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Design of Civil Engineering Frame Structures Using a Monomial/Newton Hybrid Method

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Abstract

This paper presents an application of a monomial approximation method for solving systems of nonlinear equations to the design of civil engineering frame structures. This is accomplished by solving a set of equations representing the state known as “fully-stressed design”, where each member of the structure is stressed to the maximum safe allowable level under at least one of the loading conditions acting on it. The monomial approximation method is based on the process of condensation, which has its origin in geometric programming theory. A monomial/Newton hybrid method is presented which permits some of the design variables to be free in sign, while others are strictly positive. This hybrid method is well suited to the structural design application since some variables are naturally positive and others are naturally free. The proposed method is compared to the most commonly used fully-stressed design method in practice. The hybrid method is shown to find solutions that the conventional method cannot find, while doing so with less computational effort. The impact of this approach on the activity of structural design is discussed.

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Authors and Affiliations

  1. University of Illinois at Urbana-Champaign, 117 Transportation Building, 104 S. Mathews, Urbana, IL 61801, USA

    Scott A. Burns

  2. American Institute of Steel Construction, One East Wacker Drive, Suite 3100, Chicago, IL, 60601, USA

    Keith M. Mueller

Authors
  1. Scott A. Burns
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  2. Keith M. Mueller
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Burns, S.A., Mueller, K.M. Design of Civil Engineering Frame Structures Using a Monomial/Newton Hybrid Method. Annals of Operations Research 105, 21–35 (2001). https://doi.org/10.1023/A:1013393213240

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