Disclosed herein are a tire ply steel fabric having specified weft cords, a rubber covered tire ply comprising the tire ply steel fabric, tires comprising the rubber covered tire ply, and related processes for producing a tire ply steel fabric with specific weft cords and for producing a rubber covered tire ply comprising the tire ply steel fabric. The tire ply steel fabric comprises a plurality of steel warp cords and a plurality of weft cords each weft cord having a core-sheath construction wherein the core comprises at least one filament of a non-metallic material having a specified Eb and the sheath comprises a different non-metallic material having a specified Eb that is lower than the Eb of the core material.