Method for determining arc cut corner size of steel frame infill wall

Abstract

The present application belongs to the field of civil engineering, and relates to a method for determining the size of a circular arc cut corner of a steel frame embedded filler wall. The embedded wall plate is provided with a circular arc cutout, and the circular arc cutout is located at the corner of the embedded wall plate. The steel frame embedded circular arc cut corner filler wall has good seismic performance, can delay the cracking of the wall plate, and improve the ductility of the system. The lateral stiffness of the steel frame, the lateral stiffness of the filler wall, and the width of the equivalent diagonal strut are obtained by an equivalent diagonal strut model. A group of ABAQUS finite element models are established with the size of the circular arc cut corner of the filler wall as a parameter. The width of the equivalent diagonal strut model is corrected according to the simulation results. Then, a formula for calculating the ductility coefficient of the system is derived, and a relationship curve between the circular arc cut corner and the ductility coefficient of the system is drawn. The optimal size of the circular arc cut corner is determined by the critical point. The method for determining the size of the steel frame embedded filler wall circular arc cut corner combines theoretical analysis with finite element analysis, and provides a reasonable and reliable analysis method for the application of the steel frame embedded circular arc cut corner filler wall in actual engineering.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of civil engineering and relates to a method for determining the size of a circular arc cut corner of an inlaid filler wall of a steel frame. BACKGROUND

[0002] Steel frame structures have the advantages of large column spacing and strong seismic performance, and filler walls can be flexibly divided according to the function arrangement of rooms, so inlaid filler walls of frame structures are widely used in buildings. In traditional structural design, filler walls are usually regarded as a kind of non-structural component. However, the frame and the filler wall are displaced under the action of horizontal load, and the two interact with each other, and the seismic performance of the frame becomes complex. In the early stage of loading, the filler wall improves the stiffness and horizontal bearing capacity of the frame structure; the filler wall reduces the fundamental period of the frame, which will lead to an increase in the seismic force of the frame structure, and after the filler wall fails in an earthquake, the seismic force borne by the filler wall is suddenly distributed to the adjacent components, causing early damage to the system; the filler wall also causes torsional effects and soft layer effects, and short column damage caused by filler wall restraint effects. In short, the filler wall will have an adverse effect on the seismic performance of the frame structure.

[0003] In view of the adverse interaction caused by the rigid connection of the frame and the filler wall, the current specification in China, i.e., the Code for Seismic Design of Buildings (GB 50011-2010), proposes a flexible connection method to realize the connection between the filler wall and the frame. Domestic researchers have conducted a large amount of research on the flexible connection method of the frame and the filler wall; patent CN110306694B invents a filler wall structure system and an assembled filler wall panel, which sets a first filler wall panel and a second filler wall panel in sequence along the direction perpendicular to the ground, and sets an elastic member between the first filler wall panel and the second filler wall panel, which realizes the flexible connection between the filler wall panel and the frame and has good seismic performance, but this construction method needs to precast the connecting piece in the factory, which is difficult to be widely adopted in construction; patent CN105937263B discloses an assembled steel frame filler wall system and a construction method thereof, which pre-welds connecting pieces with long circular holes on the four sides of the steel frame to weaken the interaction between the filler wall and the frame, but this method is difficult to construct and needs to position the wall panel in advance; in order to reduce the adverse effect of the filler wall on the steel frame, based on the principle of setting a notch at the corner of the filler wall to weaken the tension (compression) force zone, a steel frame inlaid circular arc cut corner filler wall is designed, and a method for determining the size of the circular arc cut corner of the inlaid filler wall of the steel frame is proposed. SUMMARY

[0004] The purpose of the present application is to provide a method for determining the size of the circular arc cut corner of the inlaid filler wall of the steel frame.

[0005] The present application is implemented by the following technical solutions:

[0006] A method for determining the size of a circular arc cut corner of an inlaid wall of a steel frame, comprising the following steps:

[0007] First, assuming the specification parameters of the main structure composed of frame columns and frame beams, the span, height and thickness of the inlaid wall panel are determined, the inlaid wall panel is provided with a circular arc cutout, and the circular arc cutout is located at the corner of the inlaid wall panel;

[0008] Second, a group of steel frame inlaid circular arc cut corner infill wall models are designed with the size of the infill wall circular arc cut corner as a parameter variable;

[0009] Third, the lateral stiffness of the steel frame inlaid circular arc cut corner infill wall is calculated according to the equivalent diagonal strut model calculation formulas (1)-(4);

[0010] System lateral stiffness: (1)

[0011] In the formula: is the lateral stiffness of the steel frame inlaid circular arc cut corner infill wall; is the lateral stiffness of the steel frame, see formula (2); is the lateral stiffness of the infill wall, see formula (4);

[0012] Lateral stiffness of steel frame: (2)

[0013] In the formula: is the bending moment of the steel frame under unit force; is the bending moment of the steel frame under load; is the span of the frame; is the elastic modulus of the steel frame; is the sectional moment of inertia of the steel column; is the force applied at the top end of the steel frame with unit displacement; is the steel column lateral stiffness correction coefficient, see formula (3);

[0014] Steel column lateral stiffness correction coefficient: (3)

[0015] is the beam-column linear stiffness ratio, ;

[0016] Infill wall lateral stiffness: (4)

[0017] In the formula: is the span of the frame; is the height of the frame; is the elastic modulus of the infill wall masonry; is the width of the diagonal strut; for the infill wall thickness;

[0018] Fourthly, the ABAQUS finite element model was established, the horizontal load was applied at the beam-column joint, and the lateral stiffness of the steel frame embedded with the circular-arc-cutting-angle infill wall was obtained through the finite element stress simulation;

[0019] Fifthly, the lateral stiffness of the steel frame embedded with the circular-arc-cutting-angle infill wall obtained through the finite element simulation was curve-fitted and corrected according to the lateral stiffness obtained according to the formulas (1)-(4), so as to determine the corrected equivalent width of the inclined strut , see formula (5);

[0020] The corrected equivalent width of the inclined strut: (5)

[0021] In the formula, is the corrected equivalent width of the inclined strut; is the diagonal length of the frame; is the radius of the circular-arc-cutting-angle, ; is the angle between the diagonal and the horizontal direction;

[0022] Sixthly, the ductility coefficient of the system was determined according to the formulas (1)-(5) , see formula (6);

[0023] The ductility coefficient of the system: (6)

[0024] In the formula, is the ductility coefficient of the frame; is the lateral stiffness of the steel frame; is the lateral stiffness of the infill wall; is the span of the frame; is the height of the frame; is the elastic modulus of the infill wall masonry; is the width of the inclined strut; is the thickness of the infill wall; is the ratio of the yield bearing capacity of the steel frame to the yield bearing capacity of the system, see formula (7);

[0025] The ratio of the yield bearing capacity of the steel frame to the yield bearing capacity of the system: (7)

[0026] In the formula, is the ratio of the yield bearing capacity of the steel frame to the yield bearing capacity of the system; is the yield bearing capacity of the steel frame; is the yield bearing capacity of the system;

[0027] Step 7, according to formula (6), the size of the circular corner cut and the ductility coefficient of the steel frame embedded with the circular corner cut infill wall are plotted The relationship curve;

[0028] Step 8, according to the critical point of the relationship curve between the size of the circular corner cut and the ductility coefficient of the system, the optimal size of the circular corner cut of the steel frame embedded with the circular corner cut infill wall is determined; The relationship curve;

[0029] Preferably, when l1 = l2, the size of the circular corner cut in the first step is in the range of (0.5-1.5)×H;

[0030] The beneficial effects of the present application are as follows: based on the principle that the notch at the corner of the infill wall can weaken the tensile (compressive) force zone, a steel frame embedded with a circular corner cut infill wall is designed, and a method for determining the size of the circular corner cut of the steel frame embedded with the infill wall is proposed; the steel frame embedded with the circular corner cut infill wall has good seismic performance, can delay the cracking of the wall panel, and improve the ductility of the system; the method for determining the size of the circular corner cut of the steel frame embedded with the infill wall combines theoretical analysis with finite element analysis, and provides a reasonable and reliable analysis method for the application of the steel frame embedded with the circular corner cut infill wall in actual engineering. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The figure is a schematic diagram of the steel frame embedded with the circular corner cut infill wall of the embodiment of the present application;

[0032] In the figure: 1, steel frame column; 2, steel frame beam; 3, infill wall; 4, stiffening rib;

[0033] Figure 2 The figure is a schematic diagram of the equivalent diagonal strut model calculation of the embodiment of the present application;

[0034] Figure 3 The figure is a relationship curve between the size of the circular corner cut and the ductility coefficient of the system of the embodiment of the present application; The relationship curve;

[0035] Figure 4 The figure is a parameter of the steel frame embedded with the circular corner cut infill wall of the embodiment of the present application. DETAILED DESCRIPTION

[0036] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments.

[0037] EMBODIMENT

[0038] A method for determining the size of the circular corner cut of the steel frame embedded with the infill wall includes the following steps:

[0039] ​The steel frame has a height of 3000 mm and a span of 4000 mm; the beam and column section sizes are H300 mm x 150 mm x 6.5 mm x 9 mm and H200 mm x 200 mm x 8 mm x 12 mm respectively; the steel material is Q355 steel; the beam-to-column linear stiffness ratio 2; the light aerated concrete (AAC) masonry infilled wall has a thickness of 100 mm, and the elastic modulus of the AAC masonry is 1745 MPa and the Poisson's ratio is 0.2;

[0040] A group of steel frame models with an embedded arc corner infilled wall are designed with the arc corner size of the infilled wall as a parameter variable, as shown in Table 1.

[0041] The lateral stiffness of the system is calculated according to formulas (1)-(5), and the calculation results are shown in Table 2. Figure 4 ;

[0042] Lateral stiffness of the system: (1)

[0043] In the formula: K is the lateral stiffness of the steel frame with an embedded arc corner infilled wall; K is the lateral stiffness of the steel frame; K is the lateral stiffness of the infilled wall;

[0044] Lateral stiffness of the steel frame:

[0045] (2)

[0046] In the formula: K is the lateral stiffness of the steel frame; K is the linear stiffness of the steel column; K is the correction coefficient of the lateral stiffness of the steel column, as shown in formula (3);

[0047] Correction coefficient of the lateral stiffness of the steel column: (3)

[0048] In the formula: K is the linear stiffness ratio of the beam and column, ;

[0049] Lateral stiffness of the infilled wall: (4)

[0050] In the formula: L is the span of the frame; H is the height of the frame; E is the elastic modulus of the infilled wall masonry; t is the thickness of the infilled wall; b is the equivalent width of the inclined strut after correction, as shown in formula (5);

[0051] Equivalent width of the inclined strut after correction:

[0052]

[0053] (5)

[0054] In the formula: This is the corrected equivalent diagonal compression bar width; The length of the frame diagonal; The radius of the tangent of the arc. ; The angle between the diagonal and the horizontal direction;

[0055] A set of ABAQUS finite element models was established based on the dimensions of the circular arc chamfer, and the ductility coefficient of the frame was obtained through simulation results. ;

[0056] The ratio of the steel frame's yield capacity to the system's yield capacity was obtained based on the simulation results. :

[0057]

[0058] Based on formulas (1)-(5) and the frame ductility coefficients obtained from finite element simulation Calculate the ductility coefficient of the system ;

[0059] System ductility coefficient:

[0060] (6)

[0061] In the formula: The frame ductility coefficient; This refers to the lateral stiffness of the steel frame; This refers to the lateral stiffness of the infill wall; For the span of the frame; The height of the frame; The elastic modulus of the infill wall masonry; This refers to the dimensions of the rounded corner. This refers to the thickness of the infill wall; This is the ratio of the steel frame's yield bearing capacity to the system's yield bearing capacity.

[0062] Draw the dimensions of the arc chamfer according to formula (6). Ductility coefficient of the infill wall with the rounded notch at the embedded corner of the steel frame Relationship curve, see Figure 3 ;

[0063] Step 8: Based on the arc chamfer dimensions and the system ductility coefficient The critical point of the relationship curve determines the optimal size of the arc chamfer of the infill wall at the embedded corner of the steel frame.

Claims

1. A method for determining the size of a circular corner cut of a steel frame infill wall, characterized in that, Comprising the following steps: First step, assuming the main structure specification parameters composed of frame column, frame beam, determine the span, height and thickness of the embedded wall, the embedded wall is provided with an arc-shaped cutout, and the arc-shaped cutout is located at the corner of the embedded wall; Second step, taking the arc cut corner size of the infilled wall and the span-height ratio as the parameter variables, a group of steel frame embedded arc cut corner infilled wall models are designed; Third step, the lateral stiffness of the steel frame embedded arc cut corner infilled wall is calculated according to the equivalent inclined strut model calculation formula (1)-(4); System lateral stiffness: K = K F + K W (1) In the formula: K is the lateral stiffness of the steel frame with the circular arc cut corner infill wall; K F K is the lateral stiffness of the steel frame, see formula (2); K W K is the lateral stiffness of the infill wall, see formula (4); Lateral stiffness of steel frames: wherein: M is the bending moment of the steel frame under the unit force; M P M is the bending moment of the steel frame under the load; L is the span of the frame; E is the elastic modulus of the steel frame; I is the sectional moment of inertia of the steel column; F is the force applied at the top of the steel frame for a unit displacement of α c is the steel column lateral stiffness correction factor, see equation (3) Steel column lateral stiffness correction factor: where: Y is the beam-to-column linear stiffness ratio, Lateral stiffness of infill wall: where: L is the span of the frame; h is the height of the frame; E w is the elastic modulus of the infill wall masonry; w0is the width of the diagonal strut; t is the thickness of the infill wall; Fourth step, the ABAQUS finite element model is established, the horizontal load is applied at the beam-column joint, and the lateral stiffness of the steel frame embedded arc cut corner infilled wall is obtained through the finite element stress simulation; Fifth step, according to the lateral stiffness of the steel frame embedded arc cut corner infilled wall obtained by the finite element simulation, the lateral stiffness obtained according to the formula (1)-(4) is curve-fitted and corrected, and the corrected equivalent inclined strut width w is determined, see formula (5); Modified equivalent oblique strut width: w = 0.3(d - 0.024l 2 cos θ + 0.28l)sin 2θ (5) In the formula: w is the corrected equivalent inclined strut width; d is the diagonal length of the frame; l is the radius of the arc cut corner, l<500mm; θ is the angle between the diagonal and the horizontal direction; Sixth step, the system ductility coefficient μ is determined according to the formula (1)-(5), see formula (6); System ductility factor: where: μ is the ductility coefficient of the system; μ f is the ductility coefficient of the frame; K F is the lateral stiffness of the steel frame; K W is the lateral stiffness of the infill wall; L is the span of the frame; h is the height of the frame; E w is the elastic modulus of the infill wall masonry; w is the width of the diagonal strut; t is the thickness of the infill wall; α is the ratio of the yield load of the steel frame to the yield load of the system, see equation (7); The ratio of the steel frame yield load capacity to the system yield load capacity is: wherein: a is the ratio of the steel frame yield load capacity to the system yield load capacity; P F is the steel frame yield load capacity; and P is the system yield load capacity; Seventh step, the relationship curve between the arc cut corner size and the ductility coefficient μ of the steel frame embedded arc cut corner infilled wall is drawn according to the formula (6); Eighth step, according to the critical point of the relationship curve between the arc cut corner size and the system ductility coefficient μ, the optimal size of the arc cut corner of the steel frame embedded arc cut corner infilled wall is determined.

2. The method for determining the size of the circular-arc cutout of a steel frame infill wall according to claim 1, wherein When l1=l2, the range of the value of the circular arc cut-off angle in the first step is

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