MIXED INTEGER PROGRAMMING FOR THE OPTIMAL (LEAST COST) DESIGN OF ECCENTRICALLY LOADED MASONRY BEARING WALLS: PART I. LOW ECCENTRICITIES

Abstract

A mixed integer approach for the least cost design of structural masonry walls with high eccentricities is developed. The integer variables in the approach are used to select the optimum values from a range of discrete block sizes, discrete grouting conditions, and discrete reinforcement levels. The structural constraints in the model are based upon the requirements of the Transformed Section type of analysis for masonry walls. The non-linear functions representing the relationships for determining the resisting capacities of the masonry element are approximated by linear functions which come very close in form and results to the original curves. Application of the model to an example problem demonstrates that in spite of the integer requirements, the approach is easily and efficiently solved using a standard software package.