Tension stiffening model for concrete beams reinforced with steel and FRP bars

Cracking is an important aspect of concrete behavior that considerably affects the overall response of concrete structures. The initiation of cracks is governed by concrete tensile properties. The propagation of cracks is a complicated phenomenon that plays a significant role in the nonlinear analysis of concrete structures. The cracking process in tension starts at a relatively low tensile strain, causing plain concrete to exhibit a gradual softening behavior. This softening is augmented by the tension stiffening of reinforcing bars. The smeared crack approach is typically combined with nonlinear finite-element analysis to generate an accurate global response. The key to such representative accurate predictions relates to material parameters, especially those of tension stiffening effects. For a complete understanding of the crack development process, tests should be performed on concrete specimens at various load histories. However, due to the difficulty of testing concrete in uniaxial tension, only limited and often conflicting results are available. The present work develops an inverse approach combining nonlinear numerical analysis and global experimental response to develop the tension stiffening model parameters needed to simulate homogenized concrete behavior in tension. The results of the study provide good model parameters to use in the case of concrete beams reinforced with steel and fiber-reinforced polymer (FRP) bars.