A simple sign convention for elastic analysis of prestressed concrete members

Abstract

Prestressed concrete members must satisfy design criteria at both service and ultimate load stages. In most cases, service load requirements control design, so the service load analysis is normally conducted first and strength is checked later. Considerable effort is expended in determining the direct stresses under service load conditions, but no consensus has yet been reached on a satisfactory method for determining the sense of the stress. For a simply supported precast concrete member without composite action, keeping track of the sense of the stress in a hand calculation is not difficult and almost any system will work. The most common approach is to use separate equations for stress at the top and bottom of the member. However, if the moment due to external load may occur in either direction or if the calculations are to be automated, the use of a clear, internally consistent system is desirable. This paper presents such a system, with its primary advantages being that it requires a single equation for computing stress, regardless of the location within the member and sense of the applied moment, and that the sense of the stress is inherent to the calculation without the need for a separate calculation. This characteristic holds true for simple or continuous members, and those that are purely precast concrete or composite with cast-in-place concrete. The system is appropriate for automation in a computer program.