Why is stranded wire more flexible than solid?

[piguy101]

This is mostly a question out of curiosity. Stranded wire is more flexible than solid core for the same wire gauge. Since they have the same cross sectional area of copper, why is stranded easier to bend? I couldn't seem to find anything on the Internet that discusses why mechanically stranded is more flexible.

[T3sl4co1l]

Think about bending itself.  If you have a rectangular cross-section, which direction is it easiest to bend in?

Now consider: how many times easier is it to bend in that direction?

If the rectangle is 1x2, say (like a 2x4, or 50x100 in the rest of the world), about how much easier is it to bend?  Like, a lot, like four times, not just twice.

And it's still harder to bend than two 2x4s stacked, i.e. a 4x4 without nails holding the 2x4s together.

What is bending?  It's compression on the inside and stretching on the outside.  The outer curve physically stretches to a greater length.  Two 2x4s nailed together, and deflected to the same angle as a single one, means the outer one is stretched as a whole -- because it's entirely along the outside -- while the inner one is all in compression, for the same reason!  Just bending a single 2x4 only compresses and stretches half and half of the single 2x4.  A pair laying together (but not bonded) both bend on their own, and there is sliding on their touching faces.

So what's the deal?  The bending moment is proportional to distance from the centroid (the point were there is neither tension nor compression).  The springiness of the material acts at this moment, too.  That is: if a point on the beam is strained by so-and-so percent, it pulls proportionally.  But that pull is already proportional to the moment, so the stiffness of the beam as a whole goes as width squared!

TL,DR: solid wire has to bend a big fat hunk of metal, while strands can slide past each other.

Tim

[piguy101]

T3sl4co1l, actually that makes a lot of sense. I forgot about the bending moment being proportional to the distance from the centroid and the possible sliding effects of the individual strands. Thanks for satisfying my curiosity. 

[Brumby]

TL,DR: solid wire has to bend a big fat hunk of metal, while strands can slide past each other.

I would have gone down that path.