Prediction of Shear Lag Effect in Thin-Walled Single-Box Multicell Box Girder Based on the Modified Warping Displacement Function

In this study, an effective and accurate theoretical analysis method for predicting the shear lag effect in the thin-walled single-box multicell box girder is presented. The modifications of longitudinal warping displacement functions at the flanges are fully investigated, including the shear lag width (bij) of flanges, the coefficients (αij) of shear lag warping functions, the deformation compatibility conditions in flanges, and the internal force balance (D). The initial shear deformation (γ03) in the top lateral cantilever flanges is innovatively introduced in multicell box girders and obtained by the designed procedure. In addition, the transverse distribution function for describing the longitudinal warping displacement is deduced and expressed in the form of the cosine function. Based on the principle of minimum potential energy, the governing differential equations are derived and solved with the associated boundary and load conditions. The accuracy and applicability of the proposed method (SL-THY2) are validated for four thin-walled single-box multicell (two- and three-cell) box girders with the results derived from the solid finite element method.

Deformation behavior of slab warping for longitudinal continuous rigid slab under temperature effect

Longitudinally coupled prefabricated slab track is prone to slab warping under the non-uniform temperature field. Analytical expressions for the displacement field of the track slab during the warping process are developed hereby based on equilibrium differential equations, and the expressions are verified through a numerical model by finite element method in ANSYS package. Through analyzing the factors such as types of temperature distribution, slab gravity, and rail weight, regulations of warping deformation for the track slab are systematically analyzed. Research shows that the displacements in the x and z directions are linearly related to the respective components during the warping deformation. The displacement in y direction has a quadratic relationship with x and z components. Temperature gradient is the pivotal factor to lead the warping of the track slab, and the type of temperature distribution has less effect on the warping displacement. If track slab remains unwarped under the effect of slab gravity, temperature gradient should be maintained in the range of –18°C/m–13°C/m. Rail weight has less influence on slab warping.

Diffraction from twisted nanowires: helicity revealed by anisotropy

The helical nature of twisted nanowires is studied by simulated X-ray diffraction. It is shown that this helicity is revealed by the anisotropy, which can be both an elastic anisotropy, through the warping displacement generated by torsion, or a shape anisotropy of the cross section. To support the analytical calculations, based on the kinematic theory of diffraction by helices, atomistic simulations of copper nanowires are performed.

Damping of Torsional Beam Vibrations by Control of Warping Displacement

Supplemental damping of torsional beam vibrations is considered by viscous bimoments acting on the axial warping displacement at the beam supports. The concept is illustrated by solving the governing eigenvalue problem for various support configurations with the applied bimoments represented as viscous boundary conditions. It is demonstrated that properly calibrated viscous bimoments introduce a significant level of supplemental damping to the targeted vibration mode and that the attainable damping can be accurately estimated from the two undamped problems associated with vanishing and infinite viscous parameters, respectively.

The Research of Box Beam Warping Displacement Function

Based on the principle of minimum potential energy, choosing warping displacement function of parabolic displacement mode, using energy variational method to deduce Box beam shear lag effect analysis of differential equation to obtain shear lag warping stress. Through the calculation of simply supported box girder model and the analyse of the stress of Wide cantilever plate, box girder roof and box girder floor Assume a new warping displacement function. Through the analysis of measured results proved the rationality of this article assumes and research value.

Uncoupled Torsion of Thin-Walled Sections

Pure bending-free torsion of a prismatic bar requires that the axis of twist be located at the shear centre of the section. However, finding the position of the shear centre in an asymmetric section is not a trivial task and corresponds to a complete bending or torsion analysis. By isolating the contribution from the axis of twist to the warping displacement distribution, the shear centre is determined from the solution to the related problem with the axis of twist at the origin. It is then necessary only to correct this solution for torsion about the shear centre rather than to re-solve the whole problem. Network theory is employed extensively in the solution.

Shear Flow in Multi-Cell Sections

Traditional shear flow calculations for thin-walled multi-cell sections subjected to bending have ignored developments in topological algebra that exploit the independence of a network topology from its physical characteristics. By treating the section as a set of thin limbs connected at end nodes, network theory originally developed for electrical circuits can be applied to the problem. Flow rules similar to those formulated by Kirchhoff almost a century and a half ago are derived from conditions of equilibrium and compatibility. Each limb of the section behaves as a flow generator which drives the flow around the network. A complete solution can be derived for shear flow and for warping displacement in every limb by solving a relatively small number of fundamental circuit equations, equal to the number of independent circuits in the network. Matrices employed in the solution can be formed directly from the section's topological description.