Rectangular Corner Column for Punching Shear 2

[Jim508]

Does anyone have experience performing the hand calculations for punching shear at corner slab-to-column connections? I'm having a hard time converting the moments and the centroid principal axes. I can provide a detailed example to work along with. I have been using ACI 421.1R and 421.2R as a guide.

Best Regards,

Jim

 

[ishvaaag]

I point to 3 publications that have info on this issue.

Postensioning Manual 5th ed
PCI
page 311

ACI 340.4R-91 Design Handbook Volume 3
Two Way Slabs
Publication SP-17(91)(S)
(all throughout)
(has examples, and aids for corner columns as well)

Design of Concrete Buildings for Earthquake and Wind Forces
Ghosh and Domel Jr.
PCA
p. 2-13 and general procedures in many examples.

Also, a trick. For shear surfaces other than rectangular in plan, draw the plan of such surfaces in autocad with, say, origin of coordinates at the corner, and make a small offset to such polyline, say, half an inch. Then close it at the edges to form a slice with the shape of the sheared surface being considered, and then, extrude this shape to the proper height (normally one would take the effective depth d-cover). Now use MASS PROPERTIES to find the center of gravity of volume with the shape of the shear surface. If will give you very approximately the position of such center of gravity, and the alignment of the axes, that for symmetrical corner setups will be quite self-evident. This way you can easily locate c.o.g. and principal axes with almost no effort, autocad will do it for you. If the slice is very thin, the position will be highly accurate.

I attach some quite diffunded figures for common cases, as of old were practiced.

If you post a pdf with your difficulties we may be of more help.

 

[slickdeals]

PCA Notes for ACI 318 also has some examples. I don't believe they have one for corner columns.

 

[ishvaaag]

above, errata: the extrusion height to be taken is Actual Depth - Relevant cover to axis, where the relevant cover to axis to be deduced is understood to be to the rebar there in tensile state.

 

[Jim508]

Hi,

Thanks for the input. I have been looking at other methods of determining the section properties for the critical sections located at a corner column, but they fail to take the rotated axes into consideration because of the asymmetry of the critical section. ACI 421.1R and ACI 421.2R provide very detailed procedures but they make many assuptions. Attached is a generic example that I started. My intention is to determine how to relate the moments about the column origin to the centroid, with respect to the centroidal principal axes. I also included pages from ACI 421.1R-08 for help. Let me know if anyone can help.

Best Regards

 

[rscassar]

It sounds like you are running into trouble with bi-axial bending in the column (obvious being a corner column).

 

[rscassar]

I didn't word that last post very well.

Does you question relate to biaxial bending of corner column and the effects on punching shear.

 

[Jim508]

Yes, we have moments on both axes but what I'm solving for is the developed shear stress for punching shear.

 

[bookowski]

Reinforced Concrete by Wight & MacGregor has some info about determining the principal axis, after you get that it is easy enough to take the components of your moments along this axis.

There's also a paper in ACI structural journal Nov-Dec 1994 by Hammill and Ghali titled 'Punching Shear Resistance of Corner Columns', unfortunately they use a square corner column so the principal axis is pretty straightforward.

 

[ishvaaag]

I am working something on this and maybe tomorrow or this weekend I may upload something about.

 

[ishvaaag]

Well, I took your pdf and reverse engineered it. I find that you seem to have taken in error the distance between center of section and center of gravity of the shearing surface. Hope have made the things well, anything manual and long is prone to error.

In my pdf I use Autocad support to ease the work and make understandable what I am making. You won't have any difficulty in duplicating it, it is only a matter of drawing a thin region with the shape of the shearing surface (closing a small offset of it with that) and you get through the command massprop great many of the magnitudes of interest to the problem. In any case, since I follow similar procedure to what you do, I hope all will be quite comprehensible.

 

[Jim508]

ishvaaag,

Thank you so much for the help! It is becoming clearer now. However, I have two more questions regarding the document you sent me.

1st: When you port the moments from the column origin to the critical section nonprincipal axes, you utilized xo & yo distances that is opposite of ACI 421.1R. When we port the shear load, we are concerned with the perpendicular distance w.r.t. the moment, correct?

2nd: I referenced Decon's Studrail Design program to compare the results. You provided principal axes moments that are different than what Decon's program provided. Decon's program uses the column origin for all points of reference, does this impact the principal axis loads? Would this be column origin principal axis moments or centroidal principal axis moments? Do you know how Decon arrived at the principal axis moments?

All help is greatly appreciated!

Best Regards,

Jim

 

[ishvaaag]

I see your answer now; To the first question it seems to me you are entirely right, for we are porting the moments perpendicularly to the named axis and so distance corresponds to be that of the other axis. Sorry, the equations are badly stated and I will correct that and repost the corrected pdf.

Respect the second question, the previous error impact the moments provided at principal axes and then when calculated we will sort any differences with Decon's results.

 

[Jim508]

ishvaaag,

Thank you for the help. Initially you mentioned Publication SP-17(91)(S)
(all throughout)
(has examples, and aids for corner columns as well)as a guide. Where can I find this publication? Does the corner column aid/examples take the rotated centroidal principal axes into consideration?

 

[ishvaaag]

I bought it once from ACI itself and followed ACI 318-89; but I think to remember from web inspection it is still being sold according to one more modern code... yes, here it is:

http://www.concrete.org/PUBS/newpubs/SP1709.htm

If this new publication has design aids or not for the issue I don't know, have not seen it.

I am finishing my corrected and revamped document for the question and soon will post it.

 

[ishvaaag]

Well I have remade the pdf document and am in better understanding of ACI ways and get accord with the worst stress by Decon; yet I don't get match their expressed moments, the definition of which should be illustrative to see.

Maybe it is a inverse port to the centroid of the moments I consider, even parallel to the I may try to ellucidate later such possibility, or just transformations of my calculation when just starting from the being applied moments, once in each direction 1 and 2.

Hope this helps.

Respect the centroidal rotated axes they are a necessary feature of the current check, since Lx and Ly for gammavy -at least for asymmetrical sections- can't be got but after their determination, since a projection of the considered shearing surface on them. Anyway the procedure in SP-17 of ACI 318-89 do not consider the rotated axes, answering the overlooked question of Jim508.

For corner columns, essentially the procedure in the old SP-17 for rectangular columns gets the additive to Vu/A stress coming from unbalanced moments M1 and M2.

In the Slabs 9.9 chart you get k'2 and k'1; if the column was square shear from moments would be k'2·M1+k'3·M2

In the Slabs 9.10 chart you start with k'2 and k'3 and c1 and c2 and get corrected k2 and k3 for rectangular corner columns; shear for moments then would be k2·M1+k3·M2

It also has at chartSlab 9.11 a correction to get less conservative values of the mechanical depth d of the slab to be considered whenever the goemetrical aspect ratio of the rectangular column (long to short side) exceeds 2.

 

[ishvaaag]

I think that from the combination for stress being used they must be moments that once applied on centroidal axes for the respective straight bendings and shearing surface second moment respect such bending axis produce the same worse stress at worse point, i.e., my point 2 in our case; i may try to ellucidate if such is the case.

Also, again o Jim508 issue, look at Fig. B2 of ACI 421.1R-99 where it is clearly seen how for corner columns the principal axes are to be taken for calculations, i.e., the M1 and M2 if understood parallel to column faces seem to be excluded, since the equilibrium is in any case made for the centroidal flexure as it is expected to happen; and this is reinforced by the fact that we pretend to use gammavy= to that of edge column, hence pretend to restore such image of behaviour that of course is not retained if we proceed with M1 and M2 along faces. Furthermore it might be stated that maybe using gammavx= to that of center column (once in principal axes) could be arguable, different from 0.4.

ACI-318 05 seems more straightforward. You determine fraction taken directly in moment at 13.5.3.2, everything else goes to moment transfer to shear, see 11.11.7.1

So no separate calculations for gammavx and gammavy etc; they might have become wary and tired of wrong interpretations. For the inner and edge columns everything is stated straight on the faces on the closed form formulations of the second moments; combination if not stated to be made as usual; and for corner columns, except for the need of finding the center of principal axes of the shearing surface (something that also happens for edge columns) no provision is made to make any shear stress but parallel to the faces, so use the closed form values of the second moments in parallel to faces' setup, or as per the image included in my first answer to this question.

 

[ishvaaag]

In the inmediate previous post, when I put ACI 318-05 was ACI 318-08. And what is eliminated is not the need of separate gammavx and gammavy, but are given a common formulation.