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Received Oct 21, 2016; Revised Dec 27, 2016; Accepted Jan 18, 2017
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1. Introduction
Structural stability has always been a key point in the design of steel structures [1–6]. It is well known that an I-beam has various buckling phenomena such as local buckling, distortion buckling, and lateral-torsional buckling, in which the lateral-torsional buckling (LTB) is also known as the global buckling. This may occur if the applied service loads exceed its LTB critical moment of the I-beam and hence, in practice design, it is important for the designers to obtain the accurate solution of the critical moment as the upper limit of buckling strength of the steel I-beams. However, until now, even for the simple-supported I-beams with doubly symmetric sections subjected to unequal end moments, the design formulas given by the codes/specifications of different countries are quite different (Figure 1) that makes the designers feel very confused. In fact, such problems also confuse those involved in the formulation of the codes/specifications. In order to avoid greater controversy, there is a trend in the specification that is the initiative to delete the relevant provisions, such as the new version of the EC3 specification [7]. However, the deletion of the relevant provisions does not mean that such problems do not exist. Therefore, it is one of the objectives of this paper to provide a more accurate design formula based on the dimensionless analytic solution, which is also the main motivation of this paper.
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Due to the complexity of the LTB phenomenon of I-beams under nonuniform distributed moment, so far only approximate analytical solutions or numerical solutions have been published.
Some approximate analytical solutions can be found in the classical text books such as Chajes [2], Chen and Atsuta [3], Trahair [4], Timoshenko and Gere [5], and Bleich...