Determinate versus indeterminant structures

I know the title sounds scary, but the part you need to know is really simple: almost all single-family houses are determinant structures. They are composed of studs, columns, simply supported joists, common rafters, valley rafters, hip rafters, headers, beams, etc. and they are all determinate structures.

So what is a determinate structure?

A determinate structure can be analyzed just on the basis of simple equilibrium equations. The analysis gives  Analyzing an indeterminate structure requires solving equilibrium equations and special methods with strange names you do not really need to know such as moment distribution.

So what does any of this have to do with single-family houses? Just this: if there is foundation distortion, the load-bearing structure will not see an increase or decrease in stress. There may be an increase in stress in the non-load bearing elements such as shown by distress in wall coverings like brick veneer and drywall, but brick veneer and drywall are not load-bearing.

This characteristic of determinate structures is very important when the foundation is expected to settle or distort as will certainly happen if the supporting soil is expensive.

The bottom line is really simple

Since the house structure is composed of determinate structural elements, foundation movement rarely has a significant adverse effect on the load-bearing structural (load-carrying) elements: rafters, joists, studs, headers, etc. (A caveat: houses will sometimes have structural elements call continuous beams. The most common is purlins used to brace rafters. Technically, continuous beams are indeterminate, but only to one degree.  

It should come as no surprise that virtually all foundation distress is cosmetic or minor functional issues such as door issues. 

Consider the following quote from an engineering textbook titled: Fundamentals of Structural Analysis by Samuel E French.

Stresses in statically determinate structures are unaffected by foundation settlements; …in fact, the elimination of such foundation problems is often a decisive factor in the choice between a determinate system and an indeterminate system for the project design. In all cases, however, diffential settlements can produce nonstructural effects such as broken windows , binding doors, and in siding; settlements may have to be considered at least to some degree even in the design of statically determinate structures. (page 17)

Consider also these three facts: (1) wood-frame structures rarely suffer structural damage due to foundation distortion, and (2) I have never seen or heard of a collapsed wood-frame structure due to expansive soils in spite of the fact that there are far more numerous than indeterminant buildings – approximately 85% of all buildings in the United States are determinant structures.

So why do determinant buildings sometimes experience severe damage and even collapse?

The list is short: fire, water to put the fire out, termite infestations if left unchecked, severe environmental loads, especially high wind as in hurricanes that in excess of 120-mph. Conventional wood-frame houses are in danger of severe damage including collapse any time wind is in excess of 120-mph. 

What is not on the list is expansive soil swelling and shrinking. Foundation settling or heaving due to expansive soil shrinking and swelling never causes structurally significant changes in determinant load-bearing structural elements. 



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