A. Ranjbaran - Associate Professor، Department of Civil Engineering, Shiraz University, Shiraz, Iran
S. Hashemi - M.Sc. Candidates ،Department of Civil Engineering, Shiraz University, Shiraz, Iran
A.R. Ghaffarian - M.Sc. Candidates Department of Civil Engineering, Shiraz University, Shiraz, Iran

In this paper mathematical formulation for buckling analysis of a column and vibration analysis of a beam is presented. The beam and column is assumed to be non-uniform and cracked. Using calculus of variations the problem is expressed as an optimization problem. A technique of optimization is used for analysis of buckling load. Considering the similarity between the governing equation for buckling and free vibration, the fundamental frequency and mode shape of the beam is computed with the same method. Several examples are solved. The results are compared with other methods. An excellent agreement was obtained.

Buckling, vibration, cracked, non-uniform, beam, column