Concrete Elasticity and tensile strength

[Yt.]

Hi, I have the following expressions to asses Concrete Elasticity and tensile strength. My problem is that they are much different between them. Which criteria would recommend me? Thanks

1-
Ec: 15000*(f'c)^0,5 [kgf/cm2]
fr: 2*(f'c)^0,5 [kgf/cm2]
---------------------------------
2-
Ec: 47000*(f'c)^0,5 [kgf/cm2]
fr: 6.3*(f'c)^0,5 [kgf/cm2]
---------------------------------
3-
Ec: 8000*(f'c^2+8)^(1/3) [kgf/cm2]
fr: 0.3*(f'c^2)^(1/3) [kgf/cm2]

 

[Yt.]

All of them are for normal concrete. Do you have other expressions?

 

[rapt]

The ones in your concrete design code.

 

[Yt.]

Sure, thanks. But this not only impact RC strength design, i need to estimate deflections in my structure and this parameters will change all i need to know.

 

[IDS]

What is the source for these equations? Check the units used in the original source. The results given for E by all three are much too low with kgf/cm2 units.

All the widely used international codes have equations for these values, and they give similar results, but you have to use the specified units.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Yt.]

I think the first are from ACI318 but with SI units, i tooked them from a book which use ACI318 for design.
The second are what we use here, the are usually written in MPa
Ec=4700*(f'c)^0.5[MPa] is intended for secant young's modulus at 0,5*f'c
fct= 0.63*(f'c)^0,5 [MPa] refers for non direct stresses.
The third are ones i found between my university notes.

If I took the first and second pairs of expressions only. i'll still get a big differences with n=Es/Ec, critical rotation, critical bending, neutral axis position, yielding beginning.

I'm only trying to get an approximation of deflections under earthquake I've been checking for effective EcIg considerations for RC, cracks influence and that's ok, but my initial values and stress-and-strain curve rely on this parameters and i think that 47000/15000~=3,1 is a big difference to start the analysis.

 

[IDS]

The results given for E by all three are much too low with kgf/cm2 units.

That's not actually right. The first one appears to be about right with kgf/cm2 units.

The second one is the ACI metric equation, which should have a factor of 4700 with MPa units.

The units of the factors are (stress)^0.5, which explains why the results you are getting differ by a factor of about 3, since you have factored by 10, rather than 10^0.5.

If you want to compare the results, use the units they were written for, then convert the results to common units.

Both 1 and 2 give an E value of about 27 GPa.

I don't know what the intended units of the third one are.


Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Yt.]

yeah, what a relief

 

[Yt.]

Reviewing this I like to say i was employing fc in MPa, that's why i got 47.000, my mistake was to simplify it sqrt(fc)/sqrt(fc) forgetting my units steps.

Thinking about the expression 4.700*sqrt(fc[MPa]) it's not just about making 4.700*sqrt(fc*10[kgf/cm2]),
this retrieves [MPa], so there should be a hidden sqrt(MPa) to achieve the result in proper units.
I mean 4.700*sqrt(fc[MPa])*sqrt([MPa]), so to change it i'll need:

4.700*sqrt(fc*10[kgf/cm2))*sqrt(10[kgf/cm2]), getting about 15.000*sqrt(fc), with fc expressed in Kgf/cm2 and also the result