Strut-and-tie modelà once again, 5

[Robbiee]

Please bear with me on this. It was nine years ago when I had my first exposure to the STM, yet never use it until recently.
Referring to attached sketches, the compression force in the strut BC is a result of the tension in the tie AB. Now, we know that stresses in the tie decrease with the development length of the bar to zero after an ld length, yet the STM assumes constant bar stresses. Doesn’t that lead to wrong results? Is not the force in BC in sketch 2 zero, while the STM gives us a force= T(AB)/ cos theta2?
It appears that I am missing something here.

 

[tolchijb]

Look at the PCI Design Handbook (6th Ed.). There is a nice example of this exact situation starting on page 6-51.

My understanding is that member BC needs to take compressive force if member CD is a tie in your model. Through statics, if you did not have member BC taking compression you would blow out the back of your column at D since CD would become a compression member and probably lacks sufficient lateral restraint.

Hope this helps.

 

[hokie66]

In strut and tie modelling, think of the members as truss members meeting at a node. Thus the forces are resolved by anchorage at the nodes, not by development along the bar. That is why anchorage is critical, not development length.

 

[kslee1000]

Ailmar:

Let me try to explain, but don't give high hope though.

The strength of bar AB is developed by bond, and the bond is usually assumed uniform throughout the development length "Ld". In turn, Ld is determined by expermiments on the instance that yielding of steel bar is imminent, and the bond starts to fail. The imminent failure causes the bar to slip (uniformly), thus the bar feels the same stress everywhere along it's length, provides as Hokie pointed out, the anchorage and end nodes are adequate to alow the stress to develop.

Your thinking is not necessary in the wrong path, just the present time research has not tilted your way yet. One day it could be though. (ie. I had similar question before, but gave up after struggled a while along the road. I don't think we are loners on this matter)

Suggest to take the face value of the code for now.

 

[fa2070]

In strut and tie modelling, think of the members as truss members meeting at a node. Thus the forces are resolved by anchorage at the nodes, not by development along the bar. That is why anchorage is critical, not development length.

Are "anchorage" and "development" not mechanically equivalent? If not, what's the difference? I thought both terms could be used interchangeably. Leaving economic/practical/labor considerations aside, for any given diagram of bending moments in pure beam zones I can anchor outside the critical sections (gray areas in Fig. 1) however I like, be with details "A", "B", "C" or "D", right?

I'm presently prototyping some concrete D-regions with the strut and tie model but cannot figure out how to anchor the ties meeting at the nodes. Typically, how are ties anchored at the nodes in strut and tie members? Are headed bars my only alternative? Where can I find a few real world examples of such details?

Thanks.

 

[hokie66]

fa2070,

There are a number of ways to anchor the tension bars in strut and tie models. Headed studs are sometimes used, bars are welded to embedded plates, and hooked bars work in certain applications. In Ailmar's example above, the AB bars should be detailed as horizontal ties and developed by continuity around the column verticals, not by bond along the length.

 

[BAretired]

Sketch #3 has a different orientation than Sketches #1 and #2. In Sketch #1 or #2, tie bar AB bends 90 degrees and continues down to point D. Corner B has to be anchored adequately to get the compression into concrete strut BC. A stout bar running horizontally inside the bend is required.

BA

 

[hokie66]

Yes, I agree, if the corbel is on a wall. But if it is on a column, the length of a horizontal bar is so limited that it is best to use the column verticals to anchor the tension, and make the AB bar into a closed horizontal tie.

 

[BAretired]

Sorry, hokie66 but I don't agree. You must have a horizontal bar to get the stress into the compression strut. If it has to be a big, fat bar to do that, so be it, but the force must be transmitted to the diagonal strut and the vertical column reinforcement only touches on the two edges of that strut.

The A-B-D bars are not restricted to just two bars. There could be four or six bars. The anchor bar running horizontally just inside the ninety degree bend is the best method of anchorage and puts the compression right into the middle of the strut.

BA

 

[Robbiee]

Thanks all for your inputs. I think Kslee1000 was the only one answered my question directly, which is: why does STM assume that stresses are constant along the tension bar, while they are not?
If tension must be considered constant because of slipping, then the whole idea of developement length is not valid.

 

[BAretired]

Ailmar,

You have a strange way of viewing this situation. It is unrealistic and unsafe to assume that bars in strut and tie models develop their capacity by bond. In general, they do not! So, if they do not, it is necessary to develop the bar force in some other way, namely by adequate anchorage. It is conservative to ignore the small contribution of bond in favor of a more positive anchorage.

The "whole idea of development length" is valid if there is enough length to develop the bar. Otherwise, the bar must be developed in a different way. Your last post suggests that you do not understand or are not prepared to accept the concept of the strut and tie model.

BA

 

[hokie66]

BA,

I didn't read Ailmar's last post that way. It seems to me he understands that anchorage is essential rather than bond, but he has just not expressed it well. But then maybe he doesn't understand, because he says kslee made it clear to him, and kslee's post only confused me.

As to our different way of detailing a corbel on a column, just as the corbel bars are not restricted to just two, neither are the column verticals.

 

[kslee1000]

Hi, Everyone Confused:

I am confused as you are as well

Let me re-state my original response with an example:
For a #4 bar, As = 0.2 si, Ds = 0.5 in, Ld = 15 in (30*Ds), Tu = 12k (at yield).
My claim is simply B (bond) = Tu/Ld = 12/15 = 0.8 ksi (800 psi) uniformly throughout the bar, as contrary to the notion that the bond stress is max at the start of the development length (2*0.8=1.6 ksi), then diminishes to zero at the end of bar (B = [1.6+0]*15/2 = 12, check too).

The uniform distribution of bond stress in under the premise that at the imminent of yielding, the slip mechanism in between bar surface and concrete is engaged to develop the yield strength, as domino, both the bar and the concrete feel the smae stress uniformly throughout the development length.

For a hooked bar, the mechanism is much more complicate. No comments on that.

Ok, guys, get out your guns & bullets ready, aim, and shoot

 

[kslee1000]

After the above excerise, for person with expertise in strut-tie method, let's look at Ailmar's question/concern closely. Both he and I could have missed something.

On case 2, say the length of bar AB >> Ld, is there a reaction at node B? If no reaction at B, is bar BC required? If not required, what is, other than CD, required to take on the force component from AC?

Please comment & explain.

 

[BAretired]

If bar ABD is adequately anchored into the column, strut BC is not required. ABD must be anchored at node A in order to develop strut AC. That would satisfy the strut and tie model.

If you do not wish to rely on the anchorage of ABD into the column, you have the option of using strut BC. If you do that, you are required by strut and tie procedures, to develop the bar at node B assuming no bond between A and B.



BA

 

[kslee1000]

BA:

The question here is if AB alone is MORE THAN adequate, why do ABD?

 

[Robbiee]

I THINK WE ARE CONVERGING. My question has nothing to do with how to achieve anchorage. My question from the beginning was: If you assume constant tension stress in the tie AB for the case where its length is equal or greater than Ld, while in fact-and because of bond- stress becomes zero at B, then STM leads to wrong results because it tells us that there is a compression in BC due to tension in AB and BD.

 

[BAretired]

The strut and tie model is an idealization which offers a method of handling large loads in regions not readily analyzed by other means. It does not provide "correct" results but I believe it provides safe results.

If bar AB is fully anchored in the column with stress tapering down to zero at node B, there is no strut BC with a known dimension and a known compression. The state of stress in the concrete around the bar is not precisely known but there is a compression field in the vicinity of the bar. The tension in bar AB, together with the horizontal component of strut AC puts moment into the column of magnitude Vu*e where e is the eccentricity of load from centerline of column.

Looking at sketch #2, I think I would be more concerned about developing the 'A' end of AB than the 'B' end.

BA

 

[kslee1000]

Ailmar:

Please check below.
By inspection, you have Tension in AB (from max at A -> 0 at B), constant Compression in AC & CB. Then the compression in CB at B triggers tension in BA & BD. So, now node B becomes an anchorge point to develop the required tension for balance. Does this make sense?

 

[hokie66]

No, it is nonsense. You have the same tension in AB all along its length. Just like any truss member. Bond doesn't come into it. As BA says, anchoring the bar at A is more difficult than anchoring at B.