ABSTRACT
Load balancing in prestressed concrete design is based on the concept of using the geometric profile of the tendon to counteract some proportion of the gravity loads on a beam in order to reduce or eliminate deflection. The funicular shape of a cable under uniformly distributed gravity loading is parabolic, and so a parabolic drape of the tendon is usually employed to balance against self-weight. The curvature of the tendon produces the upward force needed to counteract the gravity loads, but it also results in a frictional force between the tendon and duct and as a result the force in the tendon is not constant, and decreases from the jacking location along the tendon. Despite these effects being well-known, their interaction does not appear to have been reported hitherto. This paper considers the ramifications of using conventional parabolic tendon profiles in the presence of friction, and it is shown that these do not produce the desired effect of eliminating the deflection of a member under the so-called “balanced load”. Equations are derived that can be used to adjust the tendon profile to enforce a balanced load situation in the presence of friction.
