Three dimensional analysis of reinforced concrete frames with cracked beam and column elements

In the design process of reinforced concrete buildings, the serviceability limit state for lateral drift is an important design criterion that must be satisfied to prevent large second-order P –delta effects. Deformation control is also important to ensure the serviceability requirements. For accurate determination of the deflections, cracked members in the reinforced concrete structure need to be identified along with their effective flexural and shear rigidities. In this study, a computer program has been developed using the rigid diaphragm model for the three dimensional analysis of reinforced concrete frames with cracked beam and column elements. ACI, CEB and probability-based effective stiffness models are used for the effective moment of inertia of the cracked members. In the analysis, shear deformations, which can be large following crack developments, are taken into account and the variation of the shear rigidity due to cracking is considered by reduced shear stiffness models. The computer program is based on an iterative procedure which is subsequently verified experimentally through a series of reinforced concrete frame tests. A parametric study is also carried out on a four-story, three-dimensional reinforced concrete frame. The iterative analytical procedure can provide an accurate and efficient prediction of deflections of reinforced concrete structures due to cracking under service loads. The most significant feature of the proposed procedure is that the variations in the flexural stiffness of beams and columns can be observed explicitly. The procedure is efficient from the viewpoint of computational time and convergence rate, and is also more direct than the finite element method.