A method for calculating the ultimate displacement of a friction pendulum bearing under earthquake action

Abstract

The present application belongs to the field of bridge support and anti-seismic technology, and particularly relates to a limit displacement calculation method of a friction pendulum bearing under earthquake action. Based on the deformation capacity potential of the friction pendulum bearing under earthquake action, the present application proposes to allow part of the polytetrafluoroethylene pad to slide out of the concave spherical surface, but control it from causing obvious plastic damage, and establishes a limit displacement concept under earthquake action, which can truly represent the deformation performance of the friction pendulum seismic mitigation bearing under earthquake action. The present application establishes a related calculation analytical expression of the limit displacement of the friction pendulum seismic mitigation bearing under earthquake action through theoretical derivation, which has clear physical meaning and is simple and easy to operate. Compared with the design displacement capacity of the friction pendulum seismic mitigation bearing under normal use state, the limit displacement capacity under earthquake action can be improved by 50% to 150%.

Description

Technical Field

[0001] This invention belongs to the field of bridge bearing and seismic technology, and specifically relates to a method for calculating the ultimate displacement of a friction pendulum bearing under seismic action. Background Technology

[0002] Bridges are crucial nodes in transportation systems, and improving the seismic performance of bridge structures plays a vital role in enhancing the seismic resilience of transportation networks. Numerous studies have shown that employing appropriate seismic isolation and damping designs is an effective method for improving bridge seismic performance. Friction pendulum seismic isolation bearings are a high-performance and widely used type of seismic isolation bearing. They utilize the frictional force of the bearing's spherical sliding surface to create damping energy dissipation, while simultaneously using the centripetal restoring force of the spherical sliding surface to reduce the bearing's displacement response.

[0003] To ensure the mobility of the friction pendulum seismic isolation bearing under normal operating conditions and to improve the wear resistance of the bearing pads, the concave spherical surfaces of the upper and lower bearing plates are generally covered with stainless steel, forming a sliding surface with a low coefficient of friction with the PTFE bearing pads of the middle bearing plate. Under normal operating conditions, to prevent excessive compressive stress on the PTFE bearing pads, the PTFE bearing pads should always maintain complete contact with the stainless steel surfaces of the upper and lower bearing plates. Therefore, the maximum design displacement of the bearing is the displacement at which the bearing pads are about to slide out of the concave spherical surface. Existing research shows that after the friction pendulum seismic isolation bearing undergoes deformation exceeding its design displacement capacity, it will not immediately disengage; on the contrary, it still has a large capacity for continued deformation. Especially for large-tonnage friction pendulum seismic isolation bearings, the disengagement displacement can generally reach more than twice the original design displacement capacity of the bearing.

[0004] Earthquakes are accidental events; although their intensity is high, their duration is short. If, under strong earthquakes, some PTFE gaskets briefly slip out of their concave surfaces, as long as the PTFE gaskets do not suffer significant plastic damage due to increased stress, the bearing's full load-bearing capacity and function after the earthquake are still met. Therefore, using the same value as under normal operating conditions for the friction pendulum's displacement reduction and isolation capacity under earthquake loading is clearly too conservative. The displacement at which some PTFE gaskets slip out of their concave surfaces without significant plastic damage can be considered the bearing's ultimate displacement capacity under earthquake loading. However, currently, there is no established method, either domestically or internationally, for calculating the ultimate displacement capacity of friction pendulum seismic isolation bearings corresponding to earthquake loading.

[0005] Based on the above reasons, this invention proposes a method for calculating the ultimate displacement of a friction pendulum seismic isolation bearing under seismic action, establishes a control standard that allows part of the polytetrafluoroethylene gasket to slide out of the concave spherical surface without causing significant plastic damage, and derives the calculation formula for the ultimate displacement capacity corresponding to this state. Summary of the Invention

[0006] The purpose of this invention is to overcome the technical defects in the prior art, where determining the ultimate displacement of a friction pendulum under seismic loading by using the displacement reduction and isolation capacity of the friction pendulum under normal use is too conservative and does not conform to reality. This invention provides a method for calculating the ultimate displacement of a friction pendulum under seismic loading.

[0007] This invention provides a method for calculating the ultimate displacement of a friction pendulum support under seismic loading, comprising the following steps:

[0008] Step 1: Determine parameters R1 and R2 based on the design parameters of the target friction pendulum bearing vibration reduction and isolation system; where R1 represents the radius of the horizontal projection of the concave spherical surface of the bearing plate; and R2 represents the radius of the horizontal projection of the polytetrafluoroethylene bearing pad embedded in the middle bearing plate.

[0009] Step 2: Establish S and Δ D The relationship is as follows: S represents the remaining contact area between the PTFE gasket and the support plate after the PTFE gasket slides out of the support plate; Δ D The displacement increment S of the PTFE gasket sliding out of the concave spherical surface is related to Δ. D Negative correlation;

[0010] Step 3: Define the maximum displacement D of the PTFE gasket that slides out of the support plate without significant plastic damage. E ,

[0011] D E =D+Δ D，max ;

[0012] Where D represents the design displacement of the support under normal service conditions; Δ D，max This represents the maximum displacement increment of the PTFE gasket without causing significant plastic damage.

[0013] D E D represents the ultimate displacement of the friction pendulum isolation bearing under seismic loading; E =D+Δ D，max .

[0014] In the technical solution of this invention, based on the deformation potential of the friction pendulum bearing under seismic loading, the concept of "allowing part of the PTFE gasket to slide out of the concave spherical surface, but controlling it to prevent significant plastic damage" is proposed. Based on this viewpoint, the concept of limit displacement under seismic loading is established, and the formula is derived. This determination method allows the limit displacement to accurately characterize the deformation performance of the friction pendulum seismic isolation bearing under seismic loading. In the technical solution of this invention, the relevant analytical expression for calculating the limit displacement of the friction pendulum seismic isolation bearing under seismic loading is established through theoretical derivation, with clear physical meaning and simple operation.

[0015] No significant plastic damage means that within this displacement increment D, the PTFE material will not undergo significant permanent deformation or plastic deformation, thus avoiding any impact on its frictional properties, sealing function, or service life. The PTFE gasket should remain within its elastic or recoverable deformation range; residual plastic strain should not exceed 0.2%.

[0016] Preferably, in step 1 of this invention, the design parameters of the target friction pendulum support seismic isolation system include: the design vertical bearing capacity F of the support. c The design displacement D of the support and the design compressive stress σ of the support pad under normal service conditions. c .

[0017] Preferably, the friction pendulum vibration damping and isolation bearing of the present invention includes an upper support plate and a lower support plate, with a middle support plate between the upper support plate and the lower support plate, and a first polytetrafluoroethylene (PTFE) support gasket disposed between the upper support plate and the middle support plate; a second PTFE support gasket is disposed between the lower support plate and the middle support plate.

[0018] Preferably, Δ D The value range is 0-2R².

[0019] Preferably, R1 and R2 are determined according to the following formula:

[0020]

[0021] R1 = R2 + 0.5D (Equation 2)

[0022] More preferably, the support pad is made of polytetrafluoroethylene.

[0023] Preferably, the upper support plate has a first concave spherical surface on the side near the middle support plate, and the lower support plate has a second concave spherical surface on the side near the middle support plate. The horizontal projection radius of the first and second concave spherical surfaces is R1; the horizontal projection radius of the first or second polytetrafluoroethylene (PTFE) support pad is R2; and the horizontal projection of the first PTFE support pad is concentric with the horizontal projection of the first concave spherical surface.

[0024] Preferably, in this invention, D is defined. E To allow some PTFE gaskets to slide out of the concave spherical surface under seismic loading, but to control the occurrence of significant plastic damage, the friction pendulum reduces the ultimate displacement of the seismic isolation bearing.

[0025] Preferably, the formula for calculating the remaining contact area S in this invention is:

[0026]

[0027] Where α and β represent the interior angles of the triangle formed between the remaining contact area of ​​the support pad after it slides out of the support plate and the original center position.

[0028] Preferably, in this invention, the minimum contact area for the support gasket to avoid significant plastic damage is defined as S. min The maximum allowable compressive stress at which the bearing pad slides out of the spherical bearing plate without causing significant plastic damage is defined as σ. max The relationship between the two is:

[0029]

[0030] σ max / σ c The value is 1.5-2; S is determined according to the above formula. min .

[0031] More preferably,

[0032] c = Δ D +R1-R2 Equation 3

[0033]

[0034] Where c represents the straight-line distance between the center of the horizontal projection of the support pad and the center of the horizontal projection of the support plate after the support pad slides out of the support plate, which is obtained by interpolation.

[0035] Determine Δ D，max .

[0036] Preferably, for any Δ within the range (0, 2R²), D The value of the corresponding variable S can be calculated sequentially according to the above formula, and the variable S changes with Δ D As the value of variable S increases, it decreases; when the value of variable S reaches its minimum value, S... min When equation (7) is satisfied, that is, when Δ is satisfied D The maximum value Δ D,max Furthermore, the ultimate displacement D of the friction pendulum seismic isolation bearing under seismic action can be obtained according to (Equation 8). E .

[0037] The limit displacement calculation method of this invention is used in bridge bearing design to determine the dimensions of the bearing plate. Parameters such as the bearing capacity of the friction pendulum bearing, its displacement capacity under normal operating conditions, the allowable compressive stress of the PTFE gasket, and the allowable compressive stress without significant plastic damage can all be varied.

[0038] The concave spherical surfaces of the upper and lower support plates can be variable curvature surfaces or surfaces of different shapes.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] This invention, based on the deformation potential of friction pendulum bearings under seismic loading, proposes allowing a portion of the PTFE gasket to slide out of the concave spherical surface while controlling it to prevent significant plastic damage. This establishes the concept of ultimate displacement under seismic loading, accurately characterizing the deformation performance of friction pendulum seismic isolation bearings. The invention theoretically derives analytical expressions for the ultimate displacement of friction pendulum seismic isolation bearings under seismic loading, with clear physical meaning and simple operation. Compared to the design displacement capacity of friction pendulum seismic isolation bearings under normal use, the ultimate displacement capacity under seismic loading can be increased by 50% to 150%. (See attached figures.)

[0041] Figure 1 This is a structural schematic diagram of a friction pendulum seismic isolation bearing.

[0042] Figure 2 Figure showing the ultimate displacement analysis of the friction pendulum seismic isolation bearing structure under seismic loading.

[0043] Figure 3 A schematic diagram illustrating the process of the bearing pad sliding out of the bearing plate;

[0044] Figure 4 This is a graph showing the relationship between the sliding displacement of the PTFE bearing gasket and the change in the remaining contact area.

[0045] In the diagram, 1-upper support plate, 11-projection of the first concave spherical surface, 2-lower support plate.

[0046] 3-Middle support plate, 4-First concave spherical surface, 5-PTFE support pad, 51-Horizontal projection of support pad, 52-Horizontal projection of support pad after sliding out. Detailed Implementation

[0047] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0048] Unless otherwise specified, the use of terms such as "upper," "lower," "left," "right," "center," "inner," and "outer" to indicate orientation or positional relationships in the description of specific embodiments of the present invention is based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationship in which the product / equipment / device is typically placed during use. These terms are merely for the purpose of facilitating the description of the present invention or simplifying the description in specific embodiments, enabling those skilled in the art to quickly understand the solution, and do not indicate or imply that a particular device / component / element must have a specific orientation, or be constructed and operated in a specific positional relationship. Therefore, they should not be construed as limitations on the present invention.

[0049] Furthermore, the use of terms such as "horizontal," "vertical," "suspended," and "parallel" does not imply that the corresponding device / component / element must be absolutely horizontal, vertical, suspended, or parallel, but rather that it can be slightly tilted or have a deviation. For example, "horizontal" merely means that its direction is more horizontal relative to "vertical," not that the structure must be completely horizontal, but that it can be slightly tilted. Alternatively, it can be simplified to mean that the corresponding device / component / element, when set in a "horizontal," "vertical," "suspended," or "parallel" direction, can have an error / deviation of ±10% relative to the corresponding direction, more preferably within ±8%, more preferably within ±6%, more preferably within ±5%, and more preferably within ±4%. As long as the corresponding device / component / element is within the error / deviation range, it can still achieve its function in the present invention.

[0050] Furthermore, the use of terms such as "first," "second," and "third" in terminology is merely for distinguishing descriptions of identical or similar components and should not be interpreted as emphasizing or implying the relative importance of a particular component.

[0051] Furthermore, in the description of the embodiments of the present invention, "several", "more than", and "a number of" represent at least two. The number can be any number, such as two, three, four, five, six, seven, eight, or nine, and can even exceed nine.

[0052] Furthermore, in the description of the technical solution of this invention, unless otherwise explicitly specified / limited / restricted, the terms "set up," "install," "connect," "link," "provided with," "laid out," and "arranged" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to common connection methods in the art, such as welding, riveting, bolting, and threaded connections. Such connections can be mechanical, electrical, or communication connections; they can be direct connections or indirect connections through an intermediate medium; and they can refer to the internal communication between two components.

[0053] Example 1

[0054] This embodiment provides a method for calculating the ultimate displacement of a friction pendulum support under seismic loading, using a 32m span standard box girder simply supported beam of a double-track high-speed railway in a seismic zone of 9 degrees as an example.

[0055] Step 1: Determine parameters R1 and R2 based on the design parameters of the target friction pendulum bearing vibration reduction and isolation system; where R1 represents the radius of the horizontal projection of the concave spherical surface of the bearing plate; and R2 represents the radius of the horizontal projection of the polytetrafluoroethylene bearing pad embedded in the middle bearing plate.

[0056] The main beams, in phases one and two, have a total dead load of 1356 tons and utilize a friction pendulum bearing seismic isolation system. Figure 1 The diagram shown is a structural schematic of a friction pendulum support; the support is designed to withstand a vertical bearing capacity F. c Take 5000kN;

[0057] The ultimate displacement is determined based on a simplified bridge bearing system. The bridge bearing includes an upper bearing plate 1, a middle bearing plate 3, and a lower bearing plate 2. A first bearing pad is provided between the upper bearing plate 1 and the middle bearing plate 3, and a second bearing pad is provided between the lower bearing plate and the middle bearing plate. Both the first bearing pad and the second bearing pad are polytetrafluoroethylene (PTFE) bearing pads 5.

[0058] The horizontal projection 51 of the support pad is concentrically set with the projection 11 of the first concave spherical surface 4.

[0059] The design displacement capacity of the support under normal operating conditions is D, which is ±200mm in this embodiment;

[0060] Design compressive stress σ of bearing pad c In this embodiment, the value σ is taken as... c =40MPa;

[0061] Based on the above values ​​and combining with Equation 1-2, we get:

[0062]

[0063] R1=R2+0.5D=200+0.5×200=300(mm)

[0064] Where R1 represents the radius of the horizontal projection of the concave spherical surface of the support plate; R2 represents the radius of the horizontal projection of the support pad embedded in the middle support plate.

[0065] like Figure 2 The diagram shown is a simplified horizontal projection of the friction pendulum support; the dashed line represents the original position of the support pad, the solid line represents the horizontal projection 52 of the support pad after sliding out, and the shaded area represents the remaining contact area of ​​the support pad after sliding out of the support plate.

[0066] Step 2: Establish S and Δ D The relationship is as follows: S represents the remaining contact area between the PTFE gasket and the support plate after the PTFE gasket slides out of the support plate; Δ D The displacement increment S of the PTFE gasket sliding out of the concave spherical surface is related to Δ. D Negative correlation; such as Figure 4 As shown.

[0067] For each Δ D ∈(0, 400), 0-400 represents the process of the bearing pad and bearing plate being tangent from the inside to the outside.

[0068] according to

[0069] Calculate the remaining contact area S of the corresponding PTFE bearing pad, specifically, where α and β represent the interior angles of the triangle formed between the remaining contact area of ​​the bearing pad after sliding out of the bearing plate and the original center position. For example... Figure 2 As shown.

[0070] like Figure 3 As shown. It can be seen that, with Δ D As the value increases, the remaining contact area S continuously decreases.

[0071] c = Δ D +R1-R2 Equation 3

[0072]

[0073] Where c represents the straight-line distance between the center of the horizontal projection of the support pad and the center of the horizontal projection of the support plate after the support pad slides out of the support plate, which is obtained by interpolation.

[0074] Δ D，max .

[0075] Step 3: Define the maximum displacement D of the PTFE gasket that slides out of the support plate without significant plastic damage. E ,

[0076] D E =D+Δ D，max Formula 8

[0077] Where D represents the design displacement of the support under normal service conditions; Δ D，max This represents the maximum displacement increment of the PTFE gasket without causing significant plastic damage.

[0078] The minimum contact area for a bearing gasket to avoid significant plastic damage is defined as S. min The maximum allowable compressive stress at which the bearing pad slides out of the spherical bearing plate without causing significant plastic damage is defined as σ.max The relationship between the two is:

[0079]

[0080] σ max / σ c The value is 1.5-2; depending on the material of the bearing gasket, polytetrafluoroethylene is usually selected, therefore,

[0081] Take σ max =1.5σ c =60 MPa, then we can calculate:

[0082] More specifically, the corresponding Δ is obtained through interpolation. D，max =126mm, then the ultimate displacement of the support under earthquake:

[0083] D E =D+Δ D，max =326 (mm)

[0084] It is evident that by allowing some PTFE gaskets to slide out of the concave spherical surface, while controlling the PTFE gaskets to prevent significant plastic damage, the ultimate displacement capacity of the friction pendulum seismic isolation bearing under seismic loading can be increased by up to 64% compared to the bearing displacement capacity under normal use.

[0085] In a preferred embodiment of the present invention, the above-described limit displacement calculation method is used for bridge bearing design to determine the dimensions of the bearing plate. More specifically, parameters such as the bearing capacity of the friction pendulum bearing, its displacement capacity under normal operating conditions, the allowable compressive stress of the PTFE gasket, and the allowable compressive stress without significant plastic damage can all vary.

[0086] In a further preferred embodiment, the concave spherical surfaces of the upper support plate and the lower support plate can be variable curvature surfaces, or the upper support plate and the lower support plate can be surfaces of different shapes.

[0087] In a further preferred embodiment, the support pad can be made of other polymer materials in the form of a sliding plate.

[0088] This invention, based on the deformation potential of friction pendulum bearings under seismic loading, proposes allowing partial slippage of the PTFE gasket out of the concave spherical surface while controlling it to prevent significant plastic damage. It establishes the concept of ultimate displacement under seismic loading, which can realistically characterize the deformation performance of friction pendulum seismic isolation bearings under seismic loading. This invention establishes analytical expressions for calculating the ultimate displacement of friction pendulum seismic isolation bearings under seismic loading through theoretical derivation, with clear physical meaning and simple operation. Compared to the design displacement capacity of friction pendulum seismic isolation bearings under normal use, the ultimate displacement capacity under seismic loading can be increased by 50% to 150%.

[0089] The above description of the embodiments is not intended to limit the scope of the present invention. Therefore, the scope of protection of the present invention is not limited to the above embodiments. Any modifications and improvements made based on the concept of the present invention that are merely formal and not substantive, as long as they involve allowing a portion of the PTFE bearing pad to slide out of the concave spherical surface, considering the randomness and transience of seismic action, increasing the maximum allowable compressive stress of the PTFE bearing pad, controlling the PTFE from undergoing significant plastic damage, proposing the limit displacement capacity of the friction pendulum seismic isolation bearing under seismic action, and establishing a similar analytical expression based on the geometric relationship of the bearing, should all be considered to fall within the scope of protection of the present invention.

Claims

1. A method for calculating the ultimate displacement of a friction pendulum support under seismic loading, characterized in that, The steps include the following: Step 1: Determine the parameters based on the design parameters of the target friction pendulum bearing seismic isolation system. , ;in, The radius of the horizontal projection of the concave spherical surface of the support plate; The radius of the horizontal projection of the PTFE bearing gasket embedded in the middle bearing plate; Step 2, establish S and The relationship is as follows: S represents the remaining contact area between the PTFE gasket and the support plate after the PTFE gasket slides out of the support plate. S is the displacement increment of the PTFE gasket as it slides out of the concave spherical surface. Negative correlation; Step 3: Define the maximum displacement of the PTFE gasket that slides out of the support plate without significant plastic damage as the ultimate displacement. D E , Formula 8; Where D represents the design displacement of the support under normal service conditions; This represents the maximum displacement increment of the PTFE gasket without causing significant plastic damage. The minimum contact area for a bearing gasket to avoid significant plastic damage is defined as S. min The maximum allowable compressive stress at which the bearing pad slides out of the spherical bearing plate without causing significant plastic damage is defined as σ. max The relationship between the two is: Formula 7; Given 1.5-2, determine S according to Equation 7. min ;σ c This indicates the design compressive stress of the bearing pad; The formula for calculating the remaining contact area S is: Formula 6; in, and These represent the interior angles of the triangle formed between the remaining contact area of ​​the support pad after it slides out of the support plate and the original center position; Based on step 2 combined with S min Sure .

2. The method for calculating the ultimate displacement of a friction pendulum support under seismic loading according to claim 1, characterized in that, In step 1, the design parameters of the target friction pendulum support seismic isolation system include: the design vertical bearing capacity of the support. Design displacement of supports under normal operating conditions Design compressive stress of support pads .

3. The method for calculating the ultimate displacement of a friction pendulum support under seismic loading according to claim 2, characterized in that, The value range is 0-2. R 2.

4. The method for calculating the ultimate displacement of a friction pendulum support under seismic loading according to claim 2, characterized in that, , Determined according to the following formula: Formula 1 Formula 2.

5. The method for calculating the ultimate displacement of a friction pendulum support under seismic loading according to claim 1, characterized in that, The calculation methods include the following relationships: Formula 3 Formula 4 Formula 5 Where c represents the straight-line distance between the center of the horizontal projection of the support pad and the center of the horizontal projection of the support plate after the support pad slides out of the support plate. The maximum value is obtained by interpolation. .

6. The method for calculating the ultimate displacement of a friction pendulum support under seismic loading according to claim 1, characterized in that, The support pad is made of polytetrafluoroethylene.

7. The method for calculating the ultimate displacement of a friction pendulum support under seismic loading according to claim 1, characterized in that, The ultimate displacement is determined based on a simplified bridge bearing system. The bridge bearing includes an upper bearing plate, a middle bearing plate, and a lower bearing plate. A first bearing pad is provided between the upper bearing plate and the middle bearing plate, and a second bearing pad is provided between the lower bearing plate and the middle bearing plate. The horizontal projection of the first bearing pad is concentric with the horizontal projection of the upper bearing plate.

8. The method for calculating the ultimate displacement of a friction pendulum bearing under seismic loading according to any one of claims 1-7, wherein the calculation method is used for the design of friction pendulum bearings to design and determine the dimensions of the bearing plate.

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