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Re: Alternate Design Method

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Michael,

Correct...for pure bending.

If you including an axial load, then you need to include the P load in the
free-body diagram along with the T (tension steel) resultant and C
(concrete compression) resultant.  It is not just C=T.  But P=C-T.  And
the moment equation of the FBD also needs to include the moment due to the
axial load (depends on what point you take it about).

Regards,

Scott
Adrian, MI


On Wed, 2 May 2007, Michael Hemstad wrote:

> On Tue, 1 May 2007, Jim Bessley wrote:
> > Scott,
> > I understand all of that regarding your comments. I would still like to
> > find an example.
> >
> > I do, however, appreciate your comments and thoughts on the matter.
> > Jim
>
>
> Working Stress Design is not dead yet.
>
> If you're analyzing an existing section:
> 1.  Figure out the depth to reinforcing, d.
> 2. Calculate rho.
> 3. Find N, the ratio of Young's Moduli.  For your purposes, use N = 12 - fc' (about 9).
> 4. Calculate k, the depth of the compression wedge (to the neutral axis)
>
>      k = sqrt(2 rho * N + (rho * N)^2) - rho * N   (usually about 0.3)
>
> 5. Calculate j:  j = 1 - k/3   (usually about 0.9)
> 6.  Calculate allowable moment:
>
>     M = As fs j d/12
>
> If you know the reinforcing grade (yield), use fs = 0.5Fy with a maximum of 24 ksi.  If unknown:
>
> If the structure was built prior to 1954, Fy = 33 ksi; use fs = 18 ksi.
> If the structure was built after about 1985, you can safely assume Fy = 60 ksi and fs = 24 ksi.
> Between these dates, assume Fy = 40 ksi and fs = 20 ksi.
>
> The 1954 date I lifted from an old (1983) copy of the AASHTO Manual for Maintenance Inspection of Bridges.
>
> To cut down on the blitz of emails screaming about how Grade 60 steel was common before 1985, yes, it was; but there was still design being done with Grade 40.  For instance, by me, as directed by my first boss.
>
>
> If for some odd reason you're designing a new section by WSD, it's a little harder to explain by email.  When we were doing WSD, we used tables; you'd calculate M/bd^2 and enter the table, pull out a value for rho, and off you'd go.  When I programmed WSD into my calculator, it involved solving a cubic equation based on first principles.  Good fun, that.  However, if you really, really want to do it, there's a shortcut equation, hitherto unpublished, that will get you remarkably close:
>
> for M = the design moment PER FOOT OF WIDTH, in foot-kips; fs in ksi; and d in inches,
>
>    As = (M^1.04) * 11.84/(fs * d)  giving you square inches of reinforcing.
>
> I'm pretty sure it's unpublished because I curve-fit the thing, and I don't think I've told anyone.  It works great for spreadsheets.  If you have trouble, Scott can help you.
>
> HTH,
> Mike
>
>
> Michael Hemstad, P.E.
>
>
> Meyer, Borgman and Johnson, Inc.
>
> 12 South Sixth Street
> Suite 810
> Minneapolis, MN 55402
> (612) 338-0713 (main)
> (612) 604-3621 (direct)
> (612) 337-5325 (fax)
> www.mbjeng.com
>
>

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