Time-dependent serviceability behavior of reinforced concrete beams: Partial interaction tension stiffening mechanics

The partial interaction (PI) mechanics of tension stiffening governs crack widening and the consequential deflection of reinforced concrete (RC) beams and, therefore, is essential in the serviceability design of RC structures. Both behaviors are dependent on the PI global load slip behavior of the tensile reinforcement relative to the surrounding concrete at a crack face, which in turn is dependent on the local PI material bond-stress/slip relationship between the reinforcement and adjacent concrete. Due to the complexity of PI theory, it has been difficult to directly incorporate PI mechanics into design procedures. Consequently, empirical approaches to quantify effective flexural rigidities and crack widths are commonplace. While empirical approaches can be derived relatively simply for short-term loading, the influence of concrete shrinkage and creep is difficult to incorporate. In this paper, pure mechanics-based PI solutions to describe the crack spacing and tension stiffening behavior of RC beams subjected to long-term loads are derived. They only require material properties and clearly show the interaction among shrinkage, creep and bond properties. They are simple enough to use directly in design and will help in the experimental derivation of the material properties. The results of these PI analyses are used in a companion paper to develop design rules for the time-dependent serviceability deflection of RC beams and compared with test results.