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[SEAOC] Concrete Dilema

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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 

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 

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.


Eric J. Scott
ASCE-YMF Membership Chair, Sacramento
Cline, Agee, and Swedin 
Engineers and Architects