Summer 2019

ASPIRE is a quarterly magazine published by PCI in cooperation with the associations of the National Concrete Bridge Council. The editorial content focuses on the latest technology and key issues in the Concrete Bridge Industry.

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C O N C R E T E B R I D G E T E C H N O L O G Y 26 | ASPIRE Summer 2019 by R. Kent Montgomery, FIGG Design Considerations for Unbonded Post-Tensioning Tendons Pos t-tensioned concrete s truc tures are economical and durable solutions for bridges and buildings. Although most designs use internal bonded post- tensioning tendons, unbonded external and internal tendons can also be utilized. However, s truc tures with unbonded tendons exhibit fundamentally different b e h a vio r s t h a t m u s t b e c o rr e c t ly addressed to produce reliable designs. This article discusses these differences while focusing on current bridge design provisions in the United States. Types of Unbonded Tendons For bridges, the most common type of unbonded tendon is external to the cross section, anchored at each end of a span, and deviated within the span to achieve the desired profile. In the United States, this type of tendon typically uses bare strands within ducts filled with grout to provide corrosion protection. However, in other countries, external tendons with ungrouted epoxy-coated strands and individually sheathed strands have been used. Ducts have also been filled with a flexible filler, such as wax or grease, to provide corrosion protection. Details at the deviators include rigid steel pipe ducts bonded to the diaphragm and diabolos, which are radiused openings that do not result in any bond at the deviators (see the Concrete Bridge Technology article in the Fall 2015 issue of ASPIRE ® ). Tendons internal to the cross section are typically grouted and bonded, but they can also be unbonded. For decades, building elements have used unbonded sheathed strands and, more recently, the Florida Department of Transportation has used flexible filler for internal ducts rather than cementitious grout. The flexible filler does not bond the strands to the cross section but does provide corrosion resistance of the PT tendons (see the Concrete Bridge Technology article in the Winter 2017 issue of ASPIRE). Flexural Design Considerations At the service limit state, the designs for bonded and unbonded tendons are essentially the same. The tendons are tensioned, and forces are transferred to the cross section at the anchorages and tendon deviations. Whether the tendon is bonded or unbonded makes no appreciable difference for either the tendon forces or concrete stresses. Designing for the service limit state for both bonded and unbonded tendons involves selection of the tendon forces and tendon paths to achieve concrete stresses within the limits of the American Association of State Highway and Transportation Officials' AASHTO LRFD Bridge Design Specifications. 1 However, at the strength limit state, there are fundamental differences between bonded and unbonded tendon designs. For internal tendons bonded to the cross section, strain compatibility is a reasonable assumption and the stress increase in the tendons after the section cracks can be calculated from strain compatibility and material properties. Article of the AASHTO LRFD specifications presents simplified design equations that were developed using the previous considerations. These equations estimate the stress in bonded tendons at the strength limit state. Once the stress in the tendons is determined, the nominal flexural resistance is easily calculated from equations in Article and compared to the strength limit state moment demands. F o r u n b o n d e d t e n d o n s , s t r a i n compatibility is not valid and the stress in the tendons is primarily governed by global displacements of the cracked structure between bonded sections of the External tendons in grouted ducts inside the U.S. Route 181 Harbor Bridge in Corpus Christi, Tex. Photo: FIGG. Ungrouted epoxy-coated strands inside the Matoba Viaduct, which crosses the Matoba River in Japan. Photo: DYWIDAG-Systems International.

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