A seismic design method for bridges using friction pendulum bearings

Abstract

The present application relates to a seismic design method for bridges using friction pendulum bearings, which includes the following steps: obtaining the basic parameters for bridge seismic calculation; determining the additional temperature displacement at the friction pendulum bearings arranged on the bridge based on the basic parameters; determining the calculation parameters of the friction pendulum bearings according to the additional temperature displacement; establishing a dynamic equation based on the basic parameters and the calculation parameters, and solving to obtain the seismic response results. The present invention provides a seismic design method for bridges using friction pendulum bearings. Since the temperature effect will cause longitudinal additional temperature displacement at the friction pendulum bearings on the bridge, and this longitudinal additional temperature displacement has the characteristic of asynchrony, the present invention takes into account the influence of this effect on the friction pendulum bearings in seismic design, making the seismic design using friction pendulum bearings more accurate and more in line with engineering practice, improving the refinement and accuracy of bridge seismic design, as well as the reliability of the structural seismic design method.

Description

Technical Field

[0001] This application relates to the technical field of bridge engineering, and particularly relates to a bridge seismic design method using friction pendulum bearings. Background Art

[0002] With the rapid development of China's transportation industry, the construction of long-span continuous girder bridges has developed rapidly. For long-span bridges, such as a steel bridge with a length of 1000m, when the temperature changes by 10 degrees, the length of the bridge will change by 100mm. Therefore, the influence of temperature action is very significant, and the temperature deformations at different positions of the bridge are also inconsistent, with obvious asynchrony.

[0003] Existing bridge seismic design methods using friction pendulum bearings are all designed at the temperature zero point. Due to the lack of consideration of the deformation asynchrony caused by temperature action, the calculation assumptions of existing methods do not conform to the actual situation, the calculation results are inaccurate, and it may underestimate the seismic response of the bridge structure, thus resulting in insufficient structural safety reserves, endangering the operation safety of the bridge and the lives and property safety of the people. It may also overestimate the seismic response of the bridge structure, thus causing waste. Summary of the Invention

[0004] The embodiments of this application provide a bridge seismic design method using friction pendulum bearings to solve the technical problems in the related art that the bridge seismic design method does not consider temperature asynchrony, resulting in inaccurate calculation results and inaccurate seismic response results.

[0005] The embodiments of this application provide a bridge seismic design method using friction pendulum bearings. The seismic design method includes the following steps:

[0006] Obtain the basic parameters for bridge seismic calculation;

[0007] Based on the basic parameters, determine the temperature additional displacement at the friction pendulum bearings arranged on the bridge;

[0008] Determine the calculation parameters of the friction pendulum bearings according to the temperature additional displacement;

[0009] Establish a dynamic equation based on the basic parameters and the calculation parameters, and solve to obtain the seismic response result.

[0010] In some embodiments, the basic parameters at least include: the bridge finite element model, the temperature data required for bridge design, the design parameters of the friction pendulum bearings, and the seismic ground motion parameters of the bridge site area.

[0011] In some embodiments, multiple friction pendulum bearings are longitudinally arranged on the bridge. Based on the basic parameters, determine the temperature additional displacements D at different friction pendulum bearings x,i(i = 1, 2, …, n), where n is the number of piers provided with friction pendulum bearings.

[0012] In some embodiments, the calculation parameters at least include: the post-yield stiffness K2, and the calculation formula for the post-yield stiffness K2 is:

[0013]

[0014] where i = 1, 2, …, n, n is the number of piers provided with friction pendulum bearings, W is the vertical reaction force of the friction pendulum bearing under the action of dead load, and R is the equivalent curvature radius of the friction pendulum bearing.

[0015] In some embodiments, the calculation parameters at least include the pre-yield stiffness K1, and the calculation formula for the pre-yield stiffness K1 is:

[0016]

[0017] F i = K 2,i × D x,i ;

[0018]

[0019] where W is the vertical reaction force of the friction pendulum bearing under the action of dead load, μ is the sliding friction coefficient of the friction pendulum bearing, D y is the initial sliding displacement of the friction pendulum bearing, F is the restoring force of the bearing caused by the temperature additional displacement; sign(D x,i ) is the sign function, is the direction vector of the temperature additional displacement, is the direction vector of the ground motion input.

[0020] In some embodiments, the calculation parameters at least include the equivalent stiffness K eff , and the calculation formula for the equivalent stiffness K eff is:

[0021]

[0022] where W is the vertical reaction force of the friction pendulum bearing under the action of dead load, R is the equivalent curvature radius of the friction pendulum bearing, μ is the sliding friction coefficient of the friction pendulum bearing, and D d is the designed horizontal displacement of the friction pendulum bearing.

[0023] In some embodiments, the calculation parameters at least include the equivalent damping ratio ξ eff , and the calculation formula for the equivalent damping ratio ξ eff is:

[0024]

[0025] where μ is the sliding friction coefficient of the friction pendulum bearing, D d is the designed horizontal displacement of the friction pendulum bearing, and R is the equivalent radius of curvature of the friction pendulum bearing.

[0026] In some embodiments, establishing the dynamic equation based on the basic parameters and the calculation parameters and solving to obtain the seismic response result includes:

[0027] Establishing a dynamic equation based on the basic parameters and the calculation parameters;

[0028] Performing a solution calculation according to the dynamic equation;

[0029] Setting the parameter convergence condition ε and controlling the calculation result according to the parameter convergence condition ε;

[0030] If the parameter convergence condition ε is satisfied, the calculation ends and the seismic response result is obtained;

[0031] If the parameter convergence condition ε is not satisfied, iterate multiple times until the parameter convergence condition ε is satisfied.

[0032] In some embodiments, the dynamic equation is:

[0033] Mx″(t)+Cx′(t)+Kx(t)+F d =F(t);

[0034] where M is the mass matrix, C is the damping matrix, K is the stiffness matrix, F(t) is the external input dynamic load, i.e., the seismic input, and F d is the external force generated by the external boundary condition, and x(t) is the state of the structure at time t.

[0035] In some embodiments, setting the parameter convergence condition ε and controlling the calculation result according to the parameter convergence condition ε includes:

[0036] Setting the parameter convergence condition ε,

[0037] where D zz,i is the seismic displacement of the structure at the bearing, and D d is the designed horizontal displacement of the friction pendulum bearing;

[0038] If the parameter convergence condition ε is satisfied, the calculation ends and the seismic response result is obtained. The seismic response result at least includes the seismic calculated internal force F s {} of the structure, the seismic beam end displacement D be of the structure, the seismic displacement D zz,i of the structure at the bearing, and the longitudinal moment at the bottom of the pier;

[0039] If the parameter convergence condition ε is not satisfied, the structural seismic support displacement obtained from the current calculation is used to replace the design horizontal displacement D of the friction pendulum bearing d , and the calculation parameters of the friction pendulum bearing are recalculated until the parameter convergence condition ε is satisfied.

[0040] The beneficial effects brought by the technical solution provided by this application include:

[0041] This application provides a seismic design method for bridges using friction pendulum bearings. Since temperature effects will cause longitudinal temperature additional displacements at the friction pendulum bearings on the bridge, and this longitudinal temperature additional displacement has the characteristic of asynchrony, the embodiments of this application consider the influence of temperature asynchrony effects on the friction pendulum bearings in seismic design, making the seismic design using friction pendulum bearings more accurate and more in line with engineering practice, improving the refinement and accuracy of bridge seismic design, as well as the reliability of the structural seismic design method. Description of the Drawings

[0042] In order to more clearly illustrate the technical solutions in the embodiments of this application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of this application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0043] Figure 1 It is a flowchart of the steps of the seismic design method for bridges using friction pendulum bearings in an embodiment of the present invention.

[0044] Figure 2 It is an elevation layout diagram of a bridge in an embodiment of the present invention.

[0045] Figure 3 It is a schematic diagram of the seismic motion parameters in the bridge site area of a bridge in an embodiment of the present invention.

[0046] Figure 4 It is a schematic diagram of the temperature additional displacement in an embodiment of the present invention.

[0047] Reference Signs:

[0048] 1, main beam; 2, bridge pier; 3, fixed bearing; 4, friction pendulum bearing; 5, expansion bearing. Detailed Embodiments

[0049] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the following will clearly and completely describe the technical solutions in the embodiments of this application with reference to the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are some, but not all, of the embodiments of this application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in this application without creative efforts fall within the scope of protection of this application.

[0050] See Figure 1 as shown Figure 1 This is a flowchart of the steps of a bridge seismic design method using a friction pendulum bearing in an embodiment of the present invention.

[0051] The embodiments of this application provide a bridge seismic design method using a friction pendulum bearing. The seismic design method includes the following steps:

[0052] Step S1: Obtain the basic parameters for bridge seismic calculation;

[0053] Step S2: Based on the basic parameters, determine the temperature additional displacement at the friction pendulum bearing arranged on the bridge;

[0054] Step S3: Determine the calculation parameters of the friction pendulum bearing according to the temperature additional displacement;

[0055] Step S4: Establish a dynamic equation based on the basic parameters and calculation parameters, and solve to obtain the seismic response result.

[0056] The embodiments of this application provide a bridge seismic design method using a friction pendulum bearing. Since the temperature effect will cause a longitudinal temperature additional displacement at the friction pendulum bearing on the bridge, and this longitudinal temperature additional displacement has the characteristic of asynchrony, the embodiments of this application consider the influence of the temperature asynchrony effect on the friction pendulum bearing in seismic design, making the seismic design using the friction pendulum bearing more accurate and more in line with engineering practice, improving the refinement and accuracy of bridge seismic design and the reliability of the structural seismic design method.

[0057] In some embodiments, the basic parameters in step S1 at least include: the bridge finite element model, the temperature data required for bridge design, the design parameters of the friction pendulum bearing, and the seismic ground motion parameters in the bridge site area.

[0058] The basic parameters are used for bridge seismic calculation. Of course, the basic parameters may not be limited to the above parameters and may also include other parameters for seismic calculation.

[0059] In some embodiments, in step S2, when multiple friction pendulum bearings are longitudinally arranged on the bridge, the temperature additional displacements D at different friction pendulum bearings are determined based on the basic parameters x,i(i = 1, 2, …, n), where n is the number of bridge piers provided with friction pendulum bearings. Since the temperature - induced additional displacements of different friction pendulum bearings are different, determining the temperature - induced additional displacements at different friction pendulum bearings respectively and then performing calculations further improves the accuracy of seismic design.

[0060] The temperature - induced additional displacement refers to the numerical value of the displacement influence caused by temperature at the bridge friction pendulum bearing, and the temperature - induced additional displacement is determined based on the bridge finite - element model and the temperature data required by the bridge design.

[0061] In some embodiments, in step S3, the calculation parameters at least include: the post - yield stiffness K2, and the calculation formula for the post - yield stiffness K2 is:

[0062]

[0063] where i = 1, 2, …, n, n is the number of bridge piers provided with friction pendulum bearings, W is the vertical reaction force of the friction pendulum bearing under the action of dead load, and R is the equivalent radius of curvature of the friction pendulum bearing.

[0064] In some embodiments, in step S3, the calculation parameters at least include the pre - yield stiffness K1, and the calculation formula for the pre - yield stiffness K1 is:

[0065]

[0066] F i =K 2，i ×D x，i ;

[0067]

[0068] where W is the vertical reaction force of the friction pendulum bearing under the action of dead load, μ is the sliding friction coefficient of the friction pendulum bearing, D y is the initial sliding displacement of the friction pendulum bearing, which is determined by the characteristics of the friction pendulum bearing, F is the restoring force of the bearing caused by the temperature - induced additional displacement; sign(D x,i ) is the sign function, is the direction vector of the temperature - induced additional displacement, is the direction vector of the seismic motion input.

[0069] In some embodiments, in step S3, the calculation parameters at least include the equivalent stiffness K eff ,equivalent stiffness K eff The calculation formula for is:

[0070]

[0071] where W is the vertical reaction force of the friction pendulum bearing under the action of dead load, R is the equivalent radius of curvature of the friction pendulum bearing, μ is the sliding friction coefficient of the friction pendulum bearing, Dd Design the horizontal displacement for the friction pendulum bearing. The horizontal displacement designed for the friction pendulum bearing is an unknown quantity, and an initial value can be assumed based on engineering experience or similar projects.

[0072] In some embodiments, in step S3, the calculation parameters at least include the equivalent damping ratio ξ eff , the equivalent damping ratio ξ eff The calculation formula for is:

[0073]

[0074] where μ is the sliding friction coefficient of the friction pendulum bearing, D d is the horizontal displacement designed for the friction pendulum bearing, and R is the equivalent curvature radius of the friction pendulum bearing.

[0075] The calculation parameters of the friction pendulum bearing provided by the embodiments of the present application include the post-yield stiffness K2, the pre-yield stiffness K1, the equivalent stiffness K eff , the equivalent damping ratio ξ eff , and each parameter is corrected according to the temperature additional displacement, which is more accurate and more in line with the engineering practice when solving the dynamic equation subsequently.

[0076] In some embodiments, in step S4, establish a dynamic equation based on the basic parameters and the calculation parameters, and the obtained seismic response results include:

[0077] Establish a dynamic equation based on the basic parameters and the calculation parameters;

[0078] Perform a solution calculation according to the dynamic equation;

[0079] Set the parameter convergence condition ε, and control the calculation results according to the parameter convergence condition ε;

[0080] If the parameter convergence condition ε is satisfied, the calculation ends and the seismic response results are obtained;

[0081] If the parameter convergence condition ε is not satisfied, iterate multiple times until the parameter convergence condition ε is satisfied.

[0082] Establish a dynamic equation based on the basic parameters and the calculation parameters, such as based on the bridge finite element model and the seismic ground motion parameters in the bridge site area in the basic parameters, such as based on the post-yield stiffness K2, the pre-yield stiffness K1, and the equivalent stiffness K in the calculation parameters eff , the equivalent damping ratio ξ eff Establish a dynamic equation and use it for solution calculation.

[0083] In some embodiments, the dynamic equation is:

[0084] Mx″(t)+Cx′(t)+Kx(t)+F d =F(t);

[0085] Among them, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, F(t) is the dynamic load input from the outside, that is, the ground motion input, and F d is the external force generated by the external boundary condition, and x(t) is the state of the structure at time t.

[0086] In some embodiments, a parameter convergence condition ε is set, and controlling the calculation result according to the parameter convergence condition ε includes:

[0087] Set the parameter convergence condition ε,

[0088] Among them, D zz,i is the seismic displacement of the structure's bearing, and D d is the designed horizontal displacement of the friction pendulum bearing;

[0089] If the parameter convergence condition ε is satisfied, the calculation ends and the seismic response result is obtained. The seismic response result includes at least the internal force F s {} of the structure's seismic calculation, the beam-end displacement D be of the structure's earthquake, the seismic displacement D zz,i of the structure's bearing, and the longitudinal moment at the bottom of the pier;

[0090] If the parameter convergence condition ε is not satisfied, then the seismic displacement of the structure obtained from the current calculation is used to replace the designed horizontal displacement D d of the friction pendulum bearing, and the calculation parameters of the friction pendulum bearing are recalculated until the parameter convergence condition ε is satisfied.

[0091] The parameter convergence condition ε can be formulated according to the actual situation.

[0092] As Figure 2 shown, Figure 2 is the elevation layout diagram of the bridge in an embodiment of the present invention.

[0093] Taking a 9-span continuous steel truss continuous beam bridge as an example, this steel truss continuous beam bridge includes two parts: the main girder 1 and the piers 2. There are 10 piers 2, numbered from W1 to W10 respectively. A fixed bearing 3 is arranged between the main girder 1 and the pier 2 of No. W5; a movable bearing 5 is arranged between the main girder 1 and the piers 2 of No. W1 / No. W10, a total of 2; a friction pendulum bearing 4 is arranged between the main girder 1 and the piers 2 of No. W2-W4 / No. W6-W9, a total of 7.

[0094] The span layout of this steel truss continuous beam bridge is (124 + 132 + 132 + 168 + 300 + 168 + 132 + 132 + 124) m, and the total length of the whole bridge is 1412 m.

[0095] The seismic design method of a bridge using friction pendulum bearings includes the following steps:

[0096] Step S1: Obtain the basic parameters for bridge seismic calculation.

[0097] Specifically, establish a full-bridge finite element model of the bridge, determine the bridge temperature data, and determine the ground motion parameters. Since the longitudinal length of the bridge is 1412 m, the sliding friction coefficient μ of the friction pendulum bearing is selected as 0.03, the equivalent curvature radius R of the bearing is 9.0 m, and the ground motion parameters are as Figure 3 shown.

[0098] Step S2: Based on the basic parameters, determine the temperature additional displacement at the friction pendulum bearings arranged on the bridge.

[0099] Specifically, set the heating condition and cooling condition according to the engineering practice, and determine the temperature additional displacement D x,i (i = 1, 2, …, n) at different friction pendulum bearings based on the basic parameters in Step S1, where n is the number of piers with friction pendulum bearings arranged. As Figure 4 shown.

[0100] Step S3: Determine the calculation parameters of the friction pendulum bearings according to the temperature additional displacement.

[0101] Specifically, according to the above temperature additional displacement D x,i , and after taking the envelope of it, the calculation parameters of the friction pendulum bearings considering temperature asynchronism can be determined. The calculation parameters of the friction pendulum bearings mainly include: the post-yield stiffness K2, the pre-yield stiffness K1, the equivalent stiffness K eff , the equivalent damping ratio ξ eff . The calculation parameters of each bearing at each pier are shown in Table 1. At the same time, the calculation parameters of the friction pendulum bearings without considering temperature asynchronism are also listed in Table 1.

[0102] Table 1 Calculation parameters of each bearing at each pier

[0103]

[0104] In Table 1, among the calculation parameters of each bearing considering temperature asynchronism, the value outside the parentheses is the calculation value when the direction vector of the temperature additional displacement is the same as that of the ground motion parameter, and the value inside the parentheses is the calculation value when the direction vector of the temperature additional displacement is opposite to that of the ground motion parameter.

[0105] Among them, according to relevant engineering experience, assume that the designed horizontal displacement D d of the bearing is 20 cm.

[0106] Step S4: Establish a dynamic equation based on the basic parameters and calculation parameters, and solve to obtain the seismic response results.

[0107] Specifically, according to the finite element model of the bridge and based on the above calculation parameters, the dynamic equation is solved. The parameter convergence condition is set to 0.1 according to engineering experience. After multiple iterations, the designed horizontal displacement D of the bearing is finally determined. d = 30 cm.

[0108] Under the above-mentioned designed horizontal displacement D of the bearing d condition, when considering the temperature asynchrony, the seismic response results of each bearing at the critical positions of the bridge, i.e., at each pier, are shown in Table 2. At the same time, the seismic response results without considering the temperature asynchrony are also listed in Table 2.

[0109] Table 2 Seismic response results of each bearing at each pier

[0110]

[0111] It can be seen from Table 2 that the temperature asynchrony will significantly affect the initial state of the friction pendulum bearings, resulting in the out-of-synchronization of each friction pendulum bearing under seismic loads, an increase in the overall seismic internal force response of the structure, and a decrease in the bearing displacement. Taking Pier 2 of W8 as an example, the maximum longitudinal moment of the pier can increase by 16%. From Pier 2 of W2 to Pier 9 of W, the bearing displacement decreases within 12% - 15%.

[0112] Thus, it can be seen that for the long-span continuous beam bridge with friction pendulum bearings, after considering the influence of temperature asynchrony, the seismic design of the bridge can be more refined and accurate, further ensuring the safety of the structure and avoiding unnecessary waste.

[0113] In the description of the present application, it should be noted that the orientation or positional relationship indicated by terms such as "upper" and "lower" is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present application and simplifying the description, rather than indicating or implying that the method or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus cannot be construed as a limitation to the present application. Unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, "connected" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and 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 application can be understood according to specific circumstances.

[0114] It should be noted that in this application, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or also includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising the element.

[0115] The above are only specific embodiments of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application will not be limited to these embodiments shown herein, but rather will conform to the broadest scope consistent with the principles and novel features claimed herein.

Claims

1. A seismic design method for bridges using friction pendulum bearings, characterized in that, The aseismic design method includes the following steps: Obtain the basic parameters for bridge aseismic calculation; A plurality of friction pendulum bearings are longitudinally arranged on the bridge, and based on the basic parameters, the temperature additional displacements at different friction pendulum bearings are respectively determined , , where n is the number of bridge piers provided with friction pendulum bearings; Determine the calculation parameters of the friction pendulum bearing according to the temperature additional displacement, and the calculation parameters include: the post-yield stiffness K2, and the calculation formula of the post-yield stiffness K2 is: ； Among them, , is the number of piers with friction pendulum bearings set, W is the vertical reaction force of the friction pendulum bearing under the action of dead load, and R is the equivalent curvature radius of the friction pendulum bearing; The calculation parameters further include the pre-yield stiffness K1, and the calculation formula of the pre-yield stiffness K1 is: ； ； ； Among them, \(W\) is the vertical reaction force of the friction pendulum bearing under the action of dead load, is the sliding friction coefficient of the friction pendulum bearing, \(D\) y is the initial sliding displacement of the friction pendulum bearing, is the restoring force of the bearing caused by the additional temperature displacement; \(\text{sign}(D\) x,i ) is the sign function, is the direction vector of the additional temperature displacement, is the direction vector of the earthquake ground motion input; Establish a dynamic equation based on the basic parameters and the calculation parameters, and solve to obtain the seismic response result.

2. The aseismic design method for a bridge using a friction pendulum bearing according to claim 1, characterized in that, The basic parameters at least include: the bridge finite element model, the temperature data required for bridge design, the design parameters of the friction pendulum bearing, and the seismic ground motion parameters in the bridge site area.

3. A seismic design method for bridges using friction pendulum bearings as claimed in claim 1, characterized in that, The calculation parameter also includes an equivalent stiffness K eff , and the equivalent stiffness K eff has the following calculation formula: ； Among them, W is the vertical reaction force of the friction pendulum bearing under the action of dead load, R is the equivalent radius of curvature of the friction pendulum bearing, μ is the sliding friction coefficient of the friction pendulum bearing, and D d is the designed horizontal displacement of the friction pendulum bearing.

4. The aseismic design method of a bridge adopting a friction pendulum bearing according to claim 1, characterized in that The calculation parameter further includes an equivalent damping ratio ξ eff , the equivalent damping ratio ξ eff has the following calculation formula: ； where μ is the sliding friction coefficient of the friction pendulum bearing, and D d is the designed horizontal displacement of the friction pendulum bearing, and is the equivalent radius of curvature of the friction pendulum bearing.

5. The aseismic design method for bridges using friction pendulum bearings as claimed in claim 4, characterized in that, The establishing a dynamic equation based on the basic parameters and the calculation parameters and solving to obtain the seismic response result includes: Establish a dynamic equation based on the basic parameters and the calculation parameters; Conduct a solution calculation according to the dynamic equation; Set the parameter convergence condition ɛ, and control the calculation result according to the parameter convergence condition ; If the parameter convergence condition ɛ is satisfied, the calculation ends and the seismic response result is obtained; If the parameter convergence condition ɛ is not satisfied, iterate multiple times until the parameter convergence condition ɛ is satisfied.

6. A bridge seismic design method using a friction pendulum bearing as described in claim 5, characterized in that, The dynamic equation is: ； where M is the mass matrix, is the damping matrix, is the stiffness matrix, is the dynamic load input from the outside, that is, the seismic input, and F d is the external force generated by the external boundary conditions, and x(t) is the state of the structure at time t.

7. The aseismic design method for a bridge using a friction pendulum bearing according to claim 5, characterized in that The set parameter convergence condition ɛ controls the calculation results according to the parameter convergence condition including: Set the convergence condition ɛ of the parameters, ; Among them, D zz,i is the structural seismic displacement of the bearing, and D d is the designed horizontal displacement of the friction pendulum bearing; If the parameter convergence condition ɛ is satisfied, the calculation ends and the seismic response results are obtained, and the seismic response results at least include the internal forces of the structure calculated by the earthquake , the seismic beam-end displacement of the structure , the seismic seat displacement of the structure , and the longitudinal moment at the pier bottom; If the parameter convergence condition ɛ is not satisfied, the structural seismic support displacement obtained from the current calculation is used to replace the design horizontal displacement of the friction pendulum bearing , and the calculation parameters of the friction pendulum bearing are recalculated until the parameter convergence condition ɛ is satisfied.

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