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By William R. Spillers

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2 to include "buckling" effects. 1 Discussion of Exercise 3 In linear structural analysis the equilibrium equations are written in the undeformed configuration. The classical treatment of overall truss buckling (not member buckling), on the other hand, adds to the linear formulation a nonlinearity which approximates the effect of small changes of geometry on the linear formulation in a manner similar to the method used to derive the linear response of a membrane or string. How this can be done is now indicated for a single bar one end of which is allowed to move.

Will be added in a later chapter. Nothing in this formulation implies that the structure under discussion is composed of members with two ends. Quite to the contrary, this formu­ lation is valid beyond its use in this text and can be applied to shell and solid finite elements. Finally, some remarks are in order concerning the "incidence matrix", N. 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.

12) L 3α(α-1) + 1 ψ The stiffness of the other end is obtained by replacing a by 1 — a in Eq. 12) to obtain Κ ™ = ΊΓ*α(αΛ) +ν (7 13) * 61 Automated Structural Analysis ,m = 1 —i Moment diagram Fig. 5. Beam with a hinge. 14) a2 3E/ L 3α(α-1) + 1 J THE EFFECT OF SHEAR As a final example of the generality available under the methods of this book, this section describes how shear effects can be included easily in the stiffness matrix for plane, straight uniform beams. In order to do so it is convenient to think of members connected at joints by rigid blocks as shown in Fig.

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