Shyh-Rong Kuo

Impact response of high speed rail bridges and riding comfort of rail cars

The vibration of simple and three-span continuous beams traveled by trains moving at high speeds is studied in this paper. Central to this study is the adoption of a dimensionless speed parameter S, defined as the ratio of the exciting frequency of the moving vehicles to the fundamental frequency of the beam. The numerical studies indicate that the moving load model is generally accurate for simulating the bridge response. However, the use of the sprung mass model is necessary whenever the riding comfort of rail cars is of concern. If the characteristic length, rather than the span length, is used for the continuous beam, then both the simple and continuous beams will reach their peak responses at the same critical speed S, when traveled by wheel loads of constant intervals. The rail irregularity, ballast stiffness, suspension stiffness and suspension damping can drastically affect the riding comfort of rail cars traveling over simple beams. Their effects are comparatively small for continuous beams. In conclusion, the design of a high speed rail bridge is governed primarily by the conditions of serviceability, rather than by strength.

Incrementally small-deformation theory for nonlinear analysis of structural frames

Abstract An incrementally small-deformation theory that is physically self-explainable is presented for the large-displacement nonlinear analysis of structural frames. Strictly based on the assumption of small strains, small rotations, and small displacements within each incremental step, the elastic and geometric stiffness matrices for the beam element are derived from the force–displacement relations. Due consideration is taken of the 3D rotational behavior of nodal moments. The geometric stiffness matrix derived for the element is asymmetric. However, by enforcing all the joints to remain in equilibrium in the deformed configuration, the antisymmetric parts of the geometric stiffness matrices cancel out, resulting in a symmetric stiffness matrix for the structure. Also described is the procedure for updating the element forces and geometry in an incremental-iterative analysis. The present approach in its entire set is demonstrated to be robust and efficient for solving the nonlinear, postbuckling response of structural frames.

Out-of-plane buckling of angled frames

Abstract A bending moment may be generated internally as the stress resultant of a cross-section or externally as a couple or couples of direct forces by mechanical devices. In the out-of-plane buckling analysis of angled frames, all types of moments, whether internal or external, must be specified in the buckling position. Once this condition is violated, no reliable solutions can be obtained. In this paper, emphasis is placed on the effects of external moment devices on the buckling of structural frames and members. The analytical solutions presented herein, some of which are new, are useful for theoretical as well as for practical purposes. Remarks have been given regarding solution of the same problems using the finite element method.

A reliable three-node triangular plate element satisfying rigid body rule and incremental force equilibrium condition

Abstract This paper proposes a simple method for deriving the geometric stiffness matrix (GSM) of a three‐node triangular plate element (TPE). It is found that when the GSM of the element is combined into the global one of the structure, this structural stiffness matrix becomes symmetric and satisfies both the rigid body rule and incremental force and moment equilibrium (IFE) conditions, which are basically two fundamental conditions for analysis of mechanics. The former condition has been widely used in the community of mechanics; while the latter one, to our best knowledge, has never been considered. Advantages with the GSM derived are that derivations only need simple matrix operations without cumbersome non‐linear virtual strain energy derivations and tedious numerical integrations and more appealingly, this derived GSM can be explicitly given for applications. In addition, based on IFE and the rigid body rule conditions, a reasonable GSM for the three‐node TPE must be asymmetric; however, an asymmetric matrix usually gives rise to tedious numerical calculation especially in geometrically nonlinear problems and further, greatly influences computation efficiency. Fortunately, the skew‐symmetric parts of the derived GSM can be canceled out once they are merged into the global stiffness matrix of the structure. In this regard, this structural stiffness matrix becomes a symmetric one and thus enhances its effectiveness. Finally, several examples are provided for validating the robustness of the derived GSM.

Critical Load Analysis of Undamped Nonconservative Systems Using Bieigenvalue Curves

To study the instability of an undamped nonconservative system using the finite element method, an asymmetric load matrix has to be included to account for the path-dependent nature of the applied loads, in addition to the mass matrix, elastic stiffness matrix, and geometric stiffness matrix. Before the critical loads can be determined for a structure, one basic problem in research of this sort has been the construction of load-frequency relationships from the eigenvalue equations. Traditionally, this requires solution of complex eigenvalues from the characteristic equations at many load levels, which in practice is very time consuming. In this paper, an efficient approach based on a fourth-order hyperbolic curve will be proposed for predicting the critical loads. This curve, also knoww ad the bieigenvalue curve, can be uniquely determined, once the first and second derivatives of the frequency with respect to the load parameter have been calculated for the structure under a preset load level, based on the eigensolutions for the first few or all modes of vibration. Effectiveness and accuracy of the procedure based on the bieigenvalue curve is demonstrated in the numerical study

Stability of tapered bars of circular cross-sections under semi- and quasi-tangential torques

Abstract A torque may be classified as semi- or quasi-tangential, depending on whether it is generated by two couples or one couple of direct forces. Both types of torque may cause a torsionally loaded bar to buckle at certain critical values. This paper presents an analytical approach for investigating the instability of tapered bars of circular cross-sections subjected to torques of the semi- or quasi-tangential type. The analysis results indicate that a distinction must be made in practice between the two types of torque, as their critical loads have a difference of a factor of two. For the special case of a bar with constant cross-sections, the present results reduce to those given by Ziegler.

A new buckling theory for curved beams of solid cross sections derived from rigid body and force equilibrium considerations

A new method is proposed for deriving the instability potential of initially stressed curved beams based on the rigid body and equilibrium considerations using the updated Lagrangian formulation. Starting from the rigid body rule, the virtual instability potential was derived for a spatially curved beam under real rigid displacements. Next, utilising the equilibrium equations for the boundary forces at the C1 and C2 states, another virtual instability potential was derived for the curved beam under virtual rigid displacements. Comparing the two potentials yields the one in total form for the curved beam. The present approach requires only simple integrations and analogical comparison of related virtual works, thereby avoiding the physically unclear, complicated derivations involved in previous procedures. Based on the first principles of rigid body rule and equilibrium, the derived potential energy is more concise than the conventional approach that requires the consideration of six stress components in the formulation. As an illustration, the present theory was successfully adopted in the buckling analysis of helical curved beams under radial loads.

Instability of Lightly Damped Linear Nonconservative Systems

In computing the critical load for a linear nonconservative system, one needs to construct the load-frequency curve from the characteristic equation that contains asymmetric matrices, based on the finite element formulation. Traditionally, this requires repeated solution of complex eigenvalues from the characteristic equation at many load levels, which is extremely time consuming in practice. Small damping of the Rayleigh type is assumed. A bieigenvalue curve is adopted to approximate the load-frequency curve for the first few modes of interest. Such a curve can be uniquely determined, once the derivatives of the frequency with respect to the load parameter have been calculated for a preset load level. After the bieigenvalue curve is established, the critical load can be computed by setting its first derivative equal to zero. The effectiveness of the present method is demonstrated in the numerical study.