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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: "Ed Workman" <eworkman(--nospam--at)fix.net>
• Date: Thu, 29 Jul 1999 15:43:18 -0700

```-----Original Message-----
From: james korff pe pmp <seaoc(--nospam--at)yahoo.com>
To: seaint(--nospam--at)seaint.org <seaint(--nospam--at)seaint.org>
Date: Thursday, July 29, 1999 1:03 PM
Subject: RE: Drift at top and rotation/curvature

>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.

YES
>
>. That is why the plastic hinges must be at the
>column ends, and not at the beams.

They "must" be at the columns only if (as is usual) the beams are stronger
than the columns

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

All the stuff below is good to work through to gain understanding, but the
problem could end at this point for new work.  The code is quite long winded
on what and how to calculate the effects of drift. But keep reading. It then
sez if the columns are overstressed provide confinement ties in accordance
with (the provisions for columns that ARE part of the lateral system, that
is ductile frame columns) section such and so.   Now conversely, by
providing confinement as specified by the code, the cross sections are
DEEMED capable of sufficient inelatic rotation and your remaining task is to
determine the value of the plastic moment at each end, addemup and divide by
the height to obtain (the maximum probable) shear in the column and verify
that the ties proportioned for confinement provide enough shear capacity.
>
>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.

But BOTH ends of the column are exposed to the same problem. The column is
subject to double curvature ( elastic, cracked section) and potential
plastic hinging at each end. If you are assuming the bottom (at a footing)
is free to rotate then go back and look at the collapse of the "pinned base"
columns at Cal State Northridge.

>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.

HUH???? What mandated drift??? that number looks a lot like the old elastic
drift LIMIT for design. Even concrete moment frame buildings are not
designed to drift limits, since strength of things like joint shear govern.

IF you are going to provide external confinement to allow plastic rotation,
add enough to make this a simple problem: the rotation in radians at the
face of the joint( which you can easily calculate fom strains at the
extremities), times the height is a conservative estimate of drift
capability. You can refine for sections of large difference at the two ends
by determining a point of inflection , use those two different lengths for
"height" in the above calculation and summup, but why bother? Rotation/drift
is increased by adding the effects of hinge length, curvature between the
ends etc., but if a short conservative calculation works why beat it to
death?

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

If this were rocket science maybe, but it's concrete and rebar who's
properties are certainly not exact.  You need Paulay & Priestly, which will
get you thru the hinge length hangup

```