Yield Penetration Hinge Rotation in Reinforced Concrete Beams

Structural engineers have long recognized the importance of member ductility, that is member rotation, in the design of reinforced concrete structures in order to redistribute moment and absorb energy due to dynamic, seismic, and blast loads. Understanding the rotation mechanism has been a difficult task due to the complex and variable behavior of reinforced concrete members and this is reflected in the slow but steady research progress. In this paper, the three components of the rotational mechanism of reinforced concrete beams are described. The rotation due to yield penetration of the reinforcing bars is then mathematically quantified using partial-interaction theory, which depends on the bond characteristics. The results are compared with published empirical approaches and shown to be in good agreement. Finally, a variable hinge length that is specific to the rotation limit due to fracture of the reinforcing bar, that is yield penetration, is mathematically developed.