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# Fw: Application of 3Rw/8 - How to apply

• To: "seaoc list" <seaint(--nospam--at)seaint.org>
• Subject: Fw: Application of 3Rw/8 - How to apply
• From: "T. Eric Gillham" <gk2(--nospam--at)kuentos.guam.net>
• Date: Thu, 24 Sep 1998 14:58:23 +1000

```Dennis:

I know that you asked for a reply only if I thought you were off-base, but
again, I feel that expected displacements are an important aspect of
seismic design which are often times overlooked (Northridge parking
structures?).

Just to explain a little more clearly what I meant:

The design base shear is arrived at by reducing the expected base shear by
some reduction factor, which in this particular case is Rw=6.

If the expected base shear has been reduced, then the actual deformations
which will be imposed on the structure during the real earthquake will be
greater than those which an elastic analysis, using the reduced base shear,
will show.  Let's call the displacements:

delta-er   Displacement from an elastic analysis using reduced base shear
delta-m   Displacement from an elastic analysis using magnified base shear
delta-y    Displacement at which the the structure forms a yield mechanism
(assuming
minimal redistribution to parallel systems for the sake of
simplicity)

Presumably, your frame has delta-y > delta-er.

The code expects yielding of some portions of the frame, preferrably the
girders.  Therefore, it is more than likely that

delta-m > delta-y, at least for your girders.

In my opinion, UBC94 section 2211.6.2 is REQUIRING that

delta-y(JOINT) > delta-m

If all of these assumptions are correct, then

delta-y(joint) > delta-m > delta-y (girder)

Now, looking at UBC94 section 2211.7.1.1, for a SMRF, the code requires
(among other things) that

delta-y(joint) > delta-y(girder)

which is the same relationship as above without the delat-m term.

IMO, the code DOES NOT require that delta-y(joint) > delta-y(girder)
DIRECTLY for an OMRF because of the Rw=6 factor (as opposed to Rw=12 for a
SMRF).  The code expects minimal yielding in the OMRF (as evidenced by less
reduction of the base shear) and hence does not require the stringent
detailing and relative member strength checks.  Going back up to the
relationships above, for an OMRF, it is POSSIBLE that

delta-y(girder) > delta-m

If this were the case, and the code required that

delta-y(joint) > delta-y(girder)

the joint strength requirements would be stringent indeed!  So instead,
the code uses delta-m as the limit.  Of course, some people may say that
3(Rw/8) is not necessarily accurate nor conservative enough, but that's a
whole other discussion.

So, in the end, the way I see it anyway, the code IS requiring that the
CONNECTION remain elastic, and it uses the delta-m limit as the benchmark.
My previous discussion about the girder yielding or not yielding, and this
being taken into account when determining the joint forces, was for the
following reason:

If it is the case that

delta-y(girder) > delta-er

and

[delta-y(girder)/delta-m] = .5 let's say,

then why design the connection for delta-m?  Once delta-y(girder) is
reached (delta-y calculated accounting for overstrength of the girder and
setting phi factors to 1.0) then that is ALL the moment/shear that the
girder can generate in the joint.  Proceeding to design the joint for
delta-m, and the associated moments/forces, while conservative, is not
really necessary, because those moments/forces CANNOT be generated.

Regarding the .005H limit (and the .0025H limit which I can't seem to find
in the code), those limits are for the deflection calculated using the
REDUCED BASE SHEAR.  The expected deflections during the actual seismic
event will be

delta-m=2.25*delta-er

at least according to the code.  delta-m is what should be used to check
the performance of the (presumably) non-ductile masonry elements, NOT
delta-er for reasons explained above.
So, my question was as to whether the rest of your structure was checked
for 2.25*delta-er (which is delta-m).

Hope this makes my previous post a little clearer.

Gotta get back to work!

T. Eric Gillham PE
----------
> From: Dennis S. Wish PE <wish(--nospam--at)cwia.com>
> To: seaint(--nospam--at)seaint.org
> Subject: RE: Application of 3Rw/8 - How to apply
> Date: Thursday, September 24, 1998 11:54 AM
>
> First, thanks to all who responded - especially Karim who was as specific
as
> I needed. I want to respond to Eric who raised some very good points.
> Steel is not my strong point since I design very few frames every year.
> However, my opinion is that the stress in the joint is increased by
3Rw/8,
> not to insure that the frame stays within it's elastic range, but to
insure
> that the connection is adequate for - in this case - 2.25 times the
stress
> applied between the girder and column.
> In this instance - an earthquake retrofit - the frame will only deflect
the
> by the amount of the applied short-term load. This is an Unreinforced
> Masonry building and the frame lies between columns, not piers.
Therefore,
> the frame deflection need only max out at 0.005H (compared to 0.0025H for
a
> steel frame in the plane of a wall with masonry shear piers).
> I might be misunderstanding your comments which I interpret as designing
the
> frame with the expectation of a maximum deflection of 2.25 times the
actual
> story drift. I think we are saying the same thing but comming from a
> different direction based upon stiffness (increasing the capacity of the
> connection) verses deflection which can not exceed the load applied to
it.
> Following the AISC 9th edition Welded Moment Frame (taking into account
the
> SAC revisions to the detail), each step using the increased moment and
shear
> will compare against the allowable stesses of the girder and column
sections
> used.
>
> So, I guess what I am saying is that your concern about the capacity of
the
> materials used is checked and compared within the AISC prescriptive
method
> as long as you start by increasing your maximum moment and shear by
3Rw/8.
>
> You need not respond unless I am way off with my thinking. In that case I
> would appreciate you (or anyone) explaining this to me so that I can
> understand (in as simple a terminology since I've been out of school too
> long) what the intent was behind the 3Rw/8 if different from how I
> explained.
>
> Thanks again for everyone's input.
>
> Dennis S. Wish PE
> -----Original Message-----
> From: T. Eric Gillham [mailto:gk2(--nospam--at)kuentos.guam.net]
> Sent: Wednesday, September 23, 1998 4:23 PM
> To: seaoc list
> Subject: Fw: Application of 3Rw/8 - How to apply
>
>

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