Moment‐Curvature Relationships for Partially Prestressed Concrete Beams

A simple unified set of equations is presented for the determination of stresses in cracked or uncracked partially prestressed concrete sections. A variety of concrete shapes, including rectangular beams, I‐beams, T‐beams, and inverted T‐beams, can be considered. Multiple layers of prestressing and/or reinforcing arbitrarily located anywhere within the cross section can easily be handled. Continuity of all parameters (stresses, strains, and section properties) is maintained at cracking, as the neutral axis moves from the bottom flange to the web, and again as the neutral axis moves from the web to the top flange. This allows the moment‐curvature diagram to be constructed for any partially prestressed concrete beam in the elastic range. The equations are fully compatible with those required for a time‐dependent analysis. A sample problem is included.