CN116484456A - Method for calculating reinforced concrete shear wall and novel shear wall - Google Patents
Method for calculating reinforced concrete shear wall and novel shear wall Download PDFInfo
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Abstract
The application discloses a method for calculating the maximum average compressive stress in concrete in a reinforced concrete shear wall, which considers the contribution of interaction between reinforced steel bars and the concrete to the compressive stress in the concrete; calculating the maximum average compressive stress in the shear wall concrete based on the average compressive stress born by the concrete and the contribution value of the interaction between the steel bars and the concrete to the compressive stress in the concrete; through the calculation method, the application also provides a method for judging the maximum load which can be borne by the shear wall and a method for judging the maximum reinforcement ratio of the shear wall, and finally designs the shear wall with a novel structure.
Description
Technical Field
The present application relates to the field of construction engineering, and more particularly, to a method for calculating a maximum load that can be borne by concrete in a reinforced concrete shear wall, and a shear wall of a novel structure.
Background
Reinforced concrete shear walls are currently the primary lateral force resistant members widely used in high-rise building structures. The reinforced concrete shear wall mainly bears shear force or lateral horizontal load in the structure, and has the mechanical characteristics of good integrity, high lateral stiffness and good bearing performance. In addition, the reinforced concrete shear wall has the advantages of mature construction technology and relatively low manufacturing cost.
In the existing design method, the structural form of the reinforced concrete shear wall is a wall structure formed by horizontally and vertically placed reinforced grids and concrete pouring. The arrangement of the steel bars in the shear wall in the horizontal and vertical directions is generally uniformly distributed, that is, the diameters and the pitches of the steel bars in the horizontal or vertical directions are the same.
The steel bars and the concrete work cooperatively to jointly resist the action of external load. After the external load reaches a certain degree, the concrete in the shear wall is cracked, the steel bars are in a uniaxial tension state, and the concrete is in a uniaxial compression state.
In reinforced concrete shear walls, the so-called softening phenomenon is observed, in which the concrete breaks when the average compressive stress inside is far less than its breaking strength. Since the reinforced concrete shear wall member requires simultaneous coordination of the reinforcement and the concrete, the shear wall member cannot continue to operate as long as either the reinforcement or the concrete is damaged, and thus the shear strength of the shear wall is significantly lower than expected based on the strength of the materials.
Although the shear strength of the shear wall can be increased by properly increasing the content of the reinforcing steel bars in the shear wall, namely the reinforcing steel bar arrangement rate, in practice the reinforcing steel bar arrangement rate of the reinforcing steel bars in the shear wall cannot be increased at will. Firstly, when the reinforcement ratio reaches a certain degree, the condition that the concrete reaches the material strength and is damaged can occur, so that the shear strength of the shear wall is not increased by continuously increasing the reinforcement ratio. Moreover, the concrete is damaged before the steel bar, which belongs to brittle failure, has extremely high hazard and belongs to the condition needing to be avoided in structural design.
The concrete softening mechanism is unclear, so that the failure mechanism of the shear wall is ambiguous, only the lowest reinforcement ratio (horizontal distribution reinforcement is not less than 0.25%) of the shear wall is specified in the earthquake-proof specification, but the minimum reinforcement ratio (one-side longitudinal reinforcement, 0.2%) and the maximum reinforcement ratio (reinforcement ratio of longitudinal tension reinforcement at the beam end is not more than 2.5% and reinforcement ratio of all longitudinal reinforcement of the column is not more than 5%) are specified in the specification for reinforced concrete beams and columns. Therefore, in engineering practice, the reinforcement ratio of the reinforced concrete shear wall is generally lower than that of beams and columns, so that the pressure of concrete in the shear wall is smaller when the reinforcing steel reaches a yield state and the pressure does not reach a failure state, and the ductile failure of the structure is ensured.
Therefore, based on the existing design method, it is difficult to improve the strength of the shear wall simply by improving the reinforcement ratio of the reinforcing steel bars. To improve the performance of a shear wall, it is often necessary to increase the strength of the concrete or the size of the shear wall, which is costly to improve the structural strength. In the case of shear wall sizing, it is sometimes difficult to increase the strength of the shear wall.
Disclosure of Invention
The problem to be solved by the application is: based on the found concrete softening mechanism, a method for quantitatively calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall is found, so that the maximum load which the shear wall can bear is judged, and the maximum reinforcement ratio allowed by the shear wall is calculated. On the premise of ensuring ductile damage of the shear wall, the concrete softening phenomenon is lightened by reasonably arranging the reinforcing steel bars, the maximum reinforcement ratio of the reinforcing steel bars allowed by the shear wall is improved, and the strength of the shear wall structure is improved.
The applicant has found that in the prior art design method, the conventional reinforced concrete shear wall has a structural form as shown in fig. 1, and is a wall structure formed by casting a horizontal and vertical reinforced grid and concrete. The arrangement of the steel bars in the shear wall in the horizontal and vertical directions is generally uniformly distributed, that is, the diameters and the pitches of the steel bars in the horizontal or vertical directions are the same. With this structure, the shear wall is mainly subjected to normal stress (σ) in a two-dimensional plane as shown in FIG. 2 L Sum sigma T ) And shear stress (τ) LT ) The subscripts L and T denote the longitudinal and transverse directions, respectively. Steel in shear wallThe tendons work together with the concrete so that the shear wall can carry external loads. When the load is increased, the shear wall unit can crack, the distribution form of the crack is shown as figure 2, the crack extends from the upper left part to the lower right part of the shear wall, and the included angle between the crack angle and the vertical direction is alpha D 。
The stress conditions of the steel bars and concrete of the shear wall in the broken line part in fig. 2 are shown in fig. 3. Since the concrete is cracked in a direction perpendicular to the maximum principal stress, the concrete strut in fig. 3 is in uniaxial compression after the unit is cracked, and the rebar between the cracks is in tension. The steel bar is subjected to horizontal and vertical tensile forces F in FIG. 3 T And F L Compressive stress sigma in concrete D Namely, the external load (sigma) L ，σ T And τ LT ) The component in the cracking direction can be calculated by using the molar stress circle method. R and D in the figure represent directions perpendicular and parallel to the crack, respectively. The concrete that is cracked into strips in fig. 3 is called a concrete strut. Because the concrete pressing rod is in a uniaxial pressing state, the steel bars are in a uniaxial tension state and the stress characteristics of the truss structure are the same, the model for analyzing the stress of the shear wall in FIG. 3 is called a truss model. We call this model either a classical truss model or a traditional truss model. The conventional truss model only considers the pressure of external load on concrete, and does not consider the influence of interaction of steel bars and concrete on concrete.
The simplified loading of the steel and concrete of the conventional truss model of fig. 3 is shown in fig. 4. Wherein F is L And F T The tension in the individual transverse and longitudinal bars, respectively.
As can be seen from fig. 4, the tensile force of the steel bar acts on one point and the resultant force is 0, so that the effect of the tensile steel bar on the stress distribution in the concrete is 0. This is a very important assumption in the traditional truss model: the interaction of the steel bar and the concrete has no or little negligible effect on the stress distribution in the concrete, and the conventional truss structure considers the pressure distribution in the concrete strut of fig. 3 to be uniform.
Traditional Chinese medicineThe truss model has the characteristics of clear physical meaning and simple method. However, since the compressive stress σ of the shear wall unit in the concrete is observed D The failure occurs when much less than the uniaxial compressive strength of concrete, so judging the failure of the unit according to the failure strength of the concrete material will greatly overestimate the failure strength of the unit, and analyzing the failure strength of the shear wall unit according to the conventional truss model will greatly overestimate the strength of the shear wall unit. This phenomenon is observed as softening of the concrete, which is affected by a number of factors and is difficult to quantify, and therefore the determination of the breaking strength of the shear wall units has been a difficult problem.
The present application has been made in order to solve the above technical problems. According to the new knowledge of the concrete softening mechanism, the method for calculating the maximum average compressive stress in the concrete in the reinforced concrete shear wall is provided through quantitative analysis of the concrete softening phenomenon, and the shear wall with a novel structure is designed.
The present application relates to a method of calculating the maximum average compressive stress in the concrete of a reinforced concrete shear wall, wherein: external load born by the shear wall is obtained, wherein the external load comprises normal stress and shear stress in a two-dimensional plane; calculating the average compressive stress sigma of concrete without considering the interaction between the steel bar and the concrete D The method comprises the steps of carrying out a first treatment on the surface of the Calculating the contribution value of the interaction between the reinforced steel bars and the concrete to the maximum average compressive stress in the concrete; based on the average compressive stress sigma D And calculating the maximum average compressive stress of the concrete in the shear wall by the contribution value of the interaction between the reinforced steel bars and the concrete to the maximum average compressive stress of the concrete.
A method according to the present application for calculating the maximum average compressive stress of concrete in a reinforced concrete shear wall, wherein the average compressive stress sigma of the concrete is not taken into account the interaction between the reinforcement and the concrete D The positive stress in the concrete cracking direction under the action of external load can be calculated based on the external load and the shear wall cracking angle by a molar stress circle method.
According to one of the present application, a meterMethod for calculating the maximum mean compressive stress of concrete in a reinforced concrete shear wall, said concrete having a mean compressive stress sigma without consideration of the interaction between the reinforcement and the concrete D The calculation can be based on the following formula:
wherein sigma R Is the normal stress, sigma, of the shear wall unit in the direction perpendicular to the cracking surface D For the shear wall unit to be parallel to the normal stress of the direction of the fracture surface, tau RD For shear stress, sigma, on shear wall units parallel or perpendicular to the fracture plane L Sum sigma T Average normal stress, τ, of longitudinal and transverse cross-sections of the shear wall LT Alpha is the average shear stress of the shear wall unit in the transverse and longitudinal sections D Is the angle between the shear wall crack and the vertical, also known as the cracking angle.
According to the method for calculating the maximum average compressive stress of the concrete in the reinforced concrete shear wall, the contribution value of the interaction between the reinforced steel bars and the concrete to the compressive stress in the concrete is calculated through the stress condition of the minimum structural unit of the reinforced steel bars and the concrete forming the shear wall when the shear wall is cracked under the external load.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the minimum structural unit of the shear wall is strip-shaped concrete formed when the shear wall cracks, and the concrete is also called a concrete compression bar.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the contribution value of interaction between the steel bars and the concrete to the compressive stress in the concrete is calculated based on the cracking angle of the shear wall, the maximum tensile stress and the minimum tensile stress of longitudinal steel bars and transverse steel bars in the concrete compression bar, the longitudinal reinforcement rate and the transverse reinforcement rate in the concrete compression bar, the minimum width of the concrete compression bar and the arrangement interval of the transverse steel bars and the longitudinal steel bars.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the maximum tensile stress of longitudinal and transverse steel bars in the concrete compression bar is the tensile stress of the steel bars at the cracking surface of the concrete compression bar.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the minimum tensile stress of longitudinal and transverse steel bars in the concrete compression bar is the tensile stress of the midpoints of the longitudinal and transverse steel bars embedded in the concrete.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the longitudinal reinforcement rate and the transverse reinforcement rate in the concrete compression bar are calculated based on the area, the diameter and the spacing between longitudinal and transverse reinforcing steel bars of a single transverse reinforcing steel bar and the number of layers of the reinforcing steel bar arrangement.
According to the method for calculating the maximum average compressive stress of the concrete in the reinforced concrete shear wall, the maximum average compressive stress which can be born by the concrete in the reinforced concrete shear wall is calculated based on the following formula:
wherein f Lcr And f Tcr Respectively the maximum tensile stress of longitudinal and transverse steel bars in the concrete compression bar, f L0 And f T0 The minimum tensile stress of the longitudinal steel bars and the transverse steel bars in the concrete compression bar is respectively the minimum tensile stress of the steel bars; s is S m L is the minimum width of the concrete compression bar p For the distance ρ between the intersection points of two transverse and longitudinal steel bars in the concrete compression bar L Longitudinal reinforcement rate of the concrete compression bar, ρ T The transverse reinforcement rate of the concrete compression bar is alpha D Is the angle between the shear wall crack and the vertical, also known as the cracking angle.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, when the minimum tensile stress in longitudinal and transverse steel bars is 0, the maximum load of the concrete in the reinforced concrete shear wall reaches the upper limit, and the method is calculated based on the following formula:
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the minimum width of the concrete compression bar is calculated based on the following formula:
S m ＝S L cosα D ＝S T sinα D ，
wherein S is L And S is T The spacing of the longitudinal and transverse bars, respectively.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the distance between two transverse and longitudinal steel bar intersection points in the concrete compression bar is calculated based on the following formula:
wherein S is L And S is T The spacing of the longitudinal and transverse bars, respectively.
According to the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall, the maximum tensile stress of longitudinal and transverse steel bars in the concrete compression bar and the cracking angle are calculated based on the following formula:
before the steel bar yields, the included angle alpha between the shear wall crack and the vertical direction D By approximating the direction of the principal tensile stress of the external load, the tension in the bar is approximatedThe stress can be calculated; when the reinforcing steel bar in one direction is yielded, the tensile stress is constant, and the tensile force and the cracking angle of the crack in the reinforcing steel bar in the other direction can be calculated.
The application also provides a method of calculating the maximum load that a shear wall can withstand, wherein: based on any one of the above methods for calculating the maximum average compressive stress of concrete in a reinforced concrete shear wall, adjusting the value of an external load born by the input shear wall according to a specified rule, wherein the external load comprises a normal stress and a shear stress in a two-dimensional plane; calculating the maximum average compressive stress value in the concrete in the reinforced concrete shear wall, and judging whether the maximum average compressive stress reaches the uniaxial compressive strength of the concrete material in the shear wall; when the maximum average compressive stress value is equal to the uniaxial compressive strength of the concrete material or the stress in the transverse and longitudinal steel bars reaches the yield strength, the input external load value is the maximum load which can be born by the shear wall. In this application, the external load is a combination of normal stress and shear stress, and the specification rule described in this application is not particularly limited, and a person skilled in the art can set any rule to specify input according to the requirement, and it should be noted that the input normal stress and shear stress are different in combination, and may have an influence on the value of the breaking strength.
The application also provides a method for judging the maximum reinforcement ratio of the shear wall, wherein:
based on the method for calculating the maximum load which can be borne by the reinforced concrete shear wall, inputting the reinforcement ratio of transverse reinforcements and/or longitudinal reinforcements of the shear wall, and calculating the maximum load which can be borne by the concrete in the shear wall;
adjusting the reinforcement ratio of transverse reinforcing steel bars and/or longitudinal reinforcing steel bars of the shear wall to be input, and observing the change of the maximum load bearable by concrete in the shear wall; when the reinforcement ratio of the transverse reinforcement and the longitudinal reinforcement of the shear wall is increased to a certain threshold value, the maximum load which can be born by the shear wall is kept unchanged after the threshold value is exceeded, and the threshold value is the maximum reinforcement ratio of the shear wall.
According to the method for calculating the maximum average compressive stress of the concrete in the reinforced concrete shear wall, the influence of interaction between the reinforced concrete and the concrete on the concrete compressive stress in the shear wall is considered, a calculation model of the maximum average compressive stress of the concrete in the shear wall is established, the model can be used for calculating the maximum load born by the shear wall and also can be used for calculating the maximum reinforcement ratio of the shear wall under the action of the specified form load, and the method has very important guiding significance for construction of the reinforced concrete shear wall.
The application also provides a shear wall of novel structure, wherein, the shear wall is formed by main reinforcing bar, secondary reinforcing bar and concrete placement, wherein: the main steel bars comprise a plurality of transverse main steel bars and a plurality of longitudinal main steel bars, the diameters of the transverse main steel bars or the longitudinal main steel bars are the same, the transverse main steel bars are uniformly distributed parallel to the ground, and the longitudinal main steel bars are uniformly distributed perpendicular to the ground; the secondary steel bars comprise a plurality of transverse secondary steel bars and a plurality of longitudinal secondary steel bars, and each secondary steel bar is uniformly arranged between the main steel bars; the diameter of the secondary reinforcing steel bars is smaller than that of the main reinforcing steel bars; and the reinforcement ratio of the secondary reinforcing steel bars is smaller than that of the main reinforcing steel bars.
The shear wall according to the present application, wherein the primary and secondary rebars need to satisfy the following relationship:
ρ l, times ＜ρ L, main ≤ρ L,m
ρ T, times ＜ρ T, master ≤ρ T,m
Wherein ρ is L, times And ρ T, times The reinforcement ratio, ρ, of the longitudinal and transverse secondary bars, respectively L, main And ρ T, master The reinforcement ratio, ρ, of the longitudinal and transverse main reinforcements respectively L,m And ρ T,m The maximum reinforcement ratio of the longitudinal main reinforcement and the transverse main reinforcement without secondary reinforcement is respectively set.
The shear wall of the application, wherein the transverse main reinforcement pitches are the same and the longitudinal main reinforcement pitches are the same.
The shear wall of the application, wherein the lateral secondary rebar spacing is the same and the longitudinal secondary rebar spacing is the same.
In this application, the spacing of the rebar distribution is the same in a single direction (transverse or longitudinal), but it is not required that the entire shear wall have the same spacing in both the transverse and longitudinal directions.
In another embodiment of the present application, the distance between the transverse primary rebar and the longitudinal primary rebar is the same.
In one embodiment of the present application, the lateral secondary rebar and the longitudinal secondary rebar are equally spaced.
According to the shear wall, the diameter of the secondary steel bars is smaller than one half of that of the main steel bars.
The shear wall according to the application, wherein the maximum average compressive stress in the novel shear wall concrete is calculated by the method for calculating the maximum average compressive stress of concrete in the reinforced concrete shear wall described above.
The shear wall according to the application, wherein the maximum average compressive stress of the concrete in the novel shear wall is determined by the maximum tensile stress in the main reinforcing steel bar, and can be calculated by the following formula:
wherein f is Lcr And f Tcr And the maximum tensile stress of the longitudinal main reinforcing steel bars and the transverse main reinforcing steel bars respectively.
The shear wall of the present application, wherein the maximum tensile stress and cracking angle in the main rebar is solved based on the following equation:
the utility model provides a novel shear force wall, adopted the mode of arranging of main reinforcing bar and secondary reinforcing bar, added the secondary reinforcing bar in traditional shear force wall's main steel bar structure to alleviate the degree of the uneven internal stress distribution of shear force wall concrete that leads to because of the interact between reinforcing bar and the concrete, thereby reduce the influence of main reinforcing bar and concrete interact to the biggest average compressive stress of concrete in the shear force wall, alleviateed the concrete softening phenomenon, reached the purpose that promotes shear force wall destructive strength.
The novel reinforced concrete shear wall can be calculated by adopting the method for calculating the maximum average compressive stress in concrete in the reinforced concrete shear wall, the method for calculating the maximum load which can be born by the shear wall and the method for calculating the maximum reinforcement ratio of the shear wall, and the shear strength of the novel structural shear wall can be greatly improved compared with that of the traditional shear wall under the condition of adding secondary reinforcing steel bars through calculation.
Drawings
The foregoing and other objects, features and advantages of the present application will become more apparent from the following more particular description of embodiments of the present application, as illustrated in the accompanying drawings. The accompanying drawings are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate the application and not constitute a limitation to the application. In the drawings, like reference numerals generally refer to like parts or steps.
FIG. 1 illustrates a schematic view of a conventional shear wall structure.
FIG. 2 illustrates a schematic diagram of a conventional shear wall local cell stress condition.
FIG. 3 illustrates a conventional truss model of the stress after cracking of a conventional shear wall unit.
Fig. 4 illustrates a simplified schematic diagram of the stress situation of a conventional truss model.
Fig. 5 illustrates a schematic view of the stress of a concrete strut considering the interaction of a reinforcing bar and concrete.
Fig. 6 illustrates a simplified schematic view of a stress situation of a concrete strut considering interaction of a reinforcing bar and concrete.
Fig. 7 illustrates a schematic view of the average pressure distribution in the concrete pole taking into account the interaction of the steel reinforcement and the concrete.
Fig. 8 illustrates the stress of the concrete pole after considering the interaction of the reinforcing steel bars and the concrete.
Fig. 9 illustrates a typical shear wall unit with identical bi-directional reinforcement as described in example 1 of the present application.
FIG. 10 illustrates a schematic diagram of the average stress on shear wall units of the structure of FIG. 9.
Fig. 11 illustrates the actual stress situation on the shear wall element split face of the structure of fig. 9.
Fig. 12 illustrates a schematic view of a novel shear wall structure with secondary rebar added according to the present application.
Fig. 13 illustrates a force diagram of a concrete strut in a novel shear wall after adding secondary rebar according to the present application.
Detailed Description
Specific embodiments of the present invention will be described in more detail below. It should be understood, however, that the invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. Those of skill in the art will understand that a person may refer to the same component by different names. The description and claims do not identify differences in terms of components, but rather differences in terms of the functionality of the components. As used throughout the specification and claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description hereinafter sets forth a preferred embodiment for practicing the invention, but is not intended to limit the scope of the invention, as the description proceeds with reference to the general principles of the description. The scope of the invention is defined by the appended claims.
In conventional truss models, it is generally believed that the interaction of the steel reinforcement and the concrete has no, or negligible, effect on the stress distribution in the concrete. The applicant has found that in fact the interaction (bond stress) between the steel bar and the concrete is a distributed load (as shown in fig. 5), and that fig. 5 illustrates a schematic view of the stress situation of the concrete strut taking into account the action of the steel bar and the concrete, the bond stress between the steel bar and the concrete acting on the concrete, affecting the distribution of stresses inside the concrete, resulting in an uneven distribution of stresses inside the concrete. Because of the uneven stress distribution, local compressive stress is necessarily larger than the average compressive stress, and the reduction in the breaking strength of concrete is observed from the viewpoint of the average stress.
A simplified schematic of the concrete stress situation of fig. 5 is shown in fig. 6. As can be seen from the figure, the acting forces of the longitudinal and transverse steel bars on the concrete are V respectively L And V T Both contributing to the pressure in the concrete strut. Fig. 6 shows a truss model for shear wall structures, which takes into account the influence of bond stress.
The distribution of the average compressive stress in the concrete pole after considering the influence of the interaction (bonding stress) between the steel bar and the concrete is shown in fig. 7. As can be seen from the figure, the average compressive stress of the concrete is minimal on the cross section of the concrete strut at the intersection of the longitudinal bars and the transverse bars; the average compressive stress in the cross section increases with increasing distance from the node.
Fig. 5 and 6 show the most basic characteristics of the newly proposed truss model for analyzing the breaking strength of a shear wall unit in consideration of the influence of the interaction (bonding stress) between the reinforcing steel bar and the concrete. The biggest difference between the newly proposed truss model and the traditional truss model is that the influence of interaction between the steel bars and the concrete on the internal force of the concrete is considered in the new truss model, and the interaction between the steel bars and the concrete is considered to influence the stress distribution in the concrete and contribute to the pressure in the concrete.
According to the newly proposed truss model, the applicant has analyzed the stress situation of the concrete strut in fig. 5, and fig. 8 illustrates the stress situation of the concrete strut. As can be seen from the figure, in the concrete pole, in addition to the pressure created by the external load, the interaction force between the steel bar and the concrete, i.e. the binding stress, also contributes additionally to the pressure in the concrete.
FIG. 8A L And A T The areas of the individual longitudinal and transverse bars, respectively, can be calculated from the following formula:
from the stress analysis shown in FIG. 8, it can be calculated that the maximum average stress in the concrete strut after considering the bonding stress in the newly proposed truss model is The calculation formula is as follows:
wherein f Lcr And f Tcr The tensile stresses of the longitudinal and transverse bars at the fracture surface in fig. 5, respectively, are also the maximum tensile stresses in the bars; f (f) L0 And f T0 The tensile stress at the midpoint of the longitudinal and transverse bars embedded in the concrete in fig. 5, respectively, is also the minimum tensile stress in the bars; s is S m Is the minimum width of the concrete strut in fig. 5; l (L) p The distance between the intersection points of the two transverse and longitudinal bars in fig. 5 can be calculated from the longitudinal and transverse bar spacing and the cracking angle.
If the tensile stress of the midpoints of the longitudinal and transverse steel bars embedded in the concrete is 0, the tensile force in the steel bars is fully conducted into the concrete, the maximum pressure in the concrete reaches the upper limit, and the formula (2) becomes:
this is a somewhat conservative assumption, since it is assumed that the pulling force in the rebar is fully conducted into the concrete as an upper limit for the interaction of the rebar and the concrete, which makes it possible to reach the calculated concrete pressure.
The right side of equation (3) contains two terms: mean compressive stress sigma irrespective of the influence of bond stress D And the contribution of the binding stress to the compressive stress in the concrete- (ρ) L f Lcr +ρ T f Tcr )L p sinα D cosα D /S m . As can be seen from equation 3, the concrete pressure σ is considered as compared with the conventional truss model D The actual pressure in the concrete is greater.
According to calculation, the contribution value of the bonding stress to the compressive stress in the concrete is far greater than the average compressive stress sigma in the concrete D . This is the most important recognition obtained in the research, and the research results show that the influence of the bonding stress on the stress distribution in the concrete may be an important cause of the concrete softening phenomenon, which explains the cause of the concrete softening of the reinforced concrete shear wall member.
Equation (1) gives a calculation of the maximum compressive stress in the concrete, some of the parameters being unknown. Minimum crack width
S m ＝S L cosα D ＝S T sinα D (4)
L can be calculated from FIG. 8 p Length of (2)
Wherein S is L And S is T The spacing of the longitudinal and transverse bars, respectively. Other parameters such as alpha D ，f Lcr And f Tcr The calculation of (c) will be described later for the specific case.
Example 1
This example shows an embodiment of calculating the maximum reinforcement ratio of a shear wall of the structure shown in fig. 9 by the newly proposed method of calculating the maximum average compressive stress in concrete in a reinforced concrete shear wall, the method of calculating the maximum load that the shear wall can withstand, and the method of calculating the maximum reinforcement ratio of the shear wall.
As shown in FIG. 9, one of the transverse and longitudinal reinforcement is identical and the horizontal and vertical sections are subjected to pure shear τ LT An active shear wall unit. Schematic diagrams of the average stress and actual stress on the fracture surface are shown in fig. 10 and 11.
Fig. 10 shows an analysis of the average stress on a shear wall unit of the structure shown in fig. 9. According to the external load and the symmetry of the arrangement of the steel bars in the shear wall, the cracking angle of the crack is 45 degrees, the shear stress is 0 on the section parallel and perpendicular to the crack, and only the positive stress sigma exists R Sum sigma D . Fig. 11 shows the actual stress situation on the shear wall element split face of the structure of fig. 9. In actual stress, all forces on the section where the crack is located are transmitted by the steel bars.
A balance equation of the tensile force and the shearing force can be established on the fracture surface:
since the distribution of the reinforcing bars in the unit is symmetrical and the directions of the principal tensile stress and principal compressive stress of the externally applied load are perpendicular and parallel to the cracks, respectively, the included angle (alpha) of the crack angle in the unit with the perpendicular direction D ) Also 45 degrees. From the molar stress circles, the principal tensile stress (σ R ) And principal compressive stress (sigma) D ) The direction is an angle of 45 degrees of anticlockwise rotation of the x-y axis, and
σ R ＝-σ D ＝τ LT (7)
the system of equations is then solved and the tension in the steel bar is obtained.
According to calculation, the tensile stress in the steel bars is respectively
The maximum compressive stress in the concrete at the site can then be calculated according to equation 3
When τ is LT Reaching the breaking strength tau of the unit u When the steel bar yields or the main compressive stress in the concreteReaching the uniaxial compressive strength f c ' the unit is destroyed. Thus (2)
Wherein f Ly For the yield strength of the longitudinal bars, f Ty Is the yield strength of the transverse reinforcing steel bars. Equation 10 is a calculation equation of the shear strength of the shear wall unit with the structure described in embodiment 1 of the present application.
In this application, the maximum load, i.e. the load corresponding to the shear wall when broken, is also called the breaking strength. While the form of the load includes a variety of forms such as pure shear, positive stress, and a combination of shear stresses. Generally we call the breaking strength under pure shear force as the shear strength, which is also the maximum value of the shear force that can be tolerated.
When the reinforcement ratio of the reinforcing steel bar is low, the reinforcing steel bar reaches a yield state; with the improvement of the reinforcement arrangement rate of the reinforcing steel bars, the shear strength of the units is improved; when ρ is Ly f Ly ＝ρ Ty f Ty ＝f c The maximum reinforcement ratio is reached when'/3, the strength of the unit is maximized, and the failure mode is changed from the yield of the reinforcement to the crushing of the concrete; the strength of the unit is not improved by continuously improving the reinforcement ratio of the reinforcing steel bars, but the failure mode becomes the crushing of the concrete. Therefore, when the concrete strength is not improved any more, the reinforcement ratio reaches the upper limit to meet the condition
In example 1, the applicant applied the method of calculating the maximum load that a reinforced concrete shear wall can withstand, and calculated the maximum shear force that a shear wall of the structure shown in fig. 9 can withstand, and the maximum reinforcement ratio of the shear wall. Similar analytical calculations can be performed on shear walls of other structures according to the methods described herein by those skilled in the art.
Example 2
Since the interaction between the steel bar and the concrete is found to have an important influence on the destruction of the unit, particularly the maximum reinforcement ratio and the corresponding maximum shear strength of the steel bar are seriously affected, the uneven stress distribution caused by the interaction between the steel bar and the concrete is relieved by adding the secondary steel bar into the gap of the main steel bar.
The application also provides a novel shear wall, through adding secondary reinforcing bar in traditional shear wall to alleviate the degree of shear wall concrete internal stress uneven distribution that leads to because of the interact between reinforcing bar and the concrete, lighten concrete softening phenomenon, and then improve the biggest reinforcement rate and the destruction intensity of shear wall. This example 2 shows one embodiment of a novel shear wall.
The novel shear wall in this embodiment is improved on the basis of the conventional shear wall in embodiment 1, as shown in fig. 12, the main steel bars of the shear wall in this embodiment still adopt a structure similar to that of the conventional reinforced concrete shear wall in embodiment 1, and are uniformly distributed in the transverse direction (horizontal direction) and the longitudinal direction (vertical direction) respectively, and the transverse and longitudinal distances between the main steel bars are the same. However, in this embodiment, a plurality of secondary steel bars are additionally arranged between the main steel bars, and the secondary steel bars are also uniformly arranged transversely and longitudinally, wherein the diameter of the secondary steel bars is smaller than that of the main steel bars, and the reinforcement ratio of the secondary steel bars is smaller than that of the main steel bars. The shear wall can adopt a double-layer steel bar structure, namely, as shown in fig. 12, double-layer main steel bars and secondary steel bars can be overlapped and distributed in the thickness direction of the shear wall.
Referring to the stress conditions of the concrete pressing bars in fig. 5 and 6, it can be seen that the effect between the main reinforcement, the secondary reinforcement and the concrete after the concrete unit is cracked by stress is shown in fig. 13, wherein V L And V T The effect of the main reinforcing steel bars on the concreteForce V L ' and V T ' is the force of the secondary rebar on the concrete. The secondary reinforcing steel bars share the tensile force of a part of the main reinforcing steel bars and simultaneously disturb the compressive stress in the concrete compression bar.
It can be seen in fig. 13 that the addition of secondary reinforcing fibers, while affecting the distribution of internal forces, the maximum compressive stress is determined by the tension in the primary reinforcement. The reinforcement ratio of the longitudinal main reinforcement and the transverse main reinforcement on the fracture surface is respectively ρ L, main And ρ T, master The reinforcement ratio of the longitudinal secondary reinforcement and the transverse secondary reinforcement on the fracture surface is recorded as rho L, times And ρ T, times ，
Wherein n is L, times And n T, times The number of secondary steel bars between 2 longitudinal main steel bars and 2 transverse main steel bars respectively, d L, times And d T, times The diameters of the longitudinal secondary steel bars and the transverse secondary steel bars are respectively, and d is the thickness of the shear wall.
The expression that the maximum compressive stress in concrete after the novel shear wall cracks can be obtained based on the formula 3 is that the secondary steel bar and the main steel bar have the same material characteristics, namely the same elastic modulus and yield strength
According to formula 13, under the condition that the reinforcing bars of the main reinforcing bars are the same, when the conventional shear wall and the novel shear wall unit reach the breaking strength, the tensile stress of the main reinforcing bars in the two shear walls is the same. Meanwhile, as the secondary reinforcing steel bars added in the novel shear wall bear partial tension, the main reinforcing steel bars in the novel shear wall structure have smaller tensile stress under the condition of the same load. That is, the new shear wall bears a greater load when the failure condition is reached. Therefore, after the maximum reinforcement ratio of the traditional shear wall is reached, the novel shear wall structure can continue to be provided with more reinforcements, and meanwhile, the shear strength is improved.
For the case of identical bi-directional rebar placement and pure shear, a balance equation similar to equation 6 can be established at the fracture face:
from symmetry it is known that alpha D 45 degrees. Since the primary and secondary rebars are strained the same, the tensile stress is the same. Referring to formula 11, it can be known that the load of the novel shear wall reaches the maximum
At this time, the corresponding unit shear load
τ u ＝σ R ＝(ρ L, main +ρ L, times )f Lcr ＝(ρ L, main +ρ L, times )f Tcr (16)
Substituting equation 15 into equation 16 yields
The comparison formula 10 shows that the maximum breaking strength of the novel shear wall is improved by the proportion ρ L, times /ρ L, main 。
Comparative example:
the following comparative example illustrates the performance improvement of the novel shear wall with the added secondary reinforcing steel bars, which is proposed in the application, relative to the traditional shear wall in terms of reinforcement and strength, by taking a shear wall with the same configuration of transverse reinforcing steel bars and longitudinal reinforcing steel bars as an example.
Assuming a reinforced concrete shear wall of a conventional structure, the structure is shown in fig. 9, the thickness of the shear wall is 160mm, main steel bars are uniformly distributed in the direction vertical to the ground and the direction parallel to the ground, the diameter of the main steel bars is 14mm, the distance is 113mm, and the two-layer steel bars are arranged. The yield strength of the steel bar is 400MPa, and the compressive strength of the concrete is 20MPa. The reinforcement ratio of the reinforcing steel bars is 1.67%, and the shear wall meets the formula 10.
Therefore, the reinforcement ratio at this time is the maximum reinforcement ratio of the conventional shear wall, and according to equation 8, it is known that the maximum shear force that the unit can bear is 6.67MPa. According to the traditional arrangement method of the shear wall, the shear strength of the shear wall cannot be improved even if the content of the reinforcing steel bars is continuously increased, and the maximum shear strength is 6.67MPa.
According to the method, secondary reinforcing steel bar fibers are added into the main reinforcing steel bars, so that the tension of the main reinforcing steel bars can be shared under the condition of the same external load, and the non-uniformity of the internal stress distribution of the concrete caused by interaction of the reinforcing steel bars and the concrete is reduced.
The new shear wall structure is shown in fig. 12, 2 layers of reinforcing steel fiber nets are added on the basis of fig. 9, and specifically, 2 secondary reinforcing steel bars with the diameter of 4.4mm are added in the middle of each layer of main reinforcing steel bars, and the distance is 37.6mm. The reinforcement ratio of the new shear wall in the horizontal and vertical directions is respectively improved by 20 percent compared with that of the original structure and reaches 2.04 percent.
The failure strength of the novel shear wall is shown as formula 16
τ u ＝(1+20％)ρ L f Ly ＝(1+20％)ρ T f Ty ＝0.4f' c ＝8.00MPa (18)
Therefore, the breaking strength of the novel shear wall is improved by 20% after 20% of secondary reinforcing steel fibers are added, and the traditional shear wall cannot be improved because the maximum reinforcement ratio is reached. The difference between the results is shown in Table 1.
TABLE 1 failure strength comparison of novel and conventional shear walls at different reinforcement rates
From the results in the table, the novel shear wall can improve the maximum reinforcement ratio of the shear wall on the basis of the original shear wall structure by adding the secondary reinforcement, thereby improving the maximum damage strength which can be born by the shear wall.
The basic principles of the present application have been described above in connection with specific embodiments, however, it should be noted that the advantages, benefits, effects, etc. mentioned in the present application are merely examples and not limiting, and these advantages, benefits, effects, etc. are not to be considered as necessarily possessed by the various embodiments of the present application. Furthermore, the specific details disclosed herein are for purposes of illustration and understanding only, and are not intended to be limiting, as the application is not intended to be limited to the details disclosed herein as such.
The block diagrams of the devices, apparatuses, devices, systems referred to in this application are only illustrative examples and are not intended to require or imply that the connections, arrangements, configurations must be made in the manner shown in the block diagrams. As will be appreciated by one of skill in the art, the devices, apparatuses, devices, systems may be connected, arranged, configured in any manner. Words such as "including," "comprising," "having," and the like are words of openness and mean "including but not limited to," and are used interchangeably therewith. The terms "or" and "as used herein refer to and are used interchangeably with the term" and/or "unless the context clearly indicates otherwise. The term "such as" as used herein refers to, and is used interchangeably with, the phrase "such as, but not limited to.
It is also noted that in the apparatus, devices and methods of the present application, the components or steps may be disassembled and/or assembled. Such decomposition and/or recombination should be considered as equivalent to the present application.
The previous description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other aspects without departing from the scope of the application. Thus, the present application is not intended to be limited to the aspects shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
The foregoing description has been presented for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the application to the form disclosed herein. Although a number of example aspects and embodiments have been discussed above, a person of ordinary skill in the art will recognize certain variations, modifications, alterations, additions, and subcombinations thereof.
Claims (26)
1. A method of calculating the maximum average compressive stress in concrete of a reinforced concrete shear wall, wherein:
External loads borne by the shear wall are acquired, wherein the external loads comprise normal stress (sigma L Sum sigma T ) And shear stress (τ) LT )；
Calculating the average principal compressive stress sigma of the concrete based on the external load without considering the interaction between the reinforcing steel bar and the concrete D ；
Calculating the contribution value of the interaction between the reinforced steel bars and the concrete to the maximum average compressive stress in the concrete;
based on the average principal compressive stress sigma D And calculating the maximum average compressive stress in the shear wall concrete by the contribution value of the interaction between the reinforced steel bars and the concrete to the maximum average compressive stress in the concrete.
2. The method according to claim 1, wherein the concrete has an average principal compressive stress σ irrespective of the interaction between the reinforcement and the concrete D The positive stress in the concrete cracking direction under the action of external load can be calculated based on the external load and the shear wall cracking angle by a molar stress circle method.
3. The method according to claim 2, wherein the concrete has an average principal compressive stress σ irrespective of the interaction between the reinforcement and the concrete D The calculation can be based on the following formula:
wherein sigma R Is the normal stress of the shear wall unit perpendicular to the cracking direction, σ D For shear wall units normal stresses parallel to the cracking direction, τ RD For shear stress, sigma, on shear wall units parallel or perpendicular to the fracture plane L Sum sigma T The average positive stress in the longitudinal section and the transverse section of the shear wall in the positive stress in the two-dimensional plane is respectively, and the shear stress tau LT Alpha is the average shear stress of the shear wall unit in the transverse and longitudinal sections D Is the angle between the shear wall crack and the vertical, also known as the cracking angle.
4. The method of claim 1, wherein the contribution of the interaction between the steel bar and the concrete to the pressure in the concrete is calculated from the stress of the smallest structural unit of the steel bar and the concrete forming the shear wall when the shear wall is cracked by an external load.
5. The method of claim 4, wherein the smallest structural unit of the shear wall is a strip of concrete formed when the shear wall cracks, also known as a concrete strut.
6. The method of claim 5, wherein the contribution of the interaction between the steel bars and concrete to the pressure in the concrete is calculated based on a cracking angle of the shear wall, a maximum tensile stress and a minimum tensile stress of longitudinal and transverse steel bars in the concrete strut, a longitudinal reinforcement rate and a transverse reinforcement rate in the concrete strut, a minimum width of the concrete strut, and a layout pitch of the transverse and longitudinal steel bars.
7. The method of claim 6, wherein the maximum tensile stress of the longitudinal and transverse rebars in the concrete pole is the tensile stress to which the rebars are subjected at the split face of the concrete pole.
8. The method of claim 5, wherein the minimum tensile stress of the longitudinal and transverse rebars in the concrete pole is the tensile stress of the midpoints of the longitudinal and transverse rebars embedded in the concrete.
9. The method of claim 5, wherein the longitudinal reinforcement ratio and the transverse reinforcement ratio in the concrete pole are calculated based on the area of the individual transverse and longitudinal rebars, the diameter, the spacing between the longitudinal and transverse rebars, the number of layers of the rebars are arranged.
10. The method of any one of claims 4-9, wherein the maximum average compressive stress of the concrete in the reinforced concrete shear wall is calculated based on the following equation:
wherein f Lcr And f Tcr Respectively the maximum tensile stress of longitudinal and transverse steel bars in the concrete compression bar, f L0 And f T0 The minimum tensile stress of the longitudinal steel bars and the transverse steel bars in the concrete compression bar is respectively the minimum tensile stress of the steel bars; s is S m L is the minimum width of the concrete compression bar p For the distance ρ between the intersection points of two transverse and longitudinal steel bars in the concrete compression bar L Longitudinal reinforcement rate of the concrete compression bar, ρ T The transverse reinforcement rate of the concrete compression bar is alpha D Is the angle between the shear wall crack and the vertical, also known as the cracking angle.
11. The method of claim 10, wherein the upper limit value of the maximum average principal compressive stress in the concrete in the reinforced concrete shear wall is calculated based on the following formula:
the upper limit is the maximum value of the maximum average compressive stress in the concrete in the reinforced concrete shear wall assuming that the tensile forces in the steel bars are all conducted into the concrete.
12. The method of claim 10, wherein the minimum width for the concrete strut is calculated based on the following equation:
S m ＝S L cosα D ＝S T sinα D ，
wherein S is L And S is T The spacing of the longitudinal and transverse bars, respectively.
13. The method of claim 10, wherein the distance between the intersection of two transverse and longitudinal rebars in the concrete pole is calculated based on the following equation:
wherein S is L And S is T The spacing of the longitudinal and transverse bars, respectively.
14. The method of claim 10, wherein the maximum tensile stress of the longitudinal and transverse rebars in the concrete strut and the cracking angle are calculated based on the following formula:
15. a method of calculating the maximum load that a shear wall can withstand, wherein:
Adjusting the value of an external load born by the input shear wall according to a specified rule, wherein the external load comprises normal stress and shear stress in a two-dimensional plane based on the method of any one of claims 1-14;
calculating the maximum average compressive stress value in the concrete of the reinforced concrete shear wall, and judging whether the maximum average compressive stress reaches the uniaxial compressive strength of the concrete material in the shear wall;
when the maximum average compressive stress value is equal to the uniaxial compressive strength of the concrete material or the tensile stress in the transverse and longitudinal steel bars reaches the yield strength, the input external load value is the maximum load which can be born by the shear wall.
16. A method of calculating a maximum reinforcement ratio for a shear wall, wherein:
based on the method of claim 15;
inputting the reinforcement ratio of transverse reinforcements and/or longitudinal reinforcements of the shear wall, and calculating the maximum load bearable by the shear wall;
adjusting the reinforcement ratio of the transverse reinforcing steel bars and/or the longitudinal reinforcing steel bars of the input shear wall, and observing the change of the maximum load bearable by the shear wall;
when the reinforcement ratio of the transverse reinforcement and the longitudinal reinforcement of the shear wall is increased to a certain threshold value, the maximum load which can be born by the shear wall is kept unchanged after the threshold value is exceeded, and the threshold value is the maximum reinforcement ratio of the shear wall.
17. The utility model provides a shear force wall of novel structure, wherein, the shear force wall is formed by main reinforcing bar, secondary reinforcing bar and concrete placement, wherein:
the main steel bars comprise a plurality of transverse main steel bars and a plurality of longitudinal main steel bars, and the diameters of the transverse main steel bars and/or the longitudinal main steel bars are the same;
the transverse main steel bars are uniformly distributed parallel to the ground, and the longitudinal main steel bars are uniformly distributed perpendicular to the ground;
the secondary steel bars comprise a plurality of transverse secondary steel bars and a plurality of longitudinal secondary steel bars, and each secondary steel bar is uniformly arranged between the main steel bars;
the diameter of the secondary reinforcing steel bars is smaller than that of the main reinforcing steel bars; and the reinforcement ratio of the secondary reinforcing steel bars is smaller than that of the main reinforcing steel bars.
18. The shear wall of claim 17, wherein the primary and secondary rebars are required to satisfy the relationship:
ρ l, times ＜ρ L, main ≤ρ L,m
ρ T, times ＜ρ T, master ≤ρ T,m
Wherein ρ is L, times And ρ T, times The reinforcement ratio, ρ, of the longitudinal and transverse secondary bars, respectively L, main And ρ T, master The reinforcement ratio, ρ, of the longitudinal and transverse main reinforcements respectively L,m And ρ T,m The maximum reinforcement ratio of the longitudinal main reinforcement and the transverse main reinforcement without secondary reinforcement respectively.
19. The shear wall of claim 18, wherein the plurality of transverse primary rebar pitches are the same and the plurality of longitudinal primary rebar pitches are the same.
20. The shear wall of claim 18, wherein the plurality of transverse secondary rebar pitches are the same and the plurality of longitudinal secondary rebar pitches are the same.
21. A shear wall as claimed in any one of claims 17 to 20, wherein the secondary rebars are less than half the diameter of the primary rebars.
22. A shear wall according to any one of claims 17 to 20, wherein the maximum average compressive stress in the shear wall concrete is calculated by the method of any one of claims 1 to 9.
23. The shear wall of claim 22, wherein the upper limit of the maximum average compressive stress of the concrete in the shear wall is calculated by the formula:
wherein f Lcr And f Tcr And the maximum tensile stress of the longitudinal main reinforcing steel bars and the transverse main reinforcing steel bars respectively.
24. The shear wall of claim 23, wherein the maximum tensile stress and cracking angle in the main rebar is solved based on the following equation:
25. a shear wall as claimed in any one of claims 17 to 24, in which the maximum load that the shear wall can withstand is calculated by the method of claim 15.
26. A shear wall as claimed in any one of claims 17 to 24, in which the maximum reinforcement ratio of the main reinforcement of the shear wall is calculated by the method of claim 16.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116226997A (en) * | 2023-02-21 | 2023-06-06 | 中国地震局地球物理研究所 | Method for calculating reinforced concrete shear wall and novel shear wall |
| CN116226997B (en) * | 2023-02-21 | 2023-10-27 | 中国地震局地球物理研究所 | Method for calculating reinforced concrete shear wall |
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