Optimal Slabs and Grillages of Constrained Geometry

Using extensions of Prager's theories of optimal plastic design, slabs and grillages are optimized within various geometrical constraints ensuring simplicity and practicality. The two classes of problems considered are: (1)Grillages consisting of prismatic beams of preassigned directions and length but variable spacing and balanced prestressed elastic plates having tendons of preassigned directions terminated at the edges only; and (2)slabs with curtailed negative reinforcement of preassigned length. The results given represent rigorous analytical optima as well as identical upper and lower bounds on the limit load. A comprehensive set of solutions is tabulated for rectangular domains with various boundary conditions and the moment volumes for constrained geometry are compared graphically with absolute minimum volumes of unconstrained solutions. Finally, the most economic length of negative reinforcement is calculated for rectangular slabs.