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# RE: Drift at top and rotation/curvature

• To: seaint(--nospam--at)seaint.org
• Subject: RE: Drift at top and rotation/curvature
• From: Roger Turk <73527.1356(--nospam--at)compuserve.com>
• Date: Thu, 29 Jul 1999 17:31:59 -0400

```Jim,

Just some thoughts (all assuming that a collapse mechanism has not formed):

Drift in a column in which a plastic hinge has fully formed will be
controlled by the part(s) of the structure that are still in the elastic or
elasto-plastic range, i.e., the column in which the plastic hinge has formed
will be prevented by the rest of the structure from falling over.

Moment-curvature relation will only apply to the part(s) of a structure in
the elastic or elasto-plastic range.  Once a plastic hinge has fully formed,
you are on the horizontal part of the curve and rotation can be infinite.

Isn't the drift limitation of .005h based on service loads?  Isn't the drift
limitation based on factored loads .025h and isn't this assuming
pseudo-elastic behavior?  (Pseudo-elastic behavior as I understand it is that
an elastic analysis has been performed with either factored or unfactored
loads and members have been selected so that points of maximum moments are
located where you *want* plastic hinges to form.  If my understanding is
anywhere near correct, drift would be an elastic analysis.)

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

James Korff wrote:

>>Good point.

For steel columns the solution may be more straightforward (pun
intended).

We only have to assume the point of rotation, or location of the
plastic hinge.

For concrete, it is a little more complicated - or am I missing the
forest for the trees.

The underlying reason for my question is that some existing buildings,
such as
parking structures, need to have the ends of columns confined so that
they will be able to deflect in a manner compatible with the slab
deflection during the EQ. That is why the plastic hinges must be at the
column ends, and not at the beams.

I am trying to calculate how much confinement is required to meet code
requirements.

Thus, I am trying to correlate the results of a moment curvature
analysis with the required (by code) drift at the top of the columns.

In other words, what I'm looking for is a relationship between
curvature in the plastic hinge, or hinges if there is a point of
inflection, and the code mandated drift of 0.005h.

Could it be that for such a relationship, only empirical results from
testing each individual case will give the answer?

--- Roger Turk <73527.1356(--nospam--at)compuserve.com> wrote:
> Hm-m-m.
>
> Unless I have forgotten something from Theory of Plasticity, rotation
> in a
> plastic hinge is going to continue indefinitely without increase in
> moment
> (until strain hardening range is reached) as long as the moment
> (plastic
> moment) doesn't unload into an elastic state.  (Same as elongation in
> a
> tension member stressed to yield.  Elongation will continue
> indefinitely
> without increase in load until strain hardening range is reached.)
>
> A. Roger Turk, P.E.(Structural)
> Tucson, Arizona<<

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