Moment Distribution Method on a Sway Frame. 1

[StrEng007]

I was getting different answers from my FEA and spreadsheets, so I decided to refresh some hand calculation concepts to check my work.

When doing the moment distribution method to a moment frame with lateral loading (or unequal gravity loading to cause sway), we first do a moment distribution assuming a non-sway frame. Next, we do a moment distribution assuming an applied moment that will induce the lateral drift on the frame. For equal column legs with the same base fixity, these fixed end moments are equivalent. When the bases are fixed we take this as M = 6EI∆/L²

What doesn't make sense to me, is that while performing this part of the moment distribution, we assume there is no moment at the cross-member. Why is that?

See the image below:

Why are the fixed end moments for BC and CB assumed to be non-existent? Wouldn't there be an equivalent moment from BA and CD, respectively? I'm not sure I quite understand this part of the moment distribution method (as it applies to the sway portion of the exercise).

I'm good with the rest of the procedure and can get the same answers by hand as the analysis program.

 

[Celt83]

You begin with the fixed end moments, enforcing a unit horizontal displacement at the top joints does not result in any fixed end moments of the beam as it's ends remain at the same level. One unstated simplification that tends to occur in the Moment Distribution Method (MDM) is axial deformation is ignored.

This is one of the best books on the MDM in my opinion: Moment Distribution by James Gere

 

[StrEng007]

in any fixed end moments of the beam as it's ends remain at the same level.

Umm... I guess I'll have to think about that one.

 

[Celt83]

 

[Ntaco structural]

Please review my video

https://youtu.be/cT7uwq2rs5k?feature=shared

 

[StrEng007]

Celt83,
I see, that makes sense. Thank you.

 

[StrEng007]

Celt83,
I spent some time working with the single-bay moment frame and your input helped a lot, thank you. I've got it down now and all my results comply with my analysis programs. I forgot how much accounting goes into these things when you're doing it by hand. It sure makes the portal frame method seem so attractive (yet lacking due to stiffness distribution).

Do you know if that book you referenced contains examples for a multi-bay moment frames with the moment distribution method? What I'm not sure about is the sequence to distribute and carry over for each member. With a single bay frame, it goes: column one, cross-beam, and column 2. However, what if you have 2 bays? Is that now : column 1, cross-beam 1, column 2, cross-beam 2, column 3?

 

[Celt83]

It does have a multi-bay example as well as a multi-story example:

 

[StrEng007]

Great. I'm not familiar with the link you sent me. Is the snapshot above your own personal copy, or does the archive site let you download a PDF version?

 

[Celt83]

I believe you can view a copy on the archive site after logging in (accounts are free). I have a hard copy that I found on ebay a few years ago for pretty cheap ($28), I only see a copy on Amazon currently for about $100. If it really interests you keep checking Abebooks, Ebay, etc. for a copy I've seen it as low as $12 in the past.

 

[StrEng007]

Thanks for the heads up.