Reliability Analysis Considering Material and Geometrical Nonlinearities

Structures are always subjected to aggressive environment that leads them to various forms of deterioration. Among all these the most important is the corrosion induced mainly by carbonation or chlorides. Majority of these structures exhibits significant nonlinear behavior even at low load levels. Stress strain relationships, tensile cracking, post cracking softening and interaction between concrete, steel and the environment all pave way for the complicated nonlinear response. Almost all of the data available regarding the materials, loads, detrimental phenomenon involves certain amount of uncertainty due to physical, measurement or statistical constraints. Nonlinear analysis helps to avoid overdesign and build better products. While reliability analysis provides a computationally more efficient alternative for full probabilistic analysis. In the presented work a reliability analysis has been carried out considering geometrical and material nonlinearities. A brief introduction to it is summarized below: The basic background knowledge regarding material and geometrical structural nonlinear behavior, various ways to incorporate nonlinearities in analysis especially the corotational formulation, the need for addressing uncertainties, methods for probabilistic analysis and some commonly used probabilistic distributions, sensitivity analysis and reliability analysis are all discussed first. Then a brief literature review is presented for further deep insight of the related works for the interested readers. Next, the layout of all the computational work done, the procedures adopted, the models employed and the programs developed is presented. The example problems, their results (graphical as well as tabular), and discussions are talked about. At the end, some conclusions as well as recommendations for the future work are outlined. For accomplishing the job, first of all, an algorithm addressing geometrical plus material nonlinear analysis of 2D structural elements is developed. It employs corototaional formulation to address geometrical nonlinearity. Material nonlinearity is incorporated through numerical integration across the volume of the element. Thereafter unintentional material uncertainties are addressed in probabilistic manner through Monte Carlo simulations. After that a sensitivity analysis is done. For the considered deterioration mechanism (Carbonation), a program employing CEB/fib probabilistic model code for the initiation of carbonation for the service life design is developed. For the consideration of propagation of propagation uniform corrosion rate has been assumed. The reduction in the steel cross section over the age of the structure is simulated. These results are then fed in the nonlinear analysis program and the statistics about the changes in the structural capacity are obtained. At the end, some of the important results regarding the reliability analysis are reported. From the presented work it is shown that in order to avoid computational costs it is better to find out optimum number of cross sectional strips before stepping towards probabilistic considerations. The consideration of random nature of the parameters along with their underlying probabilistic approach is extremely important. It is helpful in imagining the realistic behavior of the structures and hence more suitable design. And ultimate load is found to have a log normal probabilistic distribution when considered only the material uncertainties. The reliability analysis of the structure due to carbonation shows that reduction in the structural capacity of the structures is proportional to square root of the age of the structure same as carbonation