A design method of seismic isolation bearing based on pier damping rate

Abstract

The application relates to a design method of a seismic mitigation support based on a pier damping rate, comprising the following steps: determining a basic seismic system of a bridge; obtaining the internal force response of a pier bottom when the seismic mitigation support is arranged based on the pier damping rate, so as to obtain a second shear force based on a shear damping rate and a second bending moment based on a bending moment damping rate; establishing a bridge seismic stress and a calculation model when the seismic mitigation support is arranged, and obtaining the internal force response of the pier bottom when the seismic mitigation support is arranged based on a dynamics equation, so as to obtain a third shear force and a third bending moment based on the parameters of the seismic mitigation support; and determining the parameters of the seismic mitigation support based on the principle that the second shear force is equal to the third shear force or the second bending moment is equal to the third bending moment. The application obtains the internal force response of the pier bottom when the seismic mitigation support is arranged based on the pier damping rate and the dynamics equation respectively, and constructs a relational expression between the pier damping rate and the parameters of the seismic mitigation support based on the principle that the internal force responses are equal, so that the parameters of the seismic mitigation support can be determined quickly and accurately.

Description

Technical Field

[0001] This invention relates to the field of bridge seismic design, specifically to a method for designing seismic isolation bearings based on the pier damping rate. Background Technology

[0002] Seismic isolation bearings are the main energy-dissipating components of seismic isolation bridges. They primarily achieve the purpose of dissipating seismic energy and reducing the seismic response of the structure by extending the natural period of vibration and increasing damping. In the early stages of bridge design, when studying the rationality of the bridge's seismic resistance scheme, complex finite element analysis software is often relied upon. Based on the basic parameters that the seismic isolation bearings need to meet, the actual resistance of the bridge substructure is determined, and thus the safety of the bridge substructure is assessed. This process often requires a certain amount of iterative work and repeated communication with the seismic isolation bearing manufacturer to determine whether the seismic isolation bearings can be manufactured and implemented.

[0003] However, in related technologies, relying on finite element software leads to complex calculation processes and large computational loads, and it is also difficult to accurately determine the dynamic parameters of the seismic isolation bearings, such as the equivalent sphere center distance of the bearing sliding surface. The equivalent sphere center distance directly affects the mechanical properties and vibration reduction effect of the seismic isolation bearings. Summary of the Invention

[0004] This application provides a design method for seismic isolation bearings based on the pier damping rate, which solves the technical problems in related technologies that rely on finite element software, resulting in complex calculation processes, large computational loads, and difficulty in accurately determining the dynamic parameters of seismic isolation bearings.

[0005] This application provides a method for designing seismic isolation bearings based on the pier damping ratio, including:

[0006] The basic seismic resistance system of the bridge is determined; the bridge includes a main girder, piers, and seismic isolation bearings installed between the main girder and the piers;

[0007] The internal force response at the bottom of the pier is obtained based on the pier damping ratio when the seismic isolation bearing is installed. The pier damping ratio includes the shear damping ratio η. Q and bending moment damping ratio η M To obtain the shear damping ratio η Q The second shear force Q, based on the bending moment damping ratio η M The second bending moment M;

[0008] A seismic stress and calculation model of the bridge with the seismic isolation bearings installed is established. The internal force response of the pier bottom when the seismic isolation bearings are installed is obtained based on the dynamic equations, so as to obtain the third shear force Q' and the third bending moment M' based on the parameters of the seismic isolation bearings.

[0009] The parameters of the seismic isolation bearing are determined based on the principle that the second shear force Q is equal to the third shear force Q' or the second bending moment M is equal to the third bending moment M'.

[0010] In one embodiment, the internal force response at the bottom of the pier is obtained based on the pier damping ratio when the seismic isolation bearing is installed. The pier damping ratio includes the shear damping ratio η. Q and bending moment damping ratio η M To obtain the shear damping ratio η Q The second shear force Q, based on the bending moment damping ratio η M The second bending moment M includes:

[0011] Based on the basic seismic resistance system of the bridge without the aforementioned seismic isolation bearings, the internal force response at the bottom of the pier is obtained to obtain the first shear force Q0 and the first bending moment M0 at the bottom of the pier.

[0012] Based on the shear damping rate η of the bridge pier damping rate Q Obtain the internal force response at the bottom of the pier when the seismic isolation bearing is installed, so as to obtain the shear damping ratio η. Q The second shear force Q;

[0013] The calculation formula is: Q=(1-η Q Q0;

[0014] Based on the bending moment damping ratio η in the bridge pier damping ratio M Obtain the internal force response at the bottom of the pier when the seismic isolation bearing is installed, so as to obtain the vibration reduction ratio η based on the bending moment. M The second bending moment M;

[0015] The calculation formula is: M = (1 - η) M )M0.

[0016] In one embodiment, the step of obtaining the internal force response at the bottom of the pier based on the basic seismic resistance system of the bridge without the isolation bearings, to obtain the first shear force Q0 and the first bending moment M0 at the bottom of the pier, includes:

[0017] Based on the aforementioned basic seismic resistance system for bridges, a pier coordinate system is established for the bridge piers when the aforementioned seismic isolation bearings are not installed.

[0018] Based on the aforementioned pier coordinate system, the structural vibration mode function in the direction of seismic stress is obtained as follows:

[0019]

[0020] The frequency ω3 of the bridge pier is obtained from the structural vibration mode function as follows:

[0021]

[0022] Calculate the first shear force Q0 at the bottom of the bridge pier;

[0023] The calculation formula is:

[0024] Calculate the first bending moment M0 at the bottom of the bridge pier;

[0025] The calculation formula is:

[0026] coefficient

[0027] Where, m b It is the mass of the bridge pier, m a L is the mass of the main beam; L is the height of the pier; T is the mass of the main beam. g K represents the characteristic period in the frequency domain parameters of seismic load. h denoted as the horizontal peak ground acceleration coefficient of the fundamental ground motion in the frequency domain parameters of the seismic load, where g is the gravitational acceleration.

[0028] In one embodiment, establishing a bridge seismic stress and calculation model when the seismic isolation bearing is installed, and obtaining the internal force response at the bottom of the pier when the seismic isolation bearing is installed based on the dynamic equation, so as to obtain the third shear force Q' and the third bending moment M' based on the parameters of the seismic isolation bearing, includes:

[0029] Based on the aforementioned basic bridge seismic resistance system, a bridge seismic stress and calculation model are established when the aforementioned seismic isolation bearings are installed.

[0030] Obtain the basic parameters of the bridge seismic calculation model;

[0031] Establish the dynamic equation of the seismic calculation model and solve for the displacement amplitude X1 of the main beam, wherein the displacement amplitude X1 includes the parameters of the seismic isolation bearing;

[0032] The internal force response at the bottom of the pier when the seismic isolation bearing is installed is calculated based on the displacement amplitude X1 of the main beam to obtain the third shear force Q' and the third bending moment M' based on the parameters of the seismic isolation bearing.

[0033] The calculation formulas are: Q′=k1X1;M′=Q′L0;

[0034] Where k1 is the equivalent stiffness of the pier; L0 is the equivalent pier height.

[0035] In one embodiment, establishing the seismic stress and calculation model of the bridge includes:

[0036] A seismic stress model of the bridge is established, with the main beam as the superstructure and the piers as the substructure.

[0037] The main beam and the pier are simplified as concentrated loads;

[0038] The seismic isolation bearing is simplified to equivalent stiffness k2 and equivalent damping c2;

[0039] A seismic calculation model for the bridge is established, which is a damped system with two degrees of freedom.

[0040] In one embodiment, simplifying the main beam and the pier into concentrated loads includes:

[0041] Mass m a The main beam is simplified to a first concentrated load with an equivalent mass of m2;

[0042] Mass m b The pier with stiffness EI is simplified to a second concentrated load, with equivalent mass m1, equivalent stiffness k1, and equivalent pier height L0.

[0043] In one implementation, establishing the dynamic equations of the seismic calculation model and solving for the displacement amplitude X1 of the main beam includes:

[0044] Based on the aforementioned seismic calculation model, the seismic load p0sinωt is applied to the pier location, and the motion differential equations of a damped system with two degrees of freedom are established.

[0045] The equation of motion is:

[0046]

[0047] The displacement amplitude X1 of the main beam is calculated based on the aforementioned differential equation of motion;

[0048] The calculation formula is:

[0049]

[0050] Where p0 and ω are the time-domain parameters of the seismic load; m1 is the equivalent mass of the pier; k1 is the equivalent stiffness of the pier; m2 is the equivalent mass of the main beam; k2 is the equivalent stiffness of the seismic isolation bearing; c2 is the equivalent damping of the seismic isolation bearing; W is the bearing reaction force under dead load; H is the equivalent center-to-center distance of the bearing sliding surface; D d is the horizontal displacement of the support design; μ is the dynamic friction coefficient of the support.

[0051] In one embodiment, determining the seismic isolation bearing parameters based on the principle that the second shear force Q is equal to the third shear force Q' or the second bending moment M is equal to the third bending moment M' includes:

[0052] When the pier is a short pier, the parameters of the seismic isolation bearing are determined based on the principle that the second shear force Q and the third shear force Q' are equal;

[0053] When the pier is a high pier, the parameters of the seismic isolation bearing are determined based on the principle that the second bending moment M and the third bending moment M' are equal.

[0054] In one embodiment, the seismic isolation bearing design method based on the pier damping rate further includes:

[0055] The geometric dimensions of the seismic isolation bearing are determined based on the parameters of the seismic isolation bearing.

[0056] In one embodiment, when the seismic isolation bearing parameters include the equivalent center-to-center distance H of the bearing sliding surface, determining the geometric dimensions of the seismic isolation bearing based on the seismic isolation bearing parameters includes:

[0057] The upper and lower spherical cap radii of the seismic isolation bearing are determined based on the equivalent spherical center distance H.

[0058] The calculation formula is:

[0059] H = R1 + R2 - ΔH;

[0060] Where R1 is the radius of the upper spherical cap of the seismic isolation bearing, R2 is the radius of the lower spherical cap of the seismic isolation bearing, and ΔH is the distance between the tops of the upper and lower spherical caps.

[0061] The beneficial effects of the technical solutions provided in this application include:

[0062] This application provides a method for designing seismic isolation bearings based on the pier damping ratio. According to the basic seismic resistance system of bridges, the internal force response at the pier base when seismic isolation bearings are installed is obtained based on the pier damping ratio and dynamic equations. Based on the principle of equal internal force responses, a relationship between the pier damping ratio and the parameters of the seismic isolation bearings is constructed, allowing for rapid and accurate determination of the bearing parameters and thus quickly completing the design of the seismic isolation bearings. This embodiment does not rely on complex finite element software, reducing the computational workload of the seismic isolation bearing parameters, resulting in shorter computation time and higher computational efficiency. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1This is a flowchart illustrating a seismic isolation bearing design method based on pier damping rate in one embodiment of the present invention.

[0065] Figure 2 This is a schematic diagram of the basic seismic resistance system for bridges in one embodiment of the present invention.

[0066] Figure 3 This is a schematic diagram of the basic seismic resistance system of a bridge without seismic isolation bearings in one embodiment of the present invention.

[0067] Figure 4 This is a schematic diagram of the seismic stress and calculation model of a bridge when seismic isolation bearings are installed in one embodiment of the present invention.

[0068] Figure 5 This is a schematic diagram of the equivalent center-to-center distance of the seismic isolation bearing in one embodiment of the present invention.

[0069] In the diagram: 1. Main beam; 2. Pier; 3. Seismic isolation bearing. Detailed Implementation

[0070] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0071] This application provides a method for designing seismic isolation bearings based on the pier damping rate, which can solve the technical problems in related technologies that rely on finite element software, resulting in complex calculation processes, large computational loads, and difficulty in accurately determining the dynamic parameters of seismic isolation bearings.

[0072] Reference Figure 1 and Figure 2 ,in, Figure 1 This is a flowchart illustrating a seismic isolation bearing design method based on pier damping rate in one embodiment of the present invention. Figure 2 This is a schematic diagram of the basic seismic resistance system for bridges in one embodiment of the present invention.

[0073] This embodiment provides a method for designing seismic isolation bearings based on the pier damping ratio, including the following steps:

[0074] Step S1: Determine the basic seismic resistance system of the bridge; the bridge includes the main girder 1, the pier 2, and the seismic isolation bearings 3 installed between the main girder 1 and the pier 2;

[0075] Step S2: Obtain the internal force response at the bottom of pier 2 when the seismic isolation bearing 3 is installed, based on the pier damping ratio. The pier damping ratio includes the shear damping ratio η. Q and bending moment damping ratio η M To obtain the damping ratio η based on shear force. Q The second shear force Q, based on the bending moment damping ratio η M The second bending moment M;

[0076] Step S3: Establish the bridge seismic stress and calculation model when the seismic isolation bearing 3 is installed, and obtain the internal force response of the bottom of pier 2 when the seismic isolation bearing 3 is installed based on the dynamic equation, so as to obtain the third shear force Q' and the third bending moment M' based on the parameters of the seismic isolation bearing 3.

[0077] Step S4: Determine the parameters of the seismic isolation support 3 based on the principle that the second shear force Q is equal to the third shear force Q' or the second bending moment M is equal to the third bending moment M'.

[0078] This embodiment provides a method for designing seismic isolation bearings based on the pier damping ratio. According to the basic seismic resistance system of bridges, the internal force response at the pier base when seismic isolation bearings are installed is obtained based on the pier damping ratio and dynamic equations. Using the principle of equal internal force responses, a relationship between the pier damping ratio and the parameters of the seismic isolation bearings is constructed, allowing for rapid and accurate determination of the bearing parameters and thus quickly completing the design of the seismic isolation bearings. This embodiment does not rely on complex finite element software, reducing the computational workload of the seismic isolation bearing parameters, resulting in shorter computation time and higher computational efficiency.

[0079] The following provides a detailed explanation of each step.

[0080] like Figure 2 As shown, mass m b There are multiple piers with stiffness EI, and the mass m a The main beam 1 is evenly spaced below each pier 2 and the main beam 1. A seismic isolation bearing 3 is installed between each pier 2 and the main beam 1. The seismic isolation bearing 3 is a friction pendulum bearing.

[0081] In one embodiment, step S2 involves obtaining the internal force response at the bottom of pier 2 when the seismic isolation bearing 3 is installed, based on the pier damping rate. The pier damping rate includes the shear damping rate η. Q and bending moment damping ratio η M To obtain the damping ratio η based on shear force. Q The second shear force Q, based on the bending moment damping ratio η M The second bending moment M includes:

[0082] Step S21: Based on the basic seismic system of the bridge without the installation of the seismic isolation bearing 3, obtain the internal force response at the bottom of the pier 2 at this time, so as to obtain the first shear force Q0 and the first bending moment M0 at the bottom of the pier 2.

[0083] like Figure 3 As shown, Figure 3 This is a schematic diagram of the basic seismic resistance system of a bridge without seismic isolation bearings in one embodiment of the present invention. Figure 3 (a) The basic seismic system of the bridge without seismic isolation bearings. Figure 3 (b) is the coordinate system of the pier body.

[0084] Specifically, based on the basic seismic resistance system of bridges, a pier coordinate system is established for the bridge piers without seismic isolation bearings; the mass of main girder 1 is ma; the stiffness of pier 2 is EI, and its mass is m. b =m(h)L.

[0085] Based on the pier coordinate system, the structural vibration mode function in the direction of seismic stress is obtained as follows:

[0086]

[0087] The frequency ω3 of the bridge pier is obtained from the structural mode function:

[0088]

[0089] Calculate the first shear force Q0 at the bottom of the bridge pier;

[0090] The calculation formula is:

[0091] Calculate the first bending moment M0 at the bottom of the bridge pier;

[0092] The calculation formula is:

[0093] coefficient

[0094] Where, m b It is the mass of the bridge pier, m a L is the mass of the main beam; L is the height of the pier; T is the mass of the main beam. g K represents the characteristic period in the frequency domain parameters of seismic load. h denoted as the horizontal peak ground acceleration coefficient of the fundamental ground motion in the frequency domain parameters of the seismic load, where g is the gravitational acceleration.

[0095] Step S22: Based on the shear damping ratio η in the pier damping ratio Q Obtain the internal force response at the bottom of pier 2 when seismic isolation bearing 3 is installed, in order to obtain the shear damping ratio η. Q The second shear force Q;

[0096] The calculation formula is:

[0097] Step S23: Based on the bending moment damping ratio η in the pier damping ratio MObtain the internal force response at the bottom of pier 2 when the seismic isolation bearing 3 is installed, so as to obtain the vibration reduction ratio η based on the bending moment. M The second bending moment M;

[0098] The calculation formula is:

[0099] In one embodiment, step S3, establishing a seismic stress and calculation model of the bridge with the seismic isolation bearing 3 installed, and obtaining the internal force response at the bottom of pier 2 with the seismic isolation bearing 3 installed based on the dynamic equation, to obtain the third shear force Q' and the third bending moment M' based on the parameters of the seismic isolation bearing 3, includes:

[0100] Step S31: Based on the basic system of bridge seismic resistance, establish a bridge seismic stress and calculation model when seismic isolation bearings are installed.

[0101] like Figure 4 As shown, Figure 4 This is a schematic diagram of a bridge seismic stress and calculation model according to an embodiment of the present invention. Wherein, Figure 4 (a) is the seismic stress model. Figure 4 (b) is the seismic calculation model, where x represents displacement.

[0102] A seismic stress model of the bridge was established, with the main beam 1 as the superstructure and the pier 2 as the substructure.

[0103] The main beam 1 and pier 2 are simplified as concentrated loads.

[0104] Specifically, simplifying the main beam 1 and pier 2 into concentrated loads includes:

[0105] Mass m a The main beam 1 is simplified to the first concentrated load, with an equivalent mass m2;

[0106] Mass m b The pier 2 with stiffness EI is simplified to the second concentrated load, with equivalent mass m1, equivalent stiffness k1, and equivalent pier height L0.

[0107] The seismic isolation bearing 3 is simplified to equivalent stiffness k2 and equivalent damping c2;

[0108] A seismic calculation model for the bridge is established, which is a damped system with two degrees of freedom.

[0109] Step S32: Obtain the basic parameters of the bridge seismic calculation model.

[0110] Specifically, the basic parameters include: the equivalent mass m2 of the main beam 1; the equivalent stiffness k2, natural frequency ω2, equivalent damping ratio ζ2, and equivalent damping c2 of the seismic isolation bearing 3; and the natural frequency ω1, equivalent height L0, equivalent stiffness k1, and equivalent mass m1 of the pier 2.

[0111] Wherein, the equivalent mass of main beam 1 is m2 = m a ;

[0112] Equivalent stiffness of seismic isolation bearing 3

[0113] W is the support reaction force under constant load; H is the equivalent distance between the centers of the spheres on the sliding surface of the support; D d It is the horizontal displacement of the support design; μ is the dynamic friction coefficient of the support, with a value between 0.02 and 0.05.

[0114] The equivalent center-to-center distance H of the sliding surface of the bearing refers to the distance between the upper and lower spherical caps of the spherical sliding mechanism in the seismic isolation bearing, also known as the center-to-center offset. This distance is very important in the design of seismic isolation bearings, as it affects the mechanical properties and vibration reduction effect of the bearings.

[0115] The distance between the center of the bearing and the spheres depends on the design parameters and damping requirements of the seismic isolation bearing. A larger distance between the center of the bearing and the spheres can improve the lateral stiffness and stability of the seismic isolation bearing, and reduce its deformation and sway in the vertical direction. A smaller distance between the center of the bearing and the spheres may allow the seismic isolation bearing to have a greater longitudinal deformation capacity, thus providing better damping effect.

[0116] The natural frequency of the seismic isolation bearing 3

[0117] The equivalent damping ratio of seismic isolation bearing 3

[0118] Equivalent damping of seismic isolation bearing 3

[0119] The natural frequency of pier 2

[0120] Equivalent height of pier 2 (constant cross-section pier)

[0121] Equivalent stiffness of pier 2 (constant cross-section pier)

[0122] Equivalent mass of pier 2 (constant cross-section pier)

[0123] Step S33: Establish the dynamic equation of the seismic calculation model and solve for the displacement amplitude X1 of the main beam 1. The displacement amplitude X1 includes the parameters of the seismic isolation support.

[0124] Specifically, based on the seismic calculation model, the seismic load p0sinωt is applied to the bridge pier m1 position, and the motion differential equation of the damped system with two degrees of freedom is established.

[0125] The differential equation of motion is:

[0126]

[0127] Where p0 and ω are the time-domain parameters of the seismic load;

[0128] The displacement amplitude X1 of the main beam 1 is calculated based on the equation of motion.

[0129] The calculation formula is:

[0130]

[0131] Where p0 and ω are time-domain parameters of seismic load.

[0132] In one embodiment, T in the frequency domain parameters of seismic load g K h The parameters p0 and ω in the time domain of seismic load are mutually converted through the conversion relationship between response spectrum and power spectrum.

[0133] Specifically, T g K h These are two parameters in the frequency domain (response spectrum) of the seismic load, and p0 and ω are two parameters in the time domain (power spectrum) of the seismic load. Given the known frequency domain parameters T of the seismic load... g K h When the response spectrum and power spectrum are converted, the response spectrum can be converted into the power spectrum, and then the time-domain parameters p0 and ω of the seismic load can be obtained, and vice versa.

[0134] Step S34: Solve the internal force response at the bottom of the pier when the seismic isolation bearing 3 is set according to the displacement amplitude X1 of the main beam 1, so as to obtain the third shear force Q' and the third bending moment M' based on the seismic isolation bearing parameters.

[0135] The calculation formula is:

[0136]

[0137]

[0138] Where k1 is the equivalent stiffness of the pier; L0 is the equivalent pier height.

[0139] Of course, in other embodiments, the displacement amplitude of pier 2 can also be calculated based on the equation of motion to calculate the third shear force Q'.

[0140] In one embodiment, step S4, determining the parameters of the seismic isolation support 3 based on the principle that the second shear force Q is equal to the third shear force Q' or the second bending moment M is equal to the third bending moment M', includes:

[0141] When pier 2 is a low pier, the structure is mainly subjected to shear failure. The parameters of the seismic isolation bearing 3 are determined based on the principle that the second shear force Q and the third shear force Q' are equal.

[0142] Specifically, Q=Q′;

[0143]

[0144]

[0145] Based on the above formula and in conjunction with actual engineering projects, the dynamic friction coefficient μ of the support is selected. Using mathematical and engineering calculation software such as Maple, the three parameters of the seismic isolation support, such as the equivalent sphere center distance H, are determined.

[0146] When pier 2 is a high pier, the structure is mainly prone to bending failure. The parameters of the seismic isolation bearing 3 are determined based on the principle that the second bending moment M and the third bending moment M' are equal.

[0147] Specifically, M = M′;

[0148]

[0149]

[0150] Based on the above formula and in conjunction with actual engineering projects, the dynamic friction coefficient μ of the support is selected. Using mathematical and engineering calculation software such as Maple, the three parameters of the seismic isolation support, such as the equivalent sphere center distance H, are determined.

[0151] In one embodiment, the seismic isolation bearing design method based on the pier damping rate further includes:

[0152] Step S5: Determine the geometric dimensions of the seismic isolation bearing 3 based on the parameters of the seismic isolation bearing 3.

[0153] Based on the parameters of the seismic isolation bearing 3 calculated using the above method, the geometric dimensions of the seismic isolation bearing 3 are further determined, thereby designing a seismic isolation bearing 3 that meets the requirements.

[0154] like Figure 5 As shown, in one embodiment, when the parameters of the seismic isolation bearing 3 include the equivalent sphere center distance H of the bearing sliding surface, determining the geometric dimensions of the seismic isolation bearing 3 based on the parameters of the seismic isolation bearing 3 includes:

[0155] The upper and lower spherical cap radii of the seismic isolation bearing 3 are determined based on the equivalent center-to-center distance H.

[0156] The calculation formula is:

[0157] H = R1 + R2 - ΔH;

[0158] Where R1 is the radius of the upper spherical cap of the seismic isolation bearing, R2 is the radius of the lower spherical cap of the seismic isolation bearing, and ΔH is the distance between the tops of the upper and lower spherical caps.

[0159] In practical engineering, if we take R1 = R2 and ΔH = 0.1H, then R1 = R2 = 0.55H.

[0160] It should be noted that the sequence numbers of the embodiments in this application are merely for descriptive purposes and do not represent the superiority or inferiority of the embodiments. The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not represent a sequential order, nor do they limit "first," "second," and "third" to different types.

[0161] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0162] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0163] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish the different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0164] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for designing seismic isolation bearings based on the pier damping rate, characterized in that, include: The basic seismic resistance system of the bridge is determined; the bridge includes a main beam (1), a pier (2), and a seismic isolation bearing (3) located between the main beam (1) and the pier (2). The internal force response at the bottom of the pier (2) when the seismic isolation bearing (3) is installed is obtained based on the pier damping rate. The pier damping rate includes the shear damping rate. and bending moment damping rate To obtain the damping rate based on the shear force. Second shear force Q Based on bending moment damping ratio The second bending moment M ; A seismic stress and calculation model of the bridge with the seismic isolation bearing (3) is established. Based on the dynamic equation, the internal force response of the bottom of the pier (2) with the seismic isolation bearing (3) is obtained to obtain the third shear force based on the parameters of the seismic isolation bearing (3). Q' and the third bending moment M' ; With the second shear force Q With the third shear force Q' Equal to or the second bending moment M With the third bending moment M' Based on the principle of equality, the parameters of the seismic isolation bearing (3) are determined; The internal force response at the bottom of the pier (2) when the seismic isolation bearing (3) is installed is obtained based on the pier damping rate. The pier damping rate includes the shear damping rate. and bending moment damping rate To obtain the damping rate based on the shear force. The second shear force Q, based on the bending moment damping ratio The second bending moment M includes: Based on the basic seismic resistance system of the bridge without the isolation bearing (3), the internal force response at the bottom of the pier (2) is obtained to obtain the first shear force at the bottom of the pier (2). Q 0. First bending moment M 0; Based on the shear damping rate of the bridge pier damping rate Obtain the internal force response at the bottom of the pier (2) when the seismic isolation bearing (3) is installed, so as to obtain the shear force damping rate. Second shear force Q ; The calculation formula is: ; Based on the bending moment damping rate in the pier damping ratio The internal force response at the bottom of the pier (2) when the vibration isolation bearing (3) is installed is obtained to obtain the vibration reduction rate based on the bending moment. The second bending moment M; The calculation formula is: ; The second shear force Q With the third shear force Q' Equal to or the second bending moment M With the third bending moment M' Based on the principle of equality, the parameters of the seismic isolation bearing (3) are determined as follows: When the pier (2) is a short pier, the second shear force is used. Q With the third shear force Q' Based on the principle of equality, the parameters of the seismic isolation bearing (3) are determined; When the pier (2) is a high pier, the second bending moment is used. M With the third bending moment M' Based on the principle of equality, the parameters of the seismic isolation bearing (3) are determined.

2. The seismic isolation bearing design method based on pier damping rate as described in claim 1, characterized in that, Based on the basic seismic resistance system of the bridge without the isolation bearing (3), the internal force response at the bottom of the pier (2) is obtained to obtain the first shear force at the bottom of the pier (2). Q 0. First bending moment M 0 includes: Based on the basic seismic resistance system of the bridge, the pier coordinate system of the bridge pier (2) is established when the seismic isolation bearing (3) is not installed; Based on the aforementioned pier coordinate system, the structural vibration mode function in the direction of seismic stress is obtained as follows: ； The frequency of the bridge pier (2) is obtained based on the structural vibration mode function. for: ； Calculate the first shear force at the bottom of the pier (2). Q 0; The calculation formula is: ; Calculate the first bending moment at the bottom of the pier (2). M 0; The calculation formula is: ; coefficient ; in, m b It's the quality of the bridge piers. m a It refers to the quality of the main beam; L It refers to the height of the bridge pier; T g The characteristic period in the frequency domain parameters of seismic load. K h The horizontal peak ground acceleration coefficient of the fundamental ground motion in the frequency domain parameters of seismic load. g This is the acceleration due to gravity.

3. The seismic isolation bearing design method based on pier damping rate as described in claim 1, characterized in that, The bridge seismic stress and calculation model is established when the seismic isolation bearing (3) is installed. Based on the dynamic equation, the internal force response of the pier bottom (2) when the seismic isolation bearing (3) is installed is obtained to obtain the third shear force based on the parameters of the seismic isolation bearing (3). Q' and the third bending moment M' include: Based on the aforementioned basic bridge seismic resistance system, a bridge seismic stress and calculation model is established when the aforementioned seismic isolation bearing (3) is installed; Obtain the basic parameters of the bridge seismic calculation model; Establish the dynamic equations of the seismic calculation model of the bridge and solve for the displacement amplitude of the main beam (1). X 1. The displacement amplitude X 1 includes the parameters of the aforementioned seismic isolation bearing (3); According to the displacement amplitude of the main beam (1) X 1. Solve for the internal force response at the bottom of the pier (2) when the seismic isolation bearing (3) is installed, so as to obtain the third shear force based on the parameters of the seismic isolation bearing (3). Q' and the third bending moment M' ; The calculation formula is: ; ; in, k 1 represents the equivalent stiffness of the bridge pier; L 0 is the equivalent pier height of the bridge pier.

4. The seismic isolation bearing design method based on pier damping rate as described in claim 3, characterized in that, The establishment of the seismic stress and calculation model of the bridge includes: A seismic stress model of the bridge is established, with the main beam (1) as the superstructure and the pier (2) as the substructure. The main beam (1) and the pier (2) are simplified as concentrated loads; The seismic isolation bearing (3) is simplified to an equivalent stiffness. k 2. Equivalent Damping c 2; A seismic calculation model for the bridge is established, which is a damped system with two degrees of freedom.

5. The seismic isolation bearing design method based on pier damping rate as described in claim 4, characterized in that, The simplification of the main beam (1) and the pier (2) into concentrated loads includes: quality m a The main beam (1) is simplified to the first concentrated load, with an equivalent mass m 2; quality m b Stiffness EI The bridge pier (2) is simplified to the second concentrated load, with an equivalent mass m 1. Equivalent stiffness k 1. Equivalent pier height L 0.

6. The seismic isolation bearing design method based on pier damping rate as described in claim 3, characterized in that, The dynamic equations of the seismic calculation model are established to solve for the displacement amplitude of the main beam (1). X 1 includes: Based on the aforementioned seismic calculation model, the seismic load... Acting on the position of the bridge pier (2), establish the motion differential equations of a damped system with two degrees of freedom; The equation of motion is: ； The displacement amplitude of the main beam (1) is calculated based on the aforementioned differential equation of motion. X 1; The calculation formula is: ; ； ； in, p 0、 These are the time-domain parameters of the seismic load. m 1 is the equivalent mass of the bridge pier; k 1 is the equivalent stiffness of the bridge pier; m 2 is the equivalent mass of the main beam; k 2 is the equivalent stiffness of the seismic isolation bearing; c 2 is the equivalent damping of the seismic isolation bearing; W It is the support reaction force under constant load; H It is the equivalent sphere center distance of the sliding surface of the support; D d It refers to the horizontal displacement of the support design; μ It is the coefficient of dynamic friction of the support.

7. The seismic isolation bearing design method based on pier damping rate as described in claim 1, characterized in that, The seismic isolation bearing design method based on the pier damping ratio also includes: The geometric dimensions of the seismic isolation bearing (3) are determined based on the parameters of the seismic isolation bearing (3).

8. The seismic isolation bearing design method based on pier damping rate as described in claim 7, characterized in that, The parameters of the seismic isolation bearing (3) include the equivalent center distance of the sphere on the sliding surface of the bearing. H When determining the geometric dimensions of the seismic isolation bearing (3) based on its parameters, the process includes: According to the equivalent sphere center distance H Determine the upper and lower spherical cap radii of the seismic isolation bearing; The calculation formula is: ； in, R 1 is the radius of the upper spherical cap of the seismic isolation bearing. R 2 is the radius of the lower spherical cap of the seismic isolation bearing. It is the distance between the tops of the upper and lower crowns.

Images