Three Foundation Retrofits
This article could never have been written without the insights and guidance provided by research scientist and engineer Ed Keith. He has 44 years of shear wall testing experience with the American Plywood Association, the largest shear wall testing laboratory in the world and for all he has done for me, a kind and helpful human being.
In a typical seismic retrofit we attach all four sides of the house to the foundation but we can also retrofit with three foundations. This applies to both retrofits with and without cripple walls.
Sometimes it is not possible to use all four foundations because on one side obstructions, deteriorated foundation, mudsills embedded in concrete, etc. make it impossible. These houses can still be retrofitted by using the three foundations that are accessible using the principle of rotation discussed in this article. These same principles are used in some soft story retrofits.
The discussion below uses a cripple wall retrofit as an example, but as stated earlier it also applies to non-cripple wall retrofits.
Below is an illustration of a house floor viewed from the top. The purple lines that extend left to right are the floor joists which support the floor you walk on. The reason these lines are at an angle will be explained shortly.
How to Retrofit with Three Foundations
The solid dark lines A, B and C represent foundations with cripple walls that can be retrofitted. Wall line D has a dotted line because it is not possible to retrofit the cripple wall.
One blue arrow (the arrows represent earthquake forces) on the upper left is pushing against the side of the house. This movement is resisted by Shear Wall A.
Another blue arrow on the lower left is also pushing against the side of the house. This movement is resisted by Shear Wall C.
A red arrow on the upper left is pushing down against wall line B. This movement is resisted by Shear Wall B.
Another red arrow is pushing on wall line D, which has no shear wall to resist this force, so what happens?
This creates a situation where the entire floor tries to twist or rotate as shown by the rotating circular black arrow. The purple lines represent the floor joists (the pieces of wood that support the floor you walk on) as their ends move due to pressure from the earthquake. This movement is exaggerated for demonstration purposes.
This rotating action transfers practically all of the force to the opposite cripple wall that has had a cripple wall to shear wall conversion. This retrofit procedure is using the principle of rotation.
Earthquake Force Distribution in Retrofits with Three Foundations
The arrows represent equal amounts of earthquake force pushing each side of the house. The amount of force is determined by the base shear formula. This formula tells us the the same amount of force must be resisted equally by retrofitting all 4 sides. The remarkable thing about using rotation is that this resistance can be achieved by retrofitting 3 shear walls instead of 4.
With forces attacking from the side, 1/2 the force is resisted by shear wall A and the other half is resisted by shear wall C. With forces attacking from the top, 1/2 the force is resisted by shear wall B. When the earthquake pushes against wall line D, as mentioned earlier, this force causes the floor to twist or rotate and transfer the force into side B. In other words, shear wall B must resist ALL the force attacking sides B and D and therefore will be designed to resist twice the force as wall lines A and C.
With forces attacking from the side, 1/2 the force is resisted by shear wall A and the other half is resisted by shear wall C. With forces attacking from the top, 1/2 the force is resisted by shear wall B. When the earthquake pushes against wall line D, as mentioned earlier, this force causes the floor to twist or rotate and transfer the force into side D. In other words, shear wall C must resist ALL the force attacking the house from this direction.