Strut & tie code issues

[bugbus]

Please refer to my sketch below:

Case A is pretty straightforward. The two nodes at the supports are clearly CCT and so the node is checked with beta_n = 0.8, and the strut is checked using the strut efficiency factor based on the angle theta. Nothing controversial there.

For Case C, let's delete the reinforcement and replace it with an externally applied load, so that the node is now CCC (with beta_n = 1.0). What is then the strut efficiency factor for the diagonal strut considering it no longer crosses a tie? Is it just 1.0? The code is kind of silent on what to do in that situation.

For Case B, this is where (in my opinion) it gets even more confusing. On paper, this is a CCT node, the same as for Case A. But, in my view this is clearly closer to Case C. Assuming that the anchor plate is well proportioned, and provides a uniform stress on the back face of the node (therefore not inducing any splitting or crushing effects, etc.), then what is the difference between this case and Case C?

To my mind, the reason for using a beta_n factor of 0.8 for a CCT node is due to the non-uniformity of pressure and therefore potential for splitting or crushing on the back face of the node, which is caused by the relatively concentrated anchorage forces at the bends in the reinforcement. This is basically how beta_n is defined in the code:

Would you feel comfortable for Case B using beta_n = 1.0?

I suppose the only argument against treating this as a CCC node is due to the fact that the reinforcement carries the load passively, which is different to an external load. There must be some amount of internal strain and possible cracking to engage the reinforcement, whereas the external load is there from the beginning. But, I don't consider this to be relevant to the beta_n factor.

This now leads to the question of the strut efficiency factor for the diagonal strut for Case B. If we concede that the node itself is closer to a CCC node, would it mean that we can ignore the strut efficiency factor as we might with Case C?




I appreciate any advice in advance, thanks all!

 

[bugbus]

I've just been browsing ACI-318:

There's no specific mention of the effect of the anchor plate on the node type, so strictly it would be CCT. For a bottle-shaped strut (which this is), beta_s = 0.75 regardless of the angle, provided enough transverse reinforcement is present to control splitting.

Also, in AASHTO (more similar approach to Australian standards):

The commentary is a nice thing in the American standards, I wish the Australian ones had the same. It seems that the tensile strain field parallel to the tension ties reduces the efficiency of the struts by encouraging splitting. The smaller the angle, the less efficient. So, maybe there is some difference after all between Case B and C. AASHTO explicitly mentions that if the tie is prestressed (which I imagine is similar to Case C with the externally applied loads), the performance of the diagonal struts is improved.

I wonder, then, why ACI-318 does not take the angle between the strut and tie into account?

 

[Just Some Nerd]

In my eyes A and B are the exact same - that tie in A is gonna be developed on the other side of the node, and produce a sort of compression on that outside face regardless of if there's an anchor plate or not.

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Why yes, I do in fact have no idea what I'm talking about

 

[Settingsun]

I think C would need to have different/additional design steps relating to the reliability and stiffness of the external force. You no longer have the ductility of steel to arrest the potential crack/failure. The first step would be to consider whether unreinforced concrete is permitted in the situation.

 

[rscassar]

A & B are CCT nodes. I don't know the applicability of C. If it's a pile cap than I wouldn't be using passive resistance of the rock, and likewise a transfer wall I wouldn't be applying a diaphragm force in-lieu of a tie.

 

[bugbus]

Thanks all, appreciate the comments

Just wanted to clarify that Case C obviously isn't realistic, it was more to show a situation that contains CCC nodes only.

@Just Some Nerd, do you not think that having the discrete bars (vs the flat plate) wouldn't produce some potential for splitting or crushing? My understanding is that this is the reason for beta_n = 0.8.

 

[Just Some Nerd]

I think you're focusing on the wrong side of the node, the lower beta_n is due to strain incompatibility between tension and compression members. The non-uniform reaction from bars I don't believe is considered at all, AS and ACI both appear to assume uniform stresses at node faces, so any issues caused by the non-uniform stresses I believe is left up to the designer to account for in detailing e.g. using the anchor plate if development happens relatively close to the node. AS3600 commentary however makes it explicit that reinforcement should be fully developed with at minimum 1/2 development length of bars beyond the node, which I imagine naturally allows the stresses to become more uniform by the time they reach the node face.

See below for ACI's commentary on their beta factors (they're the exact same as ours for CCC/CCT/CTT) that mentions strain incompatibility

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Why yes, I do in fact have no idea what I'm talking about

 

[bugbus]

Thanks again ^

That's good info, I will go away and think about this a bit. I tend to agree with you now that it should still be treated as CCT even with an anchor plate.