Sunday, April 24, 2011

Column Design (Part 1)

A column in the definition of mechanical engineering does not have to be in vertical. The column is a structural member that carries an axial compressive load, and that tends to fail by elastic instability or buckling rather than by crushing the material. Buckling or elastic instability is the the failure condition in which the shape of the column is not sufficient enough to hold it straight under axial compressive load. At the point of buckling, a radical deflection of the axis of the column occurs suddenly. Then if the load is not reduced, the column will collapse. It's obviously that this kind of failure must be avoided in our machine elements design.

Columns that tends to buckle are ideally straight and relatively long and slender. If a compression member is so short, the normal failure analysis must be used rather than the method that we're going to discuss in this post.

How will we know when a member is long and slender?
The tendency for a column to buckle is dependent on the shape and the dimensions of its cross section and how it is supported.
If we take a look at the cross section of the column, the followings are important properties for buckling.
  1. The cross sectional area, A.
  2. The moment of inertia of the cross section, I, with respect to the axis about which the value of I is minimum.
  3. The least value of the radius of gyration of the cross section, r.
The radius of gyration is computed from

r = sqrt(I/A)

A column tends to buckle about the axis for which the radius of gyration and the moment of inertia are minimum.
From the above picture (thin plate h x t) , we can calculate the value of radius of gyration about x-x axis and y-y axis as shown above. From calculation, we can see that ry-y is less than rx-x because t < h. Therefore, the expected axis of buckling is y-y. We can imagine that we press a common ruler with an axial load of sufficient magnitude to cause buckling, and we can easily imagine how it will bend. The formula of radius of gyration is the tool to predict this phenomenon.

Let's explore more in the next post and make excel sheet to calculate.