Longitudinal Bulkhead are provided to add longitudinal strength to the ship.
They would be subjected to longitudinal bending (Sagging & Hogging ).
So by putting horizontal corrugation on longitudinal bulkheads we are adding up strength to them to resist bending.
How does it work ?
Second moment of Area also know as second moment of inertia is measure of the “efficiency of cross sectional shape to resist bending caused by loading .
In above figure if you notice, both the beams have the same area and even the same shape . but Beam 1 is stronger than Beam 2 because its second moment of area is high .
Second moment of Area Ic= b(h*h*h)/12 . Hence Since h is greater in case of beam 1 it will be stronger than beam 2 .
Similarly , Longitudinal Bulkheads with horizontal corrugation will have high bending resistance compared to longitudinal bulkheads with vertical corrugation