By William R. Spillers
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Additional info for Automated Structural Analysis. An Introduction
Such an approximation is intuitively appealing, extremely simple, commonly practiced, and in the spirit of the recent developments in finite element methods. 2 MEMBER STIFFNESS OBTAINED FROM THE CANTILEVER FLEXIBILITY For reasons of convenience, it is common to compute the member stiffness by first "fixing" one end of the member and finding its behavior as a cantilever. ), it is frequently quite useful. e. òc = 0). For convenience in this section it is assumed that the global ^ ^ Of00^ yl **v^ # χ' Member / Fig.
While Eqs. 1) simply describe a linear system, the description is peculiar in that it uses the matrix N twice. This multiple use of N is not necessary and is purely a matter of convenience which can be motivated most easily in terms of energy. 3) respectively. If the node method is to describe a "conservative system" then W=E or Ρδ = ΡΔ. 4) The following theorem can now be proved. 30 A General Statement of the Node Method THEOREM: that Δ = Νδ. IfW' = E and NF = P are to ho Idfor arbitrary F, it follows Proof: Since NF = P, Eq.
Zero) rm Secondary problem rfn Primary problem Fig. 2. Member loads. -AT (all joint disp. zero) Secondary problem Fig. 3. Temperature effects in a truss. 4 indicates a very simple member load problem which, while not quite in the spirit of this book, (it includes a support which is not completely fixed), illustrates the decomposition nicely. El is assumed to be constant. 5 shows a temperature problem to which the decomposition has been applied. In Fig. 6 a support problem is treated indirectly as a temperature problem.