Building Design Using Linear Programming

An approach for the preliminary minimum weight design of tall framed steel buildings is presented. The design criteria are safety against collapse and a limitation on lateral deflections under service loads in the elastic range. The method of linear programming is used to generate the solution to the preliminary design. Plastic hinge theory is used to generate the equations of constraint on the moment carrying capacity of the members. The equations of constraint are compatible with the design criteria. To simplify the solution effort in the preliminary design, a building model is used in which the design requires that plastic hinges form only in the beams. This reduces substantially the number of collapse mechanisms which must be considered. A simple linear equation of constraint on the deflection under service loads is developed by separating the contributions of the columns and beams to the flexibility of a frame, and establishing a conservative ratio between these contributions. The proposed approach is illustrated by a numerical example in which the preliminary design of a 26-story building is generated.