Influence of shear deformation on the optimal design of a column under compression

The optimal design of a column subjected to compression forces is studied. Different support conditions are considered for the column. Also, a point load at the top section, self weight and unifonnly distributed vertical loading may be included in the analysis. The beam is assumed immersed in an elastic Winkler-type soil. Conservative loading has been assumed, i.e. with constant direction and therefore follower loads situation has been disregarded. The optimal column design is described by both cross-section distribution (area; second moment, shear area etc.) along the column span and the corresponding total volume. The optimal design problem consists of detennining the cross-section distribution layout for a beam of given length, so that the column volume becomes minimum, and resultant compressive stresses are admisible. This problem is analyzed assuming a linear elastic material behavior. The column is analyzed by comparing the results obtained from the Navier-Bemoulli beam-column model, and from Timoshenko beam- column model. Special shape functions are introduced in each case