Search

Producción Científica, This work focuses on the limit analysis or plastic calculation of slender beam planar frames using a direct method based on the Virtual Works Principle (VWP). The method consists in looking for the structure’s collapse mechanism from the equilibrium equations posed by means of virtual problems in displacements. This approach, in its classic formulation, is very unsystematic and requires a convenient choice of virtual problems. In this work, it has been possible to systematize the plastic calculation of the structure by applying the theory of mechanisms to obtain, fully automatically, the equilibrium equations necessary to completely solve the structure. Also, the compatibility equations necessary to know the accumulated rotations in the plastic hinges at the instant of collapse are presented. Finally, the search for the collapse mechanism is not carried out by trial and error, but is posed by optimization based on energy criteria.

Las soluciones de forma cerrada simples para la capacidad de carga no drenada de zapatas escalonadas en suelos isotrópicos cohesivos se derivan al emplear el enfoque cinemático del análisis de límites. Se intentan utilizar tanto el mecanismo traslacional de fallas como el mecanismo modificado tipo Hill, con ángulos de incidencia variables. Se ha determinado, de forma analítica, la mejor cota superior para cada mecanismo, lo cual nos lleva a una expresión analítica para el factor de capacidad de carga. También se ha evaluado la influencia del grado de anisotropía del suelo en el valor correspondiente para el factor de capacidad de carga. Para un amplio rango de grados de anisotropía, la mejora en los valores predichos de la cota superior no garantiza el uso del mecanismo modificado del tipo Hill. En vez de eso, el mecanismo convencional de falla del tipo Hill, con un ángulo de incidencia fijo de n/4, nos entrega una expresión simple y concisa para el factor de capacidad de carga que es analíticamente equivalente al factor convencional de capacidad de carga de Prandtl-Reissner, para el caso de suelos isotrópicos multiplicado por el promedio de la suma del grado de anisotropía más la unidad. Simple closed-form solutions for the undrained bearing capacity of strip footings on anisotropic cohesive soils are derived employing kinematical approach of limit analysis. Both modified Hill-type and translational failure mechanisms, with variable wedge angles, are attempted and the best upper bound for each mechanism has been analytically determined leading to an analytical expression for the bearing capacity factor. The influence of degree of soil anisotropy on the corresponding value for the bearing capacity factor has also been evaluated. For a wide range of degree of anisotropy, the improvement in the predicted upper bound values does not warrant the use of the modified Hill-type mechanism. Instead, the conventional Hill-type failure mechanism, with a fixed wedge angle of n/4, provides a simple and concise analytical expression for the bearing capacity factor that is analytically equivalent to the conventional Prandtl - Reissner bearing capacity factor for the case of isotropic soil multiplied by the average of the sum of degree of anisotropy plus unity.