Simplified calculation method for horizontal rigidity of shock insulation support
Through the simplified load and diameter calculation method, combined with adjustment coefficients and constants, the problem of difficulty in estimating the level stiffness of the seismic isolation bearing is solved, rapid iterative calculation is realized, design efficiency is improved and accuracy requirements are met.
Patent Information
- Application Number
- CN202410993200.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-24
- Publication Date
- 2024-12-13
AI Technical Summary
In the prior art, the estimation of the horizontal stiffness of the seismic isolation support is difficult and the rapid iterative calculation cannot be performed, resulting in inefficient design.
A simplified calculation method is proposed to calculate the horizontal stiffness of the seismic isolation bearing by estimating the load borne by a single seismic isolation bearing, calculating the initial diameter and applying a simplified formula (Kh=k2k1k0(aD-b). The simplified steps include load estimation and diameter Calculate and stiffness calculation, and use adjustment coefficients and constants to optimize parameters.
It realizes rapid calculation and iteration of the horizontal stiffness of the earthquake isolation support, improves the designer's work efficiency, and the error is within 3% to meet the specification value, meeting the design accuracy requirements.
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Figure CN119129170A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of building structures, and in particular relates to a simplified calculation method for the horizontal stiffness of a seismic isolation support. Background Art
[0002] The seismic isolation structure is a structural system formed by setting a seismic isolation layer with a reset function composed of seismic isolation bearings and damping devices between the foundation and superstructure of the building (base isolation) or between the lower structure and the upper structure of the building (inter-layer isolation). The seismic isolation structure system is divided into three parts: the upper structure, the seismic isolation layer and the lower structure.
[0003] Seismic isolation technology extends the natural vibration period of the building structure, reduces the seismic energy input to the upper structure, reduces the acceleration response and interlayer deformation of the upper structure, and the deformation and energy dissipation of the building structure are mainly borne by the seismic isolation system by setting a horizontal seismic isolation layer with low horizontal stiffness but high reliability in the building structure. The upper vibration response of the seismic isolation structure is close to the motion of a rigid body, thereby avoiding the damage of the structure and non-structural components and improving the seismic performance and functional integrity of the structure. The shock absorption mechanism of seismic isolation technology: extending the period of the upper structure and increasing the damping ratio.
[0004] The seismic isolation layer is a combination of multiple separate types of seismic isolation bearings or multiple types of seismic isolation bearings, such as a combination of natural rubber seismic isolation bearings and lead-zinc rubber seismic isolation bearings. In construction projects, lead core rubber seismic isolation bearings are usually arranged around the building, and natural rubber seismic isolation bearings are arranged in the middle of the building plane.
[0005] Seismic isolation bearings include two categories: laminated rubber isolation bearings and sliding isolation bearings. Laminated rubber isolation bearings mainly include natural rubber isolation bearings (LNR), lead rubber isolation bearings (LRB), high damping ratio rubber isolation bearings (HDR), etc. At present, the horizontal stiffness of isolation bearings is directly queried by the specification, without a unified formula. It needs to be calculated and verified separately, which makes estimation difficult and it is impossible to quickly iterate the calculation of isolation bearings.
[0006] Therefore, a simplified calculation method for the horizontal stiffness of the seismic isolation bearing is urgently needed to solve the problem that the horizontal stiffness of the seismic isolation bearing is difficult to estimate and cannot be calculated quickly iteratively in the prior art. Summary of the invention
[0007] In view of the above analysis, the present invention aims to provide a simplified calculation method for the horizontal stiffness of the seismic isolation bearing, so as to solve the problems in the prior art that the horizontal stiffness of the seismic isolation bearing is difficult to estimate and fast iterative calculation cannot be performed.
[0008] The purpose of the present invention is mainly achieved through the following technical solutions:
[0009] A simplified calculation method for the horizontal stiffness of a seismic isolation bearing comprises the following steps:
[0010] Step 1: Estimate the load borne by a single isolation bearing;
[0011] An isolation support is arranged under each load-bearing column of the building, and the number of the isolation supports is n; a representative value of the gravity load borne by each isolation support is estimated to obtain a single degree of freedom mass m (unit: t);
[0012] The specific formula is:
[0013]
[0014] Where M is the representative value of the overall gravity load of the structure, in t; n is the number of isolation bearings;
[0015] Step 2: Calculate the initial diameter of the isolation bearing;
[0016] D is the diameter of the seismic isolation support, in mm, the initial diameter is D0, and in this step D=D0;
[0017] Step 3: Calculate the horizontal stiffness of the isolation bearing;
[0018] The horizontal stiffness K of the seismic isolation support h The simplified formula is: K h =k2k1k0(aD-b);K h Unit: kN / mm;
[0019] Wherein k0 is the shear modulus adjustment coefficient of the isolation bearing; k1 is the secondary shape coefficient adjustment coefficient; k2 is the lead rubber isolation bearing adjustment coefficient; a is the diameter adjustment coefficient; b is a constant; the secondary shape coefficient is S2;
[0020] Step 4: End the calculation.
[0021] Furthermore, the step 2: calculating the initial diameter of the seismic isolation bearing includes: according to the "Building Seismic Isolation Design Standard", finding the required limit value σ (unit: N / mm) of the seismic isolation bearing compressive stress specification 2 ), and estimate the vertical pressure efficiency μ of the isolation bearing; estimate the initial diameter D0 of the isolation bearing (unit: mm), and the calculation formula of D0 is:
[0022]
[0023] Where g is the acceleration due to gravity.
[0024] Furthermore, the diameter adjustment coefficient a ranges from 0.001 to 0.002, and the constant b ranges from 0.01 to 0.1.
[0025] Furthermore, the diameter adjustment coefficient a is 0.0015, 0.0016 or 0.0017; and the constant b is 0.05, 0.06 or 0.07.
[0026] Furthermore, for a G4 rubber seismic isolation bearing with a secondary shape coefficient S2=5, the seismic isolation bearing shear modulus adjustment coefficient K0=1.
[0027] Furthermore, for a G5 rubber seismic isolation bearing with a secondary shape coefficient S2=5, the seismic isolation bearing shear modulus adjustment coefficient K0=1.25.
[0028] Furthermore, for the high damping ratio rubber seismic isolation bearing, the seismic isolation bearing shear modulus adjustment coefficient K0=2.4.
[0029] Furthermore, the value of the secondary shape coefficient adjustment coefficient k1 is:
[0030] Furthermore, for the G4 lead rubber isolation bearing, the lead rubber isolation bearing adjustment coefficient k2=1.19.
[0031] Furthermore, for the G5 lead rubber isolation bearing, the lead rubber isolation bearing adjustment coefficient k2=1.15.
[0032] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:
[0033] (1) The simplified calculation method of the horizontal stiffness of the seismic isolation bearing of the present invention is simple to calculate the horizontal stiffness of the seismic isolation bearing, takes a short time, and greatly improves the work efficiency of the designer;
[0034] (2) By changing the diameter D of the isolation bearing, different horizontal stiffness K of the isolation bearing can be quickly obtained. h , thus enabling fast iteration of the calculation of the horizontal stiffness of the isolation bearings.
[0035] In the present invention, the above-mentioned technical solutions can be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the following content, and some advantages can become obvious from the description or be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the text and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.
[0037] Figure 1Schematic diagram of the flow of the calculation method of the present invention;
[0038] Figure 2 The comparison curve of the simplified calculation of horizontal stiffness of seismic isolation bearing and the stiffness of the standard method;
[0039] Figure 3 This is the example structural plan layout;
[0040] Figure 4 This is the layout diagram of the seismic isolation bearings of the seismic isolation layer.
[0041] Reference numerals:
[0042] 1-Load-bearing column; 2-Lead-zinc rubber seismic isolation bearing. DETAILED DESCRIPTION
[0043] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of the present invention and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.
[0044] A specific embodiment of the present invention, as Figure 1 As shown, a simplified calculation method for the horizontal stiffness of a seismic isolation bearing (hereinafter referred to as the calculation method) is disclosed. The calculation of the horizontal stiffness of the bearing is simple and time-saving.
[0045] The fast calculation method of this embodiment includes the following steps:
[0046] Step 1: Estimate the load on a single isolation bearing
[0047] After determining the building structure system, estimate the representative value of the overall gravity load of the structure; based on the wall column arrangement, preliminarily estimate the number of isolation bearings, estimate the representative value of the gravity load borne by each isolation bearing, and obtain the single degree of freedom mass m (unit: t).
[0048] The specific formula is:
[0049]
[0050] Where M is the representative value of the overall gravity load of the structure, in units of t; n is the number of isolation bearings.
[0051] Step 2: Estimate the initial diameter of the isolation bearing
[0052] According to the "Building Seismic Isolation Design Standard", find the required limit value of the seismic isolation bearing compressive stress σ (unit: N / mm 2 ), and estimate the vertical pressure efficiency μ of the isolation bearing:
[0053] Estimate the initial diameter D0 of the seismic isolation bearing (unit: mm) using the following calculation formula:
[0054]
[0055] Where g is the acceleration due to gravity; the diameter of the seismic isolation support is D, and in this step D=D0.
[0056] Step 3: Simplify the calculation of the horizontal stiffness of the isolation bearing
[0057] According to the Code for Seismic Design of Buildings, for verification of rare earthquakes, the equivalent stiffness and equivalent viscous damping ratio at 250% shear deformation should be used.
[0058] Equivalent horizontal stiffness K of the isolation bearing under 250% shear deformation h (Unit: kN / mm), the following simplified formula can be used to simplify the calculation:
[0059] K h =k2k1k0(aD-b)
[0060] Among them, k0 is the shear modulus adjustment coefficient of the isolation bearing; k1 is the secondary shape coefficient adjustment coefficient; k2 is the lead core rubber isolation bearing adjustment coefficient; a is the diameter adjustment coefficient; b is a constant; and D is the diameter of the isolation bearing.
[0061] The range of a is 0.001-0.002, preferably, a is 0.0015, 0.0016 or 0.0017; the range of b is 0.01-0.1, preferably, b is 0.05, 0.06 or 0.07.
[0062] k0 Value of the shear modulus adjustment coefficient of the seismic isolation bearing:
[0063] For the isolation bearing with secondary shape coefficient S2=5, the rubber isolation bearing with shear modulus Gr=0.392 (hereinafter referred to as "G4"), K0=1; for the rubber isolation bearing with shear modulus Gr=0.49 (hereinafter referred to as "G5"), K0 is the ratio of the shear stiffness of G5 to the shear stiffness of G4, that is, For high damping ratio rubber isolation bearings (HDR), take K0=2.4.
[0064] k1 quadratic shape coefficient adjustment coefficient value:
[0065] The calculation formula is:
[0066]
[0067] For example, for the quadratic shape coefficient S2 = 5.45, the value is
[0068] k2 lead rubber isolation bearing adjustment coefficient value:
[0069] G4 lead rubber isolation bearing: K2=1.19; G5 lead rubber isolation bearing, K2=1.15.
[0070] like Figure 2 As shown, according to the simplified formula of this embodiment, the equivalent horizontal stiffness K of the seismic isolation bearing under 250% shear deformation is obtained. h And compared with the standard value, the stiffness comparison curve of various types of seismic isolation bearings is obtained.
[0071] Equivalent horizontal stiffness K of the seismic isolation bearing under 250% shear deformation calculated according to the simplified formula h The comparison with the standard values is shown in Table 1 below, where a is taken as 0.0016 and b is taken as 0.06. It can be seen that except for the isolation bearing with a D of 300mm, whose stiffness error is greater than 3%, the isolation bearings with other diameters, calculated according to the simplified algorithm, are consistent with the standard values, and most of the ratios are between 0.98-1.02.
[0072] Table 1 Simplified calculation of K h Comparison with standard stiffness
[0073]
[0074]
[0075] The equivalent horizontal stiffness Kh of the seismic isolation bearing calculated by the simplified formula is compared with the standard value. The error is within 3%, which meets the estimation requirements. The simplified formula in this step is effective for the equivalent horizontal stiffness Kh of the seismic isolation bearing. h The estimation is simple and fast and by varying D, fast iterations of the isolation bearing calculations can be performed.
[0076] Step 4: Alternative calculation of equivalent stiffness of seismic isolation structure
[0077] The seismic isolation structure consists of three parts: the upper structure, the seismic isolation layer and the lower structure; the seismic isolation layer consists of seismic isolation bearings, damping devices, etc.
[0078] like Figure 3 and Figure 4 As shown in Figure 1, the equivalent horizontal stiffness of the isolation structure is the series connection of the horizontal stiffness of the isolation layer and the horizontal stiffness of the superstructure.
[0079] The calculation formula of equivalent horizontal stiffness of seismic isolation structure is:
[0080]
[0081] Among them, K t is the horizontal stiffness of the superstructure; K h is the horizontal stiffness of the isolation layer; K eq is the equivalent horizontal stiffness of the isolation structure.
[0082] In rare earthquake situations, the maximum inter-story displacement angle limit of the steel structure superstructure is the largest, which is 1 / 100; the maximum inter-story displacement limits of other structural types are all smaller than those of the steel structure. The deformation limit of the seismic isolation bearing is min(0.55D, 3h), where h is the total thickness of the rubber layer of the seismic isolation bearing, and K can be obtained. h Maximum is K t The horizontal deformation of the isolation layer is much greater than that of the superstructure, and it can be inferred that the horizontal stiffness K h Much smaller than the horizontal stiffness K of the upper structure t The overall stiffness of the structure is approximately the same as the stiffness of the isolation support. The following formula can be obtained. When simplifying the estimation, the horizontal stiffness K of the isolation structure eq The horizontal stiffness K of the isolation layer can be used h replace.
[0083]
[0084] It has been proven that the stiffness is better than K h / K t When K changes from 0.001 to 0.02, eq / K h The variation range is 0.999-0.980; when K h / K t =0.0033, K eq / K h =0.997, it can be seen that K eq With K h Basically equal. So in K eq For quick estimation, K can be replaced h , and the simplified calculation can meet the calculation accuracy requirements.
[0085] If the seismic isolation bearings of the seismic isolation layer are arranged in combination with natural rubber seismic isolation bearings and lead rubber seismic isolation bearings, the horizontal stiffness K of each seismic isolation bearing can be calculated according to the above simplified calculation formula: h , according to the number ratio of seismic isolation supports, calculate the average equivalent stiffness K of the seismic isolation layer h The equivalent average stiffness K of the isolation layer using the sliding plate isolation bearings can also be estimated based on the ratio of the number of sliding plate isolation bearings. h .
[0086] Step 5: Calculate the damping ratio of the seismic isolation structure
[0087] Calculation of damping ratio of seismic isolation bearing:
[0088] For natural rubber isolation bearings, the damping ratio of the isolation bearings is 0; the damping ratio of G4 lead-zinc rubber isolation bearings under 250% shear deformation is about 10%, and the damping ratio under 100% shear deformation is about 23%. When estimating, the damping ratio under 250% shear deformation can be considered as 10%.
[0089] For the high damping ratio seismic isolation rubber bearing (HDR), the damping ratio under 250% shear deformation is 10%, and the damping ratio under 100% shear deformation is 18%.
[0090] Considering the damage to the upper structure under rare earthquakes, that is, after using seismic isolation, the damage is generally about 0.5%-2%, as well as the initial damping ratio of the structure. For concrete structures (initial damping ratio ζ5%), if all are G4 lead-zinc rubber seismic isolation bearings, the structural damping ratio ζ under rare earthquakes is about 15%, for structures using natural rubber seismic isolation bearings, the structural damping ratio ζ is about 5%, and for structures using high damping ratio seismic isolation rubber seismic isolation bearings, the structural damping ratio ζ is about 15%.
[0091] Step 6: Calculate the period of the seismically isolated structure
[0092] The following formula is used to calculate the structural period T:
[0093]
[0094] The mass and stiffness of the entire building are determined by the equivalent stiffness K corresponding to each isolation support. eq and the corresponding mass m; since the isolation bearings are controlled by the horizontal force and deformation of rare earthquakes, the diameters of the isolation bearings do not differ much, so they can be averaged when estimating, and the calculation can be done based on a single isolation bearing and the mass of a single isolation bearing.
[0095] According to the previous analysis assumptions, the seismic isolation structure can be equivalent to a single-degree-of-freedom seismic isolation model of the seismic isolation support. According to the equivalent stiffness and the corresponding structural mass, the structural period can be quickly estimated.
[0096]
[0097] It can be seen from this calculation result that no matter whether it is a shear wall, frame-shear wall structure, frame structure or steel frame structure, the target period is basically the same for structures with the same seismic isolation bearings and basically the same superstructure weight.
[0098] Step 7: End calculation
[0099] The periodic results of the seismic isolation structure are obtained and the calculation is completed, providing data for the subsequent selection calculation of seismic isolation bearings.
[0100] Preferably, by changing the diameter D of the seismic isolation support, different seismic isolation support horizontal stiffness K can be quickly obtained. h , which enables fast iteration of the calculation of the horizontal stiffness of the isolation bearing.
[0101] The calculation method of this embodiment is illustrated below by a specific calculation example:
[0102] Step 1: Estimate the load on a single isolation bearing
[0103] Take a middle school project in Sichuan as an example. The middle school is a key defense type, with 3 floors above ground and no basement. The building area is 3,000m 2 The building height is 12.30m (from outdoor ground to the top of the main roof panel), the first floor height is 4.2m, the second floor height is 3.9m, the third floor height is 4.0m, and the main column grid dimensions are 10.8m×9.1m, 10.8m×7.8m, and 10.8m×3.8m. According to the State Council of the People's Republic of China's "Regulations on Seismic Management of Construction Projects", seismic isolation technology should be adopted, and according to the regulations of Sichuan Province, this project adopts seismic isolation technology.
[0104] like Figure 3 and Figure 4 As shown, according to the structural layout, the main structure adopts a reinforced concrete frame structure. The floor is in the form of primary and secondary beams. A seismic isolation support is set under each load-bearing column 1, and there are 26 seismic isolation supports in total.
[0105] Because seismic isolation requires adding seismic isolation layers, the actual seismic isolation structure area is:
[0106] S=2983 / 3+2983=3977m 2
[0107] Total mass of building structure:
[0108] M = 3977 × 1.65 = 6562t
[0109] The mass of each isolation bearing
[0110] m=M / n=6562 / 26=252.4t
[0111] Step 2: Initial estimate of the diameter of the isolation bearing
[0112] The compressive stress limit σ of Class B lead-zinc rubber isolation bearings is required by the specification to be:
[0113] σ=12N / mm 2
[0114] Estimate the vertical pressure efficiency μ of the isolation bearing:
[0115] The outer ring isolation bearing 1 accounts for about 2 / 3, and the inner ring isolation bearing 2 accounts for about 1 / 3. Considering that the efficiency of the outer ring isolation bearing 1 is about 0.7, the average efficiency of the isolation bearing is:
[0116] μ=(2×0.7+1) / 3=0.8
[0117] Initial estimated diameter of the isolation bearing:
[0118]
[0119] Step 3: Simplify the calculation of the horizontal stiffness of the isolation bearing
[0120] The project initially considered using G4 lead-zinc rubber seismic isolation bearings 2 as the seismic isolation bearings.
[0121] When calculating, the value of k2=1.19 is taken as the value of all lead-zinc rubber isolation bearings. The horizontal stiffness of the isolation bearings is:
[0122] K h =k2k1k0(0.0016D-0.06)
[0123] =1.19×(0.0016×572.7-0.06)
[0124] =1.019kN / m
[0125] Step 4: End calculation
[0126] Compared with the prior art, the simplified calculation method of this embodiment is simple to calculate the selection of the seismic isolation bearing, takes less time, and greatly improves the work efficiency of the designer; by changing the diameter D of the seismic isolation bearing, different horizontal stiffness K of the seismic isolation bearing can be quickly obtained. h , which enables fast iteration of the calculation of the horizontal stiffness of the isolation bearing.
[0127] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.
Claims
1. A simplified calculation method for the horizontal stiffness of a seismic isolation bearing, characterized in that: The horizontal stiffness K of the seismic isolation support h The simplified formula is: K h =k2k1k0(aD-b);K h Unit: kN / mm; Where k0 is the shear modulus adjustment coefficient of the isolation bearing; k1 is the secondary shape coefficient adjustment coefficient; k2 is the lead rubber isolation bearing adjustment coefficient; a is the diameter adjustment coefficient; b is a constant; The secondary shape coefficient is S2.
2. A simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1, characterized in that: The diameter adjustment coefficient a ranges from 0.001 to 0.
002.
3. A simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1, characterized in that: The value range of the constant b is 0.01-0.
1.
4. A simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1, characterized in that: The diameter adjustment coefficient a is 0.0015, 0.0016 or 0.0017; the constant b is 0.05, 0.06 or 0.
07.
5. The simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1 is characterized in that: For a G4 rubber seismic isolation bearing with a secondary shape coefficient S2=5, the seismic isolation bearing shear modulus adjustment coefficient K0=1.
6. A simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1, characterized in that: For a G5 rubber seismic isolation bearing with a secondary shape coefficient S2=5, the seismic isolation bearing shear modulus adjustment coefficient K0=1.
25.
7. The simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1 is characterized in that: For the high damping ratio rubber seismic isolation bearing, the seismic isolation bearing shear modulus adjustment coefficient K0=2.
4.
8. The simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1 is characterized in that: The value of the secondary shape coefficient adjustment coefficient k1 is:
9. A simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1, characterized in that: For the G4 lead rubber isolation bearing, the lead rubber isolation bearing adjustment coefficient k2=1.
19.
10. A simplified calculation method for horizontal stiffness of a seismic isolation bearing according to claim 1, characterized in that: For the G5 lead rubber isolation bearing, the lead rubber isolation bearing adjustment coefficient k2=1.15.