Strong column-weak beam design method for steel frame beam-box column under bidirectional earthquake excitations

Abstract

A strong column-weak beam design method for a steel frame beam-box column under bidirectional earthquake excitations, comprising: designing an initial frame; on the basis of a reaction spectrum CQC method calculation result of the initial frame, defining important beam-column joints and important cross sections according to a designed axial compression ratio; unifying bidirectional COF values of the important beam-column joints; determining the degree of realization of "strong column-weak beam", and proposing two quantifiable evaluation indexes P1 and P2; and counting a damage index D of the frame after elastoplastic time history analysis of multiple natural waves, and according to evaluation criteria, obtaining parameter frames conforming to a target yield mechanism, if a parameter frame satisfies the target yield mechanism, considering that the frame can realize a target "strong column-weak beam" yield mechanism in the evaluation criteria, and if the parameter frame does not satisfy the target yield mechanism, indicating that the designed frame cannot realize the "strong column-weak beam" yield mechanism conforming to the evaluation criteria under the bidirectional earthquake excitations, and needing to redesigning the frame by increasing the bidirectional COF values.

Description

"Strong Column and Weak Beam" Design Method for Steel Frame Beam-Box Columns under Bidirectional Earthquake Action Technical Field

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

[0002] "Strong column, weak beam" design is crucial for preventing structural collapse and is a key component of earthquake-resistant design worldwide. Currently, the "strong column, weak beam" design theory in Chinese standards remains limited to planar structural calculations, performing calculations only along two principal axes. However, under actual bidirectional earthquakes, spatial structures experience bidirectional forces, significantly different from the unidirectional seismic effects described in the standard planar model.

[0003] Actual earthquake damage and research have shown that under bidirectional earthquakes, column deformation, energy dissipation, and damage increase while beams decrease; beam-column substructures designed according to standard planar design cannot achieve the expected unidirectional load-bearing performance under bidirectional loads; and integral frame structures designed using the standard unidirectional "strong column, weak beam" formula cannot achieve the "strong column, weak beam" yield mechanism under bidirectional earthquakes. Therefore, research on "strong column, weak beam" under bidirectional earthquakes has important theoretical and practical significance for improving the seismic safety and collapse resistance 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 is 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 columns under bidirectional earthquake action. In addition to not considering bidirectional earthquake action, there are still the following key factors that need to be considered:

[0006] Key Factor 1: The nonlinear response characteristics of each floor of the frame structure under a major earthquake. Due to the strong nonlinear response of the frame structure under major earthquakes, its calculation model (see Figure 2(a)) changes. Current design formulas are formally based on an ideal beam-column substructure (with the inflection point at the column midpoint). This ideal model can well reflect the experimental characteristics of the beam-column substructure, but it differs significantly from the yield mechanism of the overall frame entering the elastic-plastic stage of major earthquakes: some column bases 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 reversed loads on the upper and lower column ends of the beam-column joint. Therefore, current standard formulas all assume that the upper and lower column ends are subjected to simultaneous loads, which is inaccurate and unsafe for the actual loads on the beam-column joint in the overall frame under major earthquakes.

[0007] Key Factor 2: The dynamic time-varying effect of column axial forces under large earthquakes. In my country's "strong column, weak beam" formula, the column axial pressure is taken as the column axial pressure N under the commonly encountered earthquake combination. For the middle column, because there are beams on both sides, the shear forces of the beams under lateral earthquake forces can balance each other, making the column axial pressure caused by commonly encountered earthquakes almost zero. Therefore, its true axial pressure (see Figure 2(b)) remains unchanged during the time history. Therefore, the "strong column, weak beam" formula is used to calculate 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 earthquake 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 history. In addition, due to the influence of factors such as the randomness of the earthquake motion and the change of the frame structure, it is impossible to accurately estimate the maximum axial pressure of the edge and corner columns. In this case, the "strong column and weak beam" formula for the axial pressure N 边 、N 角 Unsafe estimate.

[0008] Key Factor 3: The impact of floor slabs on the load-bearing properties of beams and columns. For beams, the combined effect of floor slabs on beams transforms pure steel beams into composite beams with higher stiffness and strength, thereby increasing the beam effect in the "strong column, weak beam" formula. For columns, since the primary method of force transmission between floor slabs and columns is direct compression of the floor slab within the column width (see Figure 2(a)), this may cause local buckling of box-type columns before reaching full plastic bending strength, thereby reducing the column resistance in the "strong column, weak beam" formula. Current code formulas do not consider the reduction in column resistance caused by floor slabs. Only the New Zealand code formula, based on the ultimate (floor slab compression) state of the composite beam of the beam-column substructure, considers the floor slab's effect on steel beam strength.

[0009] Key Factor 4: Strain hardening of beams and columns, overstrength of materials, etc. The derivation of current specification formulas is based on the ideal elastic-plastic assumption of the material constitutive structure, that is, when full plasticity is achieved, the cross-section is in a rectangular stress distribution state, and the bending stiffness of the corresponding cross-section is zero. However, after yielding, actual steel has a non-negligible secondary stiffness and strain hardening (see Figure 2(d)), and the bending stiffness of the cross-section gradually decreases with increasing yield. In addition, random factors such as the overstrength of actual steel materials and the dimensional deviation of actual beam and column components will also affect the degree of realization of the "strong column and weak beam" strategy.

[0010] Summary of the Invention

[0011] 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 earthquakes. 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 earthquakes.

[0012] To achieve the purpose of the present invention, the present invention provides a "strong column and weak beam" design method for steel frame beams and box columns under bidirectional earthquake action, comprising the following steps:

[0013] Step 1: Design the initial framework;

[0014] 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;

[0015] 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 important beam-column nodes with the height of the floors, and using the column resistance to 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 floor are kept consistent;

[0016] Step 4: Determine the degree of achieving “strong columns and weak beams”, refer to the performance-based standards C and D levels, and propose two quantifiable evaluation indicators P1 and P2;

[0017] Step 5: Statistically select twenty groups of damage indicators D of the frame after elastic-plastic time-history analysis of natural waves, and combine them with the evaluation criteria of the present invention to obtain a parameter framework that meets the target yield mechanism. If the parameters meet 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 the parameters do 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 bidirectional earthquake action, and it is necessary to return to step 3 and redesign the frame by increasing the bidirectional COF value.

[0018] 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.

[0019] Furthermore, in step 2, the important beam-column nodes are nodes where the design (standard) axial compression ratio of the initial frame is 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.

[0020] Furthermore, in step 2, the standard axial pressure ratio calculation formula is:

[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 beams of uniform cross-section:

[0024] For beams with tapered end plate flanges:

[0025] 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 and the fully plastic bending moment around the principal axis (one-way) 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 (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 two-way strong column coefficient corresponding to the two-way formula. In the above two formulas, the left formula is defined as the column resistance The right equation is the beam effect

[0026] Furthermore, in step 3, after discussing the different positions of the plastic neutral axis of the cross section in the column resistance term under bidirectional earthquake action, it is considered that the unidirectional compression bending full plastic strength M around the main axis is taken within the design axial compression ratio considered in the present invention. px is a conservative value. Based on the fully plastic strength of the column subjected to simultaneous orthogonal beam loading, and considering the inconsistency of seismic wave amplitude and phase, the beam effect in the two-way formula is conservatively taken as the square root of the sum of the squares of the fully plastic bending moments of the beams about their principal axes.

[0027] 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.

[0028] Furthermore, in step 4, the evaluation indicators P1 and P2 are expressed as follows:

[0029] For Class C "strong columns and weak beams":

[0030] For D-level "strong columns and weak beams":

[0031] L4%, L5%, and L6% represent the percentage of critical sections with damage levels of L4, L5, and L6, respectively. Damage levels are classified based on performance-based standards. The evaluation process is shown in Figure 1.

[0032] Furthermore, in step 4, the degree of “strong column and weak beam” is taken as an example to achieve D level: the frame is under 20 sets 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 article.

[0033] 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 is:

[0034] Furthermore, the application of the design method needs to meet the following requirements: 1) This design method is applicable to the case where the frame is designed with an axial compression ratio of 0.4-0.6 under common earthquake combinations; 2) The squeezing effect of floor slabs on frame columns is ignored; 3) Random factors such as excessive steel strength and dimensional deviations 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 assumed that the variable of each frame lies only in the strictness of the "strong column and weak beam" control (i.e., the two-way COF value). By evaluating the seismic performance of different two-way COF frames under major earthquakes and the stress conditions of the components, the "goodness" of the two-way COF value can be evaluated.

[0035] Compared with the existing "strong column weak beam" design method, the steel frame beam-box column "strong column weak beam" design method proposed in this invention considering bidirectional earthquake action has at least the following advantages:

[0036] 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;

[0037] 2) The bidirectional "strong column and weak beam" formula proposed in this invention is consistent with the existing standard formula. 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.

[0038] 3) The present invention proposes an unfavorable energy-consuming mechanism that can avoid the "strong beams and weak columns" and the destruction of frame columns before beams under actual earthquakes caused by ignoring four key factors under bidirectional earthquakes, which helps to reduce engineering safety hazards. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of the evaluation criteria.

[0040] Figure 2 illustrates four key factors, where (a) shows the force difference between the ideal substructure and the actual frame; (b) shows the time history comparison of the column axial force; (c) shows the floor slab compression effect; and (d) shows the strain hardening diagram.

[0041] Figure 3 is a flow chart of the bidirectional “strong column and weak beam” design method.

[0042] Figure 4 is a bidirectional bending calculation diagram.

[0043] Figure 5 is a schematic diagram of the relevant curves of the box section bidirectional 45-degree bending.

[0044] Figure 6 is a schematic diagram of the box section bidirectional bending related curves.

[0045] FIG7 is a diagram illustrating the formula.

[0046] Figure 8 Structural layout diagram, where (a) is the plan layout diagram and (b) is the elevation layout diagram.

[0047] Figure 9 shows the relationship between the bidirectional COF and damage index of the parameter framework under twenty groups of natural waves.

[0048] Figure 10 is a graph showing the statistical values ​​of the bidirectional COF-evaluation index of the parameter framework under twenty groups of natural waves.

[0049] Specific implementation methods

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only 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 making creative efforts are within the scope of protection of the present invention.

[0051] FIG3 shows a flow chart of the construction of a bidirectional "strong column weak beam" design method, and FIG1 shows a flow chart of the evaluation criteria of the present invention. Among them, the key factors 1-4 given in FIG2 are the influences that the "strong column weak beam" formula in the current specification fails to take into account. The embodiment of the present invention will establish a bidirectional earthquake design method by performing an 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 the box-section column at 45° and in any direction all indicate that this value is a partial safety value under the design axial compression ratio considered by the present invention. At the same time, after experimental phenomena and finite element parameter analysis, it is proved that the existence of the floor slab causes 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 criteria of the present invention, so the squeezing effect of the floor slab on the column is not considered.

[0052] The analysis and simplification ideas of the present invention are as follows:

[0053] 1) This bidirectional "strong column, weak beam" design method, within the commonly used design axial compression ratio range, proceeds from two aspects: formula construction and COF value determination. First, the formula construction combines theoretical analysis of column resistance and beam effects under bidirectional seismic loads with the unidirectional capacity design method of the reference standard (column resistance is not less than the beam effect). Second, the bidirectional COF value is determined through a system analysis that considers four key factors not considered in the standard: differences in large earthquake response, time-varying differences in axial pressure dynamics, combined floor slab effects, and strain hardening.

[0054] 2) Determine the structure of the bidirectional "strong column weak beam" design formula. Its main structure is still the capacity design method, requiring the column resistance Not less than beam effect Since it is a bidirectional seismic action different from the code, it is necessary to carry out the following theoretical derivation of the column resistance and beam effect under bidirectional force.

[0055] For column resistance (45° bending), based on the derivation of the full plastic strength of the box section under bidirectional compression and bending, it was found that the different beam effects and axial pressures in the orthogonal directions of the column will cause the plastic neutral axis of the section to undergo different degrees of rotation and translation. This leads to several situations in the bidirectional compression and bending calculation diagram. After the research parameters are dimensionless, they are converted into the following three-variable two-parameter equation, making it impossible to obtain a concise formula form.

[0056] 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 It is divided into the bending moment in the strong axis direction of the column section and the fully plastic pure bending strength, β and γ are the parameters of the plastic neutral axis position, as shown in Figure 4. 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.

[0057] When the 45° direction (special assumption) is taken, β=γ. Substitute into the above formula and eliminate β and γ to get M x 、M y The relationship between the 45° bending full plastic strength and axial pressure after synthesis is:

[0058] Make The curves are shown in Figure 5 (M corresponds to M in the two curves in Figure 5 x With M cp45° ), when the standard axial compression ratio is greater than 0.38, the biaxial 45° full plastic strength will be greater than the uniaxial full plastic strength. Furthermore, within the standard axial compression ratio range of the present invention, the uniaxial full plastic strength is, in most cases, a safe estimate of the biaxial 45° full plastic strength, with a small difference between the two. Therefore, when the orthogonal beam effects of box-type columns are consistent, the biaxial full plastic strength of the column can be replaced by the uniaxial full plastic strength.

[0059] When considering bending at any angle, that is, when the beam effects in the orthogonal directions of the column are inconsistent, the approximate formula is obtained by first performing numerical calculations and then curve fitting:

[0060] Among them, M cpx 、M cpy They are the full plastic strength of uniaxial bending, τ is the ratio of the standard axial compression The relevant parameters are used to make the dimensionless bidirectional bending related curve The results are shown in Figure 6. Within the studied axial compression ratio, when the angle is constant, the related curve becomes fuller as the axial compression ratio increases, that is, the ratio of the full plastic strength of biaxial bending to the full plastic strength of uniaxial bending increases; in the 45° direction, the change in the full section plastic strength of bending is the largest as the axial compression ratio increases.

[0061] To sum up, the full plastic strength of the column around the main axis in any direction is smaller than that around other axes. Therefore, using 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 is a relatively safe estimate.

[0062] 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 defaults to the two main axis directions of the main and secondary waves of the bidirectional earthquake action). As shown in Figure 7, 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 the black box (that is, 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 problem of the actual orthogonal beam effect is considered in the bidirectional formula, different seismic waves and different frame structure forms 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 being simultaneously subjected to the orthogonal beams (that is, the corner points of the black box). Therefore, the beam effect in the bidirectional formula is taken as the following formula:

[0063] in are the fully plastic bending moments of the x and y plane steel beams (unreinforced) at the intersection of the spatial beam-column node.

[0064] 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 the action of 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 Based on the proposed evaluation indicators P1 and P2, a parameter framework of the "strong column and weak beam" yield mechanism with sufficient probability and average significance to achieve the target level is statistically calculated.

[0065] 4) The resulting parametric frameworks with different bidirectional COF values ​​were designed to meet the requirements for small earthquake combination calculations. By unifying the bidirectional COF values ​​across the frameworks by increasing column thickness and increasing the strength of beams at key beam-column joints with floor height, the parametric frameworks still met the requirements for small earthquake combination design. This also adheres to the principle that beam height is determined by span in actual engineering. Therefore, the bidirectional COF values ​​were unified by adjusting beam strength rather than cross-sectional dimensions.

[0066] 5) Four key factors neglected by current codes were considered. For key factor 1, a system analysis was used, differing from the ideal beam-column substructure model used in current codes, extending the current code's design approach based on plane frames to the spatial frame level. For key factor 2, a large earthquake elasto-plastic time-history analysis method was used, differing from the current code's inadequate consideration of the time-varying effects of column axial pressure. For key factor 3, the floor slab effect in the parametric frame was considered. ① In-plane effects of the floor slab: Because the floor slab has no openings, the in-plane stiffness is assumed to be infinite, and the rigid floor slab assumption is still used. ② Out-of-plane effects of the floor slab: A composite beam fiber cross-section was used to account for the amplification of the floor slab's effect on beam stiffness and strength, while ignoring the slip between the steel beam and the concrete slab. ③ The effect of the floor slab on column resistance was ignored. For key factor 4, a bilinear kinematic hardening constitutive model was used for the steel in the calculation model to account for the secondary stiffness and strain hardening of steel, which are neglected in current codes. Furthermore, random factors such as material overstrength and dimensional deviations in actual beam-column components were assumed to be negligible.

[0067] After simplification, the "strong column and weak beam" design method for steel frame beams and box columns under bidirectional earthquake action proposed in the present invention includes the following steps:

[0068] Step 1: Design the initial framework;

[0069] 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.

[0070] 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; important beam-column nodes are nodes in the initial frame where the design axial compression ratio after the response spectrum CQC method calculation does not meet the current standard strong column and weak beam verification. In some embodiments of the present invention, the design axial compression ratio (the axial compression ratio calculated using the design value of the yield strength) is less than 0.4, and the standard axial compression ratio (the axial compression ratio calculated using the standard value of the yield strength) is less than 0.35. Important sections are all upper and lower column end sections of important beam-column nodes. The calculation formula for the standard axial compression ratio is:

[0071] In the formula

[0072] μ p ——Standard axial pressure ratio

[0073] N is the 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)

[0074] N p ——Yielding axial force of box column section at the intersection of spatial beam-column node

[0075] 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 important beam-column nodes with the height of the floors, and using the column resistance to 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 floor are kept consistent;

[0076] The relationship between the two-way COF value and the column resistance and beam effect is:

[0077] For beams of uniform cross-section:

[0078] For beams with tapered end plate flanges:

[0079] In the formula

[0080] 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

[0081] ——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

[0082] 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

[0083] COF - corresponds to the bidirectional column overdesign factor of the bidirectional formula of the present invention.

[0084] After discussing the different positions of the plastic neutral axis in the column resistance term under bidirectional earthquake action, it is considered that the unidirectional compression bending full plastic strength M around the main axis is taken within the design (standard) axial compression ratio considered in this invention. px The beam effect in the two-way formula is taken as the square root of the sum of the squares of the fully plastic bending moments of the beams about their principal axes, based on the full plastic strength of the columns subjected to orthogonal beams.

[0085] Step 4: Determine the degree of “strong columns and weak beams” achieved. Referring to the C and D grades in the “Standard for Performance-Based Seismic Design of Building Structures” released in 2022, this paper refers to these grades as “strong columns and weak beams” and proposes two quantifiable evaluation indicators, P1 and P2, which are as follows:

[0086] For Class C "strong columns and weak beams":

[0087] For D-level "strong columns and weak beams":

[0088] In the formula

[0089] L4%, L5%, L6% - the proportion 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.

[0090] 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, among which 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, among which the damage level of some column components is L5.

[0091] This paper takes C and D grades as the performance targets of the parameter framework, and corresponds their provisions in a major earthquake to the two levels of realization of the "strong column and weak beam" of this invention, and quantifies the provisions in the standard as

[0092] They indicate that important sections must meet 1): the proportion of damage level L4 does not exceed 30% (i.e., only some column members have damage level L4, and the rest of the column members have damage level L3 or below); 2): damage level L5 and above does not exceed 5%

[0093] Similarly, They respectively indicate that important 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%.

[0094] Step 5: Statistically select twenty groups of natural wave elastic-plastic time-history analysis frames’ damage index D, and combine the evaluation criteria of the present invention to derive a parameter framework that meets the target yield mechanism. If satisfied, 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 not satisfied, it indicates 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 action, and it is necessary to return to step 3 and redesign the frame by increasing the bidirectional COF value. The calculation formula for the damage index D is:

[0095] In the formula

[0096] ε max ——Maximum (compressive) strain of important sections

[0097] ε y ——Yield strain of important sections

[0098] 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 article; when achieving 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 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 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 article.

[0099] In some embodiments of the present invention, Table 1 is given for a nine-story frame with multiple parameters designed according to step 3. The initial frame structure layout diagram is shown in Figure 8. Under the action of a bidirectional earthquake, the corresponding parameter frame in Table 1 is implemented. When the bidirectional COF is 0.9, 0.95, 1.0, and 1.05 (the strong column coefficient η of the corresponding specification formula is 1.27, 1.34, 1.41, and 1.48), the parameter frame meets the "strong column and weak beam" yield mechanism to different degrees under the evaluation standard of the present invention. The statistical results are shown in Figures 9 and 10. 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 in an average sense; the parameter frame with bidirectional COF=0.95 and above can realize the C-level "strong column weak beam" yield mechanism in an average sense; 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.

[0100] Table 1 Framework parameters 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.

[0101] 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 under common earthquake combinations is 0.4-0.6 (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 steel strength and dimensional deviations 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 "strong column and weak beam" control (i.e., the two-way COF value). By evaluating the seismic performance of different two-way COF frames under major earthquakes and the stress conditions of the components, the suitability of the two-way COF value can be evaluated.

[0102] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily 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 is not limited to the embodiments shown herein but is intended to conform 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 Inversely calculate the bidirectional COF value of each node; the cross-sections of the sides, corner columns and center columns of each layer are consistent; Step 4: Determine the degree of achieving "strong columns and weak beams", refer to the performance-based standards C and D levels, and propose two quantifiable evaluation indicators P1 and P2: 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: In step 3, 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 6. The "strong column and weak beam" design method of steel frame beam-box column under bidirectional earthquake action according to claim 5 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.

7. 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 4, the performance-based standard C and D grades are the C and D grades required by the "Standard for Seismic Performance-Based Design of Building Structures" issued in 2022, and the C and D grades are defined 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 sections must meet 1): the proportion of damage level L4 does not exceed 30%; 2): the proportion of damage level L5 and above does not exceed 5%, 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%.

8. The design and method of the steel frame beam-box column "strong column weak beam" considering bidirectional earthquake action according to claim 7 is characterized in that: In step 4, the degree of "strong columns and weak beams" 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.

9. 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 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:

10. The "strong column and weak beam" design method of steel frame beam-box column under bidirectional earthquake action according to claims 1-9 is 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 considered 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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