Prestressed concrete members must satisfy design criteria at both service load 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 (tensile or compressive). 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 (for example, in a beam that is continuous or is statically determinate with an overhang) or if the calculations are to be automated, the use of a clear, internally consistent system is desirable. This paper presents such a system. Its primary advantages are that it requires a single equation for computing stress, regardless of the location within the member and the 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 members that are simple or continuous and that are purely precast concrete or composite with cast-in-place concrete. The system is well suited for automation in a computer program. The system is likely to appeal most strongly to those who have not yet conducted many analyses of prestressed concrete and who may not yet have a well-developed sense of the signs of the stresses. However, the system does not discriminate among users and offers the same benefits of simplicity and automatic generation of signs to everybody. It has been used successfully in the teaching of prestressed concrete at the University of Washington in Seattle for the past 15 years.
