Analysis of beams prestressed with hybrid (Steel/Carbon Fiber-Reinforced Polymer) tendons using the conservation of energy approach

Abstract

Durability of post-tensioned concrete members is greatly enhanced by using Carbon Fiber-Reinforced Polymer (CFRP) tendons in lieu of, or in combination with, unbonded and bonded steel tendons. However, current design and analysis methods are limiting the use of hybrid (i.e., a combination of unbonded and bonded steel and CRFP) tendons since they are only applicable to either bonded or to the rather complicated post-tensioned unbonded steel tendons. This paper presents an analytical approach developed to predict the overall response of concrete beams prestressed with hybrid tendons. The model is based on a structural idealization that uncouples the concrete beam and the unbonded tendon behaving as a trussed-beam system. The approach utilizes equilibrium equations, compatibility of deflection between beam and tendon, and the conservation of energy approach (CEA) applied at various limit states. Additionally, a simplified CEA is also presented at characteristic points for various cases including unbonded as well as hybrid tendons. Results are validated using experimental tests available in the literature indicating that CEA is a versatile and rational procedure that can accurately predict the overall flexural behavior of beams with hybrid tendons. A simplified version of the CEA using hand calculations is also developed for directly analyzing such beams with comparably accurate results.