Moment in Ring Beams at Blocking Points

Hello all! This is my first first post.

I have recently been tasked with reviewing some designs for rib and liner plate shafts. I have worked on rib and lagging shafts before but unlike those, the load is transfered to the ribs at discrete locations at the blocking points. The designs I'm reviewing state that the maximum moment in the rib is 0.86 x Thrust x rise of arc between blocking points and cites Rock Tunnelling with Steel Supports by Proctor and White. I have also seen this equation used in the Steel Sheet Piling Design Manual and the Foundation Engineering Handbook by Winterkorn and Fang, so I'm confident that it's tried and true. However, I was hoping to learn the derivation of the 0.86 for my own knowledge. Proctor and White reference Strength of Materials, Part II by Timoshenko for the derivation of the equation. I have a copy of this but find it a bit intimidating as it's been a while since I've used calculus. I'm perfectly willing to get into the weeds but want to make sure i'm starting at the right place. Can anyone point me in the right direction for better understanding this equation?

Thanks in advance!