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.

 

[Robbiee]

hokie66:
Why the tension in AB is the same along its length and why bond doesn't come into it? Tie AB is not installed in a greased sleeve.

 

[hokie66]

It could be greased and still be consistent with a truss analogy (or strut and tie) method. Strut and tie is a method of modelling in which the tensile ties meet at nodes with compression struts, providing an idealised way of designing the steel reinforcement and providing forces for checking the struts. The method is not to be taken as representing the way the structural element actually works, but is a safe and rational approach, as long as the forces are adequately anchored.

 

[BAretired]

One of the difficulties we are having is that there are too many alternate load paths with the column reinforcement continuing as it does on Sketches #1 and #2. I am attaching Sketch #4 which shows a similar situation but without the upper section of column.

It should be clear to all that this is a failure waiting to happen even if bar AB is anchored with three times the required development length. The failure surface will be below bar AB and above the column verticals.

Bar AB must be anchored at A and B. It requires a hook and a vertical leg below node B to transfer tension to the column reinforcement. The location of compression struts is not an exact science. When using the strut and tie model, the designer is free to modify the location and slope within certain limits.

BA

 

[kslee1000]

Hokie:

I agree with your latest response, that the existence of bond does not have explicit role on design theory for this case. But the bond is there does the work - develop tension in bars, only we/code opted to ignore it for the simiplicity of design process.

Ailmar:
Maybe you should try to get papers on the development of trut-tie method to see the full context. For the time being, as pointed out by Hokie, there is no harm in ignoring the bond-steel interaction in this (corbel tension bar design) regard.

 

[WpgKarl]

Wow, never saw so much emotion in a forum about strut-tie models!

Regarding the original question - in a case such as this we have a "d" region (or disturbed region) where plane sections are not plane after the load is applied = non-linear strain distribution, rather than a "b" region (or beam region), where strains are linear thru the depth and plane sections remain plane.

For example, in a deep beam, with a point load applied at the top (in the middle of the beam), there must be a tension tie at the bottom of the beam (like a tied arch). If you cut a section thru the beam near the support and near the middle, the bar tensile strains would be almost the same value. In other words, there is roughly a constant amount of tension on almost all of the length of the bar (the tension develops very rapidly from the thrust of the diagonal compression struts), b/c of the non-linear distribution of strains.

This is why it is critical to develop the bars very quickly, sometimes quicker than the development length allows for, so in this case you need use mech. anchorage at the end of the bar sticking into the corbel.

So for your corbel situation, you should weld a cross bar at the outside face of the bars running into the column (to provide immediate anchorage of the bars beyond the column face). Your other option is to weld the corbel tension tie bars to an angle, on the outside edge of the corbel.

In addition, you should provide the minimum ldh (or embedment length req'd to develop a hook in tension) running into the column. This is measured from the face of the column to the back edge of the tails (near the back edge of the column). If you have less than ldh, prorate your area of tension-tie steel.

Be very careful when using ST models - if you go down the wrong road you can have an unsafe design - there is very little re-distribution of stresses after cracking. If i were you, I would use the empirical method in the PCI Manual - you will always end up with a safe design and safe details + corbel proportions that way. (Attached is a spreadsheet I wrote for the Cdn code, but you can modify for the ACI code as well - use at your own risk).

 

[WpgKarl]

Whoops, forgot to attach it....

 

[WpgKarl]

Ok, third time - hope this works now....

 

[BAretired]

WpgKarl,

Very impressive piece of work. I will need to spend a little time digesting it.

BA

 

[Robbiee]

Thank you very much to all and a star for the help and patience.

 

[kslee1000]

Ailmar:

Please bear in mind, the design of reinforced concrete is not an exact science, rather, it is based upon ongoing researches and test results. All design methods are considered the "best match" with logical assumptions to allow for ease of understanding and use.

You started a good question, wish you have gained something after this discussion. If there is anything unclear, keep asking, or do more reading on materials that are relavent to your question. But do not confuse design with research.