Elasto-plasticity block seismic design method for continuous beam bridge with different pier heights

Abstract

The present application relates to the technical field of bridge engineering, more particularly, to an elastic-plastic block seismic design method suitable for unequal pier height continuous girder bridges. The present application provides an elastic-plastic block seismic design method for unequal pier height continuous girder bridges. Only the known basic design parameters need to be obtained, and through the method, the required elastic-plastic block design parameters at each pier can be quickly and accurately obtained, without the need for complex and time-consuming nonlinear finite element modeling and parameter analysis, effectively reducing the irregularity of the seismic response of the unequal pier height continuous girder bridge. The seismic design method proposed by the present application is beneficial to improve the seismic design and reinforcement efficiency of the unequal pier height continuous girder bridge, and has a broad engineering application prospect. The present application solves the problem of lack of reasonable elastic-plastic block seismic design method suitable for unequal pier height continuous girder bridges in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge engineering, and more particularly to an elastic-plastic block seismic design method suitable for unequal-pier-height continuous girder bridges. BACKGROUND

[0002] Unequal-pier-height continuous girder bridges are one of the most widely used bridge types in mountainous areas to adapt to the undulating terrain. Figure 1 As shown. That is, a certain unequal-pier-height three-span continuous girder bridge is shown, and the heights of the piers are unequal. Unequal pier height will lead to uneven distribution of seismic forces at each pier, especially in the case of considering damage and destruction of concrete blocks and frictional sliding of unbound plate type rubber bearings, the irregular seismic response of unequal-pier-height continuous girder bridges is more significant, mainly manifested as: the main girder undergoes plane torsion, and some piers are damaged prematurely while other piers still have sufficient resistance. The irregular seismic response characteristics make the seismic performance of unequal-pier-height continuous girder bridges extremely unbalanced, and the seismic capacity is difficult to fully develop.

[0003] The inventor considers using elastic-plastic blocks instead of traditional concrete blocks and applying them to small and medium span beam bridges. The elastic-plastic blocks have many advantages such as adjustable stiffness and strength, strong energy dissipation, easy replacement, low cost, etc. By adjusting the design parameters of the elastic-plastic blocks, the stiffness and strength differences at unequal-height piers are reduced, and the seismic inertia forces of the main girder are reasonably distributed, making the irregular continuous girder bridge uniformly withstand seismic forces.

[0004] However, the current design and calculation of unequal-pier-height continuous girder bridges generally use nonlinear seismic response analysis based on complex elastic-plastic finite element models, so the parameter values of the elastic-plastic blocks that meet the target requirements generally need to be obtained through a large number of parameter analyses, which has large calculation workload and is prone to convergence difficulties in nonlinear seismic response calculation. That is, the existing design method is not conducive to the application of design personnel in actual engineering, and therefore needs to be solved. SUMMARY

[0005] Therefore, it is necessary to provide an elastic-plastic block seismic design method suitable for unequal-pier-height continuous girder bridges to solve the problem that there is no reasonable elastic-plastic block seismic design method suitable for unequal-pier-height continuous girder bridges in the prior art.

[0006] The present application adopts the following technical solutions:

[0007] The present application discloses an elastic-plastic block seismic design method suitable for unequal-pier-height continuous girder bridges, comprising the following steps:

[0008] S1, obtaining basic design parameters of a target bridge; wherein the target bridge is a continuous beam bridge with unequal pier heights, a plurality of unbonded slab rubber bearings and a plurality of elastic-plastic fender blocks are arranged at the pier abutments of the target bridge; the basic design parameters include: an upper structure mass M, a number of lower pier abutments m, a sum of sliding friction forces of bearings at a jth pier abutment F bf_ j , a critical sliding displacement of bearings at the jth pier abutment d by_ j , an allowable lateral thrust at the jth pier abutment F p_ j , a yield displacement at the jth pier abutment d py_ j , a horizontal shear stiffness at the jth pier abutment K b_ j ; j = 1, …, m;

[0009] S2, calculating a design strength of a fender block at an ith pier abutment F s_i , i = 1, …, m-1;

[0010] wherein F s_i = F p_i - F bf_i ;

[0011] calculating a design strength of a fender block at an mth pier abutment F s_m ;

[0012] wherein,

[0013] S3, estimating a design displacement of a main beam under a design seismic action as d g0 ;

[0014] assuming that the main beam moves uniformly in a horizontal direction and does not occur in-plane torsion, based on a bearing-fender block-pier abutment series-parallel system, according to d g0 calculating a yield strength of a fender block at a jth pier abutment F sy_ j , an initial elastic stiffness of the fender block k s_ j , a design displacement ductility coefficient of the fender block μ s_ j , a design displacement ductility coefficient of the bearing μ b_ j ;

[0015] S4, calculating an equivalent damping ratio coefficient ξ all of a whole bridge system according to the bearing-fender block-pier abutment series-parallel system;

[0016] S5, calculating a response spectrum damping adjustment coefficient R all according to ξ D , and adjusting a design seismic response spectrum according to R D ;

[0017] determining an adjusted main beam design displacement d g1 in the adjusted design seismic response spectrum according to an equivalent basic period T eff of the target bridge;

[0018] S6, determine d g0 With d g1 Check if the error is within the preset range; if yes, the current round of calculation meets the requirements and proceeds to S7; if not, the current round of calculation does not meet the requirements, return to S3, and set d... g1 Re-assume the design displacement d of the main beam g0 Continue with S3 to S6;

[0019] S7, from the current round of calculation, obtain the design parameters of the stop block at the j-th pier; where the design parameters include: F s_ j F sy_ j k j ;

[0020] Based on F s_ j F sy_ j k j Calculate the physical parameters of the stop block at the j-th pier.

[0021] This method for seismic design of elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights implements the method or process according to embodiments of this disclosure.

[0022] Compared with the prior art, the present invention has the following beneficial effects:

[0023] This invention provides a seismic design method for elasto-plastic abutments in continuous beam bridges with unequal pier heights. By simply obtaining the known basic design parameters, this method can quickly and accurately determine the required elasto-plastic abutment design parameters for each pier, eliminating the need for complex and time-consuming nonlinear finite element modeling and parameter analysis. This effectively reduces the irregularity of the seismic response of continuous beam bridges with unequal pier heights. The seismic design method proposed in this invention is beneficial for improving the efficiency of seismic design and reinforcement of continuous beam bridges with unequal pier heights and has broad engineering application prospects. Attached Figure Description

[0024] Figure 1 The following is a structural diagram of a three-span continuous beam bridge with unequal pier heights in the background art.

[0025] Figure 2 This is a flowchart of the seismic design method for elastoplastic blocks applicable to continuous beam bridges with unequal pier heights in Embodiment 1 of the present invention;

[0026] Figure 3 The acceleration response spectrum designed in Embodiment 2 of the present invention and the actual wave acceleration response spectrum that matches it;

[0027] Figure 4 This is an example of comparing the maximum displacement requirements of the main beam at each pier before and after design using the method of Example 1 in Example 2 of the present invention.

[0028] Figure 5 The maximum displacement ductility coefficient of the bridge pier before and after the design in Embodiment 2 of the present application is compared by using the method in Embodiment 1.

[0029] Figure 6 The main girder displacement time-history curves at the two side abutments before the design in Embodiment 2 of the present application are compared.

[0030] Figure 7 The main girder displacement time-history curves at the two side abutments after the design in Embodiment 2 of the present application are compared. DETAILED DESCRIPTION

[0031] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0032] It should be noted that when a component is referred to as being “mounted on” another component, it can be directly on the other component or there can be a middle component. When a component is referred to as being “disposed on” another component, it can be directly disposed on the other component or there can be a middle component. When a component is referred to as being “fixed on” another component, it can be directly fixed on the other component or there can be a middle component.

[0033] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs. The terminology used in the description of the present application herein only for the purpose of describing specific embodiments of the present application, and is not intended to limit the present application. The term “or / and” used herein includes any and all combinations of one or more related listed items.

[0034] Embodiment 1

[0035] Please refer to Figure 2 , Figure 2 The flow chart of the elastic-plastic block seismic design method suitable for the unequal-pier-height continuous girder bridge in the present application.

[0036] It should be emphasized that the design object of the method is located in the elastic-plastic block of the irregular continuous beam bridge. A span of the irregular continuous beam bridge contains several piers of unequal height. The pier (the subscript corresponds to p) includes the pier and the abutment. Several unbonded slab rubber bearings (referred to as bearings, the subscript corresponds to b) and several elastic-plastic blocks (referred to as blocks, the subscript corresponds to s) are arranged at the pier. For any pier, the bearing and the block form a bearing-block parallel system, and the bearing-block parallel system and the pier form a bearing-block-pier series system; the piers are also connected to form a pier parallel system; therefore, the whole can be regarded as a bearing-block-pier series-parallel system.

[0037] In general, the method is based on the principle of force couple balance and the principle of equivalent linear method, and the design strength of the block at each pier is obtained under the construction of the bearing-block-pier series-parallel system, so as to ensure that the main beam does not undergo excessive plane torsion due to the difference in pier height, and the seismic forces acting on each pier are balanced.

[0038] As shown in Figure 2 , the method comprises the following steps:

[0039] S1, obtaining the basic design parameters of the target bridge.

[0040] The target bridge is a continuous beam bridge with unequal pier heights, and several unbonded slab rubber bearings and several elastic-plastic blocks are arranged at the pier. The basic design parameters mainly include:

[0041] the mass of the superstructure M, the number of lower piers m, the sum of the sliding friction forces of the bearings at the jth pier F bf_ j , the critical sliding displacement of the bearings at the jth pier d by_ j , the allowable lateral thrust at the jth pier F p_ j , the yield displacement at the jth pier d py_ j , the horizontal shear stiffness at the jth pier K b_ j , the distance from the jth pier to the center of mass of the target bridge L j ; j = 1, …, m.

[0042] It should be noted that the above parameters can be obtained from the design manual of the target bridge.

[0043] More specifically,

[0044] 1. The mass of the superstructure M is the total mass of the main beam.

[0045] 2. The number of lower piers m is the total number of piers and abutments.

[0046] 3, For a pier or abutment, several bearings are set: allow the bearing to slip friction, then for a pier or abutment of any bearing, the sliding friction force is the vertical pressure of the bearing multiplied by the friction coefficient of the contact surface; again, the sliding friction force of all bearings at the pier or abutment is summed up, that is, the sum of the sliding friction force of the bearings at the pier or abutment is obtained.

[0047] It should be noted that the sum of the sliding friction force of the bearings at the jth pier or abutment F bf_ j , the design strength of the bearing F b_ j , the yield strength of the bearing F by_ j , the three values are equal.

[0048] 4, For a pier or abutment, the critical sliding displacement of the bearing is equal to the sum of the sliding friction force at this point divided by the horizontal shear stiffness of the bearing.

[0049] 5, For F p_ j , according to the jth pier or abutment, whether it is a pier or an abutment:

[0050] 5.1, if the jth pier or abutment is a pier, F p_ j Generally, 0.85 of the lateral yield strength of the pier is taken;

[0051] 5.2, if the jth pier or abutment is an abutment, further determination is needed according to the type of abutment foundation:

[0052] (i) the jth pier or abutment is a pile foundation abutment: F p_ j = α × (0.75 × V piles + V ww );

[0053] (ii) the jth pier or abutment is an enlarged foundation abutment:

[0054] In the formula, V piles represents the lateral strength of the abutment pile foundation; V ww represents the lateral strength of the abutment wing wall; P dl represents the vertical reaction at the abutment (including the weight of the abutment and the enlarged foundation); α represents an empirical coefficient, α ∈ [0.5, 1].

[0055] 6, for d py_ j , it should be noted that if the jth pier or abutment is an abutment, d py_ j is 0.

[0056] 7, for K b_ j , it is valued according to the material of the bearing at the pier or abutment.

[0057] 8, for L j , it can be obtained from the design drawings of the target bridge.

[0058] S2, calculate the design strength F of the block at the ith pier s_i , i = 1, …, m-1.

[0059] wherein, F s_i = F p_i - F bf_i ; in the formula, F p_i represents the allowable lateral thrust at the ith pier; F bf_i represents the sum of the sliding friction of the support at the ith pier.

[0060] That is, in the calculation of the design strength of the block at the first m-1 piers, the allowable lateral thrust at the pier is subtracted by the sum of the sliding friction of the support at the pier to obtain.

[0061] S2, calculate the design strength F of the block at the ith pier s_m ;

[0062] wherein, in the formula, L i represents the distance from the ith pier to the center of mass of the target bridge; L m represents the distance from the mth pier to the center of mass of the target bridge.

[0063] That is, the design strength F s_m of the block at the mth pier is obtained from the force couple balance condition, the principle of which is that the maximum design earthquake force generated by each pier on the main beam is zero at the center of the main beam.

[0064] S3, estimate the design displacement d g0 of the main beam under the design earthquake; wherein, d g0 is less than the limit displacement of the main beam;

[0065] It should be noted that in the estimation of d g0 , it is considered that: 1, the design displacement of the main beam is equal to the sum of the design displacement of the support (or block) and the design displacement of the lower pier; 2, the design displacement of the support and the block is equal.

[0066] Assuming that the main beam moves uniformly without plane torsion, based on the support-block-pier series-parallel system, according to d g0 , the yield strength F sy_ j of the block at the jth pier, the initial elastic stiffness k s_ j of the block, the design displacement ductility coefficient μ s_ j of the block, and the design displacement ductility coefficient μ b_ j of the support are calculated.

[0067] The calculation method of the above parameters can be based on the “Urban Bridge Seismic Design Specification CJJ166-2011”, which is only briefly described here:

[0068] First calculate the design displacement d of the support at the j-th pier. b_ j The design displacement d of the stop block s_ j ; where d b_ j =d s_ j .

[0069] If the j-th pier is a bridge pier, then d b_ j =d s_ j =d g0 -d py_ j ;

[0070] If the j-th pier is a bridge abutment, then d b_ j =d s_ j =d g0 .

[0071] Then, based on the yield strength F of the support at the j-th pier... by_ j Calculate the yield displacement d of the support at the j-th pier. by_ j ;in,

[0072] Next, the yield displacement d of the stop block at the j-th pier is selected. sy_ j Generally, d sy_ j Take the empirical value, but it must be less than d. g0 .

[0073] Calculate the initial elastic stiffness k of the stop block at the j-th pier. s_ j ;

[0074] in, In the formula, η represents the yield stiffness ratio of the stop; F s_ j This represents the design strength of the retaining block at the j-th pier.

[0075] Calculate the yield strength F of the retaining block at the j-th pier. sy_ j Among them, F sy_ j =k s_ j d by_ j .

[0076] Calculate the design displacement ductility coefficient μ of the retaining block at the j-th pier. s_ j The design displacement ductility coefficient μ of the support b_ j ;

[0077] in,

[0078] S4. Based on the series and parallel connection system of bearings, blocks, and piers, calculate the equivalent damping ratio coefficient ξ of the entire bridge system. all .

[0079] Specifically, S4 includes:

[0080] S401, respectively calculate the equivalent damping ratio coefficient ξ of the support at the jth pier b_ j , the equivalent damping ratio coefficient ξ of the block s_ j ;

[0081] Wherein,

[0082] In the formula, F b_ j , F s_ j Respectively represent the design strength of the support at the jth pier, the block, that is, the maximum seismic force demand of the support at the jth pier, the block under the design earthquake; F by_ j , F sy_ j Respectively represent the yield strength of the support at the jth pier, the block.

[0083] In addition, since F b_ j =F by_ j Therefore,

[0084] S402, calculate the equivalent damping ratio coefficient ξ of the support-block parallel system at the jth pier f_i ;

[0085] Wherein,

[0086] S403, calculate the equivalent damping ratio coefficient ξ of the support-block-pier series system at the jth pier d ;

[0087] Wherein, ξ d_ j = ξ f_ j + ξ p_ j ; ξ p_ j Is the equivalent damping ratio coefficient of the jth pier, ξ p_ j = 0.05;

[0088] S404, calculate the equivalent damping ratio coefficient of the pier parallel system, and take it as ξ all ;

[0089] Wherein,

[0090] S5, calculate the response spectrum damping adjustment coefficient R all According to ξ D , and adjust the design seismic response spectrum according to R D ; wherein,

[0091] According to the equivalent fundamental period T eff Of the target bridge, determine the adjusted main beam design displacement d g1 In the adjusted design seismic response spectrum; wherein, T effThe calculation is based on the secant stiffness method. The specific calculation method can be carried out in accordance with the "Code for Seismic Design of Urban Bridges CJJ166-2011", which will not be elaborated here.

[0092] S6, determine d g0 With d g1 Check if the error is within the preset range; if yes, the current round of calculation meets the requirements and proceeds to S7; if not, the current round of calculation does not meet the requirements, return to S4, and set d... g1 Re-assume the main beam design displacement d g0 Continue with S3 to S6.

[0093] The preset range is designed as follows: |d g1 -d g0 | / d g0 ≤5%. Although 5% can be adjusted, the larger the value, the lower the precision; the smaller the value, the higher the precision of the calculation, but the more calculations are required.

[0094] S7, from the current round of calculation, obtain the design parameters of the stop block at the j-th pier; where the design parameters include: F s_ j F sy_ j k j ;

[0095] Based on F s_ j F sy_ j k j Calculate the physical parameters of the stop block at the j-th pier; the physical parameters include: shape, material, and size. Specifically, the shape of the stop block includes, but is not limited to, triangular plate, X-shaped plate, H-shaped, and cylindrical bar; the material of the stop block includes, but is not limited to, metals or alloys such as steel and aluminum; the size of the stop block includes, but is not limited to, the planar dimensions and plate thickness.

[0096] It should be noted that the specific process of calculating the physical parameters based on the design parameters of the stop can be carried out in accordance with the "DB34 / T3957-2021 Technical Specification for Vibration Reduction of Building Wall-type Metal Dampers", which will not be elaborated here.

[0097] Example 2

[0098] This embodiment 2 discloses a specific application example of embodiment 1:

[0099] The target bridge in this embodiment 2 is Figure 1 The three-span continuous beam bridge with unequal pier heights shown has dimensions of 3×25 meters and a total of 4 piers: pier ①, pier ②, pier ③, and pier ④. Spread foundations are used at the abutments.

[0100] In this embodiment 2, the target bridge meets the set performance target under the design earthquake intensity as the design constraint, and the set seismic performance target is as follows:

[0101] (1) The main beam keeps uniform motion under the horizontal seismic action, that is, the displacement demand at each pier is basically consistent.

[0102] (2) The seismic demand of unequal height piers is consistent and basically keeps in the elastic response range.

[0103] Specifically, the operation steps of this embodiment 2 are as follows:

[0104] S1, the known basic design parameters of the target bridge are obtained according to the design manual of the target bridge, as shown in Table 1 below. It should be noted that: in Table 1, some parameters are listed separately for piers (subscript corresponding to c) and abutments (subscript corresponding to a). In addition, Table 1 also lists the related parameters of the design earthquake, including: from "seismic fortification intensity" to "design response spectrum characteristic period".

[0105] Table 1 Basic design parameters

[0106]

[0107]

[0108] S2: Determine the design strength of the block at ① abutment, ② pier, ③ pier as follows:

[0109] ① abutment: F s_1 = 0.5 × 2645 = 1323 kN;

[0110] ② pier: F s_2 = 0.85 × 6600 - 1997 = 3613 kN;

[0111] ③ pier: F s_3 = 0.85 × 3850 - 1997 = 1853 kN;

[0112] Determine the required block design strength at ④ abutment:

[0113] ④ abutment: F s_4 = (1853 × 12.5 + 1323 × 37.5 - 3613 × 12.5) / 37.5 = 736 kN.

[0114] S3: Estimate the design displacement of the main beam under the design earthquake as d g0 = 0.3 m, and select the yield displacement of the block as 0.04 m;

[0115] Calculate the initial elastic stiffness k s_1 ~ ks_4 The values ​​are 22723 kN / m, 63453 kN / m, 23408 kN / m, and 12646 kN / m, respectively.

[0116] The yield strength F of the retaining blocks at piers ① to ④ was calculated. sy_1 ~F sy_4 The corresponding values ​​are 909kN, 2538kN, 936kN, and 506kN.

[0117] The design displacement ductility coefficient μ of the supports at piers ① to ④ was calculated. b_1 ~μ b_4 The values ​​are 24.5, 1.5, 1.3, and 24.5 respectively.

[0118] The design displacement ductility coefficient μ of the retaining blocks at piers ① to ④ was calculated. s_1 ~μ s_4 The values ​​are 7.5, 7.1, 6.2, and 7.5 respectively.

[0119] In this way, the equivalent stiffness K of the full bridge system can be calculated first. eff Then calculate the equivalent fundamental period T. eff :

[0120] K eff =(6600×0.85+3850×0.85+1323+159+736+159) / 0.3=37532kN / m;

[0121]

[0122] S4: The equivalent damping ratio coefficient ξ of the supports at piers ① to ④ is calculated. b_1 ~ξ b_4 The percentages are 61.1%, 21.2%, 14.7%, and 61.1%, respectively; the equivalent damper coefficient ξ of the blocks at piers ① to ④. s_1 ~ξ s_4 The percentages were 37.94%, 38.40%, 39.18%, and 37.94%, respectively.

[0123] Finally, the equivalent damping ratio coefficient ξ of the full-bridge system was calculated. all It is 30.7%.

[0124] S5: Calculate the damping adjustment coefficient R of the response spectrum. D =0.463; The design seismic response spectrum was adjusted according to a 5% damping ratio correction, yielding the result corresponding to T. eff =1.34s main beam displacement d g1 It is 0.218m.

[0125] S6: Due to d g1= 0.218 m, d g0 = 0.3 m, which is 27% larger than the preset range of 5%, so return to S3 to re-assume the girder design displacement d g0 = 0.218 m, and after another round of iteration, d g1 = 0.221 m, which is 5% different from 0.218 m, so the iteration is terminated.

[0126] S7: Obtain the design parameters of the stop block in the second round of iteration:

[0127] F s_1 = 1323 kN, F s_2 = 3613 kN, F s_3 = 1865 kN, F s_4 = 736 kN;

[0128] F sy_1 = 1008 kN, F sy_2 = 2823 kN, F sy_3 = 1047 kN, F sy_4 = 561 kN;

[0129] k1 = 25210 kN / m, k2 = 70566 kN / m, k3 = 26164 kN / m, k4 = 14030 kN / m.

[0130] Based on the above parameters, the physical parameters of the stop block at each pier are designed according to the “DB34 / T 3957-2021 Technical Specification for Building Wall Type Metal Damper Seismic Reduction”.

[0131] In order to verify the rationality of the method of designing the stop block in Example 1, this Example 2 uses the nonlinear time history method to calculate the seismic response of the target bridge under the design seismic intensity: Referring to Figure 3 , 15 actual seismic waves matching the design seismic response spectrum are selected, and their average is taken as the seismic input. The test results are shown in Figures 4-7 .

[0132] 1. As can be seen from Figure 4 , it shows the comparison of the maximum displacement demand of the girder at each pier before and after the design using the method of Example 1: Before the design, the displacement demand of the girder at each pier of the target bridge under the action of the earthquake is quite different, indicating that the girder has a large plane twist; After the design using the method of Example 1, the displacement of the girder at each pier is relatively balanced, and the uniformity of the girder movement is greatly improved, and the overall displacement of the girder is greatly reduced; This proves the effectiveness of the method of Example 1 in controlling the plane twist of the girder and maintaining the uniformity of the girder movement.

[0133] 2. As can be seen from Figure 5It can be seen that it shows the maximum displacement ductility coefficient of the pier before and after the design by the method of embodiment 1: before the design, the displacement ductility demand of the pier is extremely uneven, and the displacement ductility demand of the high pier is significantly greater than that of the low pier, indicating that the high pier is more prone to damage and destruction than the low pier; and after the design by the method of embodiment 1, the displacement ductility demand of the high pier and the low pier becomes balanced, and is controlled near 1.0, that is, the pier can basically maintain an elastic response state; which proves the effectiveness of the design method of the present application in controlling the balance of the seismic response of the unequal-height piers.

[0134] 3, by Figure 6 、 Figure 7 It can be seen that it shows the comparison of the displacement time history curve of the main beam at the two abutments before and after the design by the method of embodiment 1: before the design, the displacement of the main beam at each pier and abutment cannot be consistent throughout the seismic excitation time range; and after the design by the method of embodiment 1, the displacement of the main beam at each pier and abutment is consistent throughout the seismic excitation time range, meeting the design target, further proving the rationality of the method of embodiment 1.

[0135] Embodiment 3

[0136] The present embodiment discloses a readable storage medium, and the readable storage medium stores computer program instructions. When the computer program instructions are read and run by a processor, the steps of the elastoplasticity block seismic design method for unequal-pier-height continuous girder bridges of embodiment 1 are executed.

[0137] The method of embodiment 1 can be applied in the form of software, such as a program designed to be independently run on a computer readable storage medium, which can be a U disk, and the U disk is designed to start the entire method through external triggering.

[0138] Embodiment 4

[0139] The present embodiment provides a computer terminal, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, the steps of the elastoplasticity block seismic design method for unequal-pier-height continuous girder bridges of embodiment 1 are implemented.

[0140] The method of embodiment 1 can be applied in the form of software, such as a program designed to be independently run, installed on a computer terminal, which can be a computer, a smart phone, a control system, and other Internet of Things devices, etc. The method of embodiment 1 can also be designed as an embedded program running, installed on a computer terminal, such as a single-chip microcomputer.

[0141] Any combination of the technical features in the above embodiments can be made, and for the sake of brevity, not all possible combinations are described above, however, as long as the combination of the technical features does not exist in contradiction, it shall be considered within the scope of the present disclosure.

[0142] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it shall not be understood as a limitation on the patent scope of the present application. It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these shall be within the protection scope of the present application. Therefore, the protection scope of the present application patent shall be subject to the appended claims.

Claims

1. A seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights, characterized in that: Includes the following steps, S1, Obtain the basic design parameters of the target bridge; wherein, the target bridge is a continuous beam bridge with unequal pier heights, and its piers are equipped with several unbonded plate rubber bearings and several elasto-plastic blocks; the basic design parameters include: superstructure mass M, number of substructure piers m, and the sum of sliding friction forces F of the bearings at the j-th pier. bf_ j The critical sliding displacement d of the support at the j-th pier by_ j The permissible lateral thrust F at the j-th pier p_ j Yield displacement d at the j-th pier py_ j The horizontal shear stiffness at the j-th pier and K b_ j j = 1, ..., m; S2, calculate the design strength F of the retaining block at the i-th pier. s_i , i = 1, ..., m-1; Among them, F s_i =F p_i -F bf_i ; Calculate the design strength F of the retaining block at the m-th pier. s_m ; in, S3, the estimated design displacement of the main beam under the design earthquake is d. g0 ; Assuming the main beam moves horizontally and uniformly without planar torsion, based on the series and parallel system of supports-stops-piers, according to d g0 Calculate the yield strength F of the retaining block at the j-th pier. sy_ j The initial elastic stiffness k of the stop s_ j The design displacement ductility coefficient μ of the stop block s_ j The design displacement ductility coefficient μ of the support b_ j ; S4. Based on the series and parallel connection system of bearings, blocks, and piers, calculate the equivalent damping ratio coefficient ξ of the entire bridge system. all ; S5, based on ξ all Calculate the response spectrum damping adjustment coefficient R D And based on R D Adjust the design seismic response spectrum; Based on the equivalent fundamental period T of the target bridge eff Determine the adjusted design displacement d of the main beam from the adjusted design seismic response spectrum. g1 ; S6, determine d g0 With d g1 Check if the error is within the preset range; if yes, the current round of calculation meets the requirements and proceeds to S7; if not, the current round of calculation does not meet the requirements, return to S3, and set d... g1 Re-assume the design displacement d of the main beam g0 Continue with S3 to S6; S7, from the current round of calculation, obtain the design parameters of the stop block at the j-th pier; where the design parameters include: F s_ j F sy_ j k j ; Based on F s_ j F sy_ j k j Calculate the physical parameters of the stop block at the j-th pier.

2. The seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights according to claim 1, characterized in that, In S3, d g0 Less than the ultimate displacement of the main beam.

3. The seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights according to claim 1, characterized in that, In S3 In the formula, F s_ j η represents the design strength of the retaining block at the j-th pier, η represents the yield stiffness ratio of the retaining block, and d sy_ j d represents the yield displacement of the stop block at the j-th pier; s_ j This represents the design displacement of the stop block at the j-th pier. F sy_ j =k s_ j d by_ j In the formula, d by_ j This represents the yield displacement of the support at the j-th pier. In the formula, d b_ j This represents the design displacement of the support at the j-th pier.

4. The seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights according to claim 1, characterized in that, S4 include: S401, calculate the equivalent damping ratio ξ of the support at the j-th pier. b_ j The equivalent damping ratio coefficient ξ of the stop s_ j ; in, In the formula, F b_ j F s_ j F represents the design strength of the support and stop block at the j-th pier, respectively; by_ j F sy_ j Let represent the yield strength of the support and the stop at the j-th pier, respectively; S402, Calculate the equivalent damping ratio coefficient ξ of the parallel support-stop system at the j-th pier. f_i ; in, S403, Calculate the equivalent damping ratio ξ of the series system of support-stop-pier at the j-th pier. d ; Where, ξ d_ j =ξ f_ j +ξ p_ j ξ p_ j Let be the equivalent damping ratio coefficient of the j-th pier; S404, calculate the equivalent damping ratio coefficient of the parallel pier system, and use it as ξ. all ; in, 5. The seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights according to claim 1, characterized in that, In S5, 6. The seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights according to claim 1, characterized in that, The sum of sliding friction forces F at the support of the j-th pier bf_ j Design strength F of the support b_ j Yield strength F of the support by_ j The values ​​of the three are equal.

7. The seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights according to claim 1, characterized in that, The design displacement d of the support at the j-th pier b_ j The design displacement d of the stop block s_ j The two values ​​are equal.

8. The seismic design method for elasto-plastic blocks applicable to continuous beam bridges with unequal pier heights according to claim 7, characterized in that, In S6, the preset range is: |d g1 -d g0 | / d g0 ≤5%.

9. A readable storage medium, characterized in that, The readable storage medium stores computer program instructions, which are read and executed by a processor to perform the steps of the elastoplastic block seismic design method for continuous beam bridges with unequal pier heights as described in any of claims 1-8.

10. A computer terminal, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor; when the processor executes the program, it implements the steps of the seismic design method for elastoplastic blocks applicable to continuous beam bridges with unequal pier heights as described in any one of claims 1-8.

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