“Strong Column and Weak Beam” Design Method for Steel Frame Beam-Box Column under Bidirectional Earthquake Action

Abstract

The steel frame beam-box column "strong column weak beam" design method under bidirectional earthquake provided by the present invention includes: designing an initial frame; defining important beam-column nodes and important sections according to the design axial compression ratio according to the calculation results of the response spectrum CQC method of the initial frame; unifying the bidirectional COF values ​​of important beam-column nodes; determining the degree of realization of "strong column weak beam", and proposing two quantifiable evaluation indicators P1 and P2; statistically analyzing the damage index D of the frame after the elastic-plastic time-history analysis of multiple groups of natural waves, and combining the evaluation criteria of the present invention to obtain a parameter framework that meets the target yield mechanism, if satisfied, it is considered that the framework can achieve the target "strong column weak beam" yield mechanism within the evaluation criteria of the present invention; if not satisfied, it means that the designed frame cannot achieve the "strong column weak beam" yield mechanism that meets the evaluation criteria of the present invention under bidirectional earthquake, and the frame is redesigned by increasing the bidirectional COF value. The present invention can provide a reference for the "strong column weak beam" design method of steel frame structure under bidirectional earthquake.

Description

Technical Field

[0001] The invention belongs to the field of civil engineering earthquake resistance technology, relates to a steel frame "strong column weak beam" design method, and specifically relates to a steel frame beam-box column welding node "strong column weak beam" design method under bidirectional earthquake action. Background Art

[0002] The "strong column and weak beam" design is of great significance for the collapse prevention of structures and is an important part of earthquake-resistant design in countries around the world. At present, the "strong column and weak beam" design theory in my country's specifications still remains at the level of plane structure calculation, and only performs verification in the two main axis plane directions. However, under the actual bidirectional earthquake action, the spatial structure will be in a bidirectional force state, which is very different from the unidirectional earthquake action under the standard plane model.

[0003] Actual earthquake damage and research have shown that: under bidirectional earthquake action, the deformation, energy consumption, and damage of columns increase while those of beams decrease; beam-column substructures designed according to the standard plane cannot achieve the expected force performance of unidirectional under bidirectional action; the overall frame structure designed according to the standard unidirectional "strong column and weak beam" formula cannot achieve the "strong column and weak beam" yield mechanism under bidirectional earthquake action. Therefore, conducting research on "strong column and weak beam" for bidirectional earthquake action has important theoretical and practical significance for improving the seismic safety and anti-collapse capacity of structures.

[0004] At present, the existing "strong column weak beam" design method has made some progress. It is achieved by controlling the full plastic bending bearing capacity matching relationship between the column and beam connected at the same node, that is, the full plastic strength of the column end at the intersection of the beam and column node. The sum of the two (referred to as column resistance in this article) is not less than the full plastic strength of the beam end The sum of the two (referred to as beam effect in this article) can achieve a certain degree of “strong column and weak beam” through a certain strong column coefficient.

[0005] However, the current code does not consider the bidirectional compression and bending stress state of the column under bidirectional earthquake action. In addition to not considering the bidirectional earthquake action, there are still the following key factors that need to be considered:

[0006] Key factor 1: Nonlinear response characteristics of each floor of the frame structure under a strong earthquake. Since the frame structure has a strong nonlinear response under a strong earthquake, its calculation model under a strong earthquake (see Figure 2(a)) has changed, and the current design formulas are all based on an ideal beam-column substructure (the inflection point is at the midpoint of the column). This ideal model can well reflect the experimental characteristics of the beam-column substructure, but it is very different from the yield mechanism of the overall frame entering the elastoplastic stage of a large earthquake: some column feet and beam ends of the frame have formed plastic hinges, and the inflection points of each frame column will not be located at the midpoint, resulting in uneven or even reverse forces on the upper and lower column ends of the beam-column node. Therefore, the current standard formulas all assume that the upper and lower column ends are subjected to synchronous forces, which is not accurate and unsafe for the actual forces on the beam-column nodes in the overall frame under a large earthquake.

[0007] Key factor 2: Dynamic time-varying effect of column axial force under large earthquakes. In my country's "strong column and weak beam" formula, the column axial pressure is taken as the column axial pressure N under the common earthquake combination. For the middle column, because there are beams on both sides, the shear forces of the beams under the lateral earthquake force can balance each other, making the column axial pressure caused by the common earthquake action almost zero, so its real axial pressure in the time history (see Figure 2 (b)) remains unchanged, so the “strong column weak beam” formula for its axial pressure N 中 is a conservative value; for the case where there is no beam on one side of the edge or corner column, the unbalanced shear force of the beam in the large earthquake time history causes the column axial pressure to change dramatically. The column axial pressure under the earthquake combination may underestimate the maximum axial pressure in the time history. In addition, due to the influence of factors such as the randomness of the ground motion and the change of the frame structure, it is impossible to accurately estimate the maximum axial pressure of the edge and corner columns. At this time, the "strong column and weak beam" formula for the axial pressure N 边 、N 角 Unsafe estimate.

[0008] Key factor 3: The influence of floor slab on the mechanical properties of beams and columns. For beams, the combined effect of floor slab on beams turns pure steel beams into composite beams with higher stiffness and strength, thereby increasing the beam effect in the "strong column and weak beam" formula; for columns, the main force transmission method between floor slab and column is the direct compression of floor slab within the width of column (see Figure 2 (a)) may cause local buckling of the box column before reaching full plastic bending strength, thus reducing the column resistance in the "strong column weak beam" formula. The current code formulas do not consider the reduction of the column resistance by the floor slab. Only the New Zealand code formula is based on the ultimate (floor slab compression) state of the composite beam of the beam-column substructure, and considers the effect of the floor slab on the strength of the steel beam.

[0009] Key factor 4: strain hardening of beams and columns, material overstrength, etc. The derivation of the current code formula is based on the assumption of ideal elastic-plastic material constitutive property, that is, when the material reaches full plasticity, the cross section is in a rectangular stress distribution state, and the bending stiffness of the corresponding cross section is zero. However, after the actual steel yields, there is a non-negligible secondary stiffness and strain hardening (see Figure 2(d), the cross-sectional bending stiffness gradually decreases with the increase of yield degree. In addition, random factors such as the overstrength of actual steel materials and the size deviation of actual beam-column components will also affect the degree of realization of “strong column and weak beam”. Summary of the invention

[0010] In order to solve at least one of the problems existing in the prior art, the present invention revolves around the core issue of "strong columns and weak beams" under bidirectional earthquake action. By clarifying the standard one-way "strong columns and weak beams" design ideas and summarizing the four key factors that need to be considered in the "strong columns and weak beams" design method, the bidirectional "strong columns and weak beams" design ideas of the present invention are formed by combining the four key factors, which can provide a reference for the "strong columns and weak beams" design method of steel frame structures under bidirectional earthquake action.

[0011] In order to achieve the purpose of the present invention, the present invention provides a steel frame beam-box column "strong column weak beam" design method under bidirectional earthquake action, comprising the following steps:

[0012] Step 1: Design the initial framework;

[0013] Step 2: Define important beam-column nodes and important sections according to the design (standard) axial compression ratio based on the response spectrum CQC method calculation results of the initial frame;

[0014] Step 3: Unify the bidirectional COF values ​​of important beam-column nodes by fixing the thickness of the middle column of important beam-column nodes, increasing the strength of the beams at important beam-column nodes with the height of the floors, and using the column resistance and beam effect The bidirectional COF value of each node is calculated in reverse. The cross-sections of the side, corner and center columns of each layer are kept consistent;

[0015] Step 4: Determine the degree of achieving “strong columns and weak beams”, refer to the performance-based standard C and D levels, and propose two quantifiable evaluation indicators P1 and P2;

[0016] Step 5: Statistically select twenty groups of damage indexes D of the frame after elastic-plastic time-history analysis of natural waves, and combine the evaluation criteria of the present invention to obtain a parameter framework that meets the target yield mechanism. If it meets the criteria, it is considered that the frame can achieve the target "strong column and weak beam" yield mechanism within the evaluation criteria of the present invention; if it does not meet the criteria, it means that the designed frame cannot achieve the "strong column and weak beam" yield mechanism that meets the evaluation criteria of the present invention under the action of bidirectional earthquakes, and it is necessary to return to step 3 to redesign the frame by increasing the bidirectional COF value.

[0017] Furthermore, in step 1, the initial framework is a framework designed using conventional design software to meet the first stage of structural verification under small earthquake combinations.

[0018] Furthermore, in step 2, the important beam-column nodes are nodes of the initial frame with a design (standard) axial compression ratio greater than 0.4 (0.35) after the response spectrum CQC method is calculated. The important sections are all upper and lower column end sections of the important beam-column nodes.

[0019] Furthermore, in step 2, the standard axial pressure ratio calculation formula is:

[0020]

[0021] Where N is the column axial pressure under common earthquake combinations (the axial pressure of the lower column section at the beam-column node is uniformly taken), N p It is the yield axial force of the box column section at the intersection of the spatial beam-column node.

[0022] Furthermore, in step 3, the relationship between the bidirectional COF value and the column resistance and beam effect is:

[0023] For uniform beams:

[0024]

[0025] For end plate flange tapered beams:

[0026]

[0027] Where N is the column axial pressure under common earthquake combinations (uniformly taken as the axial pressure of the lower column section at the beam-column node), N p 、M px are the yield axial force of the box column section at the intersection of the spatial beam-column node and the fully plastic bending moment around the principal axis (one-way), M vx , M vy are the full plastic bending moment of the x and y plane steel beams (unreinforced) at the intersection of the spatial beam-column node and the additional bending moment caused by the plastic hinge transfer, and COF is the bidirectional strong column coefficient corresponding to the bidirectional formula. In the above two formulas, the left formula is defined as the column resistance The right equation is the beam effect

[0028] Furthermore, in step 3, after discussing the different plastic neutral axis positions of the cross section in the column resistance term under bidirectional earthquake action, it is considered that the one-way compression bending full plastic strength M around the main axis is taken within the design axial compression ratio considered in the present invention. px Based on the full plastic strength of the column subjected to orthogonal beams at the same time, and considering the inconsistency of the amplitude and phase of the seismic wave, the beam effect in the two-way formula is conservatively taken as the square root of the sum of the squares of the full plastic bending moments of the beams around the principal axis.

[0029] Furthermore, in step 4, the performance-based standard C and D grades are the C and D grades corresponding to the requirements of the "Performance-based Design Standard for Seismic Resistance of Building Structures" issued in 2022, which are referred to as C and D grade "strong columns and weak beams" in the present invention.

[0030] Furthermore, in step 4, the evaluation indicators P1 and P2 are expressed as follows:

[0031] For C-level "strong columns and weak beams":

[0032]

[0033] For D-level "strong columns and weak beams":

[0034]

[0035] Among them, L4%, L5%, and L6% are the proportions of damage levels L4, L5, and L6 in important sections respectively. The damage level classification refers to the performance-based standard. The evaluation standard process is shown in Figure 1 .

[0036] Furthermore, in step 4, the degree of "strong column and weak beam" is taken as an example to achieve level D: the frame is under twenty groups of natural waves. or If the mean plus double the standard deviation (μ+σ) is not greater than 1, it means that the framework has sufficient probability to realize the D-level "strong column and weak beam" yield mechanism; if only the mean (μ) is not greater than 1, it means that the framework can realize the D-level "strong column and weak beam" yield mechanism in an average sense; if the statistical values ​​of the evaluation indicators are all greater than 1, it means that the framework does not meet the "strong column and weak beam" requirements of this article.

[0037] Furthermore, in step 5, the damage index D is the maximum (compressive) strain ε of all important sections in the earthquake time history. max and yield strain ε y The ratio of is:

[0038]

[0039] Furthermore, the application of the design method needs to meet the following requirements: 1) This design method is applicable to the case where the design axial compression ratio of the frame is 0.4-0.6 under common earthquake combinations; 2) The squeezing effect of the floor slab on the frame column is ignored; 3) Random factors such as excessive strength of steel and dimensional deviation of actual beam-column components are ignored; 4) The side and corner columns of each floor in the parameter frame are consistent with the center column; 5) It is considered that the variable of each frame lies only in the strictness of the control of "strong columns and weak beams" (i.e., the two-way COF value). By evaluating the seismic performance of different two-way COF frames under large earthquakes and the stress conditions of the components, the "goodness" of the two-way COF value can be evaluated.

[0040] Compared with the existing "strong column weak beam" design method, the steel frame beam-box column "strong column weak beam" design method proposed in the present invention considering bidirectional earthquake action has at least the following advantages:

[0041] 1) The present invention can accurately predict the "strong column and weak beam" yield mechanism of steel frames under bidirectional earthquakes, which is more scientific and reasonable than the existing design method based on unidirectional earthquake action;

[0042] 2) The bidirectional "strong column and weak beam" formula proposed in the present invention is consistent with the current standard formula form, and the degree of realization is also controlled by a specific coefficient COF (i.e., the strong column coefficient η in the corresponding standard), which is convenient for engineers to learn and apply in actual engineering;

[0043] 3) The present invention proposes an unfavorable energy dissipation mechanism that can avoid the "strong beams and weak columns" and the frame columns being destroyed before the beams under actual earthquakes due to ignoring four key factors under bidirectional earthquakes, which helps to reduce engineering safety hazards. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 Flowchart of evaluation criteria.

[0045] Figure 2 The following are diagrams to illustrate four key factors, among which (a) is the ideal substructure-actual frame force difference diagram; (b) is the column axial force time history comparison diagram; (c) is the floor slab compression effect diagram; and (d) is the strain hardening diagram.

[0046] Figure 3 Construct a flow chart for the bidirectional "strong column and weak beam" design method.

[0047] Figure 4 This is the calculation diagram for bidirectional compression bending.

[0048] Figure 5 It is a schematic diagram of the relevant curves for bidirectional 45-degree compression bending of a box section.

[0049] Figure 6 Schematic diagram of the relevant curves for bidirectional compression and bending of box sections.

[0050] Figure 7 A diagram illustrating the formula.

[0051] Figure 8 Structural layout diagram, where (a) is the plan layout diagram and (b) is the elevation layout diagram.

[0052] Fig. 9 The bidirectional COF-damage index relationship diagram of the parameter framework under twenty groups of natural waves.

[0053] Fig.10It is a curve chart of the statistical values ​​of bidirectional COF-evaluation index of parameter framework under twenty groups of natural waves. Specific implementation methods

[0054] 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.

[0055] Figure 3 A flow chart of the bidirectional "strong column and weak beam" design method is given. Figure 1 This is a flow chart of the evaluation criteria of the present invention. Figure 2 The key factors 1-4 given are the influences that the current specification "strong column weak beam" formula fails to consider. The embodiment of the present invention will establish a design method under bidirectional earthquakes by performing elastic-plastic time-history analysis on the system based on a frame model at the spatial level, embody the four key factors in the determination of the bidirectional COF value, and continue the capacity design method in the current specification. It is worth noting that the column resistance is represented by the full plastic strength of the column in one-way compression and bending. The theoretical derivation and experimental phenomena of box-section columns at 45° and in any direction have concluded that this value is a partial safety value under the design axial compression ratio considered by the present invention. At the same time, experimental phenomena and finite element parameter analysis have proved that the existence of the floor slab will cause the column to buckle after the important section reaches the maximum strain limit, that is, the existence of the floor slab does not affect the degree of achieving the target "strong column weak beam" under the evaluation standard of the present invention, so the squeezing effect of the floor slab on the column is not considered.

[0056] The analysis ideas and simplification ideas of the present invention are as follows:

[0057] 1) This bidirectional "strong column and weak beam" design method starts from two aspects, the construction in the form of formula and the determination of COF value, within the commonly used design axial compression ratio. First, the construction in the form of formula combines the theoretical analysis of column resistance and beam effect under bidirectional seismic action and the one-way capacity design method of the reference specification (column resistance is not less than beam effect). Secondly, the determination of the bidirectional COF value considers four key factors not considered in the specification through system analysis: difference in large earthquake response, time-varying difference in axial pressure dynamics, combined action of floor slabs, and strain hardening.

[0058] 2) Determine the structure of the bidirectional "strong column and weak beam" design formula. Its main structure is still the capacity design method, requiring the column resistance No less than beam effect Since it is a bidirectional seismic action different from the specifications, it is necessary to carry out the following theoretical derivation of the column resistance and beam effect under bidirectional force.

[0059] For the column resistance (45° bending), based on the derivation of the bidirectional compression-bending full plastic strength of the box section, it was found that due to the different beam effects and axial pressures in the orthogonal directions of the column, the plastic neutral axis of the section will undergo different degrees of rotation and translation, resulting in several situations in the bidirectional compression-bending calculation diagram and the following three-variable two-parameter equation after dimensionless research parameters, and it is impossible to obtain a simple formula form.

[0060]

[0061] Among them, N p are the column section axial force and yield axial force under common earthquake combinations, M x 、M px 、M y 、M py They are respectively the bending moment in the strong axis direction of the column section and the pure plastic bending strength. β and γ are the parameters of the plastic neutral axis position, such as Figure 4 As shown, assuming t / B≈0 (t is the thickness of the box column), the box section can be simplified into a simplified calculation model with the area concentrated on the edge line. The thin dotted line and solid line of the edge line represent the tensile and compressive areas where the stress reaches the yield strength, respectively.

[0062] When the 45° direction (special) is assumed, β = γ. Substituting into the above formula and eliminating β and γ, M x 、M y The relationship between the 45° bending full plastic strength and the axial pressure after synthesis is:

[0063]

[0064] Make Curve like Figure 5 As shown (M corresponds to Figure 5 M in the two curves x With M cp45° ), when the standard axial compression ratio is greater than 0.38, the bidirectional 45° bending full plastic strength will be greater than the unidirectional bending full plastic strength. At the same time, within the standard axial compression ratio range of the present invention, the unidirectional bending full plastic strength is a safer estimate of the bidirectional 45° bending full plastic strength in most cases, and the difference between the two is not large. Therefore, when the orthogonal beam effects of the box-type column are consistent, the bidirectional bending full plastic strength of the column can be replaced by the unidirectional bending full plastic strength.

[0065] When considering bending at any angle, that is, when the beam effect in the orthogonal direction of the column is inconsistent, the approximate formula is obtained by numerical calculation first and then curve fitting as follows:

[0066]

[0067]

[0068] Among them, Mcpx 、M cpy They are the one-way bending full plastic strength, τ is the ratio of the standard axial compression The relevant parameters are used to make the dimensionless bidirectional bending related curve Hou Ru Figure 6 As shown in the figure, within the studied axial compression ratio, when the angle is constant, as the axial compression ratio increases, the relevant curve becomes fuller, that is, the ratio of the total plastic strength of bidirectional bending to the total plastic strength of unidirectional bending becomes larger; in the 45° direction, as the axial compression ratio increases, the change in the total plastic strength of the bending section is the largest.

[0069] In summary, the full plastic strength of the column around the main axis in any direction is smaller than that around other axes. Therefore, it is a safe estimate to use the unidirectional full plastic strength of the box section instead of the bidirectional full plastic strength to consider the bidirectional stress state of the column.

[0070] As for the beam effect, since the amplitude and phase of the seismic waves in the main and secondary directions of the actual bidirectional earthquake motion are inconsistent, the probability that the beams in the two orthogonal directions simultaneously reach the maximum beam effect in their time history is very small (the present invention assumes that the two main axis directions of the main and secondary wave extension framework of the bidirectional earthquake action are assumed). Figure 7 As shown, the black scattered points are the actual beam effects in the bidirectional earthquake time history, and the full plastic strength of the steel beams in the two orthogonal directions constitutes a black box (i.e., the beam effect envelope considered by the formula), and its intersection with the horizontal and vertical axes is the beam effect in the current standard one-way formula. If the time history difference of the actual orthogonal beam effect is considered in the bidirectional formula, different earthquake waves and different frame structures will result in different most unfavorable combinations of orthogonal beam effects, and it is impossible to summarize a deterministic law. Therefore, for ease of application, the bidirectional formula of the present invention will be based on the full plastic strength of the columns subjected to the orthogonal beams at the same time (i.e., the corner points of the black box). Therefore, the beam effect in the bidirectional formula is taken as the following formula:

[0071]

[0072] in They are respectively the fully plastic bending moments of the x and y plane steel beams (unreinforced) at the intersection of the spatial beam-column node.

[0073] 3) Determine the value of bidirectional COF. Design and calculate multiple bidirectional COF parameter frameworks, and extract the damage index D of all important sections in the framework under multiple groups (e.g., twenty groups) of natural waves—the maximum (compressive) strain ε in the earthquake time history. max and yield strain ε y The parameter framework of the “strong column and weak beam” yield mechanism with sufficient probability and average significance to achieve the target grade is statistically calculated based on the proposed evaluation indicators P1 and P2.

[0074] 4) Among them, the parameter frames with different bidirectional COF values ​​should meet the verification of small earthquake combination calculation. When unifying the bidirectional COF of each frame, by increasing the column wall thickness and increasing the strength of the beams belonging to the important beam-column nodes with the floor height, the parameter frame still meets the small earthquake combination design. At the same time, it also conforms to the principle that the height of the beam is determined by the span in actual engineering. Therefore, it is chosen to adjust the beam strength rather than the cross-sectional size to unify the bidirectional COF value.

[0075] 5) Four key factors ignored by the current code are considered. For key factor 1, the system analysis is used to distinguish it from the ideal beam-column substructure model in the current code, and the design method based on the plane frame in the current code is promoted to the spatial frame level; for key factor 2, the large earthquake elastoplastic time history analysis method is used to distinguish it from the lack of consideration of the time-varying effect of column axial pressure in the current code; for key factor 3, the floor effect of the parameter frame is considered, ① the action in the plane of the floor: because there is no opening in the floor, the in-plane stiffness is considered to be infinite, and the rigid floor assumption is still used. ② The action out of the floor plane: the composite beam fiber section is used to consider the amplification of the floor on the stiffness and strength of the beam, and the slip between the steel beam and the concrete slab is ignored. ③ The influence of the floor on the column resistance is ignored; for key factor 4, the steel in the calculation model adopts the bilinear kinematic hardening constitutive method to consider the second stiffness and strain hardening of the steel ignored in the current code, and it is assumed that the influence of random factors such as material overstrength and dimensional deviation of actual beam-column components is not considered.

[0076] After simplification, the steel frame beam-box column "strong column weak beam" design method under bidirectional earthquake action proposed by the present invention includes the following steps:

[0077] Step 1: Design the initial framework;

[0078] In some embodiments of the present invention, the initial framework is a framework designed using conventional design software to meet the first stage of structural verification under small earthquake combinations.

[0079] Step 2: Define important beam-column nodes and important sections according to the design (standard) axial compression ratio based on the calculation results of the response spectrum CQC method of the initial frame; important beam-column nodes are nodes where the design axial compression ratio of the initial frame after the response spectrum CQC method calculation does not meet the current specification strong column weak beam verification. In some embodiments of the present invention, the design axial compression ratio (the axial compression ratio calculated using the yield strength design value) is less than 0.4, and the standard axial compression ratio (the axial compression ratio calculated using the yield strength standard value) is less than 0.35. The important sections are all upper and lower column end sections of the important beam-column nodes, and the calculation formula of the standard axial compression ratio is:

[0080]

[0081] In the formula

[0082] μp ——Standard axial pressure ratio

[0083] N——column axial pressure under common earthquake combinations (in some embodiments of the present invention, the axial pressure of the lower column section at the beam-column node is uniformly taken)

[0084] N p ——Yield axial force of box column section at the intersection of spatial beam-column node

[0085] Step 3: Unify the bidirectional COF values ​​of important beam-column nodes by fixing the thickness of the middle column of important beam-column nodes, increasing the strength of the beams at important beam-column nodes with the height of the floors, and using the column resistance and beam effect The bidirectional COF value of each node is calculated in reverse. The cross-sections of the side, corner and center columns of each layer are kept consistent;

[0086] The relationship between the two-way COF value and the column resistance and beam effect is:

[0087] For uniform beams:

[0088]

[0089] For end plate flange tapered beams:

[0090]

[0091] In the formula

[0092] M px ——Fully plastic bending moment of the box column section around the principal axis (one-way) at the intersection of the spatial beam-column node

[0093] ——are the fully plastic bending moments of the unreinforced steel beams in the x and y planes at the intersection of the spatial beam-column node

[0094] M vy 、M vx ——The additional bending moments caused by the transfer of plastic hinges in the x and y planes at the beam ends

[0095] COF——column overdesign factor corresponding to the bidirectional formula of the present invention.

[0096] After discussing the different plastic neutral axis positions of the cross section in the column resistance term considering the bidirectional earthquake action, it is considered that the one-way compression bending full plastic strength M around the main axis is taken within the design (standard) axial compression ratio considered in this invention. px is a conservative value. Based on the full plastic strength of the column being subjected to orthogonal beams simultaneously, the beam effect in the two-way formula is taken as the square root of the sum of the squares of the full plastic bending moments of the beams about the principal axis.

[0097] Step 4: Determine the degree of realization of "strong columns and weak beams", referring to the C and D grades in the "Standard for Seismic Performance-Based Design of Building Structures" released in 2022. The present invention calls it C and D grade "strong columns and weak beams", and proposes two quantifiable evaluation indicators P1 and P2, whose formulas are:

[0098] For C-level "strong columns and weak beams":

[0099]

[0100] For D-level "strong columns and weak beams":

[0101]

[0102] In the formula

[0103] L4%, L5%, L6%——respectively the proportion of damage levels L4, L5, and L6 in important sections. The damage level classification refers to the performance-based standard. The evaluation standard process is shown in Figure 1 .

[0104] Among them, the "Standard for Seismic Performance-Based Design of Building Structures" stipulates that C-level frames must meet the following requirements under major earthquakes: the damage level of column components is within the range of L3-L4, and the damage level of some column components is L4; D-level frames must meet the following requirements under major earthquakes: the damage level of column components is within the range of L4-L5, and the damage level of some column components is L5.

[0105] The present invention takes C and D grades as the performance targets of the parameter framework, corresponds their provisions in a large earthquake to the two levels of realization of the "strong column and weak beam" of the present invention, and quantifies the provisions in the standard as

[0106] They indicate that important sections must meet 1): the proportion of damage level L4 does not exceed 30% (i.e., only some column components have damage level L4, and most of the other column components have damage level L3 or below); 2): damage level L5 and above does not exceed 5%

[0107] Similarly, They respectively indicate that the important cross-sections must meet the following requirements: 1) the proportion of damage level L5 does not exceed 30%, and 2) the proportion of damage level L6 does not exceed 5%.

[0108] Step 5: Statistically select twenty groups of natural wave elastic-plastic time-history analysis frame damage index D, and combine the evaluation criteria of the present invention to obtain the parameter framework that meets the target yield mechanism. If it meets the criteria, it is considered that the frame can achieve the target "strong column weak beam" yield mechanism within the evaluation criteria of the present invention; if it does not meet the criteria, it means that the designed frame cannot achieve the "strong column weak beam" yield mechanism that meets the evaluation criteria of the present invention under the action of bidirectional earthquakes, and it is necessary to return to step 3 to redesign the frame by increasing the bidirectional COF value. The calculation formula of the damage index D is:

[0109]

[0110] In the formula

[0111] ε max ——Maximum (compressive) strain of important cross sections

[0112] ε y ——Yield strain of important sections

[0113] In this step, the degree of "strong column and weak beam" is taken as an example to achieve D level: the frame is under multiple groups of natural waves. or If the mean plus double the standard deviation (μ+σ) is not greater than 1, it means that the framework has sufficient probability to realize the D-level "strong column weak beam" yield mechanism; if only the mean (μ) is not greater than 1, it means that the framework can realize the D-level "strong column weak beam" yield mechanism in an average sense; if the statistical values ​​of the evaluation indicators are all greater than 1, it means that the framework does not meet the "strong column weak beam" requirements of this paper; when achieving the C level, the framework is or If the mean plus double the standard deviation (μ+σ) is not greater than 1, it means that the framework has sufficient probability to realize the C-level "strong column and weak beam" yield mechanism; if only the mean (μ) is not greater than 1, it means that the framework can realize the C-level "strong column and weak beam" yield mechanism in an average sense; if the statistical values ​​of the evaluation indicators are all greater than 1, it means that the framework does not meet the "strong column and weak beam" requirements of this article.

[0114] In some embodiments of the present invention, Table 1 shows a nine-layer frame with multiple parameters designed according to step 3, and the initial frame structure layout diagram is shown in Figure 8 , under bidirectional earthquake action, the corresponding parameter framework in Table 1 is implemented. When the bidirectional COF is 0.9, 0.95, 1.0, and 1.05 (corresponding to the strong column coefficient η of the specification formula is 1.27, 1.34, 1.41, and 1.48), the parameter framework meets the "strong column and weak beam" yield mechanism to different degrees under the evaluation standard of the present invention. The statistical results are as follows: Fig. 9 , 10As shown. Specifically, the parameter frame with bidirectional COF=0.85 and below does not meet the "strong column weak beam" requirements of this article, the parameter frame with bidirectional COF=0.9 and above can realize the D-level "strong column weak beam" yield mechanism on average, the parameter frame with bidirectional COF=0.95 and above can realize the C-level "strong column weak beam" yield mechanism on average, the parameter frame with bidirectional COF=1.0 and above has sufficient probability to realize the D-level "strong column weak beam" yield mechanism, the parameter frame with bidirectional COF=1.05 and above has sufficient probability to realize the C-level "strong column weak beam" yield mechanism, and it is shown that the strong column coefficient in the current specification formula needs to be improved.

[0115] Table 1 Framework parameters

[0116]

[0117] Note: The main cycles are the first, second and third order cycles, t c is the column thickness, f yb is the strength of beams at each layer.

[0118] The application of the design method provided by the aforementioned embodiment of the present invention needs to meet the following requirements: 1) This design method is applicable to the case where the design axial compression ratio of the frame is 0.4-0.6 under common earthquake combinations (the corresponding standard axial compression ratio is 0.35-0.55); 2) Ignore the squeezing effect of the floor slab on the frame column; 3) Ignore random factors such as excessive strength of steel and dimensional deviation of actual beam-column components; 4) The side and corner columns of each floor in the parameter frame are consistent with the center column; 5) It is considered that the variable of each frame lies only in the strictness of the control of "strong columns and weak beams" (i.e., the two-way COF value). By evaluating the seismic performance of different two-way COF frames under large earthquakes and the stress conditions of the components, the suitability of the two-way COF value can be evaluated.

[0119] 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. The "strong column and weak beam" design method of steel frame beam-box column under bidirectional earthquake action is characterized by: The following steps are involved: Step 1: Design the initial framework; Step 2: Define important beam-column nodes and important sections according to the design axial compression ratio based on the calculation results of the response spectrum CQC method of the initial frame. Important beam-column nodes are nodes of the initial frame whose design axial compression ratio does not meet the current specification strong column and weak beam verification after the response spectrum CQC method calculation. Important sections are all upper and lower column end sections of important beam-column nodes; Step 3: Unify the bidirectional COF values ​​of important beam-column nodes by fixing the thickness of the middle column of important beam-column nodes, increasing the strength of the beams at important beam-column nodes with the height of the floors, and using the column resistance and beam effect The bidirectional COF value of each node is calculated in reverse; the cross-sections of the side, corner and middle columns of each layer are kept consistent; the relationship between the bidirectional COF value and the column resistance and beam effect is: For uniform beams: For end plate flange tapered beams: Where N is the column axial pressure under the common earthquake combination, N p 、M px are the yield axial force and the fully plastic bending moment around the principal axis of the box column section at the intersection of the spatial beam-column node, M vx , M vy are the full plastic bending moment of the x and y plane steel beams at the intersection of the spatial beam-column node and the additional bending moment caused by the plastic hinge transfer. COF is the bidirectional strong column coefficient corresponding to the bidirectional formula. In the above two formulas, the left formula is defined as the column resistance The right equation is the beam effect Step 4: Determine the degree of realization of "strong columns and weak beams", refer to the performance-based standard C and D levels, and propose two quantifiable evaluation indicators P1 and P2: the performance-based standard C and D levels are the C and D levels required by the "Standard for Seismic Performance-Based Design of Building Structures" released in 2022, and define C and D levels as "strong columns and weak beams"; The evaluation indicators P1 and P2 are as follows: For Class C "Strong Column Weak Beam": For D-level "strong columns and weak beams": Among them, L4%, L5%, and L6% are the proportions of damage levels L4, L5, and L6 in important sections, respectively. They respectively indicate that the important cross-sections must meet 1): the proportion of damage level L4 does not exceed 30%; 2): Damage level L5 and above does not exceed 5%, They respectively indicate that the important sections must meet 1) that the proportion of damage level L5 does not exceed 30%, 2) that the proportion of damage level L6 does not exceed 5%; the degree of "strong column and weak beam" mentioned above is taken as an example to achieve level D: the frame is under multiple groups of natural waves or If the mean plus double the standard deviation μ+σ is not greater than 1, it means that the framework has sufficient probability to realize the D-level "strong column and weak beam" yield mechanism; if only the mean μ is not greater than 1, it means that the framework can realize the D-level "strong column and weak beam" yield mechanism in an average sense; if the statistical values ​​of the evaluation indicators are all greater than 1, it means that the framework does not meet the "strong column and weak beam" requirements; Step 5: Statistically select multiple groups of natural wave elastic-plastic time-history analysis frame damage index D, and combine the evaluation criteria to obtain the parameter framework that meets the target yield mechanism. If it meets the criteria, it is considered that the framework can achieve the target "strong column weak beam" yield mechanism; if it does not meet the criteria, it means that the designed frame cannot achieve the "strong column weak beam" yield mechanism that meets the evaluation criteria under bidirectional earthquake action, and it is necessary to return to step 3 to redesign the frame by increasing the bidirectional COF value.

2. The "strong column and weak beam" design method of steel frame beam-box column under bidirectional earthquake action according to claim 1 is characterized in that: In step 1, the initial frame is a frame that satisfies the first stage of structural verification under small earthquake combinations.

3. The "strong column and weak beam" design method of steel frame beam-box column under bidirectional earthquake action according to claim 1 is characterized in that: In step 2, the important beam-column nodes are nodes of the initial frame having a standard axial compression ratio greater than 0.35 after the response spectrum CQC method is calculated.

4. The "strong column and weak beam" design method for steel frame beams and box columns under bidirectional earthquake action according to claim 3 is characterized in that: The standard axial pressure ratio μ p The calculation formula is: Where N is the column axial pressure under the common earthquake combination, N p It is the yield axial force of the box column section at the intersection of the spatial beam-column node.

5. The "strong column and weak beam" design method of steel frame beam-box column under bidirectional earthquake action according to claim 1 is characterized in that: The one-way bending full plastic strength M around the main axis within the design axial compression ratio or standard axial compression ratio px As a conservative value, it is based on the full plastic strength of the column subjected to simultaneous orthogonal beams, and the beam effect in the two-way formula is taken as the square root of the sum of the squares of the full plastic bending moments of the beams about their principal axes.

6. The "strong column and weak beam" design method for steel frame beams and box columns under bidirectional earthquake action according to claim 1 is characterized in that: In step 5, the damage index D is the maximum compressive strain ε of all important sections in the earthquake time history. max and yield strain ε y The ratio of is:

7. The "strong column and weak beam" design method of steel frame beam-box column under bidirectional earthquake action according to any one of claims 1 to 6, characterized in that: The application of the design method needs to meet the following requirements: 1) This design method is applicable to the case where the design axial compression ratio of the frame is 0.4-0.6 under common earthquake combinations, and the corresponding standard axial compression ratio is 0.35-0.55; 2) The squeezing effect of the floor on the frame column is ignored; 3) Random factors such as excessive strength of steel and dimensional deviation of actual beam-column components are ignored; 4) The side and corner columns of each floor in the parameter frame are consistent with the middle column; 5) It is believed that the variable of each frame lies only in the strictness of the "strong column and weak beam" control. By evaluating the seismic performance of different two-way COF frames under large earthquakes and the stress conditions of the components, the appropriateness of the two-way COF value can be evaluated.

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