Shear Wall with Large Overturning Moment

[TTJT]

Hi All,

I have mostly done small residential/commercial projects and have been grandually moving up to more complex structures.

I am currenlty designing a three storey motel which will be primarily framed using load bearing masonry walls and cast insitu floors. The size of the structure is 100'x50' and has 6 units per floor. Please see attached sketch.

The lateral load analysis in the north/south direction is not a problem because of all the load bearing party walls. In the E-W direction it is a much bigger problem as I only have 2-12 foot walls on one side of the structure. Although I only have shear walls on one side, the party walls in the N-S direction and rigid diaphragm are able to handle all the torsion.

My main problem now is that the overturning moment in the E-W shear walls are very high and I don't have enough dead load. One colleague has advised that I can design the foundation wall as a beam to resist the overturning. He also advised that I could link the foundation wall to the N-S load bearing walls to capture more dead load.

I wanted to get some clarity on the analysis.

1. I am planning to analyse the foundation wall in the same way you would analyse the footing for a cantilever retaining wall. This would mean that a section of the foundation wall will be the heel and another section will be the toe. The moment in the toe is as a result of the soil pressure pushing up and the moment in the heel will just be the weight of the foundation wall acting like a cantilever from the shear wall. Is this the correct procedure?

2. I am not sure how to analyze the foundation links to take advantage of the weight of the load bearing walls in the N-S direction. How much of the walls in the N-S can I use?

Thanks

 

[BAretired]

1. Yes, that seems to be the correct procedure. Make sure the foundation is stiff enough to act as a rigid body.

2. You could use 25' of the N-S walls if the foundation under them is designed to span 50'. Otherwise, it depends on the capacity of the N-S foundations to act as a beam.

You could also use the weight (or submerged weight if you have a high water table) of earth above the footings sloping out from footing to surface at an angle of, say 30^o from vertical.

BA

 

[TTJT]

Thanks BA

1. For point 1. What would you consider "stiff enough". I was simply going to keep my deflections to L/240 (2L/480) where L is the cantilevered length.

For point 2, I don't understand your comment about the foundation spanning 50'. When checking the capacity of N-S foundations to act like a beam, how exactly it is to be analyzed. Do I "cantilever" the N-S foundation walls from the E-W Shear wall foundation wall and apply the dead load of the walls and slabs above? I'd have to detail these beams to carry as much load as required to hold the shear wall down. Alternatively do I apply a uplift force on the foundation link at the face of the shear wall and check the N-S wall for overturning due to this uplift force?

 

[structSU10]

If you want to be more 'exact' you could model it in an FEA program. model the foundation as a beam with nodes that you define with spring supports equal to the tributary area of the spring times the subgrade modulus per you geotech. Apply the loads, and get the moment and shear diagram for the foundation, which takes into account relative stiffness with the soil - it will result in smaller forces usually. You could even model a beam running perpendicular that represents the NS foundation, spring supported, and it will 'grab' the portion that is effective based on relative stiffness for you as well. I hope that is somewhat clear.

 

[BAretired]

1. For point 1. What would you consider "stiff enough". I was simply going to keep my deflections to L/240 (2L/480) where L is the cantilevered length.

Sounds good to me.

For point 2, I don't understand your comment about the foundation spanning 50'. They don't span 50' unless you need to utilize the full reaction which is equivalent to 25' of wall. If you need only 10' of N-S wall to hold down the E-W wall, the N-S foundation must be capable of spanning 20'(not precise).

When checking the capacity of N-S foundations to act like a beam, how exactly it is to be analyzed. Do I "cantilever" the N-S foundation walls from the E-W Shear wall foundation wall and apply the dead load of the walls and slabs above? There is no cantilever. The N-S foundation has a virtual "span" of two times the tributary length of wall which you are counting on harnessing in order to stabilize the E-W wall. There is no precise answer to your initial question, i.e. "how much of the N-S wall can I use?".

I'd have to detail these beams to carry as much load as required to hold the shear wall down. Yes, you would, but you are not obliged to use all of the walls. I would be inclined to consider the exterior walls only for maximum effect. If you need more, look at the next pair but I would be surprised if you need more. Alternatively do I apply a uplift force on the foundation link at the face of the shear wall and check the N-S wall for overturning due to this uplift force? No.


BA

 

[TTJT]

Thanks BA

I think I understand the analysis now. If I need 10 feet (lenght) of wall weight then the foundation must span 20 feet as a simply supported beam with tension at the base of the foundation wall (max. at midspan). Almost like there is no soil under this virtual span. At one end of the span, the reaction will be used to hold down the shear wall. What happens at the other end of the span. Am I to design the foundation to handle the other reaction?

 

[BAretired]

No, an upward load at one end of a beam on an elastic foundation cannot cause additional downward load somewhere along the span.

BA