Probabilistic Stability Analysis of Portal and Gabled Steel Frames with Flexible Connections and Supports

There are various factors in the analysis and design of the steel frames that uncertainties in any one of them can have a significant effect on the structural safety. The rotational stiffness of the bases and beam-to-column connections and also, the transitional stiffness of the bracing system can be considered as examples of these variables. In this paper, firstly, based on the exact solution of the governing differential equation for an Euler-Bernoulli beam, the stability matrix of portal and gabled steel frames with flexible connections and supports and non-prismatic members are derived. It should be added, the flexibility of connections and supports are molded by the linear rotational or transitional springs. The accuracy of the proposed approach in the deterministic stability analysis with numerical examples verified. Then, by using of the Monte-Carlo simulation method, the probability of failure of mentioned frames for the stability is estimated. The rotational stiffness of the beam-to-column connections and bases and also, the transitional stiffness of lateral support are considered as the random variables in the stochastic stability analysis. Accordingly, by using of the presented formulation the buckling loads of the simulated frames for the hundred thousand times obtained and the effects of various coefficients of variations and different probabilistic distribution functions for random variables in the buckling resistance of the foregoing frames estimated. Moreover, the sensitivity of the probability of failure for the stability of frames with respect to uncertainty of the stiffness of the connections and supports investigated.