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Precomposite Stresses in Reinforced Steel Sections

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Matt Muhlenkamp wrote:

"When strengthening a steel section (an open-web joist, beam, or girder
in my
most recent case), I always did the following (ASD):
1. assume a more or less permanent load (mainly the DL taken by the
member),
and compute the stresses and deflection due to this load on the original
section.
2. compute the additional stresses and deflection based on the
reinforced
section (due mainly to LL and any additional DL - like permanent
mechanical
equipment)
3. add the two together (at appropriate points on the section) to
determine
the total stress, and compare with allowable.  If the section is
overstressed, then require some load removal prior to reinforcing (e.g.
jacking to remove some DL).
 
Recently, an engineer in my office told me he only checks the 1st
condition.
In step 2, he puts the entire DL + LL on the new reinforced (i.e.
increased)
section, and doesn't consider the locked in stresses due to the
permanent
load on the original section.
 
While I know AISC ASD allows this for composite beams, it seems this is
based on certain approximations and simplifications.  I just think that
it
cannot be correct in an elastic approach to the problem, especially when
considering things like coverplating, etc.   (I know using a plastic
section
approach would make a big difference, but I only talking elastic in this
case)
 
Any thoughts?
  
Thanks,
 
Matt"


Matt,
I have a couple thoughts on your question.  First of all, remember that
in truth elastic stresses are only an average of the stresses that
actually are present in a piece of steel.  Residual stresses may range
up to yield, which if you think about it is a big part of the reason for
the rounded corner at the yield point on a stress-strain plot.  So,
working stress design is just a way (albeit a nice simple way) of
assigning a satisfactory safety factor; it isn't necessarily an accurate
representation of what is actually happening in a piece of steel.

So, the idea of using the entire composite section to resist all loads
isn't as bad as it at first seems, because at ultimate it will all
redistribute, and WSD is, as I alluded to, merely a convenient means to
apply a factor of safety to the ultimate strength.  This logic works AS
LONG AS your governing failure mode is yield.  If your section is
unbraced, or inadequately braced, or has slender bits subject to local
buckling, then all bets are off.  Also, of course, any deflection
calculation based on all the load on the composite section is garbage,
and often we care as much about deflection as we do about strength.

This all being said, I still can't bring myself to do it.  I still put
DL on the original piece, apportion LL between the two based on
stiffness, and end up throwing a lot of steel at it.  I know it's
conservative, and nice and stiff.  I justify it by reminding myself that
the steel is a very small part of a retrofit like this; the fit-up and
welding represent the vast majority of the cost.

HTH

Mike Hemstad, P.E., S.E.
TKDA
St. Paul, Minnesota

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