Nonlinear Stability Analysis of Long-Span Suspension Bridge Cable Tower

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.

Geometric imperfections play a significant role in the evaluation of the buckling capacity of thin-walled structures. Since the pattern and distribution of such imperfections take a random variation, the determination of a critical imperfect shape that leads to the minimum buckling load becomes a challenge. In this study, an optimization technique based on binary coded genetic algorithms is used together with a nonlinear finite element model to identify the critical imperfection pattern for thin-walled welded structures. The finite element model is based on a consistent sub-parametric shell element that accounts for the effect of both geometric and material nonlinearities. The binary coded genetic algorithm is used as the optimization means to arrive at the imperfection pattern leading to the near globally minimum buckling load. A previously developed mathematical model is employed to describe the imperfection bulges associated with lines of weldment. The method is demonstrated by considering the nonlinear stability analysis of both a circular cylinder subjected to pure axial compressive load and a conical tank under hydrostatic pressure. The combined genetic algorithm – finite element code is used to determine the critical imperfection bulge patterns for the two problems, as well as their associated buckling loads.

A method of analysis is presented to predict the behavior of prestressed concrete structures with internal or external tendons up to ultimate. The structure is modeled as an assemblage of plane frame members connected at nodes. The prestressing tendon is treated as a member with a small moment of inertia connected to the structural nodes with short arms. Because the centroidal axis changes with cracking and time-dependent effects, the nodes are located on an arbitrarily chosen axis called the reference axis. The analysis includes the effects of tension stiffening, and geometric and material nonlinearities. Any nonlinear stress–strain relationship for concrete and reinforcements can be applied. The analysis accounts for friction and slip of external tendons at deviators, variation of tendon eccentricity with applied load (geometric nonlinearity), and opening of joints in precast segmental construction. The computer program developed to perform the analysis method is verified using experiments on simple and...

Stall Flutter Analysis of High-Aspect-Ratio Composite Wing

Membrane materials are widely used in construction engineering with small mass and high flexibility, which presents strong geometric nonlinearity in vibration. In this paper, an improved multiscale perturbation method is used to solve the aerostatics stability of membrane roofs on closed and open structures by quantifying the effect of geometric nonlinearity on the single-mode aeroelastic instability wind velocity. Results show that the critical wind velocities of two models are smaller when the geometrical nonlinearity of the membrane material is neglected. In addition, under normal wind load, the influence of geometrical nonlinearity of the membrane on the aerodynamic stability of the roof can be neglected. However, under strong wind load, when the roof deformation reaches 3% of the span, the influence of geometric nonlinearity should be considered and the influence increases with the decrease of transverse and downwind span of the membrane roof. The results obtained in this paper have an important theoretical reference value for the design membrane structures.

Nonlinear aerostatic stability analysis of suspension bridges

Effects of material and geometric non-linearities on the collapse load of masonry arches

The objective of this study is to investigate the possible collapse mechanisms of reinforced concrete columns. Analyses are performed to study the effect of both material and geometrical nonlinearities in the post peak response of flexural columns. Discussion is mainly focussed on the restoring force characteristics, especially in large deformation range, of RC columns having high shear capacity. It is suggested that the ultimate failure is governed by bending.

We analyze transient finite electroelastodynamic deformations of a perfect electrically conducting undamped clamped–clamped beam, a clamped–clamped parabolic arch and a clamped–clamped bell-shaped arch suspended over a flat rigid semi-infinite perfect conductor. The pull-in instability in a beam and the pull-in and the snap-through instabilities in the two arches due to time-dependent potential difference between the two electrodes have been studied. The potential difference is applied either suddenly or is increased linearly in time. Since the time scale of the transient electric forces is very small as compared to that of the mechanical forces, inertia effects only in the mechanical deformations are considered. Effects of both material and geometric nonlinearities are incorporated in the problem formulation and solution; however, damping due to the interaction of the structure with the surrounding medium is neglected. The coupled nonlinear partial differential equations for mechanical deformations are solved numerically by the finite element method and those for the electrical problem by the boundary element method. The Coulomb pressure due to the potential difference between the two electrodes is a nonlinear function of the a priori unknown distance between them. The potential difference that induces either the pull-in instability in a beam or the snap-through followed by the pull-in instabilities in an arch has been computed. Wherever possible these results are compared with those available in the literature. With a decrease in the rate of the applied potential difference, the pull-in and the snap-through parameters approach those for a static problem. Also, for large rates of increase in the potential difference between the two electrodes, the snap-through instability in an arch is suppressed and only the pull-in instability occurs.

Free‐standing, unanchored liquid‐storage tanks have the tendency to lift off their base under the overturning influence of the hydrodynamic wall pressures generated during earthquakes. Fundamental to the analysis of these systems is a detailed investigation of the behavior of the partially uplifted base plate. As a step to such an investigation, a comprehensive analysis is made herein of the uplifting resistance of a uniformly loaded semiinfinite prismatic beam that rests on a rigid base. The analysis used represents an improvement over the previously proposed methods in that it provides for the effects of both material and geometric nonlinearities in a realistic and cost‐effective manner. The results presented demonstrate the importance to the load‐carrying mechanism of the membrane forces induced by the constraining action of the tank wall. An in‐depth parametric study elucidates the effects of the various system parameters on the uplifting resistance of the beam.

In this paper we reviewed the research on the dynamic response of forced vibrations of orthotropic membranes, which applies in the membrane structural engineering. We applied the large deflection theory of membranes, the D’Alembert’s principle and the momentum theorem to derive the fundamental equations of forced vibrations of orthotropic membranes, which we solved according to the Lindstedt Poincaré Perturbation Method, and obtained the formula of impact load and nonlinear forced vibration deflection of rectangular membranes with four edges fixed. Then a numerical computation method for the equation was applied. The results of practical examples are shown and discussed in the paper. This paper provide a method for analyzing some practical engineering problems and furthermore the nonlinear governing equations of forced vibration and the solving method provide some theoretical foundation for the .research relating to the solving of membrane structures under dynamic loads by comprehensively considering the effects of material nonlinearity, geometric nonlinearity and viscous damping.

Combined Effects of Geometric and Material Non-linearities on One Dimensional Structural Members

In this paper, the numerical model developed in the previous paper is used to study the seismic performance of elevated liquid-filled steel conical tanks. A number of conical tanks which are classified as tall or broad tanks according to the ratio of the tank radius to its height are considered. The consistent shell element is used to model the tank surfaces, while the coupled boundary-shell element formulation is employed to obtain the fluid added-mass which simulates the dynamic pressure resulting from a seismic motion. Linear springs are used to model the supporting towers. The natural frequencies of the liquid-filled tanks due to both horizontal and vertical excitations are evaluated. This is followed by a non-linear dynamic analysis, using an appropriately scaled real input ground motion, and which includes the effect of both geometric and material non-linearities. Thin-walled structures of this kind may exhibit inelastic behaviour and a tendency to develop localized buckles, thus diminishing stiffness. The consequence could lead to overall instability of the structure. In general, time-history analyses indicate that liquid-filled conical tanks, often possessing apparently adequate safety factors under hydrostatic loading, are shown to be very sensitive to seismic loading when ground motion frequencies contain those of the fundamental frequencies of the vessels themselves. © 1997 John Wiley & Sons, Ltd.

Typical steel moment-frame structures in the United States comprise a few seismic frames and many gravity frames, which include “continuous columns” that are pin-connected to beams. These continuous columns, which are often ignored in seismic design, can improve the seismic performance of the structure. This study investigates the effects of continuous columns on the structural stability and seismic response of building frames. Stability coefficients representing the separate and combined effects of geometric and material nonlinearities are used with a simplified modeling technique, which separates the shear-type and flexural-type lateral-force-resisting systems in moment frames. Relationships between continuous column stiffness ratio and the stability coefficients, inter-story drift, and the drift concentration factor are presented. It is shown that for realistic structures, the columns in the seismic frames are generally sufficient to prevent unstable response and large drift concentrations, and the inclusion of gravity continuous column stiffness tends to decrease both the drift concentration and inter-story drift.

Geometric and material non-linear behaviour of beam-columns