Optimum Tendon Placement for Post Tensioned S.S. Beam with Variable Eccentricity

Abstract

A challenging problem for a direct search design methods was introduced in this work. Pattern Search PS method was used to find the optimum designed section of a prestressed simply supported post tensioned beam with variable tendon eccentricity. Flexural and geometrical design constraints were used to get the optimum sectional properties of the beam. Then, new constraints concerning the placement of the tendon through the longitudinal section of the beam were introduced and involved through finding the optimum results. A single objective function was used since a multi objective optimization procedure could not be run with nonlinear constraints, and optimizing a post tensioned beam with variable eccentricity represents a highly constraints problem. Another optimization method was used here only to check the validity of the procedure adopted using PS, the results were compared for the methods and a good agreement were found between them. Apparently, using the additional constraints of the tendon placement causes a lot of difficulties to find the optimum results, as it was noticed through the elapsed time of the solution, although, both methods gave a reliable and practical optimum values, and this is due to the robust use of the design constraints to limit the optimum designed variables within the ACI code 2011 limits. Increasing the efficiency of the solution was gained through using a lot of design constraints, in addition to the basic design constraints needed in the flexural design, to avoid trapping in local optima.