Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering

First Advisor

G. Z. Voyiadjis


In this study a post-cracking formulation for the analysis of reinforced concrete structures has been proposed. The secant stiffness formulation considers the following nonlinearities: effects of tension-stiffening in concrete along the reinforcing direction(s), aggregate interlock model with variable shear based on crack confining stresses, and reduction of concrete compressive strength and stiffness after cracking as a function of stresses or strains. The cracking model is capable of simulating the effects of multiple non-orthogonal cracks at a point. This total stiffness formulation treats concrete unloading and reloading along a secant path and is capable of simulating the post-peak strain softening response. The reinforcement is treated as an elasto-plastic material with possible strain-hardening having uniaxial stiffness properties. Perfect bond is assumed between concrete and steel. The proposed nonlinear inelastic secant stiffness model has been implemented into a special purpose finite element program. Implicit and explicit layering procedures have been incorporated in conjunction with shell elements. These layering procedures enable the geometric modelling of different materials through the cross-section. Procedures to compute the variation in the transverse shear stress through the cross section in the implicit layering procedure have been adopted. The transverse shear stress distribution through the cross-section are better represented with these layering procedures and have been included in the material model. The progress of material nonlinearities through the cross section, such as concrete cracking or crushing, are simulated more effectively with these layering procedures. The capabilities of this 'three-dimensional' material model have been explored by simulating a number of experimental test specimens subjected to various loadings and comparing the analytical predictions with appropriate test results and design code provisions. These examples include a number of panels and wall specimen subjected to in-plane loads; beams and slab specimens which are subjected to out-of-plane loads and a slab element representing the connection region of fiat plate column joints subjected to a combination of loads. The results of these studies indicate that the analytical model is capable of capturing the dominant deformational response characteristics and predicting the appropriate failure modes.