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By Sorensen D.C., Wets R.J.-B. (eds.)

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Additional resources for Algorithms and Theory in Filtering and Control, part 1

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These equations can then be solved at low cost using a digital computer. While elegant and systematic, this is not a fruitful way to proceed when working by hand since humans do not perform this type of task well. The approach taken in this section will be to explain some basic principles of truss behavior and then show how these principles can be used to solve trusses without solving large systems of equations. 1 A plane truss with three unknown reactions M"_"ments must sum (0 zet» about the Jeft support Forces must sum to zero an the honzontal and vertical direcuons Sec.

Statically determinate structures. When the equations of statics imply a unique set of internal member forces and moments for an arbitrary set of external loads, a structure is said to be statically determinate. The word arbitrary is important here. A structure may perform well under one set of loads but still be technically unstable. 1 performs well under an upward vertical load but cannot carry a horizontal load component and for that reason is regarded to be (geometrically) unstable. 2. Statically indeterminate structures.

9 Mecnoel of section* Sec. V3 Geometric Instability This section contains the final example in this tact of a structure which is geometrically unstable. As suggested eariier, in the case of a geometrically unstable structure the equilibrium equations have no solutkm. (That is obvkws in Ae case of Fig. 10. ) On the other hand, it is more common to think of an unstable structure kinematically in terms of collapse. 10 A C f o i c trierifrUftafcfc Twmm unstable structure possesses the possibility of a rigid body motion which implies potential collapse.

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