How to check for maximum steel ratio

[RomelV]

I have this computation for singly reinforced rectangular beam and found that

rho_max = (3/7) * 0.85 * f'c * beta_1 / fy

That is based on ACI 318 strain of tension steel of 0.004 and concrete of 0.003.

The same formula actually was posted by user JAE (Structural) in this thread:

http://www.eng-tips.com/viewthread.cfm?qid=136515

However I found that in many situations, this value of rho_max will go lower than who_balance which I think is not reasonable.

Example, I have this (I am doing SI here but please disregard on that and let's just compare the results)
f'c = 21 MPa, fy = 276 MPa and beta_1 = 0.85

I have these results:
rho_balance = 0.85 * f'c * beta_1 * 600 / [ fy (600 + fy) ] = 0.03765

And for rho_max in the above formula, I get rho_max = 0.02356 only which is less than rho_balance.

So how can I check if I'm not going above maximum permissible reinforcement if using the of concrete won't get me there.

Is there anything or something that I miss or other thing that I need to look for?

 

[JedClampett]

In general, your reinforcing shouldn't approach rho balance. As I'm sure you know, that's where the concrete crushes simultaneously as the steel yields. In construction, that's bad. You want the steel to yield first, so you get a ductile failure. The old limit was .75 times rho balance. This came out to about .017 or so percent steel. And you didn't even want to run up too close to that. Anything over 1.5% makes me nervous.
Now the code uses limits set by ductility. Your reduction is more if your section is less ductile. But I would still follow the old limits by either deepening or widening your section. If you're over 1.5% rethink your design.

 

[RomelV]

Oh my bad... At the back of my head I always thought that rho_max should be greater than rho_balance when in fact, it should not be. I get these things mixed up in my head. Thank you for your reply. Is 0.015 not too small for an upper bound?

 

[JedClampett]

No, .015 is a pretty hefty amount of steel. As I said, if I'm in that range, I'm getting uncomfortable.
Usually deflection or shear takes care of it on its own, but every once in a while, I end up in that range.

 

[hokie66]

Agree with Jed. The maximum flexural steel percentage varies a bit with the grade of steel and the strength of concrete, but with Grade 60 (or 400 MPa) steel, the maximum should be about 0.015.