Prestressed Concrete - Design of Reinforced Concrete - page 585

important if the members and thus the tendons are short, but if they are long, the percent-
age is much less important.

Friction along the Ducts Used in Posttensioning
There are losses in posttensioning due to friction between the tendons and the surrounding
ducts. In other words, the stress in the tendons gradually falls off as the distance from the
tension points increases due to friction between the tendons and the surrounding material.
These losses are due to the so-called length and curvature effects.
The length effect is the friction that would have existed if the cable had been straight
and not curved. Actually, it is impossible to have a perfectly straight duct in posttensioned
construction, and the result is friction, called the length effect or sometimes the wobble ef-
fect . The magnitude of this friction is dependent on the stress in the tendons, their length,
the workmanship for the particular member in question, and the coefficient of friction be-
tween the materials.
The curvature effect is the amount of friction that occurs in addition to the unplanned
wobble effect. The resulting loss is due to the coefficient of friction between the materials
caused by the pressure on the concrete from the tendons, which is dependent on the stress
and the angle change in the curved tendons.
It is possible to reduce frictional losses substantially in prestressing by several meth-
ods. These include jacking from both ends, overstressing the tendons initially, and lubri-
cating unbonded cables.
The ACI Code (18.6.2) requires that frictional losses for posttensioned members be
computed with wobble and curvature coefficients experimentally obtained and verified
during the prestressing operation. Furthermore, the Code provides Equations 18-1 and 18-
2 (in Section 18.6.2.1) for making the calculations. The ACI Commentary (R18.6.2) pro-
vides values of the friction coefficients for use in the equations.

19.8 ULTIMATE STRENGTH OF PRESTRESSED SECTIONS

Considerable emphasis is given to the ultimate strength of prestressed sections, the objective
being to obtain a satisfactory factor of safety against collapse. You might wonder why it is
necessary in prestress work to consider both working-stress and ultimate-strength situations.
The answer lies in the tremendous change that occurs in a prestressed member's behavior after
tensile cracks occur. Before the cracks begin to form, the entire cross section of a prestressed
member is effective in resisting forces, but after the tensile cracks begin to develop, the
cracked part is not effective in resisting tensile forces. Cracking is usually assumed to o ccu r
when calculated tensile stresses equal the modulus of rupture of the concrete (about ).
Another question that might enter your mind at this time is this: “What effect do the
prestress forces have on the ultimate strength of a section?” The answer to the question is
quite simple. An ultimate-strength analysis is based on the assumption that the prestress-
ing strands are stressed above their yield point. If the strands have yielded, the tensile side
of the section has cracked and the theoretical ultimate resisting moment is the same as for
a nonprestressed beam constructed with the same concrete and reinforcing.
The theoretical calculation of ultimate capacities for prestressed sections is not such a
routine thing as it is for ordinary reinforced concrete members. The high-strength steels

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