Assumptions in design of total losses in tendon stress of 35,000 psi for pretensioning and 25,000 psi for posttensioning to allow for elastic shortening, frictional losses, slip at anchorages, shrinkage, creep, and relaxation of the prestressing steel usually gives satisfactory results. Losses greater or smaller than these values have little effect on the design strength but can affect service-load behavior, such as cracking load, deflection, and camber.
Elastic Shortening of Concrete. In pretensioned members, when the tendons are released from fixed abutments and the steel stress is transferred to the concrete by bond, the concrete shortens under the compressive stress. The decrease in unit stress in the tendons equals PsEs /AcEc nÆ’c, where Es is the modulus of elasticity of the steel, psi; Ec the modulus of elasticity of the concrete psi; n the modular ratio, Es /Ec; Æ’c the unit stress in the concrete, psi; Ps the prestressing force applied by the tendons; and Ac the cross-sectional area of the member.
In posttensioned members, the loss due to elastic shortening can be eliminated by using the members as a reaction in tensioning the tendons.
Frictional Losses. In posttensioned members, there may be a loss of prestress where curved tendons rub against their enclosure. The loss may be computed in terms of a curvature-friction coefficient . Losses due to unintentional misalignment may be calculated from a wobble-friction coefficient K (per lin ft). Since the coefficients vary considerably, they should, if possible, be determined experimentally.
A safe range of these coefficients for estimates is given in the Commentary on ACI 318-99, American Concrete Institute.
Frictional losses can be reduced by tensioning the tendons at both ends, or by initial use of a larger jacking force which is then eased off to the required initial force for anchorage.
Slip at Anchorages. For posttensioned members, prestress loss may occur at the anchorages during the anchoring. For example, seating of wedges may permit some shortening of the tendons. If tests of a specific anchorage device indicate a shortening L, the decrease in unit stress in the prestressing steel is equal to EsL/L, where L is the length of the tendon. This loss can be reduced or eliminated by overtensioning initially by an additional strain equal to the estimated shortening.
Shrinkage of Concrete. Change in length of a member caused by concrete shrinkage results in a prestress loss over a period of time. This change can be determined from tests or experience. Generally, the loss is greater for pretensioned members than for posttensioned members, which are prestressed after much of the shrinkage has occurred. Assuming a shrinkage of 0.0002 in / in of length for a pretensioned member, the loss in tension in the tendons is 0.0002Es 0.0002 30 106 6000 psi.
Creep of Concrete. Change in length of concrete under sustained load induces a prestress loss proportional to the load over a period of time depending greatly on the aggregate used. This loss may be several times the elastic shortening. An estimate of this loss may be made with an estimated creep coefficient Ccr equal to the ratio of additional long-time deformation to initial elastic deformation determined by test. The loss in tension for axial prestress in the steel is, therefore, equal to CcrnÆ’c. Values ranging from 1.5 to 2.0 have been recommended for Ccr. Relaxation of Prestressing Steel. A decrease in stress under constant high strain occurs with some prestressing steels. Steel tensioned to 60% of its ultimate strength may relax and lose as much as 3% of the prestressing force. This type of loss may be reduced by temporary overtensioning, which artificially accelerates relaxation, reducing the loss that will occur later at lower stresses.
(P. Zia et al., Estimating Prestress Loss, Concrete International, June 1979, p. 32, American Concrete Institute; PCI Design Handbook, Precast / Prestressed Concrete Institute.)