Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.

Machine Design

How-to, in-depth technical articles for machine design engineers

Chemical Engineering

The industry gateway for chemical engineering and plant operations.

Desktop Engineering

Design, simulation, test, prototyping and high performance computing.

more free magazines
Imperfections in Columns

Consider a curved column with an initial shape w0(x) that is under an axial load F,

        

Enforcing the moment equilibrium of the free-body yields the equation,

The governing equation for the transverse displacement w can then be expressed as,

The above equation contains a non-homogeneous term -Fw0/EI. To simplify the problem, we assume that the initial curve is a simple half sine wave with an amplitude a,

The general solution is found to be,

where is the critical load of a straight column.