Note that the skin effect:
http://en.wikipedia.org/wiki/Skin_effect/
is highly dependent on AC frequency.
So for a power wire example (the CommScope copper grounding wire replacement example) at 50Hz or 60Hz, the skin depth is on the order of 10mm:
http://en.wikipedia.org/wiki/File:Skin_depth_by_Zureks.png/
In other words, until the cable diameter is over 20mm, the skin depth is the whole wire; 10mm radius in from each side => 20mm diameter.
For the case in point (thin copper over steel core) the photos from CommScope show multi-wire (stranded) conductors with each strand being composed of a steel core with a thin layer of copper. Even if each strand was 3 mm and the copper was insignificant in cross-section, the skin depth of steel (from the chart above) is still deeper than the wire is thick. The cable does not act like a single solid (steel) wire until it is tightly twisted - crushed really - to eliminate the air gaps between strands.
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So for a power wire example (the CommScope copper grounding wire replacement example) at 50Hz or 60Hz, the skin depth is on the order of 10mm: http://en.wikipedia.org/wiki/File:Skin_depth_by_Zureks.png/
In other words, until the cable diameter is over 20mm, the skin depth is the whole wire; 10mm radius in from each side => 20mm diameter.
For the case in point (thin copper over steel core) the photos from CommScope show multi-wire (stranded) conductors with each strand being composed of a steel core with a thin layer of copper. Even if each strand was 3 mm and the copper was insignificant in cross-section, the skin depth of steel (from the chart above) is still deeper than the wire is thick. The cable does not act like a single solid (steel) wire until it is tightly twisted - crushed really - to eliminate the air gaps between strands.