The behaviour of structures at elevated temperatures is profoundly different from that at ambient state. Local buckling of beam flange outstands and local buckling of beam web, which experiences a non-uniform temperature variation, are important because the mechanical properties of the steel are degraded non-uniformly from their ambient values. Developing a formulation representing the mechanics of the potential failure zone in the column web in the compression region of the connection due to the large compressive forces developed during fire, predicting the critical temperature in a connection that causes failure of the bolts, end plate and column flange in the tension zone of the connection and elastic analysis of a panel zone in a rigid or semi-rigid joint in a steel frame, are presented in this book. In order to model the structural response of a composite beam restrained by cooler members a partial interaction analysis is developed. The generic techniques that are developed in this book provide a structural model for the response of beams and beam-to-column connections in fire and can be especially useful to professionals in Structural and Fire Engineering fields.