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# RE: Drift at top and rotation/curvature

• To: "'seaint(--nospam--at)seaint.org'" <seaint(--nospam--at)seaint.org>
• Subject: RE: Drift at top and rotation/curvature
• From: "Fredericks, Douglas/SAC" <DFreder1(--nospam--at)CH2M.com>
• Date: Thu, 29 Jul 1999 15:24:20 -0600

```In the bridge world, at least in California, we do this all the time.  In
fact, the days of checking seismic forces appears to be over.  Now
(theroretically, at least) we check only column displacements and then make
sure the structure is strong enough to handle the forces generated from the
column plastic hinging.

The drift is made up of two things, the rotation in the plastic hinge times
the plastic hinge length, and the elastic deflection of the column from the
top of the plastic hinge to the bottom of the bridge soffit (or to the
bottom of the slab in your case).

The moment curvature curve is simplified into a bi-linear curve.  The slope
of the first part will get you the elastic effective stiffness (EI).  Using
P/Delta = 12EI/L^3 (for a fixed-fixed) column will get you the elastic
displacement.

The second part of the curve represents the curvature in the plastic hinge.
The curvature after yielding times the plastic  hinge length gives you the
plastic deflection.

I'm probably not explaining this very well, its a little complicated for an
email.  Another reference to check, besides Priestley and Seible, is the
Caltrans Seismic Design Criteria,  which will supposedly be placed on their
website soon at http://tresc.dot.ca.gov/earthquake_engineering/oee.html .

> -----Original Message-----
> From:	james korff pe pmp [SMTP:seaoc(--nospam--at)yahoo.com]
> Sent:	Thursday, July 29, 1999 1:01 PM
> To:	seaint(--nospam--at)seaint.org
> Subject:	RE: Drift at top and rotation/curvature
>
> 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
> >
> >
>
> ===
> James Korff, PE, PMP
> Structural Composite Consultants
> 985 E. Hillsdale Blvd, Suite 128, Foster City, CA 94404
> Phone 650-796-8997 / Fax 650-345-1355
>
> "May the DISPLACEMENT be With You !!"
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>

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