ACI 360R-10 - Calculating Beta and Fy Units Error/Confusion

[jacktbg]

I'm trying to follow this to get a finger to the wind on whether I can apply a few thousand pound pointload (on a steel plate) onto my 7" reinforced slab...

https://socwisconsin.org/wp-content/uploads/2016/09/GRDSLAB-Slab-on-Grade-Semi-Tractor.pdf

All online calculators I can find have a minimum dowel size of 3/4". The actual dowel size and spacing is 5/8" and 16" spacing...

Where I'm coming up short is the bearing stress on dowels. When you calculate Beta, you use the equation B = (Kc*db/(4*Eb*ib))^(1/4)

My numbers are B=(1.5E^6 psi * .3125 in / (4*2.9E^6 psi * .0155 in^4))^(1/4)

Every example I can find has that work out as unitless, but how can it be perfectly unitless with the in^4 in the denominator??

When I then take what I get (and assume I just calculate the number and calll it unitless) and put it into the fd(actual) calculation I get

fd actual = kc*Pc*(2+Bz)/(4B^3*Eb*Ib)

fd actual = 1.5e^6 psi * 731.78 lbs * (2+.1204*.125 in)/(4*.1204^3*2.9e^6 psi * .0155 in^4)

My number ends up astronomical and the units are nonsensical. Can anyone help me figure out where I'm going wrong???

Thanks a million!

 

[lexpatrie]

Seems like a good question for a structural engineer to consult with you on....

Throwing a spreadsheet at the problem without knowing what it's doing isn't generally wise, and the units in concrete are frequently "baked" into the various coefficients, i.e square root of f[sub]c[/sub]' generally has units of psi, not psi[sup]1/2[/sup], so that can lead you astray.

 

[jacktbg]

Thanks! I appreciate the advice. Yeah just to be totally clear, this is for work and I had a professional S.E. coworker review my work at the end and help me verify, and this was also not an official design. We have a new building we're constructing and I was trying to determine if the slab we have in a room is relatively future proof for some equipment we may someday put in, or if they should be pouring footings there up front which would have been a change order and a whole political thing with the costs and delays associated with it... Was more looking for a finger to the wind on whether it was worth taking up the chain as if it needed a footing later (which would be an SE's job to check) we would have had to cut up the slab and dowel and epoxy in rebar etc, wheras if we catch it now it's just a deeper hole and some rebar up front. We found that the slab was fine for a few thousand pounds with the equipment in question on a steel plate, should we acquire it.

Reason I was the one doing it was just that I was a structural engineer (EIT, not an S.E. or PE) in my former life but a long time ago. I was always residential though and don't think I ever needed to check a big load on a slab, we would have just designed a proper footing had there been a question. Again, I wouldn't be doing any official structural work these days, it was more a "will this be a problem down the line most likely" and I felt comfortable trying to find out for myself since I had access to the plans for the building.

The coefficient not being truly unitless, was throwing me off... I don't remember encountering very many equations in the NDS, or misc. standards that ever used so many coefficients that had to use weird units to get the end product of the equation to work out in sensible units. I appreciate the insight! I would still love for my own curiosity to understand the how the units in this ACI 360R-10 equation work out, but I was able to get the professional help I needed to at least determine my original question.

 

[lexpatrie]

There tends to be implicit unit conversion in a lot of the goofy equations, so from a strict standpoint (and it bugs me slightly too) it isn't very clear what the units on the constant are to make the units "work" but the definitions tend to give units, as I recall, but like sqrt (fcprime), used for a lot of things has goofy units.

The metric equations have different coefficients on all the equations that handle those goofy unit issues as well.

Most of the other codes this doesn't happen, so it's perhaps easier to forget the highjinks in the Concrete code.

On your issue, they could also possibly use moment redistribution to get the slab to pass.