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During the construction stage of the steel-concrete composite box girder, the steel tub-girder has to support its weight, the self-weight of the wet concrete, and other construction loads. To improve the torsional stiffness of the steel tub-girder, the top flange bracing is often used to connect the top flanges to make “semi-closed” cross sections. The steel tub-girder with top flange bracing can form a closed shear flow under torsion, and thereby causing the distortion effect. However, the distortional behavior of this type of structure remains unclear. In this paper, the equivalent thickness of the fictitious top flange is first derived based on the restrained torsion theory. Subsequently, the errors of distortion loads given by the conventional load decomposition method which ignores the effect of warping restraint are derived, and are further verified by finite element analysis. It is demonstrated that the effect of warping restraint on the distortion is significant in the continuous tub-girder bridges with the top flange bracing. Therefore, the corresponding correction coefficients for the distortion loads caused by eccentric vertical loads and the girder axis curvature are proposed, and the simplified formulas for estimating these correction coefficients are established based on parametric analyses. Finally, the calculation method for the internal force of cross frames is modified and the accuracy of the proposed method is validated with results from finite element analysis.

This paper considers nonlinear dynamics of tethered three-body formation system with their centre of mass staying on a circular orbit around the Earth, and applies the theory of space manifold dynamics to deal with the nonlinear dynamical behaviors of the equilibrium configurations of the system. Compared with the classical circular restricted three body system, sixteen equilibrium configurations are obtained globally from the geometry of pseudo-potential energy surface, four of which were omitted in the previous research. The periodic Lyapunov orbits and their invariant manifolds near the hyperbolic equilibria are presented, and an iteration procedure for identifying Lyapunov orbit is proposed based on the differential correction algorithm. The non-transversal intersections between invariant manifolds are addressed to generate homoclinic and heteroclinic trajectories between the Lyapunov orbits. (3,3)-and (2,1)-heteroclinic trajectories from the neighborhood of one collinear equilibrium to that of another one, and (3,6)- and (2,1)-homoclinic trajectories from and to the neighborhood of the same equilibrium, are obtained based on the Poincare mapping technique.

This paper presents a new method of hierarchical control for large-scale linear time-varying systems via the single-term Walsh series (STWS). Certainly, the STWS method has definite advantages over the Walsh function (WF) method and block-pulse function (BPF) method. Both the discrete values and block-pulse values of the results are obtained for any length of time and selecting any positive integer as the number of intervals. The proposed method is simple and computationally advantageous. An illustrative example is given to the solutions obtained by the hierarchically recursive method together with those obtained by the globally recursive method.

This paper presents a development of the hierarchical optimal control for distributed parameter systems via block pulse operator. The proposed algorithm enables one to solve optimal control of distributed parameter systems with hierarchical structure and as a result, the resulting solutions are piecewise constant with minimal mean-square error, The algorithm is simple in form and computationally advantageous. An illustrative example shows the applicability of the proposed method in practice.

This paper proposes a hierarchical recursive algorithm for non-linear optimal control systems through combining the improved new predication method of large-scale system theory with the single-term Walsh series approach. Piecewise constant and discrete-time solutions with minimal mean-square error are obtained, and the proposed method has merits in both computation and efficiency. The numerical examples show that the proposed method is very effective even for systems with lower dimensions.