Construction method and system of four-fold line restoring force model of beam-column joint and storage medium

Abstract

The application discloses a beam-column joint four-fold line restoring force model construction method and system, and a storage medium. The method comprises the following steps: determining basic parameters; calculating characteristic point parameters based on the basic parameters and a static skeleton curve characteristic point parameter calculation formula; calculating the strain rate required in each loading stage in a loading system; performing material mechanics performance conversion on the characteristic point parameters by using a material dynamic increase coefficient calculated by the strain rate, generating material dynamic mechanics performance indexes, introducing the material dynamic mechanics indexes into the static skeleton curve characteristic point parameter calculation formula to generate a dynamic skeleton curve characteristic point calculation formula; equivalently converting variable axial force of the beam-column joint into fixed axial force, substituting the fixed axial force into the dynamic skeleton curve characteristic point calculation formula to generate a symmetrical skeleton curve; performing asymmetry correction on characteristic points of the symmetrical skeleton curve to generate an asymmetrical skeleton curve; and based on the asymmetrical skeleton curve, calculating loading and unloading stiffness and correcting the loading and unloading stiffness by using a damage index to form a pinch effect, and drawing a multi-linear hysteretic curve.

Description

Technical Field

[0001] This invention relates to the field of beam-column joint restoring force model technology, and in particular to a method, system and storage medium for constructing a four-segmented restoring force model of a beam-column joint considering dynamic loads with varying rates and axial forces. Background Technology

[0002] In reinforced concrete frame structures, beam-column joints are important components. When subjected to external loads, beam-column joints are in a state of combined shear and compression stress, often becoming the weakest part of the structure and extremely prone to damage and failure.

[0003] Under seismic loading, beam-column joints are subjected to complex dynamic loads with varying rates and axial forces due to the multidimensionality, randomness, and inherent irregularities of seismic motion. Existing research indicates that under dynamic loads, the load-bearing capacity and energy dissipation capacity of beam-column joints gradually increase, while strength and stiffness degradation intensifies and ductility decreases. Furthermore, the short duration and highly dynamic characteristics of dynamic loads affect the failure mechanism of beam-column joints, making them more brittle. This also leads to reduced deformation performance and increased cyclic damage rate, resulting in current code provisions being deemed unsafe. Dynamic loads with varying rates and axial forces are a significant cause of damage and failure in beam-column joints.

[0004] However, there is currently no theoretical summary or specific construction method for restoring force models applicable to the dynamic seismic performance analysis of beam-column joints under varying rates and axial forces. Most existing restoring force models are based on quasi-static studies and are fitted using corresponding experimental results, rather than being based on the physical and mechanical characteristics of the components, thus having limited applicability. How to provide an accurate, effective, and highly applicable method for constructing restoring force models for beam-column joints under varying rates and axial forces is a problem that researchers in this field urgently need to solve. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an accurate, effective, and highly applicable method for constructing a four-segmented restoring force model for beam-column joints under variable-rate and variable-axial-force conditions.

[0006] To achieve the above objectives, the present invention provides a method for constructing a four-segment restoring force model of a beam-column joint, comprising the following steps:

[0007] Determine the basic parameters, which include the geometric dimensions, reinforcement information, loading regime, static material parameters, and material constitutive model of the beam-column joint;

[0008] Based on the aforementioned basic parameters and the formula for calculating the characteristic point parameters of the static skeleton curve, the characteristic point parameters are calculated, including the cracking point, yield point, peak point, and ultimate failure point.

[0009] Calculate the strain rate required for each loading stage in the loading regime, use the material dynamic amplification factor calculated by the strain rate to convert the characteristic point parameters into material mechanical properties, generate material dynamic mechanical property index, and introduce the material dynamic mechanical property index into the calculation formula of the static skeleton curve characteristic point parameter to generate the dynamic skeleton curve characteristic point calculation formula.

[0010] The variable axial force of the beam-column joint is equivalent to a fixed axial force, and the fixed axial force is substituted into the calculation formula of the feature point of the dynamic skeleton curve to generate a symmetrical skeleton curve.

[0011] The feature points of the symmetrical skeleton curve are modified to be asymmetric to generate an asymmetric skeleton curve.

[0012] Based on the asymmetric skeleton curve, the loading and unloading stiffness is calculated and corrected with the damage index to form a pinching effect, and a multilinear hysteresis curve is plotted.

[0013] The calculation formula based on the basic parameters and the static skeleton curve feature point parameters calculates the feature point parameters, including:

[0014] Calculate the cracking load and cracking displacement, where the formula for calculating the cracking load is as follows:

[0015]

[0016] In the formula, P cr Indicates cracking load, f ts E represents the static tensile strength of concrete. c The modulus of elasticity of concrete is represented by h; the cross-sectional height is represented by x. cr This represents the height of the compression zone of the cross-section at the time of cracking, and x cr The equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint when it is in a critical state of impending cracking is obtained by combining the formulas. i This represents the distance from the strip of concrete to the central axis; a′ s This represents the distance from the point of application of the resultant force of the compressed steel reinforcement to the edge of the cross section; a s Indicates the distance from the point of application of the resultant force of the tensile reinforcement to the edge of the cross section; A s A′ represents the cross-sectional area of ​​the tensile reinforcement. s σ represents the cross-sectional area of ​​the compressed reinforcing steel; c (ε ci ) represents the strip concrete stress, determined based on the constitutive model; E s b represents the elastic modulus of the steel reinforcement; b represents the cross-sectional width; L b Indicates the calculated length of the beam end;

[0017] The formula for calculating crack displacement is as follows:

[0018]

[0019] In the formula, ⊿ cr Indicates the crack displacement, φ cr Indicates crack curvature; d b f is the diameter of the longitudinal reinforcement; ys The static yield strength of the steel reinforcement;

[0020] Calculate the yield load and yield displacement, where:

[0021] The formula for calculating yield load is as follows:

[0022]

[0023] In the formula, P y Indicates yield load, x y This represents the height of the compression zone in the cross-section when the steel reinforcement yields, and x y The equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint at the first yielding of the steel reinforcement in the compression zone is obtained by combining the formulas.

[0024] The formula for calculating the yield displacement is as follows:

[0025]

[0026] In the formula, ⊿ y φ represents the yield displacement. y Indicates the yield curvature;

[0027] Calculate the peak load and peak displacement, where:

[0028] The formula for calculating peak load is as follows:

[0029]

[0030] In the formula, P m Indicates peak load. f us x represents the static ultimate strength of the steel reinforcement; m This represents the height of the compression zone of the section under peak load, and x m The equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint under the maximum load is obtained by combining the formulas.

[0031] The formula for calculating the peak displacement is as follows:

[0032]

[0033] In the formula, ⊿m Indicates peak displacement. h0 represents the effective height of the cross section; μ s μ′ s Indicates the reinforcement ratio of tensile and compressive steel bars; f ys f′ ys Indicates the static yield strength of tensile and compressive reinforcement; N represents the column end pressure; f cs Indicates the static compressive strength of concrete;

[0034] Calculate the failure load and failure displacement, where:

[0035] The formula for calculating the failure load is as follows:

[0036] P u =0.85·P m ,

[0037] In the formula, P u Indicates the destructive load;

[0038] The formula for calculating the failure displacement is as follows:

[0039]

[0040] In the formula, ⊿ u Indicates destructive displacement. φ u It represents the limiting curvature.

[0041] The material dynamic amplification factor includes: the dynamic amplification factor of concrete tensile strength, the dynamic amplification factor of concrete compressive strength, the dynamic amplification factor of steel yield strength, and the dynamic amplification factor of steel ultimate strength.

[0042] The strain rate includes elastic strain rate and plastic strain rate. The material dynamic amplification factor calculated using the strain rate to convert the material mechanical properties of the characteristic points includes: converting the parameters of the cracking point and the yield point using the material dynamic amplification factor calculated using the elastic strain rate; and converting the parameters of the peak point and the failure point using the material dynamic amplification factor calculated using the plastic strain rate.

[0043] In the step of converting the variable axial force of the beam-column joint into a fixed axial force, the equivalent formula is as follows:

[0044]

[0045] In the formula, N′ represents the equivalent fixed-axis force under variable-axis force loading; T represents the loading time; N(t) represents the variable-axis force loading function, which is determined by the loading regime.

[0046] The step of performing asymmetric correction on the feature points of the symmetrical skeleton curve further includes:

[0047] The relationship between load and displacement is defined as follows:

[0048] R(u,z) = αk0u + (1-α)k0z

[0049] In the formula, R(u,z) represents the load at the feature point, including cracking load, yield load, peak load and failure load; k0 represents the initial elastic stiffness; α represents the stiffness ratio after yielding; u represents the displacement at the feature point, including cracking displacement, yield displacement, peak displacement and failure displacement; z represents the shape control displacement.

[0050] The maximum value z of the shape-controlled displacement max The peak displacement is set as the value, and asymmetric correction is performed using the asymmetric control parameter δ to generate the corrected positive and negative peak displacements, as follows:

[0051]

[0052] In the formula This represents the corrected positive peak displacement. This represents the corrected negative peak displacement, where β, γ, and n represent shape control parameters; ν represents the parameter describing strength degradation, v = 1 + δ v w; w represents the energy dissipation of the skeleton curve under load. p(Δ) represents the characteristic point load function; Δ u Indicates the displacement prior to correction; δ v δ represents the strength degradation parameter; δ represents the asymmetric control parameter.

[0053] Substitute the corrected positive and negative peak displacements into the relationship between load and displacement to generate the corrected positive and negative peak loads;

[0054] Using the corrected positive and negative peak loads, the corrected loads and displacements at other feature points are calculated through stiffness calculations.

[0055] The step of calculating loading and unloading stiffness based on the asymmetric skeleton curve and correcting it with a damage index to form a pinching effect, and drawing a multilinear hysteresis curve further includes:

[0056] The unloading stiffness is calculated as follows: In the formula, K represents the unloading stiffness, K0 represents the elastic stiffness; Δ represents the component displacement; Δ i The displacement amplitude of the i-th loading level is determined based on the loading regime; a and b are coefficients related to strain rate effect and variable axial force.

[0057] The reloading stiffness is calculated as follows: In the formula, K′ represents the reload stiffness;

[0058] The damage index is calculated as follows: In the formula, Δ m Indicates peak displacement; Δ y Indicates the yield displacement; Δ u Represents the failure displacement; ∑E i Indicates the energy consumption of the skeleton curve. p(Δ) represents the characteristic point load function; Q y For yield strength, A represents the cross-sectional area at the beam end;

[0059] On the other hand, the present invention also provides a system for constructing a four-segment restoring force model of a beam-column joint, characterized in that it employs the above-mentioned method for constructing a four-segment restoring force model of a beam-column joint, comprising:

[0060] The parameter input module is used to determine the basic parameters, which include the geometric dimensions, reinforcement information, loading regime, material static parameters, and material constitutive model of the beam-column joint.

[0061] The feature point calculation module is used to calculate feature point parameters based on the basic parameters and the static skeleton curve feature point parameter calculation formula. The feature points include cracking point, yield point, peak point and ultimate failure point.

[0062] The strain rate effect coupling module is used to calculate the strain rate required for each loading stage in the loading regime, use the material dynamic amplification factor calculated by the strain rate to convert the characteristic point parameters into material mechanical properties, generate material dynamic mechanical property indexes, and introduce the material dynamic mechanical property indexes into the calculation formula of the static skeleton curve characteristic point parameters to generate the dynamic skeleton curve characteristic point calculation formula.

[0063] The variable axial force equivalent processing module is used to convert the variable axial force of the beam-column joint into a fixed axial force, and substitute the fixed axial force into the calculation formula of the feature point of the dynamic skeleton curve to generate a symmetrical skeleton curve.

[0064] An asymmetric correction module is used to perform asymmetric correction on the feature points of the symmetrical skeleton curve to generate an asymmetric skeleton curve.

[0065] The hysteresis curve generation module is used to calculate the loading and unloading stiffness based on the asymmetric skeleton curve and correct it with the damage index to form a pinching effect, and draw a multilinear hysteresis curve.

[0066] In another aspect, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method for constructing a four-segment restoring force model of a beam-column joint.

[0067] In another aspect, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described method for constructing a four-segment restoring force model of a beam-column node.

[0068] As can be seen from the above solutions, the advantages of the present invention are:

[0069] The restoring force model constructed by the four-segment restoring force model of the beam-column joint of this invention contains four characteristic points in its skeleton curve: cracking point, yield point, peak point, and ultimate failure point. It considers various deformation stages of the beam-column joint component and can accurately reflect the actual change process of the mechanical properties of the beam-column joint component. The strain rate effect is introduced into the restoring force model, which can consider the changes in the material mechanical properties caused by the change in strain rate level, and thus more accurately reflect the influence of the strain rate effect on the seismic performance of the beam-column joint component. The introduction of variable axial force into the restoring force model can analyze the changes in the seismic performance of the beam-column joint under variable axial force. The asymmetry of the restoring force model is considered, and the idea of ​​introducing asymmetry into the restoring force model under dynamic load is proposed. Attached Figure Description

[0070] Figure 1 This is a flowchart of the method for constructing the four-segment restoring force model of beam-column joints according to the present invention;

[0071] Figure 2A This is a cross-sectional view of the beam-column joint in the prior art;

[0072] Figure 2B for Figure 2A Cross-sectional view along the 1-1 direction;

[0073] Figure 2C for Figure 2A Cross-sectional view along the 2-2 direction;

[0074] Figure 3 This is a schematic diagram of the loading system in the prior art used in this invention;

[0075] Figure 4 for Figure 1 Flowchart of step S20;

[0076] Figure 5 for Figure 1 Flowchart of step S30;

[0077] Figure 6 for Figure 1Flowchart of step S50;

[0078] Figure 7 This is a schematic diagram of the hysteresis curve generated by the four-segment restoring force model construction method for beam-column joints of the present invention;

[0079] Figure 8 for Figure 1 Flowchart of step S60;

[0080] Figure 9 This is a structural diagram of the beam-column joint four-segment restoring force model construction system of the present invention;

[0081] In the attached figures, the following labels are used:

[0082] 100-Beam-column joint;

[0083] 101 - Stirrups in column section;

[0084] 102 - Stirrups in the core area of ​​node;

[0085] 103 - Stirrups in beam section;

[0086] 104 - Longitudinal reinforcement of beam section;

[0087] 105 - Longitudinal reinforcement of column section;

[0088] 200-Beam-Column Joint Four-Segment Line Restoring Force Model Construction System;

[0089] 20 - Parameter Input Module;

[0090] 21-Feature point calculation module;

[0091] 22-Strain rate effect coupling module;

[0092] 23- Variable Axis Force Equivalent Processing Module;

[0093] 24-Asymmetric correction module;

[0094] 25 - Hysteresis Curve Generation Module;

[0095] S10~S60, S200~S203, S300~S301, S500~S503, S600~S604 - Steps. Detailed Implementation

[0096] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments to further understand the purpose, solution and effect of the present invention, but it is not intended to limit the scope of protection of the appended claims.

[0097] References to "embodiment," "another embodiment," "this embodiment," etc., in the specification refer to embodiments that may include specific features, structures, or characteristics, but not every embodiment must include these specific features, structures, or characteristics. Furthermore, such expressions do not refer to the same embodiment. Moreover, when describing specific features, structures, or characteristics in conjunction with embodiments, whether or not explicitly described, it is indicated that incorporating such features, structures, or characteristics into other embodiments is within the knowledge of those skilled in the art.

[0098] The specification and subsequent claims use certain terms to refer to specific components or parts. Those skilled in the art will understand that users or manufacturers may use different names or terms to refer to the same component or part. This specification and claims do not distinguish components or parts by differences in name, but rather by differences in function. The terms "comprising" and "including" used throughout the specification and claims are open-ended and should be interpreted as "including but not limited to". Furthermore, the term "connection" here includes any direct and indirect electrical connection means. Indirect electrical connection means include connections via other means.

[0099] Figure 1 A flowchart of a method for constructing a four-segment restoring force model of a beam-column joint according to an embodiment of the present invention is provided, including:

[0100] S10: Determine basic parameters;

[0101] S20: Calculates feature point parameters based on the formula for calculating the basic parameters and the feature point parameters of the static skeleton curve;

[0102] S30: Calculate the required strain rate for each loading stage in the loading regime, use the material dynamic amplification factor calculated by the strain rate to convert the characteristic point parameters into material mechanical properties, generate material dynamic mechanical property indexes, and introduce the material dynamic mechanical indexes into the static skeleton curve characteristic point parameter calculation formula to generate the dynamic skeleton curve characteristic point calculation formula.

[0103] S40: The variable axial force of the beam-column joint is equivalent to the fixed axial force. The fixed axial force is substituted into the calculation formula of the characteristic point of the dynamic skeleton curve to generate a symmetrical skeleton curve.

[0104] S50: Perform asymmetric correction on the feature points of the symmetrical skeleton curve to generate an asymmetric skeleton curve;

[0105] S60: Based on the asymmetric skeleton curve, calculate the loading and unloading stiffness and correct it with the damage index to form a pinching effect, and draw a multilinear hysteresis curve.

[0106] In step S10:

[0107] The basic parameters include the geometric dimensions of the beam-column joint, reinforcement information, loading regime, static material parameters, and material constitutive model. Specifically, such as... Figures 2A to 2C As shown, determine the beam-column cross-sectional dimensions b×h (b represents the cross-sectional width, h represents the cross-sectional height) for beam-column node 100; calculate the beam end length L. b Reinforcement information for beams, columns, and core areas of joints; loading regime, such as... Figure 3 As shown; static mechanical property parameters of steel reinforcement and concrete, such as the elastic modulus E of concrete. c Elastic modulus E of steel bars s Static yield strength f of steel reinforcement ys static tensile strength of concrete f ts Static ultimate strength f of steel reinforcement us and the static compressive strength f of concrete cs Wait; constitutive models of reinforced concrete materials. It should be noted that Figure 2 and... Figure 3 These are merely illustrative diagrams in the prior art and are not intended to be included within the scope of protection of this invention.

[0108] The relevant calculation formulas for the constitutive model of beam-column joint materials (including steel reinforcement and concrete) are shown in equations (1) and (2) below:

[0109] Concrete constitutive model:

[0110]

[0111] In equation (1), σ c ε represents the compressive stress in concrete. c Indicates the corresponding σ c The concrete compressive strain; f′c represents the compressive strength of the concrete cylinder, taken as 79% of the compressive strength of the concrete cube; K represents the strength enhancement factor of the confined concrete. Z m This represents the slope of the strain softening segment of concrete. ε cu ρ represents the ultimate compressive strain of concrete. s Indicates the volumetric reinforcement ratio of stirrups; f yh "h" represents the yield strength of the stirrups; "h" represents the width of the core concrete zone; S h Indicates the spacing between stirrups.

[0112] Reinforced steel constitutive model:

[0113]

[0114] In equation (2), E s Indicates the elastic modulus of the steel reinforcement; f y E represents the yield strength of the reinforcing steel.st This represents the deformation modulus, with a value of 0.01E. s ;ε s ε represents the strain of the reinforcing steel. y ε represents the yield strain of the steel reinforcement; y2 This indicates the initial strain during the reinforcement phase.

[0115] In step S20:

[0116] Based on the construction of the beam-column joint and the calculation formulas for the characteristic point parameters of the proposed skeleton curve (as shown in formulas (3) to (16) below), calculate the parameter values ​​of the four characteristic points: cracking point, yield point, peak point, and ultimate failure point. The characteristic point parameters include load and displacement.

[0117] Specifically, such as Figure 4 As shown, step S20 further includes:

[0118] S200: Calculate the cracking load and cracking displacement, where:

[0119] The formulas for calculating cracking load are as follows: (3) to (5).

[0120]

[0121] In the above formula, P cr Indicates cracking load, f ts E represents the static tensile strength of concrete. c The modulus of elasticity of concrete is represented by h; the cross-sectional height is represented by x. cr The height of the compression zone at the time of cracking is represented by the formulas (i.e., formulas (3) and (4)) for the equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint when it is about to crack. i This represents the distance from the strip of concrete to the central axis; a′ s This represents the distance from the point of application of the resultant force of the compressed steel reinforcement to the edge of the cross section; a s Indicates the distance from the point of application of the resultant force of the tensile reinforcement to the edge of the cross section; A s A′ represents the cross-sectional area of ​​the tensile reinforcement. s σ represents the cross-sectional area of ​​the compressed reinforcing steel; c (ε ci ) represents the strip concrete stress, determined based on the constitutive model; E s b represents the elastic modulus of the steel reinforcement; b represents the cross-sectional width; L b This indicates the calculated length of the beam end.

[0122] The formula for calculating crack displacement is as follows (6).

[0123]

[0124] In equation (6), P represents cr Crack displacement, φ cr Indicates crack curvature; d b f is the diameter of the longitudinal reinforcement; ys This represents the static yield strength of the steel reinforcement.

[0125] S201: Calculate the yield load and yield displacement, where:

[0126] The formulas for calculating yield load are as follows: (7) to (9).

[0127]

[0128] In the above formula, x y x represents the height of the compression zone of the section when the steel bar yields. y The equations (7) and (8) are obtained by using the formulas for the equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the joint beam-column joint when the steel reinforcement in the compression zone yields for the first time.

[0129] The formula for calculating the yield displacement is as follows (10).

[0130]

[0131] In the formula, φ y Indicates the yield curvature.

[0132] Step S202: Calculate the peak load and peak displacement, where:

[0133] The formulas for calculating peak load are as follows: (11) to (13).

[0134]

[0135] In the above formula, P m Indicates peak load. f us x represents the static ultimate strength of the steel reinforcement; m Indicates the height of the compression zone of the section at peak load, x m The equations (i.e., equations (11) and (12)) are obtained by using the formulas for the equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint when it is subjected to the maximum load.

[0136] The formula for calculating the peak displacement is shown in equation (14).

[0137]

[0138] In equation (14), h0 represents the effective height of the cross section; μ s μ′ s Indicates the reinforcement ratio of tensile and compressive steel bars; fys f′ ys Indicates the static yield strength of tensile and compressive reinforcement; N represents the column end pressure; f cs It represents the static compressive strength of concrete.

[0139] S204: Calculate the failure load and failure displacement, where:

[0140] The formula for calculating the failure load is as follows (15).

[0141] P u =0.85·P m (15),

[0142] In equation (15), P u P represents the destructive load. m This represents the peak load.

[0143] The formula for calculating the failure displacement is as follows (16).

[0144]

[0145] In equation (16), ⊿ u Indicates destructive displacement. φ u It represents the limiting curvature.

[0146] In step S30:

[0147] The strain rate required for each loading stage is calculated based on the proposed strain rate calculation method. The material dynamic amplification factor (DIF) is calculated using the strain rate. The material dynamic amplification factor is used to transform the static mechanical property index of the material into the dynamic mechanical property index. The dynamic mechanical property index is introduced into the calculation formula of the characteristic point parameter of the static skeleton curve to generate the calculation formula of the characteristic point parameter of the dynamic skeleton curve.

[0148] Strain rate includes elastic strain rate and plastic strain rate, such as Figure 5 As shown, step S30 further includes:

[0149] S300: The material dynamics amplification factor calculated using elastic strain rate is used to convert the parameters of the cracking point and yield point into material mechanical properties;

[0150] S301: The material dynamics amplification factor calculated using plastic strain rate is used to convert the parameters at the peak point and failure point into material mechanical properties.

[0151] In step S300, the elastic strain rate is calculated using the following formulas (17) and (18). The material dynamic amplification factor obtained from the elastic strain rate is used for the conversion of material mechanical properties between the crack point parameter and the yield point parameter.

[0152]

[0153] In the above formula, V represents the elastic strain rate, and V represents the loading rate at the beam end, such as... Figure 3 The loading regime shown represents the rate at which the load is applied to the beam end displacement level; ε1 represents the yield strain of the steel reinforcement; PSD1 represents the beam end yield displacement Δ. y ;

[0154] In step S301, the formula for calculating the plastic strain rate is as shown in equation (19).

[0155]

[0156] In equation (9) above, Represents plastic strain rate, Δl′=l1+l2-L b ;

[0157] The formula for the transformation of dynamic mechanical properties of materials is as follows (20):

[0158] f d =DIF·f s (20),

[0159] In equation (20), f d Indicates the dynamic strength of a material (e.g., dynamic tensile strength of concrete, dynamic compressive strength of concrete, dynamic yield strength of steel reinforcement, and dynamic ultimate strength of steel reinforcement); f s It represents the static strength of the material (e.g., static tensile strength of concrete, static compressive strength of concrete, static yield strength of steel reinforcement, and static ultimate strength of steel reinforcement); DIF represents the dynamic amplification factor.

[0160] Specifically, the dynamic increase factor of materials includes: the dynamic increase factor of concrete tensile strength, the dynamic increase factor of concrete compressive strength, the dynamic increase factor of steel yield strength, and the dynamic increase factor of steel ultimate strength, and the calculation formulas are as follows: (21) to (24):

[0161] Dynamic increase factor (DIF) of concrete tensile strength ft ):

[0162]

[0163] In equation (21), f td Indicates the dynamic tensile strength of concrete; f ts Indicates the static tensile strength of concrete; The strain rate is represented by (including elastic strain rate as shown in equation (18) above and plastic strain rate as shown in equation (19) above); The value is 3×10 -6 s -1 ;f cs This represents the static compressive strength of concrete; f0 is 10 MPa.

[0164] Dynamic increase factor (DIF) of concrete compressive strength fc ):

[0165]

[0166] In equation (22), f cd Indicates the dynamic compressive strength of concrete; f cs Indicates the static compressive strength of concrete; The value is 3×10 -6 s -1 f0 takes a value of 10 MPa.

[0167] Dynamic increase factor (DIF) of steel bar yield strength fy ):

[0168]

[0169] In equation (23), f yd Indicates the dynamic yield strength of the steel reinforcement; f ys Indicates the static yield strength of the steel reinforcement; The value is 5×10 -5 s -1 .

[0170] Dynamic amplification factor (DIF) of ultimate strength of steel reinforcement fu ):

[0171]

[0172] In equation (24), f ud Indicates the dynamic ultimate strength of steel reinforcement; f us Indicates the static ultimate strength of the steel reinforcement; The value is 5×10 -5 s -1 .

[0173] In step S40:

[0174] In the step of converting the variable axial force of the beam-column joint into a fixed axial force, the equivalent formula for the variable axial force is as follows (25):

[0175]

[0176] In equation (25), N′ represents the equivalent fixed-axis force under variable-axis loading; T represents the loading time; N(t) represents the variable-axis loading function, which is obtained by means of... Figure 3 The loading system is determined.

[0177] In step S50:

[0178] like Figure 6 As shown, step S50 further includes:

[0179] S500: Define the relationship between load and displacement as follows (26):

[0180] R(u,z)=αk0u+(1-α)k0z (26),

[0181] In equation (26), R(u,z) represents the load at the characteristic point, including cracking load, yield load, peak load and failure load; k0 represents the initial elastic stiffness; α represents the stiffness ratio after yielding; u represents the displacement at the characteristic point, including cracking displacement, yield displacement, peak displacement and failure displacement; z represents the shape control displacement.

[0182] S501: Set the maximum value z of the shape control displacement. max The peak displacement is set and asymmetric correction is performed using the asymmetric control parameter δ to generate the corrected positive and negative peak displacements, as shown in equations (27) and (28) below:

[0183]

[0184] In the above formula This represents the corrected positive peak displacement. This represents the corrected negative peak displacement, where β, γ, and n represent shape control parameters; ν represents the parameter describing strength degradation, ν = 1 + δ v w; w represents the energy dissipation of the skeleton curve under load. p(Δ) represents the characteristic point load function; Δ u Indicates the displacement prior to correction; δ v δ represents the strength degradation parameter; δ represents the asymmetric control parameter.

[0185] By selecting the various control parameters mentioned above in Table 1, the corrected positive and negative peak displacements are calculated using equations (27) and (28).

[0186] Table 1. Specifications for the values ​​of each control parameter

[0187]

[0188] S502: Substitute the corrected positive and negative peak displacements into the load-displacement relationship to generate the corrected positive and negative peak loads.

[0189] S503: Utilizing modified positive and negative peak loads The loads and displacements of other feature points are calculated by stiffness calculation, as shown in equations (29) to (40).

[0190] Asymmetric cracking characteristic point parameters (including corrected cracking load and cracking displacement):

[0191]

[0192] in, This indicates the corrected positive cracking load. This represents the corrected negative cracking load. Corrected positive crack displacement, Corrected negative crack displacement.

[0193] Asymmetric yield characteristic point parameters (including corrected yield load and yield displacement):

[0194]

[0195] in, This represents the corrected positive yield load. This represents the modified negative yield load. This represents the corrected positive yield displacement. This represents the corrected negative yield displacement.

[0196] Asymmetric failure characteristic point parameters (including corrected failure load and failure displacement):

[0197]

[0198]

[0199] in, This indicates the corrected positive failure load. This indicates the corrected negative failure load. This indicates the corrected positive failure displacement. This represents the corrected negative failure displacement.

[0200] In step S60:

[0201] Based on the established asymmetric skeleton curve, the loading and unloading stiffness of the dynamic skeleton curve at each stage is calculated by considering the loading and unloading stiffness calculation formula with variable rate and variable axial force. The loading and unloading stiffness value is then corrected at the cracking load using the damage index calculation formula, thus forming an inflection point (inflection point) reflecting the pinching effect of the hysteresis curve. The calculated loading and unloading stiffness values ​​are used to plot the stiffness change curve, i.e., the hysteresis curve, as shown below. Figure 7 As shown. By Figure 7 It can be seen that the hysteresis loop of the hysteresis curve can be generated by 6 segments of broken lines, which can fit the actual shape of the hysteresis loop to the greatest extent. Furthermore, the hysteresis rule is described in 4 stages, taking into account the complete deformation process of the beam-column joint. Figure 7 In the diagram, the horizontal axis Δ represents displacement, and the vertical axis P represents load. The hysteresis rule is as follows:

[0202] (1) During the cracking stage, the hysteresis path of the beam-column joint is along the skeleton curve.

[0203] (2) Numbers 1-4 represent the hysteresis path of the beam-column joint during the yielding stage. In this stage, the hysteresis path deviates from the skeleton curve, and the loading and unloading stiffness shows significant degradation. 1→2 and 3→4 represent the unloading path, and 2→3 and 4→1 represent the reloading path. The complete hysteresis path is: 1→2→3→4→1

[0204] (3) Numbers 5-14 represent the hysteresis path of the beam-column joint during the peak stage. The loading and unloading stiffness of the hysteresis path during this stage are calculated separately with the inflection point at the cracking load (such as points 6, 8, 11 and 13) as the boundary. 5→6 and 10→11 represent the unloading path, 6→7 and 11→12 represent the unloading path after the inflection point, 7→8 and 12→13 represent the reloading path, and 8→9 and 13→14 represent the reloading path after the inflection point. The complete hysteresis path is: 5→6→7→8→9→10→11→12→13→14.

[0205] (4) During the destruction phase, the hysteresis path is similar to that during the peak phase, such as... Figure 7 As shown.

[0206] Specifically, such as Figure 8 As shown, step S60 further includes:

[0207] S600: Calculate the unloading stiffness as shown in equation (41).

[0208]

[0209] In equation (41), K represents the unloading stiffness, K0 represents the elastic stiffness; Δ represents the displacement of the beam-column joint member; Δ i Represents the displacement magnitude of the i-th loading level, based on, as... Figure 3 The loading regime shown is determined; a and b are coefficients related to strain rate effect and variable axial force, preferably... Represents the rate of change of axial compression ratio, based on, for example Figure 3 The loading regime shown is determined; The value is 10 -5 s -1 ;

[0210] S601: Calculate the reloading stiffness as shown in equation (42).

[0211]

[0212] In equation (42), K′ represents the reloading stiffness;

[0213] S602: Calculate the damage index as shown in equation (43).

[0214]

[0215] In equation (43), Δ m Indicates peak displacement; Δ y Indicates the yield displacement; Δ u Represents the failure displacement; ∑E i Indicates the energy consumption of the skeleton curve. p(Δ) represents the characteristic point load function; Q y For yield strength, A represents the cross-sectional area at the beam end.

[0216] S603: Calculate the unloading stiffness K1 after the inflection point is generated, as shown in equation (44):

[0217] K1=K·(1-D) (44),

[0218] In equation (44), D represents the damage index; K represents the unloading stiffness.

[0219] S604: Calculate the reloading stiffness K′1 after the inflection point is generated, as shown in equation (45):

[0220] K′1=K′·(1-D) (45),

[0221] In equation (45), K′1 represents the reload stiffness.

[0222] The following are system embodiments corresponding to the above method embodiments. This embodiment can be implemented in conjunction with the above embodiments. The relevant technical details mentioned in the above embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above embodiments.

[0223] like Figure 9 The figure shown is a structural schematic diagram of a beam-column joint four-fold line restoring force model construction system 200 provided in another embodiment of the present invention.

[0224] The system 200 for constructing the four-segmented restoring force model of beam-column joints includes:

[0225] The parameter input module 20 is used to determine the basic parameters, which include the geometric dimensions of the beam-column joint, reinforcement information, loading regime, material static parameters, and material constitutive model.

[0226] Feature point calculation module 21 is used to calculate feature point parameters based on the basic parameters and the static skeleton curve feature point parameter calculation formula. The feature points include cracking point, yield point, peak point and ultimate failure point.

[0227] The strain rate effect coupling module 22 is used to calculate the strain rate required for each loading stage in the loading regime. It uses the material dynamic amplification factor calculated by strain rate to convert the characteristic point parameters into material mechanical properties, generates material dynamic mechanical property index, and introduces the material dynamic mechanical index into the static skeleton curve characteristic point parameter calculation formula to generate the dynamic skeleton curve characteristic point calculation formula.

[0228] The variable axial force equivalent processing module 23 is used to convert the variable axial force of the beam-column joint into a fixed axial force, and substitute the fixed axial force into the calculation formula of the feature point of the dynamic skeleton curve to generate a symmetrical skeleton curve.

[0229] The asymmetric correction module 24 is used to perform asymmetric correction on the feature points of the symmetric skeleton curve to generate an asymmetric skeleton curve.

[0230] The hysteresis curve generation module 25 is used to calculate loading and unloading stiffness based on the asymmetric skeleton curve and correct it with the damage index to form a pinching effect, and draw a multilinear hysteresis curve.

[0231] Furthermore, those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the beam-column joint four-segment restoring force model construction system 200 can be referred to the corresponding process in the aforementioned beam-column joint four-segment restoring force model construction method embodiment, and will not be repeated here.

[0232] In another embodiment, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for constructing a four-segment restoring force model of a beam-column joint (e.g., Figure 1 The steps are shown below.

[0233] Furthermore, this invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method for constructing a four-segmented restoring force model of beam-column joints (e.g., Figure 1 The steps are shown below.

[0234] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms fall within the scope of protection of the present invention.

Claims

1. A method for constructing a four-segmented restoring force model for beam-column joints, characterized in that, Includes the following steps: Determine the basic parameters, which include the geometric dimensions, reinforcement information, loading regime, static material parameters, and material constitutive model of the beam-column joint; Based on the aforementioned basic parameters and the formula for calculating the characteristic point parameters of the static skeleton curve, the characteristic point parameters are calculated, including the cracking point, yield point, peak point, and ultimate failure point. Calculate the strain rate required for each loading stage in the loading regime, use the material dynamic amplification factor calculated by the strain rate to convert the characteristic point parameters into material mechanical properties, generate material dynamic mechanical property index, and introduce the material dynamic mechanical property index into the calculation formula of the static skeleton curve characteristic point parameter to generate the dynamic skeleton curve characteristic point calculation formula. The variable axial force of the beam-column joint is equivalent to a fixed axial force, and the fixed axial force is substituted into the calculation formula of the feature point of the dynamic skeleton curve to generate a symmetrical skeleton curve. The feature points of the symmetrical skeleton curve are modified to be asymmetric to generate an asymmetric skeleton curve. Based on the asymmetric skeleton curve, the loading and unloading stiffness is calculated and corrected with the damage index to form a pinching effect, and a multilinear hysteresis curve is plotted.

2. The method for constructing a four-segment restoring force model for beam-column joints according to claim 1, characterized in that, The calculation formula based on the basic parameters and the static skeleton curve feature point parameters calculates the feature point parameters, including: Calculate the cracking load and cracking displacement, where: The formula for calculating cracking load is as follows: In the formula, P cr Indicates cracking load. f ts E represents the static tensile strength of concrete. c The modulus of elasticity of concrete is represented by h; the cross-sectional height is represented by x. cr This represents the height of the compression zone of the cross-section at the time of cracking, and x cr The equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint when it is in a critical state of impending cracking is obtained by combining the formulas. i This represents the distance from the strip of concrete to the central axis; a′ s This represents the distance from the point of application of the resultant force of the compressed steel reinforcement to the edge of the cross section; a s Indicates the distance from the point of application of the resultant force of the tensile reinforcement to the edge of the cross section; A s A′ represents the cross-sectional area of ​​the tensile reinforcement. s σ represents the cross-sectional area of ​​the compressed reinforcing steel; c (ε ci ) represents the strip concrete stress, determined based on the constitutive model; E s b represents the elastic modulus of the steel reinforcement; b represents the cross-sectional width; L b Indicates the calculated length of the beam end; The formula for calculating crack displacement is as follows: In the formula, ⊿ cr Indicates the crack displacement, φ cr Indicates crack curvature; d b f is the diameter of the longitudinal reinforcement; ys The static yield strength of the steel reinforcement; Calculate the yield load and yield displacement, where: The formula for calculating yield load is as follows: In the formula, P y Indicates yield load, x y This represents the height of the compression zone in the cross-section when the steel reinforcement yields, and x y The equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint at the first yielding of the steel reinforcement in the compression zone is obtained by combining the formulas. The formula for calculating the yield displacement is as follows: In the formula, ⊿ y φ represents the yield displacement. y Indicates the yield curvature; Calculate the peak load and peak displacement, where: The formula for calculating peak load is as follows: In the formula, P m Indicates peak load. f us x represents the static ultimate strength of the steel reinforcement; m This represents the height of the compression zone of the section under peak load, and x m The equilibrium relationship between the internal forces and bending moments of the reinforced concrete beam at the beam-column joint under the maximum load is obtained by combining the formulas. The formula for calculating the peak displacement is as follows: In the formula, ⊿ m Indicates peak displacement. h0 represents the effective height of the cross section; μ s μ′ s Indicates the reinforcement ratio of tensile and compressive steel bars; f ys f′ ys Indicates the static yield strength of tensile and compressive reinforcement; N represents the column end pressure; f cs Indicates the static compressive strength of concrete; Calculate the failure load and failure displacement, where: The formula for calculating the failure load is as follows: P u =0.85·P m , In the formula, P u Indicates the destructive load; The formula for calculating the failure displacement is as follows: In the formula, ⊿ u Indicates destructive displacement. φ u It represents the limiting curvature.

3. The method for constructing a four-segment restoring force model for beam-column joints according to claim 1, characterized in that, The material dynamic amplification factor includes: the dynamic amplification factor of concrete tensile strength, the dynamic amplification factor of concrete compressive strength, the dynamic amplification factor of steel yield strength, and the dynamic amplification factor of steel ultimate strength.

4. The method for constructing a four-segment restoring force model for beam-column joints according to claim 1, characterized in that, The strain rate includes elastic strain rate and plastic strain rate. The conversion of the material mechanical properties of the feature point using the material dynamic amplification factor calculated using the strain rate includes: The material dynamic amplification factor calculated using the elastic strain rate is used to convert the parameters of the cracking point and the yield point into material mechanical properties. The material dynamic amplification factor calculated using the plastic strain rate is used to convert the parameters of the peak point and the failure point into material mechanical properties.

5. The method for constructing a four-segment restoring force model for beam-column joints according to claim 1, characterized in that, In the step of converting the variable axial force of the beam-column joint into a fixed axial force, the equivalent formula is as follows: In the formula, N′ represents the equivalent fixed-axis force under variable-axis force loading; T represents the loading time; N(t) represents the variable-axis force loading function, which is determined by the loading regime.

6. The method for constructing a four-segment restoring force model for beam-column joints according to claim 1, characterized in that, The step of performing asymmetric correction on the feature points of the symmetrical skeleton curve further includes: The relationship between load and displacement is defined as follows: R(u,z) = αk0u + (1-α)k0z In the formula, R(u,z) represents the load at the feature point, including cracking load, yield load, peak load and failure load; k0 represents the initial elastic stiffness; α represents the stiffness ratio after yielding; u represents the displacement at the feature point, including cracking displacement, yield displacement, peak displacement and failure displacement; z represents the shape control displacement. The maximum value z of the shape-controlled displacement max The peak displacement is set as the value, and asymmetric correction is performed using the asymmetric control parameter δ to generate the corrected positive and negative peak displacements, as follows: In the formula, This represents the corrected positive peak displacement. This represents the corrected negative peak displacement, where β, γ, and n represent shape control parameters; ν represents the parameter describing strength degradation, v = 1 + δ v w; w represents the energy dissipation of the skeleton curve under load. p(Δ) represents the characteristic point load function; Δ u Indicates the displacement prior to correction; δ v δ represents the strength degradation parameter; δ represents the asymmetric control parameter. Substitute the corrected positive and negative peak displacements into the relationship between load and displacement to generate the corrected positive and negative peak loads; Using the corrected positive and negative peak loads, the corrected loads and displacements at other feature points are calculated through stiffness calculations.

7. The method for constructing a four-segment restoring force model for beam-column joints according to claim 1, characterized in that, The step of calculating loading and unloading stiffness based on the asymmetric skeleton curve and correcting it with a damage index to form a pinching effect, and drawing a multilinear hysteresis curve further includes: The unloading stiffness is calculated as follows: In the formula, K represents the unloading stiffness, K0 represents the elastic stiffness; Δ represents the component displacement; Δ i The displacement amplitude of the i-th loading level is determined based on the loading regime; a and b are coefficients related to strain rate effect and variable axial force. The reloading stiffness is calculated as follows: In the formula, K′ represents the reload stiffness; The damage index is calculated as follows: In the formula, Δ m Indicates peak displacement; Δ y Indicates the yield displacement; Δ u Represents the failure displacement; ∑E i Indicates the energy consumption of the skeleton curve. p(Δ) represents the characteristic point load function; Q y For yield strength, A represents the cross-sectional area at the beam end.

8. A system for constructing a four-segmented restoring force model for beam-column joints, characterized in that, The method for constructing a four-segment restoring force model for beam-column joints according to any one of claims 1 to 7 includes: The parameter input module is used to determine the basic parameters, which include the geometric dimensions, reinforcement information, loading regime, material static parameters, and material constitutive model of the beam-column joint. The feature point calculation module is used to calculate feature point parameters based on the basic parameters and the static skeleton curve feature point parameter calculation formula. The feature points include cracking point, yield point, peak point and ultimate failure point. The strain rate effect coupling module is used to calculate the strain rate required for each loading stage in the loading regime, use the material dynamic amplification factor calculated by the strain rate to convert the characteristic point parameters into material mechanical properties, generate material dynamic mechanical property indexes, and introduce the material dynamic mechanical property indexes into the calculation formula of the static skeleton curve characteristic point parameters to generate the dynamic skeleton curve characteristic point calculation formula. The variable axial force equivalent processing module is used to convert the variable axial force of the beam-column joint into a fixed axial force, and substitute the fixed axial force into the calculation formula of the feature point of the dynamic skeleton curve to generate a symmetrical skeleton curve. An asymmetric correction module is used to perform asymmetric correction on the feature points of the symmetrical skeleton curve to generate an asymmetric skeleton curve. The hysteresis curve generation module is used to calculate the loading and unloading stiffness based on the asymmetric skeleton curve and correct it with the damage index to form a pinching effect, and draw a multilinear hysteresis curve.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for constructing a four-segment restoring force model of a beam-column joint as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for constructing a four-segment restoring force model of a beam-column joint as described in any one of claims 1 to 7.

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