Prestress Losses
General Discussion
ACI 318, Section 20.3.2.6.1 states that prestress losses shall be considered in the calculation of the effective tensile stress in the prestressed reinforcement, fse, and shall include (a) through (f):
(a) Prestressed reinforcement seating at transfer
(b) Elastic shortening of concrete
(c) Creep of concrete
(d) Shrinkage of concrete
(e) Relaxation of prestressed reinforcement
(f) Friction loss due to intended or unintended curvature in post-tensioning tendons
Further, the commentary to Section 20.3.2.6.1 states that the actual losses, whether greater or smaller than the calculated values, have little effect on the design strength of the member, but affect service load behavior (deflections, camber, cracking load) and connections. Additionally, at service loads, the overestimation of prestress losses can be almost as detrimental as underestimation because the former can result in excessive camber and horizontal movement.
Losses for pretensioned members are typically divided into initial and long term. Initial losses include elastic shortening, anchorage seating and form or abutment deformations. Long term losses include concrete creep and shrinkage, along with steel relaxation, and are further subdivided into simplified and detailed. Simplified methods for long term losses are appropriate for most designs. Detailed long term loss methods are available for unusual situations or where more accuracy is warranted. Detailed methods can also be used when losses at times other than the end of the service life of the member are required.
Initial Losses
Initial losses are typically defined as those losses at release or stripping, however, with the appropriate equations, losses can be calculated at any time t. For the calculation of initial losses, there are four components to be considered. These include the following:
1.Chuck seating, also called chuck slippage
2. Bed shortening (for self-stressing beds) or bulkhead deflection (for fixed-abutment or non-self-stressing beds)
3. Elastic shortening
4. Steel relaxation
The first two terms, chuck seating/slippage and bed shortening/bulkhead deflection, are typically the responsibility of the precaster, and should be included in the stressing calculations. The second two terms, elastic shortening and steel relaxation, are typically the responsibility of the design engineer.
Initial elastic shortening is usually the same as that calculated for final losses, with the exception for members that are cast and stripped in a different orientation than final. Walls and spandrels are examples of this type of member. In these cases, there will be a different elastic shortening component for initial and final losses, as the fcir term in the ES equation is dependent on both the orientation of the member and the externally applied loads. Note that elastic shortening is instantaneous but not necessarily constant.
In the case of steel relaxation, the loss calculation requires an equation that takes time into account. Suitable time-dependent equations for steel relaxation can be found in ACI 423.10R-16 and PCI Committee on Prestress Losses (1975). Creep and shrinkage are usually neglected at release.
Lump Sum Losses
Lump sum losses are essentially equivalent to user defined losses. This type of loss calculation has historical usage in building and transportation specifications. For pretensioned strand, they are generally in the range of:
25 to 35 ksi (PCI),
35 ksi (ACI), or
6000 + 16fcps + 0.04fpi (psi) (FHWA)
Long Term Losses - Simplified
Simplified long term losses are based on time-dependent properties of concrete and steel, including concrete creep and shrinkage and steel relaxation. These methods of loss calculation are complicated due to interdependency of rate of loss of one factor which is altered by other factors. They are also hampered by lack of time dependent information of material properties, loading and support conditions, environmental factors, and curing methods.
Two common methods are published in the PCI Handbook method (Zia et al. 1979), and the AASHTO LRFD specification. The AASHTO LRFD simplified method is an estimate of time-dependent losses, using approximations and assumptions to simplify the detailed AASHTO LRFD method (Tadros et al. 2003).
Long Term Losses - Detailed
Long term detailed loss calculations can be further subdivided into two categories: age-adjusted effective modulus methods and incremental time-step methods.
Age-adjusted effective modulus methods consider the effects of concrete creep and shrinkage and can also include differential shrinkage of concretes in composite systems and thermal effects. One such creep and shrinkage model can be found in the AASHTO LRFD detailed method (Tadros et al. 2003). These methods adjust the concrete modulus of elasticity to account for both the elastic and time-dependent creep strains.
Incremental time-step methods are based on the superposition of elastic and creep strains resulting from increments of stress. Each load increment has associated elastic and creep strains. At any point in time, the total strain can be calculated as the summation of the elastic and creep strains for all loads plus shrinkage strains. One such model is defined in PCI Committee on Prestress Losses (1975).
Hand Calculation
References
ACI Committee 423. Guide to Estimating Prestress Losses. ACI 423.10R-16. Farmington Hills, MI: ACI.
PCI Industry Handbook Committee, PCI Design Handbook, 8th Ed., PCI, Chicago, 2017.
PCI Committee on Prestress Losses. 1975. “Recommendations for Estimating Prestress Losses.” PCI Journal 25 (4) July-August: 43-75
Tadros, M. K.; Al-Omaishi, N.; Seguirant, S. J.; and Gallt, J. G., 2003, “Prestress Losses in Pretensioned High-Strength Concrete Bridge Girders,” NCHRP Report 496, Transportation Research Board, Washington, DC.
Zia, Paul, H. K. Preston, N. L. Scott, and E. B. Workman. 1979. “Estimating Prestress Losses.” Concrete International 1 (6) (June): 32–38.