Column unbraced length

[SE80]

I am analyzing an existing warehouse with columns that are 30' high to the roof. Problem is the columns are made up of 3 different sections. The first 10' of the columns are W8, the second 10' are HSS 8x8 and the last 10' are W8 again. What would be the un-braced length for each 10' section if the only lateral supported is at the roof.

 

[ToadJones]

This is bizarre.
I didn't think architects designed warehouses.

I guess in a way you are looking at a step-column.

 

[Michel60]

Good morning SE80,
I believe in trying the simplest thing first. Would the column satisfy your design requirements if it were only a W8x section? If not as TJ suggest it's a stepped column of some sort. I looked at the "Guide to Stability Design Criteria for Metal Structures" but the references there where appropriate to reducing columns steps, not smaller-stronger-smaller. There might be something out there on non-prismatic shapes to help you find a direction.

regards,
Michel

 

[WillisV]

Just analyze it with the direct analysis method. No issues with separate shapes. Model it with an initial sinewave bow equal to L/500, split it into several segments, reduce the stiffness, run a second order analysis - done.

 

[structSU10]

I would think finite difference approach would be a good way to go to determine the K factor for such a thing. Use a 4 pivotal point, then a 7 pivotal point approach, with richardson extrapolation, to get your value. This is also assuming the intermediate column connections are sufficient for the second order loads, most likely needing to be rigid connections.

I'm attaching a paper on finite difference of non-prismatic columns to give an idea, but this case is simpler.

 

[JAE]

Are there any wall girts attached to the column? If so they might provide bracing in their longitudinal direction.

I'd second WillsV's recommendation too.

 

[ToadJones]

and dont forgot your notional loads

 

[structSU10]

I just looked at a similar problem, and if you assume the weakest section for buckling, as pointed out by Michel60, you will be conservative as K would tend to go below 1 (as long as pin-pin is a sufficient assumption).

What WillisV is saying would be appropriate as well. You can check the connection for whatever second order forces from the analysis to make sure they are sufficient as well.

 

[fancypants]

I would look at it as a weak axis W8 unless the section modulus is greater than the tube. I think i would be more concerned with how they are stuck together.

 

[WillisV]

@Toad - no need for notional loads if you model the deformed shape as I suggested.

 

[ToadJones]

Willis- ahh yes, good point.

 

[JoshPlumSE]

What you describe sounds very similar to a stepped column or a tapered column. There is a "hand-calc" method for solving this type of problem called the "Method of Successive Approximations". It's described in the AISC Design Guide 25 for design of web tapered members. And, also in Timoshenko and Gere's Theory of Elastic Stability.

Though I'd have to say that it is probably easier to set up, as WillisV suggests, a computer model and solve it using hte direct analsyis method.

 

[SE80]

Thanks everyone for the responses.

Regarding the direct analysis method, can you analyse it in RAM Elements?

 

[asixth]

Are you sure the middle is a hss or have plates been welded to the flange of the W8 to create a box section in the middle. It is an interesting concept to increase the ry locally over the middle third but i guess it has merit because thats where buckling would occur. May need to solve this one by first principles, timoshenko and gere would be the textbook i'd consult too.

 

[TLycan]

If you want to get the K-factor for the non-prismatic section I do the following by using FEM program:

I model the column as a hinge roller , roller in the gravity direction (to use K=1 in Euler equation).
I add a load on the top of the column and I run the bucking analysis
I get the Euler bucking load
From the Euler equation I get the RIGHT Inertia of the non-prismatic column

From then I can use the monograph or what ever method to get the K-factor