Nonlinear Pile Behavior in Integral Abutment Bridges, HR-227, Part 1, 1982

The highway departments of all fifty states were contacted to find the extent of application of integral abutment bridges, to survey the different guidelines used for analysis and design of integral abutment bridges, and to assess the performance of such bridges through the years. The variation in design assumptions and length limitations among the various states in their approach to the use of integral abutments is discussed. The problems associated with lateral displacements at the abutment, and the solutions developed by the different states for most of the ill effects of abutment movements are summarized in the report. An algorithm based on a state-of-the-art nonlinear finite element procedure was developed and used to study piling stresses and pile-soil interaction in integral abutment bridges. The finite element idealization consists of beam-column elements with geometric and material nonlinearities for the pile and nonlinear springs for the soil. An idealized soil model (modified Ramberg-Osgood model) was introduced in this investigation to obtain the tangent stiffness of the nonlinear spring elements. Several numerical examples are presented in order to establish the reliability of the finite element model and the computer software developed. Three problems with analytical solutions were first solved and compared with theoretical solutions. A 40 ft H pile (HP 10 X 42) in six typical Iowa soils was then analyzed by first applying a horizontal displacement (to simulate bridge motion) and no rotation at the top and then applying a vertical load V incrementally until failure occurred. Based on the numerical results, the failure mechanisms were generalized to be of two types: (a) lateral type failure and (b) vertical type failure. It appears that most piles in Iowa soils (sand, soft clay and stiff clay) failed when the applied vertical load reached the ultimate soil frictional resistance (vertical type failure). In very stiff clays, however, the lateral type failure occurs before vertical type failure because the soil is sufficiently stiff to force a plastic hinge to form in the pile as the specified lateral displacement is applied. Preliminary results from this investigation showed that the vertical load-carrying capacity of H piles is not significantly affected by lateral displacements of 2 inches in soft clay, stiff clay, loose sand, medium sand and dense sand. However, in very stiff clay (average blow count of 50 from standard penetration tests), it was found that the vertical load carrying capacity of the H pile is reduced by about 50 percent for 2 inches of lateral displacement and by about 20 percent for lateral displacement of 1 inch. On the basis of the preliminary results of this investigation, the 265-feet length limitation in Iowa for integral abutment concrete bridges appears to be very conservative.

Using the Natural Period of a Structure as an Indicator of the Significance of Second-Order Effects

This study investigates the feasibility of predicting the momentamplification in beam-column elements of steel moment-resisting frames using the structure's natural period. Unlike previous methods, which perform moment-amplification on a story-by-story basis, this study develops and tests two models that aim to predict a global amplification factor indicative of the largest relevant instance of local moment amplification in the structure. To thisend, a variety of two-dimensional frames is investigated using first and secondorder finite element analysis. The observed moment amplification is then compared with the predicted amplification based on the structure's natural period, which is calculated by first-order finite element analysis. As a benchmark, design moment amplification factors are calculated for each story using the story stiffness approach, and serve to demonstrate the relativeconservatism and accuracy of the proposed models with respect to current practice in design. The study finds that the observed moment amplification factors may vastly exceed expectations when internal member stresses are initially very small. Where the internal stresses are small relative to the member capacities, thesecases are inconsequential for design. To qualify the significance of the observed amplification factors, two parameters are used: the second-order moment normalized to the plastic moment capacity, and the combined flexural and axial stress interaction equations developed by AISC

Fastener-Based Computational Models of Cold-Formed Steel Shear Walls

Cold-formed steel (CFS) combined with wood sheathing, such as oriented strand board (OSB), forms shear walls that can provide lateral resistance to seismic forces. The ability to accurately predict building deformations in damaged states under seismic excitations is a must for modern performance-based seismic design. However, few static or dynamic tests have been conducted on the non-linear behavior of CFS shear walls. Thus, the purpose of this research work is to provide and demonstrate a fastener-based computational model of CFS wall models that incorporates essential nonlinearities that may eventually lead to improvement of the current seismic design requirements. The approach is based on the understanding that complex interaction of the fasteners with the sheathing is an important factor in the non-linear behavior of the shear wall. The computational model consists of beam-column elements for the CFS framing and a rigid diaphragm for the sheathing. The framing and sheathing are connected with non-linear zero-length fastener elements to capture the OSB sheathing damage surrounding the fastener area. Employing computational programs such as OpenSees and MATLAB, 4 ft. x 9 ft., 8 ft. x 9 ft. and 12 ft. x 9 ft. shear wall models are created, and monotonic lateral forces are applied to the computer models. The output data are then compared and analyzed with the available results of physical testing. The results indicate that the OpenSees model can accurately capture the initial stiffness, strength and non-linear behavior of the shear walls.

Análisis de elementos viga-columna en régimen no lineal con deformación por cortante

El hormigón estructural sigue siendo sin duda uno de los materiales más utilizados en construcción debido a su resistencia, rigidez y flexibilidad para diseñar estructuras. El cálculo de estructuras de hormigón, utilizando vigas y vigas-columna, es complejo debido a los fenómenos de acoplamiento entre esfuerzos y al comportamiento no lineal del material. Los modelos más empleados para su análisis son el de Bernoulli-Euler y el de Timoshenko, indicándose en la literatura la conveniencia de usar el segundo cuando la relación canto/luz no es pequeña o los elementos están fuertemente armados. El objetivo fundamental de esta tesis es el análisis de elementos viga y viga-columna en régimen no lineal con deformación por cortante, aplicando el concepto de Pieza Lineal Equivalente (PLE). Concepto éste que consiste básicamente en resolver el problema de una pieza en régimen no lineal, transformándolo en uno lineal equivalente, de modo que ambas piezas tengan la misma deformada y los mismos esfuerzos. Para ello, se hizo en primer lugar un estudio comparado de: las distintas propuestas que aplican la deformación por cortante, de los distintos modelos constitutivos y seccionales del hormigón estructural y de los métodos de cálculo no lineal aplicando el método de elementos finitos (MEF). Teniendo en cuenta que la resolución del problema no lineal se basa en la resolución de sucesivos problemas lineales empleando un proceso de homotopía, los problemas lineales de la viga y viga-columna de Timoshenko, se resuelven mediante MEF, utilizando soluciones nodalmente exactas (SNE) y acción repartida equivalente de cualquier orden. Se obtiene así, con muy pocos elementos finitos, una excelente aproximación de la solución, no sólo en los nodos sino en el interior de los elementos. Se introduce el concepto PLE para el análisis de una barra, de material no lineal, sometida a acciones axiales, y se extiende el mismo para el análisis no lineal de vigas y vigas-columna con deformación por cortante. Cabe señalar que para estos últimos, la solución de una pieza en régimen no lineal es igual a la de una en régimen lineal, cuyas rigideces son constantes a trozos, y donde además hay que añadir momentos y cargas puntuales ficticias en los nodos, así como, un momento distribuido ficticio en toda la pieza. Se han desarrollado dos métodos para el análisis: uno para problemas isostáticos y otro general, aplicable tanto a problemas isostáticos como hiperestáticos. El primero determina de entrada la PLE, realizándose a continuación el cálculo por MEF-SNE de dicha pieza, que ahora está en régimen lineal. El general utiliza una homotopía que transforma de manera iterativa, unas leyes constitutivas lineales en las leyes no lineales del material. Cuando se combina con el MEF, la pieza lineal equivalente y la solución del problema original quedan determinadas al final de todo el proceso. Si bien el método general es un procedimiento próximo al de Newton- Raphson, presenta sobre éste la ventaja de permitir visualizar las deformaciones de la pieza en régimen no lineal, de manera tanto cualitativa como cuantitativa, ya que es posible observar en cada paso del proceso la modificación de rigideces (a flexión y cortante) y asimismo la evolución de las acciones ficticias. Por otra parte, los resultados obtenidos comparados con los publicados en la literatura, indican que el concepto PLE ofrece una forma directa y eficiente para analizar con muy buena precisión los problemas asociados a vigas y vigas-columna en las que por su tipología los efectos del cortante no pueden ser despreciados. ABSTRACT The structural concrete clearly remains the most used material in construction due to its strength, rigidity and structural design flexibility. The calculation of concrete structures using beams and beam-column is complex as consequence of the coupling phenomena between stresses and of its nonlinear behaviour. The models most commonly used for analysis are the Bernoulli-Euler and Timoshenko. The second model is strongly recommended when the relationship thickness/span is not small or in case the elements are heavily reinforced. The main objective of this thesis is to analyse the beam and beam-column elements with shear deformation in nonlinear regime, applying the concept of Equivalent Linear Structural Element (ELSE). This concept is basically to solve the problem of a structural element in nonlinear regime, transforming it into an equivalent linear structural element, so that both elements have the same deformations and the same stresses. Firstly, a comparative study of the various proposals of applying shear deformation, of various constitutive and sectional models of structural concrete, and of the nonlinear calculation methods (using finite element methods) was carried out. Considering that the resolution of nonlinear problem is based on solving the successive linear problem, using homotopy process, the linear problem of Timoshenko beam and beam-columns is resolved by FEM, using the exact nodal solutions (ENS) and equivalent distributed load of any order. Thus, the accurate solution approximation can be obtained with very few finite elements for not only nodes, but also for inside of elements. The concept ELSE is introduced to analyse a bar of nonlinear material, subjected to axial forces. The same bar is then used for other nonlinear beam and beam-column analysis with shear deformation. It is noted that, for the last analyses, the solution of a structural element in nonlinear regime is equal to that of linear regime, in which the piecewise-stiffness is constant, the moments and fictitious point loads need to be added at nodes of each element, as well as the fictitious distributed moment on element. Two methods have been developed for analysis: one for isostatic problem and other more general, applicable for both isostatic and hiperstatic problem. The first method determines the ELSE, and then the calculation of this piece is performed by FEM-ENS that now is in linear regime. The general method uses the homotopy that transforms iteratively linear constitutive laws into nonlinear laws of material. When combined with FEM, the ELSE and the solution of the original problem are determined at the end of the whole process. The general method is well known as a procedure closed to Newton-Raphson procedure but presents an advantage that allows displaying deformations of the piece in nonlinear regime, in both qualitative and quantitative way. Since it is possible to observe the modification of stiffness (flexural and shear) in each step of process and also the evolution of the fictitious actions. Moreover, the results compared with those published in the literature indicate that the ELSE concept offers a direct and efficient way to analyze with very good accuracy the problems associated with beams and beams columns in which, by typology, the effects of shear cannot be neglected.

Typical performance of gallager-type error-correcting codes

The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this method, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.