Uncertainty Quantification in Modeling of Steel Structures using Timoshenko Beam

Abstract

This paper quantifies the uncertainty emanated from modeling steel structures using a Timoshenko beam. Using continuous beams to model building structures is a conventional approach in structural dynamic analyses. The use of Timoshenko beams, as a class of continuous beam models, in lieu of finite element models significantly expedites the computations. In turn, the reduction in the computational cost facilitates probabilistic, online identification and rapid damage detection of building structures in the aftermath of a seismic event. The prerequisite for structural identification using this method is the quantification of uncertainties that arise as a result of approximating the structure with a continuous beam, which is the primary objective of this research. To this end, an automated system is developed and subsequently employed to design 1000 finite element models of building structures followed by eigen-analyses to determine their natural frequencies and mode shapes. Thereafter, the residual of the eigen-equation of the Timoshenko beam given the frequency and mode shape from the exact finite element model is computed for each structure. Statistical analysis of these residuals for various structures leads to the distribution type, mean, and standard deviation for the probability distribution of the model error. The results show that the error is nearly insensitive to the height and dimensions of the plan, but is heavily dependent on the structural system. The results also show that the error standard deviation for steel moment-resisting frame systems is 3.5 times smaller than that of the steel concentrically-braced systems. This indicates that the Timoshenko beam model class provides a better estimation of steel moment-resisting frame systems.

Keywords

• timoshenko beam
• characteristic equation
• probabilistic analysis
• bayesian identification
• finite element