CN107621440B - Finite element simulation method for bonding performance between prestressed tendon and concrete - Google Patents
Finite element simulation method for bonding performance between prestressed tendon and concrete Download PDFInfo
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Abstract
The invention discloses a finite element simulation method for the bonding performance between a prestressed tendon and concrete and provides an equivalent simulation method for the bonding slippage of the prestressed tendon. Firstly, giving a principle of determining the integral slip plane and the effective working plane of the prestressed tendon, establishing a stress balance relation of a prestressed tendon interface microcell, and providing a calculation method of the ultimate cohesive force of the prestressed tendon; secondly, an equivalent principle of the ultimate bonding force of the prestressed tendon is given, a calculation formula of the equivalent maximum bonding stress of the single prestressed tendon is deduced, a BPE bonding slippage model is updated, the attribute of a spring unit for simulating bonding slippage is determined, and the equivalent bonding slippage finite element simulation of the single prestressed tendon is realized; on the basis, the finite element simulation of the prestressed tendon bonding slippage is realized based on the principle that the single prestressed tendon equivalent bonding force is superposed to obtain the prestressed tendon bonding force, and the single prestressed tendon average slippage is used as the prestressed tendon slippage. Finally, the accuracy of the method is verified by combining the existing test results.
Description
Technical Field
The invention relates to a finite element simulation analysis method, in particular to a finite element simulation method for the bonding performance between a prestressed tendon and concrete.
Background
As prestressed concrete structures are widely used in various large projects, safety problems are more and more prominent, and the bonding performance between prestressed tendons and concrete is an important factor influencing the safe use of the structures. The bonding properties of the rebar to concrete in a structure depend on the rebar diameter and the rebar surface geometry. At present, a large amount of simulation researches are carried out aiming at the bonding performance of common steel bars in the structure, and related methods are mature. However, the prestressed tendons in the structure mostly adopt twisted steel strands, and the bonding performance of the twisted steel strands is different from that of common steel bars. The documents "Analysis of the bond floor between stressed strands and concrete in fire, Jamal Khalaf, Zhuahui Huang, Construction and Building Materials,128(2016) 12-23" propose a finite element simulation method of the bonding performance of single prestressed steel strands and concrete, predict the bonding performance of prestressed tendons under the influence of different factors, and verify the bonding performance through test data. The method is only limited to the bonding performance of single prestressed steel strand and concrete, and in actual engineering, especially in large-span prestressed concrete bridges, the steel strands are often arranged in bundles. The binding force of the prestressed bundles is contributed by a plurality of steel strands and the slurry in the prestressed duct together, and is not simply superposed by the binding force of the plurality of steel strands. Tests show that the bonding stress of the prestressed tendons is lower than the sum of the bonding stresses of a plurality of single prestressed tendons, and the nonlinearity of the relationship is more remarkable when the number of the steel strands is larger. At present, the research on the bonding performance of the prestressed tendons still stays in a test level, and no prestressed tendon bonding performance simulation method is reported at present. In different structures, the number of the steel strands in the prestressed tendons is different from the spatial arrangement mode, the cost for testing the bonding performance of various prestressed tendons completely by means of tests is too high, and the actual requirements are difficult to meet. Therefore, the invention provides a finite element simulation method for the bonding performance between the prestressed tendon and the concrete.
Disclosure of Invention
Aiming at the problems and avoiding the defects in the field of research, the invention provides a finite element simulation method for the bonding performance between a prestressed tendon and concrete, which is realized by commercial ANSYS software, has better precision and can effectively simulate the bonding performance of the prestressed tendon.
The technical scheme adopted by the invention for solving the technical problems is as follows: a finite element simulation method for the binding performance between a prestressed tendon and concrete. The method mainly comprises the following steps: firstly, giving out the principle of determining the integral slip plane and the effective working plane of the prestressed tendon, and establishing a calculation formula of the ultimate cohesive force of the prestressed tendon and the equivalent maximum cohesive stress of a single prestressed tendon in the prestressed tendon; then, the attribute of the spring unit for simulating the bonding slippage is determined, and the equivalent bonding slippage finite element simulation of a single prestressed tendon is realized; on the basis, determining a bonding slip curve in the prestressed tendon drawing process; and finally, verifying the precision of the method by combining the existing test results. The method comprises the following specific steps:
step 1: and establishing a geometric model.
According to an actual engineering structure, determining geometric parameters of a model, wherein the geometric model of the concrete and the grouting body in the prestressed duct is obtained by adopting a separated modeling method; the establishment of the geometrical model of the prestressed tendons can be realized by two steps, firstly, concrete is split at the position of the steel strand by adopting a solid splitting method, and then a plurality of lines with the same geometrical parameters as the steel strand are created at the splitting position again to serve as the geometrical model of the prestressed tendons; the geometric model of the common steel bar is obtained by the same method. The bonding slippage between the concrete and the grouting body is not considered in the model, and the concrete and the grouting body are considered to be completely bonded; neglecting the bonding slippage between the common steel bar and the concrete, and adopting a method for establishing a constraint equation to connect the common steel bar and the concrete.
Step 2: and determining the integral sliding surface and effective working surface of the prestressed beam. The method specifically comprises the following steps: the contact surface of the steel strand and the surrounding concrete and the effective working area and the bonding force of the concrete slurry between the steel strands are formed (see the innovation point in detail).
And step 3: and determining the ultimate binding force of the prestressed tendons and the equivalent maximum binding stress of the single prestressed tendons in the prestressed tendons. Establishing a stress balance relation of the micro units of the prestressed tendon interface, and providing a calculation method of the ultimate binding force of the prestressed tendon; on the basis, an equivalent principle of the ultimate bonding force of the prestressed tendons is given, and the equivalent maximum bonding stress of the single prestressed tendon is deduced according to the equivalent principle (see the innovation point of the invention).
And 4, step 4: defining the constitutive relation of the unit type and the material.
1) Concrete and grouting material are simulated by a three-dimensional Solid unit Solid65, and a Hongnestad material constitutive model is adopted.
2) A single steel strand in the prestressed bundle is simulated by adopting a Link8 unit, a common steel bar is simulated by adopting a Link8 unit, and the steel strand and the common steel bar are made of simplified Menegotto constitutive models.
3) The binding slip relationship between the single steel strand in the prestressed bundle and the concrete is simulated by a COMBIN39 nonlinear spring unit, and the unit property is defined by the binding slip (F-S) relationship between the steel strand and the concrete unit as shown in the following steps.
And 5: and defining the property of the spring unit between the single steel strand and the concrete in the prestressed beam.
Firstly, based on the equivalent maximum bonding stress tau of a single steel strand in a prestressed beammaxAnd calculating a formula, updating the BPE bonding slippage model, deducing the bonding slippage (F-S) relationship between the steel strand unit and the concrete unit, obtaining the attribute of a spring unit for simulating the bonding slippage between the single steel strand and the concrete, and further establishing the bonding slippage relationship between the single steel strand and the concrete. The method comprises the following specific steps:
the bonding slippage between the single steel strand and the concrete is simulated by adopting a COMBIN39 spring unit, and specifically, three spring units with zero length are adopted to be connected between the superposed nodes of the steel strand and the concrete unit. Among the three springs, the normal and transverse tangential spring deformations are negligible with respect to the longitudinal one, so that the stiffness coefficients K of the springs in these two directions can be taken to be infinite. The bonding slippage between the steel strand and the concrete is mainly simulated by a longitudinal spring, the unit property of the bonding slippage is obtained by the bonding slippage (F-S) relationship between a single steel strand unit and a concrete unit, wherein the bonding force F between the single steel strand unit and the concrete unit is calculated by the following formula:
F＝Ar·τ＝π·br·lr·τ (1)
in the formula, ArIs the unit surface area of the tendon, brIs the unit diameter of the tendonrThe length of a prestressed tendon unit is shown, tau is the bonding stress between the prestressed tendon and a concrete unit, and can be determined according to a BPE bonding slippage model:
in the formula, τmaxIs the equivalent maximum bonding stress of a single steel strand in a prestressed strand, S1、S2、S3、S4、τ2α detailed descriptionThe literature "Analysis of the bond after between stressed structures and confidential fire, Jamal Khalaf, Zhaohui Huang, Construction and Building Materials,128(2016) 12-23".
Step 6: and defining grid division and loading modes.
①, grid division, the quality of the grid will influence the calculation accuracy and convergence, regular hexahedron units are adopted as much as possible, and for the areas with strong nonlinear response, the units are not suitable to be too small in size for avoiding stress concentration and cracking in advance.
②, defining the loading mode of the model, adopting graded loading in the model, applying the load to the end node of the prestressed tendon, avoiding applying the constraint directly to the concrete node in the model, and adding a rigid backing plate at each side of the model for applying the constraint.
And 7: finite element solving and post-processing.
①, defining analysis type and solving control options, setting parameters such as maximum number of balance iteration and convergence criterion to carry out finite element solving calculation.
② extracting results and post-processing, extracting section stress cloud charts under various levels of load models, extracting load slip curves of each steel strand, and taking the average value as the load slip curve of the prestressed tendons.
And 8: and determining a prestressed tendon bonding slip curve and verifying the accuracy of the prestressed tendon bonding slip curve. The binding force of the prestressed tendons is obtained by superposing equivalent binding forces of the single prestressed tendons, and the average sliding value of the single prestressed tendons is obtained by sliding the prestressed tendons; the accuracy of the method is verified by combining the existing experimental data.
The invention is innovated in providing an equivalent simulation method of the bonding slippage of the prestressed tendon, which mainly comprises two aspects of the second step and the third step, wherein ① provides the determination principle of the integral slippage surface and the effective working surface of the prestressed tendon;
(1) the principle of determining the overall sliding surface and the effective working surface of the prestressed tendon specifically comprises the contact surface of the steel strand and the surrounding concrete, the effective working area of concrete slurry among the steel strands and the binding power. The tendon adhesion slip may be equivalent to an adhesion slip between an assembly of the tendon and the inner concrete and the surrounding concrete, as shown in fig. 1. The binding mechanism of the prestressed tendon and the single prestressed tendon is similar, and the prestressed tendon and the single prestressed tendon are composed of chemical adhesive force, mechanical engaging force and friction force, but the two are mainly different in effective working surface, the effective working surface of the single prestressed tendon is the outer surface of the steel strand, and the effective working surface of the prestressed tendon is the outer surface of the assembly; the effective working area of the prestressed tendons is smaller than the sum of the single prestressed tendons with the same number, and the nonlinearity of the relation is more obvious when the number of the steel strands is larger.
The contact surface of the steel strand and the surrounding concrete is the arc surface of the combined body in figure 1, which is called as a mechanical occlusal surface AυIt mainly bears the concrete occlusion between the steel strand ribs and is also acted by friction force. According to the profile characteristics of the prestressed tendon assembly, a mechanical occlusal surface AυCan be expressed as:
Aυ＝lv·lω＝ns·lg·lω(3)
in the formula IvFor the width of the mechanical engaging surface of the tendon, /)gThe width of the concrete engaging surface between the single steel wire and the rib is 1/4 circumferences of the steel wire, nsThe number of steel wires of the mechanical occlusal surface lωIs the length of the peripheral steel wire of the steel strand, /)dIs the length of the middle steel wire of the steel strand, and theta is the included angle between the peripheral steel wire and the central steel wire of the steel strand, as shown in fig. 2.
The effective working surface of the concrete slurry between the steel strands is the section of the assembly in fig. 1, which is called the friction surface afMainly bearing the frictional resistance of the concrete interface, and the expression is as follows:
Af＝lf·lω(5)
lf＝nj·l'f+ns·lm(6)
l'f＝2d-ds(7)
in the formula IfWidth of friction surface of prestressed tendonmIs the width of the friction surface of the concrete between the single steel wire and the rib, and has the value of 1/2 circumference l'fIs a single section width, njIs the number of sections, d is the diameter of the steel strand, dsThe diameter of the steel wire in the steel strand.
(2) Establishing a stress balance relation of the micro units of the prestressed tendon interface based on a determination method for the bonding force composition on the effective working surface and different working surfaces of the prestressed tendon, and providing a calculation method for the ultimate bonding force of the prestressed tendon; on the basis, the equivalent principle of the ultimate bonding force of the prestressed tendons is given, and the equivalent maximum bonding stress tau of the single prestressed tendon is deduced according to the equivalent principlemaxAnd (4) calculating a formula. Tensile force F of steel strandpThe relative slip trend appears under the action, and the chemical adhesive force gradually disappears along with the generation of the slip, so that the structure bonding performance is slightly influenced; the sliding and rotation of the steel strand are restricted by the concrete between the ribs, and oblique extrusion force perpendicular to the ribs is generated at the contact surface of the steel strand and can be decomposed into radial compressive stress sigmanWith axial shear stress upsilonsAs shown in fig. 3; taking the micro unit of the contact surface of the prestressed tendon and the concrete at the position x away from the free end of the test piece for stress analysis, as shown in figure 4; local tensile force FxOne part transmits to the concrete unit of congealing on every side and makes it reach extreme condition, and another part transmits for next little unit, and until the tensile force through the whole concrete unit that transmits of prestressing tendons, then whole stress transmission process finishes, has to prestressing tendons unit atress:
dFx-lv·υs(x)·dx-μ·lf·σn(x)·dx＝0 (8)
in the formula, FxIs the tensile force, sigma, on the tendon microcell at the point xn(x)、υs(x) Respectively the normal stress and the shear stress of the concrete at the point x, and the formula (8) is arranged:
wherein tau (x) is bonding stress at the contact surface of the dx section, and the oblique extrusion stress sigma of the prestressed tendon unit on the dx sectionm(x) From Eurocode 2 formula:
k＝1.05·Ec·εc0/fc, (11)
in the formula (f)cIs the ultimate compressive strength of concrete, epsilonc0Strain corresponding to maximum stress, EcThe average positive stress sigma of dx section in the process of reaching the limit state is the elastic modulus of the concreteca(x) Comprises the following steps:
in the formula, epsiloncuFor ultimate strain of concrete, the oblique extrusion stress on dx section is decomposed into positive stress sigman(x) Comprises the following steps:
σn(x)＝σca(x)·sinθ (14)
in the formula, theta is an included angle between an outer wire and an inner wire of the steel strand, and the shear stress caused by the oblique extrusion stress is as follows:
the maximum bonding force F of the tendon at the effective bonding length ls：
Maximum binding force F based on integral sliding of prestressed beamsEvenly distributing the steel wire to each steel strand to constructEquivalent maximum bonding stress tau of single steel strandmaxCalculating the formula:
wherein n is the number of the steel strands, d is the diameter of the steel strands, ldThe effective bonding length of the steel strand.
Has the advantages that: the invention provides an equivalent simulation method for binding and sliding of a prestressed tendon, which gives a principle of determining the integral sliding surface and the effective working surface of the prestressed tendon, establishes a calculation formula for the ultimate binding force of the prestressed tendon and the equivalent maximum binding stress of a single prestressed tendon, updates a BPE binding and sliding model, defines the attribute of a spring unit for simulating the binding and sliding and realizes the finite element simulation of the binding and sliding of the prestressed tendon. The simulation method can accurately predict the bonding performance of the prestressed tendon, and save a large amount of test time and expenditure. The whole numerical simulation method flow is shown in fig. 5.
Drawings
FIG. 1 shows a pre-stressing tendon combination of the present invention.
FIG. 2 is a schematic diagram of the stress of the steel strand in the invention.
Fig. 3 is a schematic diagram of the stress analysis of the tendon in the present invention.
Fig. 4 is a schematic view of the stress analysis of the prestressed tendons and the concrete units in the invention.
FIG. 5 is a flow chart of a numerical simulation method according to the present invention.
FIG. 6 is a schematic cross-sectional view of a test piece according to the present invention.
FIG. 7 shows the constitutive relation of concrete in the present invention.
FIG. 8 shows the constitutive relation of the steel strand and the steel bar in the present invention.
Fig. 9 is a schematic view of the spring unit connection according to the present invention.
FIG. 10 is a BPE bond slip model employed in the present invention.
FIG. 11 is a schematic diagram of a 3D finite element model constructed in the present invention.
FIG. 12 is a 1-1 section stress cloud of the model of the present invention at each loading step.
FIG. 13 is a load-slip diagram of the tendon in the present invention.
Detailed Description
The technique of the present invention was used to simulate a specimen of a prestressed tendon having an effective bond length of 470mm in the documents "Secondary and oxygen in post-tension bridge systems, Elie El Zghayar, Kevin R.Mackie.ACI Structural journal.2013,110(4): 629-638". The simulation method of the present example includes the steps of:
step 1: and establishing a geometric model.
1) The geometric parameters of the structure are determined. The geometric dimensions of the test pieces were 470 mm. times.1981 mm. times.610 mm, using
The stretching length of the stretching end of the (seven) steel stranded wire is 250mm, and the stretching length of the free end of the (seven) steel stranded wire is 100 mm. The test piece adopts a concrete cuboid with the strength of C50, adopts a grouting material with the strength of 50MPa and HRB400 common steel bars, the section characteristics and the main parameters of the test piece are detailed in figure 6, and the mechanical properties of the concrete and the steel strand are shown in table 1.
2) Establishing 1/4 geometric models of concrete and grouting body respectively by using ANSYS finite element software and a separate modeling method according to structural symmetry; the establishment of the prestressed tendon geometric model can be realized by two steps, firstly, concrete is split at the position of the steel strand by adopting a solid splitting method, and then a plurality of lines with the same geometric parameters as the steel strand are created at the splitting position as the prestressed tendon geometric model; the geometric model of the common steel bar is obtained by the same method.
Step 2: and determining the integral sliding surface and effective working surface of the prestressed beam. Mechanical occlusal surface width l of prestressed tendonv70.65mm, the width l of the friction surface of the prestressed tendonf220.65mm, the effective working surface length of the prestressed tendons is 475.8 mm.
And step 3: and determining the ultimate binding force of the prestressed tendons and the equivalent maximum binding stress of the single prestressed tendons in the prestressed tendons. According to the calculation formula, the ultimate bonding force of the prestressed tendon and the equivalent maximum bonding stress of the single prestressed tendon in the prestressed tendon are 772.7KN and 4.98Mpa respectively.
And 4, step 4: defining the constitutive relation of the unit type and the material.
1) Simulating concrete and a grouting material by using a three-dimensional Solid unit Solid 65; the concrete unit property determination comprises two parts of concrete damage criterion and material property setting.
1.1) defining a concrete failure criterion, wherein the concrete failure criterion adopts an ANSYS default Willam-Warnker five-parameter failure criterion, and the shear transfer coefficient of an open crack in the concrete material parameter setting is βt0.5 is taken, and the shear transfer coefficient of the closed fracture is taken to be 0.95. Uniaxial crushing stress f to make the calculation easy to convergecTaken as-1, indicating Solid65 cells were crushed closed. Close [ Options ] at computation time]Of [ extra displacement ]]And (6) selecting options. KEYOPT (7) is assumed to be 1, and semi-brittle fracture is more likely to be converged.
1.2) defining concrete material properties; the concrete stress-strain relationship is shown in fig. 7, the formula specified in GB 50010-2002 is adopted for the rising section, and the treatment method of Hongnestad is adopted for the falling section, that is:
wherein n is 2 or epsilon0＝0.002、εcuAs 0.0033, a series of data points are input here to fit, and it is necessary to pay attention to the fact that the input concrete elastic modulus must be the initial elastic modulus.
2) The steel strand in the prestressed bundle is simulated by adopting a Link8 unit, and the common steel bar is also simulated by adopting a Link8 unit; the steel strands and the steel bars adopt a simplified Menegotto constitutive model as shown in FIG. 8.
3) The binding slip relationship between the steel strand and the concrete in the prestressed tendon is simulated by a COMBIN39 nonlinear spring unit, and the unit property is defined by the binding slip (F-S) relationship between the steel strand and the concrete unit as shown in the following steps.
And 5: and defining the property of the spring unit between the single steel strand and the concrete in the prestressed beam.
The bonding slippage between the single steel strand and the concrete is simulated by adopting a COMBIN39 spring unit, and specifically, three spring units with zero length are adopted to be connected between the superposed nodes of the steel strand and the concrete unit. Among the three springs, the normal and transverse tangential spring deformations are negligible with respect to the longitudinal one, so that the stiffness coefficients K of the springs in these two directions can be taken to be infinite. The bonding slippage between the steel strand and the concrete is mainly simulated by a longitudinal spring, the unit property of the bonding slippage is obtained by the bonding slippage (F-S) relationship between a single steel strand unit and a concrete unit, wherein the bonding force F between the single steel strand unit and the concrete unit is calculated by the following formula:
F＝Ar·τ＝π·br·lr·τ (2)
in the formula, ArIs the unit surface area of the tendon, brIs the unit diameter of the tendonrThe unit length of the prestressed tendon and the unit bonding stress of the prestressed tendon and the concrete are shown as tau, and can be determined according to a BPE bonding slippage model (see figure 10):
in the formula, τmaxThe remaining parameters for the maximum bonding stress equivalent for a single strand in a prestressed strand are known from the literature "Analysis of the bond after stressed strands and reinforcement in, Jamal Khalaf, zhahui Huang, Construction and Building Materials,128(2016) 12-23": 0.25mm for S1, 0.5mm for S2, 3.5mm for S3, 8.0mm for S4,. tau.2＝0.35τmax，α＝0.1。
Will taumaxSubstituting 4.98MP into the BPE bonding slippage model to obtain a bonding slippage (F-S) curve between the steel strand unit and the concrete unit, introducing the bonding slippage curve into the finite element model, defining the attribute of the spring unit, and realizing finite element simulation of the bonding slippage of the single steel strand and the concrete.
Step 6: and defining grid division and loading modes.
① grid division, firstly, generating a 1/4 finite element model of concrete and grouting body by adopting a volume sweep command (vssweep), then, setting the length of a prestressed tendon unit to be consistent with that of a grouting body unit, carrying out grid division on steel strands in a prestressed tendon, and finally, obtaining the whole finite element model by a mirror image (vsymm) command, thereby ensuring that the concrete unit can be divided into regular hexahedron units and is in one-to-one correspondence with node coordinates of the steel strands (convenient for arranging nonlinear spring units), wherein the finite element model of the prestressed tendon test piece is shown in figure 11.
②, defining a loading mode of the model, adding a rigid base plate on each side of the model for applying constraint, applying load on the prestressed tendon tensioning end node, applying load to the model in a grading manner by adopting a time command, wherein the primary load is 5KN, and the load is increased by 10KN in each grade after reaching 20 KN.
And 7: finite element solving and post-processing.
①, defining the model analysis type as static analysis, setting the current sub-step number and the maximum balance iteration number as 200 and 40 respectively, taking the node displacement as the convergence check standard, setting the convergence error as 0.05, carrying out finite element solution, applying a primary load of 5KN, and if the obtained node displacement u is obtainednLess than the maximum displacement u allowed by the programsThen go to the next step, otherwise, when u is appliednGreater than usThe program will report an error, end the calculation and extract the result of the last step.
② extracting results and post-processing, extracting 1-1 section stress cloud pictures (see figure 12) of the model under each level of load, respectively extracting load sliding curves of the free end and the tensioning end node of each steel strand, and taking the average value of the load sliding curves as the integral bonding sliding curve of the prestressed tendons (see figure 13).
And 8: and determining a prestressed tendon bonding slip curve and verifying the accuracy of the prestressed tendon bonding slip curve.
According to the finite element simulation result, the stress cloud picture and the bonding slip curve of the bonding area of the model are analyzed, and it can be seen from the stress cloud picture that the stress is gradually transmitted from the tensioning end to the free end along with the increase of the load, and the chemical adhesive force between the prestressed beam and the grouting body is continuously lost in the process. With increasing slippage, the adhesion is imparted by the machineThe occlusal force and the friction force are born, when the maximum adhesive force is reached, the adhesive slip curve enters a gentle section, the slip amount is obviously increased, and the load is basically kept unchanged. The final stage of adhesion is mainly provided by friction, namely residual stress shown in a stress cloud chart, and the steel strand is pulled out. In addition, as can be seen from the bonding slip curve, when the effective bonding length of the test piece is 470mm, the maximum bonding stress which can be borne by the whole prestressed tendon is 114 × 7-798 KN, and the average maximum bonding force of each steel strand is Fmb114KN less than the ultimate tensile force F of a single tendonpThe test piece is judged to be pulled out and damaged at 260KN, and the result is consistent with the conclusion of the literature.
Further verifying the correctness of the analysis method, respectively establishing test pieces with effective bonding lengths of 622mm, 965mm and 1219mm in the literature by adopting the method, wherein the obtained bonding slip curve is shown in fig. 13, and when the effective bonding length is 622mm, the average maximum bonding force of each steel strand is 153.8KN, which means that the prestressed beam is still pulled out and damaged; when the effective bonding length is 1219mm, the average maximum bonding force of each steel strand reaches 266.3KN and exceeds the ultimate tensile force FpAt 260KN, the prestressed tendons break and break; when the effective bonding length is 965mm, the maximum bonding force of each steel strand is 244.3KN on average, and the ultimate tensile force which can be borne by the prestressed tendons reaches 91.7% GUTS (ultimate tensile strength), which shows that the bonding force required by re-anchoring can be provided when the effective bonding length is more than 965mm, and the bonding force is identical to the conclusion of the literature and has higher precision.
TABLE 1 mechanical Properties of concrete and Steel strand
Claims (2)
1. A finite element simulation method for bonding performance between a prestressed tendon and concrete is characterized by comprising the following steps:
step 1: establishing a geometric model; according to an actual engineering structure, determining geometric parameters of a model, wherein the geometric model of the concrete and the grouting body in the prestressed duct is obtained by adopting a separated modeling method; the establishment of the geometrical model of the prestressed tendons can be realized by two steps, firstly, concrete is split at the position of the steel strand by adopting a solid splitting method, then a plurality of lines with the same geometrical parameters as the steel strand are created at the splitting position again to serve as the geometrical model of the prestressed tendons, and the geometrical model of the common steel bars is obtained by adopting the same method; in the model, the bonding slippage between the concrete and the grout body is not considered, the concrete and the grout body are considered to be completely bonded, the bonding slippage between the common steel bar and the concrete is ignored, and the common steel bar and the concrete are connected by adopting a method for establishing a constraint equation;
step 2: determining the composition of the integral sliding surface and the effective working surface of the prestressed beam; the method specifically comprises the following steps: the contact surface of the steel strand and the surrounding concrete and the effective working area and the bonding force of concrete slurry among the steel strands are formed;
and step 3: determining the ultimate bonding force of the prestressed tendons and the equivalent maximum bonding stress of the single prestressed tendons in the prestressed tendons; establishing a stress balance relation of the micro units of the prestressed tendon interface, and providing a calculation method of the ultimate binding force of the prestressed tendon; on the basis, an equivalent principle of the ultimate bonding force of the prestressed tendons is given, and the equivalent maximum bonding stress of the single prestressed tendon is deduced according to the equivalent principle;
and 4, step 4: defining a unit type and material constitutive relation;
1) concrete and grouting material are simulated by a three-dimensional Solid unit Solid65, and a Hongnestad material constitutive model is adopted;
2) the steel strand in the prestressed bundle is simulated by adopting a Link8 unit, the common steel bar is simulated by adopting a Link8 unit, and the steel strand and the common steel bar are made of a simplified Menegotto constitutive model;
3) simulating the bonding slip relationship between the steel strand and the concrete in the prestressed tendon by using a COMBIN39 nonlinear spring unit, wherein the unit property is defined by the bonding slip relationship between the steel strand and the concrete unit;
and 5: defining the attribute of a spring unit between a single steel strand and concrete in a prestressed strand;
firstly, based on the equivalent maximum bonding stress tau of a single steel strand in a prestressed beammaxCalculating formula, updating BPE bonding slip model, and deducingObtaining the property of a spring unit for simulating the bonding slippage between a single steel strand and concrete according to the bonding slippage relation between the steel strand unit and the concrete unit, and further realizing the finite element simulation of the equivalent bonding slippage of the single steel strand in the prestressed bundle;
the bonding slippage between the single steel strand and the concrete is simulated by adopting a COMBIN39 spring unit, and specifically, three spring units with zero length are adopted to be connected between the superposed nodes of the steel strand and the concrete unit; among the three springs, the deformation of the springs in the normal direction and the transverse direction is negligible relative to the deformation in the longitudinal direction, so that the stiffness coefficients K of the springs in the two directions can be infinitely large; the bonding slippage between the steel strand and the concrete is mainly simulated by a longitudinal spring, the unit property of the bonding slippage is obtained by the bonding slippage relation between a single steel strand and a concrete unit, wherein the bonding force F between the single steel strand and the concrete unit is calculated by the following formula:
F＝Ar·τ＝π·br·lr·τ (1)
in the formula, ArIs the unit surface area of the tendon, brIs the unit diameter of the tendonrThe length of a prestressed tendon unit is shown, tau is the bonding stress between the prestressed tendon and a concrete unit, and can be determined according to a BPE bonding slippage model:
in the formula, τmaxIs the equivalent maximum bonding stress of a single steel strand in the prestressed strand, S is the slip value corresponding to tau, S1To correspond to τmaxSlip value of (S)2Is the slip value, tau, at the end of the parallel section in the bond slip model3And S3Respectively the residual stress and the corresponding slip value;
step 6: defining a grid dividing and loading mode;
①, grid division, wherein the quality of the grid will affect the calculation accuracy and convergence, regular hexahedron units are adopted as much as possible, and for the areas with strong nonlinear response, the units are not suitable to be too small in size for avoiding stress concentration and cracking in advance;
②, defining the loading mode of the model, wherein the model adopts graded loading, and the load is applied to the end node of the prestressed tendon;
and 7: finite element solving and post-processing;
①, solving, defining analysis types and solving control options, setting the maximum number of balanced iterations and convergence criterion parameters to carry out finite element solving calculation;
②, extracting results and post-processing, extracting section stress cloud charts under various levels of load models, extracting load slip curves of each steel strand, and taking the average value of the load slip curves as the load slip curves of the prestressed tendons;
and 8: determining a prestressed tendon bonding sliding curve and verifying the precision of the curve, wherein the prestressed tendon bonding force is obtained by superposing equivalent bonding forces of single prestressed tendons, and the prestressed tendon sliding is obtained by taking the average sliding value of the single prestressed tendons; the accuracy of the method is verified by combining the prestressed tendon binding force and prestressed tendon sliding data of the existing experiment.
2. A finite element simulation method of bonding performance between a prestressed tendon and concrete according to claim 1, wherein an equivalent simulation method of bonding sliding of the prestressed tendon is provided, which mainly comprises two aspects of steps 2 and 3, wherein ① provides a principle of determining an integral sliding surface and an effective working surface of the prestressed tendon;
(1) the method specifically comprises the steps that the principle of determining the overall sliding surface and the effective working surface of the prestressed tendons is determined, and the principle specifically comprises the contact surface of steel strands and surrounding concrete, the effective working area of concrete slurry among the steel strands and the binding power; the prestressed tendon bonding slippage can be equivalent to the bonding slippage between a combination body formed by the prestressed tendon and the internal slurry and the surrounding concrete; the binding mechanism of the prestressed tendons is similar to that of the single prestressed tendon, the prestressed tendons and the single prestressed tendon are composed of chemical adhesive force, mechanical engaging force and friction force, but the two prestressed tendons are mainly different in effective working surface, the effective working surface of the single prestressed tendon is the outer surface of the steel strand, the effective working surface of the prestressed tendons is the outer surface of the combined body, the effective working area of the prestressed tendons is smaller than the sum of the single prestressed tendons in the same number, and the number of the steel strands is more, so that the nonlinearity of the relation is more obvious;
the contact surface of the steel strand and the surrounding concrete is the cambered surface of the combination body, which is called as a mechanical occlusal surface AυThe steel strand is mainly used for bearing the concrete occlusion effect among the steel strand ribs and is also under the action of friction force; according to the profile characteristics of the prestressed tendon assembly, a mechanical occlusal surface AυCan be expressed as:
Aυ＝lv·lω＝ns·lg·lω(3)
in the formula IvFor the width of the mechanical engaging surface of the tendon, /)gThe width of the concrete engaging surface between the single steel wire and the rib is 1/4 circumferences of the steel wire, nsThe number of steel wires of the mechanical occlusal surface lωIs the length of the peripheral steel wire of the steel strand, /)dThe length of the middle steel wire of the steel strand is regarded as theta, and the included angle between the peripheral steel wire and the central steel wire of the steel strand is regarded as theta;
the effective working surface of the concrete slurry between the steel strands is the tangent plane of the assembly, called friction surface AfMainly bearing the frictional resistance of the concrete interface, and the expression is as follows:
Af＝lf·lω(5)
lf＝nj·l'f+ns·lm(6)
l'f＝2d-ds(7)
in the formula IfWidth of friction surface of prestressed tendonmIs the width of the friction surface of the concrete between the single steel wire and the rib, and has the value of 1/2 circumference l'fIs a single section width, njIs the number of sections, d is the diameter of the steel strand, dsIs a steel strandThe diameter of the medium steel wire;
(2) establishing a stress balance relation of the micro units of the prestressed tendon interface based on a determination method for the bonding force composition on the effective working surface and different working surfaces of the prestressed tendon, and providing a calculation method for the ultimate bonding force of the prestressed tendon; on the basis, the equivalent principle of the ultimate bonding force of the prestressed tendons is given, and the equivalent maximum bonding stress tau of the single steel strand is deduced according to the equivalent principlemaxCalculating a formula; tensile force F of steel strandpThe relative slip trend appears under the action, and the chemical adhesive force gradually disappears along with the generation of the slip, so that the structure bonding performance is slightly influenced; the sliding and rotation of the steel strand are restricted by the concrete between the ribs, and oblique extrusion force perpendicular to the ribs is generated at the contact surface of the steel strand and can be decomposed into radial compressive stress sigmanWith axial shear stress upsilons(ii) a Taking the micro unit of the contact surface of the prestressed tendon and the concrete at the position of the free end x of the test piece for stress analysis, and carrying out tensile force F on the micro unit of the prestressed tendonxOne part transmits to the concrete unit of congealing on every side and makes it reach extreme condition, and another part transmits for next little unit, and until the tensile force through the whole concrete unit that transmits of prestressing tendons, then whole stress transmission process finishes, has to prestressing tendons unit atress:
dFx-lv·υs(x)·dx-μ·lf·σn(x)·dx＝0 (8)
in the formula, FxIs the tensile force, sigma, on the tendon microcell at the point xn(x)、υs(x) Respectively, the normal stress and the shear stress of the concrete at the point x, and the formula (8) can be obtained by arranging:
wherein tau (x) is bonding stress at the contact surface of the dx section, and the oblique extrusion stress sigma of the prestressed tendon unit on the dx sectionm(x) From Eurocode 2 formula:
k＝1.05·Ec·εc0/f’c(11)
of formula (II) to'cIs the ultimate compressive strength of concrete, epsilonc0For ultimate strain of concrete, EcIs the modulus of elasticity, ε, of concretec(x) For the concrete strain of the dx section, the mean positive stress sigma of the dx section in the process of reaching the limit stateca(x) Comprises the following steps:
in the formula, epsilonc0For ultimate strain of concrete, the oblique extrusion stress on dx section is decomposed into positive stress sigman(x) Comprises the following steps:
σn(x)＝σca(x)·sinθ (14)
in the formula, theta is an included angle between an outer wire and an inner wire of the steel strand, and the shear stress caused by the oblique extrusion stress is as follows:
in the formula, ucIs the shear stress of concrete, ftThe tensile strength of the concrete axle center;
the maximum bonding force F of the tendon at the effective bonding length ls：
Maximum binding force F based on integral sliding of prestressed beamsEvenly distributing the stress to each steel strand to establish the equivalent maximum bonding stress tau of the single steel strandmaxCalculating the formula:
wherein n is the number of the steel strands, d is the diameter of the steel strands, ldThe effective bonding length of the steel strand.
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| CN110108864B (en) * | 2019-05-21 | 2022-01-28 | 湖南城市学院 | Nondestructive testing system and method for prestressed concrete beam |
| CN113111559A (en) * | 2021-04-21 | 2021-07-13 | 中国十七冶集团有限公司 | Finite element simulation method for bonding slippage of steel-concrete composite structure |
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