Shear strength/capacity of deep beams 2

[dave_89]

Hello,

I have a practical question about shear strength of deep beams that are not a typical transfer beams but a continuos membrane through several stories.
Flexural capacity is not a thing that concerns me but shear is.
When you look at the examples that are attached to this message, there is plenty of shear cross-section area through the full height of the walls. But if we look at the wall as a deep beam and say that everything that happens in the area that is higher than the span of the beam (roughly one storey above)is a dead weight than shear becomes a governing design condition (drawings on the right). I'm interested in your thoughts on this topic because it's something that happens regularly in multi-storey residential buildings.

Thank you all for your comments and thoughts!

 

[NOLAscience]

What is this made of?

 

[KootK]

You have the right idea in that the shear situation is not adequately captured by the full depth of the multi-story walls. The approach for this that I'm familiar with is to:

1) Model the walls with strut and tie modelling.

2) Assume that the struts can be no steeper than common code recommendations.

3) Allow my shear resistance to dealt with by the vertical components in the diagonal struts.

 

[HTURKAK]

The shear should not be a concern for the cases shown on your sketch ..You can check the nominal shear strength as per ACI 318 11.5 and provide minimum ρt and ρl if Vu ≤ 0.5 * Φ * αc* λ *√fc * Acv in accordance with Table 11.6.1.

If i were , my concern would be the flexural reinf. when the deep beam was simple drop beam when 2nd storey conc. is fresh.. and props shall be provided for the 2nd and 4th sketch during 2 storey concreting..

Is this a tunnel formwork system ? ( parallel wall system , with steel tunnel formwork ?).

 

[dave_89]

@Nolascience
These are concrete walls.

@KootK
I'm not sure I understand what you are saying. The upper part of the wall is a wall without horizontal stresses

If you check the sketches that I posted, can you confirm that I understood you properly? The cross section area that acts as a shear area is only in the height of the strut?
When you check the other sketch - it says that whatever is in the upper portion of the deep beam it acts as a dead weight and it doesn't contribute to the shear strength of the wall.

If I make a calculation with this assumptions that active part of the deep beam is as high as it's span is h=l, I get a certain shear capacity or VRdmax (eurocode). I have a hard time believing that if the wall is 10 stories high it will fail in shear. But according to the theory that is available to me, it says so. I hope I explained it a little better.

When you compare the masonry wall with lintel (similar but in smaller scale) you calculate the lintel shear and flexural strength only with the masonry that is below the fictional compression arch.

Can this analogy be used in the concrete deep beam from the example in the first post?

Bottom line, is there even a need to calculate the shear strength in deep beams like the ones in the example, where we have n-number of stories with full concrete wall?

@HTURKAK
I will look into ACI and try to implement this check. But still not sure what shear strength area to choose for calculation. Maybe it will be clear when I read it.
Yeah, I always keep the props until the second story gets 70% of compressive strength and starts to act as a deep beam.
No particular formwork system, just something that occurs a lot and want to make sure that I'm thinking straight and want opinios of other professional on this topic.

Thank you all for your comments, I really appreciate it.

 

[le99]

I think you are mistaken in assuming the wall has a uniform load throughout its height, in reality, it's not. I think, for gravity loads, the wall should be designed story-wise to reflect the factual strength demand.

 

[KootK]

I'm not sure I understand what you are saying. The upper part of the wall is a wall without horizontal stresses. If you check the sketches that I posted, can you confirm that I understood you properly?

You understand properly.

The cross section area that acts as a shear area is only in the height of the strut?

Sort of. The way to design something like this is via strut and tie design, not cross sectional methods. In the context of strut and tie design, your shear capacity becomes the vertical component of your diagonal strut compression capacity per my previous sketch.

I have a hard time believing that if the wall is 10 stories high it will fail in shear. But according to the theory that is available to me, it says so.

I agree with the theory. The trick is to recognize that shear, being a complementary phenomenon, is as much about horizontal shearing action as vertical shearing action. In the horizontal sense, shear is about the transfer of axial force between the zones of axial tension and compression within the member (see sketch below). As such, the shear capacity outside of those zones is of limited use in resisting shear.

When you compare the masonry wall with lintel (similar but in smaller scale) you calculate the lintel shear and flexural strength only with the masonry that is below the fictional compression arch.

This is pretty much identical to what I've been describing. The vertical component of the arch leg compression resistance is the shear resistance mechanism.

Bottom line, is there even a need to calculate the shear strength in deep beams like the ones in the example, where we have n-number of stories with full concrete wall?

Absolutely. The entire height of the walls will not be effective in resisting shear. In this, I disagree strongly with HTURKAK.

 

[KootK]

You CAN use the entire height of the wall in shear if, and only if, you also use the entire height of the wall in flexure as illustrated below. In practice, this will be similar to le99's recommendation I suspect.

 

[dave_89]

@KootK and @le99

Thank you for your answers, guys.

I agree with the theory. The trick is to recognize that shear, being a complementary phenomenon, is as much about horizontal shearing action as vertical shearing action. In the horizontal sense, shear is about the transfer of axial force between the zones of axial tension and compression within the member (see sketch below). As such, the shear capacity outside of those zones is of limited use in resisting shear.

Sorry if I'm not thinking straight, but could you direct me to some kind of theoretical book or paper that explains this? I'm not sure that I understood this completely.

You CAN use the entire height of the wall in shear if, and only if, you also use the entire height of the wall in flexure as illustrated below. In practice, this will be similar to le99's recommendation I suspect.

Then I should reinforce the wall according to this strut and tie sketch that you have drawn? How can I force the wall to act like this? You think that a wall would perform like separate storeys if you reinforce it this way?

 

[KootK]

Sorry if I'm not thinking straight, but could you direct me to some kind of theoretical book or paper that explains this? I'm not sure that I understood this completely.

Sure. Start with this free article and then the book shown below.

Then I should reinforce the wall according to this strut and tie sketch that you have drawn?

I believe that is one good way to handle the situation, yes.

How can I force the wall to act like this?

You establish a strut and tie model that we expect to be a reasonable reflection of elastic stresses in the wall. This is made somewhat easy for you by simply following the code guidelines for strut and tie modelling which attempt to accomplish similar aims. This is how I arrived at my 55 degree strut angle. It's the maximally steep strut allowed by my jurisdictions concrete code.

You think that a wall would perform like separate storeys if you reinforce it this way?

At the ultimate limit state, yes. It may, however, take a lot of cracking and redistribution to get to that point which is why I prefer the first, single story model that I posted.

 

[ALK2415]

My understanding, Shear Wall design should be treated in segments rather than full depth [multistory height]
because of the each slab/level diaphragm (lateral stiffness/rigidity) which will provide restrain/constraint the full depth of the building shear wall actual behavior [under lateral wind/seismic loadings]
check this similar mechanism (for steel frame with infill steel plate)
Link

 

[dave_89]

Sure. Start with this free article and then the book shown below.

Thanks, I will check this out and get back here if I have more questions.

Rest of your answer is very well understood now. I share your opinion on the topic of ultimate limit state.
Designing it as single storey is definitely on the safe side.
I have read the book you pasted, I'll check it again, it's been a long time.