Blast pressures can cause severe damage to building structures. Moreover, in numerous occasions, the affected structure will experience a significant fire ensuing from a blast event. It is therefore imperative that key facilities that may be exposed to these multi-hazard scenarios are properly designed against their actions. Besides, current structural fire design methods are restricted to smaller compartments. Nevertheless, the travelling fire methodology which considers a more realistic evolution of temperatures can be used for the assessment of larger compartments. In this study, a series of non-linear finite element analyses were carried out on prototypical office steel frames. Parametric analyses were conducted to determine the effects of blast pressure, fire size, direction of fire travel, and maximum compartment temperature on the steel frames. The study revealed that increased blast pressures decreased the resistance of the frame to the travelling fires. Also, the response of the frame may be different for different directions of fire travel. The results also showed that smaller fire sizes with longer total fire durations can result in higher structural deformations and damage. The study demonstrates the importance of considering travelling fires in multi-hazard scenarios.