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Re: Effective Section - ACI 318

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These values for the "effective" moment of inertia are only used in
section 10.11.1 of the ACI 318-02 code (at least to my knowledge).  They
are listed as "permitted" values to be used when doing second-order (i.e.
magnified moments) analysis, but are also generally used as a reasonable
approximation (depending on loading level) when doing general analysis of
frames for things like deflections and other serviability
requirements (there is a similar recommendation for moment
of inertia values in an ACI publication for analyzing two-way flat plate
systems for lateral loads when using the equivalent frame method).

Now as to where they come from...just take a look at the commentary for
section 10.11.1.  It stateds:

"The moments of inertia were taken as 0.875 times those in Reference
10.28."

And reference 10.28 is MacGregor, J.G., and Hage, S.E., "Stability
Analysis and Design Concrete," Proceedings, ASCE, V. 103, No. ST 10, Oct.
1977.

With regards to use of these values during service loads checks, the
commentary further comments:

"The magnified service loads and deflections by a second-order analysis
should also be computerd using service loads.  The moments of inertia of
the structural members in the service load analysis should, therefore, be
representative of the degree of cracking at the various service load
levels investigated.  Unless a more accurate estimate of the degree of
cracking at design service load level is available, it is satisfactory to
use 1/0.70 = 1.43 time the moment of inerita given in 10.11.1 for service
load analyses."

Thus, it would appear the intent of the ACI 318 code is that the moment of
inertia values that you cited are meant as an alternative to a more
detailed determination for use in second-order strength analysis/design
applications.  If you then want to use those values to do a second order
analysis for the purposes of determining say deflections, then you
actually should multiple those values by 1.43.

Now, I would also surmise that to some degree, those values are meant to
be an "average" set of values that reflect a large range effective
moment of inertia values that depend largely on to what degree the
concrete has cracked.  In otherwords, they are likely meant to be a
conservative value that can easily be used if you don't want to spend the
time and effort to do a more detailed determination of the degree of
concrete cracking and the associated effective moment of inertia.

HTH,

Scott
Ypsilanti, MI


On Mon, 1 Sep 2003, Prof. A R Chandrasekaran wrote:

> Dear Friends,
>
> I would be thankful if some of you could explain the background to the
> clause of ACI as quoted below:
>
> The specifications of ACI 318 RM - 02 for moment of
> inertia of members are
> ------------------------------------------
> beams    0.35 Ig (gross moment of inertia)
> columns  0.70 Ig
> walls uncracked 0.70 Ig    cracked  0.35 Ig
> Flat slabs and flat plates   0.25 Ig
> --------------------------------------------
> Is it based on analytical/experimental research or is it empirical ? Could
> you suggest any References for me
> to become more familiar with this topic ?
>
> I have some experience of system identification studies -
> trying to fit analytical model to match experimental results.
> In particular for a RCC framed structure (TG framed foundation) we carried
> out extensive experiments after the structure was built and operated under
> actual loads.
> The structure was analysed as a space frame as well as by using 3D solid
> finite elements. The gross section of the concrete was used with static
> modulus of elasticity.
> The best fit was obtained when using an effective factor of 0.65. In one
> sense, ACI 316 gave us confidence that the effective factor should be less
> than unity but it was not possible to assign different factors for beams and
> columns
> to confirm ACI values. 3D analysis could predict frequencies and mode shapes
> near the operating range of frequency (50 Hz) and space frame analysis could
> not do so.
>
> Thanks.
> A R Chandrasekaran
>
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