes identifying the sensitive parameters that have the greatest impact on the stability of the gantry-wall tie-foundation system. Step 3: Calculate the standard value N of the axial force generated by the dead load based on the parametric calculation model. Gk and the standard value of axial force N generated by construction live load Qk Simultaneously calculate the standard value of wind load ω k and the standard value M of the bending moment generated in the gantry uprights wk ; Step 4: N Gk N Qk M wk and wind load standard value ω k The parameterized calculation model is input, load effects are combined according to the load code, and initial bending defect values ​​are introduced. A coordinated stress analysis of the gantry-wall tie-foundation system is performed, and the design value N of the axial force acting on the gantry uprights is obtained through iterative calculation. d With bending moment design value M d Design value of internal force R of wall tie d and the design value of the reaction force F of the pole foundation d ; Step 5: Design axial force N d and bending moment design value M d The stability bearing capacity of the gantry is verified by using the design value R of the internal force of the wall ties. d As input for verifying the strength of wall ties and their connections, the design value of the foundation reaction force F of the uprights is used. d As input for verifying the foundation bearing capacity; Step 6: Based on the results of various verifications and sensitivity analysis, generate a safety bearing capacity assessment report. This report should include at least the safety factor for each verification, the primary failure modes of the gantry-wall tie-foundation system, and control recommendations for the sensitivity parameters.

2. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 1, characterized in that, Step two, specifically, involves obtaining the preset initial bending defect value, including: S2.1 Perform linear buckling analysis on the parametric calculation model and extract its first N buckling mode vectors {φ1, φ2, ..., φ N } and the corresponding eigenvalues ​​λ1, λ2, ..., λ N ; S2.2 Based on the first N buckling modes, the Monte Carlo simulation method is used to generate M sets of random geometric defect samples that conform to the Gaussian random field distribution; M takes a value of not less than 100 sets to ensure the statistical representativeness of the samples; S2.3 Construct an optimization model with the linear combination of the Nth order buckling mode vectors as variables. The objective function of the optimization model is to find the defect distribution pattern that minimizes the second-order elastic stability coefficient of the gantry upright under the unfavorable load distribution condition in step two among M groups of random defect samples. S2.

4. The optimization model is solved by using a sequential quadratic programming algorithm. The solution corresponding to the most unfavorable initial bending defect distribution pattern is selected as the optimal solution, which is the preset initial bending defect value.

3. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 1, characterized in that, Step four, the iterative calculation specifically includes: S4.1 Within each load increment step, based on the determinant sign of the current tangent stiffness matrix and the rate of change of the residual norm of the current iteration step, dynamically select either the spherical arc length method or the cylindrical arc length method to control the iteration path; use the spherical arc length method when the determinant sign changes, and use the cylindrical arc length method in other cases. S4.2 In each iteration step, the tangent stiffness matrix is ​​updated using the Breuden-Fletcher-Goldfarb-Shanno formula in the quasi-Newton method to reduce the computational cost of directly forming the accurate tangent stiffness matrix. S4.3 Introduce an error indicator based on the energy norm to monitor the convergence of the iteration process. When the indicator is below the first tolerance limit, the incremental step is determined to be converged. When the number of iterations exceeds the preset value and convergence is not achieved, and the error indicator shows an oscillation or divergence trend, the load step size reduction algorithm is automatically triggered to halve the current load incremental step size and recalculate from the starting point of the incremental step.

4. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 1, characterized in that, The construction live load distribution conditions of the load parameters in step one are dynamically determined in the following way: S1.1 Based on image recognition or sensor networks, obtain real-time information on the location and weight of building materials, equipment and personnel stacked on the operating platform; S1.

2. Grid the platform working surface, use the position and weight information as prior knowledge, and use the Markov chain Monte Carlo method to simulate and generate multiple possible future load distribution states, with no less than 50 simulations. S1.

3. Multiple load distribution states are used as candidate working conditions and input into the parametric calculation model for parallel calculation. The working condition that maximizes the combined effect of bending moment and axial force of the gantry upright is selected as the unfavorable load distribution working condition in step two.

5. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 1, characterized in that, The method for determining the range of foundation stiffness variation in step two is as follows: Pressure sensors and displacement sensors are installed at the bottom of the pole foundation. When a known load increment ΔF is applied, the foundation settlement increment ΔS is measured. Calculate the foundation reaction coefficient K based on the measured data. 实测 =ΔF / (A×ΔS), where A is the area of ​​the pole pad; K based on multiple field measurements 实测 The normality test is used to determine the data distribution type. If it conforms to a normal distribution, its mean μ is calculated. K and standard deviation σ K And set the range of foundation stiffness variation to [μ K -2σ K μ K +2σ K If the distribution does not conform to a normal distribution, then the quantile method is used to determine the range of variation as [P]. 10 P 90 ], P 10 P is the 10th percentile. 90 The 90th percentile is used for parameter sensitivity analysis in step two.

6. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 2, characterized in that, The method for generating random geometric defect samples in step S2.2 includes: S2.2.

1. The Latin hypercube sampling method is used to generate M sets of high-dimensional sample points in the amplitude space of the first N buckling modes; S2.2.2 Assign a weight to each group of sample points based on the Mahalanobis distance between that sample point and the mean point; S2.2.3 In the optimization model of step S2.3, the weights are used as weighting coefficients to construct a weighted objective function.

7. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 3, characterized in that, Step four of the iterative calculation also includes: S4.4 When using the arc length method for iteration, simultaneously monitor the ratio U / V of the lateral displacement U at the top of the gantry to the vertical displacement V. S4.5 When the rate of change of the U / V ratio in three consecutive iterations is less than the second tolerance limit, and the change in the total potential energy of the system is less than 1 × 10⁻⁶ of the initial value of the total potential energy in three consecutive iterations. -5 When the change in the total potential energy of the system tends to be stable, the incremental step is determined to converge in advance, and the next load step is entered.

8. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 1, characterized in that, The method for verifying the stability and load-bearing capacity of the gantry in step five is as follows: S5.1 Extract the design value of the internal force (N) of the most dangerous section of the upright from the convergence result of the iterative calculation. d M d ); S5.2 Plot the MN correlation curve for this cross section. This curve is accurately generated by the fiber model method that takes into account material nonlinearity and geometric defects. S5.3, Design internal force value (N) d M d The point is plotted on the MN correlation curve, and the distance from the point to the curve is calculated as the reliability index β1. The stability is judged by whether the value of β1 is greater than the target reliability index β2.

9. The method for calculating the safe bearing capacity of a gantry crane for construction as described in claim 1, characterized in that, The safety bearing capacity assessment report generated in step six also includes: S6.1 Based on the sensitivity analysis results, identify the top three sensitivity parameters that have the greatest impact on system performance; S6.2 For each sensitive parameter, automatically generate its monitoring and measurement plan during the construction process, including suggestions for the layout of measuring points, measurement frequency and alarm threshold; S6.3 Output the monitoring and measurement scheme and evaluation report together.