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N S Trahair – 1st expert on this subject based on the ideXlab platform
non linear Biaxial Bending of steel z beamsThin-walled Structures, 2018Co-Authors: N S TrahairAbstract:
Abstract Confusion as to the way in which the Bending of Z-section beams has been described has led to misleading descriptions of the limiting moments of beams which undergo non-linear Biaxial Bending and twisting as being elastic buckling moments. Further difficulties arise from the use of the same symbols to describe both the principal and the rectangular axes of Z-sections. A constrained beam with restraints which prevent lateral displacement of the compression region does not buckle laterally, and only needs to be designed against in-plane failure. A beam with restraints which prevent lateral displacement of the tension region should be designed against lateral-distortional buckling, which may be approximated by lateral buckling with an enforced centre of rotation. An unconstrained beam bent about its minor principal axis does not buckle laterally, and should be designed against in-plane failure. An unconstrained beam bent about its major principal axis may buckle laterally. An unconstrained beam under Biaxial Bending deflects and twists as soon as loading commences and reaches very large deformations as a limiting moment is approached. The large deformations cause premature yielding before the limiting moment is reached. Pre-buckling effects reduce these large deformations somewhat, but not sufficiently that the limiting moment can be safely used in first yield design. Instead, interaction equations may be used. The linear interaction equation is unnecessarily conservative, and may be replaced by a parabolic interaction equation.
Biaxial Bending and torsion of steel equal angle section beamsJournal of Structural Engineering-asce, 2007Co-Authors: N S TrahairAbstract:
Although steel single angle sections are commonly used as beams to support distributed loads which cause Biaxial Bending and torsion, their behavior may be extremely complicated, and the accurate prediction of their strengths very difficult. Further, many design codes do not have design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. This paper is one of a series on the behavior and design of single angle section steel beams. Two previous papers have studied the Biaxial Bending and torsion of restrained beams, a third has studied the lateral buckling of unrestrained beams, a fourth the Biaxial Bending of unrestrained beams, and a fifth and sixth the buckling and torsion of unrestrained beams. In each paper, simple design methods have been developed. In this present paper, an approximate method of predicting the second-order deflections and twist rotations of steel equal angle section beams under Biaxial Bending and torsion is developed. This method is then used to determine the approximate maximum Biaxial Bending moments in such beams, which are then used with the section moment capacity proposals of the first paper and the lateral buckling proposals of the third paper to approximate the member capacities.
Biaxial Bending of steel angle section beamsJournal of Structural Engineering-asce, 2004Co-Authors: N S TrahairAbstract:
The loads applied to angle beams usually act out of the principal planes so that they cause simultaneous Biaxial Bending about both principal axes. The general practice for designing unbraced beams…
Cengiz Dundar – 2nd expert on this subject based on the ideXlab platform
behaviour of reinforced and concrete encased composite columns subjected to Biaxial Bending and axial loadBuilding and Environment, 2008Co-Authors: Cengiz Dundar, Serkan Tokgoz, Kamil A Tanrikulu, Tarik BaranAbstract:
An experimental investigation of the behaviour of reinforced concrete columns and a theoretical procedure for analysis of both short and slender reinforced and composite columns of arbitrarily shaped cross section subjected to Biaxial Bending and axial load are presented. In the proposed procedure, nonlinear stress–strain relations are assumed for concrete, reinforcing steel and structural steel materials. The compression zone of the concrete section and the entire section of the structural steel are divided into adequate number of segments in order to use various stress–strain models for the analysis. The slenderness effect of the member is taken into account by using the Moment Magnification Method. The proposed procedure was compared with test results of 12 square and three L-shaped reinforced concrete columns subjected to short-term axial load and Biaxial Bending, and also some experimental results available in the literature for composite columns compared with the theoretical results obtained by the proposed procedure and a good degree of accuracy was obtained.
arbitrarily shaped reinforced concrete members subject to Biaxial Bending and axial loadComputers & Structures, 1993Co-Authors: Cengiz Dundar, B SahinAbstract:
Abstract An approach to the ultimate strength calculation and the dimensioning of arbitrarily shaped reinforced concrete sections, subject to combined Biaxial Bending and axial compression, is presented. The analysis is performed in accordance with the American Concrete Institute (ACI) code. A computer program is presented for rapid design of arbitrarily shaped reinforced concrete members under Biaxial Bending and axial load. In the proposed method the equilibrium equations are expressed in terms of the three unknowns, e.g. location of neutral axis and amount of total reinforcement area within the cross-section, which lead to three simultaneous nonlinear algebraic equations which are solved by a procedure based on the Newton-Raphson method. One design problem, available in the literature, is solved by this program to provide possible design procedures. A listing of the computer program is given in the Appendix.
concrete box sections under Biaxial Bending and axial loadJournal of Structural Engineering-asce, 1990Co-Authors: Cengiz DundarAbstract:
A computer program is developed for ultimate strength design of concrete box sections subjected to Biaxial Bending and axial load. The distribution of steel reinforcement is assumed to be symmetric in the section. In the analysis the equilibrium equations are expressed in terms of the three unknowns describing the location of the modified axis and the total reinforcement area within the cross section, which leads to three simultaneous nonlinear algebraic equations that are solved by a procedure based on the Newton-Raphson method. It is observed that the iterative algorithm used in the program converges rapidly for many different problem tested, and execution time of the program is small; hence the program can be run many times with different reinforcement arrangements and the most suitable reinforcement pattern among them can be chosen.
H P Hong – 3rd expert on this subject based on the ideXlab platform
strength of slender reinforced concrete columns under Biaxial BendingJournal of Structural Engineering-asce, 2001Co-Authors: H P HongAbstract:
A simple approach is proposed in this paper for estimating the strength of a slender reinforced concrete column under Biaxial Bending and axial load. The model considers the nonlinear stress-strain relations of concrete and reinforcing steel, and can be used for slender reinforced concrete column with arbitrary cross section. The problem of finding the strength of the slender reinforced concrete column is formulated as a nonlinearly constrained optimization problem. The method is capable of predicting the slender column strength. Its use for design purposes is also outlined. The predicted results obtained from the proposed method compare well with experimental results found in the literature.
Short reinforced concrete column capacity under Biaxial Bending and axial loadCanadian Journal of Civil Engineering, 2000Co-Authors: H P HongAbstract:
The paper describes the development of a simple theoretical approach in estimating the capacity of short reinforced concrete (RC) columns under Biaxial Bending and axial load. The developed approach considers the nonlinear stress-strain relations of concrete and reinforcing steel and does not make the assumption about the limiting strain of extreme compression fiber of concrete. The solution is obtained using a nonlinearly constrained optimization algorithm. The approach was used to estimate the theoretical capacities of many tested RC columns found in the literature. A probabilistic analysis of the modeling errors was carried out using the ratios of the test-to-predicted results. The probabilistic analysis was extended to include two simplified theoretical methods: the reciprocal load method given by Bresler and the failure surface method given by Hsu.Key words: Biaxial Bending, modeling error, optimization, probability distribution.