Strut & Tie - Offset Column design 2

[KutEng]

I have been a long time lurker on eng-tips and have finally found the need to make a post for myself.

I have recently become familiar with Strut & Tie modeling and am currently faced with designing an offset column attached below. I have tried designing without a drop panel and my tie forces were far too high so added the drop panel in to increase the angle between the strut (black) and the ties (red). I know it would be ideal to have my bottom tie at node C however we do not detail reinforcement in the bottom of our drop panels at our firm.

I am wondering if my current model is reasonable (or even possible) with node B being midway through my strut. Am I missing additional struts or ties? Is this even a Strut & Tie problem or can I use standard methods of analysis? I am having trouble finding the resultant tie forces as I get different results when using the sum of all forces/moments or using simple trig so I'm assuming I am missing elements somewhere.

Any help would be greatly appreciated. Thanks.

 

[rapt]

steveh49

If you get rid of the drop, the lines probably end up as a jumbled mess on the ground after the compression failure in the columns. There needs to be sufficient depth to make sure that the compression can distribute over the full width of the column assuming the full column dimension was needed in the first place. Usually based on about a 30 degree angle of distribution.

Otherwise you end up with something like what happened with the Opal building in Sydney (one of its many problems)!

 

[Settingsun]

Rapt, are you referring to my question in the 5th post in this topic? I thought if you got rid of the drop then you could get rid of all the ties too, suggesting the problem had been over-simplified.

 

[rapt]

steveh49.

Yes, that comment and KootK's reply.

The drop is not causing the need for the ties. The eccentricity is. I do not think S/T can give a solution in that case either, but you still need sufficient depth for the load transfer.

 

[KootK]

This is an implicit requirement of S&T design. CCT nodes have lower capacity because there is tension in one direction which 'activates' the tie. The opposite of the strength increase when concrete is confined with transverse compression.

I agree with that wholeheartedly and I'm glad that you mentioned it. In a similar vein, I see the situation as analogous to the middle case below. It was never my intention to suggest that, for the purpose of nodal compression efficiency, the node should be treated as CCC. I was merely trying to explain how I visualize the load path in these situations such that one would not need a four member node in order to account for resistance coming from both the tension and compression sides of the node. In retrospect, however, I can see how my statements implied full CCC node treatment so, in that respect, I'm grateful for your clarification.

 

[KootK]

I'm not sure if I'm interpreting the statements of others correctly on this front but, one thing that I would not agree with, is any opposition to the use of STM for this condition. In my opinion:

1) STM is the perfect tool for something like this. Heck, we invented STM to address such, obviously non-Bernoulli situations. I think that OP came knocking on just the right door with this.

2) Yeah, the STM is not the end of the design. There are moments in the slab that need to be dealt with both from the perspective of strength and stiffness. The sketch below, repeated from above, makes that necessity pretty clear I think. But, at some point, I think that our obligation is to stick to OP's particular question and trust that he knows his craft well enough to handle the parts of the problem outside the scope of the original ask. Somewhere in the structure there are likely two or more footings that need to generate tension / compression couple to counter this offset column business. But I certainly don't feel compelled to point that out to OP or to suggest that STM may not be an appropriate tool here for that reason.

3) As Steve49 intimated, my experience of practice in the industry leads me to believe that conditions like this are ubiquitous. If there ever was a time where we could have vetoed this kind of thing out of hand, the sun set on that option long, long ago.

 

[Settingsun]

Strut and tie is fine here. In the first response, I was trying the be a bit socratic. If no btm steel was a firm requirement, I wanted the OP to be able to prove that's ok. The model in the original post was a bit short of that.

We don't know the magnitude of the column load but, if close to the column capacity (if the columns aren't oversized), S&T will fail if the strut through the slab is too flat. The strut area will be smaller than the column area, and the shallow angle to the tie(s) will mean you can only use a small fraction of f'c.

I think generally it would be easier to design for the combined loads ie include the slab loading in the model. You then don't have to keep track of whether other loads cause transverse tension in struts and don't have to interpret co-located struts at different angles from various loads. But eyeballing this case should be doable.

KootK, I was pretty sure I was the only one reading the ccc/cct stuff that way but better safe than sorry.

If we take away the upper column and replace with a live load, I daresay many (most?) designers wouldn't look twice, rightly or wrongly. The load just goes 'straight into the column'. (But if it's a moving heavy load, the slab would be thicker so maybe I'm just rambling now.)

 

[rapt]

Ar Engineer's original post said it could not work without the drop as the tie forces are too high with a 200 thick slab. What he has not check is vertical force transfer through a 200mm depth which likely also fails.

Adding a drop does not reduce the tie forces required to produce the same moment couple at the face of the drop, so the tie forces are still too high.

Adding the drop adds requirements for vertical ties in a 200mm thick slab.

The rotation required in a 200 thick slab to generate this tension/compression force couple would be enormous. All the drop does is move it to the edge of the drop and introduce an upward component of force at the edge of the drop that causes more rotation if that is possible.

The drop needs to extend the full length of the span either side to give it a chance of making the design work.

 

[KutEng]

I'm definitely glad I asked this as I have seen similar offset columns done before in our firm yet no one seems to bat an eye as to the care that evidently needs to be taken in designing such an offset. At least now I know I'm not crazy when I go challenging the senior engineer's designs (or lack of). Although those buildings are still standing to this day I guess so maybe we are the crazy ones.

In case you were all wondering my column force is approximately 5100 kN and my tie reinforcements were up at 10N32's which had me a bit shaky. But thanks to some sort of miracle, the architects decided to remove the offset without us even mentioning it so I guess we can all sleep at night knowing there's one less offset in the world.

Kootk, in all honesty, your analogy made me think for a moment that I could consider all CCT nodes as CCC. I decided, however, to stay on the conservative side though and stuck with CCT.

Rapt, could the tension/compression couple cause shear failure along a horizontal plane within the slab? What would I need to check for to make sure this coupling is ok?

Another thing I've been wondering with these offset columns which I'll probably need to start a new thread for is whether punching shear comes into play here. From my understanding (Read: I am far from punching shear mastery), if your column lies within your critical perimeter, you do not need to consider it however there will definitely be some prying force due to the offset. Would this not be considered a mechanism of punching shear?

 

[rapt]

Ar Engineer,

RE Horizontal shear, Technically yes, but I would have thought you stress limits at compression stress nodes would limit the amount of force you can transfer before this would happen.

In your case, 10N32's is equivalent to 4000KN. How could your concrete strut transfer that? Assuming a generous half depth of the slab and a 1000mm width that gives you 40MPa concrete stress at the node.

RE Punching shear, it would depend on how much overlap there is. The big worry for me in your case is the compression stress in the columns. If you had the case with only the slab and no drop panel, the compression needs to transfer from the column above to below. It will distribute at about 30 degrees to the vertical, so if that is the 300 dimension of the column we can see on the drawing, then only about 250 * 900 (from 300 / 2 + 100) of the full column width will be taking the full compression. If it is the 900mm dimension, then only 500 * 300 (from 900 / 2 + 100) of the column will be taking the full load.

So if your column is working hard at 900 * 300 it is working a lot harder on the reduced dimensions. And the rotation you are getting to make the S/T work, there is a big moment induced in the column as well!

Yes, the overhang part could try to punch through, especially if you have compression problems in the column below, and a lot of rotation due to the extreme flexibility of the slab providing the S/T transfer.

It is a wonder how a lot of concrete buildings stand up! Most times the factors of safety involved and redistribution save them. Sometimes they do not!

 

[KutEng]

I assumed the strut to be the same dimensions as my columns above and below (900x300) with 40mpa giving me a factored strut capacity of:
0.65 (Concrete reduction factor) x 1 (prismatic strut reduction factor) x 0.9 x 40Mpa x 900mm x 300mm = 6318kN capacity

As for my node capacity: 0.65 x 0.8(CCT node) x 0.9 x 40Mpa x 900mm x 300mm = 5054.4kN capacity

I'm unsure how you got a 40MPa stress - I got a stress of 15Mpa for my 900x300 strut.

 

[Retrograde]

So if your column is working hard at 900 * 300 it is working a lot harder on the reduced dimensions.

But as slenderness is not an issue on the reduced section it might not be working harder at all.

 

[Settingsun]

But thanks to some sort of miracle, the architects decided to remove the offset without us even mentioning it so I guess we can all sleep at night knowing there's one less offset in the world.

Could it have been an error, or had they specifically mentioned it before? Either way, it's a good reminder that we should speak up if someone is steering us towards non-optimal structures. There may be good reasons or there may be no reason and they're happy to change.

x 1 (prismatic strut reduction factor)

Is this a prismatic strut? Looks as though it could diverge through the thickness of the thickened slab. In which case, be careful with ignoring slight geometry effects as they can add up. Eg in this case, the slope of the strut has three effects: increase of strut force compared to column force (the strut force is the hypotenuse of the force triangle); the strut width is less than the column width (the column is the hypotenuse); and the strut efficiency factor is less than one.

 

[rapt]

Ar Engineer

I am talking about the compression in the bottom of the slab forming the compression part of the moment couple in the slab.

 

[KutEng]

Rapt,

I see the issue now. Would I be able to consider bottom reo to take some of this stress? Either considering the reo within the strut or by adding a horizontal tie to the left of that node as KootK has shown in his sketch?

Steveh49,

No, the architect claimed they needed the offset to get their kitchen layout to work, which apparently was more of a priority than the structural requirements of the building... must be a new code clause?

In terms of the prismatic strut, if my column over and column under are the same dimensions can I not assume my bearing area/node width is the same and thus my strut will be prismatic?

 

[rapt]

KootK has shown a diagram of possible strut forces. You have to dimension the struts to take these forces and transfer the forces to different struts at nodes. There is a an angled compression strut from the bottom to the slab at the right. You have to dimension this strut to meet the strut in the slab and make sure the compression stresses are ok. That is before anything gets into the horizontal struts in the slab.

Then when it goes into the slab, stress in the compression reinforcement will develop over a length, it does not happen immediately.

RE you last question, you cannot assume anything. Work out how the forces can transfer through the concrete over the depth available.

 

[Settingsun]

From the AS 3600 commentary (C7.2.1):
"Compressive stress fields try to diverge. If, and only if, they cannot diverge due to the geometry, a prismatic strut develops."

Also have a look at Figure 7.2.1(c) in the code. The bottle shape is shown despite equal bearing areas top and bottom.

 

[calvinandhobbes10]

Very interesting posts on strut and tie methodology, thanks. I am not sure about a flat slab, likely very thin, being used to resolve the Pe force couple, because the resisting arm (“truss” depth) is so small, even if it checks via strut and tie. Also concerned about resolving the force couple into the lateral system.

Ar, should you encounter an offset column condition again, perhaps consider a floor-to-floor sloped column (or just make it a rectangular prism enclosing the plan areas of the above and below columns). As i see it, this is much more rigid load path and with less shearing penalty on the shear-core walls.

Of course, as you experienced in this case—-eliminating column offsets is the best route!

 

[KootK]

Kootk, in all honesty, your analogy made me think for a moment that I could consider all CCT nodes as CCC. I decided, however, to stay on the conservative side though and stuck with CCT.

Wherever you have a significant mass of concrete available in the slab opposite the tie, you surely could consider the nodes as CCC via one of two options:

1) Just ditch the tie entirely and say that the strut leans against that opposing concrete. I suspect that this is why most of these things tend to work in the first place. Certainly, if it's me though, I'd be tossing in the tie for good measure anyhow.

2) You could de-bond the tie over the width of the crossing node/strut. In that way, you retain the nodal efficiency of a CCC node and the node and strut would just slide past the tie. I've never heard of anyone doing this but I don't see why it couldn't be done. Similar things are done in the world of precast regularly.

Another thing I've been wondering with these offset columns which I'll probably need to start a new thread for is whether punching shear comes into play here. From my understanding (Read: I am far from punching shear mastery), if your column lies within your critical perimeter, you do not need to consider it however there will definitely be some prying force due to the offset. Would this not be considered a mechanism of punching shear?

This thread of my own speaks to pretty much exactly your concern I believe: Link. This is, in my opinion, another one of the significant benefits of the thickening approach. You'll effectively force the critical shear perimeter for the delivery of slab moments to be the perimeter of the drop.

Lastly, with all of this discussion of slab moments, I think that it's prudent to recognize that any moment stemming from joint eccentricity may well end up in the columns. In something like this, the columns may be competitively stiff compared to the slabs with respect to absorbing moments. And, so long as this doesn't blow out the columns, this can do nice things for the amount of moment that goes into the slab. See the struts drawn in black in the sketch below.

...could the tension/compression couple cause shear failure along a horizontal plane within the slab? What would I need to check for to make sure this coupling is ok?

There is horizontal shear but I see no need for any special checking of it. You'll check the slab for vertical shear under a load case that considers the requisite slab moments and that will govern over any horizontal shear plane. Checking the vertical shear should automatically satisfy horizontal shear.

 

[KootK]

..and with less shearing penalty on the shear-core walls.

I disagree with this. If anything, I believe that OP's solution will result in less impact on the shear walls than would either walked columns or sloped columns. Dealing with the eccentricity in a thickening is rather like dealing with it via a transfer beam. The eccentricity manifests itself as corrections to the gravity loads carried through the system, much as jayrod was thinking at the top.

Also it appears (and maybe my analysis is a bit rusty) the lower column will see a slightly amplified force due to the restoring compression struct on the right side.

 

[calvinandhobbes10]

Dealing with the eccentricity in a thickening is rather like dealing with it via a transfer beam.

Agree that either transfer beam or sloped column resolves forces for offset columns. However, transfer beam approach means an 8” thick slab column strip (20” in vicinty of carried column) is essentially acting as the transfer beam. the backspan moment at the righthand edge of drop is your critical section and likely now the weakest link, not to mention deflection-critical. KootK, you seem to command a great deal of knowledge in this—-does that column strip backspan not give you any concern? Would it be different for 20-stories above the offset versus 2-stories?

I suspect that this is why most of these things tend to work in the first place.

This.