CN114169060A - Performance analysis method for damaged reinforced concrete section - Google Patents
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Abstract
The invention belongs to the technical field of civil engineering, and relates to a performance analysis method for a damaged reinforced concrete section. The method is based on the method of running finite element elastoplasticity analysis and MATLAB programming post-processing in OpenSees, can quantitatively determine the damage state of the concerned section, respectively considers the influence of earthquake damage on concrete fibers and steel bar fibers on the section, and shows the influence of earthquake action on member concrete and steel bars in more detail. Calculating the M of the section by considering the influence of earthquake damage on concrete fiber and steel bar fiber and combining with MATLAB programminguAnd phiuAnd further calculating the M-phi relation of the damage section through MATLAB programming. The skeleton curve of the cross section can be obtained,quantitatively determining the mechanical property of the damaged section, and evaluating the attenuation and residual performance of the component performance.
Description
Technical Field
The invention belongs to the technical field of civil engineering, relates to a performance analysis method for a damaged Reinforced Concrete section, and particularly relates to a performance analysis method for a damaged Reinforced Concrete (RC) section based on OpenSees and MATLAB.
Background
China has wide territory and a plurality of earthquake zones are distributed in China, so the earthquake is frequent. The structure may experience multiple earthquakes within a design reference period, and each earthquake causes different degrees of damage to the structure, thereby resulting in the reduction of the earthquake resistance of the structure, so that the earthquake resistance evaluation of the earthquake-caused damaged structure (i.e. earthquake damage structure) has certain necessity and important significance. In urban areas, RC frame structures are widely built. And post-earthquake field investigation reports (e.g., Wenchuan earthquake, Lushan earthquake) show that: under the action of earthquake, the RC frame structure is mostly in slight-moderate damage, and the damage of the RC frame structure is always concentrated on the end points of the beam columns. Therefore, the residual seismic performance of the damaged beam column member can be quantitatively analyzed by analyzing the section performance of the concentrated damaged part of the beam column, so that the accurate judgment on the seismic performance of the seismic damage structure is facilitated, and the rescue and reconstruction work of the disaster area after the earthquake is facilitated.
The section analysis can determine the bending moment-curvature (M-phi) relation of the key section of the member according to the size of the member, the material properties of concrete and steel bars and the configuration condition of the steel bars, thereby determining the mechanical properties of the member, and comprises the following steps: section stiffness, yield moment, yield curvature, ultimate moment and ultimate curvature.
The conventional techniques have the following problems:
the damage of the beam column under the action of the earthquake is divided into an apparent damage and an internal damage, and the degree of the damage can be judged by the apparent damage with naked eyes, but the internal damage is invisible. Meanwhile, due to the uncertainty of seismic oscillation, the section damage has the uncertainty of damage degree and the uncertainty of damage distribution, so that the influence of the damage on the section performance is difficult to quantitatively consider. At present, the main method for determining the mechanical property of a damaged section is to count the damage degree and the mechanical property (rigidity and strength) attenuation degree thereof based on the existing cyclic reciprocating test of the RC bending member, and fit a relational expression of the section property attenuation and the damage degree through regression analysis. However, this method does not take into account the effect of the size and material of the component on the performance degradation, and therefore results obtained using regression analysis are more discrete. In practical applications, even if the damage degree of the two members is the same, the mechanical properties, the cross-sectional dimensions and the arrangement of the reinforcing steel bars of the members are different from those of the concrete material, but the mechanical properties are different from each other. Therefore, if an accurate evaluation is desired for the performance of the damaged section, the damaged section needs to be analyzed. However, common section analysis software such as XTRACT, openses, etc. can only perform section analysis on intact members to obtain the M- Φ relationship of intact sections, and cannot determine the M- Φ relationship of damaged sections.
Disclosure of Invention
Aiming at the defects of the existing section analysis technology, the invention aims to solve the problem of quantitatively analyzing the performance of the damaged section, thereby considering the influence of damage on the performance of concrete and steel bars and the area of the section, obtaining the M-phi relation of the damaged section and evaluating the mechanical properties (rigidity, yield strength and deformation, ultimate strength and deformation) of the damaged section. A section performance analysis method of a damaged RC section based on OpenSees and MATLAB is provided.
A performance analysis method for damaged reinforced concrete sections comprises the following steps:
(1) establishing a finite element model: according to structural design parameters, a finite element model is established in OpenSees by adopting beam-column units and Fiber sections (Fiber Secion), and a selected seismic acceleration time course is input to carry out elasto-plastic time course analysis.
(2) Output fiber stress strain: and outputting the stress strain of a fiber beam unit (which is called a fiber for short in the invention) of the damaged section to be analyzed by using a reorder Element command of OpenSees. Due to the fact that the number of the cross-section fibers is large, in order to be capable of quickly constructing an OpenSees output command stream, a script program capable of quickly outputting fiber positions according to the cross-section size and the reinforcing steel bar configuration condition is compiled by using MATLAB.
(3) Calculating the fiber damage: and (3) reading the stress-strain data output in the step (2) by using MATLAB, and calculating the damage of the concrete and the reinforcing steel bar fibers in the MATLAB by programming. Specifically, the damage of the concrete is calculated by adopting the attenuation of the elastic modulus of the concrete, and the damage of the reinforcing steel bar is calculated by adopting accumulated fatigue.
(4) Determining the cross-section damage state: and (4) determining the influence of the damage on the concrete and the reinforcing steel bar fibers in the step (5) according to the fiber damage calculated in the step (3). Specifically, for concrete fibers, damage affects the constitutive relation (elastic modulus and yield strength) of the concrete fibers. For reinforcing steel fibers, the damage results in a reduction in reinforcing steel fiber area. When the damage of a certain fiber is equal to 1, the fiber is not considered in step (5).
(5) Calculating ultimate bearing capacity and ultimate deformation: through the damage states of the concrete and the reinforcing steel fibers determined in the step (4), the states of the damaged sections (section size, fiber constitutive relation and fiber area) can be determined, and the ultimate bending resistance bearing capacity (M) of the damaged sections is calculated in an MATLAB (matrix laboratory) in a programming modeu) And ultimate curvature (. PHI.)u)。
(6) And (3) carrying out damage section performance analysis: determining a curvature increment interval, and performing increment analysis on the curvature (ranging from 0 to phi)u) And programming and determining the moment of the damaged section under each level of curvature in MATLAB so as to obtain the M-phi relation of the damaged section.
The difference between the step (6) and the step (5) is that only the ultimate performance point of the section is determined in the step (5), and the section rigidity, yield strength, displacement and section skeleton curve concerned in engineering application cannot be obtained, and the parameters can be obtained after the section performance analysis is carried out in the step (6), so that the influence of earthquake damage on the performance of concrete and steel bars and the area of the section is considered. And in the calculation process, the curvature of the cross section in the step (5) is unknown, the strain of a certain fiber is known, and the curvature of the cross section and the strain of the fiber need to be calculated by assuming the height of a compression area. The curvature of the cross-section in step (6) is known and the strain of the fiber needs to be calculated assuming a compression zone height.
The invention has the following beneficial effects:
1. the method is based on the method of running finite element elastoplasticity analysis and MATLAB programming post-processing in OpenSees, can quantitatively determine the damage state of the concerned section, respectively considers the influence of earthquake damage on concrete fibers and steel bar fibers on the section, and shows the influence of earthquake action on member concrete and steel bars in more detail.
2. Concrete fiber and steel bar fiber by considering earthquake damageInfluence of (D) in combination with MATLAB Programming to calculate M of the sectionuAnd phiuAnd further calculating the M-phi relation of the damage section through MATLAB programming. The skeleton curve of the cross section can be obtained, the mechanical property of the damaged cross section can be quantitatively determined, and the attenuation and residual performance of the component performance can be evaluated.
3. By adopting the damaged RC section analysis method provided by the invention, the residual anti-seismic performance of the key component of the RC structure after earthquake can be quantitatively evaluated, so that the anti-seismic performance of the RC structure after earthquake is evaluated, and the reconstruction work of a disaster area after earthquake is guided.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a comparison of the constitutive relation of the materials before and after a certain concrete fiber selected in the example is damaged.
FIG. 3 illustrates the lesion state of a selected cross-section of the embodiment.
Fig. 4 is a schematic cross-sectional stress-strain distribution.
FIG. 5 is a comparison of the results of the cross-sectional analysis before and after the cross-sectional damage of the specific example.
Fig. 6 is a schematic diagram of determining yield moment and yield curvature.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings. The flow of a performance analysis method for a damaged reinforced concrete section is shown in figure 1, and the method comprises the following specific steps:
(1) according to structural design parameters, a finite element model is established in OpenSees, a forceBeamColumn unit is selected as the column in the embodiment, concentrated plastic areas can be defined at two ends of the unit by the unit, a nonliner BeamColumn unit with 5 integration points is selected as the beam, and a proper unit can be selected according to requirements. Concrete is represented by using a Concrete02 material, the material can consider the constraint effect of stirrups, the constraint effect of the stirrups on the Concrete in the core area is calculated according to the formula (1-4), and Steel02 material is used for representing the Steel bars. Setting node mass according to transverse live load and self-weight of the structure, setting Rayleigh damping according to a formula (5), setting the damping ratio to be 5%, inputting a selected seismic wave acceleration time course, setting a convergence criterion and a calculation step length, and performing elastoplasticity time course analysis.
ε0＝0.002K (1)
Wherein epsilon0Is the yield strain of the concrete in the core area, K considers the concrete strength enhancement coefficient of the stirrup constraint effect, fc' yield strength, ε, of concrete in core and protected zonescIs the concrete strain, fcIs epsiloncCorresponding stress, Z is the slope of the strain softening section, ρsIs the volume hoop ratio, fyhIs the yield strength of the stirrup, h' the concrete width of the core area from the outer edge of the stirrup, ShIs the spacing of the stirrups.
Cn＝a0Mn+a1Kn (5)
Wherein C isnIs a structural damping matrix of0And a1To be undetermined coefficient, MnAnd KnThe array is a mass array and a rigidity array of the structure.
(2) And outputting the stress strain of the concrete fiber and the reinforcing steel bar fiber on the section to be analyzed by utilizing a reorder Element command of OpenSees.
(3) And reading the output stress strain data by using a dlmread command in the MATLAB, and programming and calculating the damage of the concrete and the steel bar fiber in the MATLAB according to formulas (6-8), wherein script programs for calculating the damage of the concrete fiber and the damage of the steel bar fiber are respectively compiled.
Wherein DcIs damage to concrete fibers, ErIs the reloading elastic modulus of the concrete material, Ec0Is the initial modulus of elasticity of the concrete.
Wherein DsIs damage to reinforcing steel bar fibers (2N)f)kThe fatigue life of the k-th half cycle is calculated by equation (8), and n is the number of half cycles.
Wherein epsilonaIs the strain amplitude of the half cycle, M and M are the fatigue ductility coefficient and the fatigue ductility index, respectively, and the values of M and M in the examples are 0.065 and-0.281.
(4) Determining the constitutive relation of the damaged concrete fibers according to the fiber damage calculated in the step (3), and calculating according to the following formula:
wherein σdAnd ε is the stress strain εrFor the intersection of the reloaded curve with the abscissa, ε is calculated according to equation (10)mFor the maximum strain in the history of fiber loading, f0And (epsilon) is the constitutive relation of undamaged concrete.
Wherein sigmamIs the maximum stress in the history of fiber loading. FIG. 2 shows a comparison of the material constitutive relation before and after a certain concrete fiber damage selected in the example. Calculating the area of the damaged reinforcing steel bar fiber according to the formula (11):
wherein A issdIs the area of the damaged bar, D is the diameter of the intact bar, DsIs a damage to the reinforcing steel fibers.
(5) Determining the damage of the concrete and the reinforcing steel fibers through the step (4), so that the damage state of the section can be determined, wherein fig. 3 shows the damage state of the section of a certain embodiment, and the ultimate bending resistance bearing capacity (M) of the damaged section is calculated in a programming mode in MATLABu) And corresponding curvature (phi)u)。
The program calculation assumes the following:
(1) the cross-sectional limit condition is defined as the ultimate compressive strain reached by the concrete fibers in the core area closest to the compressed longitudinal ribs.
(2) A flat section assumption is used.
(3) The tensile strength of the concrete in the tension zone is neglected.
Calculating M of lesion cross-section using MATLAB programminguAnd phiuThe process is as follows:
step 1: assume a compression zone height (x in FIG. 4)0) Determining the position of a neutral axis;
step2, determining the limit strain of the concrete fiber in the core area according to the limit state, and further determining the section curvature phi according to the height of the compression area;
step 3: calculating the strain of each fiber according to the equation (12) on the basis of the assumption of the flat section, and calculating the stress of the fiber according to the fiber constitutive relation after damage;
εi＝xiφ (12)
wherein epsiloniIs the strain of the ith fiber, xiPhi is the distance of the ith fiber from the neutral axis and phi is the section curvature determined in Step 2.
Step 4: calculating the cross-sectional internal force from the fiber stress and the fiber area, and determining whether the internal or external force is reached (N in FIG. 4)ex) And (4) balancing. The standard for judging balance is whether the relative error of the internal force and the external force is less than 5 percent (the allowable error is flexible)Determining that 5% is selected in the embodiment), if the external force is balanced, executing Step5, otherwise, executing Step1-Step4 again;
step 5: the section center is taken as a moment according to the stress of each fiber. Then obtaining the M of the sectionuAnd phiu。
(6) Determining a curvature increasing interval and performing incremental analysis on the curvature (ranging from 0 to phi)u) The selection of the curvature increment is flexibly determined, and the curvature calculation interval is selected as
The steps for programming the relationship of damage section M- Φ in MATLAB are as follows:
the difference between the step (6) and the step (5) is that the curvature of the cross section in the step (5) is unknown, the strain of a certain fiber is known, and the cross section curvature needs to be calculated by assuming the height of a compression area, so that the strain of the fiber is calculated. The curvature of the cross-section in step (6) is known and the strain of the fiber needs to be calculated assuming a compression zone height.
Step 1: determining an initial curvature
Step2: assume a compression zone height (x in FIG. 4)0) Determining the position of a neutral axis;
step 3: calculating the strain of each fiber according to the assumption of the flat section, and determining the fiber stress according to the constitutive relation of the damaged fibers;
step 4: calculating the cross-sectional internal force according to the fiber stress and area, and determining whether the internal or external force is reached (N in FIG. 4)ex) And (4) balancing. The standard for judging balance is whether the relative error of the internal force and the external force is less than 5 percent. If the internal and external forces are balanced, executing Step5, otherwise, executing Step2-Step 4;
step 5: the section center is taken as a moment according to the stress of each fiber. A set of M-phi data pairs for the cross-section is obtained.
Step 6: increasing the curvature, and circularly executing Step2-Step6 to finally obtain the M-phi relation of the lesion section.
Fig. 5 shows a comparison of the analysis results of the cross section before and after damage according to one embodiment, the yield curvature and the yield moment can be determined according to the energy dissipation equivalence principle (as shown in fig. 6), and table 1 shows a comparison of the mechanical properties of the cross section before and after damage. Compared with the intact section, the yield moment and the ultimate moment of the damaged section are respectively attenuated by 11 percent and 4 percent, and the equivalent stiffness is attenuated by 34 percent.
The equivalent stiffness in table 1 is calculated as equation (13):
in the formula KeffFor equivalent stiffness, MyTo yield moment,. phiyIs the yield curvature.
TABLE 1 comparison of analysis of the front and rear Cross sections of the lesions
Claims (5)
1. A performance analysis method for damaged reinforced concrete sections is characterized by comprising the following steps:
(1) establishing a finite element model: according to structural design parameters, establishing a finite element model in OpenSees by adopting beam-column units and Fiber sections (Fiber Secion), inputting a selected seismic acceleration time course, and performing elasto-plastic time course analysis;
(2) output fiber stress strain: outputting the stress strain of the fiber beam unit of the damaged section to be analyzed by utilizing a reorder Element command of OpenSees; because the number of the fibers of the section is large, in order to quickly construct an OpenSees output command stream, a script program capable of quickly outputting the fiber position according to the section size and the reinforcing steel bar configuration condition is compiled by using MATLAB;
(3) calculating the fiber damage: reading the stress-strain data output in the step (2) by using MATLAB, and calculating the damage of concrete and reinforcing steel bar fibers in the MATLAB by programming; specifically, the damage of the concrete is calculated by adopting the attenuation of the elastic modulus of the concrete, and the damage of the reinforcing steel bar is calculated by adopting accumulated fatigue;
wherein DcIs damage to concrete fibers, ErIs the reloading elastic modulus of the concrete material, Ec0Is the initial modulus of elasticity of the concrete;
wherein DsIs damage to reinforcing steel bar fibers (2N)f)kIs the fatigue life of the kth half cycle calculated according to equation (8), n is the number of half cycles;
wherein epsilonaIs the strain amplitude of the half cycle, and M are the fatigue ductility coefficient and the fatigue ductility index, respectively;
(4) determining the cross-section damage state: determining the influence of the damage on the concrete and the reinforcing steel bar fibers in the step (5) according to the fiber damage calculated in the step (3); specifically, for concrete fibers, damage affects the constitutive relation (elastic modulus and yield strength) of the concrete fibers; for reinforcing steel bar fibers, the area of the reinforcing steel bar fibers is reduced due to damage; when the damage of a certain fiber is equal to 1, the fiber is not considered in the step (5);
(5) calculating ultimate bearing capacity and ultimate deformation: through the damage states of the concrete and the reinforcing steel fibers determined in the step (4), the states of the damaged sections (section size, fiber constitutive relation and fiber area) can be determined, and the ultimate bending resistance bearing capacity (M) of the damaged sections is calculated in an MATLAB (matrix laboratory) in a programming modeu) And ultimate curvature (. PHI.)u)；
(6) And (3) carrying out damage section performance analysis: determining an incremental interval of curvature, for curvaturePerforming incremental analysis (ranging from 0 to phi)u) And programming and determining the moment of the damaged section under each level of curvature in MATLAB so as to obtain the M-phi relation of the damaged section.
2. A method for analyzing the performance of a damaged reinforced concrete section according to claim 1, wherein the specific operation of the step (4) is as follows:
wherein σdAnd ε is the stress strain εrFor the intersection of the reloaded curve with the abscissa, ε is calculated according to equation (10)mFor the maximum strain in the history of fiber loading, f0(epsilon) is the constitutive relation of undamaged concrete;
wherein sigmamLoading the fiber with the maximum stress in history; FIG. 2 shows a comparison of the material constitutive relation before and after a certain concrete fiber damage selected in the example; calculating the area of the damaged reinforcing steel bar fiber according to the formula (11):
wherein A issdIs the area of the damaged bar, D is the diameter of the intact bar, DsIs a damage to the reinforcing steel fibers.
3. A method for analyzing the performance of a damaged reinforced concrete section according to claim 1 or 2, wherein the specific operation of the step (6) is as follows:
step 1: determining an initial curvature;
step2: assuming a compression zone height, determining a neutral axis position;
step 3: calculating the strain of each fiber according to the assumption of the flat section, and determining the fiber stress according to the constitutive relation of the damaged fibers;
step 4: calculating the internal force of the section according to the fiber stress and the area, and judging whether the internal and external force balance is achieved; judging whether the relative error of the internal force and the external force is less than 5% or not according to the balance standard; if the internal and external forces are balanced, executing Step5, otherwise, executing Step2-Step 4;
step 5: taking a moment from the center of the cross section according to the stress of each fiber; a group of M-phi data pairs of the cross section can be obtained;
step 6: increasing the curvature, and circularly executing Step2-Step6 to finally obtain the M-phi relation of the lesion section.
4. A method for analyzing the performance of a damaged reinforced concrete section according to claim 1 or 2, wherein the specific operation of the step (5) is as follows:
assume the following:
(1) the section limit state is defined as that the concrete fiber in the core area closest to the compressed longitudinal bar reaches the limit compression strain;
(2) adopting a flat section assumption;
(3) neglecting the tensile strength of the concrete in the tension area;
calculating M of lesion cross-section using MATLAB programminguAnd phiuThe process is as follows:
step 1: assume a compression zone height (x in FIG. 4)0) Determining the position of a neutral axis;
step2, determining the limit strain of the concrete fiber in the core area according to the limit state, and further determining the section curvature phi according to the height of the compression area;
step 3: calculating the strain of each fiber according to the equation (12) on the basis of the assumption of the flat section, and calculating the stress of the fiber according to the fiber constitutive relation after damage;
εi＝xiφ (12)
wherein epsiloniIs the strain of the ith fiber, xiIs the distance of the ith fiber from the neutral axis, phi is determined in Step2A fixed cross-sectional curvature;
step 4: calculating the cross-sectional internal force from the fiber stress and the fiber area, and determining whether the internal or external force is reached (N in FIG. 4)ex) Balancing; judging whether the relative error of the internal force and the external force is less than 5 percent (the allowable error is flexibly determined, 5 percent is selected in the embodiment), if the external force is balanced, executing Step5, otherwise, executing Step1-Step4 again;
step 5: taking a moment from the center of the cross section according to the stress of each fiber; then obtaining the M of the sectionuAnd phiu。
5. A method for analyzing the performance of a damaged reinforced concrete section according to claim 3, wherein the specific operation of the step (5) is as follows:
assume the following:
(1) the section limit state is defined as that the concrete fiber in the core area closest to the compressed longitudinal bar reaches the limit compression strain;
(2) adopting a flat section assumption;
(3) neglecting the tensile strength of the concrete in the tension area;
calculating M of lesion cross-section using MATLAB programminguAnd phiuThe process is as follows:
step 1: assume a compression zone height (x in FIG. 4)0) Determining the position of a neutral axis;
step2, determining the limit strain of the concrete fiber in the core area according to the limit state, and further determining the section curvature phi according to the height of the compression area;
step 3: calculating the strain of each fiber according to the equation (12) on the basis of the assumption of the flat section, and calculating the stress of the fiber according to the fiber constitutive relation after damage;
εi＝xiφ (12)
wherein epsiloniIs the strain of the ith fiber, xiPhi is the distance of the ith fiber from the neutral axis, phi is the section curvature determined in Step 2;
step 4: calculating the cross-sectional internal force from the fiber stress and the fiber area, and determining whether the internal or external force is reached (N in FIG. 4)ex) Balancing;judging whether the relative error of the internal force and the external force is less than 5 percent (the allowable error is flexibly determined, 5 percent is selected in the embodiment), if the external force is balanced, executing Step5, otherwise, executing Step1-Step4 again;
step 5: taking a moment from the center of the cross section according to the stress of each fiber; then obtaining the M of the sectionuAnd phiu。
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