Parametric analysis of steel structure support end gusset plate based on secondary development of ABAQUS
Parametric analysis of steel structure support end gusset plate based on secondary development of ABAQUS
Official Account: Non-Deconstructive · Author: Zhou Wenqi (Venchy)
Strong nodes and weak components are the general principles of building structure design.Steel structure node connection In the design of steel structure, there are two main ways of connecting beam-column nodes with diagonal braces, as shown in Figure 1 and Figure 2.Among them, the node connection method shown in Figure 1 basically maintains the original shape of the component at the node, and its load-bearing capacity is relatively reliable.However, its production and construction are relatively complex, and the sizes of the rods supported by the beams and columns need to match.Node 2 only needs a node plate to connect to the component, which is easy to construct. The diagonal brace can use rods of any cross-section, which solves this problem.Compared with node 1, its force is closer to an ideal hinge and will not produce a large secondary bending moment in the structure [1].At the same time, the stiffness of node 2 is also smaller than node 1, which will not cause the support deformation to be too concentrated in the middle of the support, which is beneficial to improving the low-cycle fatigue life of the support.However, the current research on the mechanical performance of plate gusset plates is not comprehensive.
Figure 1 Node 1
Figure 2 Node 2
Figure 3 Finite element model of node 2
Whitmore proposed that the axial force of the diagonal brace propagates according to a diffusion angle of 30°, and based on this, the effective width of the gusset plate is determined to determine the bearing capacity of the gusset plate [2].Tsai et al. found that the deformation shape of the gusset plate at the connection between the herringbone support and the beam is similar to the buckling shape when the end of the gusset plate has only a low rotational stiffness provided by the support, which is inconsistent with the assumption that the end of the gusset plate has infinite rotational stiffness commonly used in analysis [3].Zhang Wenyuan and others simulated a large number of nodes with different member sizes. Based on the effective length of the gusset plate, the thickness of the gusset plate, the support angle, and the stability theory of steel, they proposed a recommended formula for the bearing capacity of plate gusset plates based on the simulation results [4][5].
This article establishes different models through secondary development of ABAQUS, conducts parametric analysis of plate gusset plates, studies the relevant factors that affect the mechanical performance of plate gusset plates, and gives relevant design suggestions.
1 Model overview and ABAQUS parametric modeling
1.1 Overview of analysis model
The structural model in this article is shown in Figures 2 and 3: among them, the cross-section dimensions of beams and columns in all models remain unchanged, and the beam cross-section is I1000×350×50×70. The column cross-section size is 700×700×350×350×50×70. The diagonal brace cross-section is I700×700×80×70.The cross-section of the connection part between the gusset plate and the diagonal brace is the same as that of the diagonal brace.
In abaqus, Q235 is selected as the steel material, the elastic model is 2.06×105MPa, the Poisson’s ratio is 0.3, and the bifold line model is selected as the material.The model is modeled using solid unit C3D8R.The beam end and column end sections are rigidly connected, and the axial force of the diagonal brace is applied to the end of the diagonal brace.Loading is divided into two analysis steps.The first analysis step uses standard general, which is a preload of 0.01N/mm2. The second analysis step uses standard riks, which applies gradually increasing axial force to the end of the diagonal brace to determine the critical buckling load of the gusset plate.
1.2 ABAQUS parametric modeling
The workload of building a large number of models using the GUI that comes with abaqus/cae is huge. Therefore, this article uses the abaqus scripting interface, which is customized and developed based on the Python language.Using this interface for parametric modeling of nodes can greatly improve the efficiency of node analysis.
Based on the Python language, the abaqus script interface adds many new object models, corresponding to various functions of the abaqus/cae gui interface.This article defines the relevant parameters of the gusset plate as basic variables. The main objects used in the parametric modeling process are as follows: (1) ConstrainedSketch: used to create sketch objects. (2) Material.Density/Elastic/Plastic: used to define material properties. (3) BaseSolidExtrude: used to create Part based on sketch. (4) rootAssembly.Instance.translate/rotate/merge: used for movement, rotation and merging when assembling objects. (5) StaticStep/ StaticRiksStep: used to define analysis steps (6) PartitionCellByPlaneThreePoints/setElementType/ seedPart/ generateMesh: used to cut models and divide meshes (7) Pressure/EncastreBC: Define loads and boundary conditions (8) Job: Define computing model
2 Ultimate bearing capacity of nodes
2.1 Bearing capacity of gusset plates with different geometric dimensions
This paper established 15 models based on the length Lb of the gusset plate corresponding to the diagonal brace flange extending into the gusset plate and the angle α (as shown in Figure 2).The specific parameters of each model are shown in Table 1.
Table 1 Model numbers with gusset plate size as variable
According to a large number of numerical simulations in literature [4], the calculated length coefficient of the gusset plate is given.The calculation is based on formula 1 to calculate the steel structure length coefficient μ, and then combined with the steel structure specifications to determine the corresponding stability coefficient ψ, and the bearing capacity of the gusset plate is obtained according to formula 2.
Appendix F of “Code for Design of Steel Structures” (GB 50017-2003) [7] gives the calculation formula for the bearing capacity of truss structure gusset plates under the action of diagonal web members.
Based on the steel structure design specifications, literature [4] and the numerical simulation results of this article, the ultimate bearing capacity of the gusset plate under various geometric parameters is shown in Figure 4.
Figure 4 Buckling loads obtained by various calculation methods
From a numerical perspective, the bearing capacity of the gusset plate calculated according to the steel structure code is the smallest.Therefore, the bearing capacity of generally supported plate gusset plates designed in accordance with Appendix F of the Steel Structure Code is conservative.The bearing capacity of the gusset plate calculated according to the specifications and literature [4] increases with the increase of the diagonal bracing flange extension length Lb.The analysis of numerical simulation shows that when the extension length Lb of the diagonal brace is 200~600mm, the bearing capacity of the gusset plate increases with the increase of the extension length, and the trend is similar to the results calculated in the literature [4].However, when the extension length Lb is greater than 600mm, the bearing capacity of the gusset plate tends to remain unchanged.
Judging from the size of α, the bearing capacity of the gusset plate at each angle calculated according to the literature [4] is similar; the bearing capacity at 30 degrees and 45 degrees calculated according to the specification is similar and smaller; in the results of numerical simulation, the bearing capacity of the gusset plate when α is 30 degrees and 45 degrees is similar, and when α is 60 degrees, its bearing capacity is about 20% smaller than the other two angles.
2.2 Destruction form
Figures 5 to 12 show the stress cloud diagrams of model428, model4108, model3108 and model6108 before and after node buckling.
Figure 5 model428(1)
Figure 6 model428(2)
Figure 7 model4108(1)
Figure 8 model4108(2)
Figure 9 model3108(1)
Figure 10 model3108(2)
Figure 11 model6108 (1)
Figure 12 model6108(2)
Comparing Figure 5 and Figure 6, when the extension length Lb of the diagonal brace is 200mm, the gusset plate buckles at the two flange ends of the diagonal brace.In the area other than the local damage of the gusset plate, the stress of the gusset plate in the extension part of the diagonal brace web is larger, but it decreases with the increase of the distance from the diagonal brace flange.The gusset plate stresses in other areas are smaller.
Comparing Figure 7 and Figure 8, when the extension length Lb of the diagonal brace is 1000mm, the gusset plate undergoes overall buckling at the end of the diagonal brace.At the same time, the damage to the gusset plate is not limited to the gusset plate. The beam and column webs connected to the gusset plate are all damaged, and the internal force value of the beam and column flange is not large.It shows that under this failure mode, the gusset plate has a great influence on the stress of the beam and column webs connected to it.Comparing Figure 9 and Figure 10, the failure shape of the gusset plate of model3108 is similar to that of model4108, but the buckling part is biased towards the column side.
Comparing Figure 11 and Figure 12, the model6108 node buckling did not occur on the gusset plate, but at the end of the gusset plate at the interface between the gusset plate and the beam. Local buckling failure of the beam occurred. The internal force of the gusset plate close to the beam side was larger, but it did not yield.It shows that when the internal force is too large, in addition to causing damage to the gusset plate itself, the plate gusset plate can also cause local damage to the beam.
Figure 13 (a) Damage form of the model in literature [4]
Figure 13(b) model4108 and reference [4] model displacement load curve
The results calculated according to the literature [4] in Figure 4 are quite different from the results of the numerical simulation in this paper, which is also related to the failure form of the gusset plate.Figure 13a shows the stress distribution of the gusset plate after node buckling based on the geometric parameters of the gusset plate modeled in literature [4] and model4108.This node does not consider the effect of beams and columns on the gusset plate, and only imposes constraints on the boundaries of the gusset plate.Compare Figure 6, Figure 8 and Figure 13.In Figure 13, the damage to the gusset plate mainly occurs at the intersection between the diagonal brace and the gusset plate.The failure form of the gusset plate in Figure 13(a) is similar to Figure 6, but is quite different from the failure form of the gusset plate in Figure 8.At the same time, comparing the displacement load curves of model 4108 and the literature 4 model (Figure 13b), the ultimate bearing capacity of the literature [4] model is 33000kN, which is much larger than the numerical model in this paper, but its deformation capacity is poor. When the displacement is 3.5mm, the node loses its bearing capacity.In Figure 4, the bearing capacity of nodes with similar failure forms to Figure 13 is similar to that of Reference [4], while the bearing capacity of nodes with different failure forms from Figure 13 is quite different from that of Reference [4].Therefore, the different damage forms caused by different boundary conditions make the calculation results of some nodes in this paper and the literature [4] quite different.
- Internal force transfer between diagonal braces and gusset plates
From the perspective of force transmission, the internal force transmission from the node plate to the node beam-column node can be divided into two parts.The first is the internal force transfer between the diagonal brace and the gusset plate.The second is the internal force transfer between the gusset plates and beams and columns.For the convenience of observation, the total axial force of the orthogonal section of the node as shown in Figure 14 is defined as Na, the axial force borne by the node flange section is Nf, and the axial force borne by the node plate section is Nw, that is, Na=Nf+Nw.Nf=ΣNfi。
In order to study the internal force transfer between the diagonal brace and the gusset plate, as shown in Figure 14, the axial force Na of each section when the node buckles under the action of axial pressure is extracted according to Ln, and the internal force distribution diagram is shown in Figures 15 to 17.In order to study the distribution ratio of the axial force borne by the diagonal brace flange part and the gusset plate part of each joint section, the relationship curve between the axial force Nf and Ln of the joint flange part of each joint model is extracted, as shown in Figures 18 to 20.The relationship between the axial force Nw and Ln borne by the gusset plate is shown in Figures 21 to 23.
Figure 14: Each orthogonal section for extracting axial force
Figure 15 Axial force of node orthogonal section when α=30°
Figure 16 Relationship between Na and Ln when α=45°
Figure 17 Relationship between Na and Ln when α=60°
Figure 18 Relationship between Nf and Ln when α=30°
Figure 19 Relationship between Nf and Ln when α=45°
Figure 20 Relationship between Nf and Ln when α=60°
Figure 21 Relationship between Nw and Ln when α=30°
Figure 22 Relationship between Nw and Ln when α=45
Figure 23 Relationship between Nw and Ln when α=60°
3.1 When the joint plate and flange are jointly stressed, the attenuation trend of the joint orthogonal section axial force Na with Ln
The gusset plate plays the role of interconnecting the beams, columns and diagonal braces.The internal force of the diagonal brace is transmitted to the beams and columns connected to it through the node. From Figure 15 to Figure 17, the changing trend of the axial force on the node plate is obtained:
(1) When Ln is less than 800mm, the change of the axial force Na of each orthogonal section of the node along Ln is not obvious.When Ln is greater than 800mm, the axial force Na of each orthogonal section decreases as Ln increases.It can be found from Figure 14 that when Ln is less than 800mm, the orthogonal section of the node cannot intersect with the beams and columns, dx and dy are both 0, and the axial force of the diagonal brace cannot be transmitted to the beams and columns.When dx and dy are greater than 0, the axial force of the diagonal brace borne by the gusset plate can be partially transmitted to the beams and columns.The axial force on the gusset plate shared by the beams and columns increases with the increase of dx and dy.
(2) The internal force transmitted from the gusset plate to the beams and columns does not change with the change of the extension length Lb of the diagonal brace.When Ln is 0, the axial force of the orthogonal section of the node is equivalent to the buckling load of the node.In Figures 15 to 17, the curves with Lb of 200 and 400 are almost coincident; the models with Lb of 600, 800, and 1000 are also nearly coincident.It shows that the extension length Lb of the diagonal brace has no effect on the node normal section axial force Na.
(3) The greater the axial force of the orthogonal section, the faster the internal force transmitted from the gusset plate to the beams and columns decays with Ln.As shown in the curves in Figures 15 to 17, the efficiency of the axial force distribution curve along Ln of the model with a buckling load of 24000kN is significantly greater than that of the model with a buckling load of 16000kN.
3.2 When the node flange part transmits internal force to the node plate, the axial force Nf borne by the node flange section decreases with Ln.
In the section Lb where the diagonal brace flange extends, the axial force Na on the orthogonal cross section consists of two parts: the axial force Nw of the gusset plate and the axial force Nf of the diagonal brace flange part.The reduced axial force in the flange part is transferred to the gusset plate through the shear stress between the flange and the gusset plate.From Figure 18 to Figure 20, the curve relationship between the axial force Nf and Ln borne by the flange part of the diagonal brace is obtained.
The flange axial force Nf gradually decreases as the length Ln increases, and the relationship between the two approaches linearity.The axial force borne by the flange is transmitted to the gusset plate in the form of shear stress, so the shear stress values at various positions of the gusset plate and the flange tend to be constant.At the same time, comparing the slopes of each curve, when the length of Lb is larger, the slope of the curve is smaller, indicating that under the same flange axial force, the shear stress on the interface between the flange and the gusset plate decreases as Lb increases.
Taking model428 and model4108 as an example, the interface between the flange and the gusset plate of model428 has to bear an axial force of 7409kN on the flange part at a length of Lb=200mm, and its shear stress is τ=132.5Mpa.Although model 4108 has to bear an axial force of 14260kN on the flange section, its shear stress is only τ=50.92Mpa.Considering the influence of axial force and shear force, model428 is prone to local instability failure due to excessive shear stress at the interface between the gusset plate and the flange (Figure 5, Figure 6), while model 4108 suffers from overall instability failure of the gusset plate at Lb (Figure 7, Figure 8), and its critical load is much larger than model428.The failure principle of other nodes with Lb equal to 200mm and 400mm is the same as model428.Therefore, it is recommended that when checking nodes, the bearing capacity of the interface between the node plate and the flange should be considered to avoid local damage to the node.
3.3 Distribution of axial force Nw borne by the gusset plate section along Ln
The total axial force Na of the node orthogonal section, minus the axial force Nf of the flange section where the diagonal bracing flange extends into the section, is the axial force Nw borne by the node plate.The relationship curve between the axial force Nw and Ln borne by the gusset plate section is shown in Figures 21 to 23.It can be found that the peak internal force of each curve occurs at Ln = Lb, that is, when the overall buckling failure of the gusset plate occurs, the maximum position of the axial force Nw of the gusset plate of each model occurs at the length of the diagonal brace extending into the gusset plate Ln = Lb.When the node buckling load is the same, the greater the length of Lb, the smaller the maximum axial force Nw that the node plate bears at Ln.Since there are flange constraints in the range from Ln=0 to Ln=Lb, and the maximum axial force of the gusset plate does not occur in this section, the overall buckling of the gusset plate cannot occur in this section.When Ln>Lb, the gusset plate axial force Nw tends to decrease.When Ln=Lb, the gusset plate not only has to bear the axial force of the gusset plate itself, but also the internal force transmitted to the gusset plate from the flange end. The maximum stress of the gusset plate easily occurs on the section with Ln=Lb.Therefore, when checking the overall stability of the joint plate, it is necessary to use the cross section of Ln=Lb as the control section for checking the overall stability of the joint plate.However, on the section with Ln=Lb, the internal force distribution of the gusset plate is not uniform, and the calculated width of the section needs to be converted.
3.4 Internal force transfer between gusset plates and beams and columns
In Figures 7 to 10, when the plate gusset plate is damaged as a whole, the beam web and the gusset plate connected to the gusset plate are jointly damaged.In Figures 11 and 12, due to the excessive internal force at the plate end of the plate gusset plate, the beam web was damaged first.Therefore, it is necessary to ensure the strength of the beams and columns directly connected to the plate gusset plate.
Table 2 Internal force distribution of beams and columns in each model
The interface between each node plate and the beams and columns is transmitted to the beams and columns around the node in the form of shear force and axial force, as shown in Figure 24.Extract the axial force (Fby, Fcx) and shear force (Fbx, Fcy) on the interface between the gusset plate and the beam-column when each node buckles. Their values are shown in Table 2.The horizontal component of the diagonal brace is composed of the shear force at the interface between the gusset plate and the beam and the axial force at the interface between the gusset plate and the column, that is, ΣFx= Fbx+ Fcx.In the same way, the vertical component ΣFy= Fby+Fcy.Calculate the resultant force in a certain direction shared by the axial force and shear force of the node plate in each node. As shown in Table 2, it is found that when the boundary conditions are the same, when the diagonal brace is at a certain rotation angle, the distribution ratio of beam shear force to column axial force and column shear force to beam axial force is close to a fixed value.For example, when α is 30 degrees, the ratio of the joint horizontal force shared by each node plate and the beam interface to the total horizontal force is 0.77.Therefore, when carrying out design work, it is recommended to distribute the axial force of the diagonal brace according to a certain proportion and apply it to the beams and columns connected to the gusset plate respectively.Check the local stability of beam and column webs.
In addition to the horizontal and vertical components of the gusset plate, the bending moment generated by the eccentricity of the intersection point between the gusset plate and the centerline of the beam and column where the gusset plate bears the axial force (e as shown in Figure 24) can also easily have a greater impact on the stress of the gusset plate and its surrounding beams and columns.In order to maintain the uniformity of the size of the gusset plate, the eccentricity of the intersection point between the axial force of each α=60-degree model and the beam-column centerline in this paper reaches 450 mmm. Therefore, the large eccentricity produced by it on the node causes the model with each α=60-degree gusset plate to produce a bending moment of Mb=1500kN·m at the interface between the gusset plate and the beam.According to the calculation formula of the internal force under the eccentric compression of the gusset plate, such a large bending moment causes a huge local compressive stress at the end of the gusset plate, causing local damage to the web of the beam at the end of the gusset plate (Figure 11, Figure 12).Therefore, during the design process, eccentricity should be avoided at the intersection between the axial force of the diagonal brace and the centerline of the beam and column.If it cannot be avoided, or when the diagonal brace section is subjected to a large bending moment, the stress at the end of the gusset plate should be checked to avoid large stress at the end of the gusset plate, causing local damage to the beam as shown in Figure 11 and Figure 12.
Figure 24 Internal force transfer between gusset plates and beams and columns
4Conclusions and suggestions
Through the analysis of the bearing capacity and internal force transmission of gusset plates under different geometric dimensions, the following conclusions can be drawn:
(1) The damage of the gusset plate can be divided into local damage and overall damage of the gusset plate.Among them, local damage includes local damage to the gusset plate and local damage to the beams and columns connected to the gusset plate.
(2) Due to the large axial force borne by the flange part of the gusset plate, when the length of the interface between the diagonal brace flange and the gusset plate is too small, it is easy to cause large shear stress between the two interfaces, causing local damage to the interface between the flange and the gusset plate.Therefore, it is recommended to check the bearing capacity of the interface between the flange and the gusset plate during design.
(3) The section with the largest internal force of the gusset plate is located at the end of the flange. When checking the overall stability of the gusset plate, the flange end section can be used as the control section of the gusset plate.
(4) The horizontal and vertical component forces on the interface between the gusset plate and beams and columns are transmitted in the form of shear force and axial force on the interface between the gusset plate and beams and columns.And the horizontal component force and vertical component force are transferred into axial force and shear force on the interface according to a certain proportion.When the entire gusset plate is damaged, the beam-column webs and the gusset plate will be damaged together. It is recommended that the stability check be performed on the beam-column webs connected to the gusset plate.Reinforce beam and column webs if necessary.
(5) When the eccentricity of the intersection between the axial force and the beam-column centerline is large, it is easy to cause a large bending moment at the interface between the gusset plate and the beam-column, causing the beam column to generate large stress at the end of the gusset plate, causing local damage to the gusset plate.Therefore, when such eccentricity is unavoidable or a large bending moment occurs on the diagonal brace section, it is recommended to check the bending moment at the interface between the gusset plate and the beam column to ensure the local stability of the beam column.
References [1] Zhang Wenyuan, Chen Shixi, Zhang Yaochun. Research on low-cycle fatigue analysis and design methods of braces and beam-column plate connection nodes [J], Engineering Mechanics, 2011, 28 (1): 96-104. [2]Whitemore,R.E. Experimental investigation of stresses in gusset plate[R].Tennessee: University of Tennessee,1952. [3]Tsai K C,Hsiao BC.Pesudo-dynamic test of full-scale CFT/BRB frame-PART II:Seismic performance of buckling-restrained braces and connections[J].Earthquake Engineering and Structural Dynamics,2008,37(7):1099-1115. [4] Zhang Wenyuan, Du Peng Analysis of compression performance of braces and beam-column plate connection nodes [J]. Engineering Mechanics, 2013, 30 (2): 219-225. [5] Zhang Wenyuan, Chen Shixi, et al. Stability analysis of gusset plates under the pressure of support shafts [J]. Journal of Harbin Institute of Technology, 2012, 44 (2): 1-6. [6]abaqus scripting user’s manual,version 6.12,Hibbitt,Karkssin&Sorensen,Inc,2012 [7] GB50017-2003. Steel structure design specifications [S]. Beijing: China Planning Press, 2003.
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