Punching Shear with Moment 4

[dik]

In literature I was looking at, they use the formula:

and they use gamma v equal to 0.4. Can anyone explain the term? The article uses ACI, and I'm not familiar with the value. Thanks in advance.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[hetgen]

Below is the formula for γ_v, For square column γ_v 0.4

But it should be taken as 1.0 for an unreinforced slab or slab with insufficient reinforcement within the transfer width.

 

[dik]

Thanks hetgen... that's the condition I have... SOG with temp (I assume) reinforcing only... and thanks for a source of the material... I'd not encountered the expression before and was wondering why it was there... using 1.0 was intuitive, only.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[Agent666]

Josh, I believe you've misinterpreted that statement. Thats only saying in tests by those authors they found the ratio was 0.4. It is not saying always use 0.4 as I believe you've stated/interpreted.

The gamma_v at 0.4 is only true for square columns as hetgen has noted. If you read further in the clause you quoted, it notes the tests being referenced where the 0.6/0.4 ratio was determined was using square columns.

As noted previously, you work out gamma_f from the relationships in ACI (other codes are similar), then gamma_v = 1- gamma_f as noted in clause 8.4.4.2.2 of ACI318-19.

https://engineervsheep.com

 

[dik]

Try again... there was an error due to the Beta values...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[dik]

and SMath...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[KootK]

...but maybe I've misinterpreted what you meant.

Indeed. I'll elaborate then. I took dik's question to be, effectively:

I wish to be conservative in my punching shear design and arbitrarily manipulate the expression to accomplish that, assuming for this one aspect of design that 100% of the unbalanced moment will need to be transmitted via punching shear. That, even though I will still be a good engineer and design the other aspects of the connection appropriately. What is the intent of gamma_v and how should I manipulate it to accomplish this goal?

Taken in that context, I contend that these two statements are, in fact, true:

1) Setting gamma_v to unity would indeed be how one would go about accomplishing that goal and;

2) Setting gamma_v to unity would be universally conservative for the punching shear check.

 

[Agent666]

So you'd set gamma_f to 1 as well?

https://engineervsheep.com

 

[KootK]

So you'd set gamma_f to 1 as well?

Not unless it was my intent to also be very conservative with that for some reason as well. Normally, I'd calculate gamma_f per them fancy modern design methods that you mentioned. Inherent in my response to dik was my assumption that he generally knows his stuff as well, of better, than I do and therefore requires little hand holding. That's a function of the two decades over which we've been collaborating here I suppose.

 

[KootK]

The reality is reliance on unreinforced structures for transferring punching shear leaves one on shaky ground, I'm not aware of any rules in codes or otherwise that allow for the assessment of this.

As you probably know, ACI does touch on plain concrete punching shear. That said, I still agree with your assessment that it feel sketchy:

1) To my knowledge, they don't revisit the gamma_v thing for plain concrete.

2) Without rebar, it's difficult to see how moments would be transmitted across the joint unless it's via the axial load prestressing effect of the columns as I mentioned earlier.

3) Even if I designed a footing or slab as unreinforced, I'm not sure that I'd ever feel comfortable guaranteeing the absence of crack right over/under the columns.

Frankly, I'm kind of amazed that this provision even exists for two-way shear as it's range of practical application would seem to be almost non-existent.

 

[Agent666]

At least you're not implying 100% of unbalanced moment in shear and zero in flexure which is what I thought you were implying, you'd still have 100% in shear and 60% in moment using your conservative method.

However, I believe that approach does border somewhat on madness, overestimating the shear contribution of punching shear by 2.5 times for common square column geometry. There's conservative and there's being so overly conservative, but each to their own, we all got to get to sleep at night.

Any grad making that type of overestimate on a new design would face some serious 'what the hell' type of explanation depending on the implications (if it were to drive the slab to be considerably thicker for example, when it would have otherwise worked had it been calculated correctly).

You're working out gamma_f anyway using the given the fancy one liner equations you reference, that's a few seconds work at most to get it right, so you can then work out gamma_v correctly by subtracting gamma_f from 1, that's another few seconds work. No need to guess at it being 1 to be conservative. Sure if it works under that, go for gold, but if it doesn't ....? It's a situation where working it out wrong, and working it out right take the same amount of time.

I'm not trying to be argumentative; but I see BS and I call it out as such. It's simply my opinion that in certain situations others would be ill advised to follow the gamma_v=1.0 advice especially when the calculation is so fundamentally simple that a 10 year old could do it, and especially if someone is trying to justify an existing detail (as seems to be the intent) and you're trying to effectively sharpen your pencil to decide if it does truly work or not.

https://engineervsheep.com

 

[KootK]

No need to guess at it being 1 to be conservative. Sure if it works under that, go for gold, but if it doesn't ....?

If it doesn't work, find another solution. Failure is failure. I agree that, in conventional situations, setting gamma_v to unity would be prohibitively conservative. But, then, dik's situation isn't conventional. Heck, unless I'm mistaken, his column is really steel. I actually feel that punching shear is the wrong tool to bring to bear in this situation and would prefer to tackle it as shown below, as a steel anchorage problem.

 

[KootK]

I disagree, this simply isn't how it works in terms of modern design methods for punching shear.

I'm familiar with said modern design methods and that's how I do thing in routine design. Playing devil's advocate, however, and setting economy aside, what is the terrible thing that would occur if one set gamma_v to 1.00 and gamma_f to 0.00? Wouldn't we expect the gamma_f moment to redistribute and simply add to the punching shear flexural burden that would already be designed for it?

I don't know how things work in New Zealand but, in North America, slab designers struggle with punching shear and relish whatever relief we can get from gamma_f. Baring some minor congestion issues, however, the reverse is not true: we're not struggling to deal with the gamma_f moments. Obviously, setting gamma_v to 0.00 and gamma_f to 1.00 would be ill-advised owing to punching shear being the brittle failure mechanism.

 

[dik]

To digress... I'm not setting gamma_f equal to zero... I'm just maxing out gamma_v for a worst case scenario for shear. I wasn't aware of the formula, but it was of a familiar form that I understood what they were trying to do; I just didn't know why the coefficient was introduced. Knowing it's there, I fully appreciate the intent. In reality?, the moment transferred will be 100%, part by flexure and part by shear with the total equal to 100%. I just chose to max the shear since it is plain concrete, but there is limited reinforcing. In addition, I've sort of arbitrarily reduced the concrete thickness by 50mm assuming the slab is cast on soil (which it is). I'm comfortable that the method selected is safe, albeit, analytically a little 'flakey'. The slab is well constructed, ableit 40 years old, and crack free for more than 8' around the installation... I sleep like a baby... maybe it's the straight Scotch...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik