Development Length in Thin Sections

[WAstruc10]

I have a situation with a #3 bar embedded within the wall of a thin concrete shell. Essentially, the bar is centered within a "wall" that is only 2" thick. While Chapter 12 of the ACI seems to indicate that only a minimum cover requirement (3/8" I believe) is required to use the typical development length equations, I am concerned that a "bursting" failure of the sidewalls may preclude a typical bond failure. Is anyone aware of research or other resources that have looked specifically at thin sections? Much thanks.

 

[Bbird]

Having seen some spectacular design failures I know the Middle East architecture can pose really serious challenges for the structural engineer.

In the case of embedding #3 bar ( or 10mm dia) in a 2" (50mm) thick shell I would look for possible shear/bond failure of a portion of the shell structure being torn away by a group of reinforcement. By looking at the assumed failed perimeter and evaluate its shear capacity against the fully developed reinforcement stress one can know the risk involved.

The spacing of the #3 bar is an important consideration. It is not difficult to sketch out for a vulnerable zone of failure after one has completed the analysis. In tension reinforcement tend to straighten itself in the shell and this factor should be examined too, possibly using the cracked section (concrete tensile zone ignored in the evaluation of second moment of area) in the analysis to get a more accurate picture of the deflection. As the rebar is located centrally the actual second moment of area in service condition can be considerably lower than that derived from a uncracked full section.

 

[WAstruc10]

Perhaps I complicated the question by saying "shell." It is actually a hollow "box" with thin walls. Single rebar will be doweled in from the top of the "box" and centered in the 2" thick vertical walls. It is analogous to lifting loops embedded in the thin side of a (really) thin vertical panel. The force on the bar is straight pullout. I am questioning whether the typical ACI development length equations still apply or if a nontypical "bursting" could occur due to radial bonding stresses. The ACI equations account for rebar with small cover in one direction, as for a beam, but does this necessarily apply for really thin walls with (almost) minimum cover on two opposite faces? Thanks again,

 

[ishvaaag]

If you remain in doubt after anything you get you can reinforce around your embedment to avoid the very local failure.

Say two slightly angled lesser diameter (2 or 3 mm diameter?) bars, various around the height of the stirrup.

><·><

Once you have the geometries and the maximum expected imperfections the thing should be modelizable under some hypotheses (say, anchorage by the final 40% of the embedment and parabolic imperfection causing a spalling force in the rest of the insert). This you may do even in 2D analysis, taking a horizontal band as subject to the force the parabollic imperfection is imparting on it, and seeing if it generates forces able to spall the concrete by ejection of a triangular prism at 30 or 45 deg.

Maybe it is even easier to concrete some models and test the thing.

 

[Bbird]

WAstruc10

ACI 349 code relating to Nuclear safety structures provides a good coverage on the steel bar anchorage pull out calculation. The failure mode is often assumed to be a prism and not bursting of the concrete.

It appear to me that it is easier for a row of bars to tear the concrete out by tension than one bar plugs out with the concrete. In a row format the pull out force is multiplied by the number of bars but the shear perimeter is restricted to three sides (left, right and bottom sides of the row).

Thus if a steel bar is embedded to a sufficient depth then the design would work as sufficient amount of concrete can be made to participate in sharing the load. However this is not possible in your case of dowelling #3 bar into 2&quot; (50mm) thick concrete.

From experience the dowel depth of the #3 (10mm) bar will be around 10&quot; to 12&quot; (250 to 300mm) and grouted by epoxy grade material. Assuming a tensile stress of 1 N/mm2 (used in British code for serviceability check, ACI 349 allows about 1.5N/mm2 for grade 30N/mm2 concrete, 1N/mm2=145 psi)the tensile resistance of the concrete from the two parallel sides (say 12&quot; or 300mm embedded length) of the bar is just about to balance the yield strength of the high yield rebar estimated to be about 3 tonnes (metric tonnes is roughly similar to Imperial ton). One can say the single bar grouted at 300mm depth is safe.

However if 5 bars are grouted, say @ 12&quot; (300mm) centres, then perimeter increase over a single bar is only 300% and this cannot match the capacity of the 5 fold increase in reforcing bar.

There are also risk in drilling a 2&quot; wall for a #3 bar to 12&quot; depth as any inaccuracy of the hole's verticality and dimension can create an imperfect failure plane initiating the failure prematurely. The reliablity of getting a consistent tensile strength from a 2&quot; thick wall is, needless to say, questionable.

The code may not deliberately set out to cover the difficult situation in your case. However I believe a reasonable assessment should be possible with the information already published by the code.