A novel interval matrix stiffness method for the analysis of steel frames with uncertain semi-rigid connections

The static analysis of steel frames with uncertain semi-rigid connections is addressed. The effects of connection flexibility are incorporated into the frame model by means of rotational springs at the end nodes of beams. Assuming an idealized linear-elastic behaviour, the initial stiffness of rotational springs is expressed in terms of the so-called fixity factor which is considered uncertain to take into account the large scatter of connection stiffness and capacity, evidenced by experimental measures. Specifically, the fixity factors are modelled as interval variables whose bounds are consistent with the limits assigned by Eurocode 3 for different types of steel semi-rigid connections. Within the framework of the so-called Improved Interval Analysis via Extra Unitary Interval, a novel interval matrix stiffness method is developed by incorporating the interval fixity factors into the classical deterministic formulation. The lower bound and upper bound of the interval structural response are estimated by applying a sensitivity-based procedure. A single-storey frame and a five-storey frame with uncertain semi-rigid beam-to-column connections are analyzed to validate the proposed approach as well as to investigate the influence of the uncertain connection stiffness on structural behaviour.