Structural Analysis

“Due to imperfection, there’s no truly straight column in real life.”

Thus the column will buckle at some critical load whereas the compressive force exerts exactly through its geometrical center.

Leonhard Euler, Swiss mathematician, invented his equation that presents the relationship between buckling load and stiffness properties of the pinned end column:

But the thing is Euler’s formula works well with LONG column only.

So how to determine type of the column? (Of course, not purely by its length!)

Let’s talk the easy way.

Column length defined by its failure mode.

Wait a minute! Slenderness ratio takes important part in this story, doesn’t it?

Yes, it does.

Slenderness ratio is the ratio between effective length of the column (kL) and its radius of gyration (r).

The value of ‘k’ depends upon support condition on column ends.

Consider this free body diagram of column buckling.buckling_derive