A method for calculating the initial rotational stiffness and bending-shear capacity of prefabricated beam-column joints

Abstract

The present invention discloses a method for calculating the initial rotational stiffness and bending-shear bearing capacity of an assembled beam-column node. The method for calculating the initial rotational stiffness includes the following steps: analyzing the components constituting the initial rotational stiffness of the node and establishing a spring model of the node stiffness; calculating the equivalent spring stiffness of the upper flange cover, the inclined end plate and the upper flange plate; calculating the equivalent spring stiffness of the high-strength bolts connecting the upper flange cover and the inclined end plate; calculating the equivalent spring stiffness of the high-strength bolt connection of the upper flange cover and the high-strength bolt connection of the inclined end plate, and considering the contribution of the stiffening ribs to the initial rotational stiffness of the hybrid connection node, according to the spring model of the node stiffness, preliminarily completing the calculation of the initial rotational stiffness at the hybrid connection node; calculating the rotational stiffness of the cantilever beam section, and calculating the initial rotational stiffness through the spring model of the node stiffness. A method for calculating the bearing capacity of an assembled steel frame beam-column node under bending and shearing is also provided. The present invention has the advantage of high calculation accuracy.

Description

Technical Field

[0001] The present invention relates to the field of structural engineering in civil engineering, and in particular to a method for calculating the initial rotational stiffness of assembled steel frame beam-column nodes and a method for calculating the bearing capacity under bending and shearing action. Background Art

[0002] In prefabricated steel structures, joints are the weakest points in steel structure connections, so the study of connection nodes has become an important part of steel structure research. Among them, steel frame joints with cantilever beam segments are widely used due to their many advantages, including factory-installed beam-column welding, guaranteed weld quality, on-site high-strength bolt connections, convenient and quick installation, reliable node force transmission, good seismic performance, good energy dissipation capacity, and the ability to meet the seismic design requirements of "strong nodes and weak components" and "strong columns and weak beams." However, domestic research on steel frame joints with cantilever beam segments started later than overseas research, with a relatively small proportion of research on the component method and a relatively limited scope of application. The lack of research on their initial rotational stiffness and bearing capacity has greatly restricted the application of steel frame joints with cantilever beam segments. Summary of the Invention

[0003] The present invention provides a method for calculating the initial rotational stiffness of an assembled steel frame beam-column node and a method for calculating the bearing capacity of an assembled steel frame beam-column node under bending and shearing. The method of the present invention can be used to obtain the initial rotational stiffness and bearing capacity of an assembled steel frame beam-column node, thus solving the research gap in the prior art on the initial rotational stiffness and bearing capacity of steel frame nodes.

[0004] The prefabricated steel frame beam-column joint described in this invention includes a steel beam and a column with a cantilevered beam section. Two inclined end plates are positioned between the steel beam and the cantilevered beam section. The top surfaces of the inclined end plates are flush with the upper flange of the steel beam. The bottom surfaces of the inclined end plates extend beyond the lower flange, where stiffening ribs are provided. The two inclined end plates are connected by high-strength bolts, and the upper flange cover is fixed to the cantilevered beam section and the top of the steel beam's upper flange using high-strength bolts. This joint achieves the goals of convenient and fast installation, reliable force transmission, and excellent seismic performance, and has strong engineering application value.

[0005] The present invention provides a method for calculating the initial rotational stiffness of a prefabricated steel frame beam-column node, comprising the steps of:

[0006] Step 1: Determine a schematic diagram of a prefabricated steel frame beam-column joint, analyze the components of the joint's initial rotational stiffness, and propose a spring model for the joint's stiffness;

[0007] Step 2: Calculate the equivalent spring stiffness K of the upper flange cover, inclined end plate, and upper flange plate p , K1 and K2, K p1 and K p2;

[0008] Step 3: Calculate the equivalent spring stiffness K of the high-strength bolts connecting the upper flange cover and the inclined end plate i,bolt ;

[0009] Step 4: Calculate the equivalent spring stiffness K of the upper flange cover high-strength bolt connection and the inclined end plate high-strength bolt connection g , K d , and considering the contribution of stiffeners to the initial rotational stiffness of the hybrid connection node, the initial rotational stiffness K of the hybrid connection node is preliminarily completed using the component method based on the spring model of the node stiffness. n Calculation of

[0010] Step 5: Calculate the rotational stiffness K of the cantilever beam segment c , the rotational stiffness K of the cantilever beam segment c , initial rotational stiffness K at the hybrid connection node n The initial rotational stiffness K of the assembled steel frame beam-column node is calculated using a spring model of the node stiffness.

[0011] Furthermore, the step 2 specifically includes:

[0012] The calculation method for the equivalent spring stiffness of the upper flange cover adopts the calculation model of plate stiffness. Through experimental testing and numerical simulation, it is found that the equivalent spring stiffness depends on three main stiffness mechanisms: load bearing, bending and shear of the plate. The model that explains these three stiffnesses is:

[0013]

[0014] Where K br,p is the compressive stiffness, K b,p is the bending stiffness, K v,p shear stiffness;

[0015]

[0016]

[0017]

[0018] Where, t p is the thickness of the plate, d b is the diameter of high-strength bolt, L e is the end distance of high-strength bolts, E is the elastic modulus of the material, G is the shear modulus of the material, f y is the design value of steel strength, usually 0.7f u , f u is the ultimate strength of steel;

[0019] Inclined end plates K1 and K2, upper flange plate K p1 and K p2 The calculation method of the equivalent spring stiffness is the same as that of the upper flange cover.

[0020] Furthermore, the step three specifically includes:

[0021] The equivalent spring stiffness of a high-strength bolt includes compressive stiffness and shear stiffness. The equivalent spring stiffness of a high-strength bolt is mainly affected by the compression and shear resistance inside the high-strength bolt rod. Therefore, assuming that two springs are connected in series, the calculation is:

[0022]

[0023] Where K br,bolt High-strength bolt compressive stiffness, K v,bolt High-strength bolt shear stiffness;

[0024] High-strength bolt compressive stiffness K br,bolt The calculation formula is:

[0025]

[0026] Where t1 is the thickness of the connected top plate, t2 is the thickness of the connected bottom plate, and β b It represents the proportional correction factor of the total bending moment on the high-strength bolt, usually taken as β b =0.7, E bolt is the elastic modulus of high-strength bolts;

[0027] The shear stiffness of the high-strength bolt is determined by assuming that the high-strength bolt is a Timoshenko beam with a circular cross-section and a fixed end. The shear stiffness of the high-strength bolt K v,bolt Calculation formula:

[0028]

[0029] Where, I bolt The moment of inertia of the high-strength bolt axis intersection surface, d b is the diameter of high-strength bolt, L bolt is the length of high-strength bolt, L bolt =t1+t2; t1 is the thickness of the connected top plate, t2 is the thickness of the connected bottom plate, E bolt is the elastic modulus of the high-strength bolt, Φ is the coefficient, which can be calculated as follows:

[0030]

[0031] Where G bolt is the shear modulus of the high-strength bolt, κ is the shear coefficient of a circular cross section, ν is Poisson's ratio, A bolt is the cross-sectional area of ​​high-strength bolts.

[0032] Furthermore, the step 4 specifically includes:

[0033] According to the composition of the initial rotational stiffness of the hybrid connection node, it can be obtained that the hybrid connection node spring is composed of a spring connected by high-strength bolts of the cover plate and a spring connected by high-strength bolts of the inclined end plate. Among them, the spring connected by high-strength bolts of the cover plate is composed of the upper flange plate spring of the cantilever beam segment, a high-strength bolt spring, a cover plate spring, a high-strength bolt spring and the upper flange plate spring of the steel beam segment. The spring connected by high-strength bolts of the inclined end plate is composed of the inclined end plate spring of the cantilever beam segment, a high-strength bolt spring and the inclined end plate spring of the steel beam segment. Using the component method and considering the influence of the stiffening ribs, the initial rotational stiffness K at the hybrid connection node is preliminarily completed. n Calculation.

[0034] The equivalent spring stiffness of the cover plate high-strength bolt connection and the inclined end plate high-strength bolt connection are K g , K d , according to the spring model of the node stiffness under the decomposition of the component, two calculation formulas for the connection stiffness can be obtained:

[0035]

[0036]

[0037] Where K p is the equivalent spring stiffness of the cover, K b1 is the equivalent spring stiffness of the cover plate high-strength bolt group, K p1 is the equivalent spring stiffness of the upper flange plate of the cantilever beam segment, K p2 is the equivalent spring stiffness of the upper flange plate of the steel beam segment; K b2 is the equivalent spring stiffness of the high-strength bolt group of the inclined end plate, K1 is the equivalent spring stiffness of the inclined end plate of the cantilever beam section, and K2 is the equivalent spring stiffness of the inclined end plate of the steel beam section;

[0038] According to step 2 and step 3, K can be obtained g and K d Under the node spring stiffness model, considering the initial rotation stiffness contributed by the stiffener, the initial rotation stiffness K at the hybrid connection node is n for:

[0039]

[0040] Where K n is the initial rotational stiffness at the hybrid connection node, K d is the equivalent spring stiffness of the high-strength bolt connection of the inclined end plate, K gis the equivalent spring stiffness of the cover plate high-strength bolt connection, mK d is the equivalent spring stiffness contributed by the stiffener and the inclined end plate (K is expressed by multiplying a certain magnification factor m, which can usually be taken as 1.58, and h is the height of the high-strength bolt tension area in the length direction of the inclined end plate. According to multiple verifications, the neutral wheelbase is 0.40~0.60H from the upper flange, that is, h = 0.40~0.60H, where H is the height of the cantilever beam section.

[0041] Furthermore, the step five specifically includes:

[0042] According to the knowledge of material mechanics, calculate the rotational stiffness K of the cantilever beam segment c :

[0043]

[0044] Where, E is the elastic modulus of the cantilever beam segment, I is the section moment of inertia of the cantilever beam segment, and L is the length of the cantilever segment;

[0045] Then, through the spring model of node stiffness, the initial rotation stiffness K of a prefabricated steel frame beam-column node is calculated as:

[0046]

[0047] A method for calculating the bearing capacity of a prefabricated steel frame beam-column node under bending and shearing action comprises the following steps:

[0048] Step 1: Determine the minimum thickness t of the inclined end plate based on the condition that the high-strength bolts of the inclined end plate of the node are not subject to prying force. f,min ;

[0049] Step 2: When the beam is subjected to shear force only, calculate the shear force N on the high-strength bolts of the inclined end plate vj ;

[0050] Step 3: When the beam is subjected only to bending moment, and the bending moment is negative, calculate the tensile force Nt′ on the control bolts on the inclined end plate. tn ;

[0051] Step 4: When the beam is only subjected to bending moment, and the bending moment is positive, calculate the tensile force N on the control bolts on the inclined end plate. tn ;

[0052] Step 5: When the beam is subjected to bending moment and shear force, and the bending moment is negative, calculate the tensile force N' on the control bolts on the inclined end plate. tn1 and shear force N′ vj1 ;

[0053] Step 6: When the beam is subjected to bending moment and shear force, and the bending moment is positive, calculate the tensile force N on the control bolts on the inclined end plate.tn2 and shear force N vj2 ;

[0054] Step 7: Verify whether the bearing capacity of the high-strength bolts at the node meets the safety requirements based on the shear bearing capacity and bending bearing capacity of the high-strength bolts.

[0055] Furthermore, the step 1 specifically includes:

[0056] The minimum thickness of the inclined end plate to prevent the high-strength bolts of the inclined end plate of the node from being pried is:

[0057]

[0058] Where A s is the tensile stress area of ​​the high-strength bolt, R s is the radius of the high-strength bolt in the tensile stress zone, a is the length of the inclined end plate, b is the width of the inclined end plate, L b is the elongation length of the high-strength bolt, which is the grip length (total thickness of the material and the washer) plus half of the sum of the height of the high-strength bolt head and the height of the nut. s is the horizontal distance from the centroid of the high-strength bolt to the fillet weld.

[0059] Furthermore, the step 2 specifically includes:

[0060] For this prefabricated steel frame beam-column node, the height of the cantilever beam section is H, and the high-strength bolts of the inclined end plate are all friction-type high-strength bolts. When the beam is only subjected to shear force, the shear force is independently borne by the high-strength bolts of the inclined end plate. Since the end plate of this node is placed at an angle, the vertical shear force along the length direction of the inclined end plate is the shear force on the high-strength bolt group, and the vertical shear force along the thickness direction of the inclined end plate is the pressure on the high-strength bolt group. Under the action of shear force V, a high-strength bolt of the inclined end plate is subjected to a vertical downward force of V. j The shear force N vj for:

[0061] N v =V sinα

[0062]

[0063] Where N v is the vertical component of the shear force V acting on the beam, α is the angle between the inclined end plate and the neutral axis of the beam, α = 30°~60°, and j is the number of high-strength bolts in the inclined end plate.

[0064] Furthermore, the step three specifically includes:

[0065] When the beam is only subjected to negative bending moment, the high-strength bolts on the inclined end plate are subjected to linear distribution of tension and compression. According to multiple calculations, the neutral axis (the position where the positive stress is 0) is 0.40 to 0.60H away from the upper flange, where H is the height of the cantilever beam section.

[0066] According to empirical calculations, the cover plate is less affected by the bending moment, and it can be approximately regarded as the high-strength bolts of the inclined end plate bearing all the bending moments. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0067] The distance from the neutral axis of the beam (i.e., the point where the normal stress is 0) to the upper flange of the beam is 0.40 to 0.60H. The high-strength bolts on the inclined end plate only bear tension, not pressure, and the pressure is borne by the inclined end plate itself. The distance y from each row of high-strength bolts to the neutral axis is calculated by the difference between the distance from each row of high-strength bolts in the tension zone of the inclined end plate to the upper flange of the beam and the distance from the neutral axis to the upper flange of the beam. i , it can be deduced that the load on each row of tensile high-strength bolts in the inclined end plate is:

[0068]

[0069] Where n is the number of high-strength bolts in the tension zone of the inclined end plate, N′ ti is the tensile force on the high-strength bolts of the inclined end plate in the i-th row from the neutral axis in the tensile zone of the inclined end plate, y i is the distance between the i-th row of high-strength bolts in the tension zone of the inclined end plate and the neutral axis of the inclined end plate, and M1 is the negative bending moment on the beam;

[0070] At this time, the high-strength bolt on the inclined end plate that is subject to the maximum tensile force is the high-strength bolt on the outer layer of the end plate closest to the upper flange. This high-strength bolt is subject to a tensile force N' tn for:

[0071]

[0072] Furthermore, the step 4 specifically includes:

[0073] When the beam is subjected only to positive bending moment, the high-strength bolts on the inclined end plate are subjected to linear distribution of tension and compression, and the neutral axis (the position where the positive stress is 0) is 0.40~0.60H away from the upper flange, where H is the height of the cantilever beam section.

[0074] According to empirical calculations, the cover plate is less affected by the bending moment, and it can be approximately regarded as the high-strength bolts of the inclined end plate bearing all the bending moments. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0075] The distance from the neutral axis of the beam (i.e., the point where the normal stress is 0) to the upper flange of the beam is 0.40 to 0.60H. The high-strength bolts on the inclined end plate only bear tension, not pressure, and the pressure is borne by the inclined end plate itself. The distance y from each row of high-strength bolts to the neutral axis is calculated from the difference between the distance from each row of high-strength bolts in the tension zone of the inclined end plate to the upper flange of the beam and the distance from the neutral axis to the upper flange of the beam. i, At the same time, the force on each row of tensile high-strength bolts in the inclined end plate can be deduced as:

[0076]

[0077] Where n is the number of high-strength bolts in the tension zone of the inclined end plate, N ti is the tensile force on the high-strength bolts of the inclined end plate in the i-th row from the neutral axis in the tensile zone of the inclined end plate, y i is the distance between the i-th row of high-strength bolts in the inclined end plate tension zone and the neutral axis of the end plate, and M is the positive bending moment on the beam;

[0078] At this time, the high-strength bolt on the inclined end plate that is subject to the maximum tensile force is the high-strength bolt on the outer layer of the inclined end plate closest to the lower flange. This high-strength bolt is subject to a tensile force N tn for:

[0079]

[0080] Furthermore, the step five specifically includes:

[0081] For the assembled steel frame beam-column node, the height of the cantilever beam section is H, and the bolts of the upper flange cover plate of the beam are all friction-type high-strength bolts. When the beam-column node is subjected to bending moment and shear force at the same time, it can be regarded as the superposition of steps 2 and 3. The inclined end plate high-strength bolts bear the shear force of the beam alone. Under the action of shear force V, one inclined end plate high-strength bolt is subjected to a vertical downward force of V. j The shear force is N vj The high-strength bolts of the cover plate and the high-strength bolts of the inclined end plate jointly bear the bending moment of the beam. According to empirical calculations, the cover plate is less affected by the bending moment, and it can be approximately regarded as the high-strength bolts of the inclined end plate bearing all the bending moments. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0082] There are two situations in which the beam is subjected to positive bending moment and negative bending moment. When the beam is subjected to negative bending moment and vertical downward shear force:

[0083] The control bolt is the high-strength bolt of the inclined end plate closest to the upper flange of the beam, and the control bolt is subjected to a tensile force N' tn1 and shear force N′ vj1 for:

[0084]

[0085] N′vj1 =N vj

[0086] Where M1 is the negative bending moment applied to the beam when the beam is subjected to the combined action of bending moment and shear force.

[0087] Furthermore, the step six specifically includes:

[0088] For the assembled steel frame beam-column node, the height of the cantilever beam section is H, and the bolts of the upper flange cover plate of the beam are all friction-type high-strength bolts. When the beam-column node is subjected to bending moment and shear force at the same time, it can be regarded as the superposition of steps 2 and 4. The inclined end plate high-strength bolts bear the shear force of the beam alone. Under the action of shear force V, one inclined end plate high-strength bolt is subjected to a vertical downward force of V. j The shear force is N vj The high-strength bolts on the cover plate and the high-strength bolts on the inclined end plate jointly bear the bending moment applied to the beam. According to empirical calculations, the cover plate is less affected by the bending moment and can be approximately regarded as the high-strength bolts on the inclined end plate bearing all the bending moments. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0089] There are two situations in which the beam is subjected to positive bending moment and negative bending moment. When the beam is subjected to positive bending moment and vertical downward shear force:

[0090] The control bolt is the high-strength bolt of the inclined end plate closest to the lower flange of the beam, and the control bolt is subjected to a tensile force N tn2 and shear force N vj2 for:

[0091]

[0092] N vj2 =N vj

[0093] Where M2 is the positive bending moment applied to the beam when the beam is subjected to the combined action of bending moment and shear force.

[0094] Furthermore, the step seven specifically includes:

[0095] Shear bearing capacity of high-strength bolts and tensile bearing capacity Calculated according to the specification:

[0096]

[0097]

[0098] When a high-strength bolt friction connection is subjected to both the shear force between the friction surfaces and the external tension in the bolt rod axis direction, the bearing capacity shall meet the following requirements:

[0099]

[0100] Where N T The tensile force in the direction of the bolt rod axis borne by the high-strength bolt, N V The friction type connection of high-strength bolts bears the shear force between the friction surfaces. k is the hole coefficient, which is 1.0 for standard round holes and 0.85 for large round holes. The internal force perpendicular to the long hole is 0.7, and the internal force parallel to the long slot is 0.6. f is the number of friction surfaces transmitting force, μ is the anti-slip coefficient of the friction surface, and P is the pre-tension of a high-strength bolt;

[0101] The arrangement of high-strength bolts on the end plate is designed based on the above relationship between the tension and shear forces on the high-strength bolts and the shear bearing capacity and tensile bearing capacity.

[0102] Compared with the prior art, the present invention can at least achieve the following beneficial effects:

[0103] (1) The present invention is applied to an assembled steel frame beam-column node, which includes an end plate, high-strength bolts, a cover plate and stiffening ribs. The cover plate and the end plate are connected with high-strength bolts, which avoids on-site welding and is easy to install. The use of inclined end plates makes the overall assembly simple and reduces the use of auxiliary supports. The upper flange is added with a cover plate to improve the node stiffness and bearing capacity. The lower flange end plate is extended and provided with stiffening ribs, which can improve the initial rotational stiffness of the node, fully resist bending moment, and optimize the force performance of the node.

[0104] (2) The present invention proposes a method for calculating the initial rotational stiffness of the beam-column joint of an assembled steel frame, which uses the basic theories of steel structure and component method and has the advantages of clear concepts and high calculation accuracy.

[0105] (3) The method for calculating the bearing capacity of the beam-column node of an assembled steel frame under bending and shearing action of the present invention has the advantages of clear concepts and high calculation accuracy, and can reasonably design the arrangement of high-strength bolts on the end plate to meet the bearing capacity requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0106] Figure 1 This is a schematic diagram of the location of a node domain in a prefabricated steel frame beam-column node in an embodiment of the present invention.

[0107] Figure 2 Schematic diagram of components constituting the initial rotational stiffness of a prefabricated steel frame beam-column node in an embodiment of the present invention.

[0108] Figure 3 Schematic diagram of a node spring model of the initial rotational stiffness of a hybrid connection node in an embodiment of the present invention.

[0109] Figure 4 This is a schematic diagram of the spring model composition of the node stiffness of the initial rotational stiffness of an assembled steel frame beam-column node in an embodiment of the present invention.

[0110] Figure 5 This is a schematic diagram of an assembled steel frame beam-column node in an embodiment of the present invention when the beam is only subjected to shear force.

[0111] Figure 6 This is a schematic diagram of the actual stress conditions of the inclined end plate high-strength bolt group when the beam in the assembled steel frame beam-column node is subjected to shear force in an embodiment of the present invention.

[0112] Figure 7 This is a schematic diagram of an assembled steel frame beam-column node in an embodiment of the present invention when the beam is only subjected to negative bending moment.

[0113] Figure 8 This is a schematic diagram of the actual force on the high-strength bolts of the inclined end plate when the beam in the assembled steel frame beam-column node is subjected to negative bending moment in an embodiment of the present invention.

[0114] Figure 9 This is a schematic diagram of the actual force on the high-strength bolts of the inclined end plate when the beam in the assembled steel frame beam-column node is subjected to positive bending moment in an embodiment of the present invention.

[0115] Figure 10 This is a flow chart of a method for calculating the initial rotational stiffness of a prefabricated steel frame beam-column node in an embodiment of the present invention.

[0116] Figure 11 This is a flow chart of a method for calculating the bearing capacity of a prefabricated steel frame beam-column node under bending and shearing action in an embodiment of the present invention. DETAILED DESCRIPTION

[0117] To clarify the calculation method of the invention patent, the following provides a clear and complete description of the calculation method in the invention patent through examples. Obviously, the described embodiments are only a portion of the embodiments in the invention patent, not all of them. Based on the embodiments in the invention patent, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the invention patent.

[0118] The following embodiments of the present invention provide a method for calculating the initial rotational stiffness of a prefabricated steel frame beam-column node and a method for calculating the bearing capacity under bending and shearing action.

[0119] Example 1

[0120] The prefabricated steel frame beam-column node comprises a steel column, a cantilever beam section, a steel beam, a lower flange stiffening rib, a steel beam end plate, a cantilever beam section end plate, and an upper flange cover plate. One end of the cantilever beam section is fixedly connected to the steel column, the cantilever beam section end plate is disposed at the end of the cantilever beam section, and the steel beam end plate is disposed at the end of the steel beam. The cantilever beam section end plate and the steel beam end plate are connected by high-strength bolts. Lower flange stiffening ribs are disposed between the lower flange of the cantilever beam section and the cantilever beam section end plate, and between the lower flange of the steel beam and the steel beam end plate. The upper flange cover plate is fixed to the top of the cantilever beam section and the upper flange of the steel beam by high-strength bolts. The inclined end plate is connected to the cover plate by high-strength bolts, and the inclined placement of the end plate facilitates assembly of the steel beam.

[0121] Example 2

[0122] This embodiment provides a method for calculating the initial rotational stiffness of a prefabricated steel frame beam-column node, comprising the following steps:

[0123] Step 1: Determine a schematic diagram of a prefabricated steel frame beam-column joint, analyze the components of the joint's initial rotational stiffness, and propose a spring model for the joint's stiffness;

[0124] In an embodiment of the present invention, the node domain obtained by determining Figure 1 As shown, the components of the node initial rotation stiffness are as follows Figure 2 shown.

[0125] Step 2: Calculate the equivalent spring stiffness K of the upper flange cover, inclined end plate, and upper flange plate p , K1 and K2, K p1 and K p2 ;

[0126] In an embodiment of the present invention, the step 2 specifically includes:

[0127] The calculation method for the equivalent spring stiffness of the upper flange cover adopts the calculation model of plate stiffness. Through experimental testing and numerical simulation, it is found that the equivalent spring stiffness depends on three main stiffness mechanisms: load bearing, bending and shear of the plate. The model that explains these three stiffnesses is:

[0128]

[0129] Where K br,p is the compressive stiffness, K b,p is the bending stiffness, K v,p shear stiffness;

[0130]

[0131]

[0132]

[0133] Where, t p is the thickness of the plate, d b is the diameter of high-strength bolt, L e is the end distance of high-strength bolts, E is the elastic modulus of the material, G is the shear modulus of the material, f y is the design value of steel strength, usually 0.7f u , f u is the ultimate strength of steel;

[0134] Inclined end plates K1 and K2, upper flange plate K p1 and K p2 The calculation method of the equivalent spring stiffness is the same as that of the upper flange cover.

[0135] In this embodiment, relevant parameters and calculation results are given in Table 1:

[0136] Table 1:

[0137] Upper flange cover Inclined end plates Upper flange plate <![CDATA[f u (MPa)]]> 370 370 370 <![CDATA[f y (MPa)]]> 259 259 259 E(MPa) 210000 210000 210000 G(MPa) 80769 80769 80769 <![CDATA[t p (mm)]]> 14 30 13 <![CDATA[d b (mm)]]> 24 30 24 <![CDATA[L e (mm)]]> 48 60 48 <![CDATA[K br,p (KN·m -1 )]]> 0.416 1.065 0.386 <![CDATA[K b,p (KN·m -1 )]]> 317.520 680.400 294.840 <![CDATA[K v,p (KN·m -1 )]]> 11.313 24.243 10.505 <![CDATA[K p (KN·m -1 )]]> 0.401 1.019 0.372

[0138] Step 3: Calculate the equivalent spring stiffness K of the high-strength bolts connecting the upper flange cover and the inclined end plate i,bolt .

[0139] The equivalent spring stiffness of a high-strength bolt includes compressive stiffness and shear stiffness. The equivalent spring stiffness of a high-strength bolt is mainly affected by the compression and shear resistance inside the high-strength bolt rod. Therefore, assuming that two springs are connected in series, the calculation is:

[0140]

[0141] Where K br,bolt High-strength bolt compressive stiffness, K v,bolt High-strength bolt shear stiffness;

[0142] High-strength bolt compressive stiffness K br,bolt The calculation formula is:

[0143]

[0144] Where t1 is the thickness of the connected top plate, t2 is the thickness of the connected bottom plate, and β b Expresses the proportional correction factor of the total bending moment on the high-strength bolt, E bolt is the elastic modulus of high-strength bolts;

[0145] The shear stiffness of the high-strength bolt is determined by assuming that the high-strength bolt is a Timoshenko beam with a circular cross-section and a fixed end. The shear stiffness of the high-strength bolt K v,bolt Calculation formula:

[0146]

[0147] Where, I bolt is the moment of inertia of the high-strength bolt axis intersection surface, d b is the diameter of high-strength bolt, L bolt is the length of high-strength bolt, L bolt =t1+t2; t1 is the thickness of the connected top plate, t2 is the thickness of the connected bottom plate, E bolt is the elastic modulus of the high-strength bolt, Φ is the coefficient, which can be calculated as follows:

[0148]

[0149] Where G bolt is the shear modulus of the high-strength bolt, κ is the shear coefficient of a circular cross section, ν is Poisson's ratio, A bolt is the cross-sectional area of ​​high-strength bolts.

[0150] In this embodiment, relevant parameters and calculation results are given in Tables 2 and 3:

[0151] Table 2:

[0152]

[0153] Table 3:

[0154]

[0155] Step 4: Based on the composition of the initial rotational stiffness of the hybrid connection node, such as Figure 3 As shown, it can be obtained that the hybrid connection node spring is composed of a spring connected by high-strength bolts of the cover plate and a spring connected by high-strength bolts of the inclined end plate. Among them, the spring connected by high-strength bolts of the cover plate includes the upper flange plate spring of the cantilever beam segment, a high-strength bolt spring, a cover plate spring, a high-strength bolt spring and the upper flange plate spring of the steel beam segment. The spring connected by high-strength bolts of the inclined end plate is composed of the inclined end plate spring of the cantilever beam segment, a high-strength bolt spring and the inclined end plate spring of the steel beam segment. Using the component method and considering the influence of the stiffening ribs, the initial rotation stiffness K at the hybrid connection node is preliminarily completed. n Calculation.

[0156] The equivalent spring stiffness of the cover plate high-strength bolt connection and the end plate high-strength bolt connection are K g , K d , according to the spring model of the node stiffness under the decomposition of the component, two calculation formulas for the connection stiffness can be obtained:

[0157]

[0158]

[0159] Where K p is the equivalent spring stiffness of the cover, K b1 is the equivalent spring stiffness of the cover plate high-strength bolt group, K p1 is the equivalent spring stiffness of the upper flange plate of the cantilever beam segment, K p2 is the equivalent spring stiffness of the upper flange plate of the steel beam segment; K b2 is the equivalent spring stiffness of the high-strength bolt group of the inclined end plate, K1 is the equivalent spring stiffness of the inclined end plate of the cantilever beam section, and K2 is the equivalent spring stiffness of the inclined end plate of the steel beam section;

[0160] According to step 2 and step 3, K can be obtained g and K d Under the node spring stiffness model, considering the initial rotation stiffness contributed by the stiffener, the initial rotation stiffness K at the hybrid connection node is n for:

[0161]

[0162] Where K n is the initial rotational stiffness at the hybrid connection node, K d is the equivalent spring stiffness of the high-strength bolt connection of the inclined end plate, K g is the equivalent spring stiffness of the upper flange cover high-strength bolt connection, mK d is the stiffness contributed by the stiffener and the inclined end plate (K d It is expressed by multiplying by a certain magnification factor m, which can usually be taken as 1.58), h is the height of the tension area of ​​the high-strength bolts in the length direction of the inclined end plate, and according to multiple verifications, the neutral wheelbase is 0.40~0.60H from the upper flange, that is, h=0.40~0.60H, where H is the height of the cantilever beam section. In this embodiment, the neutral wheelbase is 0.58H from the upper flange.

[0163] In this embodiment, relevant parameters and calculation results are given in Table 4:

[0164] Table 4:

[0165] <![CDATA[K p (KN·m -1 )]]> 0.401 <![CDATA[K b1 (KN·m -1 )]]> 1.396 <![CDATA[K p1 (KN·m -1 )]]> 0.372 <![CDATA[K p2 (KN·m -1 )]]> 0.372 <![CDATA[K b2 (KN·m -1 )]]> 1.865 <![CDATA[K1(KN·m -1 )]]> 1.019 <![CDATA[K2(KN·m -1 )]]> 1.019 H(mm) 400 h(mm) 232 m 1.58 <![CDATA[K g (KN·m -1 )]]> 0.116 <![CDATA[K d (KN·m -1 )]]> 0.400 <![CDATA[K n (KN·m·rad -1 )]]> 5291.867

[0166] Step 5: Calculate the rotational stiffness K of the cantilever beam segment c , the rotational stiffness K of the cantilever beam segment c , initial rotational stiffness K at the hybrid connection node n The initial rotational stiffness K of a prefabricated steel frame beam-column joint is calculated using a spring model of joint stiffness.

[0167] According to the knowledge of material mechanics, calculate the rotational stiffness K of the cantilever beam segment c:

[0168]

[0169] Where, E is the elastic modulus of the cantilever beam segment, I is the section moment of inertia of the cantilever beam segment, and L is the length of the cantilever segment;

[0170] Then, through the model of node spring stiffness, such as Figure 4 As shown in the figure, the initial rotation stiffness K of a prefabricated steel frame beam-column joint is calculated as:

[0171]

[0172] In this embodiment, relevant parameters and calculation results are given in Table 5:

[0173] Table 5:

[0174] E(MPa) 210000 H(mm) 400 Cross-sectional dimensions H400×200×8×13 <![CDATA[I(mm 4 )]]> 2.296×10 L(mm) 400 <![CDATA[K c (KN·m·rad -1 )]]> 361620 <![CDATA[K(KN·m·rad -1 )]]> 5215.544

[0175] Example 3

[0176] This embodiment provides a method for calculating the bearing capacity of a prefabricated steel frame beam-column node under bending and shearing, comprising the following steps:

[0177] Step 1: Determine the minimum thickness t of the inclined end plate based on the condition that the high-strength bolts of the inclined end plate of the node are not subject to prying force. f,min .

[0178] The minimum thickness of the inclined end plate to prevent the high-strength bolts of the inclined end plate of the node from being pried is:

[0179]

[0180] Where A s is the tensile stress area of ​​the high-strength bolt, R s is the radius of the high-strength bolt in the tensile stress zone, a is the length of the inclined end plate, b is the width of the inclined end plate, L b is the elongation length of the high-strength bolt, which is the grip length (total thickness of the material and the washer) plus half of the sum of the height of the high-strength bolt head and the height of the nut. s is the horizontal distance from the centroid of the high-strength bolt to the fillet weld.

[0181] In this embodiment, relevant parameters and calculation results are given in Table 6:

[0182] Table 6:

[0183] a(mm) b(mm) <![CDATA[L b (mm)]]> s(mm) <![CDATA[R s (mm)]]> <![CDATA[A s (mm 2 )]]> <![CDATA[t f,min (mm)]]> 780 180 80 41.5 20 314 14.157

[0184] Step 2: When the beam is subjected to shear force only, calculate the shear force N on the high-strength bolts of the inclined end plate vj ;

[0185] For this assembled steel frame beam-column joint, the height of the cantilever beam section is H, and the inclined end plate bolts are all friction-type high-strength bolts. When the beam is only subjected to shear force, the shear force is independently borne by the inclined end plate high-strength bolts. Figure 5 、 Figure 6 As shown, since the node end plate is placed at an angle, the vertical shear force along the length direction of the inclined end plate is the shear force on the high-strength bolt group, and the vertical shear force along the thickness direction of the inclined end plate is the pressure on the high-strength bolt group. Under the action of the shear force V, the vertical downward force on a high-strength bolt of the inclined end plate is V j The shear force N vj for:

[0186] N v =V sinα

[0187]

[0188] Where N v is the vertical component of the shear force V acting on the beam, α is the angle between the inclined end plate and the neutral axis of the beam, α = 30° to 60°, in this embodiment α = 45°, and j is the number of high-strength bolts on the inclined end plate.

[0189] Step 3: When the beam is subjected only to bending moment, and the bending moment is negative, calculate the tensile force N' on the control bolts on the inclined end plate. tn ;

[0190] In this embodiment, when the beam is subjected only to negative bending moment, the high-strength bolts on the inclined end plates are subjected to a linear distribution of tension and compression. Based on multiple calculations, the neutral axis (the location where the normal stress is zero) is 0.40 to 0.60 H from the upper flange, where H is the height of the cantilever beam section. In this embodiment, the neutral axis is 0.58 H from the upper flange. Empirically, the cover plate is less affected by bending moment, so the high-strength bolts on the inclined end plates can be considered to bear all bending moment. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0191] The distance from the neutral axis of the beam (i.e. the point where the normal stress is 0) to the upper flange of the beam is 0.40 to 0.60H. The high-strength bolts on the inclined end plate only bear tension, not pressure, and the pressure is borne by the inclined end plate itself. Figure 7 、 Figure 8 As shown in the figure, the distance y from each row of high-strength bolts to the neutral axis is obtained by the difference between the distance from each row of high-strength bolts in the tension zone of the inclined end plate to the upper flange of the beam and the distance from the neutral axis to the upper flange of the beam. i , it can be deduced that the load on each row of tensile high-strength bolts in the inclined end plate is:

[0192]

[0193] Where n is the number of high-strength bolts in the tension zone of the inclined end plate, N′ ti is the tensile force on the high-strength bolts of the inclined end plate in the i-th row from the neutral axis in the tensile zone of the inclined end plate, y i is the distance between the i-th row of high-strength bolts in the inclined end plate tension zone and the neutral axis of the end plate, and M is the negative bending moment on the beam;

[0194] At this time, the high-strength bolt on the inclined end plate that is subject to the maximum tensile force is the high-strength bolt on the outer layer of the inclined end plate closest to the upper flange. This high-strength bolt is subject to a tensile force N' tn for:

[0195]

[0196] Step 4: When the beam is only subjected to bending moment, and the bending moment is positive, calculate the tensile force N on the control bolts on the inclined end plate. tn ;

[0197] In this embodiment, when the beam is subjected only to positive bending moments, the high-strength bolts on the inclined end plates are subjected to a linear distribution of tension and compression, with the neutral axis (the location where the normal stress is zero) located 0.40 to 0.60 H from the upper flange, where H is the height of the cantilever beam section. In this embodiment, the neutral axis is 0.58 H from the upper flange. Empirically, the cover plate is less affected by bending moments, so the high-strength bolts on the inclined end plates can be considered to bear all bending moments. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0198] The distance from the neutral axis of the beam (i.e. the point where the normal stress is 0) to the upper flange of the beam is 0.40 to 0.60H. The high-strength bolts on the inclined end plate only bear tension and not pressure, while the pressure is borne by the inclined end plate itself. Figure 9 As shown in the figure, the distance y from each row of high-strength bolts to the neutral axis is obtained by the difference between the distance from each row of high-strength bolts in the tension zone of the inclined end plate to the upper flange of the beam and the distance from the neutral axis to the upper flange of the beam. i , it can be deduced that the forces acting on the tensile high-strength bolts in each row of the inclined end plate are:

[0199]

[0200] Where n is the number of high-strength bolts in the tension zone of the end plate, N ti is the tensile force on the high-strength bolts of the inclined end plate in the i-th row from the neutral axis in the tensile zone of the inclined end plate, y i is the distance between the i-th row of high-strength bolts in the tension zone of the inclined end plate and the neutral axis of the inclined end plate, and M is the positive bending moment on the beam;

[0201] At this time, the high-strength bolt on the inclined end plate that is subject to the maximum tensile force is the high-strength bolt on the outer layer of the inclined end plate closest to the lower flange. This high-strength bolt is subject to a tensile force N tn for:

[0202]

[0203] Step 5: When the beam is subjected to bending moment and shear force, and the bending moment is negative, calculate the tensile force N' on the control bolts on the inclined end plate. tn1 and shear force N′ vj1 .

[0204] For the assembled steel frame beam-column node, the cantilever beam section height is H, and the flange cover bolts on the beam are all friction-type high-strength bolts. When the beam-column node is subjected to bending moment and shear force at the same time, it can be regarded as the superposition of steps 2 and 3. The inclined end plate bolts bear the shear force of the beam alone. Under the action of shear force V, one inclined end plate high-strength bolt is subjected to a vertical downward force of V and a shear force of N. vj The high-strength bolts of the cover plate and the high-strength bolts of the inclined end plate jointly bear the bending moment of the beam. According to empirical calculations, the cover plate is less affected by the bending moment, and it can be approximately regarded as the high-strength bolts of the inclined end plate bearing all the bending moments. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0205] There are two situations in which the beam is subjected to positive bending moment and negative bending moment. When the beam is subjected to negative bending moment and vertical downward shear force:

[0206] The control bolt is the high-strength bolt of the inclined end plate closest to the upper flange of the beam, and the control bolt is subjected to a tensile force N' tn1 and shear force N′ vj1 for:

[0207]

[0208] N′ vj1 =N vj

[0209] Where M1 is the negative bending moment applied to the beam when the beam is subjected to the combined action of bending moment and shear force.

[0210] Step 6: When the beam is subjected to bending moment and shear force, and the bending moment is positive, calculate the tensile force N on the control bolts on the inclined end plate. tn2 and shear force N vj2 ;

[0211] For the assembled steel frame beam-column node, the height of the cantilever beam section is H, and the bolts of the upper flange cover plate of the beam are all friction-type high-strength bolts. When the beam-column node is subjected to bending moment and shear force at the same time, it can be regarded as the superposition of steps 2 and 4. The inclined end plate high-strength bolts bear the shear force of the beam alone. Under the action of shear force V, one inclined end plate high-strength bolt is subjected to a vertical downward force of V. j The shear force is N vjThe high-strength bolts of the cover plate and the high-strength bolts of the inclined end plate jointly bear the bending moment of the beam. According to empirical calculations, the cover plate is less affected by the bending moment, and it can be approximately regarded as the high-strength bolts of the inclined end plate bearing all the bending moments. The high-strength bolts on the cover plate are arranged in two rows and four columns.

[0212] There are two situations in which the beam is subjected to positive bending moment and negative bending moment. When the beam is subjected to positive bending moment and vertical downward shear force:

[0213] The control bolt is the high-strength bolt of the inclined end plate closest to the lower flange of the beam, and the control bolt is subjected to a tensile force N tn2 and shear force N vj2 for:

[0214]

[0215] N vj2 =N vj

[0216] Where M2 is the positive bending moment applied to the beam when the beam is subjected to the combined action of bending moment and shear force.

[0217] Step 7: Verify whether the high-strength bolt bearing capacity of the node meets the safety requirements based on the shear bearing capacity and bending bearing capacity of the high-strength bolts;

[0218] Shear bearing capacity of high-strength bolts and tensile bearing capacity Calculated according to the specification:

[0219]

[0220]

[0221] When a high-strength bolt friction connection is subjected to both the shear force between the friction surfaces and the external tension in the bolt rod axis direction, the bearing capacity shall meet the following requirements:

[0222]

[0223] Where N T The tensile force in the direction of the bolt rod axis borne by the high-strength bolt, N V The friction type connection of high-strength bolts bears the shear force between the friction surfaces. k is the hole coefficient, which is 1.0 for standard round holes and 0.85 for large round holes. The internal force perpendicular to the long hole is 0.7, and the internal force parallel to the long slot is 0.6. f is the number of force transmission friction surfaces, μ is the anti-slip coefficient of the friction surface, and P is the pre-tension of a high-strength bolt.

[0224] The arrangement of high-strength bolts on the end plate is designed based on the above relationship between the tension and shear forces on the high-strength bolts and the shear bearing capacity and tensile bearing capacity.

[0225] In this embodiment, the relevant parameters and calculation results of steps 2 to 7 are given in Tables 7, 8, and 9:

[0226] Table 7:

[0227] <![CDATA[M1(KN·m)]]> <![CDATA[y1(mm)]]> <![CDATA[y2(mm)]]> <![CDATA[N′ tn1 (KN)]]> 25 118 198 93.171

[0228] Table 8:

[0229] V(KN) α(°) j <![CDATA[N v (KN)]]> <![CDATA[N′ vj1 (KN)]]> 60 45 10 42.426 4.243

[0230] Table 9:

[0231]

[0232] The bearing capacity meets the following requirements:

[0233]

[0234] 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. A method for calculating the initial rotational stiffness of a prefabricated steel frame beam-column joint, characterized in that: The node includes a steel beam and a column with a cantilever beam section, two inclined end plates are provided between the steel beam and the cantilever beam section, the top surface of the inclined end plates is flush with the upper flange of the steel beam, and the bottom surface of the inclined end plates extends outward from the lower flange and stiffening ribs are provided at the extension, and the two inclined end plates are connected by high-strength bolts, and the upper flange cover plate is fixed to the cantilever beam section and the top of the upper flange of the steel beam by high-strength bolts; The method comprises the following steps: Step 1: Determine a schematic diagram of a prefabricated steel frame beam-column joint, analyze the components of the joint's initial rotational stiffness, and propose a spring model for the joint's stiffness; Step 2: Calculate the equivalent spring stiffness K of the upper flange cover, inclined end plate, and upper flange plate p , K1 and K2, K p1 and K p2 ; Step 3: Calculate the equivalent spring stiffness K of the high-strength bolts connecting the upper flange cover and the inclined end plate i,bolt ; Step 4: Calculate the equivalent spring stiffness K of the upper flange cover high-strength bolt connection and the inclined end plate high-strength bolt connection g , K d , and considering the contribution of stiffeners to the initial rotational stiffness of the hybrid connection node, the initial rotational stiffness K of the hybrid connection node is preliminarily completed using the component method based on the spring model of the node stiffness. n Calculation of Step 5: Calculate the rotational stiffness K of the cantilever beam segment c , the rotational stiffness K of the cantilever beam segment c , initial rotational stiffness K at the hybrid connection node n The initial rotational stiffness K of the assembled steel frame beam-column node is calculated using a spring model of the node stiffness.

2. A method for calculating the initial rotational stiffness of a prefabricated steel frame beam-column node according to claim 1, characterized in that: In step 2, the equivalent spring stiffness K of the upper flange cover is p for: Where K br,p is the compressive stiffness, K b,p is the bending stiffness, K v,p shear stiffness; Inclined end plates K1 and K2, upper flange plate K p1 and K p2 The calculation method of the equivalent spring stiffness is the same as that of the upper flange cover.

3. The method for calculating the initial rotational stiffness of the beam-column joint of an assembled steel frame according to claim 1 is characterized in that: Step three includes: The equivalent spring stiffness of a high-strength bolt includes compressive stiffness and shear stiffness. Therefore, assuming two springs are connected in series, the calculation is: Where K br,bolt High-strength bolt compressive stiffness, K v,bolt High-strength bolt shear stiffness; High-strength bolt compressive stiffness K br,bolt The calculation formula is: Where t1 is the thickness of the connected top plate, t2 is the thickness of the connected bottom plate, and β b Expresses the proportional correction factor of the total bending moment on the high-strength bolt, E bolt is the elastic modulus of high-strength bolts; High-strength bolt shear stiffness K v,bolt The calculation formula is: Where, I bolt is the moment of inertia of the high-strength bolt axis intersection surface, d b is the diameter of high-strength bolt, L bolt is the length of high-strength bolt, L bolt =t1+t2, t1 is the thickness of the connected top plate, t2 is the thickness of the connected bottom plate, E bolt is the elastic modulus of the high-strength bolt, Φ is the coefficient; The calculation formula of coefficient Φ is: Where G bolt is the shear modulus of the high-strength bolt, κ is the shear coefficient of a circular cross section, ν is Poisson's ratio, A bolt is the cross-sectional area of ​​high-strength bolts.

4. A method for calculating the initial rotational stiffness of a prefabricated steel frame beam-column joint according to any one of claims 1 to 3, characterized in that: In step 4, according to the composition of the initial rotational stiffness of the hybrid connection node, it can be seen that the hybrid connection node spring is composed of a spring connected by high-strength bolts of the cover plate and a spring connected by high-strength bolts of the inclined end plate. Among them, the spring connected by high-strength bolts of the cover plate includes the upper flange plate spring of the cantilever beam segment, a high-strength bolt spring, a cover plate spring, a high-strength bolt spring and the upper flange plate spring of the steel beam segment. The spring connected by high-strength bolts of the inclined end plate includes the inclined end plate spring of the cantilever beam segment, a high-strength bolt spring and the inclined end plate spring of the steel beam segment. Using the component method and considering the influence of the stiffening ribs, the initial rotational stiffness K at the hybrid connection node is preliminarily completed. n Calculation; combined with the rotational stiffness K of the cantilever beam segment c ,According to the spring model of node stiffness, the initial rotation stiffness K of the assembled steel frame beam-column node can be obtained using the component rule; The equivalent spring stiffness of the cover plate high-strength bolt connection and the inclined end plate high-strength bolt connection are K g , K d , the calculation formulas are: Where K p is the equivalent spring stiffness of the cover, K b1 is the equivalent spring stiffness of the cover plate high-strength bolt group, K p1 is the equivalent spring stiffness of the upper flange plate of the cantilever beam segment, K p2 is the equivalent spring stiffness of the upper flange plate of the steel beam segment; K b2 is the equivalent spring stiffness of the high-strength bolt group of the inclined end plate, K1 is the equivalent spring stiffness of the inclined end plate of the cantilever beam section, and K2 is the equivalent spring stiffness of the inclined end plate of the steel beam section; According to step 2 and step 3, K can be obtained g and K d , considering the initial rotation stiffness contributed by the stiffener, the initial rotation stiffness K at the hybrid connection node n for: Where K n is the initial rotational stiffness at the hybrid connection node, K d is the equivalent spring stiffness of the high-strength bolt connection of the inclined end plate, K g is the equivalent spring stiffness of the upper flange cover high-strength bolt connection, mK d is the equivalent spring stiffness contributed by the stiffener and the inclined end plate, m is the amplification factor, h is the height of the high-strength bolt tension area in the longitudinal direction of the inclined end plate, h = 0.40~0.60H, H is the height of the cantilever beam section; According to the knowledge of material mechanics, calculate the rotational stiffness K of the cantilever beam segment c : Then the initial rotation stiffness K of a prefabricated steel frame beam-column joint is: Where E is the elastic modulus of the cantilever beam segment, I is the section moment of inertia of the cantilever beam segment, and L is the length of the cantilever beam segment.

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