TABLE OF CONTENTS The discussions in Chap. 3 were based on several simplifications such as small deflection theory, no initial imperfections and conservative boundary conditions. These simplifications were adopted in order to make the analysis simple. For actual members, however, this simplified approach does not always hold. Some of these simplifications may lead to the results on the safe side and some do not. The effects of these simplifications will be further examined in this chapter.
For the case of an ideal column (small deflection), the stability or buckling condition is essentially the same as the eigenvalue problem. Since an eigenvalue problem has some special properties, it is important to examine these properties in terms of their physical meanings in a column stability problem. Further, vibration of a column is also an eigenvalue problem, the relationship between vibration frequency and the buckling load is considered.
As a similar problem, columns on an elastic foundation are also studied in this chapter. This consideration may be useful in design of piles, train rails and concrete slabs against buckling due to thermal expansion.
In the previous chapter we have shown that the value of the critical load for a beam-column with given end conditions can also be obtained in a much simpler manner by considering the behavior of an ideal column, which is assumed to be initially perfectly straight and compressed by a centrally applied load. The prime objective of this alternative approach is that the...
