Out-of-plane stability design method for buckling-restrained braces considering bidirectional earthquake action

Abstract

The invention provides a method for designing the out-of-plane stability of a buckling-resistance support considering bidirectional earthquake action, comprising the following steps: determining the geometric dimensions of the buckling-resistance support and the node plate and the target out-of-plane displacement angle; calculating the resistance parameter and the stiffness parameter, wherein the resistance parameter includes the yield axial force of the node plate, and the stiffness parameter includes the rotational stiffness of the node plate, the ultimate bending moment of the node plate and the bending stiffness of the buckling-resistance support connection section; calculating the critical force of elastic buckling out of the buckling-resistance support plane; calculating the trigger eccentricity, and verifying whether the out-of-plane stability of the support is satisfied. If satisfied, the designed buckling-resistance support shock-absorbing system can ensure out-of-plane stability under bidirectional earthquake action; if not satisfied, the buckling-resistance support subsystem will be out-of-plane unstable under bidirectional earthquake action, and return to step 1 to redesign the buckling-resistance support shock-absorbing system. The method of the invention can accurately predict the out-of-plane ultimate load of the buckling-resistance support subsystem under bidirectional earthquake action.

Description

Technical Field

[0001] The invention belongs to the technical field of earthquake-resistant design, and in particular relates to an out-of-plane stability design method for a herringbone buckling-restrained brace considering bidirectional earthquake action. Background Art

[0002] Buckling-resistance bracing is a type of bracing that combines the functions of ordinary bracing and metal energy-absorbing damper ( Figure 1 ), in the past decade or so, has become an effective means of structural seismic control and improving structural seismic performance. The key to achieving energy dissipation of buckling-resistance braces lies in how to solve the problem of brace compressive buckling, and then give full play to its function as a structural fuse. The typical buckling failure modes of buckling-resistance braces are summarized into four types: overall buckling, local buckling, in-plane buckling of the inner core extension section, and out-of-plane buckling of the inner core extension section and the connected node plate. After decades of development, relatively mature design methods have been formed at home and abroad for the first three failure modes, and have been written into relevant standards and specifications. The extension section of the buckling-resistance brace (i.e. Figure 1 The out-of-plane bending stiffness of the transition section and connection section shown in the figure and the connected node plate are small and are not constrained by the constraint unit. These two parts are more prone to out-of-plane buckling. Most of the existing research on buckling-resistance brace seismic reduction technology is based on the plane frame theory, that is, only considering the influence of the unidirectional seismic action on the frame in the plane direction on the bearing performance of the brace. However, relevant studies have shown that buckling-resistance braces are prone to cause significant bidirectional deformation of the structural floors under bidirectional seismic action, thereby changing the geometric and physical boundary conditions at both ends of the buckling-resistance brace, which is significantly different from the existing design theory established by considering only unidirectional seismic action, resulting in buckling-resistance braces being more prone to out-of-plane instability failure than when they are only subjected to unidirectional seismic action. Considering the randomness and multi-directionality of seismic action, it is necessary to further develop the out-of-plane stability design theory of buckling-resistance braces considering bidirectional seismic action.

[0003] In terms of the out-of-plane stability design method of buckling-resistance braces, the two main design ideas currently used at home and abroad are "separate" and "integral":

[0004] The "separate" design method isolates the node plate from the buckling-resistance brace and subframe, applies the isolated support axial force to the node plate, and uses the column-strip theory to calculate the out-of-plane stability bearing capacity of the slats between the effective section of the node plate and the beam-column range, ignoring the interaction between the node plate and the brace. This method has the advantages of a simple mechanical model and easy calculation, but it completely separates the two-way deformation of the floor and the coupling of the buckling-resistance brace connection section with the node plate out-of-plane deformation and internal force, and cannot consider the impact of the two-way deformation on the out-of-plane stability of the buckling-resistance brace.

[0005] The "integrated" design method considers the node plate, buckling-resistance brace extension, buckling-resistance brace constraint section and even the frame members (beams and columns) connected to the node plate as subsystems, and studies the out-of-plane stability of the subsystem under in-plane unidirectional earthquake action. A plastic hinge theory model is established (see Figure 2 ) and the moment transfer theory model (see Figure 3 ). Although the above model takes into account the influence of the out-of-plane stiffness of the subframe and node plate on the out-of-plane stability of the buckling-restrained brace, it is still essentially a plane theory based on unidirectional earthquake action, and fails to consider the influence of the bidirectional deformation of the floor caused by bidirectional earthquake action on the out-of-plane stability of the buckling-restrained brace. In addition, the design method considers too many parameters, which makes the design very cumbersome and inconvenient for practical application. Summary of the invention

[0006] In order to solve the problem that the existing out-of-plane stability design method of anti-buckling brace cannot consider the influence of bidirectional seismic action, the present invention is based on the herringbone brace arrangement commonly used at home and abroad, and proposes a practical out-of-plane stability design method of anti-buckling brace considering bidirectional seismic action, so as to break through the theoretical limitation that the existing support frame design can only consider unidirectional seismic action.

[0007] In order to achieve the purpose of the present invention, the present invention provides a method for out-of-plane stability design of buckling-restrained braces considering bidirectional seismic action, comprising the following steps:

[0008] Step 1: Determine the geometric dimensions of the buckling-resistance brace and gusset plate and the target out-of-plane displacement angle θ;

[0009] Step 2: Calculate the resistance parameters and stiffness parameters, the resistance parameters include the yield axial force P of the node plate gy , the stiffness parameters include the rotational stiffness K of the node plate Rg , the ultimate bending moment of the node plate M gu and the bending stiffness of the buckling-restrained brace connection end; for the yield axial force of the node plate, the yield axial force of the node plate is calculated based on the 30° effective section of the node plate, where the intersection of the horizontal edge rib and the column side and the intersection of the vertical edge rib and the beam side is the equivalent bending section width b M , with the width b of the unconstrained edge of the gusset plate J The two end points extend inwards at an angle of 30° from the center rib to b M The effective cross-sectional width b is obtained e , based on the effective cross-sectional width b e Calculate the yield axial force P of the node plate gy Ignoring the shear deformation of the node plate, the rotational stiffness K of the node plate is obtained based on the rigid spring model. Rg and the ultimate bending moment M of the gusset plate gu ;

[0010] Step 3: Calculate the critical elastic buckling force P of the buckling-restrained brace out of plane cr ;

[0011] Step 4: Calculate the trigger eccentricity e tr , based on the trigger eccentricity e tr , the elastic buckling critical force P outside the buckling-restrained support plane cr , the ultimate bending moment M of the node plate gu Combined with the maximum axial pressure of the buckling restraint brace N u Verify whether the out-of-plane stability of the support is met. If so, the designed buckling-resistance brace damping system can ensure out-of-plane stability under bidirectional earthquake action. If not, the buckling-resistance brace subsystem will suffer out-of-plane instability under bidirectional earthquake action. Return to step 1 to redesign the buckling-resistance brace damping system.

[0012] Furthermore, in step 2, the calculation formula of the yield axial force of the node plate is:

[0013] P gy =b e t g f gy

[0014] Where P gy is the yield axial force of the effective section of the 30° angle of the node plate, b e is the width of the effective section formed by the 30° diffusion line of the gusset plate, t g is the gusset plate thickness, f gy is the gusset plate yield strength.

[0015] Furthermore, in step 2, the shear deformation of the node plate is ignored, and the node plate is divided into several triangular elements according to the yield line that may appear in the node plate. The rotation spring generated by inserting the anti-buckling support into the end of the node plate is defined as node ③, the end point of the horizontal side rib of the node plate is defined as node ④, the end point of the vertical side rib of the node plate is defined as node ②, the intersection of the vertical side rib and the beam side is defined as node ⑤, the intersection of the horizontal side rib and the column side is defined as node ⑥, the intersection of the beam side and the column side is defined as node ⑦, the edge of the anti-buckling support and the node plate is defined as node ①, and the lines between node ③ and node ①, node ②, node ④, node ⑤, node ⑥ and node ⑦ divide the node plate into multiple triangles. The connecting edge of two adjacent triangular elements is the yield line that may appear in the node plate. Each triangular element is regarded as a rigid body, and the concentrated force N outside the plane is applied to node ①. The lines connecting nodes ① and ② and ① and ③ and ② and ③ are defined to form a triangular element A; the lines connecting nodes ① and ④ and ① and ③ and ③ and ④ are defined to form a triangular element B; the lines connecting nodes ② and ⑤ and ③ and ⑤ and ② and ③ are defined to form a triangular element C; the lines connecting nodes ③ and ④ and ③ and ⑥ and ④ and ⑥ are defined to form a triangular element D. The rotation stiffness of node ③ of the node plate is considered to be only related to the triangular elements A, B, C, and D, then

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] In the formula, k AB ,k AC ,k BD are the rotational spring stiffnesses between triangular elements A, B, A, C, and B, D, respectively. E is the elastic modulus of the node plate material. g is the thickness of the node plate, v is the Poisson's ratio of the node plate, AB h A,AB h B are the distances from the vertices of triangle elements A and B to the yield line AB①③, AC h A,AC h C are the distances from the vertices of triangle elements A and C to the AC yield line ②③, BD h B,BD hD are the distances from the vertices of triangle elements B and D to the yield line BD ③④, AB K 11,AC K 11,BD K 11 The out-of-plane translational stiffness of the nodes provided by the triangular elements A, B, A, C, and B, D, respectively, is 13 ,l 34 ,l 23 are the distances between nodes ①③, ③④, ②③ respectively.

[0023] Furthermore, in step 2, the rotational stiffness K of the node plate is Rg The calculation formula is

[0024]

[0025] Furthermore, the ultimate bending moment of the gusset plate M gu The calculation formula is

[0026]

[0027] In the formula, f gy is the gusset plate yield strength.

[0028] Furthermore, step 2 also includes calculation of the bending stiffness of the connection section: the moment of inertia I in the out-of-plane direction is calculated according to the cross section of the buckling-restrained brace extension section, and then multiplied by the elastic modulus E of the node plate material to calculate the out-of-plane bending stiffness EI of the buckling-restrained brace extension section, and the out-of-plane bending stiffness of the buckling-restrained brace extension section is used as the bending stiffness of the connection section.

[0029] Furthermore, the calculation formula for the critical elastic buckling force outside the buckling-restrained support plane in step 3 is:

[0030]

[0031] Where P cr is the critical force of elastic buckling out of the plane of the buckling-restrained brace, l0 is the length of the brace axis from the central stiffener of the node plate, ξ is the ratio of the length from one end of the constraint unit to the root of the nearest central rib of the node plate along the brace axis to l0, and I is the out-of-plane moment of inertia of the extended connection section of the buckling-restrained brace.

[0032] Further, in step 4, the trigger eccentricity e tr The calculation formula is

[0033]

[0034] In the formula, e tris the trigger eccentricity, h is the subframe floor height, θ is the target plane displacement angle, and ξ is the ratio of the length from one end of the constraint unit to the root of the nearest node plate center rib along the support axis to l0.

[0035] Furthermore, in step 4, the expression for verifying the stability outside the support surface is:

[0036]

[0037] Where P lim is the out-of-plane ultimate load of the buckling restrained brace, N u is the maximum axial pressure of the buckling-resistance brace, M gu is the ultimate bending moment of the gusset plate, P gy is the yield axial force of the effective section of the gusset plate at an angle of 30°, P cr is the critical elastic buckling force out of the buckling-resistance brace plane, P cr is the critical elastic buckling force out of the buckling restraint plane, e tr To trigger the eccentricity.

[0038] Furthermore, the application of the design method needs to meet two conditions: the anti-buckling support subsystem satisfies the symmetrical analysis model and the frame main beam does not undergo torsional deformation under the action of earthquake. In the symmetrical analysis model, the upper and lower connecting sections of the anti-buckling support are equal in length, the upper and lower connecting sections are equal in length, the out-of-plane bending stiffness of the upper and lower connecting sections are equal, and the out-of-plane rotational stiffness of the upper and lower connected node plates is equal.

[0039] Compared with the prior art, the practical design method for out-of-plane stability of buckling-restrained braces considering bidirectional seismic action proposed in the present invention has the following advantages:

[0040] 1) It can accurately predict the out-of-plane ultimate load of the buckling-resistance brace subsystem under bidirectional earthquake action, which is more scientific and reasonable than the existing design method based on unidirectional earthquake action;

[0041] 2) A simplified method of the theoretical model based on the symmetry of the geometric and physical conditions at both ends of the support is proposed. The calculation formula is intuitive and convenient for practical engineering applications;

[0042] 3) The structural requirements of the frame beams are proposed to avoid considering the influence of the out-of-plane deformation of the sub-frames, which greatly simplifies the key influencing parameters of the out-of-plane stability of the buckling-restrained braces and reduces the potential safety hazards of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 In the figure, (a) is a schematic diagram of the anti-buckling support, (b) is a sectional view along the AA direction of (a), and (c) is a sectional view along the BB direction of (a).

[0044] Figure 2This is a conceptual diagram of the plastic hinge model theory. (a) is a schematic diagram of a buckling-restrained braced steel frame, (b) is a side view of the frame, and (c) is a schematic diagram of the AA-direction isolation body in (a).

[0045] Figure 3 It is a conceptual diagram of the moment transfer model theory. (a) is a schematic diagram of the moment transfer calculation model, (b) is the deformation diagram of the buckling-restrained braced frame under out-of-plane displacement, and (c) is a schematic diagram of the moment distribution of the buckling-restrained braced frame under out-of-plane displacement.

[0046] Figure 4 Schematic diagram of the out-of-plane stability calculation model of the anti-buckling brace subsystem proposed in the present invention, wherein (a) is a structural schematic diagram of the anti-buckling brace subframe, and (b) is a schematic diagram of the AA-direction isolation body in (a).

[0047] Figure 5 It is the deformation and force analysis diagram under bidirectional force.

[0048] Figure 6 It is a rigid spring model diagram. (a) is a schematic diagram of the force and displacement of two adjacent triangular elements. (b) is a plane schematic diagram of the triangular element without rigid body displacement. (c) is the AA section view in (a).

[0049] Figure 7 Schematic diagram of the out-of-plane deformation of the node plate proposed in the present invention.

[0050] Figure 8 Schematic diagram of an equivalent method for calculating the yield axial force of a node plate according to the present invention, (a) is a schematic diagram of a design node plate with ribbed edges, and (b) is a schematic diagram of an imaginary node plate.

[0051] Fig. 9 It is a schematic diagram of calculating the rotation stiffness of the node plate according to the present invention.

[0052] Fig.10 A schematic diagram of the dimensions of a buckling-resistance brace subsystem.

[0053] Fig.11 A flowchart of the design method proposed in the present invention.

[0054] Fig.12 A schematic diagram of the structural requirements of the node plate in the herringbone buckling-restrained braced frame according to the adaptive design method proposed in the present invention.

[0055] Fig.13 The figures are comparison diagrams of the results of the existing design method and the design method proposed in the present invention, wherein (a) is a schematic diagram of the results of the existing separate design method, (b) is a schematic diagram of the results of the existing integrated design method, and (c) is a schematic diagram of the results of the method of the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] Figure 4 The theoretical analysis model of the buckling-resistance brace stability considering bidirectional earthquake action is given in the present invention. The analysis model considering bidirectional force deformation is as follows: Figure 5 As shown. The unilateral subsystem of the herringbone anti-buckling brace subframe (abbreviated as anti-buckling brace subsystem) can be divided into five parts along the support axis: the corner node rigid domain (segments 1-2), the lower connecting segment (segments 2-3), the buckling constraint segment (segments 3-4), the upper connecting segment (segments 4-5) and the mid-node rigid domain (segments 5-6). According to the experimental phenomena of the inventor, a plastic hinge will appear at the end (2, 5) of the length of the anti-buckling brace inserted into the node plate under the condition of bidirectional force. Since a certain rotation is allowed, it is simplified here to a rotation spring with a certain rotation stiffness. In the design, in order to avoid the adverse effect of eccentric force on the structure by generating additional internal force, the extension line of the anti-buckling brace will intersect with the center axis of the beam and column at one point, namely point 1 in the figure. The corner node plate area between point 2 and point 1 has strong constraints of the beam and column and is considered to be a rigid area. The structural schematic diagram of the anti-buckling brace is shown as follows Figure 1 As shown in the figure, the intersection of the part constrained by the constraint unit (constraint segment) and the unconstrained parts at both ends usually forms a plastic hinge when subjected to bidirectional forces. However, since the out-of-plane constraint is very weak, it is regarded as an out-of-plane hinge here (points 3 and 4). Point 6 is the intersection of the extension line of the anti-buckling support and the central axis of the upper beam. The node plate has the ability to rotate out of the plane, so the rigid domain of the corner node and the lower connecting segment, and the rigid domain of the middle node and the upper connecting segment are connected by out-of-plane rotation springs to consider the out-of-plane rotation stiffness of the node plate. Since the length of the core unit reinforcement segment of the commonly used anti-buckling support inserted into the constraint member is short, it can be considered that there is usually no two-point contact between the two to produce a moment transfer effect, so the upper and lower connecting segments and the support buckling constraint segment are regarded as hinged in the out-of-plane direction.

[0058] The analysis ideas and simplification ideas of the present invention are as follows:

[0059] 1) Since the out-of-plane stability is determined by two parts, the first part is the out-of-plane elastic buckling critical force of the buckling-restrained brace, and the second part is the out-of-plane ultimate bending moment of the node plate, the solution is to calculate these two limit values ​​as the critical value for instability judgment. In order to calculate this critical value, the following steps are analyzed.

[0060] 2) Based on the existing plastic hinge model theory and experimental observations, a theoretical analysis model is proposed that can take into account the rotational stiffness of the node plate and the bidirectional seismic action. Figure 5 The mechanical parameters in the theoretical analysis model considering bidirectional earthquake action are defined as follows: EI b is the elastic bending stiffness of the lower connecting section, EI t is the elastic bending stiffness of the upper connecting section, K Rg,b K is the stiffness of the rotation spring at the end of the lower connection segment (angular node plate rotation spring), Rg,t is the stiffness of the rotation spring at the end of the upper connection segment (the rotation spring at the middle node plate). The buckling-resistance support subsystem is subjected to an out-of-plane displacement of Δ=θh. The deformation of the buckling-resistance support consists of two parts: one is the rigid body deformation, which is caused by the upper and lower connection segments rotating around the middle node plate rotation spring and the corner node plate rotation spring. The rigid body rotates, and the yield segment rotates around Figure 4 The out-of-plane hinge nodes 3 and 4 shown in the figure rotate as a rigid body, changing from the defect-free geometric configuration in the figure to a rigid body configuration; the other part is bending deformation, which is determined by the bending stiffness of the upper and lower connecting segments, plus the small displacement assumption, so that the hinge nodes 3 and 4 respectively produce y bm ,y tm The displacement changes from the rigid body configuration in the figure to the bending configuration. The bending stiffness of the constraint segment here is very large and it can be considered that there is no bending deformation. p1 ,θ p2 It represents the acute angle between a rigid body configuration and a defect-free geometric configuration, and between a rigid body configuration and a curved configuration.

[0061] 3) Based on the proposed theoretical analysis model considering bidirectional seismic effects, the out-of-plane deformation and stress conditions (mainly axial force-bending moment interaction) of each component of the anti-buckling support subsystem are derived.

[0062] 4) Ignoring the shear deformation of the node plate, based on the rigid spring model (see Figure 6 ), select a part of the adjacent triangular elements in a node plate that rotates as a rigid body with an arbitrary yield line. After the part is subjected to four forces P1, P2, P3, P4 on four nodes (①, ②, ③, ④) (the four nodes are the four vertices of the two adjacent triangular elements), the yield lines ①③ (i.e., the line between nodes ① and ③) appear as shown in the figure. The yield line divides the node plate into two triangular rigid bodies, X and Y. The rigid body spring model regards the yield line as a rotation spring with a certain rotation stiffness. XY h X and XY h Yare the distances from the vertex to the yield line of the two deformed triangular rigid bodies in the vertical XY plane projection (i.e., the shape before the out-of-plane displacement occurs). According to the out-of-plane displacement (w1, w2, w3, w4) of each X and Y node and the relative rotation angle (θ XY ), the out-of-plane translational stiffness (P i / w i ), Figure 6 Out-of-plane translational stiffness of midpoint nodes ① and ② XY K 11 , XY K 22 The expression is as follows

[0063]

[0064]

[0065] The rotation spring stiffness k XY Press the formula to take

[0066]

[0067] Similarly, the out-of-plane translational stiffness of nodes ③ and ④ is XY K 33 , XY K 44 The expression is as follows

[0068]

[0069]

[0070] Among them l ij represents the distance between nodes i and j, see Figure 6 , D is the bending stiffness of the plate per unit width, calculated as follows

[0071]

[0072] Where E and ν are the elastic modulus and Poisson’s ratio of the node plate material, respectively. g is the thickness of the gusset plate.

[0073] Among them, the node plate is divided into several triangular elements according to the possible yield line of the node plate, as shown in the following figure: Fig. 9In the present invention, the line connecting the rotation spring (point 3) generated by the end of the anti-buckling brace inserted into the node plate and the end points of the node plate side ribs (points 2 and 4), the intersection points of the side ribs and beams and columns (points 5 and 6), and the intersection points of beams and columns (point 7) is the yield line. The line connecting the edge of the anti-buckling brace and the node plate (point 1) and the aforementioned points 2 and 4 divides the node plate into several triangular elements. The connecting edge of two adjacent triangular elements is the yield line that may appear in the node plate. Each triangular element is regarded as a rigid body. Figure 7 In the example, by setting the rotational spring connection (i.e., the location where the yield line appears in the rigid spring model) and the rigid boundary conditions (rigid constraints on the edge ribs and beam-column sides) on its boundary, when the node plate satisfies the rigid boundary conditions, Figure 7 The out-of-plane translation displacement of points ②-⑦ in the figure is almost 0, so the out-of-plane concentrated force N can be applied to Figure 7 Node ①. After verification by the implementation example, Fig. 9 The rotation stiffness of node plate point ③ is approximately considered to be only related to the triangular elements A, B, C, and D (i.e., the lines connecting nodes ① and ② and ① and ③ and ② and ③; the lines connecting ① and ④ and ① and ③ and ③ and ④; the lines connecting ② and ⑤ and ③ and ⑤ and ② and ③; the lines connecting ③ and ④ and ③ and ⑥ and ④ and ⑥), and then the out-of-plane rotation stiffness of the node plate is considered.

[0074] 5) Based on safety considerations, the out-of-plane bending stiffness of the buckling-resistance brace extension section is used as the bending stiffness of the connection section. Based on the edge fiber yield design principle, a node plate stability design criterion based on yield line analysis is proposed. This design criterion involves the node plate rotation stiffness K Rg and the ultimate bending moment M gu The calculation is used as the final criterion for judging the stability of the buckling-restrained brace under bidirectional load.

[0075] 6) Use mathematical methods and symmetric analysis models to simplify the theoretical design formula obtained in the previous step to facilitate engineering applications.

[0076] Symmetric analysis model refers to Figure 4 b The calculation model given, the length of the upper and lower connecting segments is equal (ξ t =ξ b ,ξ is the length of the upper and lower connecting segments (segments 4-5 and 2-3), i.e. l 4-5 and l 2-3 The ratio of the length of the buckling-restrained brace l0, the subscripts t and b represent the upper and lower connecting segments respectively), the out-of-plane bending stiffness is equal (EI b =EI t , EI is the out-of-plane bending stiffness of the upper and lower connecting sections of the buckling-restrained brace), and the out-of-plane rotation stiffness of the upper and lower connected node plates is equal (K Rg,t =K Rg,b ,KRg is the out-of-plane rotational stiffness of the upper and lower node plates, that is, the stiffness provided by the rotation springs at points 3 and 6 in the figure). Due to the symmetrical design of the upper and lower connecting sections and the upper and lower node plates in general engineering design (materials, dimensions, etc.), this is well consistent with general engineering practice.

[0077] After simplification, the out-of-plane stability design method of buckling-restrained braces considering bidirectional seismic action proposed in the present invention includes the following steps:

[0078] Step 1: Determine the gusset plate dimensions, buckling-resistance brace geometry, and target out-of-plane displacement angle.

[0079] Among them, the size of the node plate is determined according to the maximum axial pressure of the anti-buckling brace. In some embodiments of the present invention, the size of the node plate is preliminarily determined according to 1.5 times the yield force of the anti-buckling brace. This is because the anti-buckling brace needs to consume energy in the plastic stage when working, and the force is often greater than the yield axial force. The purpose of amplifying the yield axial force and then designing it is mainly to have a certain safety redundancy. In other embodiments, the size of the node plate can be preliminarily determined by other multiples of the yield force of the anti-buckling brace.

[0080] The cross-sectional dimensions and geometric lengths of the yielding section and the strengthening section of the buckling-restrained brace are determined according to the Technical Specifications for the Application of Buckling-restrained Braces or the current local regulations according to the axial compression design method, and are determined according to the buckling-restrained brace design dimensions (i.e. Figure 1 The length, cross-section, etc. of each segment in the calculation model are determined by the assumption (6) of the anti-buckling support subsystem.

[0081] In some embodiments of the present invention, the required yield force and axial elastic stiffness requirements need to be determined based on actual design conditions, inter-story displacement angle limits, etc.

[0082] The target out-of-plane displacement angle is selected during design. In some embodiments of the present invention, the target out-of-plane displacement angle θ of the frame structure under a rare earthquake can be set to 2%. In other embodiments, the target out-of-plane displacement angle can be set to other values.

[0083] Step 2: Please refer to Figure 8 The line connecting the intersection of the horizontal edge rib and the column side and the intersection of the vertical edge rib and the beam side is the equivalent bending section width b. M , with the width b of the unconstrained edge of the gusset plate J The two end points extend inwards at an angle of 30° from the center rib to b M The effective cross-sectional width b is obtained e , calculate the yield axial force of the 30° effective section of the node plate according to this equivalent width dimension. Among them, the yield axial force P of the node plate is gy The calculation formula is:

[0084] P gy =b e t g f gy (1)

[0085] In the formula

[0086] P gy ——Yield axial force of the effective section of the gusset plate at 30° angle

[0087] b e ——Width of the effective section formed by the 30° diffusion line of the gusset plate (mm)

[0088] t g ——Node plate thickness (mm)

[0089] f gy ——Node plate yield strength (N / mm 2 )

[0090] Step 3: For Fig. 9 The rotational stiffness K of the node plate is calculated according to equations (2) to (9): Rg and the ultimate bending moment M gu , and calculate the out-of-plane moment of inertia I according to the cross-section of the buckling-restrained brace extension section, and then multiply it by the elastic modulus E of the node plate material to calculate the out-of-plane bending stiffness EI of the buckling-restrained brace extension section as the bending stiffness of the connecting section.

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] In the formula

[0100] v——Poisson's ratio of the node plate

[0101] E——Elastic modulus of the node plate

[0102] l 13 ,l 34 ,l 23——The distances between nodes ①③, ③④, ②③

[0103] AC h A,AC h C ——The distances from the vertices A and C of the triangle element to the AC yield line ②③ in the original figure

[0104] AB h A,AB h B ——The distances from the vertices A and B of the triangle element to the yield line ①③ in the original figure

[0105] BD h B,BD h D ——The distances from the vertices B and D of the triangle element to the yield line BD in the original figure

[0106] k AB ,k AC ,k BD - rotational spring stiffness between triangular elements A, B, A, C, and B, D

[0107]

[0108] K Rg ——Out-of-plane rotation stiffness of the gusset plate

[0109] M gu ——Limiting bending moment out of the plane of the gusset plate

[0110] Step 4: For Fig.10 For the buckling-resistance brace subframe in the structure, the critical elastic buckling force out of the buckling-resistance brace plane is calculated according to equation (10).

[0111]

[0112] In the formula

[0113] P cr ——Elastic buckling critical force out of the buckling-restrained brace plane (N)

[0114] l0——The length of the support axis from the center stiffener of the node plate (mm) Fig.10 )

[0115]

[0116] I——Out-of-plane moment of inertia of the buckling-restrained brace extension connection section ( Figure 1 BB section)

[0117] Step 5: Calculate the trigger eccentricity according to formula (11) (see Figure 5) and formula (12) are used to verify whether the out-of-plane stability of the support is satisfied. If so, the designed buckling-resistance brace damping system can ensure out-of-plane stability under bidirectional earthquake action. If not, the buckling-resistance brace subsystem will suffer out-of-plane instability under bidirectional earthquake action, and it is necessary to return to step 1 to redesign the buckling-resistance brace damping system.

[0118]

[0119]

[0120] In the formula, e tr is the trigger eccentricity, h is the subframe floor height (m), θ is the designed inter-story displacement angle, P lim is the out-of-plane ultimate load of the buckling restrained support (N), N u The maximum axial pressure of the anti-buckling support can be calculated as 1.5 times the support yield axial force (N), M gu is the ultimate bending moment of the gusset plate, P gy is the yield axial force of the effective section of the gusset plate at an angle of 30°, P cr is the critical force of elastic buckling out of the buckling-resistance brace plane (N).

[0121] Other parameters are calculated and defined according to equations (1) to (11).

[0122] Fig.11 The design process of the present invention is given.

[0123] The application of the practical design method for out-of-plane stability of the herringbone buckling-resistance brace proposed in the embodiment of the present invention should meet the following two prerequisites: first, the buckling-resistance brace subsystem satisfies the symmetric analysis model; second, the frame main beam does not undergo torsional deformation under the action of an earthquake, so as to avoid calculating the rotational spring stiffness of the main beam. Therefore, the structural requirements of the design method for out-of-plane stability of the buckling-resistance brace proposed in the present invention are:

[0124] 1) Ensure that the insertion length of the central rib of the gusset plates connected at both ends of the buckling restraint brace is consistent;

[0125] 2) The middle node plate should adopt double transverse stiffening rib structure, and the spacing of transverse stiffening ribs should meet Fig.12 The structural requirements shown are: that is, transverse stiffening ribs should be arranged in the middle of the frame main beam, the outer edge spacing of the transverse stiffening ribs can be equal to the column section height, the position of the stiffening ribs should correspond to the vertical side ribs and transverse ribs of the mid-node plate, the frame main beam should be equipped with secondary beams and floor slabs, and the secondary beams should be as close to the middle of the frame main beam as possible;

[0126] Although the mid-node structure proposed in the present invention is for a herringbone buckling-resistance brace steel frame, the frame beam adopts an open thin-walled I-beam, which is mainly because the torsional rigidity of the I-beam is weak and prone to twisting. When the frame beam adopts a box beam or the buckling-resistance brace is located in a reinforced concrete frame, the torsional rigidity of the beam is much greater than that of the open thin-walled I-beam, and the beam cross section is not easily distorted, so it can better meet the application conditions of the practical design method.

[0127] Fig.13 The comparison between the existing separate design method, the integral design method and the practical design method proposed by the present invention considering the bidirectional earthquake action and the finite element simulation results is given. The finite element model parameters are shown in Table 1. The parameters correspond to the key parameters calculated in the design steps and are Figure 5 , Fig.10 The parameters correspond to those of the model, and bidirectional synchronous loading is performed to simulate bidirectional earthquake action. Fig.13 The horizontal axis is the number of the 9 models, and the vertical axis is the ratio of the out-of-plane instability axial force of the buckling-restrained brace calculated by the corresponding design method to the finite element calculation result. It can be seen that the calculation results of the existing separate design method and the integral design method significantly overestimate the out-of-plane stable bearing capacity of the buckling-restrained brace, while the calculation results obtained by the practical design method of the present invention are very close to the finite element calculation results, indicating that the method of the present invention can accurately consider the influence of bidirectional seismic action on the out-of-plane stability of the buckling-restrained brace and give a correct theoretical estimate.

[0128] Table 1 Key parameters of the analysis model

[0129]

[0130] Note: The out-of-plane interlayer displacement of the model is Δ = θh.

[0131] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for out-of-plane stability of buckling-restrained braces considering bidirectional seismic action, characterized in that: The following steps are involved: Step 1: Determine the geometric dimensions of the buckling-resistance brace and gusset plate and the target out-of-plane displacement angle θ; Step 2: Calculate the resistance parameters and stiffness parameters, the resistance parameters include the yield axial force P of the node plate gy , the stiffness parameters include the rotational stiffness K of the node plate Rg , the ultimate bending moment of the node plate M gu and the bending stiffness of the buckling-restrained brace connection end; for the yield axial force of the node plate, the yield axial force of the node plate is calculated based on the 30° effective section of the node plate, where the intersection of the horizontal edge rib and the column side and the intersection of the vertical edge rib and the beam side is the equivalent bending section width b M , with the width b of the unconstrained edge of the gusset plate J The two end points extend inwards at an angle of 30° from the center rib to b M The effective cross-sectional width b is obtained e , based on the effective cross-sectional width b e Calculate the yield axial force P of the node plate gy Ignoring the shear deformation of the node plate, the rotational stiffness K of the node plate is obtained based on the rigid spring model Rg and the ultimate bending moment M of the gusset plate gu Ignore the shear deformation of the node plate, divide the node plate into several triangular elements according to the yield line that may appear in the node plate, define the rotation spring generated by the end of the anti-buckling support inserted into the node plate as node ③, define the end point of the horizontal side rib of the node plate as node ④, define the end point of the vertical side rib of the node plate as node ②, define the intersection of the vertical side rib and the beam side as node ⑤, define the intersection of the horizontal side rib and the column side as node ⑥, define the intersection of the beam side and the column side as node ⑦, define the edge of the anti-buckling support and the node plate as node ①, and divide the node plate into multiple triangular elements by the lines between node ③ and node ①, node ②, node ④, node ⑤, node ⑥ and node ⑦. The connecting edge of two adjacent triangular elements is the yield line that may appear in the node plate. Each triangular element is regarded as a rigid body, and the concentrated force N outside the plane is applied to node ①. The lines connecting nodes ① and ②, ① and ③, and ② and ③ are defined to form a triangular element A; the lines connecting nodes ① and ④, ① and ③, and ③ and ④ are defined to form a triangular element B; the lines connecting nodes ② and ⑤, ③ and ⑤, and ② and ③ are defined to form a triangular element C; the lines connecting nodes ③ and ④, ③ and ⑥, and ④ and ⑥ are defined to form a triangular element D. The rotational stiffness of node ③ of the node plate is considered to be only related to the triangular elements A, B, C, and D, then In the formula, k AB ,k AC ,k BD are the rotational spring stiffnesses between triangular elements A, B, A, C, and B, D, respectively; E is the elastic modulus of the node plate material, t g is the thickness of the node plate, v is the Poisson's ratio of the node plate, AB h A,AB h B are the distances from the vertices of triangle elements A and B to the yield line AB①③, AC h A,AC h C are the distances from the vertices of triangle elements A and C to the AC yield line ②③, BD h B,BD h D are the distances from the vertices of triangle elements B and D to the yield line BD ③④, AB K 11,AC K 11,BD K 11 The out-of-plane translational stiffness of the nodes provided by the triangular elements A, B, A, C, and B, D, respectively, is 13 ,l 34 ,l 23 are the distances between nodes ①③, ③④, ②③ respectively; the rotation stiffness K of the node plate Rg The calculation formula is The ultimate bending moment of the gusset plate M gu The calculation formula is In the formula, f gy is the gusset plate yield strength; Step 3: Calculate the critical elastic buckling force P of the buckling-restrained brace out of plane cr The calculation formula of the critical elastic buckling force outside the buckling-resistance support plane is: Where P cr is the critical force of elastic buckling out of the plane of the buckling-restrained brace, l0 is the length of the brace axis from the central stiffener of the gusset plate, ξ is the ratio of the length from one end of the constraint unit to the root of the nearest central rib of the gusset plate along the brace axis to l0, and I is the out-of-plane moment of inertia of the extended connection section of the buckling-restrained brace; Step 4: Calculate the trigger eccentricity e tr , based on the trigger eccentricity e tr , the elastic buckling critical force P outside the buckling-restrained support plane cr , the ultimate bending moment M of the node plate gu Combined with the maximum axial pressure of the buckling restraint brace N u Verify whether the out-of-plane stability of the support is met. If so, the designed buckling-resistance brace damping system can ensure out-of-plane stability under bidirectional earthquake action. If not, the buckling-resistance brace subsystem will suffer out-of-plane instability under bidirectional earthquake action. Return to step 1 to redesign the buckling-resistance brace damping system.

2. The out-of-plane stability design method of buckling-restrained braces considering bidirectional seismic action according to claim 1, characterized in that: In step 2, the calculation formula of the yield axial force of the node plate is: P gy =bet g f gy Where P gy For gusset plate 30 The yield axial force of the effective section at an angle of °, b e For gusset plate 30 °Width of the effective cross section formed by the diffusion line, t g is the gusset plate thickness, f gy is the gusset plate yield strength.

3. The out-of-plane stability design method of buckling-restrained braces considering bidirectional seismic action according to claim 1, characterized in that: Step 2 also includes the calculation of the bending stiffness of the connection section: the moment of inertia I in the out-of-plane direction is calculated according to the cross section of the buckling-restrained brace extension section, and then multiplied by the elastic modulus E of the node plate material to calculate the out-of-plane bending stiffness EI of the buckling-restrained brace extension section, and the out-of-plane bending stiffness of the buckling-restrained brace extension section is used as the bending stiffness of the connection section.

4. The out-of-plane stability design method of buckling-restrained braces considering bidirectional seismic action according to claim 1, characterized in that: In step 4, the trigger eccentricity e tr The calculation formula is In the formula, e tr is the trigger eccentricity, h is the subframe floor height, θ is the displacement angle outside the target plane, ξ It is the ratio of the length from one end of the constraint unit to the root of the nearest node plate center rib along the support axis to l0.

5. The out-of-plane stability design method of buckling-restrained braces considering bidirectional seismic action according to claim 1, characterized in that: In step 4, the expression for verifying the stability outside the support surface is: Where P lim is the out-of-plane ultimate load of the buckling restrained brace, N u is the maximum axial pressure of the buckling-resistance brace, M gu is the ultimate bending moment of the gusset plate, P gy For gusset plate 30 The yield axial force of the effective section at an angle of °, P cr is the critical elastic buckling force out of the buckling-resistance brace plane, P cr is the critical elastic buckling force out of the buckling restraint plane, e tr To trigger the eccentricity.

6. The out-of-plane stability design method of buckling-restrained braces considering bidirectional seismic action according to any one of claims 1 to 5, characterized in that: The application of the design method requires that two conditions be met: the anti-buckling support subsystem satisfies the symmetrical analysis model and the frame main beam does not undergo torsional deformation under earthquake action. In the symmetrical analysis model, the upper and lower connecting sections of the anti-buckling support are equal in length, the upper and lower connecting sections have the same length, the upper and lower connecting sections have the same out-of-plane bending stiffness, and the upper and lower connected node plates have the same out-of-plane rotational stiffness.

Images