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# Re: [SEAOC] Concrete Dilema

• To: seaoc(--nospam--at)seaoc.org
• Subject: Re: [SEAOC] Concrete Dilema
• From: "Hunt, Tom" <tom.hunt(--nospam--at)fluordaniel.com>
• Date: Mon, 15 Apr 1996 08:44:00 -0800
• Priority: Urgent

```        Eric,

As described earlier, the neutral axis in reinforced concrete
can move depending on the stress level in your beam.  Part of
your "dilemma" is to determine what you are going to use the
neutral axis calculation for.  Typically this is needed for
serviceability requirements such as crack control.  In this
case, you need to use the Unfactored Moment and the actual rebar
stress fs and not fy.  Using the working stress method here is
quite acceptable.  However, you can still use the Ultimate
Stress Method but it is a little harder and best done with a
trial and error table.

Assume a rebar stress fs, say 30ksi, then calculate "a" by
a=As*fs/.85*fc'*b, then calculate fs=M/As(d-a/2), if ASSUMED fs
does not match CALCULATED fs then guess again until they are
equal.  Now you have the correct "a" and can calculate your
neutral actual axis by a=c*B1.  You can use a simple table such
as:

|assumed|    |calc'd|     |calc'd|
|  fs   |    |  a   |     |  fs  |

In an exam, a quick and dirty way to get fs (and hence "a") is
to use fs(approx)=M/j*d*As where j is assumed to be 0.9.  This
is normally pretty close.

Thomas Hunt
Fluor Daniel
TOM.HUNT(--nospam--at)fluordaniel.com

Subject: [SEAOC] Concrete Dilema
Author:  seaoc::(SEAOCAA) at ~FABRIK
Date:    4/12/96 10:54 PM

From: seaoc(--nospam--at)seaoc.org
Date: Fri, Apr 12, 1996 10:54 PM
Subject: [SEAOC] Concrete Dilema
To: seaoc
I 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 example that I used was a concrete beam with the following
properties:

b=18"   d=37"   f'c=3000 psi   fy=60,000 psi   As=6.0 in^2
Ec=3,122,000 psi   Es=29,000,000 psi   n=9.29   k=0.333

The location I get for the neutral axis using the Ultimate Strength
method is 9.23".  The value I get using the Working Stress Method is
12.34".

I have less than a week till the exam and I would really appreciate
it if anyone can let me know which method is the correct one.

Thanks,

==============================
Eric J. Scott
escott(--nospam--at)csus.edu
ASCE-YMF Membership Chair, Sacramento
Cline, Agee, and Swedin
Engineers and Architects
==============================
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