Design method of swing building structure under effect of inverted triangle lateral load

Abstract

The invention discloses a design method for a swing building structure under the action of an inverted triangle lateral load. The design method comprises the steps that S1, parameters and working conditions of the structure are determined; s2, a hinged support is arranged at the column bottom located at the center of the structure, and a spring support is arranged at the column bottom located on the peripheral side of the structure; s3, establishing a mechanical analysis model of the structure and solving a force balance equation; s4, setting a rigid body displacement ratio target value and solving the vertical rigidity of the spring support; s5, a spring support with the rigidity is arranged in the finite element model, push-and-cover analysis is carried out, and a rigid body displacement proportion design value is solved; s6, the rigid body displacement proportion design value is compared with the rigid body displacement proportion target value, and if the rigid body displacement proportion design value is matched with the rigid body displacement proportion target value, the next step If not, returning to the step S4 to change the rigid body displacement ratio target value; and S7, elastic-plastic time-history analysis is carried out, whether the macroscopic performance index of the structure and the damage of the structure meet the requirements or not is checked, and if not, the step S1 is returned to modify the basic parameters of the structure.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake-resistant building structures, and more particularly to a design method for a swaying building structure under the action of an inverted triangle lateral load. Background Art

[0002] The main purpose of traditional earthquake-resistant structures is to control the strength and ductility of the structure. The bearing capacity is designed in case of small earthquakes, and the ductility and deformation of the structure are verified in case of large earthquakes to ensure that the structure does not collapse or break down. However, when a strong earthquake occurs, although the traditional structure can also be designed according to existing specifications to withstand a strong earthquake, the structure will be severely damaged, and it is difficult or expensive to repair the structure after the earthquake. For important engineering structures, it is not only required to effectively protect the lives and property of the people after a strong earthquake, but also emphasized that it should be able to quickly restore the normal use function of the structure after a strong earthquake to avoid causing greater indirect losses. The indirect losses and direct losses caused by strong earthquakes to building structures are at the same order of magnitude. Therefore, it is urgent to develop a resilient structure that can effectively reduce structural earthquake losses and propose its earthquake-resistant design method.

[0003] The rocking self-righting structure is an effective structural form to reduce structural earthquake damage, but the existing rocking structures have failed to achieve overall deformation control of the structure and lack of seismic design methods.

[0004] Therefore, how to provide a design method for a swaying building structure under the action of an inverted triangle lateral load so that the building structure can achieve the overall swaying function and provide strong support for engineering design is an urgent problem that technical personnel in this field need to solve. Summary of the invention

[0005] In view of this, the present invention provides a design method for an inverted triangle lateral load of a rocking building structure, aiming to solve the above technical problems.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A design method for a swaying building structure under an inverted triangle lateral load, comprising the following steps:

[0008] S1. Determine the basic parameters and working conditions of the structure;

[0009] S2. A hinge support is provided at the bottom of the column located at the center of the structure, and a spring support is provided at the bottom of the column located at the periphery of the structure;

[0010] S3. Establish a structural mechanics analysis model and solve the force balance equation;

[0011] S4, setting a target value of rigid body displacement ratio and solving the vertical stiffness of the spring support by the force balance equation in step S3;

[0012] S5. According to the vertical stiffness of the spring support obtained in step S4, the spring support is set in the finite element model and a pushover analysis is performed to solve the design value of the rigid body displacement ratio;

[0013] S6, comparing the rigid body displacement ratio design value with the rigid body displacement ratio target value, if the two match, proceed to the next step; if the two do not match, return to step S4 to change the rigid body displacement ratio target value and recalculate the vertical stiffness of the spring support;

[0014] S7, perform elastic-plastic time history analysis and verify whether the macroscopic performance index of the structure and the damage of the structure meet the requirements. If not, return to step S1 to modify the basic parameters of the structure.

[0015] The beneficial effect of the above technical solution is that the stiffness of the spring support is designed based on the force balance equation, the calculation method is relatively accurate and reliable, and the structure calculated by this method can realize the overall swing function of the building.

[0016] Preferably, in step S1, the basic parameters of the structure include the span and storey height, beam and column cross-section, floor thickness, steel type and structural damping ratio of the structure, and the working conditions include the design intensity and site type.

[0017] Preferably, in step S3, establishing the mechanical analysis model of the structure includes applying a horizontal inverted triangle lateral load to the upper structure and applying a gravity load vertically.

[0018] Preferably, in step S3, solving the force balance equation of the hinge support includes:

[0019] The inverted triangle lateral load takes the moment of the hinge support, and the formula 1 is:

[0020]

[0021] Take moment balance on the hinge support, and get equation 2:

[0022]

[0023] Introducing parameter K s : The anti-overturning moment generated by all vertical spring supports when the foundation rotates unit angle around the bottom hinge support, that is,

[0024] Then we can get formula 3 through formula 2:

[0025]

[0026] Introducing parameter K S: represents the load size of the top of the structure in the inverted triangle lateral load that needs to be applied when the upper structure has a unit lateral displacement. When the top has a lateral displacement of (u1+u2+u3),

[0027] P′=K′ S (u1+u2+u3), then according to formula 3, we can get formula 4:

[0028]

[0029] Introduce parameter Φ: represents the ratio of the horizontal displacement at the center of gravity to the horizontal displacement at the vertex, then u4=Φu, substitute into formula 4 to get formula 5:

[0030]

[0031] Substitute h = nh c Formula 6:

[0032]

[0033] Calculate the lateral stiffness of the foundation fixed structure when the lateral load is inverted triangle.

[0034] Formula 7, calculate the vertex displacement when the foundation is fixed (using the unit load method):

[0035]

[0036] Formula 8: The load K at the top of the structure in the inverted triangle load required when the top displacement is 1 sf :

[0037] u1+u2=1

[0038]

[0039] Introduce parameter θ3: represents the rigid body displacement rotation angle, calculate the anti-overturning moment K generated by all vertical spring supports when the foundation produces a unit rotation angle around the bottom hinge support s , Formula 9:

[0040]

[0041] Calculate the load K at the top of the structure in the inverted triangle load required to be applied when the upper structure undergoes unit lateral displacement s ', Formula 10:

[0042] u1+u2+u3=1

[0043]

[0044] Combining equation 6 with equation 10, we get equation 11:

[0045]

[0046] Preferably, in step S3, the moment of the lateral load on the hinge support can also be used to calculate the resultant force of the lateral load:

[0047]

[0048] The resultant force of the lateral load acts on the hinge support

[0049]

[0050] Preferably, in step S5, the pushover analysis method includes modal pushover, lateral loading, uniform loading or concentrated load applied at the vertex.

[0051] Preferably, in step S7, the elastoplastic time history analysis includes time history analysis results under no less than 7 seismic waves; response spectrum analysis is used for small earthquakes, and macro performance indicators and structural damage are verified. If the requirements are not met, return to step S1 to modify the basic parameters of the structure.

[0052] Preferably, the macroscopic performance indicators include inter-story displacement angle and acceleration.

[0053] Preferably, the structure includes assembled prefabricated components of the building superstructure, a vertical assembled load-bearing component located in the middle, a hinge support at the bottom, and vertical tension and compression spring supports located on all sides.

[0054] It can be seen from the above technical solution that, compared with the prior art, the present invention discloses a design method for a swaying building structure under the action of an inverted triangle lateral load, in which the stiffness of the spring support is designed based on the force balance equation, and the calculation method is relatively accurate and reliable. The structure calculated by this method can realize the overall swaying function of the building. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0056] Figure 1 A design flow chart of the swing assembled building structure under lateral load provided by the present invention;

[0057] Figure 2 A schematic diagram of the building structure provided by the present invention;

[0058] Figure 3 A diagram of the building structure mechanics model provided by the present invention;

[0059] Figure 4 A schematic diagram of parameters of the hinge support force balance equation provided by the present invention;

[0060] Figure 5 A schematic diagram of a two-dimensional structure of a building provided by the present invention;

[0061] Figure 6 A schematic diagram of base deformation of the structure provided by the present invention under earthquake action.

[0062] Figure 7 is a finite element time history analysis response spectrum curve in an embodiment of the present invention;

[0063] Figure 8 It is a finite element three-dimensional structure diagram in an embodiment of the present invention;

[0064] Fig. 9 It is a diagram of the overall deformation of the structure under earthquake action in an embodiment of the present invention.

[0065] in,

[0066] 1-Hinged support; 2-Spring support. DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0068] See attached Figures 1 to 6 The embodiment of the present invention discloses a design method for an inverted triangle lateral load of a swaying building structure, comprising the following steps:

[0069] S1. Determine the basic parameters and working conditions of the structure;

[0070] The basic parameters of the structure include the span and floor height, beam and column cross-section, floor thickness, steel type and structural damping ratio; the working conditions include the design intensity and site type.

[0071] In this embodiment, if Figure 5 As shown, the upper structure is a 9-story steel frame structure with a floor height of 5m, a span of 4m, a floor thickness of 120mm, a damping ratio of 0.04, and a dead load of 5kN / m 2 , Live load 2kN / m 2 ; Q345 steel is used for frame beams, frame columns and steel supports, and its parameter values ​​are: elastic modulus is 2.06Gpa, Poisson's ratio is 0.3, and density is 7850kg / m3 , the yield strength is 345MPa, the tensile strength is 470Mpa, and the basic size parameters of the structure are shown in the following table:

[0072]

[0073] Working conditions: The design intensity is 8 degrees 0.2g, the site category is Class III Group 2, and the site characteristic period is 0.55s.

[0074] S2. A rotatable hinge support 1 is provided at the bottom of the column located at the center of the structure, and a vertical tension and compression spring support 2 is provided at the bottom of the column located at the periphery of the structure (when the bottom of the columns at the periphery of the structure is at the same height as the bottom of the column at the center, horizontal constraints can be provided at the bottom of the columns at the periphery);

[0075] S3. Establish a structural mechanics analysis model and apply an inverted triangle lateral load to the upper structure, apply a gravity load vertically, and solve the force balance equation; from the perspective of engineering practicality, in order to simplify the derivation, it is assumed that the structure is a symmetrical structure. The structural stress conditions of this embodiment are as follows: Figure 4 As shown;

[0076] Figure 4 middle:

[0077] V S1 、V S2 : Vertical reaction force of spring supports on both sides (direction as shown in the figure, V S1 is the vertical reaction force of the left spring support, V S2 is the vertical reaction force of the right spring support, generally V S2 >V S1 , the direction is upward)

[0078] G: representative value of gravity load of superstructure;

[0079] u1: horizontal displacement of the top caused by bending deformation;

[0080] u2: horizontal displacement of the top caused by shear deformation;

[0081] u3: horizontal displacement of the top caused by the rotation of the rigid body;

[0082] u4: initial eccentricity of the superstructure gravity load;

[0083] h c : Floor height;

[0084] n: number of floors (including underground);

[0085] b: The distance from the left spring support to the right spring support;

[0086] u: total horizontal displacement of the top, u=u1+u2+u3;

[0087] K: slope of the inverted triangle load,

[0088]

[0089] Figure 3 is the mechanical model of the structure, Figure 3 Figure (I) shows the situation where the spring support and the rotating support are at different heights but no horizontal constraint is set at the spring support, (II) shows the situation where the spring support and the rotating support are at the same height and no horizontal constraint is set at the spring support, and (III) shows the situation where the spring support and the rotating support are at the same height but a horizontal constraint is set at the spring support.

[0090] Solve the force balance equation for the hinge support:

[0091] The lateral load of the inverted triangle on the hinged support is taken as the moment M r , we get formula 1:

[0092]

[0093] Take moment balance on the hinge support, and get equation 2:

[0094]

[0095] Introducing parameter K s : The anti-overturning moment generated by all vertical spring supports when the foundation rotates unit angle around the bottom hinge support, that is,

[0096] Then we can get formula 3 through formula 2:

[0097]

[0098] Introducing parameter K′ S : represents the load size of the top of the structure in the inverted triangle lateral load that needs to be applied when the upper structure has a unit lateral displacement. When the top has a lateral displacement of (u1+u2+u3),

[0099] P′=K′ S (u1+u2+u3), then according to formula 3, we can get formula 4:

[0100]

[0101] Introduce parameter Φ: represents the ratio of the horizontal displacement at the center of gravity to the horizontal displacement at the vertex, then u4=Φu, substitute into formula 4 to get formula 5:

[0102]

[0103] Substitute h = nh c Formula 6:

[0104]

[0105] Calculate the lateral stiffness of the foundation fixed structure when the lateral load is inverted triangle.

[0106] Formula 7, calculate the vertex displacement when the foundation is fixed (using the unit load method):

[0107]

[0108] Formula 8: The load K at the top of the structure in the inverted triangle load required when the top displacement is 1 sf :

[0109] u1+u2=1

[0110]

[0111] Introduce parameter θ3: represents the rigid body displacement rotation angle, calculate the anti-overturning moment K generated by all vertical spring supports when the foundation produces a unit rotation angle around the bottom hinge support s , Formula 9:

[0112]

[0113] Calculate the load K at the top of the structure in the inverted triangle load required to be applied when the upper structure undergoes unit lateral displacement s ', Formula 10:

[0114] u1+u2+u3=1

[0115]

[0116] Combining equation 6 with equation 10, we get equation 11:

[0117]

[0118] In order to further optimize the above technical solution, in step S3, the moment of the inverted triangle lateral load on the hinge support in the force balance equation can also be obtained in the following manner:

[0119] Find the resultant force of the lateral load:

[0120]

[0121] The resultant force of the lateral load takes the moment of the hinge support:

[0122]

[0123] S4. Set the target value of rigid body displacement ratio And the vertical stiffness of the spring support is solved by the force balance equation in step S3;

[0124] The target value of the rigid body displacement ratio in this embodiment Set to 70%, the K sf =1.358kN / mm, calculate and get Φ=0.5, G=5556.49kN, h=45m, substitute the value into formula 9 to get K S is 4776.77×103kn·m, so the spring stiffness is

[0125] S5, according to the vertical stiffness of the spring support obtained in step S4, the spring support is set in the finite element model and a pushover analysis is performed, a finite element model of the structure is established and the support is set as a spring support with the above stiffness, and then a finite element pushover analysis is performed to obtain a design value of the rigid body displacement ratio;

[0126] In this embodiment, the elastic stiffness of the telescopic spring in the spring support is 49.758 kN / mm, and then the top of the structure is horizontally pushed over 50 mm to obtain a rigid body displacement ratio of 69.37%.

[0127] S6. Compare the design value of rigid body displacement ratio with the target value of rigid body displacement ratio Compare them, and if the two match, proceed to the next step; if the two do not match, return to step S4 to change the target value of the rigid body displacement ratio and recalculate the vertical stiffness of the spring support;

[0128] After the above calculations, the rigid body displacement ratio of 69.37% obtained by the finite element pushover analysis is consistent with the set target rigid body displacement ratio of 70%, achieving the target rigid body displacement ratio and meeting the requirements.

[0129] S7, perform elastic-plastic time history analysis and verify whether the macroscopic performance indicators such as inter-layer displacement angle, acceleration and structural damage meet the requirements. If not, return to step S1 to modify the basic parameters of the structure.

[0130] When conducting elastic-plastic time history analysis, the time history analysis results under no less than 7 seismic waves should be obtained; response spectrum analysis can be used for small earthquakes.

[0131] The inter-story displacement angles of each layer of the steel frame structure in this embodiment under large, medium and small earthquakes (minus the rigid body displacement angle) are shown in the table below, which meet the design requirements.

[0132]

[0133] The rigid body displacement ratio of each floor of the steel frame structure in this embodiment under large, medium and small earthquakes is shown in the table below, which meets the design requirements.

[0134]

[0135] In order to further optimize the above technical solution, the methods for pushover analysis of spring supports include modal pushover, inverted triangle loading, uniform loading or concentrated load applied at the vertex.

[0136] In order to further optimize the above technical solution, the structure includes assembled prefabricated components of the building superstructure, vertical assembled load-bearing components located in the middle, hinged supports at the bottom and vertical tension and compression spring supports located on all sides.

[0137] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0138] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for a swaying building structure under an inverted triangle lateral load, characterized in that: The following steps are involved: S1. Determine the basic parameters and working conditions of the structure; S2. A hinge support is provided at the bottom of the column located at the center of the structure, and a spring support is provided at the bottom of the column located at the periphery of the structure; S3. Establish a mechanical analysis model of the structure and solve the force balance equation; S4, setting a target value of rigid body displacement ratio and solving the vertical stiffness of the spring support by the force balance equation in step S3; S5. According to the vertical stiffness of the spring support obtained in step S4, the spring support is set in the finite element model and a pushover analysis is performed to solve the design value of the rigid body displacement ratio; S6, comparing the rigid body displacement ratio design value with the rigid body displacement ratio target value, if the two match, proceed to the next step; if the two do not match, return to step S4 to change the rigid body displacement ratio target value and recalculate the vertical stiffness of the spring support; S7, perform elastic-plastic time history analysis and verify whether the macroscopic performance index of the structure and the damage of the structure meet the requirements. If not, return to step S1 to modify the basic parameters of the structure.

2. The design method of a swaying building structure under an inverted triangle lateral load according to claim 1, characterized in that: In step S1, the basic parameters of the structure include the span and floor height, beam and column sections, floor thickness, steel type and structural damping ratio, and the working conditions include the design intensity and site type.

3. The design method of a swaying building structure under an inverted triangle lateral load according to claim 1, characterized in that: In step S3, establishing a mechanical analysis model of the structure includes applying a horizontal inverted triangle lateral load to the upper structure and applying a vertical gravity load.

4. The design method of a swaying building structure under inverted triangle lateral load according to claim 3 is characterized in that: In step S3, solving the force balance equation of the hinge support includes: The inverted triangle lateral load takes the moment of the hinge support, and the formula 1 is: Take moment balance on the hinge support, and get equation 2: The anti-overturning moment generated by the spring support when the foundation rotates unit angle around the bottom hinge support is introduced, and equation 3 is obtained: The load size at the top of the structure in the inverted triangle load required to be applied when the upper structure undergoes unit lateral displacement is introduced, and formula 4 is obtained: Introducing the ratio of the horizontal displacement at the center of gravity to the horizontal displacement at the vertex, we get Formula 5: Substitute h = nh c Formula 6: Calculation of the lateral stiffness of the foundation fixed structure when using an inverted triangle lateral load: The vertex displacement when the foundation is fixed, formula 7: When the vertex displacement is 1, the load size at the top of the structure in the inverted triangle load required to be applied is as follows: u1+u2=1 The rigid body displacement rotation angle is introduced to calculate the anti-overturning moment generated by the vertical spring support when the foundation produces a unit rotation angle around the bottom hinge support. Formula 9: The load size at the top of the structure in the inverted triangle lateral load that needs to be applied when the upper structure undergoes unit lateral displacement is as follows: u1+u2+u3=1 Combining equation 6 with equation 10, we get equation 11:

5. The design method of a swaying building structure under inverted triangle lateral load according to claim 4, characterized in that: In step S3, the moment of the lateral load on the hinged support can also be used to calculate the resultant force of the lateral load: The resultant force of the lateral load takes the moment of the hinge support:

6. The design method of a swaying building structure under an inverted triangle lateral load according to claim 1, characterized in that: In step S5, the pushover analysis method includes modal pushover, lateral loading, uniform loading or concentrated load applied at the vertex.

7. The design method of a swaying building structure under inverted triangle lateral load according to claim 1, characterized in that: In step S7, the elastoplastic time history analysis includes the time history analysis results under no less than 7 seismic waves; the response spectrum analysis is used for small earthquakes, and the macro performance indicators and structural damage are verified. If the requirements are not met, the process returns to step S1 to modify the basic parameters of the structure.

8. The design method of a swaying building structure under inverted triangle lateral load according to claim 7, characterized in that: Macroscopic performance indicators include inter-story displacement angle and acceleration.

9. The design method of a swaying building structure under an inverted triangle lateral load according to any one of claims 1 to 8, characterized in that: The structure includes assembled prefabricated components of the building superstructure, vertical assembled load-bearing components located in the middle, hinged supports at the bottom and vertical tension and compression spring supports located on all sides.

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