TABLE OF CONTENTS The procedure in obtaining analytical solutions from the basic differential equation (3.19) has been discussed in the previous sections. The analytical solutions describe the complete lewd-deflection behavior of linear elastic beam-columns. However, one problem of structural stability analysis which occupies a central position is the computation of the critical load P E. It is not always required to obtain the complete load-deflection behavior. It is apparent from the previous examples that the value of the critical load for a simply supported beam-column is not affected by the magnitude of applied loads which induce a bending moment in the beam-column. Whether the bending moment is induced by initial imperfection or by transverse load, or by any other cause such as eccentricity of compressive loading, the critical, or Euler buckling load cannot be exceeded in a real or imperfect column without producing a buckled shape of large deflections.
It is natural to expect that this critical load for a linear elastic column may be obtained directly and easily from a simplified and idealized column rather than from a real column, or beam-column.
The following assumptions and idealization are made for the idealized column:
The column is perfectly straight;
The load is applied along the center line;
No transverse load is present;
The material is homogeneous and free of initial stress.
Although the idealized column is a special case of the beam-column described earlier, its behavior is rather different from that of a beam-column. The main...
