It has always been recognized that the approximate Eq. (18-3) in ACI 318-77 for the stress in bonded prestressing steel at flexural ultimate, fps was in general conservative. A more precise value for fps and hence for the flexural strength, can be obtained by solving the equations of equilibrium of forces and of compatibility of strains across the section, making use of the actual stress-strain relationship for the prestressing steel. Until the advent of the computer and the programmable calculator, this was a time-consuming process and hence was little used. In a 1977 paper, Naaman2 discussed the more precise approach. He showed how more accurate values of flexural strength could readily be obtained using a computer to solve the equations of equilibrium and compatibility, if the stress-strain curve for the prestressing steel were expressed algebraically. Since the time of Naaman's studies, there has been an explosion in the availability and the capabilities of small programmable electronic calculators. These machines now make it feasible and economic for any engineer to use the more precise method of calculation for flexural strength, with consequent economic advantages.
