This was a deduction by my design manager for the project we’re working on at the moment. I will not disclose the name of the project but I tried to capture the behaviour in the simplified structure that I analysed so that I can share the lessons we learned.
In multilevel structures where supports of the lateral load resisting system extend below ground at different levels, there are two ways to model the building supports: it’s either rigid (either pinned or fixed) or flexible (on springs).
Before we break down this topic piece by piece, let us first remind ourselves once more of the basics.
- Fact 1: There is no such thing as perfectly pinned or perfectly fixed support condition. The idea of infinitely rigid supports where rotation and translation is nil is just an ideal condition. There is only a certain degree of fixity to every support including the ends of beams with a minimum amount of reinforcement such as a beam framing to a girder.
- Fact 2: The correct way to model a soil support is by springs whether by area (the subgrade modulus) or by point springs (commonly used for piles). However, spring is not the best representation of friction, more of that on succeeding posts.
As a trial system, I made a simple model in ETABS where the geometry and loadings are the same except for the support conditions so that the comparison would be apple to apple. The loads applied are only lateral loads. The lateral load resisting system are 300mm thick walls founded on different levels. I labeled each wall with piers P1, P2, P3, and P4 from left to right respectively.
Walls Founded on Rigid Supports
For a rigid support, the inner walls or that part of the lateral load resisting system supported on a higher elevation will take most of the lateral load and thus will incur larger shears, bending moments and axial loads. In the sample model captured below, the walls in the middle are fully engaged such that the total lateral load of 3000 kN is absorbed in the upper level of support. See snapshots of resulting axial, shear, and bending moment diagrams of piers.
Walls Founded on Springs
If we use springs, 16.40% of the total lateral load of 3000 kN is absorbed at lower level supports. And compared to the rigid model, the shear and bending moments of middle walls are lesser. See snapshots of resulting axial, shear, and bending moment diagrams of piers with springs as soil support.
As a summary, I tabulated the resulting pier forces per type of model for each wall.
If we use the rigid model, most likely the inner walls will have a conservative design and the same would be true to the raft supporting it, while the wall at the sides, with little participation will not be carrying much lateral load and so might produce a smaller requirement and so will be the raft.
If we use the model with springs, the lateral load going to the inner walls will be lesser since the walls founded on the deeper levels will be engaged as well. Translated to the raft design, the raft supporting the walls in the middle might not be that conservative compared to the rigid model but the reinforcement in the raft for the deeper level will beef up.
So which is which? The one with the rigid supports or the one with springs?
For me if time allows, it’s good to investigate both conditions. Use the model with the rigid support to design the inner walls and the inner raft and use the model with springs to design the outer walls and the raft supporting it.
Note again that this is only a very simple model and that it doesn’t represent the actual framing system of a building. It will take a lot of trial runs and iterative design works before finally figuring out what type of supports will be used. And in some cases, the design results using either a rigid or flexible base doesn’t vary that much which only supports the conclusion that the type of support for such condition doesn’t really matter at all.