Research Article
Dec 1975
Optimal Slabs and Grillages of Constrained Geometry
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VIEW THE REPLYPublication: Journal of the Engineering Mechanics Division
Volume 101, Issue 6
Abstract
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.
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Published In
Journal of the Engineering Mechanics Division
Volume 101 • Issue 6 • December 1975
Pages: 755 - 770
Copyright
© 1975 American Society of Civil Engineers.
History
Published in print: Dec 1975
Published online: Feb 3, 2021
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George I.N. Rozvany, M.ASCE
Reader, Monash Univ., Clayton, Victoria, Australia
Robin D. Hill
Ph.D. Candidates, Monash Univ., Clayton, Victoria, Australia
Chinappa Gangadharaiah
Ph.D. Candidate, Monash Univ., Clayton, Victoria, Australia
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