Strut & Tie Modelling: Nodal Stresses & Mohr's Circle 2

[handoflion]

Hi All,

I'm doing a quick strut and tie analysis and ran into an issue with the numbers that I can't seem to get my head around.

See attached rough hand calcs.

I'm working out the stresses at a non-hydrostatic node, in my first trial I have a support width of 282.3 mm. I work out the principal compressive stress in the node to be 27.2 MPa, which exceeds the allowable stress of 21.6 MPa.

I then increase the support width to 500 mm to check to see if this works. I adjust my geometry and again go through working out the principal stress. As you can see, my guess of 500 mm results in the normal stresses on the two faces being almost equal to each other. This results in a Mohr's circle with an origin of 65.7 MPa and a radius of 54.1 MPa. The maximum principal stress is 119.8 MPa and minimum is 11.6 MPa - what's going on here???

Is someone able to explain this anomaly, or more likely, point out the error in my ways?

Thanks in advance.

Robbie

 

[TehMightyEngineer]

[Summon KootK] Strut and tie models are definitely not my specialty.

Professional and Structural Engineer (ME, NH, MA)
American Concrete Industries

http://www.americanconcrete.com

 

[KootK]

I'll certainly help if I can.

1) It would be great to see the STM model of the entire structure under consideration for context.

2) It would be great to see the node in the context of it's surrounding struts, ties, and supports for context.

3) I've never seen a node with shear on it.

4) A triangular node generally has compression on all three faces.

5) What country's code is being used? I've not encountered a Mohr's circle approach in the past.

I suspect that rectifying #3 and #4 will go along way to resolving the issues.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[handoflion]

Hi KootK,

Thanks for your help, for some reason it took posting this to realise that one of the forces I was using was incorrect !

Nevertheless, here are some answers to your questions:

1) See attached screenshot of the strut and tie model - basically a cantilever wall.
2) I've also zoomed in on the node and shown the CORRECT forces - I would be interested in your take of how I treat nodes with more than 3 forces as i'm fairly new to this type of analysis.
3) The shear arises from the fact that the surface of the node is not perpendicular to the strut force (non-hydrostatic). The strut force therefore is broken down into a normal force and a shear force.
4) In this case I have five compression forces entering one node, hence I have a pentagonal node - I break this down into 3 triangles to allow me to work out the principal stresses in the node.
5) I'm based in Australia and therefore am using AS3600-2009. As far as I understand it, when evaluating the capacity of a node, you have to make sure that the principal compressive stress is less than the allowable stress in the concrete. Mohr's circle is used to work out the principal stresses with a non-hydrostatic node.

Just out of interest, I did a quick analysis of my triangle using both the correct and incorrect forces and varied the width of the reaction (see attached graphs). Interestingly the correct forces resulted in a fairly smooth graph, but using the incorrect reaction resulted in some vertical asymptotes - hence why I was getting huge stresses!

Interested in your thoughts regarding the above

Robbie

 

[ukbridge]

This by far the best available guide for STM IMO

https://www.concretecentre.com/Publications-Software/Publications/Strut-and-tie-Models.aspx.

I'm interested in your question but havent got that much experience with the method unfortunately! Some of the more complex/advanced applications described in the publication are very interesting.

 

[KootK]

I'm glad that you've got it sorted out handoflion. Before we close off, I'd like to propose an alternate model that I believe would have some significant advantages including:

1) Simplicity. No CCCCC nodes.

2) Rational reinforcement layout. No need for diagonal reinforcing at member one.

Below, I've shown your model and mine for comparison's sake.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[handoflion]

Yes would love to avoid that CCCCC node haha, but there was one little bit of information I left out that means I need the two struts as shown. The wall turns the corner (by about 30 degrees) at nodes 4 and 5 (see attached 3D model). I'm taking out the out-of-plane forces in the slab diaphragms above and below. Is there an easier way to deal with CCCCC etc. nodes? I suspect not...

Robbie.

 

[KootK]

Cool. The same simplification still applies at the compression reaction and left of the compression reaction. Death to the CCCCC node.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[handoflion]

Awesome, thanks for your help with this, much appreciated!

 

[KootK]

Actually, even with the simplification, you might still be stuck with a 4C node. Tackling the two nodes at the bend looks like a nightmare. I'd be inclined consider this as two separate trusses that only have shear connection at the bend. That would get you back to a 3C and eliminate the difficult analysis and detailing at those two tricky nodes. The down side is that your slab reactions would jump up a fair bit since the moment formerly delivered from the dogleg to the backspan would need to go 100% into the slab couple.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.