A calculation method for the bearing capacity of beam-column welded and bolted joints based on energy method considering floor slip effect

Abstract

The present invention belongs to the field of civil engineering, and relates to a calculation method that considers the influence of floor slabs on the bearing capacity of nodes in the calculation of the bearing capacity of welded-on and bolted-on nodes. It is characterized in that the bending stiffness and bearing capacity of the steel beams are significantly improved after the floor slabs are combined with the steel beams, and it is more conducive to accurate analysis to comprehensively consider the effect of the floor slabs in the calculation of the bearing capacity of welded-on and bolted-on nodes. By converting the effective width of the compressed concrete slab into the equivalent converted cross-sectional width of the steel material, and further considering the slip effect caused by the insufficient shear connectors of the composite beams in actual engineering, the total potential energy is summed, and the calculation formula for the bearing capacity of welded-on and bolted-on nodes is derived on the basis of the energy method. The present invention is a new method for calculating the bearing capacity of welded-on and bolted-on nodes. The calculation process is concise and clear, and it provides a scientific and effective calculation method for determining the elastic critical bending moment of welded-on and bolted-on nodes and improving the safety of steel structures of welded-on and bolted-on nodes.

Description

Technical Field

[0001] The invention belongs to the field of civil engineering and relates to a calculation method for considering the influence of floor slab on the node bearing capacity in the calculation of the bearing capacity of an upper welded and lower bolted node. Background Art

[0002] For general multi-story steel structures, the floor slab can not only transfer the upper vertical load to the beams and columns, but also provide horizontal support for the vertical components of the structure. The combination of the floor slab and the steel beam significantly improves the bending stiffness and bearing capacity of the steel beam. The plastic neutral axis of the composite beam section formed is shifted upward compared to the steel beam section, which improves the ability of the upper flange of the beam to resist bending moments. While protecting the upper flange of the beam, it weakens the lower flange. After the structure without floor slab enters the yield stage as a whole, it shows good ductility due to the formation of a beam hinge mechanism, but the steel structure with floor slab may form a column hinge mechanism, which reduces the ductility of the structure. That is, the steel frame designed without considering the floor slab may not meet the requirements of "strong columns and weak beams" in the actual structure.

[0003] The upper and lower flanges of the welded-on-top and bolted-on node beams are connected by butt welds and spliced ​​plates respectively. This connection method not only ensures the flatness of the upper flange of the beam, facilitates floor slab laying, but also facilitates the installation and positioning of the node. Therefore, it is more conducive to obtaining accurate analysis results to comprehensively consider the effect of the floor slab in the bearing capacity calculation of the welded-on-top and bolted-on node. However, there is no reliable calculation method for this aspect at present. Summary of the invention

[0004] The purpose of the present invention is to propose a node bearing capacity calculation method for upper welded and lower bolted nodes under uniform load, which takes into account the existence of floor slabs and the sliding effect.

[0005] The present invention is achieved through the following technical solutions:

[0006] Step 1: When the composite beam is subjected to positive bending moment and the cross-section is analyzed according to the elastic theory, the effective width of the compressed concrete slab should be converted into the equivalent converted cross-section width of the steel material according to the principle that the cross-section strain is the same and the total internal force is unchanged:

[0007] Effective section width b of composite beam e for:

[0008] b e =b 0 +b 1 +b 2 (1)

[0009] Where: b 0 is the width of the upper flange of the steel beam, b 1 , b 2 Take 1 / 6 of the beam span l and the flange plate thickness h c The smaller value of 6 times;

[0010] Determine the converted section width b of the composite beam eq :

[0011] b eq =b e / α E (2)

[0012]

[0013] Where: E s , E c is the elastic modulus of steel and floor concrete;

[0014] Step 2: The slip effect of the steel-concrete composite beam cannot be ignored. When slip occurs at the interface of the composite beam, the stiffness of the composite beam will be reduced. Determine the stiffness reduction factor ξ:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] EI=E s A 0 / A 1 (11)

[0023] Where: EI is the bending stiffness calculated by applying the conversion section method to the composite beam section, I s and I c Respectively represent the converted moments of inertia of the steel beam and concrete slab sections, d c A represents the distance from the centroid of the steel beam to the centroid of the concrete flange. s and A c is the converted cross-sectional area of ​​the steel beam and concrete slab, and p represents the spacing of the stud connectors;

[0024] At the joint of the upper weld and lower bolt, I s is the net section inertia moment after deducting the high-strength bolt holes:

[0025]

[0026] In the formula, b represents the cross-sectional width of the steel beam, H b Indicates the cross-sectional height of the steel beam, t wb Indicates the web thickness of the steel beam, t Fb represents the thickness of the steel beam flange, n FP is the number of high-strength bolts arranged on the flange section. When parallel arrangement is adopted, it is 2. Fb Indicates the diameter of the high-strength bolt hole on the flange, y i It indicates the distance from the center of the high-strength bolt hole on the web to the neutral axis of the steel beam section;

[0027]

[0028] In the formula, and Respectively represent the distances from the centroid of the steel beam and the concrete slab to the bottom surface of the steel beam;

[0029] Step 3: Calculate the total potential energy under uniform load according to the energy method:

[0030]

[0031]

[0032] Total potential energy ∏=U+V (16)

[0033] According to the single variable total potential energy equation, in Fourier series form Express the modal test function, substitute it into the total potential energy formula, and finally find the critical moment of buckling according to the stationary value principle of potential energy:

[0034]

[0035] Where: h is the cross-sectional height of the converted cross section at the node connection, I y , I w is the moment of inertia of the converted section about the weak axis and the warping moment of inertia of the cross section, d c A represents the distance from the centroid of the steel beam to the centroid of the concrete flange. s and A c is the cross-sectional area of ​​the steel beam and concrete slab, G is the shear modulus of the material, I t is the torsional moment of inertia of the component.

[0036] The beneficial effects of the present invention are as follows: in order to solve the problem of how to calculate the bearing capacity of nodes in general multi-story steel structures with welded-on and bolted-on nodes, a node bearing capacity calculation method based on the energy method and taking into account the floor slip effect is reasonably proposed. This provides theoretical guidance to compensate for the problem that the floor section bending stiffness is not considered in the node model design process. This provides a scientific and effective calculation method for determining the elastic critical bending moment of welded-on and bolted-on nodes and improving the safety of steel structures with welded-on and bolted-on nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a side elevation view of a steel frame with upper welded and lower bolted nodes provided by an embodiment of the present invention;

[0038] Figure 2 is a cross-sectional profile calculated according to an embodiment of the present invention; DETAILED DESCRIPTION

[0039] The present invention will be further described below with reference to the accompanying drawings and by way of embodiments.

[0040] Example

[0041] A calculation method considering the influence of floor slab on the bearing capacity of nodes in the calculation of the bearing capacity of upper welded and lower bolted nodes is taken as an example. A single-frame two-span three-story plane steel frame model is used as an example. The column spacing is 6m, the floor height is 3.3m, the steel columns are made of Q345B steel with a cross-sectional size of HW350×350×12×19, the steel beams are made of Q235B steel with a cross-sectional size of HN400×200×8×13, the cantilever beam length is 0.4m, the web splicing plate thickness is 8mm, the lower flange splicing plate thickness is 12mm, the splicing bolts are 10.9-grade M20 high-strength bolts, friction type connection is adopted, the bolt reserved hole diameter is 22mm, and the bolt connection spacing is 0.1m.

[0042] A bearing capacity calculation method for a welded-on-top and bolted-on-bottom node includes the following steps:

[0043] Step 1: Determine the effective cross-sectional width of the composite beam and convert it into the equivalent cross-sectional width of the steel material:

[0044] Effective section width b of composite beam e for:

[0045] b e =b 0 +b 1 +b 2 =0.2+1+0.96=2.16m

[0046] Determine the converted section width b of the composite beam eq :

[0047]

[0048]

[0049] Step 2: Determine the stiffness reduction factor:

[0050]

[0051] It can be seen that when the spacing between the stud connectors is 0.1m, the composite beam is close to being fully connected and the stiffness reduction factor can be ignored.

[0052] Step 3: Calculate the total potential energy according to the energy method:

[0053]

[0054] Although the specific calculation method of the present invention is described above in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Technical personnel in the relevant field should understand that various modifications or variations that can be made by technical personnel in the field without creative work on the basis of the design of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for calculating the bearing capacity of beam-column welded and bolted joints based on energy method considering the floor slip effect, characterized in that: The upper flange of the node is connected by butt welds, one side of the lower flange is connected by fillet welds, the other side is connected by bolts, and the web is connected by high-strength bolts. The method for determining the critical moment of buckling of the node includes the following steps: Step 1: Determine the converted section width of the composite beam: Effective section width b of composite beam e for: <h2 style=";text-align:left;direction:ltr">b<h2 style=";text-align:left;direction:ltr"> e <h2 style=";text-align:left;direction:ltr"> =b0+b1+b2 (1) Where: b0 is the width of the upper flange of the steel beam, b1 and b2 are 1 / 6 of the beam span l and the flange plate thickness h c The smaller value of 6 times; Determine the converted section width b of the composite beam eq : b eq =b e / a E (2) Where: E s , E c is the elastic modulus of steel and floor concrete; Step 2: Determine the stiffness reduction factor: EI=E s A0 / A1 (11) Where: h is the cross-sectional height of the converted cross-section at the node connection, EI is the bending stiffness calculated by applying the converted cross-section method to the composite beam cross-section, I s and I c Respectively represent the converted moments of inertia of the steel beam and concrete slab sections, d c A represents the distance from the centroid of the steel beam to the centroid of the concrete flange. s and A c is the converted cross-sectional area of ​​the steel beam and concrete slab, and p represents the spacing of the stud connectors; At the joint of the upper weld and lower bolt, I s is the net section inertia moment after deducting the high-strength bolt holes: In the formula, b represents the cross-sectional width of the steel beam, H b Indicates the cross-sectional height of the steel beam, t wb Indicates the web thickness of the steel beam, t Fb represents the thickness of the steel beam flange, n FP is the number of high-strength bolts arranged on the flange section. When parallel arrangement is adopted, it is 2. Fb Indicates the diameter of the high-strength bolt hole on the flange, y i It indicates the distance from the center of the high-strength bolt hole on the web to the neutral axis of the steel beam section; In the formula, and Respectively represent the distances from the centroid of the steel beam and the concrete slab to the bottom surface of the steel beam; Step 3: Calculate the total potential energy of flexural-torsional buckling at the node: Strain Energy: Load potential energy: Total potential energy ∏=U+V(16) Where u is the lateral displacement of the shear center of the cross section at the node connection, θ is the torsion angle of the cross section around the shear center, Substituting into the total potential energy formula (16), the critical moment of buckling is obtained: Where: I y , I w is the moment of inertia of the converted section about the weak axis and the warping moment of inertia of the cross section, d c A represents the distance from the centroid of the steel beam to the centroid of the concrete flange. s and A c is the cross-sectional area of ​​the steel beam and concrete slab, G is the shear modulus of the material, I t is the torsional moment of inertia of the component.

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