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This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force F , bending moment M and distributed load q (or concentrated load P) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads. [ABSTRACT FROM AUTHOR]

In this paper we have discussed the frictional buckling behavior of a slender rod constrained in a horizontal cylinder. Buckling and post-buckling behaviors including the onset of helical buckling and subsequent axial force transfer are interpreted in a new way. Helical buckling and concomitant low force transfer efficiency which would prevent further axial extended reach is important to engineering structures, such as coiled tubing operations in petroleum industry. By means of the beam-column method, new governing differential equation of frictional buckling are derived to predict critical buckling force. We also investigate the transfer efficiency of axial force quantifying the effect of axial friction on rod lockup phenomenon in post-buckling analyses by perturbation solution. The coupling effect between axial force and friction is solved for the first time in this paper. The bending moment at the lock-up limit which would cause the rod to rupture is also analyzed. Finally, we have compared the proposed model with experimental results to verify its validity. Through these analyses, we have provided another interpretation to the existing experiment and numerical simulation results of frictional buckling. The derived results are simple and convenient for a problem in industrial practice. • New buckling differential equations of frictionally, cylindrically restrained rod are derived. • Critical buckling loads of frictional buckling are solved from the new buckling equations. • Analytical solutions about axial force transfer efficiency are derived by perturbation solution. • Good agreement is found between the theory and experimental results. [ABSTRACT FROM AUTHOR]