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A simple methodology for the solution of beams prestressed or partially prestressed with external or unbonded tendons in the linear elastic cracked and uncracked range of behavior is described. It leads to equations allowing the computation of stresses in the concrete section, the tensile reinforcing steel, the compression reinforcing steel, and the prestressing steel. In particular, it is shown that the stress in unbonded tendons is a function of the applied loading, the steel profile, and the ratio of the crack width (or crack band width) to the span. These factors can all be accounted for through the use of a strain reduction coefficient ê for the uncracked range of behavior and a similar coefficient êc for the cracked range of behavior. It is shown that, when the strain reduction coefficients ê and êc are taken equal to unity, the solutions developed here revert to the solutions developed earlier for partially prestressed beams with bonded tendons.

Design considerations of externally prestressed large-span reinforced concrete girders with tendons completely outside the cross section are dealt with. The analyzed systems are two-chord structural systems. The lower, downward convex tensioned chord usually consists only of prestressing tendons, while the upper, compressed chord is a reinforced concrete straight-line or upward convex polygonal girder. The desired configuration of tendons is achieved by compressed elements interconnecting the two chords at suitable distances. In such a way, the rise of tendons can be several times larger than the height of the reinforced concrete section, thus greatly increasing their efficiency compared to the classical internally or externally prestressed girders. An important characteristic of such structural systems is that adding a very small prestressing force reduces the deformation. Therefore, the dead load deflection can be easily controlled by the suitable choice of prestressing force. The time-dependent deflection is not considerably greater than the elastic one, even for a very high creep and shrinkage, as it is also primarily governed by the shape and deformation of tendons. Because of such properties, these structural systems are exceptionally favorable for roof structures of medium and very large spans but can also be successfully used for highway bridges. Due to the significant reduction of the chords' cross-sectional areas and the bending stiffness of such structural systems, the design has to be done using the second-order theory. The criteria for cases when it is notnecessary are discussed. Besides the theoretical analysis, some experiences in design and construction of the new hangar at the Belgrade International Airport in Yugoslavia, whose 135.80 m (445 ft) span main roof reinforced concrete girders are externally prestressed with tendons free in space outside the concrete cross section, are also presented.

The behavior of two segmental concrete girders incorporating external tendons was compared to that of a similar girder with internal tendons. The girders were 31 ft long and consisted of 11 match-cast segments. Test variable was the location of the tendon ducts. In the first girder, the ducts were embedded in the girder cross section. The ducts of the second girder were external to the concrete cross section except at pier segments and intermediate deviation diaphragms. The third girder was similar to the second except that portions of the external ducts were embedded in a second-stage concrete cast. The segments included multiple shear keys and were dry jointed. All ducts were grouted. Each girder was simply supported over a 30-ft span and loaded statically to destruction under a two point load. The first and third girders attained their respective flexural strengths predicted by the classic bending theory for monolithic girders with bonded tendons. The second girder exceeded the flexural strength predicted by the provisions of the AASHTO specifications for members with unbonded tendons.

A nonlinear finite element analysis was conducted to examine the full range of behavior of segmentally precast box girder construction with external post-tensioning tendons. A primary objective of the study was to examine the effect of dry joints (without epoxy) on the strength and ductility of box girder construction. A secondary consideration was the influence of supplemental bonded internal tendons on the behavior of the structure.

The purpose of this investigation was to examine the forces developing in the dome of a prestressed concrete nuclear containment structure due to prestressing of vertical tendons. A computer program was developed for personal computers to evaluate the effect of prestressing forces. A parametric study was conducted, using the program, to examine the effects of dimensions, prestressing force, properties of tendons, etc. on the resulting stresses in the dome.