The U.S. transmission grid is rapidly aging with 70% of transmission lines older than 25 years. Maintenance of transmission lines has traditionally involved visual inspection of line degradation, which is costly and time consuming given the large size of the grid. The objective of this study is to model the sag degradation of transmission lines over time by calculating and predicting the inelastic elongation in conductors. Using inelastic elongation as a health index, we analyze the sag degradation of transmission lines under various environmental and operational scenarios representing the impact of climate change and large-scale electrification. We employ historical atmospheric and operational data to calculate thermal and mechanical stresses acting on transmission lines, and physics-based models to calculate inelastic elongation accumulated in a conductor given the long-term stress profile. Sensitivity analysis is performed on the severity and frequency of extreme weather events as well as the magnitude of power flow on transmission lines. The obtained results show that inelastic elongation can serve as a quantifiable and predictable health index to inform inspection and maintenance decisions. Sensitivity analysis results show that an additional increase in power flow leads to the maximum rate of increase in inelastic elongation, which is further compounded by inelastic elongation due to severe weather events.