Calculation of Preliminary Area of Steel for Slab
Calculation of Preliminary Area of Steel for Slab
(OP)
Could someone please provide me a quick, if preliminary, formula for finding the area of steel required for a foundation, for instance, if I have the factored moment, effective depth and width. Please also provide the reference for the formula. My fc' is 4000 psi. I am
thinking that
As = Mu/b*d^2
but the units do not seem consistent.
thinking that
As = Mu/b*d^2
but the units do not seem consistent.






RE: Calculation of Preliminary Area of Steel for Slab
the 0.81 comes from approximating d-a/2 to 0.9d and multiplying that by the phi factor of 0.9
There is no need for b in the equation since that only factors into the compressive stress block depth, a. a is accounted for in the 0.9d as noted above.
Hope this helps.
RE: Calculation of Preliminary Area of Steel for Slab
It should be Mu/(0.81*fy*d)
RE: Calculation of Preliminary Area of Steel for Slab
RE: Calculation of Preliminary Area of Steel for Slab
StructuralEIT, could you please provide a reference for the formula you provided?
spats, your comments are noted and a thorough understanding of the formulas and how they are derived will be done before being put to use. Your commens here have provided a head start and that is much appreciated.
RE: Calculation of Preliminary Area of Steel for Slab
This is a conservative assumption.
Just plug in 0.9d for d-a/2 in the phiMn formula and solve for As, nothing more complicated than that.
RE: Calculation of Preliminary Area of Steel for Slab
ρ = 0.85 f'c/fy (1 – √(1-(28.32Mu/(øbd²f'c)))
As = ρbd
where Mu = ft-k, f'c & fy = ksi, and b & d = inches.
ø = 0.9 for bending.
Where tension steel required by analysis, ACI 318 requires:
As≥(200/fy)bd or As 1/3 greater than req'd. by analysis, otherwise
As≥0.0018Ag, where Ag is gross area of the footing.
Hope this helps.
RE: Calculation of Preliminary Area of Steel for Slab
As others have stated, there are a number of other things that can dictate the required steel in a slab. I would suggest you do some reading on the matter so that you can come up with an accurate prediction.
RE: Calculation of Preliminary Area of Steel for Slab
I use As req= Mu/4d for a ball park check (note: Mu in k-ft, and d in inches)
StrlEIT is also applicable.
RE: Calculation of Preliminary Area of Steel for Slab
JKStruct, you hit the head on the nail! I was exactly looking for a rule of thumb, and wanted confirmation that it was As req = Mu/4d. Could you point out a reference for this, or show how this was derived?
RE: Calculation of Preliminary Area of Steel for Slab
where jd = d - a/2
like StructuralEIT said, assume jd = 0.9d
then As = Mu / phi fy 0.9d
= Mu / [0.9 (60 ksi) 0.9 d / 12 ]
Note 12 for unit conversion
= Mu / 4.05 d
Much math and derivation omitted here but understand the concept of whitney stress block and the anticipated depth. Long hand derivation involves solving a quadratic equation for a.
I use As,est = Mu / 4.0d all the time.
For Masonry, As,est is M/1.8d for 60 ksi steel and M/1.48d for 40 ksi reinforcing. M is the service level load not ultimate. Try to derive these. Very similar.
RE: Calculation of Preliminary Area of Steel for Slab
phiMn=AsFyjd (and divide by 12 to get answer in kip-ft)
Mu=phiMn
Fy=60
j=.9 (roughly)
Substitute and solve (divide by 12 to get 4.05d on the right)
This rule of thumb may not be conservative, due to j=.9 Therefore, use ACI as the reference for final calculation
RE: Calculation of Preliminary Area of Steel for Slab
RE: Calculation of Preliminary Area of Steel for Slab
Reinforced Conrete Buildings of Moderate Size and Height"
It's put out by PCA, it's a great reference for stuff like this. It uses As=Mu/4d.