Strut and tie model

[Aldar]

Hi to all,
could someone help me with the strut and tie model. I need to design a big foundation. I attach the picture of the problem. thank you.

 

[ishvaaag]

Because he has not drawn any moment reaction, I am supposing there's no moment restraint there. Also, it would be rare find a reasonable structural "tee" of 35 cm depth able to sustain a moment in the order of +1500 m·tonf

 

[ishvaaag]

Well, more approximately, 1300 m·tonf moment. Something in the 400 m·tonf uses about 1.2 or more depth, say 1300, we have only 35 cm; a reasonable weight neither is able to balance significantly that moment, maybe reduce it by 100 m·tonf; we have an unbalanced moment of aorund 1200 m·tonf making the thing rotating counterclockwise around the hinge, actual, or notional plastic.

 

[Aldar]

which moment are you talking about (1200 m.tonf) around what point? you don't consider the weight of the foundation? if i understood you right, you take the moment aroudn the point where the force R is applied ( by the force of 774t*1.6m), am i right? the weight of the foundation is 223ton times the moment arm of 6.8m = 1516ton.m.
Anyways the stability of the foundation is not a question. The question is the flow of stresses inside.
P.S: The T beam will take only the compression forces.

 

[ishvaaag]

In any case, for the thickness I did the calculation it was not converging, it was rotating; since I didn't peserve the model (was not nice enough for that) I can't aduce what weight-thickness I was counting on, one that we couldn't estimate because the thickness was not presented in the sketch. It must be in the order of 5 m deep by your estimate of 223 ton. Also point of application of the loads is not shown annotated.

If you place the remaining dimensions, with the thickness etc we can see if stays stable or not.

Respect the strut and tie scheme, once stable, you will be guided to a one close good approximation by looking the principal stresses then developing. You may still then establish some others that are also feasible, but further from the real behaviour.

The effect of friction will need to be mimicked either through forces or the more suitable devices provided by the software for boundary conditions. The produced strut and tie schemes will be strongly dependent on the assumptions for the boundary conditions. Then in order to properly produce the model, we need also the properties of allowable soil strength, and friction at the interface, plus if the loads are assumed factored or not etc.

 

[paddingtongreen]

This looks like an impossible question to answer. Without the information on the concrete, it is not possible to calculate the pressure on the soil and thus you can't calculate the friction because it is proportional to the pressure. The soil to the left will be in compression as well as friction as the foundation tries to slide up the hill. Finally, it will be necessary to equate the stiffnesses of the soil and the T beam to their portion of the loads. The force needed to deform the soil a given amount and the force needed to deflect the T beam the same amount must equal the applied forces.




Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[BAretired]

The concept is to decrease some of the 1080 to the left by soil friction and bearing capacity, and the remaining force to apply to the T beam. Was i clear_?

Yes, you were clear in describing your concept, but unless we know how much the T Beam deflects under lateral load, we don't know how much force goes to the soil in friction and passive pressure. If the T Beam is very rigid, the soil forces will be negligible.

BA

 

[ishvaaag]

I agree with paddington, concrete data is also neccesary, not only because of the stiffness issue, but also because of the strength, because you will need stress parameters to show that the strut and tie scheme you are drawing abides withn the described scope of the reinforced concrete practice, if not the code.

Since I by whatever the reason have some custom of being a dissonant voice sometimes, I also point to the fact of that strut and tie, useful that it maybe, it is, and may be more, entirely superseded by proper FEM analysis. Any strut and tie model is shown to be only a guess (it maybe a simplifying and interesting one) but of less interest than the other, if only because the former is less in accord with the laws that rule the behaviour of the structural materials than the other. I in particular (with the most simple exceptions as say deep footings, caps or beams) dislike the complications brougth by some practical rules to find the scheme in equilibrium, whereas you can do better the other way.

 

[hokie66]

The contribution of the soil in resisting these forces is negligible. So we must assume the left reaction is rigid. The block is stable, as the mass of the concrete prevent rotation counterclockwise around the left support. The only problem to be solved is how the right side of the block resists the 774 ton force. Ishvaaag's favoured FEM analysis could be helpful, but I think unnecessary. There are several strut and tie models which could be considered. It's just a corbel design, and the force is a long way from the edge, which is good. The hanging bars in the top of the slot will be the crux of the design.

 

[BAretired]

I agree with hokie. Attached is one possibility for struts and ties around the trench area. Struts are shown in green. Ties have red circles at each end.

Are there any better ideas?

BA

 

[hokie66]

BA's way is the way I approach corbel design. There probably should be another diagonal under the trench to complete the truss analogy.

 

[Aldar]

why do you think the soil contribution is negligible? the bearing capacity of the soil is around 25-30 ton/m2. so the horizontal reaction of soil would be around 175-210 tons. So if taking it into account my strut and tie model is shown in the picture.

 

[hokie66]

Converted to my units, the soil bearing capacity you nominated is about 250 kPa, so it is soil, not rock. Some movement is required to develop that capacity, and the passive capacity of the soil would vary with depth. The deformations would not be consistent, so I would discount any assistance from the soil. Even with your numbers, it is less than 20% of the required reaction, so not worth the risk. Other than that, your model looks like BA's. Anchorage of the ties and confinement of the struts is what you have to work out now.

 

[Aldar]

and i have a question regarding the angle between the struts and ties. I found different values of min and max angles. some say min should be 25 and some 45. COuld you tell what is the angle you use? what angle i should use for this problem?

 

[BAretired]

I have modified your sketch to show an additional 62t load representing the weight of the concrete block to the right of the trench. As mentioned earlier by hokie, Strut e-f is needed to carry the shear of 62t. Strut f-h is needed to take the horizontal component of e-f. But Tie d-h lies along the same line as f-h so the angle between those two is zero. Is that a problem? At the moment, I don't think so, but it does seem a bit unusual.

On the left of the trench, if you are going to attribute some of the resistance to the soil, perhaps you should add Strut a-c.

BA

 

[TLHS]

Aldar: As far as the allowable angles between your features, I suspect it's defined in your code. It's one of the things defined in the Canadian code, certainly. While the truss analogy in general is fairly consistent, there are different ways to calculate things like strut size, node dimensions and other things of that sort, and how angles effect resistances. This will all depend on the underlying studies and assumptions used to develop your code, so you should really just refer back to those rather than depend on what anyone says here. Just because someone gives you a value doesn't mean its compatible with the way your code calculates strut and tie resistances.

BAretired: There isn't anything wrong, conceptually, with struts and ties overlapping. It just means that, depending on the load conditions, that area could have a load reversal. When he does his truss analysis for the load cases he needs to check it should clarify that area. It may be that it never reverses and it's always tension or compression and he just needs to check worst case, or it may be that he needs to design it as a strut in one case and a tie in another.