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# Punching Shear with Moment4

## Punching Shear with Moment

(OP)
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

### RE: Punching Shear with Moment

I believe that gamma v represents the share of the unbalanced moment at your column going through the punching shear mechanism. The remainder is thought to be transferred by direct flexure (as you would in a moment frame).

### RE: Punching Shear with Moment

According to my college text. This equation is based on some research by Hanson and Hanson.

Gamma v represents the portion of unbalanced moment that is transferred by shear stresses. It sounds like setting gamma_v to 0.4 was done relatively arbitrarily, but that it helped to better match their test results.

### RE: Punching Shear with Moment

(OP)
Thanks, gentlemen... if you are transferring the total moment, would the value be 1.0? I'm looking at a small jib crane mounted to a slab on grade...

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

-Dik

### RE: Punching Shear with Moment

indeed it would. Curious, why do you want to do that?

### RE: Punching Shear with Moment

(OP)
the load is very small, and the client doensn't want to construct a real foundation... I've looked at the numbers and there is lots of capacity.

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

-Dik

### RE: Punching Shear with Moment

The idea is that most of the moment will be transferred through regular flexure and won't affect the shear stresses in the punching shear perimeter. And, only a portion of the moment is manifested as shear stresses at the punching perimeter.

If you have an unusual situation where traditional flexure can't occur then sure it would be 100% transferred via these shear stresses. I cannot easily visualize a situation where this would occur.... Though I've never really taken a "deep dive" into this theory before.

### RE: Punching Shear with Moment

So like column connection to an unreinforced footing or something?

### RE: Punching Shear with Moment

You don't just choose arbitrarily how much unbalanced moment is transferred by either the flexure or eccentricity of shear mechanisms. There are formulas and rules for determining gamma_v in most codes, usually being based on the geometry of the connection (column size) and whether you have internal, corner or edge conditions. I suggest you read your local code to see how this is treated in your area, simply arbitrarily assigning some factor as others have implied as okay isn't the intent.

### RE: Punching Shear with Moment

Thank you KootK! I was racking my brain and couldn't come up with a valid case where someone might think the moment should be transferred entirely by shear stresses.

Maybe even column to footing connection where the footing has no top steel?

### RE: Punching Shear with Moment

#### Quote (Agent666)

...simply arbitrarily assigning some factor as others have implied as okay isn't the intent.

Are these "others" that you speak of me and JP? Or the authors of whatever reference dik's looking at? I hope it's the latter as my role here is simply to help dik interpret what he's seeing, not pass judgment on whether or not it's appropriate for whatever his condition is. The 0.40 value may well be associated with a particular condition, or range of conditions. And I'm privy to none of that.

#### Quote (JP)

Thank you KootK! I was racking my brain and couldn't come up with a valid case where someone might think the moment should be transferred entirely by shear stresses.

Welcome. Even then some of the moment would likely be transferred by flexure as a result of the axial load in the column prestressing the joint and providing tension capacity. And, of course, if the moment would actually lift part of the column cross section from the footing, that's a whole different kettle of fish as well.

If somebody wants to assign 100% of the moment to the punching shear mechanism, I struggle to see how that's not a conservative choice in most cases.

#### Quote (JP)

Maybe even column to footing connection where the footing has no top steel?

Interesting, given that would represent most footings. Your starter dowels would point the undesirable way but, even at that, I'm sure that there's still some moment capacity in the joint.

### RE: Punching Shear with Moment

It was referring to you mostly in this thread suggesting in the factor arbitrarily by confirming you could use a gamma_v of 1.0 in KootK (Structural)9 Apr 21 19:28 post. That was my interpretation of the advice being offered, that you could arbitrarily assign all of the moment to shear or flexure mechanisms, but maybe I've misinterpreted what you meant. I was simply stating this advice is not actually correct in terms of how punching shear works or is designed for.

Some portion of the unbalanced moment still transfers via flexure even if the underlying structure is unreinforced. 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.

#### Quote (kootk)

If somebody wants to assign 100% of the moment to the punching shear mechanism, I struggle to see how that's not a conservative choice.
I disagree, this simply isn't how it works in terms of modern design methods for punching shear.
For your classical punching shear formulations at no point would the gamma_v factor = 1 for example, nor gamma_f = 1.0 (the portion of unbalanced moment transferred (gamma_f = 1-gamma_v)).

### RE: Punching Shear with Moment

(OP)

#### Quote (So like column connection to an unreinforced footing or something?)

I think that's how it will behave...

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

-Dik

### RE: Punching Shear with Moment

(OP)

#### Quote (You don't just choose arbitrarily how much unbalanced moment is transferred by either the flexure or eccentricity of shear mechanisms.)

Agree... but shear transfer is far more critical... if it works for that, then it easily works for flexure. I'm already conservative because the effective thickness of the SOG has been reduced by 2" for all calcs... I'm comfy... this one, the formula made sense, except for the factor, and I had no idea why it was introduced. I've used a factor of 1.0 and it's still safe.

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

-Dik

### RE: Punching Shear with Moment

(OP)
Thanks, gentlemen... design problem solved. Only difference is that I'm using Hilti epoxy on a bolt circle rather than LePages PL Premium...

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

-Dik

### RE: Punching Shear with Moment

I should point out that the 0.4 may have been "somewhat arbitrary" in the Hanson and Hanson paper per the text book I was looking at. But, it sounds like it was done that way to better match their test data.

Now that the ACI code has that 0.4 is the only value given in the current version of ACI code (actually the commentary) it's pretty much a lock that you should use that here in the US. That being said, if someone is concerned that this isn't sufficient then he/she could arbitrarily use a higher amount to add conservatism to his/her punching shear check. That's conservative.

### RE: Punching Shear with Moment

(OP)
Thanks Josh... that's what I did. I just didn't know why the value was there; I hadn't considered it as a 'fudge' factor.

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

-Dik

### RE: Punching Shear with Moment

#### Quote:

Now that the ACI code has that 0.4 is the only value given in the current version of ACI code (actually the commentary) it's pretty much a lock that you should use that here in the US. That being said, if someone is concerned that this isn't sufficient then he/she could arbitrarily use a higher amount to add conservatism to his/her punching shear check. That's conservative.

Can you provide a reference for this being fixed at 0.4? I cannot seem to find this in ACI318-19.

My reading of clauses 8.4.2.2.4 & 8.4.2.2.6 is that it is still worked out indirectly form the gamma_f factor unless I'm missing something obvious. This is the way it has always been?

### RE: Punching Shear with Moment

It's the commentary to 8.4.4.2:

#### Quote (R8.4.4.2.2)

Hanson and Hanson (1968) found that when moment is transferred between a column and a slab, 60 percent of the moment should be considered transferred by flexure across the perimeter of the critical section defined in 22.6.4.1, and 40 percnt by eccentricity of the shear about the centroid of the critical section.

### RE: Punching Shear with Moment

Actually, my quote is from the 2014 version of the code, not the 2019 version.

### RE: Punching Shear with Moment

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

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

### RE: Punching Shear with Moment

(OP)

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

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

### RE: Punching Shear with Moment

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.

### RE: Punching Shear with Moment

#### Quote (Agent666)

...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.

### RE: Punching Shear with Moment

So you'd set gamma_f to 1 as well?

### RE: Punching Shear with Moment

#### Quote (Agent666)

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.

### RE: Punching Shear with Moment

#### Quote (Agent666)

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.

### RE: Punching Shear with Moment

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.

### RE: Punching Shear with Moment

#### Quote (Agent666)

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.

### RE: Punching Shear with Moment

#### Quote (Agent666)

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.

### RE: Punching Shear with Moment

(OP)
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

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