Method for analyzing integral swing structure with asymmetrical rigidity around strong axis and weak axis of structure

Abstract

The invention discloses a method for analyzing an integral swing structure with asymmetrical rigidity around a strong axis and a weak axis of the structure. The method comprises the following steps: S1, designing an upper structure; s2, calculating the shear force of the base; s3, the shear bearing capacity of the vertical tension-compression energy dissipation limiting support is designed; s4, establishing a mechanical analysis model, and solving a force balance equation; s5, a rigid body displacement proportion u3 / u is preset, and the basic rotation rigidity KSy of the upper structure around the weak axis side is solved; s6, calculating the rigidity of the vertical bearing damping body according to the axial force of the bottom of the upper structure under the action of the gravity load; s7, the basic rotation rigidity Ksx of the upper structure around the strong axis side is calculated; s8, the basic rotation rigidity Ksx of the side, around the strong axis, of the upper structure is substituted into the force balance equation, the lateral stiffness of the side, around the strong axis, of the upper structure is calculated, and the section size of a beam or a column is adjusted; s9, a vertical tension and compression energy consumption limiting support is designed; s10, estimating a damping ratio, and carrying out earthquake time history response analysis; and checking whether a corresponding limit value and a performance target of the specification are met.

Description

Technical Field

[0001] The present invention relates to the technical field of structural engineering, in particular to an analysis method for an overall rocking structure with asymmetric stiffness around a strong axis and a weak axis of the structure. Background Art

[0002] As a new type of earthquake-resistant structural system, self-righting structures, by incorporating the concept of restorative design, can effectively reduce residual deformation under earthquake action and enhance the structural recovery capability after an earthquake. Swaying self-righting structures, when subjected to an earthquake, reset themselves through their own weight or self-righting components. Previous studies have shown that the swaying structure reduces the seismic action and the structural ductility design requirements, minimizing earthquake damage, saving structural costs, and significantly alleviating post-earthquake damage and residual deformation. Traditional earthquake-resistant structures primarily aim to control their strength and ductility, designing for bearing capacity during minor earthquakes and verifying their ductility and deformation during major earthquakes to ensure they do not collapse. However, during a strong earthquake, although traditional structures can withstand strong earthquakes according to existing design specifications, they can still sustain severe damage, making post-earthquake repair difficult or expensive. Important engineering structures are not only required to effectively protect people's lives and property after a strong earthquake, but also to be able to quickly restore their normal function to avoid further indirect losses. Therefore, there is an urgent need to develop resilient structures that can effectively mitigate structural earthquake damage and propose seismic design methods.

[0003] The rocking self-righting structure is an effective structural form for reducing earthquake damage to structures. However, existing rocking structures have failed to achieve overall deformation control of the structure and lack their seismic design methods. This patent is based on a self-righting rocking structure with unequal stiffness around the strong axis and weak axis of the structure proposed by the applicant, and establishes its seismic design method to provide strong support for its early design and application in engineering. Summary of the Invention

[0004] The present invention provides an analysis method for an overall rocking structure with asymmetric stiffness around the strong axis and weak axis of the structure, aiming to solve the above technical problems.

[0005] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0006] A method for analyzing an overall rocking structure with asymmetric stiffness about a strong axis and a weak axis of the structure is characterized by comprising the following steps:

[0007] S1: Design the superstructure with fixed foundation and determine the basic parameters and working conditions of the superstructure;

[0008] S2: Calculate the shear force at the base of the superstructure;

[0009] S3: Design the shear bearing capacity of vertical tension and compression energy dissipation limit bearings;

[0010] S4: Establish a simplified mechanical analysis model and solve the force balance equation;

[0011] S5: Preset the rigid body displacement ratio u3 / u, and solve the foundation rotation stiffness K around the weak axis of the superstructure. Sy ;

[0012] S6: Based on the magnitude of the axial force at the bottom of the superstructure under the action of gravity load and the planar layout of the vertical tension and compression energy absorbing limit bearing, the stiffness of the vertical load-bearing and shock-absorbing body of the vertical tension and compression energy absorbing limit bearing is calculated proportionally;

[0013] S7: Calculate the foundation rotation stiffness K of the superstructure around the strong axis using the stiffness of the vertical load-bearing shock absorber in step 6. sx ;

[0014] S8: Foundation rotation stiffness K around the strong axis on one side of the superstructure sx Substitute the force balance equation solved in step S4 to calculate the lateral stiffness of the superstructure around the strong axis.

[0015] S9: Adjust the cross-sectional dimensions of the beams or columns on the side of the superstructure around the strong axis according to the lateral stiffness of the superstructure around the strong axis;

[0016] S10: Design vertical tension and compression energy dissipation limit bearings based on the shear bearing capacity calculation results in S3 and the stiffness of the vertical load-bearing and shock-absorbing body in S6;

[0017] S11: Establish a finite element model and perform a pushover analysis based on the stiffness of the vertical load-bearing shock-absorbing body to verify whether the rigid body displacement ratio meets the requirements. If not, return to step 5 to reset the rigid body displacement ratio u3 / u;

[0018] S12: Estimate the damping ratio and perform earthquake time-history response analysis;

[0019] S13: Based on the results of the earthquake time-history response analysis, check whether the corresponding limits and performance targets of the specifications are met. If not, adjust the stiffness of the load-bearing shock-absorbing body and the additional damping ratio and re-analyze.

[0020] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong and weak axes of the structure. Furthermore, when the vertical acceleration control requirements of the superstructure are considered, the vertical first natural vibration period T of the superstructure is calculated. 竖向 and compared with the average response spectrum dominant period Tg of the considered site type; if T 竖向 If it is equal to or close to Tg, the stiffness of the vertical load-bearing shock-absorbing body needs to be recalculated.

[0021] The present invention provides a method for analyzing an overall rocking structure with asymmetric stiffness around the strong axis and weak axis of the structure. Further, in step S11, according to the calculated stiffness value of the vertical load-bearing shock-absorbing body and according to the formula The first natural vibration cycle T of the upper structure 竖向 Calculation of

[0022]

[0023] in,

[0024] T 竖向 : vertical natural vibration period of the superstructure;

[0025] m: total mass of the superstructure;

[0026] k n : Stiffness of the nth vertical load-bearing shock-absorbing body.

[0027] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong axis and weak axis of the structure. Further, in S3, the shear bearing capacity of the vertical tension-compression energy absorbing limit support is calculated based on the thickness of the guide limit body of the vertical tension-compression energy absorbing limit support to ensure that the vertical tension-compression energy absorbing limit support does not suffer horizontal shear failure.

[0028] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong axis and weak axis of the structure. Further, in step S4, a mechanical analysis model is established, including replacing the upper structure with a frame unit, replacing the vertical tension and compression energy-absorbing limit supports with linear spring units, and applying a horizontal inverted triangle lateral load and a vertical gravity load to the upper structure.

[0029] The present invention provides a method for analyzing an overall rocking structure with asymmetric stiffness about the strong and weak axes of the structure. Further, in step S4, solving the force balance equation includes solving the force balance equation of the intermediate vertical tension and compression energy dissipation limit support. In the following formula, the vertical tension and compression energy dissipation limit support is referred to as the "spring support."

[0030] The moment of the inverted triangle lateral load on the middle spring support is obtained as formula ①:

[0031]

[0032]

[0033] in,

[0034] P′: load magnitude at the top of the structure in the inverted triangle load;

[0035] n: number of layers;

[0036] h: height from the top of the structure to the spring support, h = nh c ;

[0037] h c : Floor height;

[0038] Secondly, take the moment balance of the middle spring support and get formula ②:

[0039]

[0040] in,

[0041] G: Representative value of gravity load of superstructure;

[0042] u4: initial eccentricity of the superstructure gravity load;

[0043] V S1 、V S2 : Vertical reaction force of spring supports on both sides, V S1 is the vertical reaction force of the left spring support, V S2 is the vertical reaction force of the right spring support, and the upward direction is positive;

[0044] L: The distance from the spring supports on both sides to the central spring support;

[0045] Secondly, the anti-overturning moment generated by the spring support when the foundation rotates unit angle around the bottom middle spring is introduced, and formula ③ is obtained:

[0046]

[0047] in,

[0048] K S : represents the anti-overturning moment generated by all vertical spring supports when the foundation produces a unit rotation angle around the bottom middle spring support, that is, the foundation rotation stiffness;

[0049] u3: horizontal displacement of the top caused by the rotation of the rigid body;

[0050] Secondly, the load size at the top of the structure in the inverted triangle load required to be applied when the superstructure undergoes unit lateral displacement is introduced, and formula ④ is obtained:

[0051]

[0052] in,

[0053] K' S : represents the load size at the top of the structure in the inverted triangle load required to be applied when the upper structure unit moves sideways;

[0054] u1: horizontal displacement of the top caused by bending deformation;

[0055] u2: horizontal displacement of the top caused by shear deformation;

[0056] Secondly, the ratio of the horizontal displacement at the center of gravity to the horizontal displacement at the vertex is introduced to obtain formula ⑤:

[0057]

[0058] in,

[0059] u: total lateral displacement of the top, its value is u1+u2+u3=u;

[0060] Φ: ratio of horizontal displacement at the center of gravity to horizontal displacement at the vertex, u4 = Φu;

[0061] Next, substitute formula ⑥:

[0062]

[0063] Secondly, calculate the load size of the top of the inverted triangle load required for a unit displacement at the top of the superstructure when the foundation is fixed: the vertex displacement when the foundation is fixed, and get formula 7:

[0064]

[0065] in,

[0066] EI: bending stiffness of the upper structure lateral members;

[0067] GA: shear stiffness of the upper structure lateral members;

[0068] μ: cross-sectional shape coefficient caused by uneven shear stress distribution;

[0069] Secondly, the load size at the top of the structure in the inverted triangle load that needs to be applied when the vertex displacement is 1 is obtained as ⑧:

[0070] u1+u2=1

[0071]

[0072] in,

[0073] K sf : The load size at the top of the inverted triangle load required to produce a unit displacement at the top of the superstructure when the foundation is fixed;

[0074] Secondly, the rigid body displacement angle is introduced to calculate the anti-overturning moment generated by the other vertical spring supports when the foundation produces a unit rotation angle around the bottom middle spring support, and formula 9 is obtained:

[0075]

[0076] in,

[0077] θ3: rigid body displacement angle, its value is θ3 = u3 / h;

[0078] Calculate the load K' at the top of the structure in the inverted triangle load required to apply when the upper structure undergoes unit lateral displacement S

[0079] u1+u2+u3=1

[0080]

[0081] Combining equations ⑥ and ⑩, we get Mode

[0082]

[0083] in,

[0084] Mode The right side of the equation The preset rigid body displacement ratio of the superstructure.

[0085] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong axis and weak axis of the structure. Further, in step S6, the stiffness of the vertical load-bearing shock-absorbing body is calculated proportionally according to the axial force at the bottom of the superstructure under the vertical gravity load and the planar layout of the superstructure, that is, according to the size of the vertical loaded area.

[0086] The present invention provides an analysis method for an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure. Further, the steps for designing and calculating the proportional distribution of stiffness between the vertical load-bearing and shock-absorbing bodies are as follows:

[0087] By calculating the formula Get the foundation rotation stiffness Ks

[0088] According to the axial force under the vertical gravity load and the upper plane configuration, the following ratios are taken:

[0089]

[0090] Take moment balance for the middle spring support and calculate the spring stiffness based on the spring stiffness ratio. Take the frame structure as an example:

[0091]

[0092] in,

[0093] x, y: proportionality constants;

[0094] L: span length

[0095] K1, K2, K3: three different vertical load-bearing shock-absorbing body stiffness;

[0096] a: The number of spans of the axis being calculated c: The number of spans of the axis on the other side.

[0097] The present invention provides an analysis method for an overall rocking structure with asymmetric stiffness around the strong axis and weak axis of the structure. Further, establishing a mechanical analysis model also includes replacing the upper structure with a frame unit, replacing the vertical tension and compression energy-absorbing limit supports with linear spring units, and applying horizontal concentrated lateral loads and vertical gravity loads to the upper structure.

[0098] The present invention provides an analysis method for an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure. Further, solving the force balance equation includes solving the force balance equation of the intermediate vertical tension and compression energy dissipation limit support. In the following formula, the vertical tension and compression energy dissipation limit support is referred to as the "spring support".

[0099] First, take the moment balance of the middle spring support and get the formula

[0100]

[0101] in,

[0102] P: Top concentrated load

[0103] G: Representative value of gravity load of superstructure;

[0104] u4: initial eccentricity of the superstructure gravity load;

[0105] V S1 、V S2 : Vertical reaction force of spring supports on both sides, V S1 is the vertical reaction force of the left spring support, V S2 is the vertical reaction force of the right spring support, and the upward direction is positive;

[0106] L: The distance from the spring supports on both sides to the central spring support;

[0107] Secondly, the anti-overturning moment generated by the spring support when the foundation rotates unit angle around the bottom middle spring is introduced, and the formula is obtained:

[0108]

[0109] in,

[0110] K S : represents the anti-overturning moment generated by all vertical spring supports when the foundation produces a unit rotation angle around the bottom middle spring support, that is, the foundation rotation stiffness;

[0111] u3: horizontal displacement of the top caused by the rotation of the rigid body;

[0112] Secondly, the horizontal concentrated load required to be applied when the upper structure undergoes unit lateral displacement is introduced, and the formula is obtained:

[0113]

[0114] in,

[0115] K' S : represents the magnitude of the horizontal concentrated load required to be applied when the upper structure unit moves laterally;

[0116] u1: horizontal displacement of the top caused by bending deformation;

[0117] u2: horizontal displacement of the top caused by shear deformation;

[0118] Secondly, the ratio of the horizontal displacement at the center of gravity to the horizontal displacement at the vertex is introduced to obtain the formula

[0119]

[0120] in,

[0121] u: total lateral displacement of the top, its value is u1+u2+u3=u;

[0122] Φ: ratio of horizontal displacement at the center of gravity to horizontal displacement at the vertex, u4 = Φu;

[0123] Secondly, we can get the formula by moving the terms

[0124]

[0125] Secondly, calculate the lateral stiffness of the foundation-fixed structure when using horizontal concentrated load: When the vertex displacement of the foundation is fixed, the formula is

[0126]

[0127] in,

[0128] EI: bending stiffness of the upper structure lateral members;

[0129] GA: shear stiffness of the upper structure lateral members;

[0130] μ: cross-sectional shape coefficient caused by uneven shear stress distribution;

[0131] Secondly, the magnitude of the horizontal concentrated load required when the vertex displacement is 1 is:

[0132] u1+u2=1

[0133]

[0134] in,

[0135] Ksf : lateral stiffness of the superstructure when the foundation is fixed;

[0136] Secondly, the rigid body displacement 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 center spring, and the formula is:

[0137]

[0138] in,

[0139] θ3: rigid body displacement angle, its value is θ3 = u3 / h;

[0140] Calculate the load K' on the top of the structure in the horizontal concentrated load required to apply when the upper structure undergoes unit lateral displacement S

[0141] u1+u2+u3=1

[0142]

[0143] Joint Style and Formula Mode

[0144]

[0145] in,

[0146] Mode The right side of the equation The preset rigid body displacement ratio of the superstructure.

[0147] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong axis and weak axis of the structure. Furthermore, in step S5, after presetting the rigid body displacement ratio, the upper structure can also be taken to perform calculations around the strong axis. Subsequently, the rotational stiffness around the weak axis is calculated in the same way, and then the cross-section of the beam or column around the weak axis is adjusted.

[0148] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong axis and weak axis of the structure. Further, in step S6, according to theoretical calculations and finite element analysis results, the vertical load-bearing shock-absorbing body at the intersection of the weak axis and the strong axis only bears pressure, so it can be designed as a compressive vertical load-bearing shock-absorbing body.

[0149] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong axis and weak axis of the structure. Furthermore, the stiffness of the vertical load-bearing shock-absorbing body of the vertical tension-compression energy-absorbing limit support is proportional to the size of the vertical load it bears, ensuring that the initial compression deformation of all vertical load-bearing shock-absorbing bodies of the support layer is the same, and the stiffness of the vertical load-bearing shock-absorbing bodies of all vertical tension-compression energy-absorbing limit supports are basically symmetrically arranged around the strong axis and weak axis of the support layer at the bottom of the structure, ensuring that the structure can achieve an ideal rotational rocking deformation mode around the strong axis and weak axis during an earthquake.

[0150] The present invention provides a method for analyzing an overall swaying structure with asymmetric stiffness around the strong axis and weak axis of the structure. Furthermore, the superstructure adopts a building structure, an industrial cylindrical structure, an offshore structure or a nuclear industry structure; the superstructure selectively adds supports or metal, viscoelastic, viscous, eddy current or tuned mass damper energy dissipation and shock absorption devices.

[0151] The present invention provides an analysis method for an overall rocking structure with asymmetric stiffness around the strong axis and weak axis of the structure. Further, the vertical load-bearing shock-absorbing body is a coil spring, laminated rubber or disc spring.

[0152] The present invention provides an overall rocking structure analysis method with asymmetric stiffness around the strong axis and weak axis of the structure. Furthermore, a damper is provided on the vertical tensile and compressive energy-absorbing limit support, and the damper is a viscoelastic damper, a metal damper, a viscous fluid damper, an eddy current damper or a tuned mass damper.

[0153] Compared with the prior art, the present invention has the following beneficial effects:

[0154] 1. Compared with the previous self-resetting swing structure, the present invention is based on holistic thinking and focuses on the rigid body swing deformation of the entire structure. It avoids the addition of a large number of self-resetting and energy-consuming nodes in the previous self-resetting swing structure, simplifies the design process of this type of structure, and is conducive to its application in actual engineering.

[0155] 2. Compared with the previous self-resetting swing structure, the present invention is based on holistic thinking, and there is no need to consider the special design of filling walls, floor slabs, etc. to adapt to the deformation requirements of the swing structure;

[0156] 3. Compared with the previous self-resetting rocking structure, the present invention is not limited to the central symmetrical structure, and provides a feasible design method for the structure with asymmetric stiffness of the strong and weak axes; BRIEF DESCRIPTION OF THE DRAWINGS

[0157] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0158] Figure 1 The accompanying drawing is a flow chart of the design analysis method provided by the present invention;

[0159] Figure 2 The accompanying drawing is a three-dimensional schematic diagram of a vertical tension-compression energy dissipation limit support provided by an embodiment of the present invention;

[0160] Figure 3 The accompanying drawing is a schematic diagram of a mechanical model of a superstructure provided by the present invention under the action of a horizontal inverted triangle lateral load and a vertical gravity load;

[0161] Figure 4 The accompanying drawing is a schematic diagram of a mechanical model of the superstructure provided by the present invention under the action of a horizontal concentrated lateral load and a vertical gravity load;

[0162] Figure 5 The accompanying figure is an undeformed finite element model of the superstructure provided by the present invention before pushover analysis (A)

[0163] Deformation diagram of the finite element model after pushover analysis (B);

[0164] Figure 6 The accompanying drawing is a schematic diagram of a self-resetting rocking structure with unequal stiffness around the strong axis and weak axis of the structure provided by the present invention;

[0165] Reference numerals:

[0166] 1. Superstructure; 2. Vertical tension and compression energy-absorbing limit bearing; 21. Vertical load-bearing shock-absorbing body; 22. Guide limit body; 22a. Upper sleeve; 22b. Lower sleeve; 23. Viscous fluid damper; 24. Upper connecting plate; 25. Lower connecting plate; 3. Foundation. DETAILED DESCRIPTION

[0167] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0168] Figure 1 This is a flow chart of a method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure provided by the present invention. This embodiment is designed according to this flow chart.

[0169] Figure 2A three-dimensional schematic diagram of a vertical tensile and compressive energy-absorbing limit bearing provided in an embodiment of the present invention. The vertical tensile and compressive energy-absorbing limit bearing 2 comprises a vertical load-bearing damper 21, a guide limiter 22, and a damper 23, arranged in parallel. The guide limiter 22 comprises an upper sleeve 22a and a lower sleeve 22b. In this embodiment, the vertical load-bearing damper 21 utilizes a coil spring, the guide limiter 22 utilizes a guide limiter sleeve, and the damper 23 utilizes a viscous fluid damper. The coil spring is attached to the outer circumference of the guide limiter sleeve. The guide sleeve 22 consists of an upper sleeve 22a and a lower sleeve 22b. The outer diameter of the upper sleeve 22a is smaller than the inner diameter of the lower sleeve 22b. The upper sleeve 22a is inserted into the lower sleeve 22b. When the compression deformation of the vertical tensile and compressive energy-absorbing limit support 2 exceeds the design value, the upper sleeve 22a contacts the lower connecting plate 25 to prevent the vertical tensile and compressive energy-absorbing limit support 2 from further compressive deformation, and a 2mm gap is left between the two. Fine stone concrete is poured inside the upper sleeve 22a to improve its shear bearing capacity. The lower sleeve 22b is a hollow thin-walled cylinder. The coil spring, guide limit sleeve and viscous fluid damper are welded to the upper connecting plate 24 and the lower connecting plate 25 at both ends respectively. The upper connecting plate 24 and the lower connecting plate 25 can be connected to the upper structure 1 and the foundation 3 respectively using the connection methods currently available in actual projects.

[0170] In order to further optimize the technical solution of the present invention, the design principles of the vertical load-bearing shock-absorbing body stiffness 2 include the rigid body displacement ratio, the vertical load area size, and the vertical acceleration control.

[0171] To further optimize the technical solution of the present invention, the vertical load-bearing shock-absorbing body stiffness 21 of the vertical tensile-compression energy-absorbing limit support 2 is proportional to the magnitude of the vertical load it bears, that is, the initial vertical compression deformation of all supports under the action of gravity load is basically the same. The stiffness of the vertical load-bearing shock-absorbing body 21 of all vertical tensile-compression energy-absorbing limit supports 2 is basically symmetrically arranged around the centroid of the support layer at the bottom of the structure, with the position of the support layer after compression deformation under the action of vertical gravity load as the initial position. During a strong earthquake, the overall swing self-resetting structure generates a controlled rotational swing around the centroid position of its support layer to reduce the structure's own deformation. After a strong earthquake, the structure basically remains intact or only suffers minor repairable damage, and achieves self-reset under the action of gravity load, quickly restoring the structure's usability.

[0172] In order to further optimize the technical solution of the present invention, the present invention provides a specific embodiment of a method for analyzing an overall rocking structure with asymmetric stiffness around the strong axis and weak axis of the structure.

[0173] The traditional superstructure is designed according to the specifications and its simplified finite element model is established based on the SAP2000 program. In this example, L=5m, four spans in the strong axis (x direction), two spans in the weak axis (y direction), a floor height of 4m, a total of 10 floors, and a dead load of 4.5kN / m 2 , live load 2kN / m2 The damping ratio is 2%, the seismic fortification intensity is 8 degrees 0.3g, the characteristic period is 0.55s, the structure is made of Q345 steel, and the basic structural size parameters are shown in Table 1.

[0174] Table 1. Basic structural dimensions

[0175]

[0176] In order to further optimize the technical solution and verify the displacement ratio of the upper structure rigid body under the inverted triangle load, the vertical acceleration control requirements of the upper structure are not considered for the time being. The rigid body ratio in the calculation formula is preset to 80%. The upper structure with a fixed foundation is pushed over to obtain the load size K at the top of the inverted triangle load required for the upper structure to undergo unit displacement at the top around the weak axis when the foundation is fixed. sfy is 2.726kN / m, through The foundation rotation stiffness K of the superstructure around the weak axis can be calculated sy =4647140.0kN.m / rad, and then according to the vertical gravity load it bears and the plane layout of the superstructure, K1:K2:K3=1:2:4, where a=4, c=2

[0177] Substituting into the formula:

[0178] The coil spring stiffness can be obtained as K3 = 15.48 kN / mm, K2 = 7.74 kN / mm, K1 = 3.87 kN / mm;

[0179] To further optimize the technical solution, a pushover analysis of the superstructure with the above-mentioned spring stiffness arranged at the column base around the weak axis was conducted. The study showed that the overall structure produced a rotational and rocking deformation mode around the strong axis of the support layer. The pushover analysis showed that the rigid body displacement accounted for 79%, which was in line with the preset proportion value.

[0180] To further optimize the technical solution, the formula is used to calculate the foundation rotation stiffness of the superstructure around the strong axis, where a = 2, c = 4

[0181] Substituting into the formula:

[0182] The foundation rotation stiffness K of the superstructure around the strong axis is obtained sx =1548000.0kN.m / rad, the preset rigid body displacement accounts for 80%, through the formula The load size K at the top of the inverted triangle load required for the superstructure to undergo unit displacement at the top around the strong axis can be calculated. sfx It is 0.713kN / m.

[0183] According to K sfxThe basic dimensional parameters of the superstructure after adjusting the beam section around the strong axis are shown in Table 2.

[0184] Table 2. Basic structural dimensions after adjustment using the inverted triangle load formula

[0185]

[0186] After pushover analysis and adjustment, the rigid body displacement around the strong axis of the structure accounted for 77%, which is in line with the preset value.

[0187] In order to further optimize the technical solution and verify the displacement ratio of the upper structure rigid body under the action of horizontal load, the vertical acceleration control requirements of the upper structure are not considered for the time being. The rigid body ratio in the calculation formula is set to 80%. The upper structure with a fixed foundation is pushed over to obtain the horizontal load K required for the upper structure to undergo unit displacement around the weak axis when the foundation is fixed. sfy is 2.726kN / m, a=4, c=2, through the formula The foundation rotation stiffness K of the superstructure around the weak axis can be calculated sy =4524000.0kN.m / rad, and then according to the vertical gravity load it bears and the plane layout of the superstructure, K1:K2:K3=1:2:4, where a=4, c=2

[0188] Substituting into the formula:

[0189] The coil spring stiffness can be obtained as K3 = 15.08 kN / mm, K2 = 7.54 kN / mm, K1 = 3.77 kN / mm;

[0190] To further optimize the technical solution, a pushover analysis of the superstructure with the above-mentioned spring stiffness arranged at the column base around the weak axis was conducted. The study showed that the overall structure produced a rotational rocking deformation mode around the weak axis of the support layer, and the pushover analysis showed that the rigid body displacement accounted for 79%, which was in line with the preset proportion value.

[0191] To further optimize the technical solution, the foundation rotation stiffness of the superstructure around the strong axis is calculated by substituting the formula, where a = 2, c = 4;

[0192] Substituting into the formula:

[0193] The foundation rotation stiffness K of the superstructure around the strong axis is obtained sx =1508000.0kN.m / rad, the preset rigid body displacement accounts for 80%, through the formula The horizontal load required for the superstructure to undergo unit displacement at the top around the strong axis (i.e., the lateral stiffness of the superstructure) K can be calculated. sfy It is 2.648kN / m.

[0194] According to K sfx The basic dimensional parameters of the superstructure after adjusting the beam section around the strong axis are shown in Table 2.

[0195] Table 2. Basic structural dimensions after adjustment based on the horizontal concentrated load formula

[0196]

[0197] After pushover adjustment, the rigid body displacement of the structure around the strong axis accounts for 77%, which is in line with the preset value.

[0198] The embodiments described above are merely descriptions of preferred implementations of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. An analysis method for an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure, characterized by: The following steps are involved: S1: Design the superstructure with fixed foundation and determine the basic parameters and working conditions of the superstructure; S2: Calculate the shear force at the base of the superstructure; S3: Design the shear bearing capacity of vertical tension and compression energy dissipation limit bearings; S4: Establish a simplified mechanical analysis model and solve the force balance equation; S5: Preset the rigid body displacement ratio u3 / u, and solve the foundation rotation stiffness K around the weak axis of the superstructure. Sy ; S6: Calculate the stiffness of the vertical load-bearing and shock-absorbing body of the vertical tension-compression energy-absorbing limit bearing in proportion to the axial force at the bottom of the superstructure under gravity load and the plane layout of the vertical tension-compression energy-absorbing limit bearing; S7: Calculate the foundation rotation stiffness K of the superstructure around the strong axis using the stiffness of the vertical load-bearing shock absorber in step 6. sx ; S8: Foundation rotation stiffness K around the strong axis on one side of the superstructure sx Substitute the force balance equation solved in step S4 to calculate the lateral stiffness of the superstructure around the strong axis. S9: Adjust the cross-sectional dimensions of the beams or columns on the side of the superstructure around the strong axis according to the lateral stiffness of the superstructure around the strong axis; S10: Design vertical tension and compression energy dissipation limit bearings based on the shear bearing capacity calculation results in S3 and the stiffness of the vertical load-bearing and shock-absorbing body in S6; S11: Establish a finite element model and perform a pushover analysis based on the stiffness of the vertical load-bearing shock-absorbing body to verify whether the rigid body displacement ratio meets the requirements. If not, return to step 5 to reset the rigid body displacement ratio u3 / u; S12: Estimate the damping ratio and perform earthquake time-history response analysis; S13: Based on the results of the earthquake time-history response analysis, check whether the corresponding limits and performance targets of the specifications are met. If not, adjust the stiffness of the load-bearing shock-absorbing body and the additional damping ratio and re-analyze.

2. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: When the vertical acceleration control requirement is considered for the superstructure, the vertical first natural vibration period T of the superstructure is calculated. 竖向 and compared with the average response spectrum dominant period Tg of the considered site type; if T 竖向 If it is equal to or close to Tg, the stiffness of the vertical load-bearing shock-absorbing body needs to be recalculated.

3. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: In step S11, according to the calculated value of the vertical load-bearing shock-absorbing body stiffness and according to the formula The first vertical natural vibration cycle T of the upper structure 竖向 Calculation of in, T 竖向 : vertical natural vibration period of the superstructure; m: total mass of the superstructure; k n : Stiffness of the nth vertical load-bearing shock-absorbing body.

4. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: In S3, the shear bearing capacity of the vertical tension-compression energy absorption limit bearing is calculated according to the thickness of the guide limit body of the vertical tension-compression energy absorption limit bearing to ensure that the vertical tension-compression energy absorption limit bearing does not suffer horizontal shear failure.

5. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: In step S4, establishing a mechanical analysis model includes replacing the upper structure with frame units, replacing the vertical tension and compression energy-absorbing limit supports with linear spring units, and applying horizontal inverted triangle lateral loads and vertical gravity loads to the upper structure.

6. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 5, characterized in that: In step S4, solving the force balance equation includes solving the force balance equation of the middle vertical tension and compression energy dissipation limit support. In the following formula, the vertical tension and compression energy dissipation limit support is referred to as the "spring support". The moment of the inverted triangle lateral load on the middle spring support is obtained as formula ①: in, P′: load magnitude at the top of the structure in the inverted triangle load; n: number of layers; h: height from the top of the structure to the spring support, h = nh c ; h c : Floor height; Secondly, take the moment balance of the middle spring support and get formula ②: in, G: Representative value of gravity load of superstructure; u4: initial eccentricity of the superstructure gravity load; V S1 、V S2 : Vertical reaction force of spring supports on both sides, V S1 is the vertical reaction force of the left spring support, V S2 is the vertical reaction force of the right spring support, and the upward direction is positive; L: The distance from the spring supports on both sides to the central spring support; Secondly, the anti-overturning moment generated by the spring support when the foundation rotates unit angle around the bottom middle spring is introduced, and formula ③ is obtained: in, K S : represents the anti-overturning moment generated by all vertical spring supports when the foundation produces a unit rotation angle around the bottom middle spring support, that is, the foundation rotation stiffness; u3: horizontal displacement of the top caused by the rotation of the rigid body; Secondly, the load size at the top of the structure in the inverted triangle load required to be applied when the superstructure undergoes unit lateral displacement is introduced, and formula ④ is obtained: in, K ' S : represents the load size at the top of the structure in the inverted triangle load required to be applied when the upper structure unit moves sideways; u1: horizontal displacement of the top caused by bending deformation; u2: horizontal displacement of the top caused by shear deformation; Secondly, the ratio of the horizontal displacement at the center of gravity to the horizontal displacement at the vertex is introduced to obtain formula ⑤: in, u: total lateral displacement of the top, its value is u1+u2+u3=u; Φ: ratio of horizontal displacement at the center of gravity to horizontal displacement at the vertex, u4 = Φu; Next, substitute formula ⑥: Secondly, calculate the load size of the top of the inverted triangle load required for a unit displacement at the top of the superstructure when the foundation is fixed: the vertex displacement when the foundation is fixed, and get formula 7: in, EI: bending stiffness of the upper structure lateral members; GA: shear stiffness of the upper structure lateral members; μ: cross-sectional shape coefficient caused by uneven shear stress distribution; Secondly, the load size at the top of the structure in the inverted triangle load that needs to be applied when the vertex displacement is 1 is obtained as ⑧: u1+u2=1 in, K sf : The load size at the top of the inverted triangle load required to produce a unit displacement at the top of the superstructure when the foundation is fixed; Secondly, the rigid body displacement angle is introduced to calculate the anti-overturning moment generated by the other vertical spring supports when the foundation produces a unit rotation angle around the bottom middle spring support, and formula 9 is obtained: in, θ3: rigid body displacement angle, its value is θ3 = u3 / h; Calculate the load K at the top of the structure in the inverted triangle load required to apply when the upper structure undergoes unit lateral displacement ' S u1+u2+u3=1 Combined with the formula ⑥ Formula Mode in, Mode The right side of the equation The preset rigid body displacement ratio of the superstructure.

7. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: In step S6, the stiffness of the vertical load-bearing shock-absorbing body is calculated in proportion to the axial force of the bottom of the superstructure under the vertical gravity load and the planar layout of the superstructure, that is, according to the size of the vertical loaded area.

8. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 7, characterized in that: The design and calculation steps for the proportional distribution of the stiffness of the vertical load-bearing and shock-absorbing bodies are as follows: By calculating the formula Get the foundation rotation stiffness Ks According to the axial force under the vertical gravity load and the upper plane configuration, the following ratios are taken: Take moment balance for the middle spring support and calculate the spring stiffness based on the spring stiffness ratio. Take the frame structure as an example: in, x, y: proportionality constants; L: span length K1, K2, K3: three different vertical load-bearing shock-absorbing body stiffness; a: The number of spans of the axis being calculated c: The number of spans of the axis on the other side.

9. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: Establishing the mechanical analysis model also includes replacing the upper structure with frame units, replacing the vertical tension and compression energy-absorbing limit supports with linear spring units, and applying horizontal concentrated lateral loads and vertical gravity loads to the upper structure.

10. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 9, characterized in that: Solving the force balance equation includes solving the force balance equation of the intermediate vertical tension and compression energy dissipation limit support. In the following formula, the vertical tension and compression energy dissipation limit support is referred to as the "spring support"; First, take the moment balance of the middle spring support and get the formula in, P: Top concentrated load G: Representative value of gravity load of superstructure; u4: initial eccentricity of the superstructure gravity load; V S1 、V S2 : Vertical reaction force of spring supports on both sides, V S1 is the vertical reaction force of the left spring support, V S2 is the vertical reaction force of the right spring support, and the upward direction is positive; L: The distance from the spring supports on both sides to the central spring support; Secondly, the anti-overturning moment generated by the spring support when the foundation rotates unit angle around the bottom middle spring is introduced, and the formula is obtained: in, K S : represents the anti-overturning moment generated by all vertical spring supports when the foundation produces a unit rotation angle around the bottom middle spring support, that is, the foundation rotation stiffness; u3: horizontal displacement of the top caused by the rotation of the rigid body; Secondly, the horizontal concentrated load required to be applied when the upper structure undergoes unit lateral displacement is introduced, and the formula is obtained: in, K ' S : represents the magnitude of the horizontal concentrated load required to be applied when the upper structure unit moves laterally; u1: horizontal displacement of the top caused by bending deformation; u2: horizontal displacement of the top caused by shear deformation; Secondly, the ratio of the horizontal displacement at the center of gravity to the horizontal displacement at the vertex is introduced to obtain the formula in, u: total lateral displacement of the top, its value is u1+u2+u3=u; Φ: ratio of horizontal displacement at the center of gravity to horizontal displacement at the vertex, u4 = Φu; Secondly, we can get the formula by moving the terms Secondly, calculate the lateral stiffness of the foundation-fixed structure when using horizontal concentrated load: When the vertex displacement of the foundation is fixed, the formula is in, EI: bending stiffness of the upper structure lateral members; GA: shear stiffness of the upper structure lateral members; μ: cross-sectional shape coefficient caused by uneven shear stress distribution; Secondly, the magnitude of the horizontal concentrated load required when the vertex displacement is 1 is: u1+u2=1 in, K sf : lateral stiffness of the superstructure when the foundation is fixed; Secondly, the rigid body displacement 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 center spring, and the formula is: in, θ3: rigid body displacement angle, its value is θ3 = u3 / h; Calculate the load K at the top of the structure in the horizontal concentrated load required to apply when the superstructure undergoes unit lateral displacement ' S u1+u2+u3=1 Joint Style and Formula Mode in, Mode The right side of the equation The preset rigid body displacement ratio of the superstructure.

11. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: In step S5, after the rigid body displacement ratio is preset, the upper structure around the strong axis can also be taken for calculation. Subsequently, the rotational stiffness around the weak axis is calculated in the same way and the cross section of the beam or column around the weak axis is adjusted.

12. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: In step S6, according to theoretical calculation and finite element analysis results, the vertical load-bearing shock-absorbing body at the intersection of the weak axis and the strong axis only bears pressure, so it can be designed as a compressive vertical load-bearing shock-absorbing body.

13. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: The stiffness of the vertical load-bearing shock-absorbing body of the vertical tensile and compressive energy-absorbing limit bearing is proportional to the size of the vertical load it bears, ensuring that the initial compression deformation of all vertical load-bearing shock-absorbing bodies in the support layer is the same. The stiffness of the vertical load-bearing shock-absorbing bodies of all vertical tensile and compressive energy-absorbing limit bearings is basically symmetrical around the strong axis and weak axis of the support layer at the bottom of the structure, ensuring that the structure can achieve an ideal rotational and rocking deformation mode around the strong axis and weak axis during an earthquake.

14. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: The superstructure adopts a building structure, an industrial cylindrical structure, an offshore structure or a nuclear industry structure; the superstructure is selectively provided with supports or metal, viscoelastic, viscous, eddy current or tuned mass damper energy dissipation and vibration reduction devices.

15. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: The vertical load-bearing shock-absorbing body is a coil spring, a laminated rubber or a disc spring.

16. The method for analyzing an overall rocking structure with asymmetric stiffness around the strong and weak axes of the structure according to claim 1, characterized in that: The vertical tension and compression energy dissipation limit support is provided with a damper, and the damper is a viscoelastic damper, a metal damper, a viscous fluid damper, an eddy current damper or a tuned mass damper.

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