Wedge-shaped section variable-form bending-shear-resistant model and design method

Abstract

The invention relates to a wedge-shaped section variable-form bending-shear-resistant model and a design method. A cracking surface and a pressure-bearing surface of the model are perpendicular to each other at an intersection point, obliquely extend by the length of the same proportion Km and then are converted into a forward stress surface. Wherein Km is a variable form coefficient and is controlled by the bending-shear ratio on the cross section. On the basis of a wedge-shaped section deformation form bending-shear resistance model, the reinforcement ratio, the deformation form coefficient Km, the shear bearing capacity VR and the bending bearing capacity MR on the section can be calculated in sequence, and calculation judgment and design adjustment are conducted in time in the process till a bending-resistant and shear-resistant coupling calculation result meeting the requirement is obtained. According to the method, bending resistance and shearing resistance calculation models are unified, accurate calculation of the section bending resistance and shearing resistance coupling problem is achieved, the problems that a traditional bending resistance and shearing resistance calculation method is poor in relevance, lack of theoretical basis and unreliable in calculation and design are solved, and innovation of the design theory and development of the structure technology are further promoted.

Description

Technical Field

[0001] The invention relates to the technical field of civil engineering, and in particular to a wedge-shaped cross-section deformable bending and shearing resistance model and a design method. Background Art

[0002] Under the action of shear force, the component will produce oblique principal tensile stress and principal compressive stress inside. When the principal tensile stress exceeds the tensile ultimate strength of the material, three forms of oblique cracks will appear.

[0003] The shear resistance of the member section is based on the concrete bearing pressure, combined with longitudinal reinforcement, vertical stirrups and bent reinforcement, etc., to form a bearing system to control the free generation and excessive development of oblique cracks, and is calculated according to the following formula.

[0004] V d ≤V R =V cz +V sg +V sw

[0005] Among them, V d 、V R are the cross-section design shear force and shear bearing capacity respectively; V cz V is the shear bearing capacity of the longitudinal reinforcement section; sg 、V sw are the shear bearing capacity of vertical stirrups and bent steel bars respectively.

[0006] The traditional method for implementing the calculation according to the above formula comes from a combination of semi-empirical and semi-theoretical methods. Although it basically reflects the characteristics of cross-section shear failure, the model cannot fully reflect the equilibrium relationship of cross-section forces, and the formula is not based on theoretical deduction results. The calculation results have always been controversial.

[0007] Recently, the shear failure characteristics of components were analyzed. The upper end of the shear diagonal crack has an area that is both sheared and compressed. A wedge-shaped section shear model was proposed to solve the problem that the traditional method lacks a theoretical basis, and the calculation and design are inaccurate and unreliable. However, the model description is more suitable for near the support point, and the problem that the bending moment on the section affects the shape and bearing capacity of the diagonal crack, that is, the coupling problem of bending and shear, has not yet been solved. Summary of the invention

[0008] The purpose of the present invention is to provide a wedge-shaped section deformable bending and shear resistance model and design method in order to solve the above problems.

[0009] The purpose of the present invention is achieved through the following technical solutions:

[0010] When a component is destroyed under the action of bending moment and shear force, a deformed oblique crack will appear. The deformed bending and shear model and design method of the wedge-shaped section is based on the deformed bending and shear model of the wedge-shaped section, which more clearly expresses the physical and geometric meanings of the bending and shear resistance of the section, and performs accurate bending and shear resistance calculations.

[0011] First, the bending and shear failure characteristics of the component are further analyzed. The wedge-shaped section will soften due to the bending moment on the section. Positive stress surfaces appear at the ends of the crack surface and the pressure surface. This phenomenon will be aggravated with the increase of the shear span ratio until a complete positive stress surface is formed. The study further proposes a wedge-shaped section deformable bending and shear model. The bending and shear model has a deformable crack surface and a deformable pressure surface. The crack surface and the pressure surface intersect each other and are perpendicular to each other at the intersection. The crack surface extends obliquely downward for a certain length and then turns positive downward to extend to the bottom of the component. The pressure surface extends obliquely upward for a certain length and then turns positive upward to extend to the top of the component. Then, a design method based on the wedge-shaped section deformable bending and shear model is formed to perform accurate model size calculation, bending and shear calculation and design judgment.

[0012] Furthermore, the following basic settings are made for the deformed bending-shear model of the wedge-shaped section: (1) The intersection of the deformed crack surface and the deformed pressure surface is the zero point of the section strain. (2) The ratio of the length of the deformed crack surface and the deformed pressure surface extending obliquely to a certain length to the length of the length of the deformed crack surface extending obliquely to the full length of the component edge adopts the same deformed coefficient K. m .

[0013] Furthermore, the shear bearing capacity V of the wedge-shaped section deformation bending shear model 1 is R The calculation is as follows:

[0014] V R =V cz +V sg +V sw

[0015] Among them, V cz is the shear bearing capacity of longitudinal reinforcement 4; V sg V is the shear bearing capacity of vertical stirrup 5; sw is the shear bearing capacity of the bent steel bar 6.

[0016]

[0017] N d =σ c bx c -σ sz A′ sz

[0018]

[0019]

[0020]

[0021] Where C is the horizontal projection length of the crack surface extending obliquely to the full length of the component edge; h0 is the calculated height of the section; b is the calculated width of the section; x c is the position of the zero point of the cross-section superimposed strain. c Calculate the stress of the concrete on the bearing surface; σ sz , A sz Calculate stress and area for longitudinal reinforcement of crack surface; σ sj , A sj ,θ sj Calculate stress, area, and acute angle with the normal line of the cross section for bent bars. N d Design the cross section for the axial forces.

[0022]

[0023] Among them, q d is the design vertical pressure of the section; σ sg Calculate the stress of vertical stirrups on the crack surface; μ sg is the reinforcement ratio of vertical stirrups on the crack surface.

[0024] V sw =Σσ sj A sj sinθ sj

[0025] Deduced:

[0026]

[0027] The most unfavorable value of horizontal projection length C:

[0028]

[0029]

[0030] Shear bearing capacity V R The most unfavorable value:

[0031]

[0032] Among them, V′ R It is the shear capacity of the orthogonal reinforcement without taking into account the shear capacity of the bent reinforcement.

[0033] Furthermore, based on the shear bearing capacity V R The calculation of the most unfavorable value is for the bending bearing capacity M of the wedge-shaped section deformed bending-shear model 1 RThe calculation is as follows:

[0034] M R =M cz +M sg +M sw

[0035] Among them, M cz M is the bending bearing capacity of the longitudinal reinforcement; sg M is the bending bearing capacity of vertical stirrups; sw It is the bending bearing capacity of bent steel bars.

[0036]

[0037]

[0038] M sw =∑σ sj A sj d sj

[0039] Among them, d sj The distance between the bent reinforcement and the cross section to calculate the moment equilibrium point.

[0040] Deduced:

[0041] Bending bearing capacity M R The most unfavorable value:

[0042]

[0043] Among them, M′ R It is the flexural capacity of the orthogonal reinforcement without taking into account the flexural capacity of the bent reinforcement.

[0044] Furthermore, based on the shear bearing capacity V R The most unfavorable value, bending bearing capacity M R The calculation of the most unfavorable value for the deformation coefficient K m The calculation is as follows:

[0045]

[0046]

[0047]

[0048] Where m is the bending-shear ratio of the orthogonal reinforcement; M d is the cross-section design bending moment; V d is the cross-section design shear force; M′ d The effective design bending moment of the section after deducting the bending bearing capacity of the bent reinforcement; V′ d The effective design shear force of the section is calculated by deducting the shear bearing capacity of the bent reinforcement.

[0049] Furthermore, the deformation coefficient K m The following instructions are given for use:

[0050] (1) In actual use, the deformation coefficient K m The calculation of shear bearing capacity V R , flexural bearing capacity M R before the calculation of .

[0051] (2) When K m →0, its mechanical meaning is: when the shear force on the section is 0 or the shear span ratio is large enough ( Desirable ), the wedge-shaped section is single and converted into a bending-resistant normal section.

[0052] (3) When K m =1, its mechanical meaning is: the bending moment on the section always participates in the shear calculation But the shear span ratio is small enough The wedge-shaped section is simplified and there is no longer a positive rotation part.

[0053] Furthermore, the following explanation is given for the use of the reinforcement ratio on the cross section:

[0054] (1) In actual use, the calculation of the reinforcement ratio on the cross section should be based on the variable shape coefficient K m , shear bearing capacity V R , flexural bearing capacity M R before the calculation of .

[0055] (2) There is an effective value for the longitudinal reinforcement ratio and the vertical stirrup reinforcement ratio under the deformation state of the wedge-shaped section. When this effective value is exceeded, the calculated value of the section shear bearing capacity decreases, but in reality it no longer increases. Therefore, in actual use, when k sz (μ sz +μ N )≥0.5, take k sz (μ sz +μ N )=0.5; when k sg (μ sg +μ q )≥0.5, take k sg (μ sg +μ q )=0.5.

[0056] Further, the calculation of the bending and shear bearing capacity is explained as follows:

[0057] Based on the shear bearing capacity V R , shear bearing capacity M RThe calculation of the most unfavorable value shows that the shear bearing capacity has a maximum value. sz (μ sz +μ N )≥0.5 and k sg (μ sg +μ q )≥0.5, the bending shear bearing capacity can be directly calculated according to the following formula:

[0058]

[0059] V R =0.5σ c oeLh m +∑σ sj A sj sinθ sj

[0060]

[0061] Further, the following explanation is given for the use of the calculation of bending and shear bearing capacity:

[0062] (1) When V d ≤V R And M d ≤M R When the design meets the requirements;

[0063] (2) When V d >V R or M d >M R The design needs to be adjusted.

[0064] Furthermore, a computer design program set in a memory and a processor is developed for the wedge-shaped section deformable bending and shearing model 1 and the design method. The design program is connected with the structural calculation, and the reinforcement ratio on the section, the deformable coefficient K m , shear bearing capacity V R , flexural bearing capacity M R , and in the process, the calculation results are judged and the calculation content is reset in time until the results that meet the requirements are obtained and output. The design program consists of a series of subroutines or functional modules, which can perform different calculation selections and combinations, and can be used to support other design processes. At the same time, the wedge-shaped section deformable bending and shear resistance model and design method of the present invention also provide an idea for section bending and shear resistance calculation. Under this idea, technicians do not need to deduce analytical calculation formulas, but can use a cyclic iteration method to gradually correct the calculation until the calculation results meet the requirements.

[0065] The beneficial technical effects of the present invention are embodied in the following aspects:

[0066] This application proposes accurate model size calculation, bending calculation and shear calculation formulas, and realizes the accurate calculation of the cross-section bending and shear coupling problems; at the same time, it clarifies the significance of traditional bending calculation and shear calculation, and unifies the bending calculation and shear calculation models.

[0067] This application solves the problem that the traditional method adopts a combination of semi-empirical and semi-theoretical methods, lacks a comprehensive expression that reflects the force balance of the cross-section, lacks theoretical deduction, and calculation and design have always been controversial.

[0068] This application further promoted the innovation of design theory and the development of structural technology, and achieved remarkable technical, economic and social effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a schematic diagram of the bending-shear model of the wedge-shaped section deformation;

[0070] Figure 2 This is a schematic diagram of the overall layout of the light T-beam;

[0071] Figure 3 This is a schematic diagram of the bending and shear resistance near the support point of a light T-beam;

[0072] Figure 4 Schematic diagram of the bending and shear resistance of a light T-beam at 1 / 4 of the span.

[0073] In the figure: 1- bending and shear model; 2- variable cracking surface; 3- variable pressure surface; 4- longitudinal reinforcement; 5- vertical stirrups; 6- bent reinforcement; 7- light T-beam; 8- web; 9- support point; 10- longitudinal main reinforcement; 11- longitudinal distribution reinforcement. DETAILED DESCRIPTION

[0074] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The following embodiments are carried out based on the technical solution of the present invention, and provide detailed implementation methods, specific operation processes and quantitative calculation results, but the protection scope of the present invention is not limited to the following embodiments.

[0075] Example 1

[0076] See also Figure 2 In order to meet the development requirements of standardization, systematization, modularization and assembly in the industrialized construction of highways, a theoretical span of 25m reinforced concrete light T-beam 7 is designed, the beam height is 1.605m, the web 8 is 0.22m thick, the concrete strength grade is C70, and the four horizontal beams form a 12.75m wide bridge. Calculate the bending and shear bearing capacity near the support 9.

[0077] See also Figure 1 , Figure 3 ,calculate:

[0078] b=0.22m,h0=1.505m.

[0079] The longitudinal reinforcement 4 is composed of the longitudinal main reinforcement 10 and the longitudinal distribution reinforcement 11. Taking into account the longitudinal equivalent part of the bent reinforcement 6, the calculation is:

[0080] k sz =10.8198;μ sz =0.02438; μ N =0. k sz (μ sz +μ N )=0.2638<0.5.

[0081] The vertical stirrup 5 is a double stirrup. Calculation:

[0082] k sg =10.8198;μ sg =0.01028; μ q =0. k sg (μ sg +μ q )=0.1112<0.5.

[0083] Calculate the most unfavorable value of the horizontal projection length C of the deformed crack surface 2: C = 1.9889m.

[0084] Calculate the shear force at a distance C from the support point 9: V d =2.0018MN, V′ d =1.6014MN.

[0085] Calculate the bending moment at distance C from the support 9: M d =3.9813MN·M,M′ d =3.1850MN·M.

[0086] Calculate the shear span ratio of the orthogonal reinforcement at a distance C from the support point 9:

[0087] Calculate the bending-shear section deformation coefficient at a distance C from the support point 9: K m =0.7918.

[0088] Calculate the most unfavorable shear bearing capacity at a distance C from the support point 9: V R =2.5797MN.

[0089] Calculate the most unfavorable bending bearing capacity at a distance C from the support point 9: M R =5.1306MN·M.

[0090] Design judgment: Yes V d <V R And M d <MR , the design meets the requirements.

[0091] By using the deformable bending and shear resistance model and design method of the wedge-shaped section of the present invention, the most unfavorable bending and shear resistance capacity of the wedge-shaped section near the support point 1.9889m of the light T-beam 7 is accurately calculated, proving that the end bending and shear resistance design of the light T-beam 7 meets the requirements.

[0092] Example 2

[0093] See also Figure 2 , the structural conditions are the same as those in Example 1. Calculate the bending and shear bearing capacity at 1 / 4 span.

[0094] See also Figure 1 , Figure 4 ,calculate:

[0095] b=0.22m,h0=1.505m.

[0096] The longitudinal reinforcement 4 is composed of longitudinal main reinforcement 10 and longitudinal distribution reinforcement 11. Calculation:

[0097] k sz =10.8198;μ sz =0.04452; μ N =0. k sz (μ sz +μ N )=0.4817<0.5.

[0098] The vertical stirrup 5 is a double stirrup. Calculation:

[0099] k sg =10.8198;μ sg =0.01028; μ q =0. k sg (μ sg +μ q )=0.1112<0.5.

[0100] Calculate the most unfavorable value of the horizontal projection length C of the crack surface 2 at 1 / 4 span: C = 2.1260m.

[0101] Calculate the shear force at 1 / 4 span: V d =0.8107MN, V′ d =0.8107MN.

[0102] Calculate the bending moment at 1 / 4 span: M d =5.0088MN·M,M′ d =5.0088MN·M.

[0103] Calculate the shear span ratio of the orthogonal reinforcement at 1 / 4 span:

[0104] Calculate the bending-shear section deformation coefficient at 1 / 4 span: K m =0.2918.

[0105] It can be seen that in Example 2, compared with Example 1, the calculation position is moved toward the mid-span, the shear span ratio is increased, the most unfavorable bending-shear section has a smaller oblique part and an increased positive part, which is manifested as an increased slope of the crack surface. This is consistent with the damage that occurs when the beam is actually used.

[0106] Calculate the most unfavorable shear bearing capacity at 1 / 4 span: V R =0.9231MN.

[0107] Calculate the most unfavorable bending bearing capacity at 1 / 4 span: M R =5.7032MN·M.

[0108] Design judgment: Yes V d <V R And M d <M R , the design meets the requirements.

[0109] By using the wedge-shaped section deformable bending and shear resistance model and design method of the present invention, the most unfavorable wedge-shaped section bending and shear resistance bearing capacity at 1 / 4 span of the light T-beam 7 is accurately calculated, proving that the bending and shear resistance design of the light T-beam 7 at 1 / 4 span meets the requirements.

Claims

1. A wedge-shaped section deformable bending and shear model, characterized in that: The wedge-shaped section deformable bending and shear resistance model has a crack surface and a pressure-bearing surface with variable shapes. The crack surface and the pressure-bearing surface intersect with each other and are perpendicular to each other at the intersection. The crack surface extends obliquely downward for a certain length and then turns positive to extend downward to the bottom of the component. The pressure-bearing surface extends obliquely upward for a certain length and then turns positive to extend upward to the top of the component. The extension length changes according to the change of the bending moment and shear force ratio on the section.

2. The wedge-shaped cross-section deformable bending and shearing model according to claim 1, characterized in that: The intersection of the crack surface and the pressure surface of the wedge-shaped section deformation bending and shear model is the cross-section strain 0 point. The ratio of the crack surface and the pressure surface extending obliquely for a certain length to the full length of the oblique extension to the edge of the component adopts the same deformation coefficient K. m .

3. A design method for a wedge-shaped cross-section deformable bending-shear model according to claim 1, characterized in that: Shear bearing capacity V R Calculated according to the following formula: V R =V cz +V sg +V sw Among them, V cz V is the shear bearing capacity of the longitudinal reinforcement; sg V is the shear bearing capacity of vertical stirrups; sw is the shear bearing capacity of the bent steel bar; the shear bearing capacity of the longitudinal steel bar V cz Calculated according to the following formula: N d =s c bx c -s sz A ′ sz Where C is the horizontal projection length of the crack surface extending obliquely to the full length of the component edge; h0 is the calculated height of the section; b is the calculated width of the section; x c is the position of the zero point of the cross-sectional superimposed strain, σ c Calculate the stress of the concrete on the bearing surface; σ sz , A sz Calculate stress and area for longitudinal reinforcement of crack surface; σ sj , A sj ,θ sj Calculate stress, area, and acute angle with the normal line of the cross section for the bent steel bar, N d Design the axial forces for the cross section; Shear bearing capacity of vertical stirrups V sg Calculated according to the following formula: Among them, q d is the design vertical pressure of the section; σ sg Calculate the stress of vertical stirrups on the crack surface; μ sg is the reinforcement ratio of vertical stirrups on the crack surface; Shear bearing capacity of bent steel bar V sw Calculated according to the following formula: V sw =∑σ sj A sj sinθ sj ; The most unfavorable value of the horizontal projection length C is calculated according to the following formula: Shear bearing capacity V R The most unfavorable value is calculated according to the following formula: Among them, V R ′ It is the shear capacity of the orthogonal reinforcement without taking into account the shear capacity of the bent reinforcement.

4. The design method of a wedge-shaped cross-section deformable bending-shear model according to claim 3 is characterized in that: Based on the shear bearing capacity V R The calculation of the most unfavorable value, the bending bearing capacity M R Calculated according to the following formula: M R =M cz +M sg +M sw Among them, M cz M is the bending bearing capacity of the longitudinal reinforcement; sg M is the bending bearing capacity of vertical stirrups; sw The bending bearing capacity of the bent steel bar; Longitudinal reinforcement bending bearing capacity M cz Calculated according to the following formula: Longitudinal reinforcement bending bearing capacity M sg Calculated according to the following formula: Bending bearing capacity of bent steel bar M sw Calculated according to the following formula: Among them, d sj The distance between the bent reinforcement and the cross section to calculate the moment equilibrium point.

5. The design method of a wedge-shaped cross-section deformable bending-shear model according to claim 3 is characterized in that: Based on the shear bearing capacity V R The calculation of the most unfavorable value, the bending bearing capacity M R The most unfavorable value is calculated according to the following formula: Among them, M ′ R It is the flexural capacity of the orthogonal reinforcement without taking into account the flexural capacity of the bent reinforcement.

6. A wedge-shaped cross-section deformable bending and shearing resistance model and design method according to claim 3, characterized in that: The deformation coefficient K m Calculated according to the following formula: Where m is the bending-shear ratio of the orthogonal reinforcement; M d is the cross-section design bending moment; V d is the cross-section design shear force; M ′ d The effective design bending moment of the section after deducting the bending bearing capacity of the bent reinforcement; V d ′ The effective design shear force of the section is calculated by deducting the shear bearing capacity of the bent reinforcement.

7. The design method of a wedge-shaped cross-section deformable bending-shear model according to claim 3, characterized in that: When K m →0, its mechanical meaning is: when the shear force on the section is 0 or the shear span ratio is large enough ( Desirable ), the wedge-shaped section is single and converted into a bending-resistant normal section.

8. The design method of a wedge-shaped cross-section deformable bending-shear model according to claim 3 is characterized in that: When K m =1, its mechanical meaning is: the bending moment on the section always participates in the shear calculation But the shear span ratio is small enough The wedge-shaped section is simplified and there is no longer a positive rotation part.

9. The design method of a wedge-shaped cross-section deformable bending-shear model according to claim 3, characterized in that: Based on the shear bearing capacity V R , shear bearing capacity M R The calculation of the most unfavorable value, the longitudinal reinforcement ratio and the vertical stirrup reinforcement ratio under the deformation of the wedge section have an effective value; when k sz (μ sz +μ N )≥0.5, take k sg (μ sg +μ q )=0.5; when k sz (μ sz +μ N )≥0.5, take k sg (μ sg +μ q )=0.5; Based on the shear bearing capacity V R , shear bearing capacity M R The calculation of the most unfavorable value, the shear bearing capacity has a maximum value; when k sz (μ sz +μ N )≥0.5 and k sg (μ sg +μ q )≥0.5, the shear bearing capacity V R , shear bearing capacity M R The maximum value is calculated using the following formula: Design judgment is carried out according to the following rules: (1) When V d ≤V R And M d ≤M R When the design meets the requirements; (2) When V d >V R or M d >M R The design needs to be adjusted.

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