Stability Design Methods Of Stepped Column Frames Considering The Interaction Between Columns

The stepped column is a kind of common component in industrial buildings,which has the advantages of reasonable structure and material saving,and is widely used in industrial plants.Because of the column section changes significantly along the height direction and is subjected to the force in the column that is the loads of the crane,the buckling of the stepped column is significantly different from the ordinary constant section column.For the stable design of stepped columns,the effective length factor calculation methods of stepped column that provided by current design codes can not accurately to account for the interaction effect among the columns,the calculation methods can not accurately consider the limited constraints at the stepped column end and to account for the influence of the roof inclination angle of stepped column,thereby may cause the partial unsafe design,which has a great limitation.For this reason,the stiffness matrix of stepped column was obtained by using the rotational displacement equations of the constant cross member,and the influence of axial force on the stiffness is determined.Based on the concept of layer stability,then used to determine the effective length factors formula considering the interaction effect among columns.The results show that the formula has high precision and is somewhat safe,it can be used to calculate the multi-span frames and different column height frames as well.A practical method to account for the influence of the roof inclination angle for pitched-roof portal frames with stepped columns is also presented.In addition,the second-order effect of the stepped column is analyzed and the formulas for the amplification coefficients of the lateral shift and the bending moment of the stepped column frame are derived.Based on the calculation of the effective length factors and the study of the second order effect,this paper presents the method of checking the stability design of the stepped column frame,which provides a reference for the design and application of practical engineering.In practical engineering,there are still a large number of complex frames composed of stepped columns and constant section columns.In this paper,the calculating formulas of the effective length factors,layer lateral displacement amplification coefficient and layer bending moment amplification coefficient are also given.The analysis shows that the method presented in this paper has great precision and can meet the practical design requirements.