Theoretical Study And Computer Simulation On The Buckling Of Double-layer Portal Frame

With the fast development of construction industry, the portal frame, as one of the light-weight structures, is widely used in industrial plants, airplane garages, bridges, gymnasiums and exhibition halls etc. The buckling problem has been an active subject in the solid mechanics and engineering and has been drew much attention to. Based on this, the static and dynamic buckling problem of double-layer portal frame is studied by theoretical analysis and computational simulation.1. The present research on the static and dynamic buckling of portal frame is simply stated and analyzed, and the main method and conclusion are summarized.2. The governing equation of the double-layer portal frame is derived by using the Hamilton principle. The static buckling problem of no-sway and lateral sway double-layer portal frame in different constraint conditions is studied theoretically. The equation is solved by using the definite conditions, the analyzing expression of critical buckling condition on the static buckling and the bucking mode equation are given. The buckling coefficient and the effective length factor μ of the column and critical buckling load are obtained by calculating the critical bucking conditions based on MATLAB.When the linear stiffness ratio of the beam and the column of the no-sway double-layer portal frame A range from0.1to30, the error range between the theoretical value and simulation value is less than1%. The effective length factor μ. of the column decrease with the increase of A. When A is larger than30, the error range between the theoretical value and simulation value is more than2%. The theoretical value of effective length factorμ decrease with the increase of A and approach0.5, while the simulation value of effective length factor μ increase with the increase of A. The extreme point of the effective length factor μ can be found when A is between30-40.When the linear stiffness ratio of the beam and the column of the lateral sway double-layer portal frame A range from0.1to8, the error range between the theoretical value and simulation value is less than1%. The effective length factor μ of the column decrease with the increase of A. When A is larger than15, the error range between the theoretical value and simulation value is more than5%. The theoretical value of effective length factorμ decrease with the increase of A and approach1, while the simulation value of effective length factor μ increase with the increase of A. The extreme point of the effective length factorμ can be found when A is between10-15.3. The dynamic buckling problem of no-sway double-layer portal frame in different constraint conditions is studied theoretically. The equation is solved by using the definite conditions and the analyzing expression of critical buckling condition on the dynamic buckling and the bucking mode equation are given. The buckling coefficient and the effective length factor μ of the column are obtained by calculating the critical bucking conditions based on MATLAB.4. The static and dynamic buckling of portal frame is simulated by using ANSYS. The boundary condition is divided into column hinged-hinged support and fixed-fixed support, and the double-layer portal frame is subjected to different loads on the roof of the structure that are uniform load, trapezoidal load and triangular load. Through analyzing, the conclusions can be obtained as follow:(1). When the frame is subjected to uniform load, the buckling of columns up and down of the double-layer portal frame occur at the same time. The deformation mode is shown in Fig.3and Fig.9. Tablel shows that the critical buckling loads of the frame subjected to different uniform loads are the same.(2). The critical buckling load of frame subjected to the trapezoidal load is unequal to the sum of the critical buckling loads of frame subjected to corresponding triangular load and uniform load respectively. Therefore, when the irregular loads are divided into regular loads, the corresponding critical buckling loads don’t accord with the superposition principle.