Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag

Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.

Lateral static and dynamic characteristics of thin-walled box girder

To analyze the static and dynamic behaviors of the thin-walled box girder in its lateral webs in consideration of shear lag effect and shear deformation, an approach based on the minimum potential principle is introduced in this paper. Both static and dynamic response equations as well as the corresponding natural boundary conditions of the box girder are deduced. Meanwhile, three generalized displacement functions： w （x） , U（x） and O（x） are employed and their differences in the calculus of variation are quantitatively investigated. The comparison of finite shell element results with analytical results of calculation examples validates the feasibility of the proposed approach.

A comparative study on the hull strength of a ship with thin-walled box girders

Based on the Finite Element Analysis and Thin Walled-Box girder Mechanics, two design concepts of adding box girders under main deck in order to increase the hull strength of ship are presented. By comparison and analysis on the longitudinal strength, torsion strength and deck buckling between designed concepts and the original concept, it is found that by adding box girders under the main deck, the weight of hull structure is increased by lower than 10%, but the stress on the plate of the main deck is reduced by about 10%, the stress on the plating of the second deck is reduced about 20%. The shear stress on the plating of both of the main deck and second deck is reduced, but the shear stresses in several nodes are increased. Also the capability of resisting damage to ship is obviously increased by adding box girders under the main deck. The deck buckling is also increased by more than 90%. Consequently, the box girders added under the main deck are useful and effective to increase the strength of hull and ship survivability.

Mechanics analysis of thin-walled box continuous girder with variable cross-sections in considering effect of large deflection and shear lag

In order to study the mechanics behavior of a thin-walled box continuous girder with variable crosssections,using potential variation theories,considering the effect of shear lag of flange’s stress and the nonlinear geometry of vertical displacement,and evolving five generalized displacements with the spline function,the large deflection problem of the thin-walled box continuous girder with variable cross-section was transformed to a nonlinear algebraic equation,which was solved using the Newton-Raphon iterative method.The results of the calculation show that different shear lag warp functions to the cantilever,top and bottom plate should be taken to analyze the mechanics behavior of the thin-walled box continuous girder reliably.The thin-walled box continuous girder with variable cross-sections has more reasonable stress state and is more adaptable for the longitudinal change of internal forces than that with equal crosssections.The effect of large deflection on the stress and displacement of the thin-walled box continuous girder with variable cross-sections depends on the values of the load.