Lateral-torsional buckling analysis of cantilever beam with tip lateral elastic brace under uniform and concentrated load

Zhang, Wenfu; Liu, Yingchun; Hou, Gui-Lan; Chen, Ke-Shan; Ji, Jing; Deng, Yun; Deng, Shengli

doi:10.1007/s13296-016-0052-5

Cited by 16 publications

(13 citation statements)

References 11 publications

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“…For the case of the simply supported I-beams, the following modal trial functions are proposed for the lateral deflection ( ) and twist angle ( ) [29][30][31][32][33][34][35], which can be expressed as the sum of trigonometric series as follows:…”

Section: Moment Function and Modal Trial Functions For The Simply Sumentioning

confidence: 99%

“…However, their dimensions are different, so in order to remove the dimension of so that and are both undetermined dimensionless coefficients, we introduce ℎ into the expression of ( ) in this work. This idea is proposed by the author, which is completely different from other previous research [25][26][27] as discussed in Section 3.4, and it has been used in LTB analysis of various steel beams [29][30][31][32][33][34][35]. Obviously, the above trial functions are orthogonal and satisfy the following geometric boundary conditions of the simply supported beams; that is,…”

Section: Moment Function and Modal Trial Functions For The Simply Sumentioning

confidence: 99%

“…Without loss of generality, the following new dimensionless parameters [29][30][31][32][33][34][35] are introduced:…”

Section: Dimensionless Total Potential Energymentioning

confidence: 99%

“…This definition is first proposed by Professor Zhang [29] since 2008 and later used in the LTB analysis of various steel beams [30][31][32][33][34][35].…”

Section: Remarks On Definition Of Dimensionless Critical Momentmentioning

confidence: 99%

“…Recently, based upon the author's work [29,30], we have carried out a series of research work on the dimensionless analytical solutions and design formulas of the critical moment of the LTB of the I-beams [31][32][33][34]. Recently, Zhang et al [35] derived a dimensionless analytical solution and design formula of the critical moment of the LTB of the cantilever beam with tip lateral elastic brace under uniform and concentrated load.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Liu

Chen

et al. 2017

Mathematical Problems in Engineering

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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.

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Section: Moment Function and Modal Trial Functions For The Simply Sumentioning

confidence: 99%

Section: Moment Function and Modal Trial Functions For The Simply Sumentioning

confidence: 99%

“…Without loss of generality, the following new dimensionless parameters [29][30][31][32][33][34][35] are introduced:…”

Section: Dimensionless Total Potential Energymentioning

confidence: 99%

“…This definition is first proposed by Professor Zhang [29] since 2008 and later used in the LTB analysis of various steel beams [30][31][32][33][34][35].…”

Section: Remarks On Definition Of Dimensionless Critical Momentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations