Keywords: prestressed concrete, statically indeterminate structures, primary moment, secondary moment, moment coefficient, prestressing force.

Prestressed concrete structures in most cases have become an alternative way of design in order to obtain sophisticated and economical structures. With the simple principles to give compression to the concrete so that during the service load the tensile stress will be eliminated while limiting the compressive stress within the prescribe value, prestressed concrete has become an attractive strategy for the design of concrete structures. However, some difficulties may arise in designing prestressed concrete members for statically indeterminate structures. This is due to the presence of a secondary moment when the prestressing force is applied [1,2,3]. The interaction between the secondary moment and the magnitude of prestressing force produces more challenging tasks, because the magnitude of the secondary moment might be significantly large enough and cannot be neglected.

When Lin's load balancing method [1] is used some conditions should be satisfied. First, the cable profile is assumed to be a curve or parabolic in each span of the member with no smooth transition. Therefore, the drastic change in the cable profile in continuous support is neglected in the computation so that the prestressing force can balance a part of the external loading in every span of the member. Besides this we cannot have cable eccentricities at the end supports as those eccentricities produce additional moments. This condition results in that when the prestressing force is obtained by using load balancing method, we have to check the stress to account for those two conditions. Another method to handle the secondary moment is by designing the cable profile so that the cable is coincident, i.e., the C-line coincides with the T-line, for the case without external loading. However, obtaining such profiles is not an easy task.

In this paper a simple procedure to obtain the magnitude of prestressing force in statically indeterminate concrete elements is proposed. By assuming that the total moment due to the prestress as a linear function of the magnitude of the prestressing force, as a moment coefficient, and employing the relationships between stress limitation, the magnitude of prestressing force can be obtained. The inequality equations can then be solved by defining the lower and upper bounds of the prestressing force so that when such prestressing force is applied to the members, the stress will be in the prescribed limit with the secondary moment taken into account. With this procedure the determination of the prestressing force will be simple. In addition, this method can be considered as a general procedure that can be used either for statically determinate or indeterminate structures. In statically determinate prestressed concrete structures the value of secondary moment would be zero. The economical design is achieved when the difference between the lower and the upper magnitudes of the prestressing force is small. Thought in a different way the difference between the lower and upper bound magnitudes of prestressing force defines the degree of safety. Numerical examples are then carried out to show the simplicity of the proposed design procedure.

1

T.Y. Lin, "Design of prestressed concrete structure", John Wiley & Sons, N.Y.,1963.

2

A. Naaman, "Prestressed concrete analysis and design", McGraw-Hill Book Company, N.Y, 1982.

3

J.R. Libby, "Modern prestressed concrete: design principles and construction methods", Van Nostrand Reinhold, N.Y., 1977.

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