THE usual formulæ for deflexions and bending moments in curved beams, as given in standard textbooks (e.g., Refs. 1 and 2), are not easily applied to the relatively flimsy closed rings used as stiffeners in contempory aircraft design. Two kinds of difficulty arise; one of computation, the other of principle.
Fairthorne, R.A. (1939), "The Stressing of Thin Rings: A Simplified and Complete Method for the Solution of Continuous Rings", Aircraft Engineering and Aerospace Technology, Vol. 11 No. 6, pp. 228-237. https://doi.org/10.1108/eb030495
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