Frame structure design method based on rigidity reduction

Abstract

The invention discloses a frame structure design method based on rigidity reduction. The method comprises the following steps that 1, rod end bending moments Mb and Mc and axial force Nc of frame beams and columns are obtained through calculation; step 2, obtaining actual reinforcement areas Asb0 and Asc0, section sizes and concrete strength of frame beams and columns; 3, the equivalent stiffness Kb1 of the frame beam is obtained through calculation according to the formula Kb1 = Mb0.75y / phi b0.75y; 4, the equivalent stiffness Kc1 of the frame column is obtained through calculation according to the formula Kc1 = Mc0.75y / phi c0.75y; 5, comparing the equivalent stiffness of the frame beam and the frame column with the initial flexural stiffness, and ending after the deviation is less than or equal to 15%; 6, calculating a shear force design value of the frame beam, calculating stirrups needing to be configured for the frame beam, and rechecking a shear-resistant section; and 7, calculating a shear force design value of the frame column, calculating stirrups needing to be configured for the frame column, and rechecking a shear-resistant section. Compared with the prior art, an overall calculation model of the frame structure is established, the real rigidity of a structural member is obtained through multiple iterations, section reinforcement is optimized, and the reinforcement amount is reduced; and the overall anti-seismic performance is improved.

Description

Technical Field

[0001] This invention relates to a method for designing building structures, and more particularly to a frame structure design method based on stiffness reduction. Background Technology

[0002] Reinforced concrete members operate with cracks. Chinese standards stipulate that the crack limit for reinforced concrete members under the serviceability limit state is 0.2–0.3 mm. Under the ultimate limit state, members exhibit numerous cracks, potentially exceeding 0.3 mm. Furthermore, shrinkage and creep are fundamental characteristics of reinforced concrete members; their stiffness inevitably decreases under long-term loads. Therefore, the current linear elastic design of reinforced concrete members, which calculates stiffness using the full section moment of inertia (I), is unreasonable. In current traditional frame structure design, beam and column stiffness are often taken as E without reduction according to standards. c I. Failure to consider the effects of actual reinforcement, axial compression ratio, and crack development leads to the following problems:

[0003] 1. The stiffness values ​​of beams and columns have large deviations, the internal force calculations are inaccurate, and the reinforcement is redundant or insufficient;

[0004] 2. Unreasonable stiffness distribution makes it difficult to achieve "strong column, weak beam", and columns are prone to fail before beams during earthquakes;

[0005] 3. The shear design did not take into account the overstrength effect of the reinforcement, resulting in shear failure before bending yielding and poor structural ductility. Summary of the Invention

[0006] The purpose of this invention is to provide a frame structure design method based on stiffness reduction. The technical problem to be solved is to accurately reflect the actual bending stiffness of the components by dynamically adjusting the stiffness coefficients of beams and columns, thereby obtaining the true stress state of the components and optimizing the reinforcement design.

[0007] To solve the above problems, the present invention adopts the following technical solution: a frame structure design method based on stiffness reduction, comprising the following steps:

[0008] Step 1: Establish a three-dimensional model based on the dimensions of the building structure components and the loads they are subjected to, and set the initial bending stiffness of the frame beams as K. b0 =E c I b The initial bending stiffness of the frame column is K. c0 =E c I c , of which E c I represents the elastic modulus of concrete. b I c The moments of inertia of the beam and column sections are given, and the end moments M of the frame beams and columns are calculated. b M c and axial force Nc ;

[0009] Step 2: Based on the bending moment M at the ends of the frame beams and columns. b M c and axial force N c The ultimate limit state design of flexural bearing capacity is performed to obtain the actual reinforcement area A of the frame beams and columns. sb0 A sc0 Cross-sectional dimensions and concrete strength;

[0010] Step 3: Calculate the equivalent stiffness K of the frame beam based on its actual reinforcement, cross-sectional dimensions, and concrete strength. b1 =M b0.75y / φ b0.75y ;

[0011] Step 4: Calculate the equivalent stiffness K of the frame column based on its actual reinforcement, cross-sectional dimensions, concrete strength, and axial stability. c1 =M c0.75y / φ c0.75y ;

[0012] Step 5: Compare the equivalent stiffness of the frame beams and frame columns with the initial bending stiffness. If the deviation is ≤15%, then adjust the equivalent stiffness K of the frame beams and frame columns. b1 K c1 The final actual bending stiffness of the component is used as the basis for calculating the final actual reinforcement area of ​​the component; if the deviation is >15%, the equivalent stiffness K of the frame beam and frame column is adjusted. b1 K c1 Replacement of initial bending stiffness K b0 K c0 Repeat steps one through four until the deviation is ≤15% and then stop.

[0013] Step 6: Calculate the design value of the shear force of the frame beam based on the final actual reinforcement area, calculate the stirrups required for the frame beam, and verify the shear section.

[0014] Step 7: Calculate the design value of the shear force of the frame column based on the final actual reinforcement area, calculate the stirrups required for the frame column, and verify the shear section.

[0015] Furthermore, in step one, the dimensions of the building structure components and the loads they bear are input into the Yingjianke software to create a three-dimensional model, and the bending moments M at the ends of the frame beams and columns are calculated using the Yingjianke software. b M c and axial force N c .

[0016] Furthermore, in step three, the bending moment-curvature curve of the frame beam is generated using XTRACT software to obtain the yield moment M.by and corresponding curvature φ by M b0.75y =0.75M by and corresponding M b0.75y curvature φ b0.75y Calculate the equivalent stiffness K of the frame beam. b1 =M b0.75y / φ b0.75y .

[0017] Furthermore, in step four, the bending moment-curvature curves of the frame columns are generated using XTRACT software to obtain the yield moment M under the same axial force. cy and corresponding curvature φ cy M c0.75y =0.75M cy and corresponding M c0.75y curvature φ c0.75y Calculate the equivalent stiffness K of the frame column. c1 =M c0.75y / φ c0.75y .

[0018] Furthermore, in step six, the design value of the shear force of the frame beam is calculated based on the final actual reinforcement area. The calculation yields the result, where γ is the overstrength coefficient of the reinforcing steel. The bending moment value corresponding to the bending capacity of the actual longitudinal reinforcement in the clockwise or counterclockwise direction at the left and right ends of the beam; n For the clear span of the beam, V gb Shear force generated by gravity load.

[0019] Furthermore, the overstrength coefficient of the steel reinforcement is set to 1.2.

[0020] Furthermore, in step seven, the design value of the shear force of the frame column is calculated based on the final actual reinforcement area. The calculation yields, where: H represents the bending moment value corresponding to the bending capacity of the actual longitudinal reinforcement bars arranged clockwise or counterclockwise at the top and bottom of the column; n Let η be the net height of the column, and η be the shear force amplification factor of the column.

[0021] Furthermore, the column shear force amplification system is configured based on the column's seismic resistance level.

[0022] Compared with existing technologies, this invention establishes an overall calculation model of the frame structure, obtains the true stiffness of structural components through multiple iterations, optimizes the cross-sectional reinforcement, and reduces the amount of reinforcement; calculates the shear resistance requirements based on the actual reinforcement, ensuring "strong shear and weak bending"; balances the stiffness of beams and columns, promotes the formation of a "strong column and weak beam" mechanism, and improves the overall seismic performance. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention;

[0024] Figure 2 A schematic diagram of the moment-curvature curves of a frame beam under different reinforcement ratios;

[0025] Figure 3 A schematic diagram of the moment-curvature curves of frame columns under different reinforcement ratios;

[0026] Figure 4 A schematic diagram showing the relationship between reinforcement ratio and stiffness coefficient of frame columns under different axial compression ratios;

[0027] Figure 5 This is a schematic diagram of a frame structure. Detailed Implementation

[0028] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0029] In this invention, "strong shear and weak bending" is a proactive design strategy in seismic design of structures. It artificially increases the shear capacity of beams, significantly exceeding the maximum shear force that might occur when the beam yields in bending. This forces the beams to preferentially undergo ductile bending failure (forming plastic hinges) under strong earthquakes, avoiding dangerous brittle shear failure and ensuring the overall safety of the structure and the safety of personnel under seismic loads. This is one of the important technical means to achieve the seismic fortification goal of "no damage in minor earthquakes, repairable in moderate earthquakes, and no collapse in major earthquakes."

[0030] "Strong column, weak beam" is an active seismic design strategy that artificially increases the flexural capacity of columns to significantly exceed the maximum flexural capacity of beams at the same joint, thereby forcing plastic hinges to form preferentially at the beam ends. It is a fundamental guarantee for realizing the "beam hinge energy dissipation mechanism" in frame structures and avoiding catastrophic "inter-story collapse," and is of paramount importance for protecting people's lives and property. This principle profoundly embodies the advanced concept in seismic design that "controlling failure modes takes precedence over simply increasing strength."

[0031] like Figure 1 As shown, this invention discloses a frame structure design method based on stiffness reduction. The specific design method steps are as follows:

[0032] Step 1: Input the dimensions of the building structure components and the loads they bear into the YJK structural design software to create a 3D model, and set the initial bending stiffness of the frame beams to K. b0 =E c I b The initial bending stiffness of the frame column is K. c0 =E c I c E c I represents the elastic modulus of concrete.b I c The moments of inertia of the beam and column sections are respectively; and the end moments M of the frame beams and columns are calculated using Yingjianke software. b M c and axial force N c Of course, this calculation can also be obtained using existing calculation formulas;

[0033] Step 2: Calculate the end moments M of the frame beams and columns obtained in Step 1. b M c and axial force N c According to the current specifications, the ultimate limit state design (calculation) of flexural bearing capacity is performed to obtain the actual reinforcement area A of the frame beams and columns. sb0 A sc0 The cross-sectional dimensions and concrete strength; the ultimate limit state design of flexural bearing capacity can be calculated using existing methods, for example:

[0034] For typical frame beams, the formula can be used:

[0035] M≤α1f c bx(h0-0.5x)+f′ y A′ s (h0-a′ s ),

[0036] and α1f c bx = f y A s -f′ y A′ s Calculate the required reinforcement area for the frame beam;

[0037] For general frame columns, the formula can be used:

[0038] Ne≤α1f c bx(h0-0.5x)+f′ y A′ s (h0-a′ s ),

[0039] N≤α1f c bx+f′ y A′ s Calculate the required reinforcement area for the frame columns;

[0040] In the above formula, M is the design bending moment, α1 is a coefficient related to the concrete strength grade, and f c A represents the design value of the axial compressive strength of concrete. s A s′ represents the cross-sectional area of ​​the longitudinal ordinary reinforcement in the tension and compression zones, b is the width of the rectangular section, h0 is the effective height of the section, x is the height of the concrete compression zone, and f y f y ′ represents the design values ​​of tensile and compressive strength of ordinary steel bars, a s ′ is the distance from the resultant point of the longitudinal ordinary steel reinforcement in the compression zone to the compression edge of the section, N is the design value of the axial pressure on the member, and e is the distance from the point of application of the axial pressure to the resultant point of the longitudinal ordinary steel reinforcement under tension.

[0041] Ultimate limit state design of flexural bearing capacity can also be calculated using YJK structural design software.

[0042] The ultimate limit state design of flexural bearing capacity is a conventional technology, and the appropriate calculation method can be selected according to actual needs.

[0043] After obtaining the required reinforcement area, determine the actual reinforcement area of ​​the frame beams and frame columns. Generally, the actual reinforcement area should not exceed 5% of the required reinforcement area. Of course, it can also be calculated further according to the building structure design requirements (such as seismic resistance level, wind load, etc.).

[0044] Step 3: Based on the actual reinforcement, cross-sectional dimensions, and concrete strength of the frame beam, use XTRACT software to generate the bending moment-curvature curve of the frame beam to obtain the yield moment M. by and corresponding curvature φ by M b0.75y =0.75M by and corresponding M b0.75y curvature φ b0.75y Calculate the equivalent stiffness K of the frame beam. b1 =M b0.75y / φ b0.75y M b0.75y That is, yield moment M by 0.75 times that of K b1 It is the ratio of 0.75 times the yield moment to its corresponding curvature.

[0045] Step 4: Based on the actual reinforcement, cross-sectional dimensions, concrete strength, and axial force (N) of the frame column. c The moment-curvature curves of the frame columns were generated using XTRACT software, and the yield moment M under the same axial force was obtained. cy and corresponding curvature φ cy M c0.75y =0.75M cy and corresponding M c0.75y curvature φ c0.75y Calculate the equivalent stiffness K of the frame column. c1 =M c0.75y / φ c0.75y Mc0.75y That is, yield moment M cy 0.75 times that of K c1 It is the ratio of 0.75 times the yield moment to its corresponding curvature.

[0046] Step 5: Compare the equivalent stiffness K of the frame beams and frame columns. b1 K c1 With initial bending stiffness K b0 K c0 If the deviation is ≤15%, the bending design is completed. The equivalent stiffness K of the frame beams and frame columns calculated in steps three and four is then applied. b1 K c1 The final actual bending stiffness of the component is used as the basis for calculating the final actual reinforcement area of ​​the component; if the deviation is >15%, the equivalent stiffness K of the frame beam and frame column is adjusted. b1 K c1 Replacement of initial bending stiffness K b0 K c0 Repeat steps one through four for i iterations until the deviation is ≤15%, at which point the final bending stiffness K is obtained. bi K ci The actual bending stiffness K of the component eb K ec Take the stiffness reduction factor α b =K eb / K b0 α c =K ec / K c0 ; where α b α is the stiffness reduction factor for the frame beam, ranging from 0.3 to 0.5; c This is the stiffness reduction factor for the frame columns, with a value ranging from 0.4 to 0.8.

[0047] Step 6: Calculate the design shear force of the frame beam based on the final actual reinforcement area. Where γ is the overstrength coefficient of the steel reinforcement, which is taken as 1.2; The bending moment value corresponding to the bending capacity of the actual longitudinal reinforcement in the clockwise or counterclockwise direction at the left and right ends of the beam; n For the clear span of the beam, V gb Shear force generated by gravity load; after calculating the design value of shear force of frame beam, calculate the required stirrups of frame beam according to current specifications and check the shear section;

[0048] Step 7: Calculate the design shear force of the frame columns based on the final actual reinforcement area.

[0049] in, H represents the bending moment value corresponding to the bending capacity of the actual longitudinal reinforcement bars arranged clockwise or counterclockwise at the top and bottom of the column; n η is the column clear height, and η is the column shear force amplification factor, which is determined according to the column seismic grade. After calculating the design value of the frame column shear force, the required stirrups for the frame column are calculated according to the current code, and the shear section is checked.

[0050] In steps six and seven, the current standards for calculating the required stirrups for the frame beams and columns and verifying the shear section are: "Code for Design of Concrete Structures GB 50010-2010 (2015 Edition)", "Code for Seismic Design of Buildings GB 50011-2010 (2016 Edition)", "Technical Specification for Concrete Structures of High-Rise Buildings JGJ 3-2010", "Load Code for Building Structures GB 50009-2012", and "General Specification for Engineering Structures GB 55001-2021", etc.

[0051] Taking a frame project in Shenzhen as an example, this paper illustrates the specific operation process and effects of the frame structure design method based on stiffness reduction proposed in this invention. The selected case is a 3×3 span frame structure, with each span being 8m, a total of 5 stories, each story height being 4.5m, beam cross-sections of 300×600mm, column cross-sections of 600×600mm, slab thickness of 200mm, and an additional dead load of 2.0kN / m. 2 Live load 4.0 kN / m 2 The concrete grade for both beams and columns is C30. A typical floor plan of the structure is shown below. Figure 5 As shown. Follow these steps:

[0052] 1. Initial setting of beam stiffness coefficient α b =1.0, column α c =1.0, the beam end bending moment and column bottom bending moment are calculated;

[0053] 2. After reinforcement is added, a moment-curvature curve is generated, and the equivalent stiffness K of the beam is determined. e =0.37E c I b Column equivalent stiffness

[0054] K e =0.68E c I c ;

[0055] 3. After one iteration, it converges, and finally the beam α b =0.35, column α c =0.7;

[0056] 4. The shear force was calculated based on the actual longitudinal reinforcement, and both beams and columns met the shear resistance requirements.

[0057] The calculation results show that the total amount of steel reinforcement in the building is reduced by 3.5%, with beam steel reinforcement reduced by 5.6% and column steel reinforcement increased by 0.5%. This effectively ensures the formation of the "strong shear and weak bending" and "strong column and weak beam" mechanisms, thereby improving the overall seismic performance.

[0058] As the size of the structure increases, the reduction in the amount of steel reinforcement becomes more and more obvious.

Claims

1. A frame structure design method based on stiffness reduction, characterized in that: Includes the following steps: Step 1: Establish a three-dimensional model based on the dimensions of the building structure components and the loads they are subjected to, and set the initial bending stiffness of the frame beams as K. b0 =E c I b The initial bending stiffness of the frame column is K. c0 =E c I c , of which E c I represents the elastic modulus of concrete. b I c The moments of inertia of the beam and column sections are given, and the end moments M of the frame beams and columns are calculated. b M c and axial force N c ; Step 2: Based on the bending moment M at the ends of the frame beams and columns. b M c and axial force N c The ultimate limit state design of flexural bearing capacity is performed to obtain the actual reinforcement area A of the frame beams and columns. sb0 A sc0 Cross-sectional dimensions and concrete strength; Step 3: Calculate the equivalent stiffness K of the frame beam based on its actual reinforcement, cross-sectional dimensions, and concrete strength. b1 =M b0.75y / φ b0.75y ; Step 4: Calculate the equivalent stiffness K of the frame column based on its actual reinforcement, cross-sectional dimensions, concrete strength, and axial stability. c1 =M c0.75y / φ c0.75y ; Step 5: Compare the equivalent stiffness of the frame beams and frame columns with the initial bending stiffness. If the deviation is ≤15%, then adjust the equivalent stiffness K of the frame beams and frame columns. b1 K c1 The final actual bending stiffness of the component is used as the basis for calculating the final actual reinforcement area of ​​the component; if the deviation is >15%, the equivalent stiffness K of the frame beam and frame column is adjusted. b1 K c1 Replacement of initial bending stiffness K b0 K c0 Repeat steps one through four until the deviation is ≤15% and then stop. Step 6: Calculate the design value of the shear force of the frame beam based on the final actual reinforcement area, calculate the stirrups required for the frame beam, and verify the shear section. Step 7: Calculate the design value of the shear force of the frame column based on the final actual reinforcement area, calculate the stirrups required for the frame column, and verify the shear section.

2. The frame structure design method based on stiffness reduction according to claim 1, characterized in that: In step one, the dimensions of the building structure components and the loads they bear are input into the Yingjianke software to create a 3D model, and the bending moments M at the ends of the frame beams and columns are calculated using the Yingjianke software. b M c and axial force N c .

3. The frame structure design method based on stiffness reduction according to claim 1, characterized in that: Step 3: Use XTRACT software to generate the moment-curvature curve of the frame beam to obtain the yield moment M. by and corresponding curvature φ by M b0.75y =0.75M by and corresponding M b0.75y curvature φ b0.75y Calculate the equivalent stiffness K of the frame beam. b1 =M b0.75y / φ b0.75y .

4. The frame structure design method based on stiffness reduction according to claim 1, characterized in that: Step four uses XTRACT software to generate the moment-curvature curves of the frame columns, obtaining the yield moment M under the same axial force. cy and corresponding curvature φ cy M c0.75y =0.75M cy and corresponding M c0.75y curvature φ c0.75y Calculate the equivalent stiffness K of the frame column. c1 =M c0.75y / φ c0.75y .

5. The frame structure design method based on stiffness reduction according to claim 1, characterized in that: In step six, the design value of the shear force of the frame beam is calculated based on the final actual reinforcement area. The calculation yields the result, where γ is the overstrength coefficient of the reinforcing steel. The bending moment value corresponding to the bending capacity of the actual longitudinal reinforcement in the clockwise or counterclockwise direction at the left and right ends of the beam; n For the clear span of the beam, V gb Shear force generated by gravity load.

6. The frame structure design method based on stiffness reduction according to claim 5, characterized in that: The overstrength coefficient of the steel reinforcement is set to 1.

2.

7. The frame structure design method based on stiffness reduction according to claim 1, characterized in that: In step seven, the design value of the shear force of the frame column is calculated based on the final actual reinforcement area. The calculation yields, where: H represents the bending moment value corresponding to the bending capacity of the actual longitudinal reinforcement bars arranged clockwise or counterclockwise at the top and bottom of the column; n Where η is the net height of the column, and η is the shear force amplification factor of the column.

8. The frame structure design method based on stiffness reduction according to claim 7, characterized in that: The column shear force amplification system is described in terms of value based on the column's seismic resistance level.

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