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How Do You Know You Have Foundation Problems?
I would say about 10% of the houses I go to have no foundation problems at all.  Other houses I've been to have had foundation problems for years and the home owners thought the movement would stop and things got worse.  There are certain key items to look for.  Let me go through them:

Doorways and Windows:  If there is any kind of foundation problems, it usually can be seen in the windows and doorways.  As the foundation settles, the walls of your house will shift, and it will pull the windows and doors out of square.  You can usually see where there are problems over the openings with diagonal cracks that will form.  Also, your doors won't shut properly and your windows will stick. 
Crack over door from foundation failureThe picture above shows a good example of this.  In this house, the foundation failure showed most clearly on the second floor.

Floor Slabs:  Those of us that work with concrete say there are two kinds of concrete - that which has cracked, and that which will crack.  Concrete, unlike wood or steel, is rigid.  It has almost no tensile strength, so when it is put under tension it cracks.  When concrete is placed, it's a chemical reaction that makes it set, and during this process it will shrink.  Also, during the life of the concrete it will expand and shrink due to temperature.  Just to give you an idea of the amount of movement, a 50 foot long concrete slab can expand and contract an inch during the day.  I ran into this with a concrete framed building in Washington DC where we were doing site monitoring during construction of an adjacent building.  We found the adjacent building changed in height about an inch during the day.  We did the calculations using the coefficient of thermal expansion in concrete, and it was in fact supported by the calcs.

The cracking in floor slabs can be aggravated by poor construction practices, which is pretty typical in residential construction.  Concrete should be poured in a reasonable amount of time after it is mixed (the American Concrete Institute has published standards for this), and it should be protected from getting too cold or too hot.  It's not a good idea to mix water with the concrete if it is starting to set.  The surface should be kept moist during curing.  In residential construction very little of these precautions are followed.  So, in a basement slab you will see quite a bit of cracking that won't be related to movement of the foundation. 

The Greater Atlanta Home Builder's Association's Home Owner Handbook states that cracks over 3/16" of an inch, or that have uneven edges from one side to another are of concern.  I use this as a reference, and it generally holds true.  Generally, cracks in floor slabs that are uneven from one side to another indicate floor settlement.
Crack in Concrete SlabTypical Cracking in a Basement Slab

Exterior Wall Cracks:  Foundation settlement will become very noticeable in brick veneer because the brick can't move with the foundation.  The results can be extreme as the photo below shows:
Cracking in Brick Veneer
Bowing Subwalls:  A lot of older houses were built with unreinforced concrete block walls.  If you do calculations on them, you find they shouldn't be standing.  They do stand for the most part because engineering calculations don't take into effect everything that holds a structure up.  However, many of them begin to bow after a few years.  Here's a rather extreme example that Aquaguard Basement Systems was kind enough to provide a photo of:
Bowing SubwallIf your basement wall looks like this, you probably should have it repaired.

Where is your house built?  The biggest problem houses I've seen are ones built on hills where there is a stream behind the house.  The upper part of the house is usually on good soil, and it stays put.  The lower part of the house is often on very weak soil (alluvial soil, or fill that the builder dumped to the rear), and it settles.  Combined effect is a big crack opening up halfway across the house. 

You also have to be careful of houses built on fill materials.  Many builders, especially during the housing boom when everybody seemed to want to be a builder, have no idea about compaction of fill material.  If soil is placed improperly, it starts to settle.  If you put a foundation on top of fill soil. it will crack as the soil settles.

Summary
So, to summarize, you need to look for the following issues to determine if you have foundation problems:
- Doors and windows that are not operating properly, and diagonal cracks opening above the openings.
- Cracks in concrete slabs that are uneven from side to side, or are greater than 3/16".
- Cracks in brick veneer.
- Was your house built on fill soils, or does it back up to a stream?

There are of course other indications, but the above are the big four.   

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