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# Two-way flat plate moment frame question

• To: seaint(--nospam--at)seaint.org
• Subject: Two-way flat plate moment frame question
• From: Clifford Schwinger <clifford234(--nospam--at)yahoo.com>
• Date: Tue, 21 Oct 2003 19:57:56 -0700 (PDT)

```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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