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# Re: Drift Criteria / Cracking - Wind Loads

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Drift Criteria / Cracking - Wind Loads
• From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
• Date: Tue, 30 May 2006 18:51:07 -0400 (EDT)

```Anantha:

The key (to me at least) is to read the WHOLE paragraph of the commentary.
You just quoted the last part of the paragraph.  What that paragraph
points out (to me at least) is that the second-order/moment-magnifier
analysis procedure is for doing analysis to figure out design force based
upon FACTORED loads.  It then points out that you might need to do
deflection/drift etc analysis using service loads (i.e. UNFACTORED).  As
such, it would make sense that the whole "process" that is started to be
outlined in section 10.11.1 contains a load factor...thus, those effective
I values "contain" (for lack of a better word) a load factor.  Thus, if
you use those I value for service loads, you need to "take out" the load
factor.  And an "average" load factor is around 1.43.

This will leave the columns using Ig but a beam using .5*Ig.  This is
potentially rather reasonable considering that your typical beam will NOT
have any compression force in it while a column generally will.  In
otherwords, your column that is under bending is going to in effect be
under a prestressing force (i.e. the gravity load).  Thus, a column should
have relatively little to no cracking assuming that the axial load to
bending moment ratio is high.  If it is a lightly loaded column, then this
"approximate" method likely would not be the best thing to use or as an
alternative, treat the column as if it was a beam.

That is how I look at what the commentary is saying.

In the end, I would, however, suggest doing a more detailed analysis if it
concerns you that much.  Using the formula 9-8 is the way to do that.
Where it can get complicated is if you also have an axial load.  If you
do, then that formula does not strictly address the inclusion of
compression forces.  In such a case, the degree of cracking is not just a
function of the actual service load moments relative to the cracking
moment, but rather a function of the actual service load moment PLUS axial
load relative to the cracking moment.

HTH,

Scott

On Tue, 30 May 2006, Anantha Narayan C.K. wrote:

> Greetings,
>
> This is a section from the commentary of ACI 318-02.
>
> R10.11.1 (last paragraph) " The moments of inertia of the structural members in service load analyses should, therefore, be representative of the degree of cracking at the various service levels investigated. Unless a more accurate estimate of the degree of cracking at design service load level is available, it is satisfactory to use 1.0/0.7=1.43 times the moment of inertia given in 10.1.1 for service load analyses".
>
> My question is thus. Service load levels refer to load cases and combinations with a load factor of 1.0. Does the commentary actually tell you that you can use 1.43 * [values from 10.1.1]. For a column, does this mean that you can use a 1.43 * 0.7 = 1.0 EIg for service load analyses, meaning you can use gross Ig for service load analyses. Am I correct in interpreting this?
>
> Is this not unconservative for drift if cracking occurs at service level loads? Or is the "design intent" always to be such that service level loads should not produce any cracking in the concrete?
>
> Thanks
> Anantha
>
> VTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVTVT
>
> ANANTHA NARAYAN, E.I.
> Structural Engineer
> Bliss and Nyitray Inc.
> Miami, FL - 33134
>
>
> ----- Original Message ----
> From: Scott Maxwell <smaxwell(--nospam--at)engin.umich.edu>
> To: seaint(--nospam--at)seaint.org
> Sent: Monday, 29 May, 2006 11:31:46 PM
> Subject: Re: Drift Criteria / Cracking - Wind Loads
>
>
> 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
>
>
> 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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