Solid Modeling of RC Beams: I. Data Structures and Algorithms

Abstract

Solid modeling is the process of building and analyzing geometrically complete representations of points, lines, polygons, and three‐dimensional solid objects. In a functional sense, a model is said to be geometrically complete if it is possible to answer questions about the geometry of an object with algorithmic operations that act on the underlying data representation. For this to be possible, objects must be closed, orientable, non‐self‐intersecting, bounding, and connected. This paper describes data structures and algorithms used in a solid modeling‐based methodology for the interactive design and analysis of reinforced concrete (RC) beam structures. Data structures are described for steel reinforcing‐bar trajectories and a three‐dimensional boundary representation of the concrete beam solid. After the concrete beam model is set up, the envelope of ultimate flexural strength is obtained by slicing the beam solid at selected locations and extracting the cross section. Algorithms are given for the slicing process, plus the calculation of cross‐section properties and ultimate flexural strength.