Automated Structural Analysis. An Introduction by William R. Spillers

By William R. Spillers

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It also shows two coordinate systems, the primed and the unprimed, which differ in orientation by the angle φ. t/ — y component of the vector t in the unprimed coordinate system (t)^, — x component of vector t in the primed coordinate system (t)'u — y component of vector t in the primed coordinate system With the aid of the segment (t)^ sin φ shown in Fig. e. Λ~Λ = Ä. Based upon this relationship, a hybrid rotation matrix (which contains a third component which does not transform) is constructed in the next section; Chapter 5 uses the full three dimensional form indicated in the appendix.

By this argument it is determined that the member force matrix will contain six components for each member in the structure, or and (F, + ),/ (M,+ ),/ + Fi = (M l ) y / (M, + ),* (MT)y* (ΜΓ),* FB in which the subscripts x\ y\ £ indicate components in the local coordinate system of the /th member. There is an arbitrariness in the selection of the components of F{ here, just as there is in the case of the plane frame. ) It may be noted that the components of Ft can be classified roughly as a thrust, a twisting moment, and four bending moments.

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.

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