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Re: [SEAOC] Concrete Dilema

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        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.
        
        Good luck on your exam,
        
        Thomas Hunt
        Fluor Daniel
        TOM.HUNT(--nospam--at)fluordaniel.com



______________________________ Reply Separator _________________________________
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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To: seaoc(--nospam--at)seaoc.org
Date:          Fri, 12 Apr 1996 18:50:26 -800 
Subject: [SEAOC] Concrete Dilema
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