Design Interaction Curves for Tubular Steel Beam-Columns
Authors: Wagner W.L. , Mueller W.H. , Erzurumlu H. 
Published: December 2007

This paper describes a general-purpose computer program developed to determine ultimate load capacities in tubular steel beam-columns. An analytical model and a computer method are presented also. Analytical results are compared with published test data and the experimental data obtained in this investigation.

Introduction
Previous investigators have shown that tubular members Previous investigators have shown that tubular members of annular shapes exhibit structural characteristics markedly different from wide-flange shapes when subjected to loads that cause stresses above first yield. Methods for calculating failure loads and developing interaction diagrams for wide-flange members used as beam-columns have been developed and are used in design practice currently. Because the same type of technique practice currently. Because the same type of technique for tubular members is not available now, an investigation as launched to develop an analytical tool. This took the form of a computer program that could be used to generate load displacement histories and to calculate failure loads of circular steel tubes subjected to the combined effects of axial force and flexure. This study briefly documents the development of the mathematical model and presents experimental data verifying the results of this computer program.
The computer program can account for the effects of residual stresses during the generation of moment-thrust-curvature (MP) data, the first phase in calculating beam-column failure loads. Any configuration of stress-strain relationships may be included by providing appropriate data in tabular form. However, while this investigation includes the determination of MP data, those provided by other investigators also may be put directly into the computer program. Failure loads are calculated by a numerical technique that increases the load in increments until no further load can be supported, when the beam-column is considered to have failed.
A testing program was conducted to obtain experimental data. This program comprised four model tests of circular tubes loaded eccentrically to failure. These tests and those of other investigators verified the mathematical model presented.

Computer Model
The computer model has two major components:generation of MP data anddetermination of failure loads. Details of each are described below.
The MP data characterize the behavior of column stubs. This information fundamentally defines the required stress distribution and magnitude necessary for equilibrium of a given strain condition. An open-form solution technique to determine MP relationships for circular tubes by dividing a cross-section into horizontal sectors has been developed previously. The method presented here divides the cross-section into layers of presented here divides the cross-section into layers of elements surrounding the circumference (Fig. 1a) and is more accurate and complete for element idealization. The number of layers and elements is limited only by the size of the specified arrays in the computer program. As developed, the open-form technique permits any configuration of sums-strain relationship and selected residual-stress distribution patterns (Fig. 1b) to be included directly into the solution.
JPT
P. 367