A FE procedure is proposed for spatial buckling analysis of thin-walled steel beams that are pre-stressed (PS) by spatially inclined cables. Here, the beams are simply supported, and their cross ...section can be bi/mono-symmetric. Also, the pre-stressing cables are connected to several deviators under bonded/un-bonded conditions. For lateral–torsional buckling (LTB) analysis of the PS beams, a thin-walled beam element for the steel beam and solid beam elements for the deviator members are firstly formulated using total potential energies. After that, the potential energies of two-node bonded and multi-node un-bonded cable elements are rigorously derived, and the corresponding elastic and geometric stiffness matrices are explicitly presented. Finally, the validity and accuracy of the present FE formulation are demonstrated through numerical examples, and a set of parametric studies is conducted to investigate the effects of initial tension, multi-deviators, vertical and lateral eccentricities, and flexible deviators on the LTB of the PS beams.
•LTB analysis for thin-walled beams pre-stressed by spatial cables is performed.•A FEM is formulated using mono-symmetric thin-walled beam elements and spatial un-bonded cable elements.•Effects of initial tension, deviator number and stiffness, and spatial cable profile on LTB behaviors of PS beams are investigated.
This paper intends to propose a lateral-torsional buckling (LTB) theory of pre-stressed simple/cantilever steel beams with deviators subjected to compression and end moments in which their cross ...sections are mono-symmetric, initially tensions are introduced by rectilinear single/double tendons, and discrete un-bonded/bonded deviators are taken into account. Firstly, in-plane linear solutions of the PS system are presented under combined compression and moments. After that, analytically exact buckling solutions and approximate Ritz solutions are obtained based on the total potential energies derived. As a result, it is demonstrated that both exact and Ritz solutions by this study are very well matched with FE solutions by Abaqus. In addition, pre-tension effects on LTB behaviors of the PS beams are investigated with increase of the number of deviators.
•Spatial buckling theory of PS steel beams with mono-symmetric thin-walled sections are formulated depending on discretely un-bonded/bonded deviators.•Analytically exact and approximate Ritz solutions on LTB loads of simple/cantliver PS beams are compared with FE solutions by Abaqus.•The closed-form solutions by Ritz method could serve as design formula because they are so simple and predict LTB loads accurately.
A FE formulation has been newly presented for the lateral-torsional buckling (LTB) analysis of an externally pre-stressed (PS) steel beam, possessing deviators under non-uniform bending moments. ...Firstly, the total potential energies of the PS mono-symmetric thin-walled beams in possession of un-bonded/bonded deviators are derived depending on the number of deviators. Afterwards, the in-plane solutions of the PS mono-symmetric simple/cantilever beams under the lateral load can be analytically derived through the use of discontinuous functions. A simplified FE procedure is then developed based on the total potential energy, taking into consideration the effects of double tendons. Finally, the critical buckling loads of simple and cantilever PS mono-symmetric beams which were subjected to the non-uniform moments with the increasing of deviators are evaluated using the FEM and Rayleigh-Ritz method. As a result, the FE solutions were found to be very well matched to solutions by Ritz method and Abaqus. Additionally, the effects of double tendons, eccentricity, and the initial tension on LTB of the PS beam system were investigated with the increase of un-bonded/bonded deviators.
We develop a novel lateral–torsional buckling theory for pre-stressed (PS) steel H-beams with or without a deviator by using the total potential energy derived from the second order terms of ...semi-tangential rotations, the analytically derived exact solutions are presented and compared with the approximate solutions produced by the Ritz method and FEM. In this work, we particularly focus on the buckling characteristics of simple and cantilever PS beams under three loading conditions: initial tension only, compression, and quasi/semi-tangential moments. In addition, we demonstrate how these quasi- and semi-tangential moments are generated based on semi-tangential rotations. Furthermore, we verify that in-plane load distributions and spatial buckling loads under the conditions of a rectilinear cable with an un-bonded deviator are exactly the same as under the conditions of a rectilinear cable with a bonded deviator. Finally, a deviator’s effect on the buckling strengths of the PS system with double tendons under external loading is examined.
•A LTB theory for PS steel beams with one un-bonded/bonded deviator under compression and end moments is formulated.•The effects of the deviator on buckling of a PS beam are investigated under simple/cantilever conditions.•Two types of analytical solutions for buckling of a PS system are given, the results match the solutions given by FE analysis well.
A lateral–torsional buckling theory of mono-symmetric thin-walled beams pre-stressed by rectilinear tendon cables was proposed considering bonded/un-bonded deviators. It was assumed that ...simple/cantilever steel beams would be subjected to a combined compressive force and bending moment caused by double tendon cables, rigidly connected to discrete deviators. As a result, total potential energies of the pre-stressed (PS) system were newly derived depending on the number of deviators. Buckled equilibrium equations were analytically solved and compared with FE solutions by Abaqus. Through buckling analysis, stabilizing effects of deviators were demonstrated on lateral–torsional buckling (LTB) strength of mono-symmetric PS steel beams pre-stressed by tendon cables. In addition, it was found that LTB loads of mono-symmetric simple beams pre-stressed by single tendon with deviators were identical to those of PS cantilever beams under warping free conditions.
•A LTB theory of PS beams with mono-symmetric thin-walled sections due to initial tensions is formulated with deviators.•It is demonstrated that analytical solutions on LTB of simple/cantilever PS beams are accurate and valid.•LTB loads of the PS mono-symmetric beams under initial tension are drastically increased with increase of deviators.•It is observed that LTB loads of simply-supported PS beams are identical to cantilever PS beams with a warping-free end.
This study intends to answer how nonlinear beam theories could be rigorously derived when based on three hypotheses: Haringx/Reissner, Engesser, and Ziegler. For this purpose, Reissner formulation is ...first summarized for an elastic beam segment undergoing large displacements and strains, and the nonlinear equations obtained are compactly converted into a non-dimensional form using two parameters of shear-flexibility and extensibility. After that, conjugate strain measures corresponding to axial and shear forces based on Engesser and Ziegler's assumptions are consistently derived, and the resulting governing equations are presented in a dimensionless form. Finally, nonlinear problems of extensible and shearable cantilever beams are solved using the 4th order Runge-Kutta method combined with a shooting method. Shear-deformation and extensibility effects are addressed through two examples showing large deflections and post-buckling behaviors of cantilever beams.
A lateral-torsional buckling (LTB) experimental study has been firstly investigated for an externally pre-stressed (PS) steel beam with/without un-bonded central deviator. Analytical and numerical ...studies related to elastic LTB of the PS beam are abundant. However, an experimental study focusing on LTB behaviors of the PS steel beam is newly presented in this study. Six full-scale experimental specimens consisting of two usual steel beams without tendon bar, two PS steel beams under vertical loadings and two PS steel beams under increasing tendon force were tested. Load–strain/displacement behaviors of the specimens were obtained by measuring stains, lateral and vertical displacements. The numerical study of the geometric and material nonlinear behaviors of PS steel beams was evaluated based on the Riks method using ABAQUS. Finally, numerical and experimental results of load–strain/displacement behaviors of the usual and PS beams were investigated. The experimental and numerical results indicated that the LTB strength of steel beams could be greatly improved by prestressing system.
