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RE: Two-way flat plate moment frame question

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I am sure that if you ask any two engineers they will disagree as to an
appropriate "effective width" of slab beams to be used for lateral
analysis.  Your best bet is to go out and look in academic databases.
There you will find a variety of options to choose from.  We use a set
of recommendations similar to a paper by Jacob Grossman ACI v94, no 2
(march-april) 1997.  

There is no "correct" method.  Most do not have allowances for
reinforcing etc and are just geometry based.  

The two things to worry about are strength and serviceability.  For
serviceability you just need a method that is proven to be close.  A
variation of Grossman's formula have been used to design several hundred
highrise buildings in NYC (+30 stories).  Whatever your choice make sure
it is justified by experiment.  Computer modelling, especially elastic
finite element, does not well describe the stiffness of the system.

For strength, things are a little easier as your guess is, to some
extent, self fulfilling.  You end up putting in reinforcing based on
your choice of width and your "real" effective width depends on the
amount of reinforcing (stiffness) you provide.  

Punching shear is the worry.  Be careful and be conservative.

The worst thing you can do is ignore that there is a lateral slab beam.
Presuming you have reinforcing, the beam is there, it will attract
moment and it will increase punching shear stresses.  If you don't use
it for your lateral system, or the code won't let you, that is your
choice.  But you should assume something for a punching shear check.

Craig

-----Original Message-----
From: Clifford Schwinger [mailto:clifford234(--nospam--at)yahoo.com] 
Sent: Tuesday, October 21, 2003 10:58 PM
To: seaint(--nospam--at)seaint.org
Subject: Two-way flat plate moment frame question


I have a question about "slab-beams" in non
post-tensioned two-way flat plate moment frames.

Section 13.5.1.2 in ACI 318-02 has this somewhat vague
statement: "For lateral loads, analysis of frames
shall take into account effects of cracking and
reinforcement on stiffness of frame members."

The commentary doesn't really clarify anything except
to say "For nonprestressed slabs, it is normally
appropriate to reduce slab bending stiffness to
between one-half and one-quarter of the uncracked
stiffness."   One-half to one-quarter the stiffness of
what? The full tributary width of the slab framing
into the columns on the moment frame?

The commentary statement seems to imply that when you
have building with square column bays (let's say 30' x
30') then the moment of inertia of the equivalent
"beam" in my moment frame is equal to 0.25 x "I"gross
where "I"gross is the gross  moment of inertia of
entire tributary width of the floor slab framing into
the column (i.e., a 30' wide "slab-beam"). 

This seems to agree with section 10.11.1 where
simplified approximate moments of inertia for various
moment frame components are listed.  For flat plates
and flat slabs "I"effective = 0.25 x "I"gross.

What isn't stated is a clear definition as to the
width of the moment frame "slab-beam" member for which
"I"gross is computed.  Is the width of the "slab-beam"
equal to the full tributary width of the slab that
frames into the columns in the direction for which the
moment frame is being analyzed - or is it something
less?

If the full tributary width of slab is considered as
the "I"gross beam width then how is the column
stiffness (or beam stiffness?) modified to account for
the torsional flexibility of the slab-to-column
connection?  Is the torsional flexibility accounted
for in the "0.25" factor that's applied to "I"gross? 
I'm figuring that maybe the "0.25" factor is comprised
of the product of two numbers - 0.5 x.0.5 = 0.25.  The
first "0.5" being an adjustment that modifies the
effective width of the "slab-beam" to one-half the
actual slab width (this modification reduces the beam
width to account for the torsional flexibility of the slab-to-column
connection).  The second "0.5" factor may be an adjustment for
converting "I"gross to "I"effective.

I don't want to overestimate the stiffness of the
moment frame beams, but then again I don't want to underestimate the
stiffnesses of the slab-beams either.  If you underestimate stiffness of
flat-plate moment frame slab-beams, the column k-factors will quickly go
through the roof (due to the wimpy beams)!

Does any of this make sense?

TIA,

Cliff Schwinger


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