Looking for ACI reference of the attached formula 3

[Blackstar123]

I'm reviewing the design calculation of anchoring to concrete checks, submitted by another design firm.
The designer has calculated the pull out capacity of L bolts using the following formula, which is contrary to the one given in Chapter 17.

I am having difficulty finding out the reference of the above formula in regards with "anchor bolts". As I understand the pull out strength of anchor bolt is governed by the bearing on the L part only, and any bond stress developed due to friction is ignored.

Before I asked the designer to furnish the said reference, I want to ask if someone here could point me in the right direction.

 

[JStephen]

From an old general reference book, I find allowable bond stress for "plain bars (must be hooked)" given as 0.045fc', and it references ACI 318-51.
In AWWA D100-79, the bond stress for anchor bolts is given as 1.5*sqrt(fc')<160, in psi units, and I assume that was based on the current ACI code at the time, or perhaps one cycle older.

 

[JLNJ]

It looks to be just the bond stress on the surface area of the bolt itself.

 

[centondollar]

That formula is the equation for the bond capacity of a reinforcement bar.

I do not know the specifics of how pull out strength is handled in ACI, but "bearing on the L-part" (I assume you are referring to a hook at the end of a reinforcement bar), or a washer plate, is not the only thing providing resistance against pullout. Assuming that bond exists between the anchor bolt and the concrete (i.e., it is placed before casting), the bond capacity due to friction is significant, and is used to calculate anchorage lengths and development lengths.

You can solve the maximum anchorage length first from the force balance: "A_s_rebar * F_yd = f_bd*perimeter_rebar*l_b_max --> l_b_max= ...", and then calculate the bond capacity; you will find that it depends only on bar diameter and yield strength (and is restricted by the maximum anchorage length "l_b_max").

The solution provided by the engineer in question, assuming that loading is static (bond is not abruptly increased and decreased due to cyclic load), seems reasonable.

 

[JoshPlumSE]

I recall seeing "bond stress" calculations like this related to WSD of masonry reinforcement.... though I don't have the reference anymore. I think it was a design guide related to the 1997 UBC masonry requirements.

Opening up the 1997 UBC (yes, I'm that old!), I see the following that looks pretty close in the Masonry - working stress chapter:
Section 2107.1.5 embedded anchor bolts.

 

[WARose]

In older ACI 318 codes (circa the 50's through about '63)....for plain bars, allowable bond is given this way:

(4) For plain bars the allowable bond stresses shall be one-half of those permitted for bars conforming to ASTM A305 but not
more than 160 psi.

[Requirements for A305]

(1) For tension bars with sizes and deformation conforming to ASTM A305:

-Top Bars[sup]*[/sup]: 3.4√F'c/(D) nor 350 psi
-Bars other than top bars: 4.8√F'c/(D) nor 500 psi

*Top Bars, in reference to bond, are horizontal bars so placed that more than 12 in. of concrete is cast in the member below the bar.

And this was working stress design by the way.

In any case, no one should be using this in modern structural calculations. (I.e. for new concrete structures.) Anchorage based on bond stress has been history for quite a while. (As this approach is inadequate as per testing.)

 

[centondollar]

Anchorage based on bond stress (force balance between the bar and the surrounding concrete) is how flexural reinforcement (and other reinforcement) is curtailed. It is not an inadequate concept, but it may provide non-conservative results for dynamic loading (which causes "slippage" and thus irreversible loss of bond).

Washer plates or bent bars (creating capacity through the bearing effect of the end-plate or bent bar) add to capacity, of course.

 

[WARose]

Anchorage based on bond stress (force balance between the bar and the surrounding concrete) is how flexural reinforcement (and other reinforcement) is curtailed.

We aren't talking rebar, we are talking anchors. The failure mode there can be from numerous other things (including bending on the L/J shape) before any "bond" strength kicks in. (The chemical adhesion that constitutes "bond" is unreliable in any case.) Furthermore rebar is ribbed. The bearing forces on the ribs provide the anchorage.

 

[JoshPlumSE]

WARose -

I tend to agree.... Unless Centondollar can point to a modern code equation where this comes from.

My comments about masonry rebar from the 1997 UBC, rather it was a guess (a relatively wild one) about where that could have come from.

Note: My favorite part of the image is the blue text that says "See ACI". No reference to which code document, which report, what section or year. Sigh..... I suppose I shouldn't criticize too much. It's easy to put together a spreadsheet or something and not document the source of it all that well. But, it does make me chuckle every time I look at it.

 

[WARose]

Note: My favorite part of the image is the blue text that says "See ACI". No reference to which code document, which report, what section or year. Sigh..... I suppose I shouldn't criticize too much. It's easy to put together a spreadsheet or something and not document the source of it all that well. But, it does make me chuckle every time I look at it.

Yeah, I use to bang heads with the people at one place I worked at where just citing the code section wasn't enough for archived calcs....they wanted the code practically reproduced and stuck in the calcs as well. "See ACI" would have been nice.

 

[JStephen]

I was able to spot this online. This is ACI 318-63, Section 13, Bond and Anchorage, Working Stress Design.
The second image shows 318-58 at the top, that 58 is the page number, not the year.
On the second image, they say plain bars are half the deformed bars above.
And yes, it's my understanding that this has been outdated for years as noted above.
My understanding- used for bolts, you considered bond stress on the straight shaft only, but were required to have the bend- but didn't figure any strength contribution from it, either.
D is bar diameter in inches, fc' should be psi.

 

[Blackstar123]

Thank you everyone for your valuable insight.

I understand the basics of the given expression and know that it’s the principal theory behind the development length expressions of deformed bars. I am seeing it first time used for anchor bolts however. The calculation in question is for a PEB structure, still in the construction phase and I could not think of a reason why not to use the design provision as per the latest code (or at least code issued in this century).

My firm is responsible for design of RCC foundations and other concrete structure. PEB supplier submitted these calculations after we proposed to replace the L bolts with hex nut anchor bolts to meet the demand. They claimed that they have also performed the pull out check and found the anchor bolt assembly adequate. Calculations were carried assuming a commonly used concrete strength in their region, i.e., f’c = 35 MPa for UAE. This strength is not according to our proposal, however, for arguments sake, I’ve calculated the following numbers based on their assumption.

Based on the submitted calculations (which is based on ASD methodology as most of you have implied) as per unknown ACI Code
Service Capacity = 51.63 KN
Service Demand (0.6D-W) = 57.6 KN (Calculated by myself. Incidentally, calculation sheet does not provide the service load with which they are comparing the capacities)
DCR = 1.1 > 1.0

As per ACI 318-19 -17.6.3
Ultimate Capacity = 61.2 KN
Ultimate Demand (0.9D-1.6W) = 93.25 KN
DCR = 1.52 > 1.0

I can’t make sense of the difference in demand capacity ratios from the two methods. Seems like something is not right here.

P.S. Wind Loads provided by supplier are for basic wind speed.

 

[centondollar]

WARose:
"We aren't talking rebar, we are talking anchors. The failure mode there can be from numerous other things (including bending on the L/J shape) before any "bond" strength kicks in. (The chemical adhesion that constitutes "bond" is unreliable in any case.) Furthermore rebar is ribbed. The bearing forces on the ribs provide the anchorage. "

Anchors are often ribbed, at least where I practice, and using rebar with a threaded end (from a manufacturer of such items) is not unusual either. Furthermore, the original poster did not ask about "all checks relating to all failure modes": he specifically adressed pull-out, and that is countered by bond stress and bearing. As long as splitting failure, cone failure and edge breakout is checked (for anchors purely in tension) separately, the pull-out check reduces to either a bond strength calculation or a combination of bond strength and bearing (where the bearing is typically given by a washer plate or factory-welded "mushroom head" at the tip of the anchor) strength.

PS. The primary source of bond is not chemical adhesion, but rather the mechanical interlock of aggregate between ribs and the shear stress along the tips of the ribs. These two mechanisms are at play when curtailment of ordinary reinforcement is assessed (and, in fact, the mechanical interlock is not explicitly accounted for in code equations in e.g. Eurocode 1991-1-1 chapter 8), and I see no reason to assume why the same principles would not be applicable in this case.

 

[WARose]

Anchors are often ribbed, at least where I practice...

You must practice in a strange place. Maybe I am behind the times, but I can't think of the last time I've seen ribbed anchor bolts.

PS. The primary source of bond is not chemical adhesion, but rather the mechanical interlock of aggregate between ribs and the shear stress along the tips of the ribs.

Not when we are talking smooth bars. (And only smooth bars.) My concrete texts (especially the older ones, and I've got texts going back to the 70's and earlier) make clear that chemical adhesion & mechanical friction between the steel and concrete were the primary considerations for what I posted. Granted there are a lot of variables (including what happens after cracking).....but adhesion was clearly part of the thought process.

 

[canwesteng]

Note that if using bond stress here (assuming they are deformed bar and not smooth) you should consider a different breakout cone, probably more sore . I would be surprised if the assumptions made here were carried over to the breakout calculation.