0
RESEARCH PAPERS

A General Formulation of the Optimal Frame Problem

[+] Author and Article Information
D. E. Grierson, M. Z. Cohn

University of Waterloo, Waterloo, Ontario, Canada

J. Appl. Mech 37(2), 356-360 (Jun 01, 1970) (5 pages) doi:10.1115/1.3408513 History: Received June 10, 1969; Revised January 19, 1970; Online April 06, 2010

Abstract

Optimal design techniques have been extensively applied to steel structures and, to a lesser degree, to reinforced concrete structures. In the latter case, for given geometry and preassigned stiffnesses, optimal designs have been found which simultaneously satisfy (a) limit equilibrium (plastic limit stage), (b) serviceability (elastic limit stage), and (c) optimality (minimum material consumption). The limitations to these designs are: 1. A subsequent check of plastic compatibility may invalidate the design. 2. The resulting member stiffnesses may differ appreciably from the preassigned values. 3. A different geometry may result in a better solution while still satisfying all design criteria. The present paper attempts to eliminate these limitations through a more general formulation of the optimal frame problem wherein design plastic moments, member stiffnesses, and frame geometry are all treated as variables and are found for simultaneous satisfaction of (a) optimality, (b) limit equilibrium, (c) serviceability, (d) plastic compatibility, and (e) elastic compatibility. With some simplifying assumptions to linearize the problem, the general formulation is illustrated for a reinforced concrete continuous beam example. The resulting optimal design is compared with conventional elastic and plastic designs with respect to safety, serviceability, compatibility, and efficiency.

Copyright © 1970 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In