Reliability of Frame and Shear Wall Structural Systems. I: Static
Loading
Ahmed Ghobarah
Abstract:
An efficient and accurate algorithm is developed to evaluate the reliability of a steel frame and reinforced concrete shear wall structural system subjected to static loading. In a companion paper, the algorithm is extended to consider dynamic loading, including seismic loading. The concept integrates the finite-element method and the first-order reliability method, leading to a stochastic finite element-based approach.
In the deterministic finite-element representation, the steel frame is represented by
beam-column elements and the shear walls are represented by plate elements. The stiffness matrix for the combined system is then developed. The deterministic finite-element algorithm is verified using a commercially available computer program. The deterministic algorithm is then extended to consider the uncertainty in the random variables. The reliability of a steel frame with and without the presence of reinforced concrete shear walls is evaluated for the strength and serviceability performance functions. The results are verified using Monte Carlo simulations. The algorithm quantitatively confirms the beneficial effect of shear walls, particularly when the steel frame is weak in satisfying the serviceability requirement of lateral deflection. The algorithm can be used to estimate the reliability of any complicated structural system consisting of different structural elements and materials when subjected to static loading. The procedure will be useful in the performance-based design guidelines under development by the profession. keywords:Limit states; Simulation; Shear walls; Static loads; Steel frames; Finite element method.
Introduction
The realistic reliability analysis of complicated structural systems consisting of different types of structural elements and materials is a major challenge to our profession. In most cases, the limit state or performance function (a functional relationship between the load- and resistance-related variables and the performance criterion) is implicit in evaluating the reliability of such systems. The analytical technique most frequently used to capture the mechanical behavior of complicated structural systems consisting of different materials appears to be the finite-element method (FEM)-based approach. Finite-element analysis is a powerful tool commonly used in many engineering disciplines to analyze simple or complicated structural systems. With this approach, it is straightforward to consider complicated geometric arrangements，various sources of nonlinearity, different materials, and the load path to failure. However, the deterministic
finite-element method fails to consider the uncertainty in the variables, and thus cannot be used for reliability analysis. On the other hand, the available reliability methods fail to represent structures as realistically as possible. If the basic variables are uncertain, every quantity computed during the deterministic analysis is also uncertain. The currently available reliability methods can still be used if the uncertainty in the response can be tracked in terms of the
