Plain concrete shear strength

[901STR]

On ACI 318-11, chapter 22, section 22.5.4 we have the equation for beam-action shear as: Vn = (4/3)*λ*(sqrt(f'c))*b*h.
Chapter 22 has no references at all, but the commentary indicated the expression is derived from v=VQ/Ib (Mech of Materials equation for shear stress). I suspect the 4/3 part comes from multiplying the shear stress from Chapter 11 (2*sqrt(f'c)) by 2/3. 2/3 being the inverse of 3/2 - the maximum stress shear for a rectangular cross section. However, since we have not references, I am not entirely sure if this is how ACI arrived at the 4/3 value.

Here is my question: Since the shear capacity for plain concrete is based on the Mech of Materials equation v=VQ/Ib, is it also subjected to its limitations? The Mech of Materials equation is only correct for a beam that is much deeper than it is wide (h ≥ 2b). for example, if the beam is much more shallow than it is wide (h≈b/4), the shear stress varies along the width of the section, and the maxim shear stress is about 2 times the average of the cross section.
Most of the time I see plan concrete in is foundations, and they are typically wider than they are deep.

 

[DaveAtkins]

I don't think it is helpful to think about shear STRESS when using that equation. The equation is for ultimate shear STRENGTH, so that is how you should look at it.

DaveAtkins

 

[KootK]

I suspect the 4/3 part comes from multiplying the shear stress from Chapter 11 (2*sqrt(f'c)) by 2/3. 2/3 being the inverse of 3/2 - the maximum stress shear for a rectangular cross section.

This is my assumption/understanding as well.

Since the shear capacity for plain concrete is based on the Mech of Materials equation v=VQ/Ib, is it also subjected to its limitations?

I would think so. Frankly, it's a very interesting point that I'd not considered before.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[901STR]

Thanks for the feedback, Kootk.

DaveAtkins, normally I would agree with you however the commentary to that section specifically mentions STRESS and references the STRESS equation c=VQ/Ib. so, in this case, we are warranted in discussing stress.

 

[mike20793]

Isn't there a separate equation when two way action needs to be considered?

 

[901STR]

mike20793, you are correct. there is a separate equation for 2 way action. The case I'm looking is strictly one-way action.
Also, the 2-way action includes the 4/3 term... so I assume it also takes into account a similar stress.

 

[mike20793]

I see what you mean now. I guess chalk it up to another part of ACI's terrible shear methodology. Just out of curiosity, how does the Eurocode handle this case?

 

[901STR]

I'm not too familiar with Eurocode, and I do not have a readily available copy with me.
I really wish we had some references for Chapter 22, but none are listed.