Flexural-torsional behavior of beams both in static and dynamics has been the subject of several papers in the recent past. In [1] flexural-torsional couplings in the motion of a cantilever beam was considered, limiting the model to linear warping. An approach based on the extension of the Vlasov theory to the nonlinear field is found in [2]; however, due to the complexity of the problem, several simplifying assumptions have been used. More recently in [3] the description of the mechanical behaviour of beams with open cross-sections is dealt with in a rigorous manner by extending in nonlinear field the Vlasov theory. The nonlinear effects of the torsional curvature on the elongation of the longitudinal fibers and the nonlinear warping of the section are considered. The model obtained is very complex and missing any possibility of recognizing the mechanical meaning of the different numerous terms. With the aim to study cases in which the torsional curvature is prevailing with respect to the flexural ones, the model in [3] has been specialized to describe the behavior of a cantilever beam and in particular with a monosymmetric cross-section. The simplified equations make it possible to stress the role of the nonlinear terms due to nonlinear warping and torsional elongation of the longitudinal fibers. The attention is focused on the response to static forces and on the stability of the equilibrium branches. Analytical results are compared with results of different nonlinear FE models and mainly with experimental results. Numerical and experimental investigation confirms the importance of the new nonlinear contributions and permits to validate the model developed [3]. In particular the model furnishes values of critical loads in flexural-torsional stability that the classical nonlinear one-dimensional beam models are not able to describe correctly. From a technical point of view it has been shown that the literature results for the critical loads are very far from the results obtained by means of the refined model proposed. In one case – flexural torsional buckling along symmetry cross section axis – is almost double the correct one, i.e. not in favour of safety. In another case - flexural torsional buckling along no symmetry axis – is almost half the correct one, in favour of safety. References [1] Crespo da Silva, M.R.M., Glynn, C.C., 1978. Nonlinear flexural-flexural-torsional dynamics of inextensional beams. - I. Equations of motion'. J. Struct. Mech.. 6(4), 437-448. [2] Ghobarah, A.A., Tso, W.K., 1971. A non-linear thin-walled beam theory. Int. J. Mech. Sci. 13, 1025-1033. [3] Di Egidio, A., Luongo, A., Vestroni, F., 2003. A nonlinear model for open cross-section thin-walled beams - Part I: Formulation. Int. J. Non-Linear Mech.. 38(7), 1067-1081.

### Nonlinear warping effects on the flexural-torsional behavior of a thin-walled open cross-section beam

#### Abstract

Flexural-torsional behavior of beams both in static and dynamics has been the subject of several papers in the recent past. In [1] flexural-torsional couplings in the motion of a cantilever beam was considered, limiting the model to linear warping. An approach based on the extension of the Vlasov theory to the nonlinear field is found in [2]; however, due to the complexity of the problem, several simplifying assumptions have been used. More recently in [3] the description of the mechanical behaviour of beams with open cross-sections is dealt with in a rigorous manner by extending in nonlinear field the Vlasov theory. The nonlinear effects of the torsional curvature on the elongation of the longitudinal fibers and the nonlinear warping of the section are considered. The model obtained is very complex and missing any possibility of recognizing the mechanical meaning of the different numerous terms. With the aim to study cases in which the torsional curvature is prevailing with respect to the flexural ones, the model in [3] has been specialized to describe the behavior of a cantilever beam and in particular with a monosymmetric cross-section. The simplified equations make it possible to stress the role of the nonlinear terms due to nonlinear warping and torsional elongation of the longitudinal fibers. The attention is focused on the response to static forces and on the stability of the equilibrium branches. Analytical results are compared with results of different nonlinear FE models and mainly with experimental results. Numerical and experimental investigation confirms the importance of the new nonlinear contributions and permits to validate the model developed [3]. In particular the model furnishes values of critical loads in flexural-torsional stability that the classical nonlinear one-dimensional beam models are not able to describe correctly. From a technical point of view it has been shown that the literature results for the critical loads are very far from the results obtained by means of the refined model proposed. In one case – flexural torsional buckling along symmetry cross section axis – is almost double the correct one, i.e. not in favour of safety. In another case - flexural torsional buckling along no symmetry axis – is almost half the correct one, in favour of safety. References [1] Crespo da Silva, M.R.M., Glynn, C.C., 1978. Nonlinear flexural-flexural-torsional dynamics of inextensional beams. - I. Equations of motion'. J. Struct. Mech.. 6(4), 437-448. [2] Ghobarah, A.A., Tso, W.K., 1971. A non-linear thin-walled beam theory. Int. J. Mech. Sci. 13, 1025-1033. [3] Di Egidio, A., Luongo, A., Vestroni, F., 2003. A nonlinear model for open cross-section thin-walled beams - Part I: Formulation. Int. J. Non-Linear Mech.. 38(7), 1067-1081.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11697/38576`
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