Design method for rigidity of shock insulation support of mountain fallen layer frame structure

Abstract

The invention relates to the field of structural seismic isolation, and discloses a design method for rigidity of a seismic isolation support of a mountain falling layer frame structure. Designing an upper structure by reducing by one degree; analyzing a non-seismic-isolation model response spectrum under the action of a fortification earthquake, and determining the shear force of a non-seismic-isolation structure base; setting the shear force ratio of the substrate to be 0.5; selecting an upper grounding shock insulation support; according to an equivalent consistent rigidity method, namely according to the fact that when the structure is subjected to horizontal lateral force, the grounding columns with different heights are subjected to the same shearing force, and after the seismic isolation supports are arranged, the equivalent rigidities of the series connection of the grounding column seismic isolation supports with different heights and the grounding columns are the same, a lower grounding seismic isolation support is determined; establishing an integral seismic isolation model, performing fortification seismic response spectrum analysis, and judging whether a seismic reduction target is met or not; and upper structure design reinforcement and seismic isolation structure wave selection are carried out, and rare earthquake seismic isolation layer checking calculation is carried out. Compared with a traditional shock insulation structure, the falling layer shock insulation structure based on the equivalent consistent rigidity concept is smaller in base shear force, and the torsion reaction is obviously improved.

Description

Technical Field

[0001] The present invention relates to the field of structural isolation, and particularly to a design method for the stiffness of isolation bearings of a mountainous stepped frame structure. Background Art

[0002] As shown in the attached Figure 1 figure, as one of the main research objects of mountainous buildings, the RC stepped frame structure forms unequal-height constraints due to terrain differences. While effectively utilizing space resources and avoiding large-scale excavation, it also has significant differences in the vertical and horizontal mass stiffness distributions, often resulting in serious damage to the upper grounding end and obvious torsional effects under seismic action.

[0003] Base isolation measures can effectively reduce the seismic response of the upper structure. However, current research mainly focuses on general flat ground structures, and there is still relatively little research on the base isolation design of stepped structures. In traditional isolation design, the isolation layer is generally at the same elevation. When designing the isolation layer, the stiffness relationship between the isolation layer and the upper structure floors is mainly considered, and the problem of how to select the stiffness of the upper and lower isolation layers under the condition of unequal-height grounding is not considered. The stepped structure has unequal-height grounding ends, and the selection of the stiffness of the upper and lower isolation layers will inevitably have a great impact on the stepped part. Summary of the Invention

[0004] The present invention aims to provide a design method for the stiffness of isolation bearings of a mountainous stepped frame structure to solve the problem that when the traditional isolation design is adopted for a mountainous stepped structure, there are unequal-height grounding ends, and obvious intra-layer deformation differences will occur at the elevation of the upper grounding end, affecting the stepped frame structure.

[0005] To achieve the above object, the present invention adopts the following technical solutions: A design method for the stiffness of isolation bearings of a mountainous stepped frame structure, including:

[0006] Step 1: Determine the seismic reduction target;

[0007] Step 2: Design the upper structure according to one degree lower in seismic fortification;

[0008] Step 3: Conduct a response spectrum analysis of the non-isolated model under the action of the fortification earthquake to determine the base shear force of the non-isolated structure;

[0009] Step 4: Set the base shear force ratio to 0.5;

[0010] Step 5: Select the upper grounding isolation bearing;

[0011] Step 6: Determine the lower grounding isolation bearing according to the equivalent uniform stiffness method, that is, according to the fact that when the structure is subjected to a horizontal lateral force, each unequal-height grounding column should receive the same shear force, and after arranging the isolation bearings, the equivalent stiffness of the series connection of the isolation bearings of the unequal-height grounding columns and the grounding columns is the same to determine the lower grounding isolation bearing;

[0012] Step 7: Establish an overall isolation model, conduct a spectrum analysis for the fortification earthquake, and determine whether the seismic reduction objective is met;

[0013] Step 8: Perform the design and reinforcement of the upper structure and select waves for the isolation structure, and conduct a check calculation for the isolation layer under rare earthquakes.

[0014] Preferably, when the check calculation in Step 8 fails, return to Step 5 to re-select the upper-ground isolation bearing or return to Step 1 to re-design the upper structure.

[0015] Preferably, when the seismic reduction objective is not met in Step 7, return to Step 5 to re-select the upper-ground isolation bearing.

[0016] Preferably, Step 6 specifically includes:

[0017] Step 61: Calculate the lateral stiffness of the dropped columns of the non-isolated dropped-story frame structure according to the equivalent column method. The formula is: In the formula, K is the lateral stiffness of the equivalent column, i j and h j are respectively the equivalent linear stiffness and equivalent height of the required equivalent column, and α j , ζ j are respectively the column end rotation capacity coefficient and the proportional coefficient between the shear force formed by the column end rotation and the shear force formed by the lateral displacement;

[0018] Step 62: According to the relationship between the horizontal stiffness and deformation of the isolation bearing: Z 4 K u = Z 5 K d = 0.5F, K u = f(K d , i 1 , i 2 , i 3 , l 1 , l 2 , l 3 ), in the formula, Z 4 is the horizontal displacement of the upper isolation bearing, Z 5 is the horizontal displacement of the lower isolation bearing, K u is the stiffness of the upper isolation bearing, and K d is the stiffness of the lower isolation bearing, and calculate the horizontal shear stiffness of the isolation bearing;

[0019] Step 63: Then, when the structure is subjected to a horizontal lateral force, each unequal-height grounded column should receive the same shear force. After arranging the isolation bearings, the equivalent stiffness of the series connection of the isolation bearings of the unequal-height grounded columns and the grounded columns is the same, and calculate the effective stiffness of the isolation bearings at the bottom of each grounded column through the following formula. The specific formula is:

[0020] Ki = K j ;

[0021]

[0022] K ib = K jb ;

[0023] Among them, K ic and K jc are respectively the lateral stiffness of the lower and upper earthing columns, and K ib and K jb are the horizontal equivalent stiffness of the lower and upper isolation bearings. K i and K j both represent the series stiffness of the column and the isolation bearing. For the upper earthing column or the equivalent column of the lower earthing, when the column line stiffness is the same, the stiffness of the equivalent column with the same earthing end is: K ic = K jc , and the equivalent stiffness of the isolation bearing is: K ib = K jb .

[0024] Preferably, the calculation method of the column height of the equivalent column is: Among them, α k is a parameter reflecting the ratio of the beam-column line stiffness of the equivalent part, and α k , k is related to the beam-column line stiffness, and i c is the line stiffness of the equivalent column part of the dropped storey, and ∑i is the sum of the line stiffnesses of the beams connected to the column.

[0025] Preferably, the calculation of the relationship between the horizontal stiffness and deformation of the isolation bearing includes: The simplified model with isolation bearings arranged at the earthing ends of the long and short columns of unequal-height columns has 5 degrees of freedom, which are the rotation Z1 at point A, the rotation Z2 at point B, the horizontal displacements Z3 at points A and B, the horizontal displacement Z4 at point E of the isolation bearing, and the horizontal displacement Z5 at point F of the bearing. The shear forces on the long and short columns are 0.5 times the horizontal F. Specifically: When a horizontal force F is applied to the right at point B, the following relationship can be obtained:

[0026] In the formula, l i is the length of the beam-column, and i i is the beam-column line stiffness. The relationship between the horizontal stiffness and deformation of the isolation bearing is: Z 4 K u = Z 5 K d = 0.5F. In the formula, Z 4 is the horizontal displacement of the upper isolation bearing, and Z 5is the horizontal displacement of the lower isolation bearing, K u is the stiffness of the upper isolation bearing, K d is the stiffness of the lower isolation bearing. According to the above formula, the stiffness K of the isolation bearing is simplified to u and K d The numerical relationship of is:

[0027] K u = f(K d , i 1 , i 2 , i 3 , l 1 , l 2 , l 3 ).

[0028] Preferably, the calculation of the series stiffness formula includes: equivalent the series model of the isolation bearing and the upper structure to a column, then the series stiffness is expressed as: Where K c is the lateral stiffness of the column, and K b is the horizontal shear stiffness of the series support.

[0029] The purpose of the present invention is to coordinate the shear force distribution of the upper and lower grounding columns of the dropped story structure and control the torsional effect of the dropped story structure. It studies how to select the stiffness of the upper and lower isolation layers of the dropped story frame structure and proposes a method for selecting the stiffness of the isolation bearing at different grounding ends of the dropped story structure; from the perspective of coordinating the horizontal shear forces of the upper and lower grounding columns of the dropped story structure, it calculates the stiffness of the isolation bearing at different elevations of the dropped story structure at different grounding ends in a relatively simple way, and then guides the layout and seismic checking of the isolation layers at unequal-height grounding ends of the dropped story frame structure; compared with the traditional isolation design method, this method can better coordinate the shear force distribution between unequal-height grounding columns and improve the torsional effect of the upper structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a schematic structural diagram of an RC dropped story frame structure in the background technology of the present invention.

[0031] Figure 2 is a schematic flow chart of an embodiment of the present invention.

[0032] Figure 3 is a schematic structural diagram of an equivalent column in an embodiment of the present invention.

[0033] Figure 4 is a schematic simplified model diagram of arranging isolation bearings on unequal-height columns in an embodiment of the present invention.

[0034] Figure 5 is a schematic diagram of a series model of unequal-height grounding columns and isolation bearings in an embodiment of the present invention.

[0035] Figure 6Schematic diagram of the horizontal displacement and deformation of the dropped-story structure in the embodiments of the present invention.

[0036] Figure 7 Diagram of the equivalent consistent stiffness coordinated displacement ratio in the embodiments of the present invention.

[0037] Figure 8 Diagram of the coordinated displacement ratio of the same bearings in the embodiments of the present invention.

[0038] Figure 9 Schematic diagram of the 7D2K2_4_6 dropped-story structure of the embodiments of the present invention along the slope direction.

[0039] Figure 10 Plan layout of the upper grounding layer in the embodiments of the present invention.

[0040] Figure 11 Response spectrum of the fortification earthquake in the embodiments of the present invention.

[0041] Figure 12 Response spectrum of the rare earthquake in the embodiments of the present invention.

[0042] Figure 13 Diagram of the base shear force of the dropped-story model structure along the slope direction in the embodiments of the present invention.

[0043] Figure 14 Diagram of the base shear force of the dropped-story model structure across the slope direction in the embodiments of the present invention.

[0044] Figure 15 Diagram of the floor shear force of the D2K1 structure in the embodiments of the present invention.

[0045] Figure 16 Diagram of the floor shear force of the D4K1 structure in the embodiments of the present invention.

[0046] Figure 17 Diagram of the floor shear force of the D2K2 structure in the embodiments of the present invention.

[0047] Figure 18 Diagram of the floor shear force of the D4K2 structure in the embodiments of the present invention.

[0048] Figure 19 Diagram of the peak value of the absolute acceleration response of the D2K1 floor in the embodiments of the present invention.

[0049] Figure 20 Diagram of the peak value of the absolute acceleration response of the D2K2 floor in the embodiments of the present invention.

[0050] Figure 21 Diagram of the peak value of the absolute acceleration response of the D4K1 floor in the embodiments of the present invention.

[0051] Figure 22 Diagram of the peak value of the absolute acceleration response of the D4K2 floor in the embodiments of the present invention.

[0052] Figure 23 It is the interlayer torsion angle diagram of the first group of structures in the embodiments of the present invention.

[0053] Figure 24 It is the interlayer torsion angle diagram of the second group of structures in the embodiments of the present invention.

[0054] Figure 25 It is the interlayer torsion angle diagram of the third group of structures in the embodiments of the present invention.

[0055] Figure 26 It is the interlayer torsion angle diagram of the fourth group of structures in the embodiments of the present invention. Detailed implementation manners

[0056] The following is a further detailed description through specific implementation manners:

[0057] Embodiment:

[0058] Equivalent consistent stiffness method:

[0059] 1. Equivalent column:

[0060] The equivalent column is specifically as shown in the appendix Figure 3 The grounded layer part under the dropped story structure is replaced by an equivalent column. The calculation method of the column height of the equivalent column is as shown in the formula:

[0061]

[0062] In the formula, α k is a parameter reflecting the ratio of the beam-column linear stiffness of the equivalent part, α k , k are related to the beam-column linear stiffness, i c is the linear stiffness of the dropped story equivalent column part, and ∑i is the sum of the linear stiffnesses of the beams connected to the column.

[0063] The equivalent lateral stiffness correction formula of the dropped story part equivalent column is:

[0064]

[0065] In the formula, K is the lateral stiffness of the equivalent column, i j and h j are respectively the equivalent linear stiffness and equivalent height of the required equivalent column, α j , ζ j are respectively the column end rotation capacity coefficient and the proportional coefficient between the shear force formed by the column end rotation and the shear force formed by the lateral displacement. Among them, the equivalent linear stiffness and equivalent height of the equivalent column are solved through the column height of the equivalent column.

[0066] 2. Calculation method for the stiffness of the unequal-height column isolation bearing

[0067] The series model of the isolation bearing and the superstructure is equivalent to a column. Through the series stiffness model, the analysis of the isolation bearing arrangement of the non-uniform-height earthing column shows that: arranging isolation bearings with different horizontal stiffnesses at the bottom of the columns with different heights can make the ratio of the lateral stiffness of the columns with different heights equal to 1, thereby adjusting the non-uniformity of the stiffness of the non-uniform-height earthing column. Therefore, it is necessary to adjust the non-uniformity of the non-uniform-height column through the isolation bearing and propose a calculation method for the lateral stiffness of the isolation bearing of the non-uniform-height earthing column.

[0068] For the isolation bearing, its force characteristics are relatively complex. It mainly undergoes horizontal shear deformation and has a large axial stiffness. When subjected to external forces, the axial deformation is very small, and at the same time, the bending deformation of the isolation bearing is also very small. Therefore, the assumptions are as follows: The isolation bearing only undergoes horizontal shear deformation; for the beam-column elements, it is considered that the non-uniform-height column mainly undergoes bending deformation and the horizontal beam element does not undergo axial deformation; the material obeys Hooke's law; the plane section assumption is considered.

[0069] Based on the above assumptions, as Figure 4 shown, the simplified model with isolation bearings arranged at both the grounding ends of the long and short columns of a single-span non-uniform-height column considers five degrees of freedom, namely the rotation angle Z1 at point A, the rotation angle Z2 at point B, the horizontal displacements Z3 at points A and B, the horizontal displacement Z4 at point E where the isolation bearing is located, and the horizontal displacement Z5 at point F where the bearing is located. In order to achieve that under the action of the horizontal force F on the non-uniform-height column, the shear force can be evenly distributed to the non-uniform-height column, that is, the shear forces borne by the long and short columns are both 0.5 times the horizontal force F.

[0070] According to the displacement method: when a horizontal force F is applied to point B to the right, the following relationships can be obtained.

[0071]

[0072] In the formula, l i is the length of the beam-column, and i i is the linear stiffness of the beam-column.

[0073] The relationship between the horizontal stiffness and deformation of the isolation bearing is:

[0074] Z 4 K u = Z 5 K d = 0.5F (6)

[0075] By obtaining the mathematical relationship between K u and K d through equations (4) and (6), one of K u or K d can be determined first and then the other. Finally, the stiffnesses of the isolation bearings K u and K d , K u is the stiffness of the upper isolation bearing, and K dThe numerical relationship of the lower isolation bearing stiffness can be expressed by Equation (7) as follows:

[0076] K u = f(K d , i 1 , i 2 , i 3 , l 1 , l 2 , l 3 ) (7)

[0077] Through the practical calculation formula of the series horizontal stiffness coefficient, the series model of the isolation bearing and the upper structure can be equivalent to a column, thus simplified to a mathematical model with three degrees of freedom fixed at both ends, as Figure 5 shown.

[0078] For the above mathematical model, the series stiffness can be expressed as:

[0079]

[0080] where K c is the lateral stiffness of the column, and K b is the horizontal shear stiffness of the series bearing.

[0081] Assume that the equivalent series stiffness of the upper and lower grounding ends are K 1 and K 2 , and K 1 = nK 2 Then the shear force ratio relationship of the upper and lower grounding columns is:

[0082]

[0083] Obviously, when the stiffness ratio of the equivalent non-uniform-height grounding columns is near 1, its shear force ratio will change significantly with the change of the lower isolation bearing stiffness. From the series stiffness model, it can be seen that the series stiffness is mainly controlled by the isolation bearing with smaller stiffness.

[0084] 3. Displacement and deformation coordination analysis at the horizontal position of the upper bearing

[0085] Due to the existence of non-uniform-height grounding in the dropped-story structure, under the action of horizontal force, obvious in-story deformation differences will occur at the elevation of the upper grounding end. And since the isolation layer is arranged at two non-uniform-height grounding ends in the dropped-story structure, it is necessary to consider the deformation problem of the bearings at different grounding ends. The deformation of the isolation bearing is directly related to its force. Further, aiming at the previous isolation bearing layout method, the deformation of the isolation bearing and the structural deformation coordination of the single-story single-span non-uniform-height grounding end are studied.

[0086] The structural horizontal displacement and deformation are as Figure 6As shown in the figure, when discussing the deformation of the isolation bearing, the consistent deformation of the isolation bearing with unequal-height grounding ends should not be simply considered. For the suspended floor structure, the relative deformation of each mass point on the same horizontal layer or horizontal plane should be considered. For the deformation of the upper grounding-end isolation bearing, the horizontal displacement coordination at the same horizontal plane should be considered. Based on the above analysis of the deformation coordination of the upper structure with unequal-height grounding ends, the deformation of the upper structure and the isolation bearing of a single-story and single-span structure with unequal-height grounding ends is assumed as follows: A frame structure with isolation bearings arranged at both grounding ends is subjected to a horizontal force F at the vertex. To simplify the analysis, it is assumed that the axial stiffness of each member is infinitely large and no axial deformation occurs; the isolation bearing only undergoes horizontal deformation, and the deformation of columns AC and BD varies linearly along the vertical direction. Based on the above assumptions, the basic deformation conditions can be obtained:

[0087]

[0088] In the formula, K u is the stiffness of the upper isolation bearing, K d is the stiffness of the lower isolation bearing, K AC , K BD are the lateral stiffnesses of columns AC and BD, and K eqAC , K eqBD are the equivalent stiffnesses of the series connection of columns AC and BD with the bearing respectively. If it is desired that the upper structure can be deformed coordinately, it is necessary to ensure that the horizontal displacement of the long column at the horizontal position of the upper grounding-end isolation bearing is the same as or close to the horizontal deformation of the upper grounding-end isolation bearing. That is, it is necessary to satisfy:

[0089]

[0090] After consulting the data, the equivalent horizontal stiffness of the lead-rubber isolation bearing LRB and the natural rubber isolation bearing LNR is generally between 0.6 kN / mm and 5 kN / mm. For a C30 concrete column with a height of 3.3 m and a cross-sectional size of 0.6 m × 0.6 m, the lateral stiffness is about 100 kN / mm, and its lateral stiffness is much greater than the horizontal stiffness of the isolation bearing. Define the ratio of the stiffness K d of the lower grounding isolation bearing to the lateral stiffness K BD of the upper grounding short column as ε, that is:

[0091]

[0092] Calculate the relationship between the coordination displacement ratio λ and ε under different column stiffness ratios η, and compare it with the structure with the same isolation bearings arranged at the upper and lower grounding ends, as shown in Figure 7 and Figure 8 shown. From Figure 7 and Figure 8It can be seen that when the stiffness ratio η of the isolated structural column is constant, the coordinated displacement ratio λ decreases as ε decreases, indicating that the deformation of the unequal-height columns at the horizontal position of the upper isolation bearing becomes more coordinated. In this paper, it is assumed that when 1.05 > λ > 0.95, the unequal-height grounding frame can meet the requirements of displacement coordination. As can be seen from the figure, the gray part is all the selectable areas that satisfy the coordinated displacement ratio λ > 0.95, and the yellow part is the area that satisfies λ > 0.95 within the parameter range of the rubber isolation bearing. The above analysis shows that the isolation bearings arranged based on the concept of equivalent uniform stiffness can not only satisfy the uniform distribution of the shear forces of the unequal-height columns but also well control the displacement coordination between the grounding end and the non-grounding end in the horizontal plane of the upper grounding end. Moreover, the smaller η is, the easier it is to satisfy the deformation coordination, which is consistent with the concept. That is, when η = 1, the unequal-height frame is transformed into a flat structure. At this time, the upper and lower grounding ends are in the same horizontal plane. When the isolation bearings are arranged by the equivalent uniform stiffness method, under the action of the horizontal force at the vertex, the horizontal displacements of the two bearings are the same, and at this time λ = 1, which is always true in theory.

[0093] 4. Verification of the equivalent uniform stiffness method

[0094] Check whether the equivalent uniform stiffness method can meet the accuracy requirements. The basic mechanical method for the check is the matrix displacement method. The principle of the matrix displacement method is to discretize the structure into a finite number of elements, establish the element stiffness matrix according to the basic assumptions, and then form the overall stiffness matrix of the discretized elements according to the equilibrium conditions and deformation conditions to establish and solve the basic equations of the displacement method. For a multi-degree-of-freedom structure, the computational amount of its matrix equation is very large. Therefore, a computer is usually used as an auxiliary means to solve the matrix equation. OpenSees has a powerful solving function. In this application, numerical models are mainly established by OpenSees to check the above-mentioned calculation of the isolation bearing stiffness to verify its accuracy. Five groups of models are designed with different parameters according to the beam-column section sizes of the single-span unequal-height frame structure, the heights of the upper and lower grounding columns, etc. The model parameters are shown in Table 1:

[0095] Table 1 Parameters of the single-story single-span unequal-height grounding frame

[0096]

[0097] Solve the sizes of the isolation bearings required to be arranged on the upper and lower grounding columns for each model under the condition that the shear forces at the upper and lower grounding ends are expected to be the same, and apply a horizontal force F = 10 kN to the model with the arranged isolation bearings. Calculate the base shear forces of each example through finite element analysis. The calculation results are shown in Table 2:

[0098] Table 2 Shear force distribution results

[0099]

[0100] Under the action of a horizontal static force applied at the top, it can be seen from the shear force distribution results at the column bases of the isolated structure and the non-isolated structure that arranging the stiffness of the isolation bearings by the equivalent uniform stiffness method can effectively and evenly distribute the base shear force of columns with different heights, achieving an even distribution of the shear force. Therefore, the isolation bearings that can be arranged by the above equivalent uniform stiffness method can not only satisfy the uniform distribution of the shear force of columns with different heights but also well control the displacement coordination between the grounded end and the non-grounded end in the horizontal plane of the upper grounding end.

[0101] A design method for the stiffness of isolation bearings of a mountainous stepped frame structure, as shown in the appendix Figure 2 shown, includes the following steps:

[0102] Step 1: Determine the seismic reduction target.

[0103] Confirm the seismic reduction target according to the "Building Isolation Design Standard" GB / T 51408-2021 (hereinafter referred to as the "Isolation Standard") issued by the Ministry of Housing and Urban-Rural Development.

[0104] Step 2: Design the upper structure by reducing the seismic fortification intensity by one degree.

[0105] Determine the seismic measures by reducing the seismic fortification intensity by one degree, that is, the base shear ratio specified in the "Isolation Standard" is less than 0.5.

[0106] Step 3: Conduct a response spectrum analysis of the non-isolated model under the action of the fortification earthquake to determine the base shear force of the non-isolated structure.

[0107] Non-isolated Model Response Spectrum Analysis is a method for analyzing the seismic response of building structures based on the response spectrum method. Non-isolated Model Response Spectrum Analysis is a method for analyzing the seismic response of building structures based on the response spectrum method. It specifically includes the following steps:

[0108] 1. Establish a structural model: Model the building into appropriate discretized elements (such as frames, walls, columns, etc.). Determine the basic parameters of the structure, such as mass, stiffness, and damping. Assume the structure is a multi-degree-of-freedom system, and then conduct a modal analysis to extract the natural frequencies and vibration modes of the structure.

[0109] 2. Select an appropriate seismic response spectrum: Select a suitable seismic response spectrum according to the seismic region where the building is located, the design seismic intensity, etc. The response spectrum usually consists of the acceleration, displacement, or velocity of the ground motion, depending on the building codes and design requirements in different regions.

[0110] 3. Modal Analysis: Calculate the natural frequencies and vibration modes of the structure through modal analysis. The seismic response of the structure is usually composed of the superposition of multiple modes. Each mode corresponds to a natural frequency, reflecting the response characteristics of the structure at that frequency.

[0111] 4. Calculate the response of each mode: According to the selected response spectrum, calculate the maximum response (usually the maximum displacement, acceleration, etc.) of each mode under the action of seismic loads. For each mode, use the response spectrum method to calculate its maximum displacement or maximum acceleration.

[0112] 5. Modal superposition: Superimpose the responses of each mode to obtain the overall response of the structure. Commonly used superposition methods include complete linear superposition and equivalent linear superposition. When superimposing, the phase relationship between different modes needs to be considered. Generally, in a non-isolated model, it is assumed that the responses between each mode are independent.

[0113] 6. Result analysis: Calculate key parameters such as the maximum displacement, acceleration, and stress of the structure through the superimposed response. Combine the requirements of the specifications to judge whether the structure meets the safety requirements of seismic design.

[0114] In the response spectrum analysis of the non-isolated model, the base shear force of the non-isolated structure is determined through the maximum response of the structure under seismic action. The base shear force refers to the horizontal force borne by the bottom of the structure (usually the ground or the foundation part), and this force is caused by the propagation of seismic waves.

[0115] Step 4: Set the base shear force ratio to 0.5.

[0116] The base shear force ratio is the ratio of the base shear force of the structure to a certain reference value under seismic action. It is usually used to measure the seismic resistance of a building during an earthquake or to compare the seismic performance of different design schemes.

[0117] Step 5: Select the upper ground isolation bearing.

[0118] Since the seismic isolation building aims at a one-degree reduction in design, it is necessary to satisfy that the base shear force F of the seismic isolation structure iso <0.5F 0 , when initially selecting the isolation bearing, F iso =0.5F 0 , the advantage of the equivalent uniform stiffness method is that the shear forces received by all grounding columns are the same. Therefore, the target base shear force of each grounding column can be obtained as: F isoi =F iso / N. In the formula, F iso is the base shear force of the seismic isolation structure, F 0 is the base shear force of the non-seismic isolation structure, F isoiis the base shear force of each column. After obtaining the base shear forces of each grounding column, appropriate isolation bearings can be selected. The equivalent consistent stiffness method determines that the equivalent stiffness of the upper grounding isolation bearing should be less than that of the lower grounding column. Therefore, first determine the size of the upper grounding isolation bearing, and then determine the size of the lower grounding isolation bearing through the equivalent consistent stiffness method, which can ensure that the upper and lower grounding isolation bearings are reasonable in the preliminary selection.

[0119] Step 6: Determine the lower grounding isolation bearing according to the equivalent consistent stiffness method.

[0120] After determining the upper grounding isolation bearing, calculate the equivalent horizontal stiffness of the lower grounding isolation bearing by the equivalent consistent stiffness method proposed above: Select the corresponding or close isolation bearing according to the calculated equivalent horizontal stiffness.

[0121] Referring to the methods introduced above, this step specifically includes:

[0122] Step: Step 61: Calculate the lateral stiffness of the dropped-story columns of the non-isolated dropped-story frame structure according to the equivalent column method. The formula is: In the formula, K is the lateral stiffness of the equivalent column, and i j and h j are the equivalent linear stiffness and equivalent height of the required equivalent column respectively. α j , ζ j are the column end rotation capacity coefficient and the proportional coefficient between the shear force formed by the column end rotation and the shear force formed by the lateral displacement respectively;

[0123] Step 62: Calculate the horizontal shear stiffness of the isolation bearing according to the relationship between the horizontal stiffness and deformation of the isolation bearing. Among them, Z 4 K u = Z 5 K d = 0.5F, K u = f(K d , i 1 , i 2 , i 3 , l 1 , l 2 , l 3 ).

[0124] Step 63: Then, when the structure is subjected to horizontal lateral forces, each unequal-height grounding column should receive the same shear force. After arranging the isolation bearings, the equivalent height of the series connection of the isolation bearings and the grounding columns of the unequal-height grounding columns is the same. Calculate the effective stiffness of the isolation bearings at the bottom of each grounding column through the following formula. The specific formula is:

[0125] K i = K j (19)

[0126]

[0127] K ib = K jb (22)

[0128]

[0129] Among them, K ic and K jc are the lateral stiffness of columns, K ib and K jb are the horizontal shear stiffness of series-connected bearings, and K i and K j both represent the series stiffness of columns and isolation bearings. Among them, for the upper grounding column or the equivalent column such as the lower grounding, if the stiffness difference between the edge column and the middle anti-column is not considered and the line stiffness of the column is the same, for the equivalent column stiffness with the same grounding end, there is: K ic = K jc , and the equivalent stiffness of the isolation bearing is: K ib = K jb .

[0130] Step 7: Establish an overall isolation model, conduct a seismic response spectrum analysis for the design earthquake, and determine whether the seismic reduction target is met.

[0131] Step 8: Carry out the design reinforcement of the superstructure and wave selection for the isolation structure, and conduct a rare earthquake check for the isolation layer.

[0132] The present invention conducts finite element simulation tests using the finite element software OpenSees. Taking different outrigger and skip-story base isolation structures as examples, dynamic time history analysis is carried out by comparing with the isolation structure with uniform stiffness and the traditional outrigger isolation structure. The naming method of the outrigger structure example is: DaKb_M_N, where Da is the number of floors of the outrigger part, Kb is the number of spans of the outrigger part, M is the number of spans of the upper grounding part, and N is the number of floors above the upper grounding. The model schematic diagrams are as shown in Figure 9 and Figure 10 shown.

[0133] According to the dual-frequency wave selection method, two artificial waves and five natural waves are selected, and all waves meet the requirements of the example model. The seismic response spectra are as shown in Figure 11 and Figure 12 shown.

[0134] The base shear force is shown in Table 3,

[0135] Table 3 Peak Base Shear Force

[0136]

[0137]

[0138] Figure 13It is the shear force diagram of the base of the stepped - down model structure in the along - slope direction. Figure 14 It is the shear force diagram of the base of the stepped - down model structure in the cross - slope direction. Compared with the traditional isolation group, for the D2K1 and D2K2 uniform stiffness group models, the shear forces of the base in the along - slope direction are reduced by 2.4% and 2% respectively, and the shear forces of the base in the cross - slope direction are reduced by 2.45% and 1.97% respectively; while for the D4K1 and D4K2 uniform stiffness groups, the shear forces of the base in the along - slope direction are reduced by 8.6% and 7.1% respectively, and the shear forces of the base in the cross - slope direction are reduced by 8.81% and 6.81% respectively. As the number of stepped - down floors increases, the reduction of the base shear force becomes more obvious.

[0139] Figure 15 、 Figure 16 、 Figure 17 、 Figure 18 They are the floor shear force diagrams of different groups of structures. The shear forces of the floors above the upper - grounded part of the uniform stiffness group models are all less than those of the traditional isolation group, which also shows that the overall shock - absorption effect of the uniform stiffness isolation design is better than that of the traditional isolation design.

[0140] Figure 19 、 Figure 20 、 Figure 21 and Figure 22 They are the peak diagrams of the floor acceleration responses of different groups of structures. The peak accelerations of the floors of the uniform stiffness group are all less than those of the traditional isolation group. The distribution characteristics of the accelerations of the two isolation structures along the floors are basically the same, both showing that: the accelerations of the floors above the upper - grounded part first decrease and then increase, reaching the maximum at the top floor.

[0141] Figure 23 、 Figure 24 、 Figure 25 and Figure 26 They are the diagrams of the inter - story torsional angles of different groups of structures.

[0142] For the base isolation design method of the stepped - down frame structure based on the concept of "equivalent uniform stiffness" proposed in the present invention, through establishing a numerical model and conducting time - history analysis, it can be known that: the isolation design method based on the concept of equivalent uniform stiffness can better improve the dynamic response of the stepped - down structure; compared with the stepped - down isolation structure based on the traditional isolation design method, the base shear force of the stepped - down isolation structure based on the concept of equivalent uniform stiffness is smaller, and the torsional response is significantly improved.

[0143] The above are only embodiments of the present invention, and common general technical solutions and / or characteristics in the solutions are not described in detail herein. It should be noted that for those skilled in the art, without departing from the technical solutions of the present invention, several deformations and improvements can be made. In the present invention, unless otherwise clearly defined and limited, terms such as "installation", "connection", "connection", "fixation" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations. The scope of protection required by this application should be based on the content of its claims, and the specific implementation manners and the like recorded in the specification can be used to explain the content of the claims.

Claims

1. The design method of the seismic isolation bearing stiffness of the mountainous layer-dropping frame structure is characterized by: include: Step 1: Determine the shock reduction target; Step 2: Design the superstructure by lowering one degree; Step 3: Analyze the response spectrum of the non-isolated model under the design earthquake to determine the base shear force of the non-isolated structure; Step 4: Set the base shear ratio to 0.5; Step 5: Select the upper ground isolation bearing; Step 6: Determine the lower grounded isolation bearing according to the equivalent consistent stiffness method, that is, when the structure is subjected to horizontal lateral force, each unequal height grounding column should be subjected to the same shear force. After the isolation bearings are arranged, the equivalent stiffness of the unequal height grounding column isolation bearings and the grounding column in series is the same to determine the lower grounded isolation bearing; Step 7: Establish an overall seismic isolation model, conduct earthquake response spectrum analysis, and determine whether the seismic reduction target is met; Step 8: Design the reinforcement of the superstructure and the isolation structure, and perform wave calculations on the isolation layer for rare earthquakes.

2. The method for designing the stiffness of the seismic isolation bearing of the mountainous floor-falling frame structure according to claim 1 is characterized by: If the calculation in step 8 fails, return to step 5 to reselect the upper ground isolation bearing or return to step 1 to redesign the upper structure.

3. The method for designing the stiffness of the seismic isolation bearing of the mountainous floor-falling frame structure according to claim 1 is characterized by: If the shock absorption target is not met in step 7, return to step 5 to reselect the upper grounded seismic isolation bearing.

4. The method for designing the stiffness of the seismic isolation bearing of the mountainous floor-falling frame structure according to claim 1 is characterized by: Step 6 specifically includes: Step 61: Calculate the lateral stiffness of the dropped-story columns of the non-seismic dropped-story frame structure according to the equivalent column method. The formula is: In the formula, K is the lateral stiffness of the equivalent column, i j and h j are the equivalent linear stiffness and equivalent height of the required equivalent column, α j , j are the column end rotation capacity coefficient and the proportionality coefficient between the shear force generated by the column end rotation and the shear force generated by the lateral displacement; Step 62: According to the relationship between the horizontal stiffness and deformation of the seismic isolation support: Z4K u =Z5K d =0.5F, K u =f(K d ,i1,i2,i3,l1,l2,l3), where Z4 is the horizontal displacement of the upper isolation support, Z5 is the horizontal displacement of the lower isolation support, and K u is the stiffness of the upper isolation support, K d is the stiffness of the lower isolation bearing, and the horizontal shear stiffness of the isolation bearing is calculated; Step 63: Then, when the structure is subjected to horizontal lateral force, each unequal height grounding column should be subjected to the same shear force. After the seismic isolation bearings are arranged, the equivalent stiffness of the seismic isolation bearings of the unequal height grounding columns and the grounding columns in series is the same, and the effective stiffness of the seismic isolation bearings at the bottom of each grounding column is calculated by the following formula, which is: K i =K j ; K ib =K jb ; Among them, K ic and K jc are the lateral stiffness of the lower and upper grounding columns, K ib and K jb is the horizontal equivalent stiffness of the lower isolation support and the upper isolation support, K i and K j Both represent the series stiffness of the lower grounding column, the upper grounding column and the seismic isolation support. For the upper grounding column or the lower grounding equivalent column, when the column line stiffness is the same, the equivalent column stiffness for the same grounding end is: K ic =K jc , the equivalent stiffness of the isolation bearing is: K ib =K jb .

5. The method for designing the stiffness of the seismic isolation bearing of the mountainous floor-falling frame structure according to claim 4 is characterized by: The column height of the equivalent column is calculated as follows: in, α k is a parameter reflecting the ratio of the linear stiffness of the equal-generation beam and column, α k , k is related to the beam-column linear stiffness i c is the linear stiffness of the column part that is replaced by the dropped floor, and ∑i is the sum of the linear stiffness of the beams connected to the column.

6. The method for designing the stiffness of the seismic isolation bearing of the mountainous floor-falling frame structure according to claim 4 is characterized by: The calculation of the relationship between the horizontal stiffness and deformation of the seismic isolation bearing includes: the simplified model in which the grounding ends of the long and short columns of unequal height are all arranged with seismic isolation bearings has 5 degrees of freedom, namely the rotation angle Z1 of point A, the rotation angle Z2 of point B, the horizontal displacement Z3 of points A and B, the horizontal displacement Z4 of point E at the seismic isolation bearing, and the horizontal displacement Z5 of point F at the bearing. The shear force on the long and short columns is 0.5 times the horizontal force F. Specifically, when point B is subjected to the horizontal force F to the right, the following relationship can be obtained: In the formula, l i is the length of the beam, i i is the beam-column linear stiffness, and the relationship between the horizontal stiffness and deformation of the isolation bearing is: Z4K u =Z5K d =0.5F, where Z4 is the horizontal displacement of the upper isolation support, Z5 is the horizontal displacement of the lower isolation support, K u is the stiffness of the upper isolation support, K d is the lower isolation bearing stiffness, and the isolation bearing stiffness K is simplified according to the above formula. u , K d The numerical relationship is: K u =f(K d ,i1,i2,i3,l1,l2,l3)。 7. The method for designing the stiffness of the seismic isolation bearing of the mountainous floor-falling frame structure according to claim 4 is characterized by: The calculation formula of the series stiffness includes: the series model of the seismic isolation support and the upper structure is equivalent to a column, and the series stiffness is expressed as: Where K c is the lateral stiffness of the column, K b is the horizontal shear stiffness of the series supports.

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