Energy-based aseismic design method for dual self-resetting support steel frame

Abstract

The invention relates to the technical field of building anti-seismic structure design, in particular to an energy-based anti-seismic design method for a double-self-resetting supporting steel frame. By means of systematic design steps, the superiority and reliability of the double-self-resetting supporting steel frame in the anti-seismic performance are guaranteed. Firstly, by obtaining basic structure information and supporting key design parameters, a performance target is set, and a clear direction is provided for subsequent aseismic design. Then, a single-degree-of-freedom system steel frame is constructed, relevant energy consumption, ductility and other parameters are calculated, and a foundation is provided for calculation of total energy consumption; by setting the horizontal load distribution coefficient and combining with the total energy consumption, the total base shear force can be accurately calculated, so that the stability of the structure under the earthquake action is ensured. In addition, according to the method, through iterative design, support key structure parameters are continuously adjusted and verified until period and performance judgment conditions are met, and the design accuracy and efficiency are greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of building seismic structure design, and specifically to an energy-based seismic design method for a dual self-centering braced steel frame. Background Art

[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 a certain degree of seismic resistance, when encountering strong earthquakes, problems such as excessive structural deformation, insufficient energy dissipation capacity, or poor self-centering effect often occur, which greatly affects the safety and reliability of buildings. Therefore, developing a braced steel frame that can significantly improve seismic performance and has good self-centering ability has become a current research hotspot.

[0003] The dual self-centering braced steel frame (DSCB) consists of a recoverable slope friction damper system and a self-centering system, namely a basalt fiber pre-tension rod system. It has a large post-activation stiffness and energy dissipation capacity, can effectively control the displacement response of the frame, reduce the effect of concentrated structural deformation, and has strong seismic resistance, so it is widely used. However, as a new type of lateral load resisting member that can be prefabricated in the factory, due to its special generalized flag-shaped hysteretic characteristics and construction form, it is difficult to directly apply existing traditional design methods, resulting in large design errors in the key brace construction parameters in DSCB, and the manufactured DSCB cannot fully exert its seismic performance.

[0004] Therefore, it can be seen that the design method of the key brace construction parameters in DSCB at the present stage still needs to be further improved. Summary of the Invention

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

[0006] To achieve the above object, the present invention 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. Obtain the basic structural information of the dual self-centering braced steel frame, obtain the key brace design parameters of the dual self-centering braced steel frame according to the basic structural information, set the performance objectives of the dual self-centering braced steel frame, and calculate the basic period T of the dual self-centering braced steel frame; the key brace design parameters include the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio βf,4 ;

[0009] S2. Based on the basic period T and the key design parameters of the braces, construct a single-degree-of-freedom steel frame of the double self-centering braced steel frame, and calculate the single-cycle hysteretic energy dissipation E of the single-degree-of-freedom steel frame D , energy amplification factor α Energy , cumulative loading ductility μ aP , and cumulative unloading ductility μ aN ;

[0010] S3. According to the single-cycle hysteretic energy dissipation E D , energy amplification factor α Energy , cumulative loading ductility μ aP , and cumulative unloading ductility μ aN calculate the total energy dissipation of the double self-centering braced steel frame;

[0011] S4. Set the horizontal load distribution coefficient of the double self-centering braced steel frame, and calculate the total base shear force of the double self-centering braced steel frame in combination with the total energy dissipation;

[0012] S5. Based on the total base shear force and the key design parameters of the braces, determine the key construction parameters of the braces of the double self-centering braced steel frame, and construct a complete double self-centering braced steel frame model accordingly, and perform finite element analysis on the double self-centering 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, execute steps S7-S8; otherwise, assign the estimated value to the basic period T, and execute steps S1-S5;

[0014] S7. Continue to perform 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, design the double self-centering braced steel frame according to the current key construction parameters of the braces; otherwise, execute steps S1-S7.

[0016] As a further solution of the present invention: The calculation formula for the basic period T of the double self-centering 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-centering braced steel frame.

[0019] As a further solution of the present invention: the parameters related to the performance target include the peak displacement angle, residual displacement angle, ductility, and peak acceleration of the double self-centering braced steel frame; setting the performance target of the double self-centering braced steel frame is to determine the standard reference values of the peak displacement angle, residual displacement angle, ductility, and peak acceleration.

[0020] As a further solution of the present invention: the single-cycle hysteretic energy dissipation E of the single-degree-of-freedom system steel frame D is calculated as follows:

[0021]

[0022] 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 represents the loading stiffness ratio of the double self-centering braced steel frame; π represents the pi; S a (T) represents the acceleration response spectrum value corresponding to the fundamental period T of the equivalent double self-centering braced steel frame; represents the power of the natural constant; a 1 represents the coefficient linearly related to the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 ; b 1 represents the coefficient linearly related to the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 ;

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

[0024]

[0025] In the formula, a 2 represents the coefficient linearly related to the fundamental period T; b 2 represents the coefficient linearly related to the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 ; c 2 represents the coefficient linearly related to the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 ; e 2 represents the coefficient linearly related to the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 ; d2 Denotes the 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 ; Denotes the power of the natural constant;

[0026] The cumulative loading ductility μ of the single-degree-of-freedom steel frame aP is calculated as follows:

[0027]

[0028] where a 3 Denotes the 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 ; b 3 Denotes the 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 ; c 3 Denotes the 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 ; d 3 Denotes the 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 ; Denotes the power of the natural constant;

[0029] The cumulative unloading ductility μ of the single-degree-of-freedom steel frame aN is calculated as follows:

[0030]

[0031] where a 4 Denotes the 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 ; b 4 Denotes the 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 ; c 4 Denotes the coefficient linearly related to the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4Coefficient in linear correlation; d 4 Denote the coefficient related to the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and strength ratio β f,4 which is in linear correlation; Denote the power of the natural constant.

[0032] As a further solution of the present invention: The calculation formula for the total energy dissipation of the double self - resetting bracing steel frame is as follows:

[0033]

[0034] In the formula, W represents the total energy dissipation of the double self - resetting bracing steel frame; M represents the total mass of the double self - resetting bracing steel frame; m i represents the mass of the i - th floor structure in the double self - resetting bracing steel frame, N represents the total number of braces in the double self - resetting bracing steel frame; u yjP represents the starting displacement when the j - th floor structure in the double self - resetting bracing steel frame is loaded; F yjP represents the starting load when the j - th floor structure in the double self - resetting bracing steel frame is loaded.

[0035] As a further solution of the present invention: 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 bracing steel frame, and select a horizontal load distribution coefficient q from this value range;

[0037] S42. Based on the selected horizontal load distribution coefficient q, calculate the horizontal seismic force coefficient of each floor structure in the double self - resetting bracing steel frame; The calculation formula for the horizontal seismic force coefficient is expressed as follows:

[0038]

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

[0040] S43. Calculate the horizontal seismic force distribution ratio of each floor structure in the dual self-centering braced steel frame based on the horizontal seismic force coefficient. The calculation formula for the horizontal seismic force distribution ratio is as follows:

[0041]

[0042] In the formula, DR j represents the horizontal seismic force distribution ratio of the j-th floor structure in the dual self-centering braced steel frame;

[0043] S44. According to the calculated horizontal seismic force distribution ratio and combined with the total energy dissipation of the dual self-centering braced steel frame, calculate the total base shear force of the dual self-centering braced steel frame through the total base shear force calculation formula. The total base shear force calculation formula is as follows:

[0044]

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

[0046] As a further solution of the present invention, the specific steps of step S5 are as follows:

[0047] S51. According to the total base shear force of the dual self-centering braced steel frame, calculate the starting load when each floor structure of the dual self-centering braced steel frame is loaded in combination with the horizontal seismic force calculation formula, and at the same time calculate the initial stiffness when each floor structure of the dual self-centering braced steel frame is loaded in combination with the initial stiffness calculation formula;

[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 when the j-th floor structure of the dual self-centering braced steel frame is loaded;

[0053] S52. Convert the starting load and initial stiffness when each floor structure of the dual self-centering braced steel frame is loaded into the starting load and initial stiffness when each floor brace of the dual self-centering braced steel frame is loaded by means of coordinate transformation;

[0054] S53. According to the selected loading stiffness ratio αk,2 、Unloading stiffness ratio α k,4 and strength ratio β f,4 , to determine the key structural parameters of each layer of bracing;

[0055] S54; Input the key design parameters of the bracing, the key structural parameters of the bracing, as well as the starting load and initial stiffness when each layer of bracing is loaded into the finite element analysis software to establish a dual self-centering bracing steel frame model;

[0056] S55. Perform finite element analysis on the dual self-centering bracing steel frame model through the finite element analysis software to obtain an estimated value T of its fundamental period T est .

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

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

[0059] S71. Sum the horizontal seismic forces when each layer of the structure is loaded and perform coordinate transformation on the summation result to convert the horizontal seismic forces of each layer of the structure into the starting forces when each layer of bracing is loaded through coordinate transformation;

[0060] S72. Set the slope angle θ of the disc spring according to the maximum starting load of the bracing and in combination with the working mechanism of the dual self-centering bracing steel frame D ;

[0061] S73. Simultaneously establish the difference between the loading stiffness K D,AB and the unloading stiffness K D,CD of each layer of bracing in the dual self-centering bracing steel frame, as well as the difference between the starting load F D,A of each layer of bracing and the load F D,D when unloading until there is no deformation between the inner and outer sleeves, construct a system of equations, and calculate the number n B of high-strength bolts, the stiffness k D of the disc spring, the initial pre-tightening force N C , the loading correction coefficient and the unloading correction coefficient

[0062]

[0063] In the formula, K j,D,AB represents the loading stiffness of the j-th layer of bracing in the dual self-centering bracing steel frame; K j,D,CD represents the unloading stiffness of the j-th layer of bracing in the dual self-centering bracing steel frame; F j,D,A represents the starting load of the j-th layer of bracing in the dual self-centering bracing steel frame; Fj,D,D represents the unloading load of the brace on the j-th floor in the double self-centering steel braced frame; θ s,j represents the inclination angle of the brace on the j-th floor in the double self-centering steel braced frame;

[0064] S74. Input the number n B of high-strength bolts, 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 into the double self-centering steel braced frame model, and continue to perform finite element analysis on the double self-centering steel braced frame model to obtain the estimated value of the target performance.

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

[0066] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0067] 1. Through a systematic design process, the present invention ensures the superiority and reliability of the double self-centering steel braced frame in seismic performance. First, by obtaining the basic structural information and key design parameters of the brace, the performance objectives are set, providing a clear direction for subsequent seismic design. Then, a single-degree-of-freedom system steel frame is constructed and related energy dissipation, ductility and other parameters are calculated, providing a basis for the calculation of the total energy dissipation. By setting the horizontal load distribution coefficient and combining it with the total energy dissipation, the total base shear force can be accurately calculated, thus ensuring the stability of the structure under earthquake action. In addition, through iterative design, the key construction parameters of the brace are continuously adjusted and verified 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 double self-centering steel braced 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 obtain the basic dynamic characteristics of the double self-centering steel braced frame more quickly and accurately.

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

[0070] 4. Introducing coefficients linearly related to key design parameters of braces such as loading stiffness ratio, unloading stiffness ratio, and strength ratio, as well as terms such as powers of natural constants, into the relevant calculation formulas of single-degree-of-freedom steel frames can more accurately describe the energy dissipation, ductility, and other characteristics of single-degree-of-freedom steel frames under earthquake action. The application of these formulas not only improves the calculation accuracy but also provides a more refined analysis method for the seismic design of double self-centering braced steel frames.

[0071] 5. The total energy dissipation calculation formula of double self-centering braced steel frames comprehensively considers factors such as the total mass of the double self-centering braced steel frame, the mass of each floor structure, the total number of braces, and the starting displacement and starting load during loading, and can more comprehensively reflect the energy dissipation of the structure under earthquake action. This comprehensive consideration not only improves the calculation accuracy but also helps designers better evaluate the seismic performance of the structure.

[0072] 6. By setting the value range of the horizontal load distribution coefficient and selecting appropriate values, the horizontal seismic force coefficient and distribution ratio of each floor structure in the double self-centering braced steel frame can be calculated more accurately, and then the total base shear force can be obtained.

[0073] 7. Step S5 provides an accurate data basis for subsequent finite element analysis by calculating the starting load and initial stiffness of each floor structure during loading in the double self-centering braced steel frame and converting them into the starting load and initial stiffness of each floor brace during loading. At the same time, by selecting appropriate loading stiffness ratio, unloading stiffness ratio, and strength ratio, the key construction parameters of each floor brace can be determined, thus ensuring that the seismic performance of the structure meets the requirements.

[0074] 8. By setting clear period judgment conditions, this method can ensure that the fundamental period of the double self-centering braced steel frame meets the design requirements. The setting of such judgment conditions not only improves the design accuracy but also avoids repeated design and modification work caused by non-compliance of the period.

[0075] 9. Step S7 calculates key parameters such as the number of high-strength bolts, the stiffness of disc springs, and the initial pre-tightening force by solving equations, providing a scientific basis for the detailed design of the double self-centering braced steel frame. At the same time, by setting parameters such as the slope angle of the disc spring and the loading and unloading correction coefficients, the structure can be ensured to have good self-centering ability and energy dissipation performance under earthquake action.

[0076] 10. By setting a performance judgment condition that the difference between the target performance and the estimated value of the target performance is within 5%, this method can ensure that the seismic performance of the double self-centering braced steel frame meets the design requirements. The setting of the judgment condition not only improves the design precision but also avoids structural safety problems caused by non-compliance of the performance. Description of the Drawings

[0077] Figure 1 This is the design flow chart of the present invention.

[0078] Figure 2 This is the hysteresis curve diagram of DSCB and equivalent traditional SCB in the present invention.

[0079] Figure 3 This is the average displacement angle response curve diagram of DSCB with a 6-story structure in the present invention.

[0080] Figure 4 This is the average displacement angle response curve diagram of DSCB with a 9-story structure in the present invention.

[0081] Figure 5 This is the average residual displacement angle response curve diagram of DSCB with a 6-story structure in the present invention.

[0082] Figure 6 This is the average residual displacement angle response curve diagram of DSCB with a 9-story structure in the present invention.

[0083] Figure 7 This is the average acceleration response curve diagram of DSCB with a 6-story structure in the present invention.

[0084] Figure 8 This is the average acceleration response curve diagram of DSCB with a 9-story structure in the present invention.

[0085] Figure 9 This is the average ductility response curve diagram of DSCB with a 6-story structure in the present invention.

[0086] Figure 10 This is the average ductility response curve diagram of DSCB with a 9-story structure in the present invention. Specific embodiments

[0087] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0088] Please refer to Figure 1 , in the embodiments of the present invention, a dual self-centering braced steel frame with a total height of 6 stories and a total height of 9 stories is designed. The specific design process includes the following steps:

[0089] I. Obtain basic information

[0090] Obtain the basic structural information of the Dual Self-Centering Braced Steel Frame (DSCB), calculate the basic period T of the DSCB according to this basic structural information, set the performance objectives of the DSCB, and obtain the key design parameters of the braces of the DSCB. The key design parameters of the braces include the loading stiffness ratio α k,2 , the unloading stiffness ratio α k,4 and the strength ratio β f,4 . The specific steps are as follows:

[0091] First, obtain the information such as the shape, size, and mass of the structures such as beams, columns, joints, bracing members, energy dissipation components, and prestressed self-centering components in the current DSCB. These information are the basic structural information of the DSCB.

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

[0093] Then, determine the performance objectives of the DSCB under medium and large earthquakes. The specific values of the performance objectives are shown in Table 1.

[0094] Table 1 Specific values of performance objectives

[0095]

[0096] Finally, according to the storey height selected for the steel frame in the basic structural information, use the following formula to calculate the basic period T of the Dual Self-Centering Braced Steel Frame:

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

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

[0099] Simplify the Dual Self-Centering Braced Steel Frame into a single-degree-of-freedom system steel frame (SDOF) according to the basic period T of the DSCB.

[0100] III. Calculate energy dissipation, amplification factor, and cumulative ductility

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

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

[0103]

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

[0105] The calculation formula for the viscous damping ratio of the traditional self-centering brace (SCB) is:

[0106]

[0107] In the formula, ζ eq,SCB represents the viscous damping ratio of the SCB; γ SCB represents the strength coefficient of the SCB; μ represents the required ductility ratio of the DSCB, usually taking a value of 6.

[0108] As Figure 2 shown, the abscissa U represents the activation displacement, and the ordinate F represents the activation load. To calculate the equivalent damping ratio of the brace in the DSCB, a curve C'D' section with the same stiffness as the AB section is drawn at the midpoint of the hysteretic unloading section (CD section) 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, the calculation of γ SCB is converted into Figure 2 the calculation of the strength coefficient γ' of the DSCB in

[0109] To calculate γ', first calculate Figure 2 the ordinate y C' of point C' in

[0110]

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

[0112] According to the ordinate y C' of point C', calculate the corresponding equivalent strength ratio β' f,4 . The calculation formula is as follows:

[0113]

[0114] Combining formula (4) to formula (6), we can get:

[0115] γ'=1-β' f,4 (7)

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

[0117]

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

[0119] To facilitate the subsequent energy-based design method for DSCB, the fitting formula of R of SDOF can be expressed as follows:

[0120]

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

[0122]

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

[0124]

[0125] However, since DSCBs under earthquakes usually undergo multiple hysteresis cycles such as reciprocating loading and unloading, the single-loop hysteresis energy dissipation cannot predict the total hysteresis energy dissipation of DSCBs under earthquakes. Therefore, the energy amplification factor is proposed:

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

[0127] The E calculated by nonlinear time history h Divide by E D , the corresponding energy amplification factor α can be obtained Enery To facilitate the subsequent energy-based seismic design of DSCB, the energy amplification factor α of 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] For the energy-based seismic design of DSCB, the μ of SDOF aP The fitting formula of the spectrum can be expressed as follows:

[0132]

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

[0134]

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

[0136]

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

[0138]

[0139] IV. Calculate the total energy dissipation

[0140] According to the single-loop hysteretic energy dissipation E D , energy amplification coefficient α Energy , cumulative loading ductility μ aP , and cumulative unloading ductility μ aN , calculate the total energy dissipation of the dual self-centering braced steel frame.

[0141] Based on the energy-based design method, calculate the base shear force and the starting load of each floor of DSCB. Assuming that all energy dissipation is provided by the braces, it is expressed by the energy balance formula as:

[0142]

[0143] F yjN =β f,4 F yjP (20)

[0144] u yjN =β f,4 u yjP (21)

[0145] Among them, u yjN represents the starting displacement when the structure of the j-th floor in the dual self-centering braced steel frame is unloaded. F yjN represents the starting load when the structure of the j-th floor in the dual self-centering braced steel frame is unloaded.

[0146] Since each layer structure of the DSCB has the same required ductility, the starting displacements of each layer structure are the same. Therefore, the formula for calculating the total energy dissipation of the double self-centering braced steel frame can be further expressed as:

[0147]

[0148] V. Calculating the total base shear

[0149] Set the horizontal load distribution coefficient of the double self-centering braced steel frame, and calculate the total base shear of the double self-centering braced steel frame in combination with the total energy dissipation.

[0150] First, set the value range of the horizontal load distribution coefficient q of the double self-centering braced steel frame, and select a horizontal load distribution coefficient q from this value range. The value of the horizontal load distribution coefficient q in the current round of loop is selected as 0.7.

[0151] Since the low energy dissipation capacity of the traditional self-centering braced frame usually leads to a large lateral displacement distribution at the top floor of the structure. Therefore, to control the displacement angle at the top floor of the structure, based on the selected horizontal load distribution coefficient q, calculate the horizontal seismic force coefficient C of each layer structure in the double self-centering braced steel frame i ; The calculation formula of the horizontal seismic force coefficient is expressed as follows:

[0152]

[0153] Next, based on the horizontal seismic force coefficient, calculate the horizontal seismic force distribution ratio of each layer structure in the double self-centering braced steel frame; the calculation formula of the horizontal seismic force distribution ratio is expressed as follows:

[0154]

[0155] Then, calculate the starting load of each layer structure in the DSCB, and the starting load is expressed as follows:

[0156] F yjP =DR j ·V y (27)

[0157]

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

[0159]

[0160] VI. Estimated value of the fundamental period of finite element analysis

[0161] Based on the total base shear force and the key design parameters of the braces, determine the key construction parameters of the braces for the dual self-centering braced steel frame, and thus construct a complete dual self-centering braced steel frame model. Then, perform a finite element analysis on this dual self-centering braced steel frame model to obtain an estimated value of the fundamental period T.

[0162] First, according to the total base shear force of the dual self-centering braced steel frame, combine with the horizontal seismic force calculation formula to calculate the starting load when each floor structure of the dual self-centering braced steel frame is loaded. At the same time, combine with the initial stiffness calculation formula to calculate the initial stiffness when each floor structure of the dual self-centering braced steel frame is loaded.

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

[0164] F yjP =DR j ·V y (30)

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

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

[0167] Next, through coordinate transformation, convert the starting load and initial stiffness when each floor structure of the dual self-centering braced steel frame is loaded into the starting load and initial stiffness when each floor brace of the dual self-centering braced steel frame is loaded.

[0168] Then, according to the selected loading stiffness ratio α k,2 、unloading stiffness ratio α k,4 and strength ratio β f,4 , determine the key construction parameters of each floor brace.

[0169] Then, input the key design parameters of the braces, the key construction parameters of the braces, as well as the starting load and initial stiffness when each floor brace is loaded into the finite element analysis software to establish a dual self-centering braced steel frame model;

[0170] Finally, perform a finite element analysis on the dual self-centering braced steel frame model through finite element software (such as Abaqus, ANSYS, etc.) to obtain an estimated value T est .

[0171] If the estimated value T est satisfies the period judgment condition then perform a finite element simulation; otherwise, assign this estimated value to the fundamental period T and execute the above steps one to six.

[0172] VII. Estimated value of the target performance of the finite element analysis

[0173] Firstly, the horizontal seismic force of each layer structure when loaded is summed and the summation result is subjected to coordinate transformation, so as to transform the horizontal seismic force of each layer structure into the starting force when each layer support is loaded through coordinate transformation.

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

[0175] Then, the loading stiffness K of each layer of support in the double self-centering support steel frame is combined. D,AB and unloading stiffness K D,CD The difference between the starting loads F of each layer support D,A Load F when unloading to inner and outer casings without deformation D,D The difference between the values ​​of the equations is constructed, and the number of high-strength bolts n is calculated by solving the equations in combination with the standard "Disc Spring (GB / T1972-2005)". B , the stiffness k of the disc spring D , initial preload N C , loading correction factor of disc spring And the unloading correction factor of the disc spring

[0176]

[0177] Finally, the number of high-strength bolts n B , the stiffness k of the disc spring D , initial preload N C , loading correction factor of disc spring And the unloading correction factor of the disc spring The input is then fed into the double self-righting braced steel frame model, and finite element analysis is continued on the double self-righting braced steel frame model to obtain an estimate of the target performance.

[0178] If the target performance is within 5% of the estimated value of the target performance, the double self-centering braced steel frame is designed according to the current key structural parameters of the support; otherwise, steps one to seven are repeated.

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

[0180] Table 2 Key structural parameters of the support of the 6-layer DSCB

[0181]

[0182] Table 3 Key structural parameters of the support of the 9-story DSCB

[0183]

[0184] Based on the data in Table 1, Table 2 and Table 3, a finite element model of the DSCB-supported steel frame was established to calculate the seismic response of the structure as Figures 3 - 10 shown. Figures 3 - 10 In [reference], DBE represents an earthquake with medium vibration intensity, simply referred to as the medium earthquake; MCE represents an earthquake with high vibration intensity, simply referred to as the major earthquake; E6 represents the DACB of a 6-story structure, and similarly, E9 represents the DACB of a 9-story structure. Figures 3 - 10 The results [of a certain study] show that the residual displacement angles of DSCB using the energy-based design method are all very small. Under the medium earthquake, the differences between the peak displacement angle and the ductility peak response and the performance target values are less than 5% of the performance target values. Under the major earthquake, the peak displacement angle and ductility are less than the performance target values, and the bracing performance is fully exerted, meeting the design requirements. At the same time, the displacement angle is evenly distributed along the building height, reducing the problems of excessive or insufficient utilization of the bracing deformation limit caused by too large or too small local floor displacement angles. Therefore, the design of DSCB using the present invention improves the recoverable performance of the structure and prevents the structure from undergoing large plastic damage during an earthquake.

[0185] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution of the present invention and its inventive concept, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

Claims

1. An energy-based double self-resetting braced steel frame seismic design method, characterized in that: The design steps include: S1. Obtain basic structural information of the double self-resetting support steel frame, obtain key support design parameters of the double self-resetting support steel frame according to the basic structural information, set performance targets of the double self-resetting support steel frame, and calculate the basic period T of the double self-resetting support steel frame; the key support design parameters include loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and intensity ratio β f,4 ; S2. Based on the basic period T and the key design parameters of the support, a single-degree-of-freedom system steel frame with double self-resetting support steel frame is constructed, and the single-loop hysteresis energy dissipation E of the single-degree-of-freedom system steel frame is calculated. D , energy magnification factor α Energy , Cumulative loading ductility μ aP , and the cumulative unloading ductility μ aN ; S3, based on single-turn hysteresis energy consumption E D , energy magnification factor α Energy , Cumulative loading ductility μ aP , and the cumulative unloading ductility μ aN Calculate the total energy consumption of the double self-righting braced steel frame; S4. Set the horizontal load distribution coefficient of the double self-centering brace steel frame, and calculate the total base shear force of the double self-centering brace steel frame in combination with the total energy consumption; S5. Based on the total base shear force and the key design parameters of the support, determine the key structural parameters of the support of the double self-centering braced steel frame, thereby constructing a complete double self-centering braced steel frame model, and perform finite element analysis on the double self-centering braced steel frame model to obtain an estimated value of the basic period T; S6. If the estimated value of the basic period T meets the period judgment condition, execute steps S7-S8; Otherwise, the estimated value is assigned to the basic period T, and steps S1-S5 are executed; S7, continue finite element analysis to obtain an estimate of the target performance; S8. If the estimated value of the target performance meets the performance judgment condition, the double self-centering braced steel frame is designed according to the current key structural parameters of the support; Otherwise, execute steps S1-S7.

2. The energy-based double self-resetting braced steel frame seismic design method according to claim 1 is characterized in that: The calculation formula of the basic period T of the double self-centering braced steel frame is as follows: T=0.0731H N 0.75 ; In the formula, H N Indicates the overall height of the double self-righting braced steel frame.

3. The energy-based double self-resetting braced steel frame seismic design method according to claim 2 is characterized in that: The parameters involved in the performance target include the peak displacement angle, residual displacement angle, ductility and peak acceleration of the double self-righting braced steel frame; setting the performance target of the double self-righting braced steel frame is to determine the standard reference values ​​of the peak displacement angle, residual displacement angle, ductility and peak acceleration.

4. The energy-based double self-resetting braced steel frame seismic design method according to claim 3 is characterized in that: Single-loop hysteresis energy dissipation E of a steel frame with a single degree of freedom D The calculation formula is as follows: Where, γ' represents the strength coefficient of the double self-centering brace steel frame; μ represents the required ductility ratio of the double self-centering brace steel frame; α k,2 represents the loading stiffness ratio of the double self-centering braced steel frame; π represents the circumference of the circle; S a (T) represents the acceleration response spectrum value corresponding to the fundamental period T of the equivalent double self-righting braced steel frame; Represents a natural constant power; a1 and b1 both represent the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 , and the intensity ratio β k,4 The linear correlation coefficients among the three; Energy amplification factor α of steel frame with single degree of freedom Energy The calculation formula is as follows: Where a2 is the coefficient linearly related to the basic period T; b2, c2, e2 and d2 are all related to the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 , and the intensity ratio β f,4 The linear correlation coefficients among the three; Represents a natural constant Power; Cumulative loading ductility μ of steel frame with single degree of freedom aP The calculation formula is as follows: Where a3, b3, c3 and d3 all represent the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 , and the intensity ratio β f,4 The linear correlation coefficients among the three; Represents a natural constant Power; Cumulative unloading ductility μ of steel frame with single degree of freedom aN The calculation formula is as follows: Where a4, b4, c4 and d4 all represent the loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 , and the intensity ratio β f,4 The linear correlation coefficients among the three; Represents a natural constant Power.

5. The energy-based double self-resetting braced steel frame seismic design method according to claim 4 is characterized in that: The total energy consumption of the double self-centering braced steel frame is calculated as follows: Where W represents the total energy consumption of the double self-centering support steel frame; M represents the total mass of the double self-centering support steel frame; m i represents the mass of the i-th layer structure in the double self-righting brace steel frame, and N represents the total number of braces in the double self-righting brace steel frame; u yjP represents the starting displacement of the j-th layer structure in the double self-centering braced steel frame when loaded; F yjP It represents the starting load when the j-th layer structure in the double self-righting braced steel frame is loaded.

6. The energy-based double self-resetting braced steel frame seismic design method according to claim 5 is characterized in that: The specific steps of step S4 are as follows: S41, setting a value range of the horizontal load distribution coefficient q of the double self-resetting support steel frame, and selecting a horizontal load distribution coefficient q from the value range; S42. Based on the selected horizontal load distribution coefficient q, calculate the horizontal seismic force coefficient of each layer structure in the double self-centering braced steel frame; the calculation formula of the horizontal seismic force coefficient is as follows: In the formula, C i represents the horizontal seismic force coefficient of the i-th floor structure in a double self-righting braced steel frame; p i represents the structural coefficient of the i-th layer structure in the double self-centering braced steel frame; p i+1 represents the structural coefficient of the i+1th floor structure in the double self-centering braced steel frame; w N represents the mass of the Nth layer structure in the double self-centering braced steel frame; h N represents the height of the Nth floor structure in the double self-centering braced steel frame; w j represents the mass of the j-th layer structure in the double self-centering braced steel frame; h j represents the height of the jth floor structure in the double self-centering braced steel frame; S43. Based on the horizontal seismic force coefficient, calculate the horizontal seismic force distribution ratio of each layer structure in the double self-righting braced steel frame; the calculation formula of the horizontal seismic force distribution ratio is expressed as follows: In the formula, DR j represents the horizontal seismic force distribution ratio of the j-th floor structure in the double self-righting braced steel frame; S44, calculating the total base shear force of the double self-centering braced steel frame by using the total base shear force calculation formula according to the calculated horizontal seismic force distribution ratio and the total energy consumption of the double self-centering braced steel frame; The total base shear force calculation formula is as follows: Where V y Represents the total base shear force of the doubly self-centering braced steel frame.

7. The energy-based double self-centering braced steel frame seismic design method according to claim 6 is characterized in that: The specific steps of step S5 are as follows: S51. Calculate the starting load of each layer of the double self-centering support steel frame when loaded based on the total base shear force of the double self-centering support steel frame and the horizontal seismic force calculation formula, and calculate the initial stiffness of each layer of the double self-centering support steel frame when loaded based on the initial stiffness calculation formula; The calculation formula of starting load is as follows: F yjP =DR j ·V y ; The initial stiffness calculation formula is as follows: k yjP =F yjP / u yjP ; In the formula, k yjP represents the initial stiffness of the j-th layer structure in the double self-righting braced steel frame when loaded; S52, converting the starting load and initial stiffness of each layer structure in the double self-centering support steel frame when loaded into the starting load and initial stiffness of each layer support in the double self-centering support steel frame when loaded by means of coordinate transformation; S53, according to the selected loading stiffness ratio α k,2 , unloading stiffness ratio α k,4 and intensity ratio β f,4 , determine the key structural parameters of each layer of support; S54； Input the key design parameters of the support, the key structural parameters of the support, and the starting load and initial stiffness of each layer of support when loaded into the finite element analysis software to establish a double self-centering support steel frame model; S55. Perform finite element analysis on the double self-centering brace steel frame model using finite element analysis software to obtain an estimated value of its basic period T est .

8. The energy-based double self-centering braced steel frame seismic design method according to claim 7 is characterized in that: The cycle judgment conditions are:

9. The energy-based double self-resetting braced steel frame seismic design method according to claim 8, characterized in that: The specific steps of step S7 are as follows: S71, summing the horizontal seismic forces of each layer of the structure when it is loaded and performing coordinate transformation on the summation result, so as to transform the horizontal seismic forces of each layer of the structure into the starting forces of each layer of the support when it is loaded through coordinate transformation; S72. According to the maximum starting load of the support and the working mechanism of the double self-reset support steel frame, set the slope angle θ of the disc spring. D ; S73、Loading stiffness K of each layer of support in the combined double self-centering support steel frame D,AB and unloading stiffness K D,CD The difference between the starting loads F of each layer support D,A Load F when unloading to inner and outer casings without deformation D,D The difference between the two is used to construct a set of equations, and the number of high-strength bolts n is calculated by solving the equations. B , the stiffness k of the disc spring D , initial preload N C , loading correction factor of disc spring And the unloading correction factor of the disc spring The system of equations is expressed as follows: In the formula, K j,D,AB K represents the loading stiffness of the j-th support in the double self-centering brace steel frame; j,D,CD F represents the unloading stiffness of the j-th support in the double self-centering brace steel frame; j,D,A F represents the starting load of the j-th support in the double self-centering brace steel frame; j,D,D represents the unloading load of the j-th support in the double self-centering braced steel frame; θ s,j represents the inclination angle of the j-th support in the double self-centering brace steel frame; S74, the number of high-strength bolts n B , the stiffness k of the disc spring D , initial preload N C , loading correction factor of disc spring And the unloading correction factor of the disc spring The input is then fed into the double self-righting braced steel frame model, and finite element analysis is continued on the double self-righting braced steel frame model to obtain an estimate of the target performance.

10. The energy-based double self-centering braced steel frame seismic design method according to claim 9, characterized in that: The performance judgment condition is that the set value of the target performance is within 5% of the estimated value of the target performance.

Images