By Anil K. Jain
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Extra resources for Algorithms for Clustering Data
First, the reactions are computed. In this case since there are time unknown reactions and three equations of equihTmum for a rigid body, t h ^ computed directly. In some cases such as the three-hinged arch discussed below there can hefourreactions to compute. In any case, given the reactions, enough free body diagrams must be taken (cuts to the structure must he made) to describe die stress resultants at every point In this particular example, four free body diagrams are required. 16 is included here to pick up the pace a little.
MB * 2368 lb' bending moment^ - k' • MB « -48 lb' Exercises Sec. 5] 13 The cantilever beam shown has a parabolic shape with vertical tangent at point A rather than the circular shape of Example 1 ,4. Find T,V,M. 14 Compote the reactions Fl and F, for the plane truss town. ) *nr < ft \1 1 \ < 1r ♦ . 1 . . ■» IS Compute the reactions F„ F* f 3 for die apace truss sfeown. 1 INTRODUCTION This relatively long chapter is concerned with a topic which is basic to any introductory text on structures: the analysis of statically determinate structures.
67-0 F v - - 2 . 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.
Algorithms for Clustering Data by Anil K. Jain