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Reinforcing existing steel members

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Keith,
There's been a lot of good discussion on this topic. 
Let me throw in my two cents' worth.

A few years ago, the firm I was at did a lot of work
in old facilities, removing and moving columns.  We
used the conservative method you describe (subtracting
stress already on the column) to account for
pre-existing or built-in load.  We suspected it was
needlessly conservative.

I think everyone agrees that for short columns, the
amount of load pre-existing on the core column is
immaterial.  The original column could be at incipient
yield; it will not affect the total capacity of the
reinforced column.  I asked Ted Galambos about this
and he concurred.  When I asked him about longer
columns he recommended the article by Brown (AISC 4th
qtr 1988).

Rick Drake wrote that if the column is long enough to
experience buckling (inelastic or elastic), its
critical buckling stress will be a function of kL/r,
not initial load.  I agree with this for the elastic
(Euler) buckling case.

The article by Brown disagrees with this for inelastic
buckling.

The article by Tide (AISC 4th qtr 1990) disagrees with
Brown.  (Actually, Tide seems to disagree with
everyone, but he can get away with it.)

I disagree with Tide, because if the core column has
significant load when reinforced, in the
inelastic-buckling range the core will yield under
lower total load than one with no built-in load.

I also disagree with Charlie's statement that
redistribution will take place, or rather the
implication behind it.  (Sorry, Charlie.)  Once the
core has yielded, its contribution to strength (its
resistance) is constant, not linearly increasing as
assumed by the code equations.  OK, so that's when
redistribution takes place; but the core's
contribution has ceased to increase with increased
bending (buckling), and the reinforcement's
contribution is still only increasing linearly with
increasing strain.  The total of these, the total
resistance, is thus less if the core was carrying
significant load before reinforcement.

Anyhow, Brown's method gives results which are
slightly more conservative than the Tide/Carter camp
would arrive at.  Admittedly it does this at the cost
of very complex mathematics; it always takes me at
least an hour just to re-read the article and
re-figure out what he's saying.  But, I agree with it
philosophically more than I do Ray Tide's analysis. 
Besides, Ted Galambos said it was the way to do it.

Mike Hemstad, P.E.
TKDA
Saint Paul, Minnesota

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