This paper shows a general model of rectangular footings to obtain the soil minimum contact area (optimal surface) that support from 1 to n columns aligned on a longitudinal axis. The proposed model considers that the soil pressure varies linearly. The recently published models have been presented individually to obtain the soil contact area for rectangular isolated footings, rectangular combined footings that support two columns, these models present the equations, but it is not guaranteed to be the minimum area. The present research complies with the models mentioned above and can be applied to footings that support 3 or more columns, and also the minimum area is guaranteed. Also, numerical problems are shown the soil minimum contact surface for rectangular isolated footings, and rectangular combined footings that support two and three columns (unrestricted on its sides, one side restricted and two opposite sides restricted).
Objective of this research is to present a mathematical model for optimal design of rectangular cross-section beams with straight haunches under the criterion of minimum cost considering the concrete cost and reinforcing steel cost, and taking into account the equations of the regulation (ACI 318S-14). This model presents the equations for a uniformly distributed load and a concentrated load located anywhere on the beam. Two examples are developed by the proposed model, one for uniformly distributed load and another for concentrated load showing the best solution for each case. The results show the following: a) The prismatic beams for uniformly distributed load have a total cost of the 8% greater, a total volume and a total weight of the 9% greater with respect to the non-prismatic beams; b) The prismatic beams for concentrated load have a total cost, a total volume and a total weight of the 6% greater with respect to the non-prismatic beams. The main conclusions are: For a smaller b width the optimal design for both models is presented. The non-prismatic beams are more economical, also these have less volume and less weight with respect to prismatic beams.
This paper shows a model for the T-shaped beams with straight haunches under uniformly distributed load that considers shear and bending deformations to obtain the fixed-end moments, carry-over and stiffness factors, which is the main part of this investigation. The methodology used is the conjugate beam method to obtain the rotations in supports and by the superposition method is solved this problems type. The current model considers only the bending deformations, and some authors consider bending and shear deformations for some proportions that are shown in tables. A comparison among the proposed approach that considers shear and bending deformations against the current model that considers bending deformations only are presented in the tables and graphics. A significant advantage of this paper over any other document is that is not limited to certain dimensions or proportions, and it can also be used for TT-shaped or TTT-shaped beams, which is commonly applied in highway bridges.
Este documento presenta un modelo matemático para obtener el área mínima de la superficie de contacto con el suelo para zapatas combinadas rectangulares asumiendo que la superficie de contacto trabaja parcialmente a compresión, es decir, una parte de del área de contacto de la zapata está sujeta a compresión y la otra parte no hay presión (presión cero). Algunos documentos presentan el costo mínimo para diseño de zapatas combinadas rectangulares, pero se considera el área de la zapata con el suelo trabajando completamente en compresión, y otros muestran las ecuaciones para las dimensiones de la zapata combinada rectangular trabajando parcialmente a compresión, pero el momento en el eje X no se considera. La metodología se desarrolla para los cinco casos de zapatas sometidas a flexión biaxial y cuatro casos de zapatas sometidas a flexión uniaxial (dos en dirección X y dos en dirección Y), tomando en cuenta las propiedades geométricas que se generan del diagrama de presiones producidas por el suelos sobre la zapata. Varios ejemplos numéricos se muestran para encontrar el área mínima de zapatas combinadas rectangulares bajo una carga axial y momentos en una o dos direcciones en cada columna. El modelo propuesto presenta una reducción significativa en el área mínima de contacto en el suelo con respecto al modelo propuesto por otros autores, si la fuerza resultante se encuentra fuera del núcleo central.
Successful supply chains manage product flows, information and funds to provide a high level of product availability to the customer. The fundamental challenge today is for supply chains to achieve coordination despite multiple ownership and increasing product variety. The objective then is to coordinate business processes from manufacturers, suppliers, transportation, warehouses, distributors, and partners to the customer in such a way that lower costs, shorter production times and product and service quality adapted to customer requirements are achieved. In the present work, a system is created that evaluates the behavior of the supply chain based on quality. To carry it out, focus groups and exploratory factor analysis with varimax rotation are used to compile the main components of quality management in the SCQM supply chain and the set of dependent variables associated with the determining factors. The results show the most valuable key factors and this is an instrument that allows their evaluation. In the development of the research, the review of impact literature is carried out, methods, techniques and tools such as interviews, document review, work with experts, brainstorming, descriptive analysis and exploratory factor analysis, diagrams or control graphs are used.
This paper presents a general model for the design to obtain the thickness and reinforcing steel areas of rectangular footings that support from 1 to “n” columns aligned on a longitudinal axis. The pressure diagram is considered linear. Some recently published papers are restricted to certain types of footings as the rectangular isolated footings, and rectangular combined footings that support two columns. The first part of this paper shows the minimum soil area that supports 1 to “n” columns aligned on a longitudinal axis. Three numerical examples are presented for design of rectangular footings subjected to an axial load and two orthogonal moments in each column that supports one, two and three columns. The main advantage of this document over other documents is: this model can be applied for one or more columns supported on a rectangular footing (unrestricted on its sides, one side restricted and two opposite sides restricted).
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