Study Of Effective Length Coefficient Of Frame Column With Semi-rigid Connections

In the stability design of frame column,the effective length l₀ is required.The effective length l₀=μl_c,hereμis known as effective length coefficient.For the frame with rigid connection,code for design of steel structures has given specific results and tables.But in fact, the connection stiffness of the practice is not completely rigid or articulated.They are all between in the completely rigid and articulated.So they are called semi-rigid connection.To the effective length of frame column with semi-rigid connections,code for design of steel structures only has general provisions to describe and has not concrete results and tables. Therefore,the problem to determine the effective length of frame column with semi-rigid connections has great significance for ensuring the reasonableness of the design.The existing formula of effective length coefficient is derived under certain assumptions.It not fully considers the factors effecting effective length coefficient.So the paper analyze possible factors effecting effective length coefficient,and study the impact of semi-rigid to effective length coefficient deeply.From the balance equation of axial compression component with semi-rigid connection,the buckling equations of sway and non-sway axial compression component with semi-rigid connection are derived.The buckling equations are solved by the software matlab,and the effective length coefficient of single component under the condition of different constraints is got.Through adopting approximate method and using rotation-displacement equations and adopting three column model,the formula of effective length coefficient of non-sway and sway frame column with semi-rigid connections are derived,In application,when the relative error of the effective length coefficient under semi-rigid and rigid conditions is less than 5%,the impact of semi-rigid can be ignored.And through amending the above formula to consider the problem that the actual force and critical bearing capacity are inconsistent when the columns are not losing stability at the same time.The results show that:for sway steel frame,the impact of semi-rigid to the effective length coefficient is significantly higher than that of non-sway frame;When the column and base hinged,the impact of semi-rigid to the effective length coefficient is significantly higher than column and base linking with rigid connection;The impact of semi-rigid to the top frame column is higher than the bottom.The effective length coefficients we get through considering the impact of semi-rigid of the paper can not only ensure the structural design more secure, and they are more in line with the actual.