Creep, Cracking and Shrinkage in Concrete Frame Structures

A mathematical model is developed for the study of time-dependent behavior of reinforced concrete structures. The model is formulated to account for creep, cracking, and drying shrinkage in the concrete. The output from the model includes forces, stresses, strains, and displacements in the structure. The model is formulated on the basis of idealizations in time and geometry. The idealization of incrementing the time is an expedient for integration of the hereditary strain-stress law for concrete. A linear law in functional form provides an accurate description of concrete strain-stress behavior within design stress ranges. The geometric idealizations are made so that the stiffness of the structure may be found. The structural members are divided into length increments, and each length increment is divided into depth increments so that bending and axial stiffness of a reinforced concrete member can be evaluated. Three examples are studied using the model: axially loaded column; reinforced concrete beams; and reinforced concrete frame.