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RE: Lateral Brace Deflection

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Mark,

   >My reading of S&J says that  Kreqd = 2*Kideal does not require an
   >additional factor of safety.  The multiplier of 2 is a
   >function of the
   >initial crookedness and does not vary based on the loading.

According to the 2ed, "When service loads are used for P in the working
stress method, a factor of safety FS must be applied to the stiffness
requirement; thus in working stress design where service load P replaces Pcr
in all equations, Kreqd=4Kideal"

The strength requirement, as they show, is unchanged because Qu is divided
by FS, just as Pu is.

However, the 4ed states, "For ASD a factor of safety FS must be applied so
that the service load P may be used instead of Pcr...however, the stiffness
required will be the same in ASD as in LRFD...Kreqd=2Kideal"

So, the FS application to convert Pu to Pcr is swapped.  I thought I
understood it the first time.  Now I will have to dig into the 4ed, too.

I also noticed that the derivation of the Abrace formula is conflicting,
even though the results are the same.  2ed starts with AEb/Lb =
2*beta*pi^2*Ec*Ic/Lc^2, which I thought was wrong.  But the 4ed shows the
same formulas, but Lc is not squared...which I think is also wrong.
K=Beta*Pcr/L = Beta*(pi^2*E*A/(L/r)^2)/L, so the L term should be cubed.
9.13.20 (4ed), the next step, shows this - as does 9.11.20 in the 2ed.



   >You should consider not only the bending
   >stiffness of the beam and the diagonal brace but also any other
   >flexibilities in the bridge structure that would have a
   >significant impact on this term.

I'm dropping the (continuous) outrigger below a deck beam.  It will hang
from the bottom chord of each truss.  The deck beam will be very stiff.  I'm
debating weather or not to weld them together to make a very deep built up
member...I'm certainly open to any advice on how to look at that...I would
think I could check the new 'I' for deflection, 'S' for stress.
Compactness, shear. LTB sound like issues I may have to consider carefully,
though...it's getting to the point where engineering time is not going to
pay for itself on that (although I find it interesting).  With L/800 there
is clearance between the outrigger and the beam enough so they do not
interfere.

   >Assuming that the transverse beams contribute to the
   >bracing of  chords for each of the trusses I would be inclined to
calculate the
   >stiffness by imposing a unit displacement inword for both truss chords
   >at the same time.

Agreed, but I think the worst case (hair splitting here) is when the trusses
buckle outward because it works with the dead load of the outrigger.  I am
also adding 0.3 wind, in accordance with AASHTO load combinations, I was
hesitant about the low factor, but it seems 100 mph design load in an 80 mph
area, with the consideration of 35 psf as if enclosed, when it is wide open,
is conservative enough.

   >vehical loads on the transverse beam that produced
   >deflections in the chord consistent with the buckling shape you are
trying to
   >suppress...these loads could be thought of as increasing the initial
crookedness
   >of the member and would not need to be considered when considering the
availible
   >stifness.

I was thinking about that crookedness FS in this case, since the outrigger
is independent, as being not required...at least to the full extent.  Since
my brace is providing 18 times the axial stiffness required, and the
outrigger is independent, the crookedness would have little bearing.  I
don't think initial crookedness of the beam would impact stiffness.
However, as Paul Ransom pointed out, construction tolerances still may be a
factor...with slip critical bolting, though, the brace should engage
properly...

   >Hopefully you will be able to show that the transverse
   >deflection of the truss chord is not significantly influenced by other
loads
   >and that the overall flexibilities of the bridge do not significantly
   >influence the stiffness of your brace.

Yes, this is the case, in my view.


Regards,

Ed Fasula