A method for calculating the shear bearing capacity of seawater sand concrete beam-column joints

Abstract

This invention relates to the field of bearing capacity calculation technology, specifically disclosing a method for calculating the shear bearing capacity of seawater-sand concrete beam-column joints. By accurately acquiring multiple basic parameters such as the component cross-sectional dimensions and the uniaxial compressive strength of the seawater-sand concrete, a dynamic calculation system for the axial compression ratio and the depth of the concrete compression zone is constructed. Through calculation and optimization of the column inclination angle, the mechanical model can reflect rapid changes in the stress state in real time. This model, utilizing a topology optimization loop, integrates transverse tensile strain, projected stirrup ratio, and brittleness degradation factor to generate a composite softening coefficient, thereby dynamically correcting the effective compressive strength and achieving accurate assessment of the joint's mechanical state. The optimal column inclination angle and shear bearing capacity derived from this method not only overcome the limitations of traditional fixed models but also provide scientific support for optimizing concrete performance under complex working conditions.

Description

Technical Field

[0001] This invention belongs to the field of bearing capacity calculation technology, and relates to a method for calculating the shear bearing capacity of seawater sand concrete beam-column joints. Background Technology

[0002] The complex grid system composed of multi-spiral stirrups significantly enhances the deformation capacity and shear toughness of the core concrete through continuous spatial constraints, becoming an important defense against extreme loads such as earthquakes. Meanwhile, the morphological characteristics of the diagonal compression members within the core area directly determine the path and efficiency of load transfer from beams and columns to the core area. As the primary load-bearing unit in the compression-tension model, the effective width, inclination angle, and load density of the diagonal compression member jointly constrain the ultimate bearing capacity and failure mode of the joint area; therefore, an accurate description of its mechanical behavior is a prerequisite for shear design.

[0003] It is worth noting that the diagonal compression members in the core area of ​​a node do not exhibit a fixed geometric posture, but rather undergo significant deflection and width evolution with dynamic adjustments in axial pressure. When the axial compression ratio at the column end changes, the confining pressure state and stress field distribution in the core area change accordingly, driving the principal compressive stress trajectory to tilt and redistribute. Traditional tension-compression member models generally presuppose a fixed empirical value for the inclination angle of the diagonal compression members, over-relying on standardized force patterns while ignoring the actual deflection effect caused by changes in the axial compression ratio. Engineering practice shows that even nodes that meet shear resistance requirements according to current specifications may still experience diagonal compression failure or constraint failure in the core area when encountering different axial compression ratio conditions, reflecting a significant deviation from simulating the compression member morphology with a fixed angle while ignoring its dynamic evolution process. Existing methods often treat the axial compression ratio as an external load condition independent of the force transmission path, failing to systematically analyze how changes in the axial compression ratio affect the actual constraint contribution of the helical stirrups and the degree of concrete softening by altering the inclination angle of the diagonal compression members. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present invention provides a method for calculating the shear bearing capacity of seawater sand concrete beam-column joints to solve the above-mentioned technical problems.

[0005] To achieve the above and other objectives, the technical solution adopted by the present invention is as follows: This invention provides a method for calculating the shear bearing capacity of seawater-sand concrete beam-column joints, the method comprising: Obtain the component cross-sectional dimensions, uniaxial compressive strength of seawater sand concrete, material brittleness degradation factor, helix diameter, helix pitch, shear reference value of multi-helix skeleton, column end axial force, column end bending moment, and column end shear force; The dynamic axial compression ratio and the depth of the concrete compression zone are calculated by combining the component cross-sectional dimensions, column end axial force, and column end bending moment. The geometric endpoints of the main inclined compression member are located at the point of application of the resultant force at the depth of the concrete compression zone to generate floating node coordinates. The initial compression member inclination angle and the initial effective width of the compression member are extracted based on the floating node coordinates. The initial column tilt angle and initial effective column width are used as the current column tilt angle and current effective column width in the topology optimization loop. The topology optimization loop includes: Extract the transverse expansion surface orthogonal to the current column inclination angle, calculate the equivalent projected stirrup ratio using the helix diameter and pitch, and generate the lateral passive constraint compressive stress; Calculate the lateral principal tensile strain based on the current column inclination angle; A composite softening coefficient is generated by combining transverse principal tensile strain, lateral passive confinement compressive stress, and material brittleness degradation factor. The current effective compressive strength is obtained by multiplying the composite softening coefficient by the uniaxial compressive strength of seawater sand concrete. Based on the current column inclination angle, current effective column width, and current effective compressive strength, extract the nodal force imbalance residual vector and the total strain energy in the core area, and then weight and sum the nodal force imbalance residual vector and the total strain energy in the core area to generate the objective function value; If the objective function value is greater than or equal to the preset convergence threshold, update the current column tilt angle and the current effective width of the column and continue to execute the topology optimization loop; If the objective function value is less than the preset convergence threshold, the loop is exited and the current column tilt angle and current effective compressive strength are locked as the optimal column tilt angle and optimal compressive strength. The shear contribution value of the main inclined compression member concrete is calculated using the optimal compression member inclination angle and optimal compressive strength. The shear contribution value of the main inclined compression member concrete is added to the shear reference value of the multi-helix skeleton to generate the total shear bearing capacity and output it.

[0006] As described above, the method for calculating the shear bearing capacity of seawater sand concrete beam-column joints provided by the present invention has at least the following beneficial effects: This invention generates lateral passive restraint compressive stress by extracting the transverse expansion surface orthogonal to the current column inclination angle and calculating the equivalent projected stirrup ratio using the helix diameter and pitch. Combining this with the calculation of the transverse principal tensile strain at the current column inclination angle, and further integrating the transverse principal tensile strain, lateral passive restraint compressive stress, and material brittleness degradation factor, a composite softening coefficient is generated. This composite softening coefficient is then multiplied by the uniaxial compressive strength of seawater sand concrete to obtain the current effective compressive strength. This allows for a reasonable assessment of the concrete compressive performance under different stress conditions, more closely reflecting the actual structural stress state.

[0007] This invention extracts the nodal force imbalance residual vector and the total strain energy of the core area based on the current column inclination angle, effective column width, and effective compressive strength. These two values ​​are then weighted and summed to generate an objective function value. When the objective function value is less than a preset convergence threshold, the loop is exited, and the current column inclination angle and effective compressive strength are locked as optimal values. Finally, the shear contribution value of the main inclined column concrete is calculated using the optimal column inclination angle and optimal compressive strength. This value is then added to the initial multi-helix skeleton shear benchmark value to generate and output the total shear capacity. This makes the assessment of the shear capacity of the nodal concrete more accurate, significantly improving the reliability of the overall structural assessment and providing more scientific technical support for engineering design. Attached Figure Description

[0008] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a schematic diagram showing the connections between the steps of the method of the present invention. Detailed Implementation

[0010] The following description, in conjunction with the implementation of this invention, is merely an example and illustration of the concept of this invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the inventive concept or exceed the scope defined in these claims, all of which should fall within the protection scope of this invention.

[0011] In traditional structural design and analysis systems, fixed geometric assumptions and force paths cannot accurately reflect the real-world performance of seawater-sand concrete under dynamic loading conditions. When the stress state of the nodal core undergoes complex morphological changes due to fluctuations in the axial compression ratio, existing models cannot dynamically couple the actual working state of the member with the mechanical calculation process, leading to significant discrepancies between the calculated results of the compression zone depth and axial compression ratio and the actual values. This static assumption mechanism is particularly rigid in multi-helical stirrup-constrained systems, easily overlooking the actual synergistic effect of the stirrups and the matrix concrete, thus affecting the accuracy of shear strength assessment of the nodal core.

[0012] For example, when the pressure load changes, the values ​​of axial force, bending moment, and shear force at the column end may vary significantly under different working conditions. Traditional systems calculate the depth of the concrete compression zone based on the assumption of a fixed axial compression ratio, which leads to deviations in the results due to the lack of consideration for the geometric adaptive adjustment of the inclined compression members during the stress process. The resulting calculation errors are particularly evident when evaluating the confinement effectiveness of multi-helix stirrups, and may cause important inclined compression member inclination adjustment characteristics to be misjudged as interference, failing to accurately reflect the actual physical state.

[0013] If the above problems are not addressed, misjudgments of the mechanical properties of the node core area will lead to a mismatch between the shear capacity assessment and the actual stress state of the member, further increasing the risk of insufficient design safety. The rigidity of the feature processing mechanism will hinder the system from capturing the dynamic impact of node inclination changes on the concrete softening coefficient and compressive strength, delaying necessary model adjustments and reducing the reliability of the overall shear performance assessment.

[0014] After introducing the basic concept of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0015] Example 1: Please see Figure 1 As shown, a method for calculating the shear bearing capacity of seawater-sand concrete beam-column joints includes: Obtain the component cross-sectional dimensions, uniaxial compressive strength of seawater sand concrete, material brittleness degradation factor, helix diameter, helix pitch, shear reference value of multi-helix skeleton, column end axial force, column end bending moment, and column end shear force.

[0016] In this embodiment of the invention, the current loading condition data of the structural design drawing database and the structural finite element analysis model are first read, and the cross-sectional width and cross-sectional height of the node components are extracted as the cross-sectional dimension parameters of the components. At the same time, the spiral diameter and pitch of the multi-spiral steel bars configured in the core area of ​​the node are obtained. Furthermore, the longitudinal column end axial force, column end bending moment and column end shear force acting on the upper and lower column end boundaries of the node are extracted synchronously from the data feedback link of the finite element analysis model. Their physical dimensions are converted into Newton, Newton multiplied by millimeter and Newton, respectively.

[0017] Next, regarding the definition of special material properties, measured data from material mix design tests were retrieved to extract the uniaxial compressive strength and splitting tensile strength of seawater sand concrete. Both are expressed in megapascals (Newtons per square millimeter). Given that seawater sand inevitably contains shell fragments and chloride ions interfere with the microscopic crystallization process of cement hydrates, this type of concrete exhibits early brittle fracture characteristics under complex stresses, differing from ordinary concrete. In this embodiment, a material brittleness degradation factor is used. The calculation formula is set as follows:

[0018] in the formula The uniaxial compressive strength of seawater sand concrete. The splitting tensile strength is the tensile strength; dividing the two yields the compressive-tensile ratio. and These represent the mass of seashells and the total mass of sea sand in the aggregate mix, both in kilograms. The preset benchmark brittleness constant is determined by the compressive-tensile ratio-brittleness calibration test of standard cement mortar without aggregate. The preset compression-tension ratio sensitivity coefficient can be obtained by regressing the fracture energy decay curves of seawater sand concrete under different compression-tension ratios, reflecting the nonlinear embrittlement characteristics caused by the weak transition zone of the aggregate interface. The impurity / defect amplification factor has a default value of 2.0; it is calibrated by microscopic image analysis based on the accelerating effect of shell content and chloride ion concentration in sea sand on the density of early-stage microcracks in concrete. The constant 10 is an empirical normalization factor derived from the compressive-tensile ratio of ordinary concrete. The median value of the typical range is rounded up. This constant can be adjusted based on the test data of seawater sand concrete. If no test data is available, take 10.

[0019] Subsequently, the shear benchmark value of the multi-helix skeleton was calculated. The calculation formula is established as follows: ; in The total number of spiral columns arranged in parallel within the node core area; The cross-sectional area of ​​a single steel bar in the j-th spiral skeleton is calculated based on the measured spiral diameter and is expressed in square millimeters. The yield strength of the extracted helical skeleton is expressed in Newtons per square millimeter. The effective height of the cross-section is calculated by subtracting the thickness of the protective layer from the cross-section height, and the unit is millimeters. The initial fixed crack is assumed to have an inclination angle, which is usually taken as 45 degrees based on experience; s is the pitch in millimeters.

[0020] Effective height of cross section The calculation formula is h is the height of the component section. The thickness of the concrete protective layer is determined in advance based on the structural design drawings or specifications.

[0021] The dynamic axial compression ratio and the depth of the concrete compression zone are calculated by combining the component cross-sectional dimensions, column end axial force, and column end bending moment, including: The nominal cross-sectional area is calculated by extracting the cross-sectional width and height from the component's cross-sectional dimensions and multiplying the cross-sectional width and height. The reference value of axial compressive bearing capacity is determined by multiplying the nominal cross-sectional area by the uniaxial compressive strength of seawater sand concrete, and the dynamic axial compression ratio is generated by dividing the axial force at the column end by the reference value of axial compressive bearing capacity. The initial eccentricity of the section is calculated by dividing the column end bending moment by the column end axial force, and the eccentric compression influence factor is extracted by dividing the section height by the initial eccentricity of the section. The eccentric compression influence factor is multiplied by the dynamic axial compression ratio to obtain the equivalent eccentric compression ratio. The equivalent eccentric compression ratio is then multiplied by the section height to define the depth of the concrete compression zone.

[0022] The geometric endpoints of the main inclined compression member are located at the point of application of the resultant force at the depth of the concrete compression zone to generate floating node coordinates. The initial compression member inclination angle and the initial effective width of the compression member are extracted based on the floating node coordinates.

[0023] Preferably, the geometric endpoints of the main inclined compression member are positioned at the point of application of the resultant force at the depth of the concrete compression zone to generate floating node coordinates. Based on these floating node coordinates, the initial compression member inclination angle and the initial effective width of the compression member are extracted, including: The offset of the point of application of the resultant force is calculated by dividing the depth of the concrete compression zone by a preset proportional coefficient. With the center of the component section as the origin of the coordinate system, the offset of the point of application of the resultant force is mapped to the beam-column intersection boundary to form the coordinates of the first floating node and the coordinates of the second floating node. Connect the coordinates of the first floating node and the coordinates of the second floating node to generate a geometric line, calculate the angle between the geometric line and the horizontal axis and extract it as the initial column inclination angle; The projection distance between the coordinates of the first floating node and the coordinates of the second floating node in the direction perpendicular to the initial column inclination angle is calculated as the effective width of the initial column.

[0024] In this embodiment of the invention, the cross-sectional width and height are extracted from the component's cross-sectional dimensions, and the nominal cross-sectional area is obtained by multiplying them by a planar scalar. Then, the nominal cross-sectional area is multiplied by the obtained uniaxial compressive strength of seawater sand concrete (in Newtons per square millimeter) to determine the reference value of the axial compressive bearing capacity of the cross-section, its dimension converted to Newtons. Next, the extracted column-end axial force (in Newtons) is divided by the reference value of the axial compressive bearing capacity to generate the dimensionless dynamic axial compression ratio n. To accurately quantify the nonlinear compression effect of bending moment on the depth of the compression zone, the system divides the extracted column-end bending moment (in Newtons per millimeter) by the column-end axial force to obtain the initial eccentricity of the cross-section, characterizing the deviation of the force from the centroid position, with the unit after cancellation being millimeters. The cross-sectional height is then divided by the initial eccentricity to extract the eccentric compression influence factor.

[0025] Based on the above parameters, the eccentric compression influence factor is multiplied by the dynamic axial compression ratio and fused into a dimensionless equivalent eccentric compression ratio. Then, it is multiplied by the section height to define the depth of the concrete compression zone under the current working condition. After determining the quantitative data of the compression zone depth, the geometric endpoints of the main inclined compression members are positioned at the point of application of the resultant force within the concrete compression zone depth to generate floating node coordinates. From these coordinates, the initial compression member inclination angle and effective width are extracted. This process first divides the concrete compression zone depth by a preset scaling factor to calculate the offset of the point of application of the resultant force, in millimeters. The preset scaling factor is a dimensionless geometric constant characterizing the stress block distribution in the plastic compression zone of seawater sand concrete, typically set to an adjustable range of 1.8 to 2.2. Next, a local two-dimensional coordinate system is established with the center of the core section of the member as the origin. The offset of the point of application of the resultant force is then calculated. Spatial mapping is performed on the beam-column intersection boundary to lock the coordinates of the first floating node representing the mechanical transmission inlet and outlet of the main diagonal compression member. Second floating node coordinates .

[0026] Then, in virtual space, the coordinates of the first floating node and the second floating node are connected to generate a geometric line, and the arctangent function is called to calculate the absolute angle between the geometric line and the horizontal reference axis. It is directly extracted as the initial column tilt angle. The unit is radians. Finally, the system uses the projected width to solve the model. The projected distance between the coordinates of the first floating node and the coordinates of the second floating node in the direction perpendicular to the initial column inclination angle is calculated as the effective width of the initial column. In the formula and The base depths represent the local pressure zones on the boundaries of the first and second floating nodes, respectively, in millimeters.

[0027] The initial column tilt angle and initial effective column width are used as the current column tilt angle and current effective column width in the topology optimization loop. The topology optimization loop includes: Extract the transverse expansion surface orthogonal to the current column inclination angle, calculate the equivalent projected stirrup ratio using the helix diameter and pitch, and generate the lateral passive restraint compressive stress, including: Establish a three-dimensional spatial mesh model of the node core area, introduce the current column inclination angle into the three-dimensional spatial mesh model and generate the corresponding normal tangent as the lateral expansion surface; Extract the solid section where the transverse expansion surface intersects with the multi-helix skeleton, and count the total area of ​​the cut reinforcing bars within the solid section; The influence area of ​​a single turn of the spiral is calculated by multiplying the spiral diameter by the spiral pitch. The reference stirrup ratio is generated by dividing the total area of ​​the cut steel bars by the influence area of ​​a single turn of the spiral. Extract the spatial angle of the multi-helix skeleton within the transverse expansion plane and calculate the square value of the direction cosine of the spatial angle. Multiply the square value of the direction cosine by the reference hoop ratio to obtain the equivalent projected hoop ratio.

[0028] Preferably, the method further includes extracting the transverse expansion surface orthogonal to the current column inclination angle, calculating the equivalent projected stirrup ratio using the helix diameter and pitch, and generating the lateral passive restraint compressive stress. Obtain the yield strength of the multi-helix skeleton; The effective core area size is obtained by extracting the cross-sectional width and height within the transverse expansion surface and performing harmonic averaging. The nominal constraint stress is obtained by multiplying the equivalent projected hoop ratio by the yield strength. Lateral passive compressive stress is generated by compensating for the nominal constraint stress with cross-sectional size effect using the effective core area size.

[0029] In this embodiment of the invention, the initial column inclination angle and the initial effective column width are assigned to the current column inclination angle and the current effective column width, respectively, thereby triggering a topology optimization loop. At the beginning of the loop, to accurately capture the spatial stress state of seawater-sand concrete during compressive expansion, the system establishes a three-dimensional spatial mesh model of the node core area based on the three-dimensional coordinate point set of the node design drawings in the background. The current column inclination angle is introduced into this three-dimensional spatial mesh model, and a corresponding normal tangent is generated along the principal tensile stress direction perpendicular to the current column inclination angle. This normal tangent is defined as the transverse expansion surface, thus simulating the real physical fracture surface of micro-cracks opening inside the concrete. Subsequently, the system uses the spatial Boolean intersection algorithm in computer graphics to extract the solid cross-section where the transverse expansion surface intersects with the pre-configured multi-helix skeleton, and counts the total area of ​​all cut reinforcing bars passing through this solid cross-section. Simultaneously, retrieve the spiral diameter obtained from the front end. And the pitch s, through the planar scalar multiplication formula The influence area of ​​a single spiral was calculated. ; cut the total area of ​​the reinforcing bars Divide by the area of ​​influence of a single spiral Generate the benchmark stirrup ratio .

[0030] Considering that the complex multi-helix mesh is distributed in three-dimensional nonlinear winding in space, not all reinforcement bars can provide full orthogonal normal constraint force. Therefore, the system further extracts the spatial angle of the multi-helix skeleton in the transverse expansion plane. And calculate the square of the direction cosine of the included angle in this space. Based on the spatial mechanics projection tensor transformation logic, the equivalent projected hoisting ratio is derived by multiplying the squared value of the direction cosine with the reference hoisting ratio and integrating. .

[0031] Spatial angle Defined as: the minimum angle between the tangent direction of the spiral reinforcement and the normal direction of the expansion surface at the intersection of the transverse expansion surface and the multi-spiral skeleton. When the spiral reinforcement intersects the expansion surface perpendicularly, =0; when parallel =90°.

[0032] After obtaining the equivalent projected hoop ratio, the system retrieves the yield strength of the multi-helix skeleton. The unit is Newtons per square millimeter. Multiplying this by the equivalent projected hoop ratio as a scalar yields the theoretical nominal constraint stress. Its dimension remains at Newtons per square millimeter following the yield strength. However, real concrete material exhibits a significant internal stress arching effect when constrained by a mesh, meaning that there are micromechanical dead zones in the concrete area between the stirrups that cannot be effectively constrained. Therefore, the cross-sectional width within the transverse expansion plane is extracted systematically. and cross-sectional height All units are millimeters, obtained through a harmonic mean variant formula. The effective core area size was calculated. Therefore, the system introduces a cross-sectional size effect compensation function. In the formula The pre-defined arch effect expansion coefficient is a dimensionless value used to characterize the degree of interference of different aggregate particle sizes on the micro-stress transmission path. Given that seawater sand contains shell fragments which can easily lead to stress concentration and local early slippage, it is recommended to set it to an adjustable range of 1.05 to 1.15. This is derived from regression analysis using finite element parameters, based on the ratio of the reinforcement cage spacing to the core area size. As the ratio of the pitch to the effective core area size increases, the arching effect intensifies. Take the larger value.

[0033] Finally, the cross-sectional size effect compensation for the nominal constraint stress is performed using the effective core area size, by calling the formula. Generate lateral passive constraint compressive stress The unit is always Newtons per square millimeter.

[0034] Calculate the lateral principal tensile strain based on the current column inclination angle, including: Obtain the shear deformation angle and longitudinal compressive strain of the node core region; Divide the shear deformation angle by a constant 2 to obtain the average shear strain; Based on the Mohr strain circle theory, a strain transformation matrix is ​​constructed by combining the average shear strain, longitudinal compressive strain and the current column inclination angle. The eigenvalues ​​of the strain transformation matrix in the direction perpendicular to the current column inclination angle are solved, and the absolute values ​​of the eigenvalues ​​are extracted as the transverse principal tensile strain.

[0035] In this embodiment of the invention, the shear deformation angle, which characterizes the overall tangential displacement of the structure, is obtained in real time by pre-setting a fiber optic strain sensor network deployed on the surface of the component or by calling the displacement field mesh differential feedback node of the finite element analysis model. And the longitudinal compressive strain characterizing the axial compressive dissipation at the column end The raw data for these two parameters were standardized into dimensionless pure strain scalar data before entering the calculation module. The system then divides the acquired shear deformation angle by a constant 2 to accurately calculate the mean shear strain. Subsequently, based on the classical Mohr's strain circle theory, combined with the mean shear strain... Longitudinal compressive strain and current strut inclination angle A two-dimensional strain transformation matrix is ​​constructed in the background to solve for the direction perpendicular to the axis of the main diagonal column (i.e., the geometric polar angle is). The deformation characteristic extreme values ​​of the cracked surface are determined. To significantly reduce the memory and computing power overhead risks caused by frequent matrix eigenvalue decomposition in the real-time topology optimization space, the system performs mathematical dimensionality reduction on the strain transformation matrix. Utilizing the partial differential geometric boundary conditions of the plane strain compatibility, an explicit variant formula for directly solving the transverse principal tensile strain is derived: The final solution outputs the transverse principal tensile strain. .

[0036] It should be added that the horizontal normal strain in the node core area is assumed. (i.e., unrestrained or minimally deformed laterally), and shear deformation angle Much greater than longitudinal strain (Right now Then the principal tensile strain in the Mohr strain circle can be approximated as:

[0037] when hour, Ignoring higher-order minor quantities, and considering the relationship between the principal strain direction and the maximum shear strain direction in the Mohr's circle, we can obtain:

[0038] This formula applies to the inclination angle of the diagonal compression bar. near Furthermore, it exhibits sufficient accuracy when shear deformation dominates. For seawater and sea sand concrete beam-column joints, the shear deformation in the core area is typically much greater than the axial compressive deformation, thus the principle of the explicit variant formula applies.

[0039] A composite softening coefficient is generated by combining the transverse principal tensile strain, lateral passive confinement compressive stress, and material brittleness degradation factor. Multiplying this composite softening coefficient by the uniaxial compressive strength of seawater sand concrete yields the current effective compressive strength, including: The relative constraint stiffness is generated by dividing the lateral passive confinement compressive stress by the uniaxial compressive strength of the seawater sand concrete. The brittle amplified tensile strain is calculated by multiplying the transverse principal tensile strain by the material brittleness degradation factor. A softening attenuation function is constructed with a preset benchmark softening constant as the numerator and the nonlinear ratio of brittle amplified tensile strain to relative constraint stiffness as the denominator. The magnitude of the softening attenuation function increases monotonically with the increase of relative constraint stiffness and decreases monotonically with the increase of brittle amplified tensile strain. The output of the softening attenuation function is extracted as a composite softening coefficient. The composite softening coefficient is then multiplied by the uniaxial compressive strength of seawater sand concrete to obtain the current effective compressive strength.

[0040] Based on the current column inclination angle, current effective column width, and current effective compressive strength, the nodal force imbalance residual vector and the total strain energy in the core area are extracted. The nodal force imbalance residual vector and the total strain energy in the core area are then weighted and summed to generate the objective function value, including: Multiply the current effective compressive strength by the current effective width and cross-sectional width of the compression member to obtain the internal force of the main diagonal compression member; The internal forces of the main diagonal compression member are decomposed along the horizontal and vertical directions, and the difference between them and the column end axial force and column end shear force is calculated to obtain the horizontal and vertical residuals. The horizontal and vertical residuals are then combined to generate the nodal force unbalance residual vector. The total strain energy in the core area is calculated by dividing the square of the internal force of the main inclined column by the elastic modulus of the seawater sand concrete and multiplying it by the length of the main inclined column corresponding to the current column inclination angle.

[0041] Preferably, the method further includes extracting the nodal force imbalance residual vector and the total strain energy in the core area based on the current column inclination angle, the current effective column width, and the current effective compressive strength, and then weighted summing the nodal force imbalance residual vector and the total strain energy in the core area to generate the objective function value. The scalar residual value is obtained by calculating the Euclidean norm of the nodal force imbalance residual vector; Obtain the section height from the component's cross-sectional dimensions, and divide the total strain energy in the core area by the section height to obtain the equivalent energy force. Obtain the first preset weight coefficient and the second preset weight coefficient, multiply the first preset weight coefficient by the scalar residual value to obtain the balance penalty term, and multiply the second preset weight coefficient by the equivalent energy force to obtain the energy dissipation term. It should be added that the first and second preset weighting coefficients are selected through parameter sensitivity analysis of several typical node examples (different axial compression ratios and stirrup ratios) to form a combination of coefficients that can make the objective function converge and stabilize and minimize the error between the predicted bearing capacity and the test results.

[0042] The objective function value is generated by summing the balance penalty term and the energy dissipation term.

[0043] In this embodiment of the invention, the transverse principal tensile strain generated in conjunction with the preceding sequence is... Lateral passive restraint compressive stress and material brittleness degradation factors Generate a composite softening coefficient. The specific calculation logic is as follows: call the uniaxial compressive strength of seawater sand concrete. Lateral passive restraint compressive stress Divide by Generate the relative constraint stiffness characterizing the three-dimensional compression crowding effect. Simultaneously, the transverse principal tensile strain With material brittleness degradation factor By performing scalar multiplication, the brittle amplified tensile strain of the abrupt change property can be calculated. Based on this, the system uses a preset benchmark softening constant. Using the numerator as the numerator and the nonlinear ratio of brittle amplified tensile strain to relative constraint stiffness as the denominator, a softening attenuation function is constructed, whose formula evolves as follows:

[0044] In the formula The ideal strength retention rate of concrete in its initial undamaged state is preset to a value range of 0.9 to 1.0, with 0.95 being the preferred value to better suit the high porosity characteristics of sea sand. is the preset crack sensitivity correction coefficient, which is a dimensionless coefficient; m is the Poisson effect expansion amplification constant, which is usually taken as 10; Indicates the composite softening coefficient; The value can be obtained by fitting the descending segment of the stress-strain curve from the axial compression test of seawater and sea sand concrete. If experimental data is unavailable, empirical values ​​can be calculated by referring to the softening coefficient of ordinary concrete. m is a theoretical derivation based on the volumetric expansion characteristics of concrete under multiaxial compression, and is taken as 50 times Poisson's ratio to amplify the inhibitory effect of lateral restraint on softening behavior. This constant is commonly found in relevant literature to be between 5 and 15.

[0045] After constitutive boundary constraints are completed, the system is based on the current column tilt angle. Current effective width of the compression bar And the currently effective compressive strength has just been obtained Extract the nodal force imbalance residual vector and the total strain energy in the core region. The system first sets the current effective compressive strength. Multiply by the current effective width of the compression bar And the cross-sectional width b, thus integrating the internal forces of the main diagonal compression members acting on the cross-section of the force transmission frame. .

[0046] Next, using the orthogonal solution mechanism of trigonometric functions, the internal forces of the main diagonal compression member are calculated. Component decomposition is performed along the horizontal and vertical directions, i.e., extraction is performed separately. and , Decompose the horizontal force and the column end shear force. By subtracting, we obtain the horizontal residual. ; Decompose the vertical force and the axial force at the end of the column. By subtracting, we obtain the vertical residual. ; The horizontal and vertical residuals are combined to generate the nodal force imbalance residual vector. .

[0047] Subsequently, the system calculates the total strain energy U in the core region based on the principle of minimum energy consumption in solid mechanics. .

[0048] Finally, the two-dimensional L2 norm of the nodal force imbalance residual vector R is obtained by following the Euclidean norm rule. scalar residual values ​​are obtained. .

[0049] Obtain the first preset weight coefficient, the second preset weight coefficient, and the section height in the component's cross-sectional dimensions; multiply the first preset weight coefficient by the scalar residual value to obtain the balance penalty term; multiply the second preset weight coefficient by the total strain energy of the core area and then divide by the section height to obtain the energy dissipation force term; and use the summation operator to merge and superimpose the balance penalty term and the energy dissipation term to generate the objective function value.

[0050] If the objective function value is greater than or equal to the preset convergence threshold, update the current column tilt angle and the current effective width of the column and continue to execute the topology optimization loop; If the objective function value is less than the preset convergence threshold, the loop is exited and the current column tilt angle and current effective compressive strength are locked as the optimal column tilt angle and optimal compressive strength. The shear contribution of the main inclined compression member concrete is calculated using the optimal compression member inclination angle and optimal compressive strength. This shear contribution is then added to the shear reference value of the multi-helix skeleton to generate and output the total shear capacity, including: The current effective width of the compression member when the loop is exited is obtained as the optimal compression member width. The optimal compressive strength is multiplied by the optimal compression member width and the cross-sectional width to obtain the optimal compression member compressive bearing capacity. The cosine value of multiplying the optimal compressive bearing capacity of the compression member by the optimal inclination angle of the compression member is used to extract the shear contribution value of the concrete of the main inclined compression member; The total shear capacity is calculated by scalar addition of the shear contribution value of the main inclined compression member concrete and the shear benchmark value of the multi-helix skeleton. The total shear capacity is output to the component bearing capacity assessment terminal.

[0051] In this embodiment of the invention, the objective function value is compared with a preset convergence threshold by magnitude; wherein, the preset convergence threshold is a physical constant characterizing the maximum allowable mechanical imbalance residual of the system. In order to achieve the best balance between the computational power consumption of topology optimization of finite element mesh and the allowable error of engineering, it is usually set to an adjustable range of 500 to 2000 Newtons.

[0052] If the objective function value is greater than or equal to the preset convergence threshold, it is determined that the virtual geometric boundary of the current inclined column has not yet formed a minimum energy dissipation equilibrium state with the external load. At this time, the system refuses to execute the output command, and calculates the tilt angle correction step size and width correction step size based on the residual feedback, thereby updating the current column tilt angle and the current column effective width, forcing the system state to roll back and continue to execute the next round of topology optimization loop; Conversely, if the objective function value is strictly less than the preset convergence threshold, it is determined that the compression-shear force transmission skeleton inside the core area has completely conformed to the actual physical fracture surface. The system immediately sends an interrupt signal to jump out of the optimization loop, and locks and extracts the current column inclination angle, current effective compressive strength, and current effective column width at the moment of loop termination as the optimal column inclination angle. Optimal compressive strength and optimal compression bar width After successfully locking the mechanical boundary, the component cross-sectional width b obtained during the front-end initialization phase is retrieved, and the result is obtained using a ternary scalar multiplication variation formula. Find the optimal compressive bearing capacity of the compression member .

[0053] Next, we introduce the spatial vector projection formula. The shear contribution value of the main inclined column is extracted by multiplying the optimal compressive bearing capacity of the column by the cosine of the optimal column inclination angle. Furthermore, the system retrieves the shear resistance benchmark value of the multi-helix skeleton. This is compared with the concrete shear contribution value of the main inclined compression member that was just extracted. Perform linear scalar addition operations using the summation formula. The total shear bearing capacity of the node core area under complex working conditions was calculated. Finally, the total shear capacity is output to an external component bearing capacity assessment terminal.

[0054] It should be noted that the interval and threshold sizes are set for ease of comparison. The size of the threshold depends on the amount of sample data and the base number set by those skilled in the art for each set of sample data, as long as it does not affect the proportional relationship between the parameter and the quantized value. Furthermore, the above formulas are all dimensionless calculations, and the formulas are derived from software simulations using a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0055] It should be understood that in the various embodiments of this application, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0056] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

[0057] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the shear bearing capacity of seawater-sand concrete beam-column joints, characterized in that, include: Obtain the component cross-sectional dimensions, uniaxial compressive strength of seawater sand concrete, material brittleness degradation factor, helix diameter, helix pitch, shear reference value of multi-helix skeleton, column end axial force, column end bending moment, and column end shear force; The dynamic axial compression ratio and the depth of the concrete compression zone are calculated by combining the component cross-sectional dimensions, column end axial force, and column end bending moment. The geometric endpoints of the main inclined compression member are located at the point of application of the resultant force at the depth of the concrete compression zone to generate floating node coordinates. The initial compression member inclination angle and the initial effective width of the compression member are extracted based on the floating node coordinates. The initial column tilt angle and initial effective column width are used as the current column tilt angle and current effective column width in the topology optimization loop. The topology optimization loop includes: Extract the transverse expansion surface orthogonal to the current column inclination angle, calculate the equivalent projected stirrup ratio using the helix diameter and pitch, and generate the lateral passive constraint compressive stress; Calculate the lateral principal tensile strain based on the current column inclination angle; A composite softening coefficient is generated by combining transverse principal tensile strain, lateral passive confinement compressive stress, and material brittleness degradation factor. The current effective compressive strength is obtained by multiplying the composite softening coefficient by the uniaxial compressive strength of seawater sand concrete. Based on the current column inclination angle, current effective column width, and current effective compressive strength, extract the nodal force imbalance residual vector and the total strain energy in the core area, and then weight and sum the nodal force imbalance residual vector and the total strain energy in the core area to generate the objective function value; If the objective function value is greater than or equal to the preset convergence threshold, update the current column tilt angle and the current effective width of the column and continue to execute the topology optimization loop; If the objective function value is less than the preset convergence threshold, the loop is exited and the current column tilt angle and current effective compressive strength are locked as the optimal column tilt angle and optimal compressive strength. The shear contribution value of the main inclined compression member concrete is calculated using the optimal compression member inclination angle and optimal compressive strength. The shear contribution value of the main inclined compression member concrete is added to the shear reference value of the multi-helix skeleton to generate the total shear bearing capacity and output it.

2. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 1, characterized in that, The dynamic axial compression ratio and the depth of the concrete compression zone are calculated by combining the component cross-sectional dimensions, column end axial force, and column end bending moment, including: The nominal cross-sectional area is calculated by extracting the cross-sectional width and height from the component's cross-sectional dimensions and multiplying the cross-sectional width and height. The reference value of axial compressive bearing capacity is determined by multiplying the nominal cross-sectional area by the uniaxial compressive strength of seawater sand concrete, and the dynamic axial compression ratio is generated by dividing the axial force at the column end by the reference value of axial compressive bearing capacity. The initial eccentricity of the section is calculated by dividing the column end bending moment by the column end axial force, and the eccentric compression influence factor is extracted by dividing the section height by the initial eccentricity of the section. The eccentric compression influence factor is multiplied by the dynamic axial compression ratio to obtain the equivalent eccentric compression ratio. The equivalent eccentric compression ratio is then multiplied by the section height to define the depth of the concrete compression zone.

3. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 2, characterized in that, The geometric endpoints of the main inclined compression member are located at the point of application of the resultant force at the depth of the concrete compression zone to generate floating node coordinates. Based on the floating node coordinates, the initial compression member inclination angle and the initial effective width of the compression member are extracted, including: The offset of the point of application of the resultant force is calculated by dividing the depth of the concrete compression zone by a preset proportional coefficient. With the center of the component section as the origin of the coordinate system, the offset of the point of application of the resultant force is mapped to the beam-column intersection boundary to form the coordinates of the first floating node and the coordinates of the second floating node. Connect the coordinates of the first floating node and the coordinates of the second floating node to generate a geometric line, calculate the angle between the geometric line and the horizontal axis and extract it as the initial column inclination angle; The projection distance between the coordinates of the first floating node and the coordinates of the second floating node in the direction perpendicular to the initial column inclination angle is calculated as the effective width of the initial column.

4. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 3, characterized in that, Extract the transverse expansion surface orthogonal to the current column inclination angle, calculate the equivalent projected stirrup ratio using the helix diameter and pitch, and generate the lateral passive restraint compressive stress, including: Establish a three-dimensional spatial mesh model of the node core area, introduce the current column inclination angle into the three-dimensional spatial mesh model and generate the corresponding normal tangent as the lateral expansion surface; Extract the solid section where the transverse expansion surface intersects with the multi-helix skeleton, and count the total area of ​​the cut reinforcing bars within the solid section; The influence area of ​​a single turn of the spiral is calculated by multiplying the spiral diameter by the spiral pitch. The reference stirrup ratio is generated by dividing the total area of ​​the cut steel bars by the influence area of ​​a single turn of the spiral. Extract the spatial angle of the multi-helix skeleton within the transverse expansion plane and calculate the square value of the direction cosine of the spatial angle. Multiply the square value of the direction cosine by the reference hoop ratio to obtain the equivalent projected hoop ratio.

5. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 4, characterized in that, Extracting the transverse expansion surface orthogonal to the current column inclination angle, calculating the equivalent projected stirrup ratio using the helix diameter and pitch, and generating lateral passive restraint compressive stress, also includes: Obtain the yield strength of the multi-helix skeleton; The effective core area size is obtained by extracting the cross-sectional width and height within the transverse expansion surface and performing harmonic averaging. The nominal constraint stress is obtained by multiplying the equivalent projected hoop ratio by the yield strength. Lateral passive compressive stress is generated by compensating for the nominal constraint stress with cross-sectional size effect using the effective core area size.

6. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 5, characterized in that, Calculate the lateral principal tensile strain based on the current column inclination angle, including: Obtain the shear deformation angle and longitudinal compressive strain of the node core region; Divide the shear deformation angle by a constant 2 to obtain the average shear strain; Based on the Mohr strain circle theory, a strain transformation matrix is ​​constructed by combining the average shear strain, longitudinal compressive strain and the current column inclination angle. The eigenvalues ​​of the strain transformation matrix in the direction perpendicular to the current column inclination angle are solved, and the absolute values ​​of the eigenvalues ​​are extracted as the transverse principal tensile strain.

7. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 6, characterized in that, A composite softening coefficient is generated by combining the transverse principal tensile strain, lateral passive confinement compressive stress, and material brittleness degradation factor. Multiplying this composite softening coefficient by the uniaxial compressive strength of seawater sand concrete yields the current effective compressive strength, including: The relative constraint stiffness is generated by dividing the lateral passive confinement compressive stress by the uniaxial compressive strength of the seawater sand concrete. The brittle amplified tensile strain is calculated by multiplying the transverse principal tensile strain by the material brittleness degradation factor. A softening attenuation function is constructed with a preset benchmark softening constant as the numerator and the nonlinear ratio of brittle amplified tensile strain to relative constraint stiffness as the denominator. The magnitude of the softening attenuation function increases monotonically with the increase of relative constraint stiffness and decreases monotonically with the increase of brittle amplified tensile strain. The output of the softening attenuation function is extracted as a composite softening coefficient. The composite softening coefficient is then multiplied by the uniaxial compressive strength of seawater sand concrete to obtain the current effective compressive strength.

8. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 7, characterized in that, Based on the current column inclination angle, current effective column width, and current effective compressive strength, the nodal force imbalance residual vector and the total strain energy in the core area are extracted. The nodal force imbalance residual vector and the total strain energy in the core area are then weighted and summed to generate the objective function value, including: Multiply the current effective compressive strength by the current effective width and cross-sectional width of the compression member to obtain the internal force of the main diagonal compression member; The internal forces of the main diagonal compression member are decomposed along the horizontal and vertical directions, and the difference between them and the column end axial force and column end shear force is calculated to obtain the horizontal and vertical residuals. The horizontal and vertical residuals are then combined to generate the nodal force unbalance residual vector. The total strain energy in the core area is calculated by dividing the square of the internal force of the main inclined column by the elastic modulus of the seawater sand concrete and multiplying it by the length of the main inclined column corresponding to the current column inclination angle.

9. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 8, characterized in that, Based on the current column inclination angle, current effective column width, and current effective compressive strength, the nodal force imbalance residual vector and the total strain energy in the core area are extracted. The nodal force imbalance residual vector and the total strain energy in the core area are then weighted and summed to generate the objective function value. This also includes: The scalar residual value is obtained by calculating the Euclidean norm of the nodal force imbalance residual vector; Obtain the section height from the component's cross-sectional dimensions, and divide the total strain energy in the core area by the section height to obtain the equivalent energy force. Obtain the first preset weight coefficient and the second preset weight coefficient, multiply the first preset weight coefficient by the scalar residual value to obtain the balance penalty term, and multiply the second preset weight coefficient by the equivalent energy force to obtain the energy dissipation term. The objective function value is generated by summing the balance penalty term and the energy dissipation term.

10. The method for calculating the shear bearing capacity of seawater sand concrete beam-column joints as described in claim 9, characterized in that, The shear contribution of the main inclined compression member concrete is calculated using the optimal compression member inclination angle and optimal compressive strength. This shear contribution is then added to the shear reference value of the multi-helix skeleton to generate and output the total shear capacity, including: The current effective width of the compression member when the loop is exited is obtained as the optimal compression member width. The optimal compressive strength is multiplied by the optimal compression member width and the cross-sectional width to obtain the optimal compression member compressive bearing capacity. The cosine value of multiplying the optimal compressive bearing capacity of the compression member by the optimal inclination angle of the compression member is used to extract the shear contribution value of the concrete of the main inclined compression member; The total shear capacity is calculated by scalar addition of the shear contribution value of the main inclined compression member concrete and the shear benchmark value of the multi-helix skeleton.

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