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RE: Post yielded beam performance

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Jerry D. Coombs wrote:

. > Be careful here.  The elongation to failure is in the 20% to 24% range. 
. >  But the ultimate strength is reached in the 12% to 16% strain range. 
. >  Beyond that point, the slope of the stress-strain curve is negative.  As 
. > loading proceeds up the new curve to a point that exceeds the new maximum 
. > point on the curve, major failure can proceed very rapidly because all of 
. > the strain hardening has been used.
. > 
. > JDC
. > 

In my original post, which Jerry Coombs refers to, I have assumed that the 
beam has been unloaded.  When steel has been stressed beyond the elastic 
limit and has been unloaded, the unloading stress-strain curve will parallel 
the original stress-strain curve between zero stress and the elastic limit, 
with the only resulting effect being that there is a residual elongation.  
Reloading the steel will have the stress-strain curve retracing the unloading 
curve up to the elastic limit, and then tracing along the stress-strain curve 
for steel which had not been unloaded.

If required elongation is in the 20% to 24% range, the ultimate strength has 
to be at a strain greater than this amount.  For A36 steel, strain at yield 
is 36,000/29,000,000 = .0012, or .12%, considerably less than the 20% 
elongation required.

A. Roger Turk, P.E.(Structural)
Tucson, Arizona