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Moment Redistribution in Concrete Frame

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richard lewis <rlewistx(--nospam--at)juno.com> wrote:
"I have a single span concrete frame I am looking at. I was wondering if
moment redistribution is applicable..."

Padmanabhan Rajendran responded:

"In continuous structures, the span moments are smaller than the support
moments. Structural collapse does not occur as soon as the the most
stressed section reaches its moment capacity. A so called plastic hinge
forms at that section and inelastic deformation begins at that section
at "constant" bending moment as the loading is increased further. The
process continues until an interior section of the span reaches its
capacity. At that point the structure is said to have become a mechanism
and is assumed to have failed.
 
If my memory of my college notes can be trusted, in continuous beam type
structures with 3 or more spans, of equal spans with each span carrying
the same magnitude of uniform loading, a plastic hinge anlysis would
show that the beam can safely carry 1.25w, where 'w' is the load
producing the largest support moment. The moment redistribution method
takes advantage of this behaviour. Thus, a beam section can be sized for
75% of the maximum support moment. ACI, conservatively, limits the
redistribution to 20%.
 
In theory, a single span frame structure does not satisfy the
assumptions involved in ACI recommendation. You may perform a plastic
hinge analysis to determine how much of moment redistribution is
possible in the frame structure you are dealing with. The redistribution
will also depend on the column base condition.
 
Rajendran"
 


Richard,
In addition to Padmanabhan Rajendran's excellent analysis above, I would
add a couple points:

First, invoking moment re-distribution basically is telling the beam to
yield and crack at the supports, or as I like to think of them, "high
shear areas."  I don't like the cracking per se, and I really don't like
it in an area of high shear.

Second, I don't know what the Code has to say about your situation, but
I would think allowing this would invalidate the sway assumptions
implicit in the usual moment-magnification equations.  And to go to a
real P-delta analysis, you've got to be pretty confident in both your
member stiffness (now cracked and varying over the length) and your
support stiffness.

Good luck.

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

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