Normal weight concrete definition in ACI seems incorrect

[Petras Surna]

According to ACI-318R-14 the formula for Ec is as below.

Normal weight concrete is 2400 kg/m3 or 150 lb per cu ft
This means the first formula applies.

That seems to be an error.
The second formula would never apply even though it states "normal weight concrete"
Can anyone please enlighten me as to the mistake I am making?

 

[r13]

The normal weight concrete often is taken as 145 pcf, then Ec = 145^1.5(33)√fc' = 57619√fc' ≅ 57000√fc'.

 

[Petras Surna]

OK, thanks a bit weird but I get it.

 

[r13]

You are welcome. Just remember that concrete properties are not exact science. Most are derived through testing and by statistics means, that is, largely average, or best fit approximation.

Also note when is a more realistic elastic modulus having significance in the results. I would say it has less structure significance for the majority of analysis and design tasks, thus an approximation is enough. But for investigation on an existing structure, with concrete weight is known, I think the elastic modulus carries more weight, especially in the analysis of deflections, and the first equation should be used.

 

[271828]

Also, they only use two significant digits. That makes it a little tricky when comparing with other specifications. Consider the following for 145 pcf and 4 ksi concrete.

ACI: Ec = 33(145^1.5)*sqrt(4000)/1000 = 3644 ksi

AISC: Ec = 145^1.5*sqrt(4) = 3492 ksi

They're about 4% different.

 

[Ron247]

I also think the 150 psf is used for the weight of reinforced concrete, more than just the weight of concrete.

 

[JoshPlumSE]

Keep in mind that when the code say, the following parameters are "permitted to be calculated by", that doesn't mean you have to use the formula. Rather the code is merely giving you formulas that you CAN use. However, neither formula is a code requirement.