Automated Structural Analysis. An Introduction by William R. Spillers

By William R. Spillers

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1)). When 8C = 0, Eq. 1) reduces to Δΐ = Νι+δΑ. 3) + Multiplying Eq. 2) by Λ^ and using Eq. 4) and from the definition of the stiffness matrix that K^iNi+QNt*)-1. 5) can be viewed formally as a transformation from the cantilever flexibility, C„ to the member stiffness Kt. 5. 3 ADDING FLEXIBILITIES TO APPROXIMATE A CURVED MEMBER As stated in the introduction to this chapter, arbitrary curved members are treated in this book only as they can be approximated by straight uniform beam segments. Still, a large class of problems can be handled in this manner.

4 SINGULAR STIFFNESS MATRICES The node method for frames as it is presented here has a tendency to appear more restricted than it really is. While it is perhaps not obvious, such problems as hinges or releases, for example, in general can be handled very simply by including their effects in member stiffness matrices. Some applications of this method are indicated in Fig. 4. When this is done, the member stiffness matrix becomes singular. V rfh fth rfh rfh rfn ΓΤΠ 1 Fig. 4. Releases included in the member stiffness matrix.

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.

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