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 Geomechanics and Engineering   Volume 14, Number 1, January20 2018 , pages 61-69 DOI: https://doi.org/10.12989/gae.2018.14.1.061 A new model for T-shaped combined footings part II: Mathematical model for design Arnulfo Luévanos-Rojas, Sandra López-Chavarria and Manuel Medina-Elizondo Abstract The first part shows the optimal contact surface for T-shaped combined footings to obtain the most economical dimensioning on the soil (optimal area). This paper presents the second part of a new model for T-shaped combined footings, this part shows a the mathematical model for design of such foundations subject to axial load and moments in two directions to each column considering the soil real pressure acting on the contact surface of the footing with one or two property lines restricted, the pressure is presented in terms of an axial load, moment around the axis \"X\" and moment around the axis \"Y\" to each column, and the methodology is developed using the principle that the derived of the moment is the shear force. The classic model considers an axial load and a moment around the axis \"X\" (transverse axis) applied to each column, i.e., the resultant force from the applied loads is located on the axis axis \"Y\" (longitudinal axis), and its position must match with the geometric center of the footing, and when the axial load and moments in two directions are presented, the maximum pressure and uniform applied throughout the contact surface of the footing is considered the same. To illustrate the validity of the new model, a numerical example is presented to obtain the design for T-shaped combined footings subjected to an axial load and moments in two directions applied to each column. The mathematical approach suggested in this paper produces results that have a tangible accuracy for all problems. Key Words mathematical model for design; T-shaped combined footings; moments; bending shear; punching shear Address Arnulfo Luévanos-Rojas, Sandra López-Chavarria and Manuel Medina-Elizondo: Universidad Autónoma de Coahuila, Blvd. Revolución No, 151 Ote, CP 27000, Torreón, Coahuila, Mexico

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