Fixed Angle Softened Truss Model for Reinforced Concrete

Abstract

A softened truss model has previously been developed for reinforced and prestressed concrete membrane elements subjected to in-plane shear and normal stresses. This existing model satisfies the three principles of mechanics of materials : two-dimensional stress equilibrium, Mohr's circular strain compatibility, and the softened biaxial constitutive laws of concrete. That is, the model can predict the strength of a membrane element as well as its load-deformation history. However, this model cannot predict the contribution of concrete observed in tests, because it is based on the assumption that the direction of the cracks (and thus, the concrete struts) is inclined at the rotating angle following the postcracking principal stresses of the concrete. This paper presents a new and more general softened truss model in which the direction of the cracks is assumed to incline at the fixed angle following the principal stresses of the applied loading. This new model, although more complex, is capable of predicting the contribution of concrete. The fixed angle softened truss model requires four constitutive laws of materials. Three have been established previously for the rotating angle softened truss model (concrete in compression, concrete in tension, and steel embedded in concrete). This paper presents the fourth constitutive law relating the average shear stress of concrete to the average shear strain.