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# Re: [SEAOC] Concrete Dilema

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: [SEAOC] Concrete Dilema
• From: CarlS95(--nospam--at)aol.com
• Date: Sun, 14 Apr 1996 02:58:47 -0400

```In a message dated 96-04-12 22:23:40 EDT, you write:

> am studying to take the PE exam on the 19th, and I have run into a
>snag on determining where the neutral axis is in a RC beam.  The
>method that I have used in the past is to simply use the expression:
>
>a=As*fy/.85*f'c*b         and         a=B1*c
>
>However, in flipping through my concrete book and Lindburg's PE
>review manual I found another method which uses a factor multiplied
>with the depth, or:
>
>c=k*d    where     k=sqrt(2*p*n+(p*n)^2)-p*n
>
>p= the steel ratio (since rho is not part of my keyboard)
>n= the modular ratio of     E (steel)/ E (conc.)
>
>I know that one expression is based on Ultimate Strength and the
>other is based on Working Stress, but since they both assume a
>cracked section shouldn't they give similar values?

The neutral axis is not a fixed location.  As the load on a beam increases,
the theoretical neutral axis moves toward the compression face.  For small
loads, the section is uncracked: the theoretical neutral axis is right in the
middle of the beam.  For working level loads, the section is cracked:  the
neutral axis moves so that the strain in the compression block balances the
strain in the steel.  The stresses and strains are assumed to be linear from
the neutral axis.  Finally, for ultimate loads, the steel and/or concrete go
plastic.  The stresses and strains are no longer linear from the neutral
axis, which is why the two formulas give different values.  This is pretty
apparent when you look at the assumed stress diagrams for the two methods.

The first formula is what is most commonly used in concrete these days.  The
second formula is common for masonry, although they are switching to ultimate
strength methods as quick as they can.

I'm itching to draw a sketch, but it doesn't seem to work very well in
E-Mail.  All I can draw are smilies : - ) and frownies : - ( .

Sorry you can't get a perfect answer:  Both formulas are correct.  If the
question comes up in the exam, read what is being asked for and if you are
hooked up to the Internet with your laptop, just pop on over to the SEAOC
Mail Server.  (Just kidding.)

Good luck.  Carl S.
...

```