5Friction LossesMonitor elongation in addition to pressure during stressingOvercoming friction:Over-tensioning (limited)Stressing from both ends
6Friction Losses Calculating losses Function of: Reference: Curvature friction coefficientAngular change over length of strandWobble friction coefficientLength from jack to point of interestReference:Post-Tensioning Manual, Appendix A
8Elastic Shortening Losses Shortening of concrete compressed during stressing as the two occur simultaneouslyIf only one strand (tendon) – no ES lossesIf multiple strands (tendons)Tendons stressed early in the sequence will suffer losses as subsequent tendons are stressedThe first strand stressed will suffer the most total lossThe last strand stressed has zero lossReasonable to take the average of first and last
9Elastic Shortening Losses Hooke’s LawΔ 𝑓 𝑝𝐸𝑆 = 𝐸 𝑝 𝜖 𝑝Change in strand stress due to elastic shortening lossStrain in strandSteel elastic modulusAssume: Perfect bond between steel and concrete 𝜖 𝑝 =𝜖 𝑐Strain in the concrete, due to compressive stress applied:𝜖 𝑐 = 𝑓 𝑐𝑔𝑝 𝐸 𝑐𝑖Concrete stress at prestressing centroidConcrete elastic modulus at time of stressingSubstitution through previous stepsΔ 𝑓 𝑝𝐸𝑆 = 𝑁−1 2𝑁 𝐸 𝑝 𝐸 𝑐𝑖 𝑓 𝑐𝑔𝑝Average of first and last strand that experience loss; the last strand tensioned has zero loss, hence the (N-1) term.
10Anchorage Devices ENCAPSULATED ANCHOR ENCAPSULATED ANCHOR STANDARD ANCHORSWEDGESSource: PTI
14Anchorage Seating Loss Calculating lossesSome of the imposed strain on the strand is lost when the wedge seats in the plateFunction of:Hardware usedType of stressing jack (Power seating, etc.)Reference: Post-Tensioning Manual, Appendix A
20Friction and Anchorage Losses The variable prestress force in the previous slide is negligible for:Strands less than 100 feet (single-end stressed)Strands less than 200 feet (both ends stressed)Reference: Bondy, K.B., “Variable Prestress Force in Unbonded Post-Tensioned Members,” Concrete International, January 1992, pp
26Concrete CreepCreep strain is calculated by a creep coefficient, 𝜓(𝑡, 𝑡 𝑖 ), that expresses creep strain as a function of elastic strain.
27Steel RelaxationA loss of stress in the steel after being held at a constant elongation (sustained tension)For low-relaxation steel (industry standard) relaxation losses are very small compared to other loss components (~1-3 ksi)