CN109344437B - Reinforced concrete complex stress component reinforcement design method based on force transmission path - Google Patents

Reinforced concrete complex stress component reinforcement design method based on force transmission path Download PDF

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CN109344437B
CN109344437B CN201810991585.6A CN201810991585A CN109344437B CN 109344437 B CN109344437 B CN 109344437B CN 201810991585 A CN201810991585 A CN 201810991585A CN 109344437 B CN109344437 B CN 109344437B
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张鹄志
徐文韬
黄垚森
杨彤麟
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Hunan University of Science and Technology
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Abstract

The invention belongs to the technical field of structural design of civil engineering, and particularly relates to a reinforcement design method for a reinforced concrete complex stressed component based on a force transmission path, which is mainly used for reinforcement design of reinforced concrete complex stressed components which do not conform to the assumption of a flat section, such as deep beams, shear walls and the like, and comprises the steps of (1) obtaining the force transmission path of the reinforced concrete complex stressed component; (2) carrying out reinforcement design on the component according to the force transmission path; (3) merging and finishing the steel bars; (4) and (5) carrying out structural design on the component. The method takes the force transmission path as a starting point to design the reinforcing bars of the reinforced concrete complex stress structural member, can change the situation that the traditional empirical design method is rough in design and low in precision and is only based on experimental statistics and insufficient in theoretical support, and provides a new technical thought for the reinforcing bar design of the complex stress structural member or novel material which is difficult to accurately solve at present.

Description

Reinforced concrete complex stress component reinforcement design method based on force transmission path
Technical Field
The invention belongs to the technical field of structural design of civil engineering, and particularly relates to a reinforcement design method for a reinforced concrete complex stressed component based on a force transmission path, which is mainly used for reinforcement design of reinforced concrete complex stressed components which do not conform to the assumption of a flat section, such as deep beams, shear walls and the like.
Background
In the structural design industry in civil engineering, for two-dimensional members with complex stress distributions, such as shear wall structures, the deformation has not been completely compliant with the flat section assumption, so it is not reasonable to simplify the design into a bar system structure.
Regarding the problem of reinforcement design of a shear wall in a reinforced concrete complex stress member, the design concept of the shear wall in China and the United states is as follows:
1) the reinforcement calculation method of the shear wall is still the reinforcement calculation according to eccentric tension or eccentric compression of a general flexural member as given in the second section of chapter 6 of the current concrete structure design Specification GB50010-2010 in China, and the reinforcement design of the rectangular, T-shaped and I-shaped eccentric compression shear wall limbs is recommended by an empirical method to calculate the compression bearing capacity of the normal section of the rectangular, T-shaped and I-shaped eccentric compression shear wall limbs in chapter 7 of the concrete structure technical Specification JGJ3-2010 in high-rise buildings, and most of the methods are based on the assumption of a flat section and are mainly based on an empirical or semi-empirical method for data correction through a series of tests.
2) The section 11.8 and the section 14 of the American 'concrete structure design Specification' ACI 318-14 also give suggestions of empirical methods, and it can be seen that the specifications of various countries mostly still use the assumption of a flat section as the basis when the reinforcement design of a shear wall is carried out, the design is carried out by analogy with a frame column, the specification of the section 23 also recommends that a tension and compression bar model method is designed and applied to the design of the shear wall, the complex stressed member is divided into a B area and a D area according to the stress characteristics of the complex stressed member, the B area represents the area which conforms to the assumption of the flat section, the D area represents the area which does not conform to the assumption of the flat section, a tension and compression bar model is established for reinforcement design, but certain defects still exist due to neglecting the non-linear characteristics of concrete members and the like.
The specifications of various countries based on the assumption of a flat section are mostly unreasonable for the reinforcement design of the shear wall, and after the scholars at home and abroad recognize this point, a stress design method is popularized. GB50010-2010 gives an experience method and a suggestion of a stress design method, proposes a two-dimensional or three-dimensional non-rod system structural member, and after the stress design value distribution of the member is obtained according to an elasticity or elastoplasticity analysis method, the reinforcement amount can be determined according to the projection of the resultant force of the main tensile stress design value in the reinforcement direction, and the reinforcement arrangement is determined according to the distribution region of the main tensile stress; ACI 318-14 also suggests that the design of wall height may be no more than 2 times its length in horizontal shear, and therefore, in the current state of the art, there is a lack of reinforcement that can be applied directly to complex stressed components. At present, most of shear wall design specifications of various countries are empirical design methods, most of the design methods are a set of theories summarized by a large number of experiments and experiences, and the design methods are unreasonable by analogy with frame columns based on flat section assumption.
Disclosure of Invention
Aiming at the technical problems, the invention provides a reinforced concrete complex stress component reinforcement design method based on a force transmission path.
The specific technical scheme is as follows:
the reinforced concrete complex stress component reinforcement design method based on the force transmission path is roughly divided into four steps:
(1) acquiring a force transmission path of a reinforced concrete complex stressed component;
(2) performing reinforcement preliminary design on the component according to the force transmission path;
(3) merging and finishing the steel bars;
(4) and (5) carrying out structural design on the component.
The detailed process is as follows:
(1) the method for acquiring the force transmission path of the complex stress component mainly comprises the following methods:
(1.1) finite element analysis method: firstly, acquiring a force transmission path which can be obtained by using a stress result of finite element analysis, establishing a coordinate system in fig. 1, and keeping a load value of a load in any direction of the coordinate system constant in a transmission channel from an acting position to a reaction position; solving the tangent line and the angle of the outer contour line of the load path on the finite element cell by using the method, such as figure 2, and then solving the outer contour line of the whole continuous force transmission path by using a streamline tracing method; first, it should be satisfied that for zero total force in any direction, at point E:
σnsinθds＝τntcosds (1)
σn、τntfor normal and tangential stresses in the x-direction at point E, there is σn、τntAnd σx、σyAnd σxyThe relationship of (1):
σn＝σxsin2θ+σycos2θ-2τxysinθcosθ (2)
τnt＝(σy-σx)sinθcosθ+τxy(cos2θ-sin2θ) (3)
change the formula (1) into
Figure GDA0002888946450000031
Substituting the formulas (2) and (3) into the formula:
Figure GDA0002888946450000032
obtaining: sigmaxtan3θ-τxytan2θ+σxtanθ-τxy＝0 (4)
Is provided with
Figure GDA0002888946450000033
Obtaining: (tan)2θ+1)(tanθ-α)＝0 (5)
Then, the included angle between the load path contour line and the x axis is obtained:
Figure GDA0002888946450000034
(1.2) evolutionary optimization algorithm
Evolutionary algorithm — ESO: the method is the basis of all calculation algorithms, and the structure gradually tends to be optimized by giving a certain unit deletion standard, deleting invalid or inefficient stress units, and then gradually improving the deletion standard to continuously optimize until the optimization stops after multiple iterations.
Genetic evolution optimization algorithm-GESO: the method is characterized in that ANSYS analysis software is used as a tool to establish a steel bar and concrete separation type model, a Link10 unit is used for simulating steel bars, a Solid65 unit is used for simulating concrete, and the concrete flow steps are as follows:
a. and (3) taking the boundary condition and the load condition of the complex stress member into consideration, and establishing a separate model of the steel bar and the concrete by using ANSYS software.
b. And dividing the finite element cells, and endowing each steel bar unit with a binary string chromosome with the length of n, wherein the genes in the chromosome are all 1.
c. And carrying out finite element analysis on the structure to obtain the structure response.
d. And calculating the sensitivity of the steel bar units, sequencing the sensitivity values, and changing genes of which the number is 1 into 0 according to an optimization target to a plurality of later units according to a certain probability.
e. And selecting a certain hybridization rate to perform hybridization operation of the whole population.
f. And if all genes in the chromosome corresponding to a certain rebar unit are 0, discarding the rebar unit.
g. And repeating the steps 3-6 until the stopping condition preset by the structure is met or the expected requirement is met, and obtaining the final topological optimization graph which is also the force transmission path graph.
Bidirectional progressive structure optimization algorithm-BESO: based on the ESO, not only can the structural inefficient or ineffective unit be deleted, but also the unit can be added in the area of the high stress unit or high sensitivity unit, so as to optimize the structure.
Genetic incremental evolution algorithm-GAESO: by utilizing the principle of 'out-of-the-best and survival of the suitable person', a genetic evolution algorithm is introduced on the basis of an incremental evolution algorithm, a finite element model is established, units are divided, an initial structure and constraint conditions are selected, then finite element analysis is carried out to enable increasing units with probability to be arranged near the units with higher fitness, loads are increased step by step, iteration is continued until the convergence conditions are met after the preset loads are reached, and therefore the structure is optimal.
(2) The concrete method for designing the reinforcing bars of the component according to the force transmission path comprises the following steps:
a. the force transmission paths obtained in the first step comprise a compression path and a tension path, and in design, the tension or compression of the force transmission paths can be judged by establishing a truss model and inputting load conditions through mechanics solving software such as a structural mechanics solver, and the stress magnitude of each force transmission path can also be obtained.
b. Because the force transmission path can not be a regular geometric figure, and the convenience and the practicability of construction are considered, the irregular force transmission path is required to be regularized and simplified, and the method specifically comprises the following steps: for each force transfer path, a set of parallel lines is used to enclose the force transfer path. For example, as shown in fig. 3 and 4, the GESO optimization results are sorted.
c. Dividing the finishing result of the step b into independent tensioned or compressed areas, and combining the stress obtained in the step a to obtain the tension or pressure of each area; reinforcement design is then performed based on the resulting force transfer path:
for a compressed region: because the reinforced concrete member, concrete mainly undertake compressive stress, the compressive stress that the reinforcing bar bore can be ignored, consequently should compare the compressive stress that this member bore and concrete compressive strength earlier, carry out the intensity check:
Figure GDA0002888946450000041
wherein N is1For pressure, A is the cross-sectional area (A is the product of the width of the force transmission path and the thickness of the component), fcThe design value is the concrete compressive strength; the fact that the size of the member and the strength grade of the concrete are reasonably selected and the next reinforcement design can be carried out is shown when the above formula is met;
along the force transfer path direction: only the minimum reinforcement ratio requirement of the compression member of the specification requirement (8.5.1 in the concrete structure design specification GB 50010-2010) is met; perpendicular to the force transmission path direction: due to the poisson effect, tension strain perpendicular to the force transmission path direction is caused by pressure strain along the force transmission path direction, so that a stirrup needs to be configured perpendicular to the force transmission path direction, the direction perpendicular to the force transmission path is restrained, and the stirrup is configured according to the stirrup configuration specification (9.3.2 in the concrete structure design specification GB 50010-2010) of a column.
For the tensioned region: the method is characterized in that the steel bar bears the tensile stress, and the specific method comprises the following steps:
N2≤fyASI
wherein N is2Is a pulling force, unit N, ASIIs the nominal area of the hot rolled steel bar and has unit mm2，fyThe tensile strength, namely the yield strength design value of the hot rolled steel bar is measured in N/mm2；
The force transmission path of the complex stress member may have a section of continuous force transmission path, and the joint between every two force transmission paths is not easy to be configured with steel bars, at this time, a steel strand can be adopted to resist tensile stress, for example, as shown in the following application example of two-span continuous deep beams, the concrete method of reinforcement configuration design is as follows:
Figure GDA0002888946450000051
wherein N is a tensile force, AsIs the nominal area of the steel strand, fpyThe design value of the tensile strength of the prestressed steel strand is shown.
(3) Merging and finishing the steel bars: in order to make the obtained result easier for engineering application, steel bars can be merged, and if the obtained result is regular, the step can be skipped to the step 4), and the specific method is as follows:
(3.1) Isointensity method:
n1fy1As1≤n2fy2As2
wherein n is1、n2Respectively the number of the steel bars before and after merging, fy1And fy2Respectively designed strength values of the steel bars before and after merging, As1And As2The area of the section of the single steel bar before and after merging is respectively.
(3.2) pitch equivalence method:
n1s1＝n2s2
in case the pitch meets the pitch requirement in the specification, s1And s2Respectively representing the steel bar spacing before and after merging. And after the merging, the maximum steel bar spacing requirement in the specification cannot be exceeded. When two or several parallel steel bars are not equal in length, but the length difference meets the following conditions, merging can be carried out:
Figure GDA0002888946450000052
in the formula I1And l2The lengths of the shortest reinforcing steel bar and the longest reinforcing steel bar before merging are respectively, and lambda is recommended to be 0.7-1.0. At this time according to length l2And (6) merging.
(4) The components are made to meet the construction requirements according to the specifications: according to the concrete structure design specification GB50010-2010, the components need to meet the following requirements;
(4.1) for the shear wall, reinforcing steel bar nets are distributed in a double-row configuration mode and are arranged along two side faces of the wall, tie bars are adopted for connection, the diameter of each tie bar is larger than or equal to 6 mm, and the distance between the tie bars is not larger than 600 mm.
(4.2) the anchoring length requirement of the steel bar:
the use of a common steel bar is preferred,
Figure GDA0002888946450000061
lab-a basic anchoring length of the tensioned reinforcement bar;
d-the diameter of the anchoring bar;
alpha is the form factor of the anchoring steel bar;
anchoring length of tension bar:
la＝ξalab
la-the anchoring length of the tensioned bar;
ξathe anchoring length correction factor is used according to the standard of 8.3.2 pieces of common steel bars.
The invention is different from the characteristics and advantages of the traditional technology:
(1) the complex stress components which do not accord with the flat section assumption are mostly calculated by adopting an empirical formula method in various countries, wherein the reinforcement calculation of the shear wall is calculated by analogy with a frame on the basis of the flat section assumption, and the reinforcement design method of the technology is a stress design method and has enough theoretical support.
(2) The reinforcement design method based on the empirical formula is generally over conservative, so that a part of cost is increased in terms of engineering economy, particularly in countries with a large population and a shear wall structure as the main design of the existing residential structure in China, the reinforcement design method increases the resource burden of China, and the novel technology can greatly save the consumption of the reinforcement so as to save a part of engineering cost.
(3) From the mechanical point of view, the ductility of the tension steel bar is difficult to be fully exerted by an empirical formula method, the invention firstly proposes that reinforcement design is carried out from a force transmission path, a force transmission path of a complex stress component is obtained by a finite element method or a genetic evolution optimization algorithm, and then the whole component is divided into a tensile stress area and a compressive stress area by the force transmission path; compared with the traditional reinforcement method for the complex stressed member, the method has clear mechanical concept, has clear and correct idea for solving the reinforcement problem of the complex stressed member which does not meet the assumption of a flat section, and fully exerts the performance of the material under the condition of ensuring the reliability of the member.
The invention has the following beneficial technical effects:
(1) the method has the advantages that the idea of designing the reinforcing bars of the reinforced concrete complex stress structural member by taking the force transmission path as a starting point is put forward for the first time, the situation that the traditional empirical design method is rough in design and low in precision and is only based on experimental statistics and insufficient in theoretical support can be changed, and a new technical thought is provided for designing the reinforcing bars of the complex stress structural member or the novel material which is difficult to solve more accurately at present.
(2) The building construction cost is reduced by about 20-40%, and resources are saved.
Drawings
FIG. 1 is a plan view of the loading path of the structure of the present invention;
FIG. 2 illustrates the cell plane stress of the present invention;
FIG. 3 is a topological graph derived from GESO of the present invention;
FIG. 4 shows the results of the finishing of the present invention;
FIG. 5 illustrates example continuous deep beam dimensions;
FIG. 6 is a force transfer path obtained by GESO according to an embodiment;
FIG. 7 is a force transfer path of the embodiment after finishing;
FIG. 8 is a reinforcement diagram of two continuous deep beams according to the embodiment.
Detailed Description
The specific technical scheme of the invention is described by combining the embodiment.
Taking two-span continuous deep beam as an example, the designed strength of concrete is C30, and the elastic modulus Ec＝3×104N/mm2Poisson ratio μ ═ 0.2, size: the section length is 2000mm, the section height is 500mm, the section width is 120mm, the protective layer thickness is 30mm, and the reinforcing steel bar strength is HRB 335. Two concentrated forces of 500kN were applied at the top of the continuous beam as shown in figure 5.
1) The force transmission path of the structure is obtained through genetic evolution optimization-GESO (genetic evolution optimization) as shown in figure 6, and the obtained force transmission path is sorted, so that the obtained sorting result is shown in figure 7.
2) Carrying out reinforcement design through a force transmission path to obtain a final reinforcement diagram
According to the design specification GB50010-2010 of concrete structures, the deep beam should be provided with double-layer steel bar nets, the diameters of the horizontally and vertically distributed steel bars should not be smaller than 8mm, and the distance between the horizontally and vertically distributed steel bars should not be larger than 200 mm. According to the structural requirements of the deep beam in the specification and the technical method, steel strands are used in a part of the tension area according to the characteristics of a force transmission path, and finally, a reinforcement distribution diagram is obtained, as shown in fig. 8, all the steel bars which are not noted in the diagram are B6.

Claims (1)

1. The reinforced concrete complex stress component reinforcement design method based on the force transmission path is characterized by comprising the following innovative steps and methods:
(1) acquiring a force transmission path of the complex stress component based on a finite element analysis method, an evolution optimization algorithm, a bidirectional progressive structure optimization algorithm and a genetic incremental evolution algorithm;
(2) based on the mechanical limit balance calculation of the force transmission path, carrying out reinforcement preliminary design on the component;
(3) merging and arranging the reinforcing steel bars based on an equal strength method and an interval equivalent method;
(4) the components are made to meet the construction requirements according to the specifications: according to the design specification GB50010-2010 of concrete structures, the components need to meet the following requirements:
a. for the shear wall, reinforcing mesh is distributed in double rows and arranged along two side surfaces of the wall, tie bars are adopted for connection, the diameter of each tie bar is more than or equal to 6 mm, and the distance between the tie bars is not more than 600 mm;
b. the anchoring length requirement of the steel bar is as follows:
Figure FDA0002888946440000011
lab-the basic anchoring length of the tensioned bars in mm;
d is the diameter of the anchoring steel bar in mm;
alpha is the form factor of the anchoring steel bar;
the anchoring length of the tensioned reinforcement bar;
la＝ξalab
la-the anchoring length of the tensioned bar, in mm;
ξathe anchoring length correction coefficient is used for the common steel bars according to the standard of 8.3.2 bars;
the specific innovative method for preliminarily designing the component reinforcement according to the force transmission path is as follows:
(2.1) the force transmission paths obtained in the step (1) comprise a compression path and a tension path, and the tension or compression of the force transmission paths is judged by establishing a truss model and inputting load conditions to obtain the stress size of each force transmission path;
(2.2) regularizing and simplifying irregular force transmission paths;
(2.3) dividing the finishing result of the step (2.2) into independent tension or compression areas, and combining the stress obtained in the step (2.1) to obtain the tension or pressure of each area; reinforcement design is then performed based on the resulting force transfer path:
2.3.a. for compressed areas: the compression stress borne by the member is compared with the concrete compression strength, and the strength is checked:
Figure FDA0002888946440000021
wherein N is1Is the pressure, in N, A is the cross-sectional area, in mm2I.e. the product of the width of the force-transmitting path and the thickness of the component, fcThe design value of the compressive strength of the concrete is the unit of N/mm2；
Along the force transfer path direction: only the minimum reinforcement ratio requirement of the compression member meeting the specification requirement is met; perpendicular to the force transmission path direction: the method comprises the following steps of configuring stirrups in a direction perpendicular to a force transmission path, constraining the direction perpendicular to the force transmission path, and specifically configuring the stirrups according to the stirrup configuration specification of a column;
2.3.b. for the tensioned region: the method for bearing the tensile stress by hot rolling the steel bar comprises the following steps:
N2≤fyASI
wherein N is2Is a pulling force, unit N, ASIIs the nominal area of the hot rolled steel bar and has unit mm2，fyThe tensile strength, namely the yield strength design value of the hot rolled steel bar is measured in N/mm2；
The force transmission path of the complex stress component may have a section of continuous force transmission path, and the joint between every two force transmission paths is not easy to be configured with steel bars, at this time, the steel strand can be adopted to resist the tensile stress, and the concrete method of the reinforcement configuration design is as follows:
Figure FDA0002888946440000022
wherein N is the pulling force in the unit of N, AsIs the nominal area of the steel strand in mm2，fpyThe design value of the tensile strength of the prestressed steel strand is the unit of N/mm2；
The concrete innovative method for merging and arranging the steel bars in the step (3) is as follows:
(3.1) Isointensity method:
n1fy1As1≤n2fy2As2
wherein n is1、n2Respectively the number of the steel bars before and after merging, fy1And fy2Respectively the strength design values of the reinforcing steel bars before and after merging, and the unit is N/mm2，As1And As2Respectively being the cross-sectional area of the single steel bar before and after merging in unit mm2；
(3.2) pitch equivalence method:
n1s1＝n2s2
in case the pitch meets the pitch requirement in the specification, s1And s2Respectively representing the steel bar spacing before and after merging, wherein the unit mm can not exceed the maximum steel bar spacing requirement in the specification after merging;
when two or several parallel steel bars are not equal in length, but the length difference meets the following conditions, merging can be carried out:
l1≥λl2
in the formula I1And l2The lengths of the shortest reinforcing steel bar and the longest reinforcing steel bar before merging are respectively, the unit mm and the lambda are 0.7-1.0, and the length l is used at the moment2And (6) merging.
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