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Mathematical Problems in Engineering
Volume 2017, Article ID 4838613, 23 pages
Research Article

Dimensionless Analytical Solution and New Design Formula for Lateral-Torsional Buckling of I-Beams under Linear Distributed Moment via Linear Stability Theory

1School of Architecture & Engineering, Nanjing Institute of Technology, Nanjing 211167, China
2Northeast Petroleum University, Daqing, Heilongjiang 163318, China

Correspondence should be addressed to Wen-Fu Zhang; moc.621@ufnew_gnahz

Received 21 October 2016; Revised 27 December 2016; Accepted 18 January 2017; Published 31 December 2017

Academic Editor: R. Emre Erkmen

Copyright © 2017 Wen-Fu Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Even for the doubly symmetric I-beams under linear distributed moment, the design formulas given by codes of different countries are quite different. This paper will derive a dimensionless analytical solution via linear stability theory and propose a new design formula of the critical moment of the lateral-torsional buckling (LTB) of the simply supported I-beams under linear distributed moment. Firstly, the assumptions of linear stability theory are reviewed, the dispute concerning the LTB energy equation is introduced, and then the thinking of Plate-Beam Theory, which can be used to fully resolve the challenge presented by Ojalvo, is presented briefly; secondly, by introducing the new dimensionless coefficient of lateral deflection, the new dimensionless critical moment and Wagner’s coefficient are derived naturally from the total potential energy. With these independent parameters, the new dimensionless analytical buckling equation is obtained; thirdly, the convergence performance of the dimensionless analytical solution is discussed by numerical solutions and its correctness is verified by the numerical results given by ANSYS; finally, a new trilinear mathematical model is proposed as the benchmark of formulating the design formula and, with the help of 1stOpt software, the four coefficients used in the proposed dimensionless design formula are determined.