ACI Appendix D - Combined Loading 1

[Once20036]

I've been looking at a situation where I need to post install an anchor into concrete to attach a plate.
I've gone through the calculations for shear (controlled by concrete breakout) and the calculations for tension (controlled by steel strength.)

In accordance with the equation sect. RD.7:
v-ult/v-allow)^(5/3) + (t-ult/t-allow)^(5/3)<1.0

I`m using this equation from the commentary because it's the published value in Hilti's design guide & I`m using Hilti bolts.

Per ACI D4.1.2, PhiNn and PhiVn are the lowest design strengths determined from all appropriate failure modes. SO, when you use the combined loading formula you end up using the concrete shear ratio and the steel tensile ratio.

This seems overly conservative because you're mixing materials. Ie, the concrete will fail based on combined concrete shear & concrete tension OR the steel will fail based on combined steel shear & steel tension, but I don't see how stressing the concrete to 75% in shear and the steel to 75% in tension will lead to a failure.

Logically, this makes sense to me, but I can't see how to get there according to the letter of the code. Am I missing something? Has anyone run across this issue before? Is there a reason to mix the two failure modes like this?

 

[ishvaaag]

It seems essentially and simply that the equations show a statistically safe statement of the available strength. You can see some charts of the kind in

Anchors in Concrete
Design and Behaviour
ACI Special Publication SP-130
Senkiw, Lancelot III, eds.

SP 130-4
Behavior of Ductile Multiple-Anchor Steel-to-Concrete Connections with Surface-Mounted Plates
Cook and Klingner
p. 108, 109, 110, 120, 121, 122

The first set of figures show the T/V points outside the eliptical interaction equation; the others how predictions according to the eliptical interaction fare against tests.

Your question is really interesting in that out of neccesity of practical adjudication of time, most of those practicing are acting as if convinced that the beautiful closed form statements in the codes are something of mathematical exactitude, whereas in most cases derive of a centuries' long process of assesment of the behaviour in practice, and anytime using every kind of fine tunings required to get the (economically) most useful statement of accepted safety to some grade of reliability. In short, our formulas are just fittings to the set of our tests and experiences, to some degree lower bound when for strength, and to the average when attempting to predict "probabilistic" behavior.

 

[Once20036]

ishvaaag,
Maybe I haven't had enough coffee yet, but I`m not sure if you're agreeing or disagreeing with me... Unfortunately I don't have access to SP-130.
I read the bit about practical adjudication of time as meaning that the code cannot possibly cover each subtle nuance such as this, and engineering judgement is required for some situations.
The second bit about these being developed over centuries & fitting the tests and experiences makes it sound as though the code should be followed, even if it isn't intuitively correct.
Can you clarify?

 

[TXStructural]

The codes are almost entirely a set of notions and contrivances developed to produce a safe structure. And that is what they intend to do. They are like a recipe which is "tried and true", but from which one cannot derive the underlying science and chemistry. You should never try to mix first principles with code kludges. The parts of the code fit together such that the completed design represents a safe structure. If you go back to first principles, you have to take it all the way and cannot rely on code assumptions or simplifications.

As to App D, and the problem presented, it does seem that combining two limit states where there is really no intersection of the sets of failures is poor engineering. You would probably want to combine two different concrete failure modes, but not the concrete breakout and the steel anchor tension failure. Where the modes do combine, such as under lateral shear where the anchor will deform and the concrete crush locally or breakout, the risk might be combined if they do depend on each other.

 

[ishvaaag]

Well, I think TXStructural has almost explained the thing as I see it. Anyway, I of course agree with engineering judgement (i.e., own understanding of science of construction) being a good thing when one thinks anyone other, code or not, in error. Yet as TXStructural says, the codes have been distilled to forfeit such worries for most cases in such way that you can produce a safe design, and deriving from the codes may end in causing more trouble than benefit; this, of course, needs be (and is) tempered by the (hopefully sage) practice of the structural design art, for, for what I know, I don't see out there any building or structure where such act of structural belief as complete compliance with the codes is extant; nor I see any present code "perfect".

There have been cases where the divergent interpretation of the structural designer or investigator has shown to be more correct than what stated in codes (Northridge connections is a commonly referred case) and as long as structural designers are held personally responsible of both following the code and keeping public safety, I have no doubt that a responsible engineer must pursue first safety, and then code, or what the interpreting official says.

So, well, I was mainly pointing that the formula even if conceptually aberrant by mixing pears and apples, through statistical experience and the actual interaction as commented by TXStructural must be adequate or otherwise we shouldn't find it in the code.

But as you see, I think even necessary that responsible structural designers retain their ability to diverge from the code and its standing interpretation by officials. Other than that, the statutory laws should make engineers only responsible of faithfully following the code.

This certainly is not the view of the legislative body where I practice (Spain) where traditionally when justified the designer can diverge from the code precises, something that the current and more modern code CTE also agrees upon by it being a performance code, this meaning, more or less, that as long you meet the performance targets in the code (as long everything goes well) you can diverge from the statements in the code, something entirely neccesary because simply some subjects are not even covered. I have found in my last structural design one of such cases, a masonry plus wood structure that not having a structural diaphragm -not my decision- is expressly excluded from the masonry specs. So you will resource to engineering judgement and science of construction every time things stay undefined ... and maybe even when they are defined.

 

[JAX91]

I agree with you. Checking the interaction ratio between two different materials is conservative, but it is what the code says we need to do. A significant portion of Appendix D is based on testing. That is why they exclude anchors with an embedment depth greater than 25" because they did not test anything above a 25" embedment. Using the interaction between the steel anchor and the concrete may also be based on their testing.

On a side note from your question, Hilti's website provides ESR reports for the design of anchors according to Appendix D. Only certain Hilti anchors have been approved for strength design. All of the ESR reports I have show the interaction ratio as V/Vu+N/Nu<1.2. You may want to make sure you are using the proper numbers from Hilti and that the type of anchor you are using has been approved for the strength design of Appendix D.