Plain concrete shear strength
Plain concrete shear strength
(OP)
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.
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.






RE: Plain concrete shear strength
DaveAtkins
RE: Plain concrete shear strength
This is my assumption/understanding as well.
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.
RE: Plain concrete shear strength
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.
RE: Plain concrete shear strength
RE: Plain concrete shear strength
Also, the 2-way action includes the 4/3 term... so I assume it also takes into account a similar stress.
RE: Plain concrete shear strength
RE: Plain concrete shear strength
I really wish we had some references for Chapter 22, but none are listed.