Michael Thonet observed during the early 19th century how wood reacted when being bent. Like other objects that are bent, the outside curve stretches while the inside compresses. The limit to the bend is the balance the material has between its ability to stretch or compress.
Imagine three parallel lines, the top line is the out side of a boards face (outside of curve), the bottom line is the inside of the boards face (inside of curve), the center line would represent the neutral point of wood movement during a bend. If the material has characteristics that allow it to stretch and compress equally then the neutral point would land equidistance between the top and bottom line. The further above the line the greater the stretching and the further below the greater the compression.
Wood basically does not have this equal balance of stretching to compressing ratio. It will compress much more than it will stretch. I have seen some suggest that a wood such as white oak will only stretch 2% of its length. That seems about right in my experience.
When wood is thin the other face has enough strength to resist stretching to the point of breaking while forcing the inner face to compress during a bend. However as the wood gets thicker it reaches a point where this is no longer possible and the outer face stretches to a point that it breaks.
So this brings us back to the three parallel lines. Michael Thonet realized that to balance these qualities in wood he would need to restrain the stretching of the outside of the wood face (top line) in order to force the neutral point closer to the outer face and move more force to the compression side (bottom line). His solution was to reinforce the outer face with a metal strap and the bending blank would be trapped between end blocks that were attached to the strap. During the bend the end blocks restrained the outer face from stretching and thus compression occurs on the inner face. Since wood in general will accept far more compression this would result in a successful bend.
If this seems a bit confusing. Just watch my youtube video on the first part of this series and you will see the strap and end block set up. Or watch this video of a chair back for a Michael Thonet chair being bent at the factory.
I hope this explains a bit as to why a strap is sometimes needed to achieve a successful bend. I will show a further technique that I use to compensate for compression problems as the wood gets even thicker as in this bend that began this discussion.