Take a piece of paper, lay it horizontally, try and bend it. It folds very easily, but take a piece of paper and hold it so the very thin edge us up, and try and bend it that same way. It will take more force or end up tearing.
Adding another plane of resistance, where some material will be in compression and tension opposed to just being compressed makes it more rigid and stronger.
This same idea can be seen in an [I-Beam](https://www.grainger.com/product/DYNAFORM-I-Beam-Isopthalic-Polyester-4AUU3), a common building material, or a[ shipping container.](https://moverfocus.com/wp-content/uploads/2019/08/Shipping-Containers.webp)
So yes, ridges add additional strength and rigidity to the luggage.
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