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# Strut and tie model comprehension problem4

## Strut and tie model comprehension problem

(OP)
Hi!

Many strut and tie models in publications are not stable trusses (the members don't necessarily form triangles), yet they are accepted as is. I was wondering why?

For example, in the first picture, from ACI 318 chapter 23, the truss seems to be missing a member. I was wondering why this member was not modeled?

I have added a member here to show what I mean:

### RE: Strut and tie model comprehension problem

That pink member is not required to satisfy equilibrium.

Stability is satisfied simply because everything is "braced" by the large mass of concrete. How could a beam like that form a mechanism?

### RE: Strut and tie model comprehension problem

You can add the pink strut if you want (and another, and another, and another) but it’s not necessary for stability in a monolithic mass of concrete.

### RE: Strut and tie model comprehension problem

(OP)
Thank you for your answers gusmurr and Tomfh. This explains the reason why they are not all triangular trusses.

I believe this beam would not have a failure mechanism with its "bracing".

The previous example was easy to calculate. However, would it be better to model complex strut and tie models as triangular trusses to calculate the load in them using a FEM software such as Advance Design America? Could it give a similar result by calculating this unstable truss using a FEM software with fixed nodes instead of pinned nodes?

### RE: Strut and tie model comprehension problem

I would avoid using fixed nodes to try to stabilised the truss model, unless you actually verify that there is negligible bending moment transmitted through the joints.

I think the usual way of getting around this stability problem is by introducing dummy members (like the pink one you showed above) with very, very small axial stiffness so that it attracts negligible load but still stabilises the truss.

(OP)

### RE: Strut and tie model comprehension problem

If the applied loads aren't equal then you'll need the additional diagonal won't you?

### RE: Strut and tie model comprehension problem

#### Quote (gusmurr)

Stability is satisfied simply because everything is "braced" by the large mass of concrete.

While it may feel more intellectually satisfying to add in the diagonal, I feel that gusmurr's comment above is the fundamental truth of the matter. The strut and tie method is a truss analogy and, like most analogies, it's imperfect. And perfect triangulation / explicit stability is one several ways in which it is imperfect. I believe that the stability of a model like this, put into equilibrium, is justified as follows:

1) Bracing loads for systems in equilibrium tend to be very small relative to the applied load.

2) It's really the horizontal shear capacity of the beam stabilizing our fictional truss. and that capacity can be expected to be massive.

Were one to remove all of the concrete other than that included in the STM model, there would indeed be a problem and, most likley, a need for something like the diagonal.

#### Quote (Agent666)

If the applied loads aren't equal then you'll need the additional diagonal won't you?

Certainly, something must be done to put the model into static equilibrium. And adding the diagonal is one way to do that. Another way, I believe, is shown below. I see a couple of advantages with that approach.

1) A simpler model that might be a bit easier to prosecute at the nodes.

2) You'd not bump up against, potentially, a diagonal strut that would trigger too shallow of a strut angle (25 deg etc) in a way that may be spurious.

3) Taken in aggregate, the diagonal and the model below both capture the same, fundamental aspect of the stress field: the strut highlighted in green gets shallower.

### RE: Strut and tie model comprehension problem

"Certainly, something must be done to put the model into static equilibrium." ... if you consider as a classical truss (with pinned joints).

But with fixed joints it is stable, and "surely" this is the understood modelling ?

### RE: Strut and tie model comprehension problem

#### Quote (rb1957)

But with fixed joints it is stable, and "surely" this is the understood modelling ?

I don't believe that to be the case rb1957. Normal rebar detailing in the joints would not support rigidity and I've yet to see anything in the literature to suggest a tacit consideration of such rigidity.

### RE: Strut and tie model comprehension problem

"fixed joints" should have been more accurately expressed as "moment capable" (ie some level of fixity, not necessarily fully fixed).

If you don't have Any moment capacity in the joints (truly pinned joints) then you have no structure.

### RE: Strut and tie model comprehension problem

#### Quote (rb1957)

"fixed joints" should have been more accurately expressed as "moment capable" (ie some level of fixity, not necessarily fully fixed).

I understood that in your initial comment. It's why I replaced "fixed" with "rigid" in by stuff. I don't much care which term is used as I understand the intent of both but I know that some folks here do get excited about precision in this arena.

#### Quote (rb1957)

If you don't have Any moment capacity in the joints (truly pinned joints) then you have no structure.

I disagree with that assertion. You have this:

#### Quote (gussmur)

Stability is satisfied simply because everything is "braced" by the large mass of concrete.

#### Quote (KootK)

It's really the horizontal shear capacity of the beam stabilizing our fictional truss. and that capacity can be expected to be massive.

Although we use a truss analogy in our STM analysis, we have to recognize that the final product here is not a truss.

Philosophically, strut and tie analyses really have more to do with capturing arching behavior than they do "trussing" behavior. The truss model is just an analytical device, it's not the whole truth of the situation.

### RE: Strut and tie model comprehension problem

If we're going to fixate on the truss model to the exclusion of all else, I suppose that one could represent it this way.

### RE: Strut and tie model comprehension problem

well, that was the original question, no ? "why is this truss considered stable ?"

The picture shows a very specific (very ideal) loading, and in this case the truss is good (with/without moment capable joints).
And doesn't need the additional diagonal member suggested.

To push the truss and say "what if it is loaded by only one load ?" or "what if one corner moves relative to the other?" isn't what the pic is trying to show.
I'm sure these cases are dealt with in other sections of your standards.

### RE: Strut and tie model comprehension problem

Given that dead symmetrical loading is an utterly realistic expectation in the wild, I feel that a little digression into asymmetric loading is germane to the discussion. One might even view the asymmetrical loading as one of the possible perturbations that would induce instability.

There was never any suggestion that one corner moves relative to the other. That's just an adjustment to the analytical model to accommodate load asymmetry while still maintaining equilibrium.

### RE: Strut and tie model comprehension problem

Somebody may have already said it/alluded to it.....but is that top boundary strut even needed? Seems like a lot of S&T models I've seen handle multiple point loads without it. (Depending on the geometry.)

### RE: Strut and tie model comprehension problem

(OP)
Thank you KootK and rb1957 for the replies.

WARose, I think the top boundary strut is important in the model since this strut represents a high compression zone (top flange of the beam).

### RE: Strut and tie model comprehension problem

#### Quote (WARose)

Somebody may have already said it/alluded to it.....but is that top boundary strut even needed?

Are you suggesting something like the model shown below instead? Certainly, for short shear span like this, I could see that having legs.

I believe that it is frowned upon to have crossing compression struts although, frankly, I've not fully understood why that should be other that the analytical complexity that it introduces. Has anybody seen examples of crossing compression struts in the literature?

### RE: Strut and tie model comprehension problem

I see stuff like this too but assume that there is a boundary strut implied if not explicitly acknowledged in the sketch.

### RE: Strut and tie model comprehension problem

#### Quote:

Are you suggesting something like the model shown below instead?

Yep.

#### Quote:

I believe that it is frowned upon to have crossing compression struts although, frankly, I've not fully understood why that should be other that the analytical complexity that it introduces. Has anybody seen examples of crossing compression struts in the literature?

I'm not sure I have. But depending on the geometry, I'm not sure you'd need it. See this pic from ACI 318-11 (Fig. RA.1.2 (b)):

### RE: Strut and tie model comprehension problem

Are you under the impression that there is no boundary strut in the model shown below? Or is your point that the boundary strut is really just the flexural compression block?

### RE: Strut and tie model comprehension problem

I would have thought that with overlapping struts, you would at least have to assess the overlapped region in the same way you'd check a node.

In fact I believe it's always possible to rejig the model to introduce two adjacent triangular nodes in the rectangular overlap region, which is more in accordance with how the standards like STM to be done.

### RE: Strut and tie model comprehension problem

I think we need to look at how the forces can actually be developed and the different load cases that are involved. Remember, no matter how we want to imagine forces developing, they will initially develop in the way the concrete wants to carry them, and that is controlled by the relative strains in the concrete on different load paths.

- For the purely vertical load case with 2 point loads, the boundary strut will develop because its length is much shorter than the diagonal strut to the far column. So the concrete shortening to develop it is much less. Once it develops and compresses and shortens there will probably be a secondary much more lightly stressed diagonal strut to the far column. But is that critical? No, so we just do the 2 interior struts plus the boundary strut. As gusmurr suggests, the bulk concrete between the struts will provide any bracing required and the forces will be relatively small. The normal vertical and horizontal side face reinforcement should handle it.

I doubt it is possible to get the 2 diagonal struts to the far columns without a boundary strut in Koots later post unless the point loads are very well separated so the boundary strut is very long, in which case not much of the load is going through the long diagonal struts anyway as most of the load will go through the short relatively steep interior struts to their nearest supports.

- But a good design will allow for somewhere between 1.5 and 5% of the vertical load as a horizontal load as well. In one direction at a time. So then we have the 2 interior struts plus the boundary strut + the pink strut in the original post for sway in each direction separately.

- If there is a possibility that the loads can be applied individually then that case must be considered separately.

- If there is a possibility that one load can be fully applied and one partially (sway case or pattern live load) then the pink diagonal strut needs to be included again for sway in each direction separately.

### RE: Strut and tie model comprehension problem

#### Quote:

Are you under the impression that there is no boundary strut in the model shown below?

Doesn't appear to be one. But I see your point as far as equilibrium goes.

### RE: Strut and tie model comprehension problem

It may be that the boundary strut is omitted from explicit consideration in sketches sometimes because it just tends to not be a big deal. Usually you've already proportioned things to get a viable compression block from the get go and turning that compression block into a boundary strut is rarely where one gets stuck.

### RE: Strut and tie model comprehension problem

2
I have been re-reading Schlaich Schlaich et al Book recently, and in this they show linear stress plots to help designers get to the optimal STM. To continue this discussion I mocked up a an example focusing on the load case being questioned. This is a 12m span with two point loads that lead to disturbed regions. Three load cases were considered. P/P, 2P/1P and 3P/1P.

Of interest from Schlaich:

Definition:

LC1 Stress Plots:

LC2: Stress Plots:

LC3 Stress Plots:

I had a little time to try a STM using the defaults in a design package, so I have included them: This is not my typical use for STM, so I have to think a bit more on their defaults. Time for the real job.

### RE: Strut and tie model comprehension problem

Thanks for doing all of that investigation work Brad805. It provides me with a perfect opportunity to discuss something that I've been thinking about for a while with regard to unbalanced loads. Namely, that a failure to consider a significant imbalance has the potential to result in designers omitting important tie elements. Thankfully, most of these things tend to be heavily dead load dominated so it probably doesn't come up much. I can't say that I've ever seen an STM design example with more than one load case considered. I guess one is just supposed to be thoughtful enough to anticipate that need on their own.

### RE: Strut and tie model comprehension problem

At which point it starts to look like a beam designed the usual way but ignoring concrete contribution to shear capacity.

PS: the FEA model is 3:1 so isn't a deep beam according to some codes.

### RE: Strut and tie model comprehension problem

(OP)
Brad805 and KootK analysis notably highlights that 1 STM model is only valid for 1 load case. Since STM models can be long to calculate, the approach could be to limit the number of STM Models while being more conservative with the load cases.

#### Quote (KootK)

Are you under the impression that there is no boundary strut in the model shown below? Or is your point that the boundary strut is really just the flexural compression block?
I believe the boundary strut can be very similar to an ACI flexural compression block if you are modeling a B-region using a strut and tie model. In the first example of this thread, this a deep beam, we are in a D-region and the flexural compression block formulas of ACI do not apply.
See 2:01 of this video: https://www.youtube.com/watch?v=9ywGx5y7r_U&ab...

#### Quote (gusmurr)

I would have thought that with overlapping struts, you would at least have to assess the overlapped region in the same way you'd check a node.
You are right. Two struts crossing would imply a CCC node.
See 18:20 of this video: https://www.youtube.com/watch?v=9ywGx5y7r_U&ab...

### RE: Strut and tie model comprehension problem

I went searching for a study on the unbalanced load question. I found one that will be of interest to those using this methodSSDB STUDY In addition to unbalance question they also considered asymmetry.

Steve, there is an interesting figure in the Schlaich report from 1987. I have included it below (avail online). I agree that the span to depth of the example beam would not be a deep beam if a uniform load were applied, but considering the point loading it has disturbed regions.

### RE: Strut and tie model comprehension problem

If D-region cannot be designed with B-region design, then how does normal beam design work?

### RE: Strut and tie model comprehension problem

Bearing loads within the span are non-event D-regions. Loading on concrete doesn't get better than that. You can make any beam entirely D-regions with enough point loads.

I have to read the asymmetric loading test report in more detail but note that they had a premature failure which they've excluded from their analysis of the accuracy of the design method. Is real world construction and loading going to be more forgiving than a laboratory?

The tested deep beams are also the usual micro scale stuff. Pretty rare to design a beam so small in my work. I wonder whether there's a scale effect. Also limited examination of variables such as the shear reinforcement.

But fundamentally I wonder whether S&T is being used in the best way. For fairly standard things like deep beams, researchers using parametric analysis to extend existing design rules from testing would be more efficient than designers doing routine S&T. Keep it as a last resort for the design office as I'm sure errors are being made in use of the method.

### RE: Strut and tie model comprehension problem

#### Quote (Logan82)

I believe the boundary strut can be very similar to an ACI flexural compression block if you are modeling a B-region using a strut and tie model. In the first example of this thread, this a deep beam, we are in a D-region and the flexural compression block formulas of ACI do not apply.

Thanks for the clarification Logan82, I agree. That said, you'll note that I took care to not use the terms ACI Compression Block or Whitney Compression Block. Rather, I just went with Flexural Compression Block. And I contend that there is a flexural compression block in all situations. The only question is that of what the appropriate treatment of that compression zone is for a particular case being considered:

1) Whitney/ACI stress block for Bernoulli regions.

2) Boundary struts for disturbed regions.

3) The old school lever arm method that I use regularly (steveh49's point regarding simplified methods).

The notion that a deep beam isn't so flexurally deep after all is really what got the whole consideration of arching/STM rolling in the first place. It's a lesson that I've not forgotten since first learning it, I assure you.

### RE: Strut and tie model comprehension problem

(OP)

#### Quote (steveh49)

But fundamentally I wonder whether S&T is being used in the best way. For fairly standard things like deep beams, researchers using parametric analysis to extend existing design rules from testing would be more efficient than designers doing routine S&T. Keep it as a last resort for the design office as I'm sure errors are being made in use of the method.
What calculation method do you suggest using for the D-regions instead of the Strut and Tie Method, such as for instance the corbels and moment resistant connections?

Interesting figure KootK regarding the flexural stresses in a deep beam.

#### Quote (KootK)

3) The old school lever arm method that I use regularly (steveh49's point regarding simplified methods).
What is the method you are referring to?

### RE: Strut and tie model comprehension problem

I know it as "The Reduced Lever Arm Method" from Park & Paulay"s tome on reinforced concrete.

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