ACI 350 - Sd factor

[JAE]

In ACI 350-06, I have to calculate an Sd factor from section 9.2.6 (equation 9-8) which lists:

Sd = [φ]fy / [γ]fs

Where
[φ] = 0.9 for flexure
fy = 60 ksi for rebar
[γ] = 1.4 (for my fluid load combination 1.4(D+F))
fs = service level stress in the rebar

The section describes fs as "the permissible stress in reinforcement as given below".

Below this, we find references to various maximum values of fs equals various values (such as 24,000) for things like hoop stress, shear stress in rebar, etc. It also lists section 10.6.4 for flexural stress.

In 10.6.4 we find for fs: "The calculated stress, fs, in reinforcment closest to a surface in tension at service loads shall not exceed that given by equations (10-4) and (10-5) and a maximum of 36,000 psi"

The two equations (10-4) and (10-5) are for fs,max. Each equation is a formula and below each there is a statement:

"but need not be less than..." and they give a value such as 17,000 psi.

Now my problem is that as I calculate Sd based on fs, I find I am chasing my tail. As I use smaller bars, or closer spacing, or larger bars, etc. I can't ever catch up to the design moment Sd x U = Sd x Mu.

I am basing Sd on a CALCULATED value of fs at service loads. As I reduce spacing, my fs gets rather small. This kicks up Sd since fs is in the denominator. I never catch up.

Should I be using the fs,max or the 17,000 psi value (as a minimum)? The 17,000 is given as a minimum of fs,max...not as a minimum of fs.

Help!!!!!

 

[JedClampett]

I don't understand why your fs is getting smaller when you decrease the spacing. Using equations 10-4 and 10-5, the spacing is in the denominator, so a decrease mans you're dividing by a smaller number and the result should be greater. This is confirmed by the charts on the right side of the page.

 

[JAE]

Jed - the fs that I calculate (M(service) divided by moment arm divided by area of steel) is the calculated fs. As you decrease spacing, your As goes up, your stress in your rebar goes down.

The question is -

Use the calculated fs (M/(As x arm))

OR

Use the fs,max which has a ceiling (equations 10-4, 10-5) and a floor: 17,000 psi or 20,000 psi.

 

[JedClampett]

For this formula, fs is the allowable maximum stress as calculated using 10.6.4.
It's not very well defined, but if you had been using the ACI 350-89 when it was in force, it would look familiar.
The result of this requirement is to encourage the use of smaller bars with a closer spacing vs. large bars spaced far apart. Which makes good sense if you think about it.

 

[JAE]

OK - I think we've figured it out -

Section 9.2.6 refers to fs and calls it the "permissible" stress in the bars. It then refers you to 10.6.4.

10.6.4 says the "calculated" stress must be less than the fs,max, which is ASSUMED BY ME to be the "permissible" stress. So I would use the permissible fs,max as my fs in the Sd equation, not the calculated fs.

The calculated fs is ONLY used to check against the fs,max and that's all.

So this makes more sense - but ACI sure isn't very clear in their wording.