Prestressed Concrete Hashemite University The Hashem ite University Departm ent of Civil Engineering Lecture Lecture 5 5 – – Losses of Losses of Prestress Prestress Dr. Hazim Dwairi Dr. Hazim Dwairi Dr Hazim Dwairi Dr Hazim Dwairi Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Types of Losses Types of Losses • Initial PS force undergoes force loss over Initial PS force undergoes force loss over a period of approximately a period of approximately 5 i d i d f f i i t l 5 t l 5 years years Losses of PS Immediate Time-dependent •Elastic shortening •Concrete Creep •Anchorage losses •Concrete Shrinkage •Friction losses •Steel Relaxation Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 1
Prestressed Concrete Hashemite University Types of Losses Types of Losses Losses of PS Concrete Steel •Elastic shortening •Relaxation •Creep •Creep •Friction F i ti •Shrinkage •Anchorage set Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete General Notes General Notes • Early failures in PS structures were due to the Early failures in PS structures were due to the inaccuracy in predicting losses over time inaccuracy in predicting losses over time. inaccuracy in predicting losses over time. inaccuracy in predicting losses over time • Losses of PS force may be grouped into: Losses of PS force may be grouped into: – Immediate during construction Immediate during construction – Time Time- -dependent over an extended period of time dependent over an extended period of time • The jacking force The jacking force P P j j (largest force applied to a (largest force applied to a tendon) is immediately reduced due to friction, tendon) is immediately reduced due to friction tendon) is immediately reduced due to friction tendon) is immediately reduced due to friction, anchorage and elastic shortening to initial force anchorage and elastic shortening to initial force P i i Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 2
Prestressed Concrete Hashemite University General Notes General Notes • As time passes by, the force reduces gradually, As time passes by, the force reduces gradually, rapidly at first but then more slowly due to rapidly at first but then more slowly due to rapidly at first but then more slowly, due to rapidly at first but then more slowly, due to creep, shrinkage and relaxation. creep, shrinkage and relaxation. • After many years, the force stabilizes to what is After many years, the force stabilizes to what is known as effective force known as effective force P P e . • For For pretensioning pretensioning, , P P j j never acts on the concrete, never acts on the concrete, but only on the anchorage of the casting bed but only on the anchorage of the casting bed, but only on the anchorage of the casting bed but only on the anchorage of the casting bed, • For post For post- -tensioning, tensioning, P P j j is fully applied to the is fully applied to the concrete only at the ends. concrete only at the ends. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete General Notes General Notes • An exact determination of the PS losses is not An exact determination of the PS losses is not feasible all the time sometimes it is reasonable feasible all the time sometimes it is reasonable feasible all the time, sometimes it is reasonable feasible all the time, sometimes it is reasonable to lump- to lump -sum loss estimates. sum loss estimates. • Exact losses affect service load behavior such Exact losses affect service load behavior such as deflection and crack width. as deflection and crack width. • Overestimation of losses leads to high PS force Overestimation of losses leads to high PS force causing excessive camber and tensile stresses. causing excessive camber and tensile stresses causing excessive camber and tensile stresses causing excessive camber and tensile stresses. • Underestimation of losses leads to little PS Underestimation of losses leads to little PS force, thus not using the system to its full force, thus not using the system to its full capacity. capacity. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 3
Prestressed Concrete Hashemite University Lum p Lum p- -sum Estim ate of Losses sum Estim ate of Losses • First introduced in the ACI code of First introduced in the ACI code of 1963 1963. The . The current ACI code doesn’t have lump current ACI code doesn’t have lump sum current ACI code doesn t have lump current ACI code doesn t have lump-sum sum sum estimates. However AASHTO and Post- estimates. However AASHTO and Post - tensioning institute (PTI) suggest lump tensioning institute (PTI) suggest lump- -sums. sums. AASHTO Lump-sum losses * Type of Steel Total Losses Total losses f’ c =27.6 MPa f’ c =34.5 MPa Pretensioned Strand Pretensioned Strand --- 310 MPa 310 MPa Post-tensioned wire or strand 221 MPa 228 MPa Bars 152 MPa 159 MPa * Losses due to friction are excluded, it should be computed according to sec. 6.5 of AASHTO and added. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Lum p Lum p- -sum Estim ate of Losses sum Estim ate of Losses PTI Lump-sum losses for post-tensioning Type of Steel Total Losses Total losses (S abs) (Slabs) F(Beams and joists) ( ea s a d jo sts) Stress relieved 270-K strands 207 MPa 241 MPa and stress relieved 240-K wire Low relaxation 270-K strands 103 MPa 138 MPa Bars 138 MPa 172 MPa • These losses are applied to only routine, These losses are applied to only routine, standard conditions of loading, normal concrete, standard conditions of loading, normal concrete, standard conditions of loading normal concrete standard conditions of loading normal concrete quality control, construction procedure and quality control, construction procedure and normal environmental conditions. normal environmental conditions. Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Dr. Hazim Dwairi 4
Prestressed Concrete Hashemite University Type of PS Losses Type of PS Losses Type Stage Stress Loss Pre Post (t i , t j ) Total Δ f Δ f pES Elastic shortening Elastic shortening At transfer At transfer At seq ential At sequential --- (ES) jacking Δ f pR (t i , t j ) Δ f pR Relaxation (R) Before After transfer and after transfer Δ f pCR (t i , t j ) Δ f pCR Creep (CR) After After transfer transfer Δ f SH (t i t j ) Δ f pSH (t i , t j ) Δ f pSH Δ f SH Shrinkage (SH) Shrinkage (SH) After After After stransfer After stransfer transfer Δ f pF Friction (F) --- At jacking --- Δ f pA Anchorage Set (A) --- At transfer --- Δ f pT (t i , t j ) Δ f pT Total Life Life Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Prestressed Concrete Concrete Total Losses Total Losses • Pretensioned Pretensioned Members: Members: � Δ f pT � Δ f = Δ f pES Δ f pES + Δ f pR Δ f pR + Δ f pCR Δ f pCR + Δ f pSH Δ f pT = pSH � Δ f pR pR = Δ f pR )+ Δ f pR pR (t t o o ,t ,t tr tr )+ pR (t t tr tr ,t ,t s ) � t o = time at jacking (usually zero) = time at jacking (usually zero) � t tr tr = time at transfer (usually = time at transfer (usually 18 18 hours) hours) � t s = time at stabilized loss (usually = time at stabilized loss (usually 5 5 years) years) • Th • Thus, Th Thus, pJ - Δ f pR - Δ f pES � f pi pi = = f f pJ pR (t t o ,t ,t tr tr ) ) - pES Elastic Shortening Relaxation Jacking stress Dr. Hazim Dwairi Dr. Hazim Dwairi The Hashemite University The Hashemite University Prestressed Concrete Prestressed Concrete Dr. Hazim Dwairi 5
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