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Re: Drift Criteria / Cracking - Wind Loads

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Anantha:

There is generally two ways that I know of to determine the effective
moment of inertia to use for cracked concrete sections.  There is the
"easy" way and the more detailed way.

The "easy" way is basically what you kind of reference in your point #1.
Section 10.11.1 of ACI 318-02 lists a set of "alternative" (alternative to
doing a more detailed calculation) effective, but approximate moments of
interia's, as a function of a percentage of Ig.  This section is really
intended for figuring out magnified moments (i.e. 2nd order analysis) of
frames, but can be used as a "lazy" way to get an effective moment of
inertia for deflection calculations that take into account cracked
sections.

The more detailed method is to use Eq. 9-8 of ACI 318-02, which is
consistent with what you seem to talk about in your point #2.  Here you
must determine Mcr (i.e. the moment where the bottom flexural tension
stress in the gross, uncracked section of the concrete reached the modulus
of rupture...i.e. in theory when a crack initiates), Ma (the actual
unfactored moment in place on the concrete cross section), Ig (the gross
moment of interia...note that it should be the transformed cross section
gross moment of interia, but many times it can be approximated with little
"error" by the non-transformed cross section moment of inertia), and Icr
(the tranformed cross section cracked moment of inertia assuming that the
crack has propigated to the neutral axis...that is the section is
comprised of the compression concrete zone that is from the neutral axis
to the extreme compression fiber and the tension steel, but NO concrete in
the tension zone "below" the neutral axis).  This equation then will
"approximate" the degree to which the cross section is cracked (i.e. how
high the crack has propagated up the cross section) as a function of the
ratio of Mcr/Ma.  The lower the actual, service moment (i.e. the closer it
is to Mcr), the closer the effective moment of inertia will be to Ig.  The
higher the actual service load moment (i.e. the further it gets from Mcr)
is the closer it will get to Icr.

As to drift limits for wind, my memory is that the codes really don't tend
to do much to address any wind drift limits.  Table 1604.3 of the 2000 IBC
does pose some limits for member deflection, not really drift per se.
But, you can use that as a "guide" to get approximate drift limits.

HTH,

Scott
Adrian, MI


On Mon, 29 May 2006, Anantha Narayan C.K. wrote:

> Greetings,
>
> I am looking for answers from experienced engineers for a few questions and this listserv has been more than helpful in many previous instances.
>
> The first question is aimed toward drift criteria for wind loading in buildings. I work in Miami and Miami-Dade county requires all buildings to be designed for wind speeds of 156 mph (3 second gust). There is no prescribed load combination to check for drift under service loads in ASCE 7-02 nor FBC 2004 except a load combo in the commentary of ASCE 7-02 which requires drift to be checked for D + 0.5 L  + 0.7 W. Typically we have been checking drift under service wind and D + L + W. Are there any other specified means of checking for drifts at service loads?
>
> The second question is aimed towards cracking in concrete at service loads. Chapter 10 in ACI gives stiffness modification factors for columns, beams and walls. However, I am going around in circles trying to figure out the accurate means of establishing cracking in concrete and its associated reduction in stiffness (increased drift). Typical buildings that we work with might not have appreciable change in stiffness due to cracking, but I do wish to understand the rationale in the code.
>
> 1. For shear walls, ACI requires you to use a stiffness modification factor of 0.7 (even prior to cracking?), run your analysis under service loads, check for cracking under service loads and then use 0.35 in case there is cracking and re-run. Also the code suggests using 1.0/0.7 = 1.43 for service load analysis. Does this mean you are increasing your stiffness to a value greater than Ig? What is the suggested means to model a realistic behavior? Why is the stiffness reduced by 20%-30% for axial members and by around 50% in flexural members? Are there any experimental values that these are based on? List of references/sources will be very helfpul in understanding the same.
>
> 2. Moment-curvature diagrams can be created for columns, beams etc. Mcr can be calculated based on Ig (not including the increase in Ig due to reinforcement) per Mcr = fr*Ig/y. Based on this and the service load moments, degree of cracking can be computed. This can then be used as a stiffness modification factor. Is this approach of any value in trying to compute accurate cracking and reduction in stiffness.
>
> I would appreciate your responses in this regard.
>
>
> VTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVT
>
> ANANTHA NARAYAN, E.I.
> Structural Engineer
> Bliss and Nyitray Inc.
> Miami, FL - 33134
>
>
>
>         VTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVT
>
>   ANANTHA NARAYAN, E.I.
>   Structural Engineer
>   Bliss and Nyitray Inc.
>   Miami, FL - 33134
>
>
>
>
>
>
>

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