The Theory of Optimal Load Transmission by Flexure

Publisher Summary This chapter outlines optimality conditions for truss-like continua in which the cross-sectional areas are proportional to the absolute value of the member forces. It has been found that the optimal moment field is the same for any one of the following three criteria: rigid-plastic grillages: prescribed ultimate load; linearly or nonlinearly elastic grillages: prescribed maximum stress; and linearly elastic grillages: prescribed value of the work of the specified loads on the actual elastic deflections. The same moment fields minimize the volume of continuously variable reinforcement in fiber-reinforced plates of constant thickness. The problem is also referred to as the “minimum moment-volume problem” because it gives a minimum value for the integral of the sum of the absolute values of principal moments, considering the set of all statically admissible moment fields for given boundary conditions and loading. The theory discussed has several useful applications, such as beam systems in floors and roofs, and reinforced concrete slabs. Another aspect of grillage design is that the quantitative implications of optimization appear to be more significant than for most other types of structures.

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