Exact solution of buckling problem of the column loaded by self-weight

摘要

This work proposes the new method of investigation the buckling problem of the uniform column under the axial distribution load,which presented by self-weight.The new method is based on the exact solution of the appropriate differential equation for the buckling of a column.The solution is expressed with dimensionless fundamental functions and initial parameters.Due to the exact solution,the formulas in an explicit form for variables of the state of a column-deflections,angular displacement,bending moment and transverse force-were defined.They generally define the stress-strain state of the column Due to the dimensionless nature of the fundamental functions the analytical form of load is defined.That has limited the problem of determination of critical load to determination the unknown non-dimensional buckling coefficient through characteristic equation.An example of determining the buckling coefficient for a hinged column was considered.The values of buckling coefficient for most popular design schemes are given.The proposed method does not require discretization od scheme and is a real alternative to applying approximate methods when solving stability problems of this class.