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Selection of the load cases in reinforced concrete corss-section design

Exact methods are presented for the problem of the convex hull in two and three dimensions. Given a set of points in the plane or in a three dimensional space, the convex hull problem consists in the determination of the points of the set which are vertices of the minumum convex polygon or polyhedron which contains all the points of the set. Both algorithms have been implemented as subroutines in Basic for PC-compatible micros, whose listings are given. Execution times of these subroutines vary almost linearly with the numbers of points of the ser, in the plane case, and with the product of the number of points by the number of vertices of the polyhedron, in the space case. These methods can be used for the selection of load cases for the design or check of reinforced concrete cross-sections submitted to symmetrical bending and compression (plane case) or to biaxial bending and compression (space case). The load caes corresponding to internal points can be eliminated as a consequence of the convexity of the interaction diagram or surface.