ishvaaag
Structural
- Aug 17, 2001
- 3,665
I am interested in thinking a moment about how reinforcement embedded in a column taking just compression, and for the purpose of debate, going on straight down into some footing below shows stresses. The ordinary code consideration would be to develop at least the compressive force standing on the rebar, as determined by some analysis in compatibility of deformations at the section in the column, and likely the brute nominal strength of the rebar.
Now, imagine we model tridimensionally the thing with its two materials, bond at the interface and so on, and the column has some height, say 3 m above the top of the footing, and the load is passed to the column by a plate welded or fitted atop the column. Assume the bond is enough to forfeit slippage, then it is clear that in the upper part of the column the steel will partake the load more or less as the compatibility of deformations analysis says, but as we near the interface between the column and footing the steel stress is influenced by the reaction of the footing against punching by the column. Since the total load applied in the footprint of the column is unable to sink in unitary terms in the same proportion that the unitary shortening does in the column, just showing some dishing action at the surface, it becomes a corollary that on compressed rebar its "tributary" load is not entering whole in the rebar, but on increased local compressive stresses in the concrete to be taken at the footprint, if you want, up to the limit signalled for them by the A1/A2 confinement ratio.
But the point here is that in the compressed rebar entering the footing there is some gradient lowering the standing stresses in the column to those standing in the footing, which are far lesser upon the far lesser compressibility of the footing, given its bigger section, for the stresses in the rebar come from the unitary deformations standing at the point, and there are far lesser. So, the practice one can see in many of the sections of the CRSI manual, where one has lots of examples where the amount of rebar being developed is less than the total in the column, i.e., you may have 12 bars of some diameter and only 4 or 6 in dowels, find a justification and even some evaluation procedure, this way. What I find interesting because I myself once found some party mandating the whole compression rebar being wholly developed wanting some increase in depth in the footing. We, except code demands otherwise, do not need to do that, we need simply to pass the loads from the column to the footing in accord to the science of construction, and if we find one scheme that satisfies it, we wouldn't be needing further compliances to meet.
And what said of some continuous rebar can be also be thought to be the case for properly spliced dowels unto the footing.
So a scheme for the checks would be
1. Only compressive force in the rebar (or at least for the hypothesis, to just determine hypothesis by hypothesis what is the real amount of rebar in dowels required, even if some are in tensile stress at some hypothesis).
2. Assume the compressive force is entirely dissipated to increased compressive forces in the concrete section at the interface; by the A1/A2 ratio, is the interface able to take the whole of the compressive stress in the upper part of the rebar in the column? Or just part?
All the part able to be met by the increased f'c by the A1/A2 ratio, as long as you have length of embedment on the column, needs not to be passed in dowels. In fact, if you determine some unitary compressive strain just a bit under the footprint of the column and within the footing, with whatever assumption of the applied loads (you could even, for example, assume the whole compatibility of deformations loads are applied at the interface) you may find that there the compression strain shows the bars embedded in the footing are not taking the loads that purportedly need to be developed in bond; and if they are not taking the brunt, the concrete has already taken in transfer in bond from some length within the lower part in the column to pass them to concrete strut action in the footing; this might go maybe beyond what the A1/A2 ratio allows for f'c growth (since the code would be a sanitized safe value for the effects of confinement).
In short, that not all, and not always the rebar in compression needs be developed in its full strength unto the footing.
Now, imagine we model tridimensionally the thing with its two materials, bond at the interface and so on, and the column has some height, say 3 m above the top of the footing, and the load is passed to the column by a plate welded or fitted atop the column. Assume the bond is enough to forfeit slippage, then it is clear that in the upper part of the column the steel will partake the load more or less as the compatibility of deformations analysis says, but as we near the interface between the column and footing the steel stress is influenced by the reaction of the footing against punching by the column. Since the total load applied in the footprint of the column is unable to sink in unitary terms in the same proportion that the unitary shortening does in the column, just showing some dishing action at the surface, it becomes a corollary that on compressed rebar its "tributary" load is not entering whole in the rebar, but on increased local compressive stresses in the concrete to be taken at the footprint, if you want, up to the limit signalled for them by the A1/A2 confinement ratio.
But the point here is that in the compressed rebar entering the footing there is some gradient lowering the standing stresses in the column to those standing in the footing, which are far lesser upon the far lesser compressibility of the footing, given its bigger section, for the stresses in the rebar come from the unitary deformations standing at the point, and there are far lesser. So, the practice one can see in many of the sections of the CRSI manual, where one has lots of examples where the amount of rebar being developed is less than the total in the column, i.e., you may have 12 bars of some diameter and only 4 or 6 in dowels, find a justification and even some evaluation procedure, this way. What I find interesting because I myself once found some party mandating the whole compression rebar being wholly developed wanting some increase in depth in the footing. We, except code demands otherwise, do not need to do that, we need simply to pass the loads from the column to the footing in accord to the science of construction, and if we find one scheme that satisfies it, we wouldn't be needing further compliances to meet.
And what said of some continuous rebar can be also be thought to be the case for properly spliced dowels unto the footing.
So a scheme for the checks would be
1. Only compressive force in the rebar (or at least for the hypothesis, to just determine hypothesis by hypothesis what is the real amount of rebar in dowels required, even if some are in tensile stress at some hypothesis).
2. Assume the compressive force is entirely dissipated to increased compressive forces in the concrete section at the interface; by the A1/A2 ratio, is the interface able to take the whole of the compressive stress in the upper part of the rebar in the column? Or just part?
All the part able to be met by the increased f'c by the A1/A2 ratio, as long as you have length of embedment on the column, needs not to be passed in dowels. In fact, if you determine some unitary compressive strain just a bit under the footprint of the column and within the footing, with whatever assumption of the applied loads (you could even, for example, assume the whole compatibility of deformations loads are applied at the interface) you may find that there the compression strain shows the bars embedded in the footing are not taking the loads that purportedly need to be developed in bond; and if they are not taking the brunt, the concrete has already taken in transfer in bond from some length within the lower part in the column to pass them to concrete strut action in the footing; this might go maybe beyond what the A1/A2 ratio allows for f'c growth (since the code would be a sanitized safe value for the effects of confinement).
In short, that not all, and not always the rebar in compression needs be developed in its full strength unto the footing.
