Diagonal compressive failure of concrete 1

[hardbutmild]

Hello,

this is my first post, I usually watch other threads and find most of the answers so thank you for that.

My question is does anyone here know where the expressions for diagonal compressive failure of concrete come from?
To clarify, I'm talking about the maximum shear resistance that an element can have before the diagonal strut fails under compression, in eurocode it's denoted as VRd,max.
Now, I do know how to get the expression from some basic statics and geometry, but I want to check how the actual experiments to confirm it were done. I want to do this because I think that the expression is valid only for elements with low ductility. Here is my reasoning behind it. In the standard procedure you basically check the strut for failure and it should be the same at any point on the strut, but at the point where the strut connects with the compression area (caused by bending) a 2D stress field occurs. In other words, if bending causes large stresses in compression area, at that point less diagonal stresses can be transferred (basically I check main stresses and not just normal and shear independently).

Why do I care for all this? Well, because of walls in earthquake. Eurocode 8 states that you should reduce this strength to 40% (that's 2,5 times reduction!) of it's basic value for high ductility class DCH (EN 1998-1 section 5.5.3.4.2 if you want to check), but no reduction for medium ductility. Further they say that this is "due to dynamic nature of the loading", but the dynamic nature is present in both ductility classes and usually tests are made by static pushing of the wall so it makes more sense that it's due to ductility.
I'm trying to figure out what really happens because this reduction is HUGE, this strength can not be increased by adding reinforcement and shear failure is non-ductile and should be avoided at all cost. It just feels very important.

I'm sorry if this is not coherent, too long or if I posted it in the wrong place. I can provide way more explanations if needed but I didn't want to put too much in the first post.
If you can give any insight into anything related to this I'd be very grateful, thank you!

 

[oldestguy]

Stay with it. In time some structural guys will show up. You are somewhat over my head, but I'm not a guy that into structures.

 

[Agent666]

The reduction in codes to shear strength in beams, walls, columns etc is due to the fact that under cyclic loading there will be cracking, member elongation, spalling of the cover concrete potentially, crushing of the confined core of concrete, and the reliance on aggregate interlock as part of the concrete shear mechanism is reduced or becomes less certain. Here in NZ we take concrete shear = 0 for higher levels of curvature (or local ductility demand at potential plastic hinges). Keep in mind ductility = controlled damage to dissipate seismic energy in simple terms.

Note this local ductility demand is quite separate to the global ductility you might use to determine the overall seismic loading on the structure. A short deep beam will undergo much more plastic rotation in the hinges than say a longer shallower beam for the same overall lateral drift.

 

[Tomfh]

Not familiar with that code but presumably higher ductility class relies more heavily on major deformations to absorb earthquake, in which case shear rupturing is a much bigger concern (since the shear capacity is not ductile, and heavily deformed concrete has reduced shear capacity)

 

[hardbutmild]

@agent666
You say that aggregate interlock can't be relied on and I agree, but aggregate interlock is a mechanism relevant to resist tension force. As you mentioned, it's usually completely neglected and that's fine because you can simply put more reinforcement. Compressive failure on the other hand can only be avoided by making a wall thicker and that's usually a problem.
You mentioned some other problems that affect shear strength like cracking. That is actually considered in eurocode for concrete already so this is a reduction in addition to that because of cracking. Spalling of the concrete cover is also considered in a way that you consider only the part of wall inside confinement reinforcement. Regarding member elongation, do you mean because of axial force? Because that's also taken into account with the basic formula.
Now regarding concrete crushing it really depends will it happen and how much will it crush because that depends on the way you detail your wall, axial force, the amount of reinforcement and as you mentioned slenderness.
However, none of those problems are specific to the cyclic nature, but rather to the fact that large plastic deformations occur, right?

Note that this reduction is specifically given ONLY for walls of high ductility (not for beams or columns, nor for any element of medium ductility). It also completely disregards the way you detailed it or anything.
Yeah I know about ductility, both local and global, but thanks for the info.
My main problem is that I feel like this could be the case for medium ductility (most often used in practice) and that it's not that dependent on "cyclic effects" but more on ductility.

Just to paint a picture what "a medium ductility" is in eurocode, it usually (now this can obviously vary) implies required curvature ductility of a wall is 5 or larger. High ductility is 7 or larger.
Also the fact that it's given only for walls and not columns doesn't make any sense to me.

@tomfh
I agree and that is certainly the case. The problem is the following, I saw an article from which that provision is taken supposedly and there they had a lot of experimental data and their conclusion is that for high ductility shear compressive strength should be 40% of basic value (that's what the code also says). BUT HERE'S THE THING, according to them for medium ductility (standard structures, like 90% in practice) this reduction is roughly 51,5% (that's their exact number and the code requires no reduction). That's HUGE! Code requires no reduction at all for those structures.
In other words, I'm not really concerned with why is there a reduction of 2,5 times for high ductility, it's why there ISN'T a reduction of 2 times for medium ductility.

Question for all of you not from europe: Is there such reduction in your code? I'm talking specifically about compressive shear strength. I know that there is a "force amplification" factor but it's independent of this phenomena.

 

[Tomfh]

Ok, I understand your point. It does seem a double standard.

What year version of Eurocode? I looked online and the versions of 1998 available on the web are 2004 edition. The 5.5.3.4.2 clause doesn't appear to differentiate between DCH and medium?

 

[hardbutmild]

What year version of Eurocode? I looked online and the versions of 1998 available on the web are 2004 edition. The 5.5.3.4.2 clause doesn't appear to differentiate between DCH and medium?

That's the last version yes. Clause doesn't say it's about DCH because the whole document is poorly written. The whole chapter 5.5 is about DCH, it's called "Design for DCH".

 

[Ron]

Aggregate interlock has little to do with tension resistance. Even in tension, the mode of failure resisted by aggregate interlock is shear.


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[hardbutmild]

Aggregate interlock has little to do with tension resistance. Even in tension, the mode of failure resisted by aggregate interlock is shear.

Imagine a member under shear force (only shear).
It will fail on a diagonal, right? It won't be cut vertically.
That's because either principal tension stress was too large or principal compression stress was too large.
I'm saying that shear failure caused by exceedance of principal TENSION stresses depends on interlock, but the one caused by exceedance of principal COMPRESSION stresses doesn't.

That's what I meant by "tension failure" or "compression failure".
We're not talking about axial tension.

 

[Agent666]

Tension capacity doesn't rely on interlock of the aggregate though, it relies on the tensile capacity of the concrete matrix (cement paste + aggregate).

Aggregate interlock is the mechanism by which shear is resisted/carried in the concrete after it cracks.

Regarding member elongation, do you mean because of axial force? Because that's also taken into account with the basic formula.

For member elongation I'm not talking about the elastic elongation or shortening due to axial load. I am referring to in a ductile system, if you are yielding the tensile reinforcement in one cycle, but in the next opposing cycle the reinforcement is not yielding in compression. The elongates the reinforcement due to the strain not being recovered in the opposing cycle. With each successive cycle this elongates the member as a result. This effect for example in terms of beams can end up pushing columns out from the floor plate and causing large cracks in the floor especially in the corners. In the worst cases a loss of support for any flooring units can occur in these regions. In walls it can mean the distribution of gravity loads changes if it also supporting continuous beams because you are in effect trying to push these beams upwards when the wall is longer. Walls often have a lesser confinement requirement than say columns.

This is a real effect and I'm not sure how its treated in any code but my own (NZS3101). Our code was amended a few years ago now to address all these lessons learned from our 2011 Christchurch and 2016 Kaikoura earthquakes. These earthquakes resulted in some regions of the response spectrum at least 2 times the design basis level earthquake. We has increased awareness of this as some of our recent earthquakes have had quite a few high profile failures in this regard, one building in particular in the 2016 events had a number of double tee units lose their seating and come down on the floor below. Thankfully this earthquake occurred near midnight and the buildings were not occupied, but people would have died for sure based on the photos (if you are interested in reading up on it google statistics house floor collapse.

It's sometimes called 'frame dilation' as well when its discussed for moment frames if you are looking for literature on the effect.

I'm talking specifically about compressive shear strength.

I've never heard of the term compressive shear strength? In our code there is some enhancement due to axial load, but its far less pronounced in ductile members.

We have for reference 3 separate levels of detailing, nominally ductile plastic regions (NDPR), limited ductile plastic regions (LDPR) and ductile plastic regions (DPR), these are based on limiting curvatures which sounds the same as what Eurocode may have. I'm sure Eurocode must have references on which there minimum recommendations are based. Perhaps delving into those will help answer why the code is the way it is.

Keep in mind that codes only prescribes the minimum requirement, if you want to go further based on what you know, research or otherwise there is no one stopping you. In this part of the world we've dealt with these rules for neglecting shear in potential hinge regions since the conception of our modern standards in the 1970's so it's not a shock to us, it's just the way things get done. We look at other codes with the more relaxed requirements around things like member confinement and being able to take concrete shear capacity when ours don't, and wish them the best for the future, we've already been there and learned our lesson so to speak.

 

[Tomfh]

I've never heard of the term compressive shear strength?

He's referring to VuMAX, where the compression struts crush.

 

[Agent666]

Ah right, it's simply termed maximum shear strength limit or something similar here.

 

[hardbutmild]

Tension capacity doesn't rely on interlock of the aggregate though, it relies on the tensile capacity of the concrete matrix (cement paste + aggregate).

I'm talking about shear induced tension. Tensile stresses because of shear forces. The thing that causes diagonal cracks. I used the term "tension" to distinguish it from "compression" or crushing. Shear can always be substituted by principal stresses. Why do you think cracks due to shear are at a diagonal? Because tension stresses caused by that force are diagonal. Just draw trajectories in a beam and you'll see failure is caused by tension. If the failure was truly due to shear crack in a beam would be vertical (just like bolts may fail)

@agent666
I never thought of that! It completely makes sense actually and should be considered, but it's not so much related to capacity, rather to forces and structural response.

I think eurocode was based off of new zealand codes (or at least that's something I heard long time ago) so they're probably similar in a way.

I checked the background documents for the provisions given by the code and their explanation is "we didn't want to put any reductions for medium ductility so that wall systems could be economical"

Now just to clarify again, we DO neglect shear strength completely, but that's not my concern at all.

The problem is maximum shear limit (the force at which crushing occurs). I have checked research and I only found some experiments, no theoretical explanation as to why does this limit drop or does it drop with rise in ductility indefinitely or is there a limit.

To further clear it up, I'll try an example. Imagine a wall. You get with standard analysis a force V acting on that wall (let's say it's 2000 kN). You increase it due to "dynamic magnification" (let's say V = 3000 kN after amplification). After that you say strength = 0 and put enough horizontal reinforcement to take the whole increased force. After that you have to check that struts don't crush. You get by your code expression (usually found in a part of code about concrete, not seismic part) that they crush at a force of 4000 kN. You think you're safe, right?
Our code says "if you have high ductility multiply it by 0,4". That would mean that crushing occurs at the force of 1600 kN. Now since 1600 < 3000 it's really bad and it'll fail way before the required ductility is achieved.
But our code also says "if you have medium ductility it remains the same". That would mean that crushing occurs at the force of 4000 kN and that you're safe. In reality it makes no sense at all to me. There should at least be some reduction to it.

Problem here is that if some reduction of that shear strength limit occurs for medium ductility structure, it'll fail in a very non ductile way! And difference between 1600 kN and 4000 kN is huge. The only way to avoid that failure is to require a thicker wall. That changes it's stiffness and so on.

No mechanisms you mentioned before actually influence the maximum shear limit (I think) so I wonder why does it reduce. Because the only documents I could find (most of them research) all say it's because of a dynamic nature of loading.
But dynamic nature makes no sense to me especially since dynamic effects occur even if you design a building to remain elastic.

As I said, I haven't been able to find any research papers explaining this and I've been looking for it on and off for a few years now.

 

[Klitor]

Before I start - Just a question hardbutmild..
You have 2 identical walls - You calculate one using DCH provisions and one using DCM - Do you think VRd is the same for both cases?

 

[hardbutmild]

You have 2 identical walls - You calculate one using DCH provisions and one using DCM - Do you think VRd is the same for both cases?

I'm talking only about VRd,max (crushing) so if the geometry and concrete class are the same, yes. So the basic value is the same!

BUT, because of different ductilities, this strength will reduce more for DCH. The question is why does it reduce?


I don't think that final strength should be the same for DCM and DCH, but if the reduction for DCH is 0,4 for DCM it should be 0,5.
Although I think it shouldn't be based only on the ductility class, but I don't know what should be considered.

 

[Klitor]

They are not the same
For DCM, VRd,max is not a fixed number
If you take a look at the DCH item you referenced, EN 1998-1 section 5.5.3.4.2(a), it says that VRd is calculated using theta angle of 45 degrees... But for DCM it is not so (you can freely select angle between 28 and 45 degrees) ... so for instance your same wall from example that has VRd,max=4000kN will have VRd,max=3350kN if you select 28 degrees.

Also, fallacy in your example is that force V is 3000kN for both DCM and DCH...
In fact q factor (or R for our north american friends) is 3.00 for DCM, and 4.50 for DCH .... So for the same building the DCM force V in the wall will be multiplied by 1.5 (4.5/3) and will be 4500kN (Also doesnt pass) ... So in essence you are reducing capacity, just in another way.

 

[hardbutmild]

@klitor
nothing you actually said has anything to do with the fact that for some reason shear strength reduces, but I'll address your post.

so for instance your same wall from example that has VRd,max=4000kN will have VRd,max=3350kN if you select 28 degrees.

It's usually considered either 45° or 39,8° for standard design. Using 22° (the lowest allowable value) seems unreasonable and you usually have to prove that you can actually provide that angle. It assumes a large redistribution of forces which is not a good idea in a critical section where dissipation is supposed to happen. It seems to me that choosing an angle different than 45° already assumes some plastic behavior and to have a same mechanism addressed by two factors seems confusing at best. Also, in earthquake walls cracks tend to be at a 45° angle.
Also, by assuming the lowest possible angle you get around 80% of the original strength. Experiments suggest that this value is closer to 50%, so it would be 2000 kN. Do you understand my point? It's not something that should be ignored since it's still just 60% of the smallest value that you suggested.

This variable inclination thing only adds to some differences in the design, but it doesn't address the problem of shear strength reduction.

And "they're not the same" is a maybe. You can chose 45° regardless and I always tend to do that when doing seismic design so yes, they are the same

So in essence you are reducing capacity, just in another way.

You're fundamentally wrong. This increase has nothing to do with the reduction of strength, it's a phenomenon on it's own. Also, the basic value is 2000, it's multiplied by 1,5 for DCM and by a larger value for DCH. So if it's 2000*1,5 for DCM for DCH it might be 2000*(3/4,5)*2,25 which gives the same value. This increase for DCH can kind of vary, but it's usually between 2 and q. For most structures (period smaller than corner period) it tends to be on a higher side. So usually DCH force is larger than that for DCM AND the strength reduction is larger.

This force has nothing to do with my question though because I'm concerned ONLY with why does strength reduce. This force part is quite easy and straightforward. My point in that simple example was only to show what the problem is since people probably aren't familiar with eurocode procedure.

 

[Klitor]

Indeed if you get multiplicator 2,25 you are just choosing the inappropriate method for calculation (in that case you should calculate this specific building using DCM).
I stand by my comment.. If you look into eg. Fardis, the point of DCM/DCH is only choosing the right method for specific structure (not some much higher level of safety, or material savings) and 0,4 is just a safeguard that you dont "accidentally" get too small shear force (and you CAN manipulate alpha0/alpha1,ε and bunch of DCH related items)

I did add strut inclination thing just as an indicator of one of EC8 many many small items that you CAN "use" to tweak you designs ... unfortunately, as you know, EC is sometimes very vague, and it is not exactly pure science
Just my 2 cents

 

[hardbutmild]

Indeed if you get multiplicator 2,25 you are just choosing the inappropriate method for calculation (in that case you should calculate this specific building using DCM).

Nonsense, the minimum value for that factor is around 2, so 2,25 or larger is the majority of cases. DCH tends to behave better in earthquakes that are unexpected since it has larger ductility and although it should be as safe or as economical it really isn't. Just look at the thing I'm talking about. Experiments show that there should be reduction of 0,4 for DCH and 0,5 for DCM. They take them for DCH, but not DCM. Same exact phenomenon in the same exact research paper! How can you claim it has the same level of safety? Also, do bear in mind that DCH doesn't require more strict regulations on the actual placement of reinforcement and it HEAVILY depends on the high level of crafstmanship, more so than DCM. In practice, they differ significantly.


Note that this increase is only for shear checks, when you determine moments they don't increase. So it makes PERFECT sense to get larger design shear for DCH. Because your structure needs to go deeper into the ductile area you need to ensure that shear doesn't govern for a longer time. Shear failure is non ductile so if you want ductility 1 you just need to ensure that it doesn't fail in shear up to idk 1,1. If you have ductility 2 you need to ensure that ductility 2 is provided and then it's allowed to fail in shear at 2,1 and so on. Larger the ductility, larger the increase of the shear force. It can be as large as elastic force, while for DCM it's half the value of elastic force.

and 0,4 is just a safeguard that you dont "accidentally" get too small shear force (and you CAN manipulate alpha0/alpha1,ε and bunch of DCH related items)

0,4 has nothing AT ALL to do with shear force. It is only related to CAPACITY. you need to consider BOTH the increase of the shear force and the decrease in the capacity. Latter doesn't exist in american codes.
0,4 isn't a safeguard it's actual result from an experiment, not a safety factor.

The point is not "how can i manipulate and trick the code". I know how to do that. The point is "WHY DOES SHEAR CAPACITY VRd,max REDUCE?". Does it have to do with the dynamic nature of earthquake? Does it have to do with ductility? If so, does it mean that if I design a system to behave in a plastic way for standard loads (no earthquake whatsoever) what is the VRd,max?


It's not a safety thing, fardis who you mentioned SPECIFICALLY says that in the designers' guide to eurocode. He says that "similar reduction should exist for DCM, but it wasn't introduced into the code because it would limit the usability of wall systems in practice". That's a very poor thing to do, you can't say "oh it's too expensive so I'll just ignore that this critical thing is in fact half as strong"

 

[Klitor]

I didnt see that one before - I was talking about the Fardis book..Why didnt you put excerpt in the beginning, it would be quicker..everything is written in it

Im putting it here if someone wants to continue, but I doubt something better can be found, excluding a email to Fardis or comitee members