Direct Minimum Weight Design of Long Span Prestressed Concrete Members

T elastic design of prestressed concrete members is based on two main assumptions: (1) sections which were plane before deformation remain plane after deformation and (2) strains remain proportional to stress. With a material like concrete, these two assumptions remain satisfactory so long as the stresses do not exceed certain limits which depend upon the strength of concrete. Both assumptions become progressively more inexact as the stresses increase beyond these limits. However, in our present state of knowledge, the elastic theory of design still remains one of the most effective methods for proportioning a prestressed concrete member. The stress Iimits are generally chosen so that the structure wil] be usable and safe under service load conditions while ultimate load conditions are satisfied and a reasonably economical use is made of the material. Prestressed concrete beams are generally classified as either short span or long span beams,' In long span beams, the self weight moment constitutes a major portion of the total moment. In all such cases, it is impractical to accomrnodate the eccentricity within the beam section given by the expression: