Cb bracing at inflection points

[kennyb04]

I have continuous beams running over columns (with shear only splices) which creates an inflection point within the beam over the column. My understanding is to not use the inflection points as the unbraced length with Cb = 1 but rather to use the entire beam span as the unbraced length and then increase the moment using Cb.

In calculating Cb for the bottom flange in compression, do you use both the positive and negative moment values in the equation? For example, if the maximum bending in the beam is the positive moment, do you use the absolute value of the positive moment or only consider the maximum of the negative moment (which would be at the column)?

Additionally, if for instance, the moments Mb and Mc are in the positive bending portion of the beam, but you are calculating Cb for the bottom flange, do you still use the moment values from the positive side of the beam or would you set any value from the positive side equal to 0 in the equation?

 

[r13]

This thread may help. Link

 

[KootK]

I'm going to assume that your top flange is braced at a relatively short interval by transverse framing or deck. If that's the case, I'd recommend the following for AISC LTB checks:

1) Check top flange, positive bending LTB based on:

a) The max positive moment within the span,

b) Unbraced length = spacing between transverse framing (or zero if continuously braced) either side of the maximum moment.

c) Cb per it's definition if you feel that the exercise is worthwhile. Usually it's not with such a small unbraced length.

2) Check bottom flange, negative bending LTB based on:

a) The max negative moment at the ends.

b) Unbraced length = beam length between supports (assuming no other physical bracing).

c) Cb per it's definition which will account for the fact that not your entire bottom flange will be in compression when the bottom flange buckles in it's first mode shape.

 

[KootK]

Note that my comments above were in reference to the portion of the main beams between supports and not the cantilevers or the suspended simple span.

 

[dik]

My favourite for plastic design and using end plate connections to transfer small moment as well as shear... splices at about 1/7 the span and use q*l²/16 for the design moment (except end spans)... no need for alternating load patterns... and HSS columns.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[kennyb04]

Thanks for the comments so far. My problem is in regards to the negative moment capacity over the column in an existing building. The new use of the building will change the Risk Category to III causing a slightly higher snow load I am checking the existing structure for. After looking through some of the Yura equations/papers, does the code indicate anywhere an acceptable use of the Case II, Cb = 3.0-(2/3)(M1/M0)-(8/3)(Mcl/(M0+M1)) equation, or does it just come down to engineering mechanics?

My understanding is the Case II equation requires the top flange to be continually braced. If I am using the full beam length as the negative unbraced length, and joists with decking above are spaced at 6'-8", would you consider that spacing to be continually braced or would decking need to be attached directly to be continually braced?

Using the AISC equation F1-1, I get a Cb of around 1.31 which is not high enough to pass the existing beam, however, with Yura's Case II I get a high enough Cb to pass the beam without adding new lateral support throughout the building. I'm just trying to determine if I can justify using Yura's alternate equation for this condition and per code.

 

[KootK]

does the code indicate anywhere an acceptable use of the Case II, Cb = 3.0-(2/3)(M1/M0)-(8/3)(Mcl/(M0+M1)) equation, or does it just come down to engineering mechanics?

Engineering mechanics. I think that Yura wrote much of the AISC standard as it pertains to LTB so I wouldn't sweat that.

If I am using the full beam length as the negative unbraced length, and joists with decking above are spaced at 6'-8", would you consider that spacing to be continually braced or would decking need to be attached directly to be continually braced?

I suspect that the joists at 6'-8" would be enough but it will depend on how long your beam is. I'd want the beam to be getting braced at at least 1/3rd points, preferably 1/4 or 1/5th points.

You might consider doing an FEM buckling analysis using something like the free software Mastan2. It's not all that time consuming and the effort required may be justifiable for an existing situation where you're hoping to get it down to "do nothing".