Displacement-based lead core damper seismic mitigation and isolation design method

Abstract

The invention relates to a displacement-based lead core damper seismic mitigation and isolation design method, which comprises the following steps of: determining an applicable bridge system, and establishing a full-bridge stress analysis model; determining design displacement ub; calculating the equivalent stiffness Ke and the equivalent damping ratio zeta e of the lead core damper; preliminarily determining a lead core damper arrangement scheme; calculating the equivalent stiffness K1 and the equivalent damping ratio zeta 1 of the pier provided with the lead core damper; if the fixed support is reserved, the equivalent stiffness K2 and the equivalent damping ratio zeta 2 of the fixed pier are calculated; enabling a bridge system to be equivalent to a single-degree-of-freedom mechanical model, and calculating a damping ratio zeta w and a damping influence coefficient eta of a full bridge; calculating the horizontal force of the top of each pier and the displacement u of a bridge system according to a full-bridge seismic mitigation and isolation analysis model; comparing ub with u, if ut; if ub, the number of the dampers is increased, and if ugt; ub, the number of the dampers is reduced. According to the method, shock absorption and isolation design is carried out on the lead core dampers without assistance of computer programs, the number of the lead core dampers is rapidly determined, and operation is convenient and rapid.

Description

Technical Field

[0001] The invention relates to the technical field of bridge seismic isolation technology, and in particular to a displacement-based lead core damper seismic isolation design method. Background Art

[0002] As a key project in the transportation system, bridges are an important part of lifeline projects. When an earthquake occurs, they are the first to be damaged. Damage to bridges will inevitably lead to traffic interruption, making disaster relief work difficult or greatly delayed, causing great losses. Therefore, it is very necessary to carry out seismic isolation design for bridges.

[0003] Lead core dampers are widely used in bridges as seismic isolation devices. The number and position of lead core dampers need to be determined in seismic isolation design. Since the lead core damper needs to undergo a certain displacement to form a hysteresis loop for energy dissipation, the displacement of the lead core damper should reach the designed displacement for full energy dissipation during seismic isolation design. At the same time, the displacement should not be too large to ensure the overall safety of the bridge system. Therefore, the number of lead core dampers needs to be adjusted repeatedly during design to achieve the ideal displacement value.

[0004] At present, the main seismic isolation design methods are response spectrum method and time history analysis method. Although the response spectrum method takes into account the frequency spectrum characteristics and can obtain the maximum response of the structure, it cannot reflect the time history of the structure under the action of seismic motion and the sustained effect of seismic motion; the time history analysis method is the main analysis method used in the design specifications. It has high calculation accuracy, but the calculation process is relatively complicated and requires reliance on computer programs for modeling and calculation. When lead core dampers are used for seismic isolation design, the number of dampers needs to be repeatedly adjusted for calculation. When using traditional design methods for time history analysis, repeated adjustment of the model is time-consuming and labor-intensive. Summary of the invention

[0005] The present invention aims to solve the deficiencies of the prior art and provides a displacement-based lead core damper seismic isolation design method.

[0006] To achieve the above object, the present invention adopts the following technical solution: a displacement-based lead core damper seismic isolation design method, comprising the following steps:

[0007] S1. Determine the applicable bridge system and establish a full bridge stress analysis model;

[0008] S2. Analyze the seismic requirements of the bridge and determine its design displacement u based on the full bridge stress model and the parameters of the lead core damper. b ;

[0009] S3, based on the design displacement u b Calculation of the equivalent stiffness K of the lead core damper e and equivalent damping ratio ζ e ;

[0010] S4. Preliminarily determine the layout of the lead core damper and convert the bridge system into a linear model;

[0011] S5. Assuming that the number of dampers installed on each pier is n, calculate the equivalent stiffness K1 and equivalent damping ratio ζ1 of the pier with lead core damper installed according to the series-parallel stiffness theory;

[0012] S6. If the fixed support is retained, there is no need to install a lead core damper on the fixed pier, and only the equivalent stiffness K2 and equivalent damping ratio ζ2 of the fixed pier are calculated;

[0013] S7. Equivalently transform the bridge system into a single-degree-of-freedom mechanical model, establish a full-bridge seismic isolation analysis model using lead core dampers, and calculate the damping ratio ζ of the full bridge. w and damping influence coefficient η;

[0014] S8. Calculate the horizontal force on the top of each pier and the displacement u of the bridge system based on the full bridge seismic isolation analysis model;

[0015] S9. Compare b and u, if u b , then increase the number of dampers. If u>u b , then reduce the number of dampers and repeat S5 to S8 until u and u b The difference meets the requirements;

[0016] S10. Determine the layout of the lead core damper through S1 to S9, use finite element software to build a full-bridge analysis model for time-history analysis, verify the rationality of the layout, and finally determine the layout of the lead core damper to complete the seismic isolation design.

[0017] In particular, in S1, the bridge system is divided into beam bridges, arch bridges, rigid frame bridges, cable-bearing bridges and combined system bridges. The stress modes and seismic isolation arrangements of each system are different and are determined according to the specific bridge type.

[0018] In particular, in S2, the parameters of the lead core damper are selected according to the bilinear restoring force model, including: the initial stiffness K of the lead core damper u , post-yield stiffness K d , the ratio of initial stiffness to yield stiffness r, the yield displacement u y , and the design displacement u b It should be ensured that the lead core damper forms a hysteresis loop to fully dissipate energy while meeting the displacement requirements of the main beam.

[0019] In particular, in S3, the equivalent stiffness K of a single lead core damper is e and equivalent damping ratio ζ e According to the equivalent linearization theory, the calculation formula is as follows: ​

[0020]

[0021] Where μ is the displacement ductility coefficient, and

[0022] In particular, in S5, each lead core damper is connected in parallel, and the effect of multiple lead core dampers is equivalent to the superposition of the effect of a single lead core damper. The new lead core damper is connected in series with the movable pier and the beam. According to the series-parallel theory, the equivalent stiffness K1 of the pier is calculated as follows:

[0023]

[0024] The equivalent damping ratio ζ1 is calculated using the modal strain energy theory, and the calculation formula is:

[0025]

[0026] In the formula, ζ s is the elastic damping ratio of the pier, K P is the horizontal stiffness of the pier itself.

[0027] In particular, in S6, the equivalent stiffness K2 and equivalent damping ratio ζ2 of the fixed pier are calculated as follows:

[0028]

[0029] In the formula, μ P is the displacement ductility ratio of the pier.

[0030] In particular, in S7, the single-degree-of-freedom mechanical model is simplified, assuming that the mass of the bridge pier is simulated by concentrated mass, half of the mass is concentrated on the main beam, and the other half is concentrated on the bottom of the pier. The main beam is a rigid body, and the damping ratio of the whole bridge is ζ w Calculate as follows:

[0031]

[0032] c=∑c i ;

[0033]

[0034] K=ΣK i ;

[0035]

[0036] Where c is the damping of the full bridge, c i , K i 、M i , iare the damping, equivalent stiffness, mass and equivalent damping ratio of the i-th pier respectively, M0 is the mass of the main beam, M is the total mass of the bridge system, and K is the overall stiffness of the bridge system.

[0037] In particular, in S8, the horizontal force on the pier top is calculated as follows:

[0038] F = α·β·η·M;

[0039]

[0040] The displacement u of the bridge system is calculated as follows:

[0041]

[0042] Where α is the peak acceleration of the earthquake; β is the dynamic amplification factor of the structure, which is calculated based on the natural vibration period of the structure and the dominant period of the earthquake; T g is the characteristic period of the seismic wave, determined according to the selected seismic wave; T e is the natural vibration period of the structure.

[0043] The beneficial effects of the present invention are as follows: the present invention realizes the seismic isolation design of lead core dampers without the assistance of computer programs, quickly determines the number of lead core dampers, and is convenient and quick to operate; relative to conventional seismic isolation design, the method can freely select the displacement generated by the lead core damper when an earthquake occurs, and the target performance is not only given by the specifications, but can also be clearly set by the owner, and the target is highly achievable, which can meet both the specification requirements and the target performance requirements; the present invention adopts simplified calculations to ensure the rapid and efficient seismic isolation design, and at the same time adopts time-history analysis for double verification to ensure the reliability and stability of the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flow chart of the method for designing the present invention;

[0045] Figure 2 A broken line restoring force model diagram of the design method of the present invention;

[0046] Figure 3 This is a layout diagram of a four-span continuous beam bridge in Example 1 of the present invention;

[0047] Figure 4 This is a diagram of the restoring force model of the lead core damper in Example 1 of the present invention;

[0048] Figure 5 This is a schematic diagram of the support arrangement in Example 1 of the present invention;

[0049] Figure 6 This is a full-bridge single-degree-of-freedom model diagram in Example 1 of the present invention;

[0050] Figure 7 is a time history curve diagram of pier top displacement under seismic waves in Example 1 of the present invention;

[0051] The following is a detailed description of the embodiments of the present invention with reference to the accompanying drawings. DETAILED DESCRIPTION

[0052] The present invention will be further described below in conjunction with embodiments:

[0053] like Figure 1 As shown, a displacement-based lead core damper seismic isolation design method includes the following steps:

[0054] S1. Determine the applicable bridge system and establish a stress analysis model for the entire bridge. Bridge systems are divided into beam bridges, arch bridges, rigid frame bridges, cable-bearing bridges and combined system bridges. The stress modes and seismic isolation arrangements of each system are different and are determined based on the specific bridge type.

[0055] S2. Analyze the seismic requirements of the bridge and determine its design displacement u based on the full bridge stress model and the parameters of the lead core damper. b ;

[0056] The parameters of the lead core damper are selected based on the bilinear restoring force model, such as Figure 2 As shown, including: the initial stiffness K of the lead core damper u , post-yield stiffness K d , the ratio of initial stiffness to yield stiffness r, the yield displacement u y , and the design displacement u b It should be ensured that the lead core damper forms a hysteresis loop to fully dissipate energy while meeting the displacement requirements of the main beam.

[0057] S3, based on the design displacement u b Calculation of the equivalent stiffness K of the lead core damper e and equivalent damping ratio ζ e ;

[0058] Equivalent stiffness K of a single lead core damper e and equivalent damping ratio ζ e According to the equivalent linearization theory, the calculation formula is as follows:

[0059]

[0060] Where μ is the displacement ductility coefficient, and

[0061] S4. Preliminarily determine the layout of the lead core damper and convert the bridge system into a linear model;

[0062] S5. Assuming that the number of dampers installed on each pier is n, calculate the equivalent stiffness K1 and equivalent damping ratio ζ1 of the pier with lead core damper installed according to the series-parallel stiffness theory;

[0063] Each lead core damper is connected in parallel, and the effect of multiple lead core dampers is equivalent to the superposition of the effect of a single lead core damper. The new lead core damper is connected in series with the movable pier and the beam. According to the series-parallel theory, the equivalent stiffness K1 of the pier is calculated as follows:

[0064]

[0065] The equivalent damping ratio ζ1 is calculated using the modal strain energy theory, and the calculation formula is:

[0066]

[0067] In the formula, ζ s is the elastic damping ratio of the pier, K P is the horizontal stiffness of the pier itself.

[0068] S6. If the fixed support is retained, there is no need to install a lead core damper on the fixed pier, and only the equivalent stiffness K2 and equivalent damping ratio ζ2 of the fixed pier are calculated;

[0069] The equivalent stiffness K2 and equivalent damping ratio ζ2 of the fixed pier are calculated as follows:

[0070]

[0071] In the formula, μ P is the displacement ductility ratio of the pier.

[0072] S7. Equivalently transform the bridge system into a single-degree-of-freedom mechanical model, establish a full-bridge seismic isolation analysis model using lead core dampers, and calculate the damping ratio ζ of the full bridge. w and damping influence coefficient η;

[0073] Simplify the single-degree-of-freedom mechanical model and assume that the pier mass is simulated by concentrated mass, half of the mass is concentrated on the main beam and the other half is concentrated on the bottom of the pier. The main beam is a rigid body and the damping ratio of the whole bridge is ζ w Calculate as follows:

[0074]

[0075] c=∑c i ;

[0076]

[0077] K=∑K i ;

[0078]

[0079] Where c is the damping of the full bridge, c i , K i 、M i , i are the damping, equivalent stiffness, mass and equivalent damping ratio of the i-th pier respectively, M0 is the mass of the main beam, M is the total mass of the bridge system, and K is the overall stiffness of the bridge system.

[0080] S8. Calculate the horizontal force on the top of each pier and the displacement u of the bridge system based on the full bridge seismic isolation analysis model;

[0081] The horizontal force on the pier top is calculated as follows:

[0082] F = α·β·η·M;

[0083]

[0084] The displacement u of the bridge system is calculated as follows:

[0085]

[0086] Where α is the peak acceleration of the earthquake; β is the dynamic amplification factor of the structure, which is calculated based on the natural vibration period of the structure and the dominant period of the earthquake; T g is the characteristic period of the seismic wave, determined according to the selected seismic wave; T e is the natural vibration period of the structure.

[0087] S9. Compare b and u, if u b , then increase the number of dampers. If u>u b , then reduce the number of dampers and repeat S5 to S8 until u and u b The difference meets the requirements;

[0088] S10. Determine the layout of the lead core damper through S1 to S9, use finite element software to build a full-bridge analysis model for time-history analysis, verify the rationality of the layout, and finally determine the layout of the lead core damper to complete the seismic isolation design.

[0089] Example 1

[0090] like Figure 3 As shown, taking a four-span continuous beam as an example, the lead core damper seismic isolation design is carried out by adopting the present invention.

[0091] S1. Determine the applicable bridge system and establish a full bridge stress analysis model;

[0092] Take a four-span continuous beam bridge with a span of (32+48+48+32) m as an example, and the site characteristic period is T g ​= 0.45s, the peak earthquake acceleration is 0.57g, and the bridge span is arranged as follows Figure 3 shown.

[0093] S2. Analyze the seismic requirements of the bridge and determine its design displacement u based on the full bridge stress model and the parameters of the lead core damper. b ;

[0094] The parameters of the lead core damper selected in this embodiment are as follows: initial stiffness K u =7879kN / m, yield displacement u y =0.06m, post-yield stiffness K d =317kN / m, the restoring force model is as follows Figure 4 In order to give full play to the energy dissipation capacity of the lead core damper and make the displacement of the main beam of this continuous beam bridge meet the requirements under the earthquake, the design displacement u b =0.23m.

[0095] S3, based on the design displacement u b Calculation of the equivalent stiffness K of the lead core damper e and equivalent damping ratio ζ e ;

[0096] For this embodiment, the displacement ductility coefficient is calculated as follows: μ = u b / u y =0.23 / 0.06=3.819, the ratio of initial stiffness to yield stiffness r=K d / K u =317 / 7879=0.0402.

[0097] The equivalent stiffness and equivalent damping ratio are calculated as follows:

[0098]

[0099] S4. Preliminarily determine the layout of the lead core damper and convert the bridge system into a linear model;

[0100] In this embodiment, the fixed bearing on the middle pier P3 is retained, and movable bearings and a lead core damper bearing are set on the other piers. The bearings are arranged as follows: Figure 5 shown.

[0101] S5. According to the series-parallel stiffness theory, calculate the equivalent stiffness K1 and equivalent damping ratio ζ1 of the bridge pier with lead core damper installed. The horizontal stiffness of the bridge pier in this embodiment is K P =2.803×10 5 kN / m.

[0102]

[0103] S6, the yield displacement of the fixed pier is 0.075 mm, no lead core damper is installed on the fixed pier, and only the equivalent stiffness K2 and equivalent damping ratio ζ2 of the fixed pier are calculated;

[0104]

[0105] S7. Equivalently transform the bridge system into a single-degree-of-freedom mechanical model, establish a full-bridge seismic isolation analysis model using lead core dampers, and calculate the damping ratio ζ of the full bridge. w , calculate the damping influence coefficient ratio η;

[0106] The single degree of freedom mechanical model of this embodiment is as follows Figure 6 As shown, it is assumed that the mass of the pier is simulated by concentrated mass, half of the mass is concentrated on the main beam, and the other half is concentrated on the bottom of the pier. The main beam is a rigid body.

[0107] The calculation formula for the damping value of each pier is: Substituting in:

[0108] Activity pier:

[0109] Fixed pier:

[0110] The full bridge damping value is c = ∑c i =4c1+c2=5160591;

[0111] The total bridge mass is

[0112] The overall stiffness of the whole bridge is K = ∑K i =3.835×10 4 kN / m;

[0113] The full bridge damping ratio is:

[0114]

[0115] The full bridge damping influence coefficient is:

[0116]

[0117] S8. Calculate the horizontal force on the top of each pier and the displacement u of the bridge system based on the full bridge seismic isolation analysis model;

[0118] The first-order natural frequency of the bridge system in this embodiment is:

[0119]

[0120] The power amplification factor is:

[0121] The horizontal force on the pier top is:

[0122] F=α·β·η·M=0.57×9.8×0.379×0.671×6915399=9843kN;

[0123] Then the displacement u of the bridge system is:

[0124]

[0125] S9. Compare b and u, if u>u b , then increase the number of dampers, if u<u b , then reduce the number of dampers and repeat the process from S4 to S7 until u and u b The difference meets the requirements;

[0126] Since u>u in this embodiment b , then the number of dampers needs to be increased. According to the force characteristics of the continuous beam in this case, the P2 and P4 piers bear a large load on the main beam, so the number of lead core dampers in the P1 and P5 piers remains unchanged, and the number of lead core dampers in the P2 and P4 piers is increased, and S5-S8 are repeated. After calculation, when 1 lead core damper is set in the P1 and P5 piers, and 3 lead core dampers are set in the P2 and P4 piers, u=u b =0.23m, meets the requirements.

[0127] S10. The above calculations can determine the layout of the lead core damper. The finite element software is used to establish a full-bridge analysis model for time-history analysis to verify the rationality of the layout.

[0128] Create a full bridge model for time history analysis and calculate the pier top displacement time history curve as follows: Figure 7 As shown, the maximum displacement is 0.221m, which is less than 10% different from the simplified calculation result. The lead core damper arrangement scheme is finally determined and the seismic isolation design is completed.

[0129] The present invention realizes the seismic isolation design of lead core dampers without the assistance of computer programs, and quickly determines the number of lead core dampers, with convenient and quick operation; compared with conventional seismic isolation design, the method can freely select the displacement generated by the lead core damper when an earthquake occurs, and the target performance is not only given by the specifications, but also can be clearly set by the owner, with strong target feasibility, which can meet both the specification requirements and the target performance requirements; the method uses simplified calculations to ensure the rapid and efficient seismic isolation design, and uses time-history analysis for double verification to ensure the reliability and stability of the calculation results.

[0130] The above is an exemplary description of the present invention. Obviously, the specific implementation of the present invention is not limited to the above-mentioned method. As long as various improvements are made using the method concept and technical solution of the present invention, or they are directly applied to other occasions without improvement, they are all within the protection scope of the present invention.

Claims

1. A displacement-based lead core damper seismic isolation design method, characterized in that: The following steps are involved: S1. Determine the applicable bridge system and establish a full bridge stress analysis model; S2. Analyze the seismic requirements of the bridge and determine its design displacement u based on the full bridge stress model and the parameters of the lead core damper. b ; S3, based on the design displacement u b Calculation of the equivalent stiffness K of the lead core damper e and equivalent damping ratio ζ e ; S4. Preliminarily determine the layout of the lead core damper and convert the bridge system into a linear model; S5. Assuming that the number of dampers installed on each pier is n, calculate the equivalent stiffness K1 and equivalent damping ratio ζ1 of the pier with lead core damper installed according to the series-parallel stiffness theory; S6. If the fixed support is retained, there is no need to install a lead core damper on the fixed pier, and only the equivalent stiffness K2 and equivalent damping ratio ζ2 of the fixed pier are calculated; S7. Equivalently transform the bridge system into a single-degree-of-freedom mechanical model, establish a full-bridge seismic isolation analysis model using lead core dampers, and calculate the damping ratio ζ of the full bridge. w and damping influence coefficient η; S8. Calculate the horizontal force on the top of each pier and the displacement u of the bridge system based on the full bridge seismic isolation analysis model; S9. Compare b and u, if u b , then increase the number of dampers. If u>u b , then reduce the number of dampers and repeat S5 to S8 until u and u b The difference meets the requirements;​ S10. Determine the layout of the lead core damper through S1 to S9, use finite element software to build a full-bridge analysis model for time-history analysis, verify the rationality of the layout, and finally determine the layout of the lead core damper to complete the seismic isolation design.

2. A displacement-based lead core damper seismic isolation design method according to claim 1, characterized in that: In S1, the bridge system is divided into beam bridges, arch bridges, rigid frame bridges, cable-bearing bridges and combined system bridges. The force mode and seismic isolation arrangement of each system are different and are determined according to the specific bridge type.

3. The displacement-based lead core damper seismic isolation design method according to claim 1, characterized in that: In S2, the parameters of the lead core damper are selected according to the bilinear restoring force model, including: the initial stiffness K of the lead core damper u , post-yield stiffness K d , the ratio of initial stiffness to yield stiffness r, the yield displacement u y , and the design displacement u b It should be ensured that the lead core damper forms a hysteresis loop to fully dissipate energy while meeting the displacement requirements of the main beam.

4. The displacement-based lead core damper seismic isolation design method according to claim 3 is characterized in that: In S3, the equivalent stiffness K of a single lead core damper is e and equivalent damping ratio ζ e According to the equivalent linearization theory, the calculation formula is as follows: Where μ is the displacement ductility coefficient, and 5. The displacement-based lead core damper seismic isolation design method according to claim 4, characterized in that: In S5, each lead core damper is connected in parallel, and the effect of multiple lead core dampers is equivalent to the superposition of the effect of a single lead core damper. The new lead core damper is connected in series with the movable pier and the beam body. According to the series-parallel theory, the equivalent stiffness K1 of the pier is calculated as follows: The equivalent damping ratio ζ1 is calculated using the modal strain energy theory, and the calculation formula is: In the formula, ζ s is the elastic damping ratio of the pier, K P is the horizontal stiffness of the pier itself.

6. A displacement-based lead core damper seismic isolation design method according to claim 5, characterized in that: In S6, the equivalent stiffness K2 and equivalent damping ratio ζ2 of the fixed pier are calculated as follows: In the formula, μ P is the displacement ductility ratio of the pier.

7. The displacement-based lead core damper seismic isolation design method according to claim 1, characterized in that: In S7, the single-degree-of-freedom mechanical model is simplified. It is assumed that the mass of the bridge pier is simulated by concentrated mass, half of the mass is concentrated on the main beam, and the other half is concentrated on the bottom of the pier. The main beam is a rigid body, and the damping ratio of the whole bridge is ζ w Calculate as follows: c=∑c i ; K=∑K i ; Where c is the damping of the full bridge, c i , K i 、M i , i are the damping, equivalent stiffness, mass and equivalent damping ratio of the i-th pier respectively, M0 is the mass of the main beam, M is the total mass of the bridge system, and K is the overall stiffness of the bridge system.

8. The displacement-based lead core damper seismic isolation design method according to claim 7, characterized in that: In S8, the horizontal force on the pier top is calculated as follows: F = α·β·η·M; The displacement u of the bridge system is calculated as follows: Where α is the peak acceleration of the earthquake; β is the dynamic amplification factor of the structure, which is calculated based on the natural vibration period of the structure and the dominant period of the earthquake; T g is the characteristic period of the seismic wave, determined according to the selected seismic wave; T e is the natural vibration period of the structure.

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