Prestressed Concrete Calculator

Prestressing locks a compressive stress into concrete so that service load tension never exceeds its modest cracking strength. The force available in service is always less than that applied at the jack, and the difference, prestress loss, is quantified here through four mechanisms. Elastic shortening occurs the instant force is transferred, as bonded tendons shorten with the concrete they compress; it follows from the modular ratio and the concrete stress at the tendon centroid, fcgp = P/Ac + P e^2 / I. Creep multiplies that same stress by a coefficient near 2.0. Shrinkage is independent of load, estimated here from a strain of 0.0005 on the strand modulus of 28,500 ksi, giving roughly 14 ksi. Steel relaxation is stress decay at constant strain, about 2.5 percent for the low-relaxation strand now standard against 6 to 8 percent for older stress-relieved product. Grade 270 seven-wire strand is jacked to about 0.70 to 0.75 of ultimate, which is why 189 ksi is a typical starting stress, and the modulus at transfer is 57,000 times the square root of the transfer strength in psi, itself about 0.8 of the 28 day value. Total losses land between 15 and 30 percent for pretensioned members and 10 to 25 percent for post-tensioned work. Results are checked against ACI 318 limits: at transfer, compression of 0.60 times the transfer strength and tension of 3 times its square root in psi; in service, sustained compression of 0.45 f'c. These are approximate lump-sum estimates that do not model ambient humidity, volume to surface ratio, or the friction and anchorage seating losses specific to post-tensioning.

The idea of precompressing concrete was attempted well before it worked. P. H. Jackson, working in San Francisco, patented tensioned tie rods through concrete blocks in 1886, and C. E. W. Doehring in Germany filed a comparable idea in 1888. Both failed for the same reason: ordinary mild steel at low stress, whose small elongation was consumed entirely by creep and shrinkage within months. The decisive insight was that loss is roughly fixed as a strain, so it can only be tolerated if the steel is stressed high enough that losing a few thousandths of strain still leaves most of the force. Eugene Freyssinet, the French engineer who had earlier used jacking to correct creep deformation in arch bridges, established this and patented his prestressing method in 1928. Freyssinet went on to develop the conical wedge anchorage in 1939 that made practical post-tensioning possible. Gustave Magnel of Ghent carried it to North America through the Walnut Lane Memorial Bridge in Philadelphia, completed in 1950 and generally regarded as the project that launched the American prestressed concrete industry. The Prestressed Concrete Institute was founded in 1954 to standardize precast products, and design provisions were absorbed into ACI 318 and into AASHTO bridge specifications. Loss estimation itself evolved from single lump-sum allowances of roughly 25,000 to 45,000 psi toward component-by-component procedures, including the widely cited recommendations published by Zia and colleagues in 1979 and the refined methods later adopted in AASHTO LRFD.