Strut and tie method maximum angle of truss 5

[ENGUCR]

Generally the truss angle of strut and tie system is restricted to a maximum limit about 60 deg. What happen if someone goes beyond this upper bound limit. What is the concept behind max limit? I am struggling with a deep pile capping beam where the strut and tie system angle is almost about 75 degress
Thanks

 

[patswfc]

I think that the "good" model represents the stress distribution in the member in reality more accurately.
It anushka's example, the D regions are at the point load at the top of the wall and the 2 supports. The compression stresses spread out from the point load down through the wall, then in the middle of the wall the compressive stresses will be fairly uniform, before the stresses concentrate to the supports.
I quick FE model would show this behaviour.

 

[sticksandtriangles]

For my own fun I did a quick FEM. As others expected the good model seems to capture the behavior of linear elastic analysis pretty well.

Vertical stress picture (notice struts form in a way consistent with "good model"

Horizontal stress picture (notice tie where expected in "good model"

 

[KootK]

I think that the fundamental difference here is that the good/bad stuff is a load spread problem where, in all likelihood, the pile cap situation is not (a sketch would help to confirm). With the pile cap situation, the load has no real cause to change direction significantly. You do get some spreading and re-concentrating of the load which is related. In some codes, that is covered by bursting stress provisions in bottle shaped struts. People complain about it all the time here as it's a detailing pain. If I recall correctly, I think that the codes of both the UK and AU have such provisions. This in no way limits your strut angle, however, because you could have a bottle shaped strut running off in any old direction.

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.

 

[rapt]

From what I see of the first FEM picture, the "good model" lines bear no relationship to the stress contours. Someone drawing those lines on it is dreaming!

Based on the "good model" you need horizontal tension reinforcement at about 20% of the depth from the top, at the kink from slope to vertical. Personally I think it is a waste of good reinforcement to put tension tie reinforcement there!

Yes, there may be bursting effects near the top where the compression stresses spread out. Yes some side face reinforcement over the full depth of the section if a beam. But tension tie reinforcement at 1/4 depth!!

 

[hokie66]

Agree, rapt. I see no merit in the "good model". As KootK said, the load has no reason to change direction, so its most likely direction is straight between points of loading and support. Sometimes, I think these new-fangled finite element models just cause confusion in interpreting how a structure actually works.

 

[rapt]

Hokie,

Agreed, stresses do not change angle suddenly without a good reason, and I cannot see one there! Maybe a gentle curve in the compression strut, but sudden angle changes. Someone is smoking something that is not good for their logic thought processes!

 

[KootK]

I think that the "good" model and the FEM results both have merit. Below, I've tinkered with proportions and orientations to create examples where I feel that the "good" model aligns well with intuition (mine at least) and what is often found in the literature. None of this changes my opinion of the original pile cap issue however.

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.

 

[hokie66]

I think the difference is that bursting at a post-tensioned anchor is a much more concentrated force in a relatively thin element than bearing of a column on a big footing/pile cap. Confinement is the issue.

 

[sticksandtriangles]

Someone drawing those lines on it is dreaming!

Haha thanks rapt. I agree the vertical lines are questionable between the "good" and "bad" model.

The main thing that made me like the relationship between the "good" model and linear elastic FEM was the presence of horizontal tension in the FEM model (horizontal stress picture). This is not captured in the "bad" model.

 

[rapt]

HGokie,

Agree the PT busting effect is very different. It is the dispersion of a very concentrated compression at the anchorage over the full width of the section causing transverse bursting stresses over a length of the member. It is very different to a pile cap situation.

 

[KootK]

It's different to the pile cap situation. It's not that different too the good/bad model situation. That was my intended point.

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.