cantilevered beam backspan- unbraced beam length

huangyhg

cantilevered beam backspan- unbraced beam length
- have several cantilevered steel beams which naturally have negative moment over a portion of its backspan.
- the top flange is continuously braced by a composite slab. however, the bottom flange (currently) is unbraced.
- trying to determine what unbraced length should be used when checking if the beam has the capacity to resist the negative moment.
- attached you will find a partial framing plan, bending moment diagram, and a blow up detail which illustrate the condition and the unbraced length i'm trying to determine.
any help you could provide on this would be greatly appreciated.
thanks
good question, chief45.  i have a feeling you are going to get a few different answers from the forum. theoretically, it is a difficult question to answer, but there are some safe routes to take.
the safest route is to brace the bottom flange at the tip of the cantilever, at the column and near the point of inflection.  then the unbraced length is the length between braces.
if you brace the bottom flange only at the column and not at the other two points, then in my humble opinion, the unbraced length is from the point of inflection to the tip of the cantilever.  i suspect others will disagree.
if you do not brace the bottom flange at the column, your structure is unstable and prone to lateral buckling.  it is not clear what the unbraced length is or even if it can be determined.
  
ba
i would provide tranverse beam at the column to make it a fully braced point. then consider the cantilever, and the back span seperately. otherwise, ba's method seems logically correct.
according to aisc 360 6.3.1
"lateral bracing shall be attached to both flanges at the brace point nearest the inflection point for beams subject to double curvature bending along the length to be braced"
i guess the nearest brace point for you is the column if you dont add any other brace point and that is also the spot that has both flanges braced, so i guess the unbraced length is the whole backspan in your case.
if you add full-depth stiffeners at the inflection point than the unbraced length is from inflection point to column.
but baretired is right you are going to get alot of different answers.
i don't think i would use the whole length as lb for negative moment, but who knows.
i believe that an inflection point cannot be considered as a braced point. right?
i would say that an inflection point should not be considered as a brace point.  this is explicitly stated in the 13th edition aisc manual and in various texts.  the unbraced length should be the distance between actual brace points for the bottom flange.
what are the beams supporting?  is it concrete filled metal deck?  if so, provide shear studs and a full depth stiffener near the inflection point and this will brace the section there.  otherwise, the unbraced length is the length between the columns.  you can get a lot of help from cb for this situation.  maybe that will solve your problem and you won't have to worry about unbraced lengths.  i just did a back-of-the-envelope check and using cb (i'm getting about 2 without diving too far into the moment diagram) you can use the full plastic moment, so unbraced length shouldn't be an issue.  you really only need cb to be about 1.3 to get up to mp.
i agree with slickdeals and structuraleit that an inflection point is not a braced point.  but it does represent the extent of compression in the bottom flange.  if the bottom flange of the beam is braced only at the columns, then the length subjected to compressive stresses is the backspan length plus the cantilever length and that is the length i would consider unbraced.
because the inflection point can move under checkerboard loading, its location should be determined with reduced live load on the span and full load on the cantilever.
in my opinion, your cantilever length of 7'-6" is too long compared to the span.   
ba
guide to stability design criteria for metal structures, t.v. galambos ed., p. 168, mine is 4th. ed.
i agree with ba retired here, but do consider inflection points as "braced" points for exactly the same reason - the compression is no longer in the bottom flange - exactly what what we are bracing for the compression stresses seen.   
mike mccann
mmc engineering
chief45,
i attach a sketch showing my version of unbraced length and buckled shape of bottom flange when braced only at the columns.
ba
i always assume the unbraced length is the entire length of the backspan, and i do use the cb factor.
daveatkins