Session Start Date

8-24-2012

Session End Date

8-25-2012

Abstract

The objective of this paper is to introduce appropriate constraints in the shape optimization of a cold- formed steel column such that the resulting optimized shapes retain the strength benefits of unconstrained optimal solutions combined with practical manufacturing and constructional needs. Unconstrained shape optimization of cold-formed steel columns, where the cross-section that maximizes axial capacity is found, has previously been performed. Here, practical manufacturing and construction constraints are introduced into the optimization algorithm. Members with three lengths: 2 ft, 4 ft, and 16 ft, are considered. Optimized sections from multiple runs show uniformity and bear a close resemblance to unconstrained results. A point-symmetric ‘S’-shaped section has maximum capacity for long columns and a singly-symmetric ‘∑’-shaped section with complex lips performs best for shorter columns. The observed strength loss from the unconstrained optimal design, to the constrained optimal design, is within ten percent. A simultaneous perturbation stochastic approximation algorithm, with the idea of injecting randomness in the gradient approximation to save computational cost, is adopted as the local optimizer. A systematic survey on a family of lipped channel cross-sections using the same amount of material was carried out. Comparison reveals that the optimized shapes have much larger capacities and exhibit the potential to seed a new generation of commercial products.

Department(s)

Civil, Architectural and Environmental Engineering

Research Center/Lab(s)

Wei-Wen Yu Center for Cold-Formed Steel Structures

Meeting Name

21st International Specialty Conference on Cold-Formed Steel Structures

Publisher

Missouri University of Science and Technology

Publication Date

8-24-2012

Document Version

Final Version

Rights

© 2012 Missouri University of Science and Technology, All rights reserved.

Document Type

Article - Conference proceedings

File Type

text

Language

English

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Constrained Shape Optimization of Cold-formed Steel Columns

The objective of this paper is to introduce appropriate constraints in the shape optimization of a cold- formed steel column such that the resulting optimized shapes retain the strength benefits of unconstrained optimal solutions combined with practical manufacturing and constructional needs. Unconstrained shape optimization of cold-formed steel columns, where the cross-section that maximizes axial capacity is found, has previously been performed. Here, practical manufacturing and construction constraints are introduced into the optimization algorithm. Members with three lengths: 2 ft, 4 ft, and 16 ft, are considered. Optimized sections from multiple runs show uniformity and bear a close resemblance to unconstrained results. A point-symmetric ‘S’-shaped section has maximum capacity for long columns and a singly-symmetric ‘∑’-shaped section with complex lips performs best for shorter columns. The observed strength loss from the unconstrained optimal design, to the constrained optimal design, is within ten percent. A simultaneous perturbation stochastic approximation algorithm, with the idea of injecting randomness in the gradient approximation to save computational cost, is adopted as the local optimizer. A systematic survey on a family of lipped channel cross-sections using the same amount of material was carried out. Comparison reveals that the optimized shapes have much larger capacities and exhibit the potential to seed a new generation of commercial products.