Analysis of Buckling Property of Portal Steel Plate Shear Wall Member Used for Steel Frame

A set of portal steel plate shear wall members are numerically studied, and effect of some factors on its buckling property and stiffeners used for avoiding its buckling is especially discussed. It is concluded that three stiffening forms presented here have a better effect on the buckling performance of the portal steel plate shear wall member. The buckling coefficient of various portal steel plate shear walls with 6m span are slightly lower than those with 4m and 5m span, which means that the increase of span will reduce the buckling performance and out of plane instability bearing performance of portal steel plate shear walls studied here. The buckling performance requirements can be met by using the stiffening form I as if thickness of the portal steel plate shear wall take as 16mm for the stell framed structures below 10 stories.


Introduction
As is well known, steel frame structures often require additional support units due to their insufficient stiffness, and cross slant support is widely used.However, for residential structures, the traditional slant support has some obvious defects or deficiencies.For example, The end connection structure of the support unit is relatively complex and the diagonal strut unit hinders wall opening,etc.[1].Hence, developing new support systems for steel framed structures has important practical significance and valuable to the progress and development of steel structure residential technology.Therefore, different steel plate shear walls are developed and studied [2][3].A steel plate shear wall with diamond shaped continuous distribution openings is put forward , and experimental research and simulation analysis of energy dissipation capacity are also conducted [4].Based on mechanical characteristics and deformation mechanism of frame structures, a new type of frame stiffness enhancement method is proposed by constraining the deformation of frame beams and columns,which is called portal steel plate shear wall [5].In order to use this new shear element more effectively, numerical analysis model is carried out for studying bearing capacity and buckling property of the new type of portal steel plate shear members.After studying the overall stress characteristics and instability characteristics of the shear element, effective methods to prevent its local instability based on extensive analysis is proposed.The study focused on the influence of different reinforcement methods on its stability.The conclusions obtained here have important guiding significance for further research on this new type of shear element.

Dimension and Basic Construction of the Portal Steel Plate Member
The fundamental geometrical dimension of the portal steel plate shear wall member which can be connected to steel frame with finite high strength bolts is shown in Figure 1.The parameters , ,  has the formula as  =  0 − 1220,  = 0.38,  = 0.12 + 600 (1) It is seen from the geometrical dimension of the portal steel plate shear wall member connected to steel frame shown in Figure 1 that width of the portal steel plate is 600mm, and the span of the plate  0 is corresponding to span  of the steel frame, which is related with height of cross section of steel column.

Figure 1. Dimension of portal steel plate shear wall member
Three form of stiffener of the portal steel plate shear wall member are shown in Figure 2. It is denoted that stiffeners are symmetrically welded on both sides of the shear wall, and  1 is wall thickness of the stiffener and ℎ 1 is height of it.
It is well denoted that the portal steel plate member as shown in Figure 1 and Figure 2 is connected with the steel frame through 9 connection points with bolts.Therefore, the force applied on the portal steel plate shear wall member will come from 9 connection points denoted as A~I in Figure 2.

Numerical Model and Verification
The finite element model of portal steel plate shear wall is established by using SHELL181 element, and bilinear follow-up strengthening is used as the material constitutive relationship.This element considers the variation of shell thickness in nonlinear analysis and supports full integration and reduced integration.For verification of the numerical model presented here, numerical simulation analysis was conducted on two specimens as shown in Figure 3.It is noted that the wall thickness of the portal steel plate as shown in Figure 3 is10mm for two specimens.The materials used for making the specimens is Q345B which has the yield strength of 340MPa, tensile strength of 440MPa and elastic modulus of 204GPa.It is seen from the curves shown in Figure 3 that the numerical results are quite consistent with the experimental results, which show that the numerical model for analysis the portal steel plate member is quite accurate.

Numerical Analysis of Buckling Property of the Portal Steel Plate Element
The steel frame in the middle span of a building with 10 stories in the actual project is selected as the analysis case.Its floor load is 4kN/m 2 , the wall weight is 2kN/m 2 , the live load is 3kN/m 2 , the basic wind pressure of wind load is 0.5kN/m 2 .Size of 10mm, 16mm and 20mm are respectively selected as thickness of the portal steel plate shear wall.The elastic modulus of the material is taken as 2.06×10 5 MPa, the yield strength is taken as 345MPa, and the Poisson's ratio is taken as 0.3, and necessary constraints and loads at nine connections are applied as shown in Figure 5.It is found that the loads that applied to the portal steel plate shear wall with different plate thickness in the steel frame are also different.The loads on the specific portal steel plate shear wall calculated by the above method are shown in Figure 5.

Load applied to the portal steel plate
According to the same methods, the loads applied to the portal steel plate shear wall for span of 5000mm and 6000mm are also obtained.Then the buckling analysis of the portal steel plates with different stiffener are finished and the buckling loads which is expressed by buckling coefficient are finally obtained as following contents.

Elastic buckling coefficient
The elastic buckling coefficient denoted as  is the ratio of the external load on the portal steel plate shear wall to the elastic buckling load, which represents the strength of the elastic buckling performance of the shear wall member.When the ideal portal steel plate shear wall (that is, without considering any defects) develops from in-plane deformation to out of plane deformation, the structure will buckle elastically.The variation of buckling coefficient with wall thickness of the portal steel plate for four case of stiffening rib settings are shown in Figure 6, in which J0 mean no stiffener, J1, J2 and J3 stand for stiffener I, stiffener II and stiffener III, respectively as shown in Figure 2. Compared with the portal steel plate shear wall without stiffening, the buckling property of the three stiffening forms have been greatly improved, which show that the three stiffening forms have a better effect on the buckling performance of the portal steel plate.For portal steel plate shear walls with the same span and the same stiffening form, the greater the plate thickness, the stronger the elastic buckling performance.Through the nonlinear buckling analysis of all kinds of portal steel plate shear walls, the load displacement curves of portal steel plate shear walls with three spans, three plate thicknesses and four stiffening forms are obtained shown in Figure 7 and Table .1.It is shown that the nonlinear buckling coefficients (denoted as ) of the three stiffened portal steel plate shear walls with thickness of 16mm are greater than 1, which means that the buckling performance requirements can be met by using the stiffening form I as if thickness of the portal steel plate shear wall take as 16mm.It is also seen that the buckling performance requirements can be met without arranging stiffeners in the plane as if a 20mm thick portal steel plate shear wall is used.
The buckling coefficient and out of plane instability ultimate bearing coefficient of various portal steel plate shear walls with 6m span are slightly lower than those with 4m and 5m span, indicating that the increase of span will reduce the buckling performance and out of plane instability bearing performance of portal steel plate shear walls.

Conclusions
Based on the results of numerical analysis of the portal steel plate shear wall member presented above, following conclusions are obtained as: (1) The elastic buckling property of the portal steel plate shear wall member with three stiffening forms may be greatly improved compared with the portal steel plate shear wall without stiffening.
(2) For portal steel plate shear walls with the same span and the same stiffening form, the greater the plate thickness, the stronger the elastic buckling performance.
(3) The buckling performance requirements can be met by using the stiffening form I as if thickness of the portal steel plate shear wall take as 16mm for the applied loads presented here.
(4) Increase of span will reduce the buckling performance and out of plane instability bearing performance of the portal steel plate shear walls.

Figure 2 .
Figure 2. Form of stiffener of portal steel plate shear wall member

Figure 5 .
Figure 5. Loads applied to portal steel plate shear wall member(L=4000)

Table 1 .
Nonlinear buckling coefficient and Ultimate bearing coefficient.