How to model Foundation Beams and remain within a Linear Static Analysis

[kellez]

Project:
I am designing the foundations of a 2 storey RC structure. The foundation i am using
is a monolithic slab (raft foundation 45cm thick), with foundation beams (45cm height) fully
embedded within the foundation slab, interconnecting all columns at the base. (see pictures)

First i want to design the foundation beams without the slab, and then i will also take that into consideration.


Modelling of Foundation Beams:
In order to model the foundation beams on elastic soil:

I have modified all fully fixed supports at the column bases -> By releasing all rotations and assigning a stiffness to the Z+ direction.
I have also added an elastic support to the foundation beams to simulate ground stiffness.


Problem
After i modified the supports all of my dead load cases and live load cases have now changed from linear static to nonlinear static analysis.
Now when i try to design the foundations the design only takes into account the seismic load combinations, the ULS and SLS combinations are not considered.

Is there any way I can properly model the foundation beams and stay within a linear static analysis?


Pictures of the type of foundation I am using

 

[JoshPlumSE]

As soon as you start using compression only springs, you are talking about a non-linear analysis of some kind. You have different stiffness when the beam moves up than you have when it moves down.

Now, if you used a 2 way spring that is active for both tension and compression then it could still be a linear analysis. Though it may not as accurately capture the soil / beam behavior.

 

[kellez]

Ok, i totally understand that.
You are right though it wouldn't be accurate to use a 2 way spring, I will stick with the one way spring.
However what exactly happens to the ULS and SLS combinations if we have a non linear analysis?

 

[molibden]

Have in mind that if you are doing response spectrum analysis (modal analysis) it is a linear analysis and your two way spring is in fact a one way. If you are doing seismic analysis with equivalent forces you can use a non linear spring.

 

[kellez]

HI,

I am doing a response spectrum analysis (modal analysis). So you suggest i should use the 2-way spring and the results should be fine?

I am having a real hard time modelling the foundations, i have tried several ways but dont seem to work.

 

[kellez]

I have just changed the spring from 1 way to 2 way having the same stiffness in the +Z and -Z direction
and the analysis changed from non-linear to linear static. i will check the results to see if they are reasonable.

I have checked the results and they are not reasonable at all,
the maximum bending moment on a beam changed from 131kNM to 258kNM (looks like it has doubled)

 

[molibden]

Response spectrum analysis (modal analysis) is in fact a linear analysis so non-linear spring is not taken into account. You can check your reaction forces and you will see that your springs are not compression only. Post some images of the model, maybe some results (moment, shear, reaction forces). It will be easier to comment.

 

[kellez]

Ok, lets see what i have done up to now. Below are the different scenarios I've tried so far.


All scenarios are carried out using the RESPONSE SPECTRUM ANALYSIS which as mentioned by molibden above its wrong because the RESPONSE SPECTRUM ANALYSIS is linear therefore the 1-way spring is not taken into account

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Scenario 1
1. Fully fixed supports at base of the columns.
2. Assign soil stiffness along the length foundation beams (at the bottom of the beams)


Observations with Scenario 1:
1. The reaction forces at the base of the columns are absorbed by the fully fixed supports and are not transferred to the foundation beams.
_____________________________________________________________________________________________________________________________________________

Scenario 2
1. Pin supports at base of the columns.
2. Assign soil stiffness along the length foundation beams (at the bottom of the beams)


Observations with Scenario 2:
1. The reaction forces at the base of the columns are absorbed by the pin supports and are not transferred to the foundation beams.
_____________________________________________________________________________________________________________________________________________

Scenario 3
1. Delete Fully fixed supports at base of the columns. (No supports at all at column base)
2. Assign soil stiffness along the length foundation beams (at the bottom of the beams)


Observations with Scenario 3:
1. The reaction forces at the base of the columns are now transferred to the foundation beams.
2. However there are no supports to hold the structure down to the ground.
_____________________________________________________________________________________________________________________________________________

Scenario 4
1. Modified supports at base of the columns:
a. Released all rotations RX RY RZ,
b. Fixed support in the UX UY and UZ+ direction,
c. Add spring with stiffness to UZ- direction (simulating soil stiffness).
2. 2. Assign soil stiffness along the length foundation beams (at the bottom of the beams)


Observations with Scenario 4:
1. The reaction forces at the base of the columns are now transferred to the foundation beams.
2. However the analysis now has become NON-LINEAR and the software does not allow the design of the foundation beams in ULS and SLS combinations
a. All dead loads and live loads are now considered as NON-LINEAR
b. Therefore ULS and SLS combinations are now NON-LINEAR
3. The software only allows the design of the foundation beams for the Response Spectrum Analysis which is linear.
_____________________________________________________________________________________________________________________________________________

Observations regarding all Scenarios
1. After summarising the whole story above i think that the correct modelling approach is Scenario 4.
2. However the main issue here is that Scenario 4 requires a NON-LINEAR analysis and the RESPONSE SPECTRUM ANALYSIS which I am using is LINEAR, and cannot be used together.
3. Therefore the main question now is, what type of analysis shall I use so that the NON-LINEAR spring is taken into account?
4. On the other hand, is it really necessary to use A NON-LINEAR analysis in order to properly transfer the reactions from the columns to the foundation beams? There must be a more straight forward way.
5. The main question now is, how can i properly transfer the reactions at the base of the columns to the foundation beams and still use a LINEAR ANALYSIS?