Buckling Equations

[ztengguy]

Just a generic question, not a project.

Why with similar columns, loads, etc does higher k factor alone control buckling, whats the controlling equation that allows that statement to be true for steel design?

 

[briancpotter]

The governing equation is the Euler buckling equation, Pi^2*E/(KL/r)^2 (Equation E3-4 in AISC). Essentially, at this point there are two possible solutions to the equations of static equilibrium, one of which has the column deformed laterally. You don't want to let your columns get to this point...

The K factor is an adjustment based on the fact that the equation only applies to a pin-pin column. Other types of ends make the column more restrained and thus require more force to buckle. So an adjustment factor is needed to make them approximate pin-pin connections.

Brian C Potter

http://simplesupports.wordpress.com

 

[structSU10]

euler buckling controls. it is defined as pi^2*E*I/(K*L)^2. Boundary conditions, brace location, and frame action all affect the K value that can be calculated using an eigenvalue analysis - either done directly with differential equations or numerical methods. It is also estimated by nomographs, but that method is crude, and can potentially yield unconservative results, mainly if a frame analysis.

What is your specific question on the matter?

 

[ztengguy]

Thanks, I thought it was Euler equation.

It was asked of me if you have a x braced frame and a moment connection frame, which will buckle first...same column, load, dims, etc.

Since a moment frame column would have K of 2, that would control corrrect?

 

[theonlynamenottaken]

Yes. A moment frame would be considered to be a "sway frame", since the top ends of the columns can translate horizontally with load, which corresponds to the higher K factor of 2. There is a very popular chart that diagrams buckling mode shapes for various column end support conditions (its in AISC as well as many steel and mechanics of materials textbooks) that illustrates this very well.