MOMENT COEFFICIENTS FOR STATICALLY INDETERMINATE PRESTRESSED CONCRETE STRUCTURES

In statically indeterminate prestressed concrete structures, prestressing force produces secondary moment in addition to primary moment due to eccentricity. This condition is different from statically determinate structures where there is no secondary moment effect and the moment due to prestressing is due to primary moment only, i.e., prestressing force times eccentricity. With the presence of secondary moment, prestressing force design becomes more complex, because the secondary moment is a function of prestressing force and the geometry of the structures. In addition, considering that in general the cable profile is parabolic or another type of curves, which also occurs at continuous supports, the load balancing method may not be used. To cope with this problem moment due to prestressing force is assumed to be the prestressing force times a β coefficient. In statically determinate structures the β coefficient equals the cable eccentricity to the center of gravity of the section. Therefore, the β coefficient can be considered as a statically indeterminate eccentricity. By assigning that the moment due to prestressing force as a function of prestressing force and by considering the allowable stress requirements at top and bottom fibers, equations can be derived to compute the prestressing force in statically indeterminate structures. From the derived equations, the upper and lower bounds of prestressing force can be determined if the section satisfy the requirements. If the optimum prestressing force is needed, the difference of lower and upper bounds should be minimum. Nevertheless, the difference of lower and upper bounds can be considered as a safety level. At the end of the paper examples are presented to show the application of the proposed method.