Energy-based seismic design method for dual self-centering steel braced frames

Abstract

The present application relates to the technical field of building seismic structure design, and particularly relates to a dual self-resetting braced steel frame seismic design method based on energy. The present application ensures the superiority and reliability of the dual self-resetting braced steel frame in seismic performance through systematic design steps. First, by obtaining basic structure information and support key design parameters, performance targets are set, providing a clear direction for subsequent seismic design. Then, a single degree of freedom system steel frame is constructed and relevant energy dissipation, ductility and other parameters are calculated, providing a basis for total energy dissipation calculation. By setting the horizontal load distribution coefficient and combining the total energy dissipation, the total base shear can be accurately calculated, thereby ensuring the stability of the structure under the action of earthquakes. In addition, the method continuously adjusts and verifies the key support structural parameters through iterative design until the period and performance judgment conditions are met, greatly improving the accuracy and efficiency of the design.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of seismic design of building structures, and particularly relates to an energy-based seismic design method for a dual self-centering braced steel frame. BACKGROUND

[0002] In the field of building structures, especially in earthquake-prone areas, it is crucial to improve the seismic performance of buildings. Although traditional steel frame braced structures have some seismic capacity, they often have problems such as excessive structural deformation, insufficient energy dissipation capacity, or poor self-centering effect when subjected to strong earthquakes, which greatly affects the safety and reliability of buildings. Therefore, developing a braced steel frame that can significantly improve the seismic performance and has good self-centering ability has become a hot research topic.

[0003] A dual self-centering braced steel frame (DSCB) is composed of a recoverable slope friction damper system and a self-centering system, i.e., a basalt fiber pre-tension rod system, which has a large post-yield stiffness and energy dissipation capacity, can effectively control the displacement response of the frame, reduce the structural deformation concentration effect, and has strong seismic capacity, so it is widely used. However, as a new type of lateral component that can be prefabricated in a factory, DSCB has special generalized flag-type hysteretic characteristics and structural form, making it difficult for existing traditional design methods to be directly applicable, resulting in large design errors in the key structural parameters of the bracing in DSCB, which makes the manufactured DSCB unable to fully exert its seismic performance.

[0004] Therefore, the design method of the key structural parameters of the bracing in DSCB at the present stage still needs to be further improved. SUMMARY

[0005] In order to avoid and overcome the technical problems existing in the prior art, the present application provides an energy-based seismic design method for a dual self-centering braced steel frame. The present application can effectively improve the accuracy of the design of the key structural parameters of the bracing in the dual self-centering braced steel frame.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0007] An energy-based seismic design method for a dual self-centering braced steel frame, comprising the following design steps:

[0008] S1, obtaining the basic structural information of the dual self-centering braced steel frame, obtaining the key design parameters of the bracing of the dual self-centering braced steel frame according to the basic structural information, setting the performance target of the dual self-centering braced steel frame, and calculating the basic period T of the dual self-centering braced steel frame; the key design parameters of the bracing include the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio βf,4 ;

[0009] S2, constructing a single degree of freedom system steel frame of the double self-resetting braced steel frame based on the basic period T and the support key design parameters, and calculating the single cycle hysteretic energy E of the single degree of freedom system steel frame D , energy amplification coefficient α Energy , cumulative loading ductility μ aP , and cumulative unloading ductility μ aN ;

[0010] S3, calculating the total energy consumption of the double self-resetting braced steel frame according to the single cycle hysteretic energy E D , energy amplification coefficient α Energy , cumulative loading ductility μ aP , and cumulative unloading ductility μ aN ;

[0011] S4, setting the horizontal load distribution coefficient of the double self-resetting braced steel frame, and combining the total energy consumption to calculate the total base shear of the double self-resetting braced steel frame;

[0012] S5, determining the support key construction parameters of the double self-resetting braced steel frame based on the total base shear and the support key design parameters, thereby constructing a complete double self-resetting braced steel frame model, and performing finite element analysis on the double self-resetting braced steel frame model to obtain an estimated value of the basic period T;

[0013] S6, if the estimated value of the basic period T meets the period judgment condition, steps S7-S8 are executed; otherwise, the estimated value is assigned to the basic period T, and steps S1-S5 are executed;

[0014] S7, continuing the finite element analysis to obtain an estimated value of the target performance;

[0015] S8, if the estimated value of the target performance meets the performance judgment condition, the double self-resetting braced steel frame is designed according to the current support key construction parameters; otherwise, steps S1-S7 are executed.

[0016] As a further scheme of the present application: the calculation formula of the basic period T of the double self-resetting braced steel frame is as follows:

[0017] T = 0.0731H N 0.75 ;

[0018] In the formula, H N represents the total height of the double self-resetting braced steel frame.

[0019] As a further scheme of the present application: the performance target involves parameters including peak displacement angle, residual displacement angle, ductility and peak acceleration of the double self-resetting braced steel frame; setting the performance target of the double self-resetting braced steel frame, namely determining the standard reference value of the peak displacement angle, residual displacement angle, ductility and peak acceleration.

[0020] As a further scheme of the present application: the energy amplification coefficient a of the single degree of freedom system steel frame D is expressed as follows:

[0021]

[0022] In the formula, γ' represents the strength coefficient of the double self-resetting braced steel frame; μ represents the demand ductility ratio of the double self-resetting braced steel frame; α k,2 represents the loading stiffness ratio of the double self-resetting braced steel frame; π represents the circular constant; S a (T) represents the acceleration response spectrum value corresponding to the fundamental period T of the equivalent double self-resetting braced steel frame; represents the natural constant ; a1 represents a coefficient linearly related to the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4 ; b1 represents a coefficient linearly related to the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4 ;

[0023] The energy amplification coefficient a of the single degree of freedom system steel frame Energy is expressed as follows:

[0024]

[0025] In the formula, a2 represents a coefficient linearly related to the fundamental period T; b2 represents a coefficient linearly related to the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4 ; c2 represents a coefficient linearly related to the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4 ; e2 represents a coefficient linearly related to the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4 ; d2 represents a coefficient linearly related to the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4 ; Representing the natural constant Power;

[0026] Cumulative loading ductility μ of a single-degree-of-freedom steel frame system aP The calculation formula is expressed as follows:

[0027]

[0028] In the formula, a3 represents the ratio of the loading stiffness α to the stiffness. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients that are linearly correlated; b3 represents the coefficients that are linearly correlated with the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients that are linearly correlated; c3 represents the coefficients that are linearly correlated with the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients that are linearly correlated; d3 represents the coefficients that are linearly correlated with the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 Coefficients showing linear correlation; Representing the natural constant Power;

[0029] Cumulative unloading ductility μ of a single-degree-of-freedom steel frame system aN The calculation formula is expressed as follows:

[0030]

[0031] In the formula, a4 represents the ratio of the loading stiffness α to the stiffness. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients that are linearly correlated; b4 represents the coefficients that are linearly correlated with the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients that are linearly correlated; c4 represents the coefficients that are linearly correlated with the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients are linearly related; d4 represents the coefficients related to the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 Coefficients showing linear correlation; Representing the natural constant Power of 1.

[0032] As a further scheme of the present application: the total energy consumption calculation formula of the double self-resetting braced steel frame is as follows:

[0033]

[0034] In the formula, W represents the total energy consumption of the double self-resetting braced steel frame; M represents the total mass of the double self-resetting braced steel frame; m i represents the mass of the i-th layer structure in the double self-resetting braced steel frame, N represents the total number of supports in the double self-resetting braced steel frame; u yjP represents the activation displacement of the j-th layer structure in the double self-resetting braced steel frame when loaded; F yjP represents the activation load of the j-th layer structure in the double self-resetting braced steel frame when loaded.

[0035] As a further scheme of the present application: the specific steps of step S4 are as follows:

[0036] S41, set the value range of the horizontal load distribution coefficient q of the double self-resetting braced steel frame, and select a horizontal load distribution coefficient q from the value range;

[0037] S42, based on the selected horizontal load distribution coefficient q, calculate the horizontal seismic force coefficient of each layer structure in the double self-resetting braced steel frame; the horizontal seismic force coefficient calculation formula is represented as follows:

[0038]

[0039] In the formula, C i represents the horizontal seismic force coefficient of the i-th layer structure in the double self-resetting braced steel frame; p i represents the structure coefficient of the i-th layer structure in the double self-resetting braced steel frame; p i+1 represents the structure coefficient of the i+1-th layer structure in the double self-resetting braced steel frame; w N represents the mass of the N-th layer structure in the double self-resetting braced steel frame; h N represents the height of the N-th layer structure in the double self-resetting braced steel frame; w j represents the mass of the j-th layer structure in the double self-resetting braced steel frame; h j represents the height of the j-th layer structure in the double self-resetting braced steel frame;

[0040] S43, based on the horizontal seismic force coefficient, calculate the horizontal seismic force distribution ratio of each layer structure in the double self-resetting braced steel frame; the calculation formula of the horizontal seismic force distribution ratio is represented as follows:

[0041]

[0042] In the formula, DR ja horizontal seismic force distribution ratio of a jth story structure in the double self-resetting braced steel frame;

[0043] S44, according to the calculated horizontal seismic force distribution ratio, combining the total energy consumption of the double self-resetting braced steel frame, calculating the total base shear of the double self-resetting braced steel frame through the total base shear calculation formula; the total base shear calculation formula is as follows:

[0044]

[0045] In the formula, V y represents the total base shear of the double self-resetting braced steel frame.

[0046] As a further scheme of the application: the specific steps of step S5 are as follows:

[0047] S51, according to the total base shear of the double self-resetting braced steel frame, combining the horizontal seismic force calculation formula to calculate the starting load of each layer structure in the double self-resetting braced steel frame when loading, and combining the initial stiffness calculation formula to calculate the initial stiffness of each layer structure in the double self-resetting braced steel frame when loading;

[0048] The starting load calculation formula is as follows:

[0049] F yjP = DR j ·V y ;

[0050] The initial stiffness calculation formula is as follows:

[0051] k yjP =F yjP / u yjP ;

[0052] In the formula, k yjP represents the initial stiffness of the jth story structure in the double self-resetting braced steel frame when loading;

[0053] S52, the starting load and initial stiffness of each layer structure in the double self-resetting braced steel frame when loading are converted into the starting load and initial stiffness of each layer support in the double self-resetting braced steel frame through coordinate transformation;

[0054] S53, according to the selected loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 , determine the support key construction parameters of each layer support;

[0055] S54; Input the key design parameters, key structural parameters, and the starting load and initial stiffness of each layer of support into the finite element analysis software to establish a double self-resetting support steel frame model.

[0056] S55. A finite element analysis was performed on the double self-resetting braced steel frame model using finite element analysis software to obtain an estimate of its fundamental period T. est .

[0057] As a further aspect of the present invention: the period determination condition is:

[0058] As a further aspect of the present invention, the specific steps of step S7 are as follows:

[0059] S71. Summing up the horizontal seismic forces of each floor structure under load and performing coordinate transformation on the summation results to convert the horizontal seismic forces of each floor structure into the starting forces of each floor support under load.

[0060] S72. Based on the maximum starting load of the support and in conjunction with the working mechanism of the double self-resetting support steel frame, set the slope angle θ of the disc spring. D ;

[0061] S73, Loading stiffness K of each layer of bracing in a combined double self-resetting steel frame D,AB With unloading stiffness K D,CD The difference, and the starting load F of each layer of support. D,A The load F that is unloaded onto the inner and outer sleeves without deformation D,D The difference is used to construct a system of equations, and the number of high-strength bolts n is calculated by solving the equations. B Stiffness k of the disc spring D Initial preload N C Load correction factor for disc springs and the unloading correction factor for disc springs

[0062]

[0063] In the formula, K j,D,AB K represents the loading stiffness of the j-th layer brace in a double self-resetting steel frame; j,D,CD F represents the unloading stiffness of the j-th layer support in a double self-resetting braced steel frame; j,D,A F represents the starting load of the j-th layer support in a double self-resetting braced steel frame; j,D,D θ represents the unloading load of the j-th layer support in a double self-resetting braced steel frame; s,j This represents the inclination angle of the j-th layer of support in a double self-resetting steel frame;

[0064] S74, the number n of high-strength bolts B , the stiffness k of the disc spring D , the initial pre-tightening force N C , the loading correction coefficient of the disc spring , and the unloading correction coefficient of the disc spring are input into the dual self-resetting braced steel frame model, and the finite element analysis of the dual self-resetting braced steel frame model is continued to obtain the estimated value of the target performance.

[0065] As a further scheme of the present application: the performance judgment condition is that the set value of the target performance and the estimated value of the target performance differ by within 5%.

[0066] Compared with the prior art, the present application has the beneficial effects that:

[0067] 1. The present application ensures the superiority and reliability of the dual self-resetting braced steel frame in seismic performance through systematic design steps. First, by obtaining basic structural information and key support design parameters, performance targets are set, providing a clear direction for subsequent seismic design. Then, a single-degree-of-freedom system steel frame is constructed and relevant energy dissipation and ductility parameters are calculated, providing a basis for total energy dissipation calculation. By setting the horizontal load distribution coefficient and combining the total energy dissipation, the total base shear can be accurately calculated, ensuring the stability of the structure under seismic action. In addition, this method iteratively designs, continuously adjusts and verifies key support structural parameters until the period and performance judgment conditions are met, greatly improving the accuracy and efficiency of the design.

[0068] 2. The basic period calculation formula directly calculates the basic period through the total height of the dual self-resetting braced steel frame, without complex calculation processes or additional parameters. This simplified calculation method not only improves the calculation efficiency, but also reduces the risk of calculation errors, enabling designers to more quickly and accurately obtain the basic dynamic characteristics of the dual self-resetting braced steel frame.

[0069] 3. By setting performance targets including peak displacement angle, residual displacement angle, ductility, and peak acceleration, as well as their standard reference values, clear and quantitative evaluation standards for the seismic performance of the dual self-resetting braced steel frame are provided, which not only helps designers better grasp the performance requirements of the structure in seismic design, but also ensures the structure has good safety and reliability under seismic action.

[0070] 4. Introducing coefficients linearly related to key design parameters such as loading stiffness ratio, unloading stiffness ratio, and strength ratio, as well as terms such as powers of the natural constant, into the relevant calculation formulas for single-degree-of-freedom steel frames allows for a more accurate description of the energy dissipation, ductility, and other characteristics of single-degree-of-freedom steel frames under seismic loading. The application of these formulas not only improves the accuracy of calculations but also provides more refined analytical tools for the seismic design of double self-centering braced steel frames.

[0071] 5. The total energy dissipation calculation formula for a double self-centering braced steel frame comprehensively considers factors such as the total mass of the double self-centering braced steel frame, the mass of each story, the total number of supports, and the initiation displacement and initiation load during loading. This comprehensive consideration not only improves the accuracy of the calculation but also helps designers better evaluate the seismic performance of the structure.

[0072] 6. By setting the range of values ​​for the horizontal load distribution coefficient and selecting appropriate values, the horizontal seismic force coefficient and distribution ratio of each layer of the double self-resetting steel frame can be calculated more accurately, thereby obtaining the total base shear force.

[0073] 7. Step S5 calculates the starting load and initial stiffness of each story in the double self-resetting braced steel frame under load, and converts these values ​​into the starting load and initial stiffness of each story's supports under load, providing an accurate data foundation for subsequent finite element analysis. Simultaneously, by selecting appropriate loading stiffness ratios, unloading stiffness ratios, and strength ratios, the key structural parameters of each story's supports can be determined, thereby ensuring that the structure's seismic performance meets requirements.

[0074] 8. By setting explicit periodicity criteria, this method ensures that the basic period of the double self-resetting support steel frame meets design requirements. This criterion not only improves design accuracy but also avoids repetitive design and modification work caused by unmet periodicity requirements.

[0075] 9. Step S7 calculates key parameters such as the number of high-strength bolts, the stiffness of the disc springs, and the initial preload by solving a system of equations, providing a scientific basis for the detailed design of the double self-resetting support steel frame. Simultaneously, by setting parameters such as the slope angle of the disc springs and the loading and unloading correction coefficients, the structure can be ensured to have good self-resetting capability and energy dissipation performance under seismic loading.

[0076] 10. By setting a performance criterion that the difference between the target performance and the estimated target performance is within 5%, this method can ensure that the seismic performance of the double self-setting braced steel frame meets the design requirements. Setting this criterion not only improves the accuracy of the design but also avoids structural safety problems caused by unmet performance requirements. Attached Figure Description

[0077] Figure 1 Design flowchart of the present application.

[0078] Figure 2 DSCB and equivalent traditional SCB hysteretic curve diagram in the present application.

[0079] Figure 3 DSCB average drift angle response curve diagram of 6-story structure in the present application.

[0080] Figure 4 DSCB average drift angle response curve diagram of 9-story structure in the present application.

[0081] Figure 5 DSCB average residual drift angle response curve diagram of 6-story structure in the present application.

[0082] Figure 6 DSCB average residual drift angle response curve diagram of 9-story structure in the present application.

[0083] Figure 7 DSCB average acceleration response curve diagram of 6-story structure in the present application.

[0084] Figure 8 DSCB average acceleration response curve diagram of 9-story structure in the present application.

[0085] Figure 9 DSCB average ductility response curve diagram of 6-story structure in the present application.

[0086] Figure 10 DSCB average ductility response curve diagram of 9-story structure in the present application. DETAILED DESCRIPTION

[0087] 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. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0088] Please refer to Figure 1 In the embodiments of the present application, a double self-resetting braced steel frame with a total height of 6 stories and a total height of 9 stories is designed, and the specific design process includes the following steps:

[0089] I. Obtain basic information

[0090] Obtaining basic structure information of a dual self-centering braced steel frame (DSCB), calculating a basic period T of the DSCB according to the basic structure information, setting a performance target of the DSCB, and obtaining bracing key design parameters of the DSCB. The bracing key design parameters include a loading stiffness ratio α k,2 , an unloading stiffness ratio α k,4 , and a strength ratio β f,4 . The specific steps are as follows:

[0091] First, the shape, size, and mass of the beams, columns, nodes, bracing members, energy dissipation elements, and prestressed resetting elements in the current DSCB are obtained, which are the basic structure information of the DSCB.

[0092] Next, the specific values of the three bracing key design parameters of the DSCB are set, that is, the loading stiffness ratio α k,2 is 0.25, the unloading stiffness ratio α k,4 is 0.4, and the strength ratio β f,4 is 0.2.

[0093] Then, the performance target of the DSCB under a moderate earthquake and a major earthquake is determined, and the specific values of the performance target are shown in Table 1.

[0094] Table 1 Specific values of performance target

[0095]

[0096] Finally, according to the selected story height of the steel frame in the basic structure information, the basic period T of the dual self-centering braced steel frame is calculated using the following formula:

[0097] T = 0.0731H N 0.75 (1)

[0098] II. Establishing a single-degree-of-freedom system steel frame

[0099] The dual self-centering braced steel frame is simplified into a single-degree-of-freedom system steel frame (SDOF) according to the basic period T of the DSCB.

[0100] III. Calculating energy dissipation, amplification coefficient, and cumulative ductility

[0101] The single-cycle hysteretic energy E D , energy amplification coefficient α Energy , cumulative loading ductility μ aP , and cumulative unloading ductility μ aN of the single-degree-of-freedom system steel frame are calculated. The specific process is as follows:

[0102] The calculation formula of the hysteretic energy E h of the DSCB is as follows:

[0103]

[0104] In the formula, t total Δx represents the total duration of seismic wave vibration. B,t Denotes the deformation of the support at time t; Δx B,t-Δt F represents the deformation at time t+1; B,t This represents the axial force borne by the support at time t.

[0105] The formula for calculating the viscous damping ratio of a conventional self-resetting bearing (SCB) is as follows:

[0106]

[0107] In the formula, ζ eq,SCB γ represents the viscous damping ratio of SCB; SCB represents the strength coefficient of SCB; μ represents the required ductility ratio of DSCB, which is usually taken as 6.

[0108] like Figure 2 As shown, the horizontal axis U represents the starting displacement, and the vertical axis F represents the starting load. To calculate the equivalent damping ratio of the support in the DSCB, a curve C'D' with the same stiffness as the AB segment is plotted at the midpoint of the hysteretic unloading section (CD segment) of the DSCB. Therefore, the hysteretic energy dissipation capacity of the equivalent SCB (the area enclosed by ABC'D') is the same as that of the DSCB (the area enclosed by ABCD). In the equivalent damping ratio of the traditional SCB, γ SCB The calculation was converted into Figure 2 Calculation of the strength coefficient γ' of DSCB.

[0109] To calculate γ', first calculate Figure 2 The ordinate of point C' is y. C' The calculation formula is as follows:

[0110]

[0111] In the formula, u y Indicates the DSCB start displacement; V y Indicates; V e Indicates; S a (T) represents the acceleration response spectrum value corresponding to the fundamental period T of the equivalent double self-resetting braced steel frame. R represents the strength reduction factor of the DSCB.

[0112] Based on the ordinate y of point C' C' Calculate the corresponding equivalent strength ratio β' f,4 The calculation formula is as follows:

[0113]

[0114] Combining equations (4) and (6), we get:

[0115] γ'=1-β' f,4 (7)

[0116] The equivalent damping of the support in the DSCB can then be obtained as shown in formula (8):

[0117]

[0118] In the formula, k represents the initial stiffness of the DSCB, which is set to 1 in SDOF.

[0119] To facilitate subsequent energy-based design methods for DSCBs, the R-fit formula for SDOF can be expressed as follows:

[0120]

[0121] The coefficients of formula (9) are calculated as follows:

[0122]

[0123] Since the hysteresis curves of the DSCB are the same in the tension and compression stages, the single-turn hysteresis energy dissipation E of the single-degree-of-freedom steel frame system is... D The calculation is as follows:

[0124]

[0125] However, because DSCBs under earthquakes typically undergo multiple hysteresis cycles such as reciprocating loading and unloading, the energy dissipation of a single hysteresis cycle cannot predict the total hysteresis energy dissipation of the DSCB under earthquakes. Therefore, an energy amplification factor is proposed:

[0126] α Energy =(E h / M) / (E D / M)=E h / E D (12)

[0127] E obtained through nonlinear time history calculation h Divide by E D The corresponding energy amplification factor α can then be obtained. Enery To facilitate subsequent energy-based seismic design of the DSCB, the energy amplification factor α of the SDOF is... Energy The fitting formula can be expressed as follows:

[0128]

[0129] The calculation formulas for each coefficient in formula (13) are as follows:

[0130]

[0131] μ for energy-based seismic design of DSCB, SDOF aP The fitting formula of the spectrum can be expressed as follows:

[0132]

[0133] The calculation formula of each coefficient in formula (15) is as follows:

[0134]

[0135] μ for energy-based seismic design of DSCB, SDOF aN The fitting formula of the spectrum can be expressed as follows:

[0136]

[0137] The calculation formula of each coefficient in formula (17) is as follows:

[0138]

[0139] Four, total energy consumption calculation

[0140] According to the single cycle hysteretic energy E D , energy amplification factor α Energy , cumulative loading ductility μ aP , and cumulative unloading ductility μ aN The total energy consumption of the double self-resetting braced steel frame is calculated.

[0141] Based on the energy-based design method, the base shear of DSCB and the starting load of each floor are calculated. Assuming that all energy consumption is provided by the support, it is expressed by the energy balance formula as follows:

[0142]

[0143] F yjN = β f,4 F yjP (20)

[0144] u yjN = β f,4 u yjP (21)

[0145] Where u yjN represents the starting displacement of the jth floor structure unloading in the double self-resetting braced steel frame. F yjN represents the starting load of the jth floor structure unloading in the double self-resetting braced steel frame.

[0146] Since each story of the DSCB has the same demand ductility, the initiation displacement of each story is the same, the total energy dissipation of the DSCB steel frame can be further expressed as:

[0147]

[0148] V. Calculate the total base shear

[0149] The total base shear of the DSCB steel frame is calculated by setting the horizontal load distribution coefficient and combining the total energy dissipation.

[0150] First, the value range of the horizontal load distribution coefficient q of the DSCB steel frame is set, and a horizontal load distribution coefficient q is selected from the value range. The value of the horizontal load distribution coefficient q in the current cycle is selected as 0.7.

[0151] Since the lower energy dissipation capacity of the traditional self-centering braced frame usually leads to a larger lateral displacement distribution of the top story displacement angle. Therefore, in order to control the displacement angle of the top story, based on the selected horizontal load distribution coefficient q, the horizontal seismic force coefficient C of each story in the DSCB steel frame is calculated i ; The horizontal seismic force coefficient calculation formula is as follows:

[0152]

[0153] Then, based on the horizontal seismic force coefficient, the horizontal seismic force distribution ratio of each story in the DSCB steel frame is calculated; The calculation formula of the horizontal seismic force distribution ratio is as follows:

[0154]

[0155] Then, the initiation load of each story in the DSCB is calculated, and the initiation load is expressed as follows:

[0156] F yjP = DR j ·V y (27)

[0157]

[0158] Finally, combining formulas (23) to (28), the total base shear of the DSCB can be obtained as follows:

[0159]

[0160] Six, estimate the basic period of finite element analysis

[0161] Based on the total base shear and the support key design parameters, the support key construction parameters of the dual self-centering braced steel frame are determined to build a complete dual self-centering braced steel frame model, and the finite element analysis is performed on the dual self-centering braced steel frame model to obtain the estimated value of the basic period T.

[0162] Firstly, according to the total base shear of the dual self-centering braced steel frame, the starting load of each layer structure loading in the dual self-centering braced steel frame is calculated by combining the horizontal seismic force calculation formula, and the initial stiffness of each layer structure loading in the dual self-centering braced steel frame is calculated by combining the initial stiffness calculation formula.

[0163] The starting load calculation formula is as follows:

[0164] F yjP =DR j ·V y (30)

[0165] The initial stiffness calculation formula is as follows:

[0166] k yjP =F yjP / u yjP (31)

[0167] Then, the starting load and the initial stiffness of each layer structure loading in the dual self-centering braced steel frame are converted into the starting load and the initial stiffness of each layer support loading in the dual self-centering braced steel frame by coordinate transformation.

[0168] Then, according to the selected loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 , the support key construction parameters of each layer support are determined.

[0169] The support key design parameters, the support key construction parameters, and the starting load and the initial stiffness of each layer support loading are input into the finite element analysis software to build a dual self-centering braced steel frame model;

[0170] Finally, the finite element analysis is performed on the dual self-centering braced steel frame model by the finite element software (such as Abaqus, ANSYS, etc.) to obtain the estimated value T est of the basic period T.

[0171] If the estimated value T est satisfies the period judgment condition , the finite element simulation is performed; otherwise, the estimated value is assigned to the basic period T, and the above steps one to six are performed.

[0172] Seven, the estimated value of the target performance of the finite element analysis

[0173] First, the horizontal seismic force of each layer structure is summed and coordinate transformation is performed on the summed result to convert the horizontal seismic force of each layer structure into the starting force of each layer support through coordinate transformation.

[0174] Next, according to the maximum starting load of the support, and in combination with the working mechanism of the dual self-resetting support steel frame, the slope angle θ of the disc spring is set D .

[0175] Then, the difference between the loading stiffness K D,AB and the unloading stiffness K D,CD of each layer support in the dual self-resetting support steel frame, and the difference between the starting load F D,A and the load F D,D unloading to the inner and outer sleeves without deformation of each layer support are constructed into an equation group, the standard “Disc Spring (GB / T1972-2005)” is combined, and the number of high-strength bolts n B , the stiffness k D of the disc spring, the initial pre-tightening force N C , the loading correction coefficient of the disc spring and the unloading correction coefficient of the disc spring

[0176]

[0177] Finally, the number of high-strength bolts n B , the stiffness k D of the disc spring, the initial pre-tightening force N C , the loading correction coefficient of the disc spring and the unloading correction coefficient of the disc spring are input into the dual self-resetting support steel frame model, and the dual self-resetting support steel frame model is further subjected to finite element analysis to obtain the estimated value of the target performance.

[0178] If the target performance and the estimated value of the target performance differ by within 5%, the dual self-resetting support steel frame is designed according to the current support key construction parameters; otherwise, the above steps 1 to 7 are repeated.

[0179] The support key construction parameters of the 6-layer DSCB calculated finally are shown in Table 2, and the support key construction parameters of the 9-layer DSCB are shown in Table 3.

[0180] Table 2 Support key construction parameters of 6-layer DSCB

[0181]

[0182] Table 3 Support key construction parameters of 9-layer DSCB

[0183]

[0184] According to the data in Table 1, Table 2 and Table 3, a finite element model of the DSCB supporting steel frame is established, and the seismic response of the structure is calculated as shown in Table 4. Figures 3-10 Figures 3-10 The DBE in Table 4 represents a moderate vibration intensity earthquake, referred to as a moderate earthquake; the MCE represents a high vibration intensity earthquake, referred to as a major earthquake; the E6 represents a DACB of a 6-story structure, and the E9 represents a DACB of a 9-story structure. Figures 3-10 The results in Table 4 show that the residual drift angles of the DSCB designed by the energy-based design method are very small, the difference between the peak drift angle and the ductility peak response under the moderate earthquake and the performance target value is less than 5% of the performance target value, the peak drift angle and the ductility under the major earthquake are less than the performance target value, the support performance is fully exerted, and the design requirements are met. Meanwhile, the drift angle is uniformly distributed along the story height, which reduces the problem of excessive local story drift angle leading to exceeding the deformation limit of the support or insufficient utilization. Therefore, the design of the DSCB by the present application improves the recoverable performance of the structure and prevents the structure from producing large plastic damage under the earthquake.

[0185] The above description is only the preferred embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can make equivalent replacement or change according to the technical solution and the inventive concept of the present application within the technical range disclosed by the present application, which should be covered in the protection scope of the present application.​

Claims

1. A seismic design method for an energy-based double self-resetting supported steel frame, characterized in that, The design process includes the following steps: S1. Obtain the basic structural information of the double self-resetting braced steel frame. Based on this information, obtain the key design parameters for the double self-resetting braced steel frame, set the performance targets, and calculate the fundamental period T. The key design parameters include the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 ; S2. Based on the fundamental period T and key support design parameters, construct a single-degree-of-freedom steel frame system with a double self-resetting support, and calculate the single-cycle hysteretic energy dissipation E of the single-degree-of-freedom steel frame system. D Energy amplification factor α Energy Cumulative loading lag μ aP and cumulative unloading ductility μ aN ; S3, based on the energy consumption E of a single-turn hysteresis loop. D Energy amplification factor α Energy Cumulative loading lag μ aP and cumulative unloading ductility μ aN Calculate the total energy consumption of the double self-resetting braced steel frame; S4. Set the horizontal load distribution coefficient of the double self-resetting steel frame, and calculate the total base shear force of the double self-resetting steel frame in combination with the total energy dissipation. S5. Based on the total base shear force and key design parameters of the support, determine the key structural parameters of the double self-resetting support steel frame, thereby constructing a complete double self-resetting support steel frame model, and performing finite element analysis on the double self-resetting support steel frame model to obtain an estimate of the fundamental period T. S6. If the estimated value of the basic period T meets the period judgment condition, then proceed to steps S7-S8. Conversely, the estimated value is assigned to the basic period T, and steps S1-S5 are executed. S7. Continue with finite element analysis to obtain an estimate of the target performance; S8. If the estimated value of the target performance meets the performance judgment conditions, then the double self-resetting support steel frame shall be designed according to the current key support structural parameters. Conversely, proceed with steps S1-S7.

2. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 1, characterized in that, The formula for calculating the fundamental period T of a double self-resetting braced steel frame is as follows: T=0.0731H N 0.75 ; In the formula, H N This indicates the total height of the double self-resetting support steel frame.

3. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 2, characterized in that, The performance targets involve parameters including the peak displacement angle, residual displacement angle, ductility, and peak acceleration of the double self-resetting braced steel frame; setting the performance targets of the double self-resetting braced steel frame means determining the standard reference values ​​for the peak displacement angle, residual displacement angle, ductility, and peak acceleration.

4. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 3, characterized in that, Single-cycle hysteretic energy dissipation E of a single-degree-of-freedom steel frame system D The calculation formula is expressed as follows: In the formula, γ' represents the strength coefficient of the double self-centering braced steel frame; μ represents the required ductility ratio of the double self-centering braced steel frame; α k,2 This indicates the loading stiffness ratio of a double self-resetting braced steel frame; π represents pi; S a (T) represents the acceleration response spectrum value corresponding to the fundamental period T of the equivalent double self-resetting supported steel frame; Representing the natural constant The power; a1 and b1 both represent the ratio of the loading stiffness to α. k,2 Unloading stiffness ratio α k,4 and strength ratio β k,4 The coefficients showing a linear correlation among the three; Energy amplification factor α of a single-degree-of-freedom steel frame system Energy The calculation formula is expressed as follows: In the formula, a2 represents the coefficient linearly related to the fundamental period T; b2, c2, e2, and d2 all represent the coefficients related to the loading stiffness ratio α. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients showing a linear correlation among the three; Representing the natural constant Power; Cumulative loading ductility μ of a single-degree-of-freedom steel frame system aP The calculation formula is expressed as follows: In the formula, a3, b3, c3, and d3 all represent the ratio of the loading stiffness α to the load stiffness. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients showing a linear correlation among the three; Representing the natural constant Power; Cumulative unloading ductility μ of a single-degree-of-freedom steel frame system aN The calculation formula is expressed as follows: In the formula, a4, b4, c4, and d4 all represent the ratio of the loading stiffness α to the stiffness. k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 The coefficients showing a linear correlation among the three; Representing the natural constant Power of 1.

5. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 4, characterized in that, The formula for calculating the total energy dissipation of a double self-resetting braced steel frame is as follows: In the formula, W represents the total energy dissipation of the double self-resetting braced steel frame; M represents the total mass of the double self-resetting braced steel frame; m i The mass of the i-th layer of the double self-resetting braced steel frame is represented by N, and the total number of supports in the double self-resetting braced steel frame is represented by N. u yjP F represents the starting displacement of the j-th layer of the double self-resetting steel frame when the structure is loaded; yjP This represents the starting load when the j-th layer of the double self-resetting steel frame is loaded.

6. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 5, characterized in that, The specific steps of step S4 are as follows: S41. Set the range of values ​​for the horizontal load distribution coefficient q of the double self-resetting support steel frame, and select a horizontal load distribution coefficient q from this range. S42. Based on the selected horizontal load distribution coefficient q, calculate the horizontal seismic force coefficient of each story in the double self-centering braced steel frame; the formula for calculating the horizontal seismic force coefficient is as follows: In the formula, C i This represents the horizontal seismic force coefficient of the i-th story structure in a double self-resetting steel frame; p i p represents the structural coefficient of the i-th layer in a double self-resetting braced steel frame; i+1 w represents the structural coefficient of the (i+1)th layer in a double self-resetting braced steel frame. N h represents the mass of the Nth layer of structure in a double self-resetting braced steel frame; N This indicates the height of the Nth layer of structure in a double self-resetting braced steel frame; w j h represents the mass of the j-th layer of the structure in a double self-resetting steel frame; j This represents the height of the j-th layer of the structure in a double self-resetting steel frame; S43. Based on the horizontal seismic force coefficient, calculate the horizontal seismic force distribution ratio of each story in a double self-setting braced steel frame; the formula for calculating the horizontal seismic force distribution ratio is as follows: In the formula, DR j This represents the horizontal seismic force distribution ratio of the j-th story structure in a double self-resetting braced steel frame; S44. Based on the calculated horizontal seismic force distribution ratio and the total energy dissipation of the double self-resetting braced steel frame, calculate the total base shear force of the double self-resetting braced steel frame using the total base shear force calculation formula. The formula for calculating the total base shear force is as follows: In the formula, V y This represents the total base shear force of the double self-resetting supported steel frame.

7. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 6, characterized in that, The specific steps of step S5 are as follows: S51. Based on the total base shear force of the double self-resetting steel frame, calculate the starting load of each floor of the double self-resetting steel frame when loaded, and combine the horizontal seismic force calculation formula. At the same time, calculate the initial stiffness of each floor of the double self-resetting steel frame when loaded, and combine the initial stiffness calculation formula. The formula for calculating the starting load is as follows: F yjP =DR j ·V y ; The formula for calculating the initial stiffness is as follows: k yjP =F yjP / u yjP ; In the formula, k yjP This represents the initial stiffness of the j-th layer of the double self-resetting steel frame under load. S52. The starting load and initial stiffness of each layer of the double self-resetting steel frame when the structure is loaded are transformed into the starting load and initial stiffness of each layer of the double self-resetting steel frame when the support is loaded by coordinate transformation. S53. Based on the selected loading stiffness ratio α k,2 Unloading stiffness ratio α k,4 and strength ratio β f,4 Determine the key structural parameters of each layer of support; S54； The key design parameters, key structural parameters, and the starting load and initial stiffness of each layer of support during loading are input into the finite element analysis software to establish a double self-resetting support steel frame model. S55. A finite element analysis was performed on the double self-resetting braced steel frame model using finite element analysis software to obtain an estimate of its fundamental period T. est .

8. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 7, characterized in that, The conditions for determining the period are:

9. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 8, characterized in that, The specific steps of step S7 are as follows: S71. Summing up the horizontal seismic forces of each floor structure under load and performing coordinate transformation on the summation results to convert the horizontal seismic forces of each floor structure into the starting forces of each floor support under load. S72. Based on the maximum starting load of the support and in conjunction with the working mechanism of the double self-resetting support steel frame, set the slope angle θ of the disc spring. D ; S73, Loading stiffness K of each layer of bracing in a combined double self-resetting steel frame D,AB With unloading stiffness K D,CD The difference, and the starting load F of each layer of support. D,A The load F that is unloaded onto the inner and outer sleeves without deformation D,D The difference is used to construct a system of equations, and the number of high-strength bolts n is calculated by solving the equations. B Stiffness k of the disc spring D Initial preload N C Load correction factor for disc springs and the unloading correction factor for disc springs The system of equations is represented as follows: In the formula, K j,D,AB K represents the loading stiffness of the j-th layer brace in a double self-resetting steel frame; j,D,CD F represents the unloading stiffness of the j-th layer support in a double self-resetting braced steel frame; j,D,A F represents the starting load of the j-th layer support in a double self-resetting braced steel frame; j,D,D This represents the unloading load of the j-th layer support in a double self-resetting braced steel frame; θ s,j This represents the inclination angle of the j-th layer of support in a double self-resetting steel frame; S74, the number of high-strength bolts n B Stiffness k of the disc spring D Initial preload N C Load correction factor for disc springs and the unloading correction factor for disc springs The data is input into the double self-resetting braced steel frame model, and finite element analysis is performed on the double self-resetting braced steel frame model to obtain an estimate of the target performance.

10. The seismic design method for an energy-based double self-resetting supported steel frame according to claim 9, characterized in that, The performance judgment condition is: the difference between the set value of the target performance and the estimated value of the target performance is within 5%.

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