Rigidity of raft and rigidity of superstructure

[RamiHabchi93]

Hi,
1-Is it good to use a flexible mat foundation with a rigid superstructure?because it is more economical. I am modeling the flexible raft as a slab on elastic soil, and have checked the differential settlement and found them in the limits.
2-Could you give me a formula that help me determine if the superstructure is rigid or flexible?(for a raft for e.g L<2L0 means the raft is rigid, with L0=sqrt(4EI/kB),is there any similar way for the superstructure?)

 

[dik]

I would think that you would want the raft to be as rigid as possible... foundations are not the place to look to economising.

Dik

 

[BridgeSmith]

In assessing the rigidity of a structure, I usually compare the forces or moments required in each component to produce the same deflection or deformation. Since I don't know the particulars of your structure, an example from my work will have to suffice:

To evaluate whether a concrete bridge abutment on steel piles should be analyzed as rigid or flexible, I calculated the force required to deflect the abutment down 1/8" at an interior pile that was assumed to provide no resistance. Then I calculated the load required to shorten the pile by the same 1/8". The ratio of the force applied to the abutment to the load applied to the pile gives an approximation of how rigid the abutment is relative to the piles. It's essentially an application of the virtual work method (which I never actually thought I'd use when I learned it in my structural analysis class). In my case, the force necessary to deflect the abutment was 20 times larger than the load required to deform the pile, so the abutment was 95% of the way to being fully rigid. That told me I could reasonably model it as an infinitely rigid beam.

I hope that helps.

 

[WARose]

1-Is it good to use a flexible mat foundation with a rigid superstructure?because it is more economical. I am modeling the flexible raft as a slab on elastic soil, and have checked the differential settlement and found them in the limits.

When it comes to mats.....you typically don't have much of a choice. The trick is to avoid differential settlement. (As much as possible. It's completely impossible to avoid some.) And it sounds like you have done that.

2-Could you give me a formula that help me determine if the superstructure is rigid or flexible?(for a raft for e.g L<2L0 means the raft is rigid, with L0=sqrt(4EI/kB),is there any similar way for the superstructure?)

There are a few in ASCE7-05.....but they are for classifying the structure as "rigid" for the purposes of seismic loading. For foundation loading I don't know what exactly would qualify as "rigid".

Even if you selected a mat with a thickness that completely precluded localized deformation......there is little chance (with most buildings) you are going to get the Center of Gravity for both the mat and the building in the same place. (Ergo the foundation would slope a bit.)