Elastic Stability Analysis Of Cantilever Column Under Uniformly Distribute Load And Floor Concentrated Load

The cantilever column is common member in engineering.For high-rise buildings, when the whole stability analysis is carried out,it can be simplified as the equivalent cantilever column model according to the characteristics of the structure.At present, there are many studies on elastic stability of cantilever columns under axial pressure at home and abroad, but few studies on axial force change and shear deformation.Energy method is an effective method to solve the problem of elastic stability which is composed of force or structure components.This paper is mainly focused on the following parts based on energy method:(1) The energy method is used to derive the shear-flexural cantilever column buckling load formula by taking the flexural deformation curve and shear deformation curve of cantilever columns under lateral uniform load as the deflection curve of which under uniformly distrib-uted load.By verifying the results with SAP2000, giving the scope of application.The formula have simply form and high precision.The parameter η in the formula are discussed and the simplified formula are fitted.(2) Approximate buckling formulas for flexural buckling of singly-stepped columns subjected to a uniformly distributed load are derived based on energy method with two trial functions:one is the column bending lateral deflection curve under lateral uniform load,another is trigonometric function.Through compared to the finite element results, the applicable scope of the two formulas are given.Using trigonometric function as the trial function, approximate buckling formulas for shear-flexural buckling of singly-stepped under uniformly distributed load are derived based on energy method. Also the formula are test and verify by the results of the finite element and the applicable scope of the two formulas are given.(3) Based on the comparative analysis of buckling critical load of cantilever column under uniformly distributed load and floor concentrated load, fitting out of the conversion coefficient ξ of floor concentrated load and uniformly distributed load with the finite element software. Research has shown that for any cantilever column under floor concentrated load to calculate the buckling critical load are available under uniform distributed load calculation formula of the critical buckling load multiplied by the coefficient factor ξ and the floor height h.