Cracking moment - CSA vs ACI 1

[EngDM]

I'm reviewing a spreadsheet from steeltools for slab on grades for use with CSA A23.3, and I came cross that the Mcr calculation according to 24.2.3.5 of ACI 318-19 is Mcr = fr*Ig/yt, CSA A23.3-14 shows the same equation, but stipulates that fr should be taken as half of the value calculated in equation 8.3 of A23.3.

I investigated the equations for fr to see if maybe ACI took the 1/2 in the equation, but no dice. This equation, for reference is 0.6λsqrt(fc') in CSA which is roughly equivalent to the 7.5λsqrt(fc') used in ACI with imperial units in equation 19.2.3.1 (in reality it is closer to using 7.2 instead of 7.5). Regardless, the 7.5>7.2 factor doesn't make up for the half.

P.S. the spreadsheet still shows a coefficient of 9 for MOR for those who use it, might be worth investigating whether changing it to 7.5 is appropriate.

Is anyone aware of why this is? I couldn't find if it was perhaps an ASD vs LSD design reason, but ACI 318 seems to be in LRFD which is comparable to how CSA does it (with phi factors).

 

[skeletron]

You reduce the modulus of rupture only in the deflection calculations when finding the effective moment of inertia (Equation 9.1). This is explained in Chapter 6 of the CAC Concrete Design Handbook. As noted on page 6-7:
-A23.3 uses the Branson equation to compute Ieff
-A23.3 uses a reduced modulus of rupture when computing the cracking moment
-the reduction reflects presence of tension due to restrained shrinkage that reduces the applied moment that causes flexural cracking
-the reduction reflects unconservative errors created because the Branson Equation is based on an incorrect mechanical model

A manual check versus S-Concrete's output indicates that Mcr (for strength) uses the full modulus of rupture as per Equation 8.3.

 

[EngDM]

You reduce the modulus of rupture only in the deflection calculations when finding the effective moment of inertia (Equation 9.1). This is explained in Chapter 6 of the CAC Concrete Design Handbook. As noted on page 6-7:
-A23.3 uses the Branson equation to compute Ieff
-A23.3 uses a reduced modulus of rupture when computing the cracking moment
-the reduction reflects presence of tension due to restrained shrinkage that reduces the applied moment that causes flexural cracking
-the reduction reflects unconservative errors created because the Branson Equation is based on an incorrect mechanical model

A manual check versus S-Concrete's output indicates that Mcr (for strength) uses the full modulus of rupture as per Equation 8.3.

Do you know where in CSA code it says only to reduce fr for deflection calculations, or is it only in the commentary on 6-7?

Subsequently, where does ACI say to take 1/2fr for deflections? Or is this a CSA thing.

 

[skeletron]

Equation 9.2 tells you to reduce fr for deflections. Follow the thread through the commentary to 6-7.

I believe this is a CSA thing (don't quote me on that) because CSA and ACI use different models for deflection. CSA uses the Branson equation, ACI uses another equation. I attended a seminar a few years back but the details are hazy. Someone else probably can chime in on this.

 

[EngDM]

Equation 9.2 tells you to reduce fr for deflections. Follow the thread through the commentary to 6-7.

I believe this is a CSA thing (don't quote me on that) because CSA and ACI use different models for deflection. CSA uses the Branson equation, ACI uses another equation. I attended a seminar a few years back but the details are hazy. Someone else probably can chime in on this.

Is there anywhere else where Mcr is referenced other than in 9.2? Without reading the commentary it can almost be interpretted that Mcr always has fr/2. Is this just one of those ambiguities in the code?

 

[skeletron]

Go read Clause 10.5.1.1...

 

[BulbTheBuilder]

How do you mark a comment as "solution"?

 

[EngDM]

How do you mark a comment as "solution"?

There is a checkmark on the right of a comment when you are the original poster, so I clicked that.