The Northridge, California earthquake of January 17, 1994 seriously damaged more than 150 steel moment resisting buildings. The most common and most serious mode of failure was the fracture of beam to column welded connections. This has raised questions and concerns about the seismic performance of welded steel moment-resisting frame (SMRF) steel structures. One SMRF that suffered connections damage in the Northridge Earthquake first is evaluated using a deterministic approach. A new degraded hysteretic connection model, which incorporates the effects of brittle weld failure, is developed based on experimental data. Nonlinear dynamic time domain analyses of this SMRF are performed using ground motions representing the Northridge Earthquake. Predicted and observed connections are compared, and limitations of deterministic modeling are addressed. In the stochastic approach, a detailed uncertainty analysis is conducted for the building, and probability distributions of maximum roof displacement angle and maximum inter-story drift angle are constructed. Building fragilities are constructed. These results are useful for condition assessment and performance-based design.