Stability Analysis Of Stepped Columns And Framed Columns Supporting Laterally Leaning Columns

This paper is mainly composed of four parts.â… Theoretical derivation is presented to determine the moment amplification factor of singly-stepped columns and proposed formulas with good accuracy are presented. Based on the assumption that the interaction between upper and lower segments of singly-stepped columns remains unchanged from elastic to elastic-plastic stage, an investigation into elastic-plastic load-carrying capacity of the dominating columns of stepped columns is carried out. Comparing it with the capacity of the stepped columns analyzed as an overall structure, we find that the change of interaction between upper and lower columns from elastic to elastic-plastic stage increases always the overall load-carrying capacity of the stepped columns. At last this paper carried out an investigation into elastic-plastic load-carrying capacity of stepped columns. Compared with it, the result of current code method is conservative.â…¡An investigation into elastic-plastic load-carrying capacity of the framed columns supporting laterally leaning columns is carried out. Comparing it with the result of the current code method, we can find that, the stability coefficient of framed columns should not only be determined by an amplified effective length, but also the column curve used should be lowered down. A modified imperfection factor is proposed to predict the reduced column capacity using the current equation for column stability coefficient. Also this paper reveals that the total load-capacity may be much greater than the cross-section yield strength of the framed column itself when the slenderness is small.â…¢The code gets the limited value of width-thickness ratio of flange elements in I-section struts based on principles as follows. The elastic-plastic critical stress of plate elements should be equal to the stress level of struts failed, this stress maybe a little low; the flange of the I-section is assumed to be hinged with the web. The elastic-plastic load-carrying capacity of struts with the overall initial deformation, of which all the plate elements take the largest width-thickness ratio limits according to the code is analyzed by finite element method. Comparing it with the result of the same struts but with both overall and local initial deformation, we can find that the reduction of the capacity caused by the local initial deformation is at most by 10% of the capacity of the strut with only overall initial deformation, which deduces that the limit given by the code is reasonable.â…£Portal frames with overhead cranes are modeled as a one-span two-story frame in this paper; The lower beam is hinged onto two columns to model the connecting effect of the crane bridge. Buckling analysis is carried out on the idealized frame. It is revealed that the buckling loads of columns in the same story, due to the interaction between upper and lower story, increase or decrease with identical percentage. This means that the columns in a story behave as a unified identity to join the interaction between stories. Based on this observation on the buckling behavior, a mergence method, in which all columns are merged as a mega-column and the rotational restraints of the beam is summed up, is proposed, and is found to be very accurate.