K-factor Selection

[aswierski]

First, some background info...

Our client's standards state that vertical fixed ladder supports shall not exceed ten feet. Upon inspection of already-installed ladders on this particular site (designed by other firms), we noticed that many of the actual support spans exceed ten feet (approx. 12'-20' spans). I have been asked by the client to analyze the ladders to see what our maximum allowable spacing really is.

Now, the part I'm confused with is the selection of a reasonable K-factor for the weak axis slenderness. I know that the base is fixed and the top is pinned per my FBD on sheet 2 of the attached pdf, giving me a K value of 0.8. That makes perfect sense to me for the strong axis, but along the y-axis (same axis as rungs) I'm not sure what to use. In my attached calcs I used 0.8 for K for both directions, but I think this may be over-conservative as the rungs are essentially acting as braces in the y direction. What are your thoughts?

 

[aswierski]

Another few things to add...

The rungs are spaced at 12" O.C. and are welded to the side rails. I also included two channel sizes for the side rails (C3x4.1 and C3x5) in my calcs because those are the two shapes that are installed in the field.

 

[strucguy]

I would use K = 1 and L = 1'-0" for buckling about weak axis. But, I seriously doubt if that controls the strength.

 

[aswierski]

@strucguy:

That was my first inclination. Doing that would result in the strong axis governing the max support span.

 

[JAE]

Check out AISC 13th edition - spec section Appendix 6.

I would agree that you would have one check be k=1.0 and L = 12" for the individual channel, but overall, the whole latter could bend between ladder connections to the supporting wall or whatever.

This makes the two channels work together so you might have a 20 foot value for L and a k = 1.0 with two channels working together. This would probably control.

You could assume that all the rungs created a sort of Vierendeel truss and created a stronger condition - to verify that I guess I'd do a second order analysis on the ladder.