Arch Beam Roark's Formulas for Stress and Strain

[Struct123ure]

I have a arch steel beam very similar to the example attached from page 292 of 7th ed Textbook by Roark's ... The example says "To obtain the rotation of the arch at the point of attachment of the bar, we first calculate the loads on the portion to the right of the loading and then establish an equivalent symmetric arch (see Fig. 9.10)."
My question is how does he establish the equivalent symmetric arch below?


I have attached the example from Roarks Formulas For Stress & Strain by C. Young, G. Budynas(7ed).

 

[rb1957]

rotate the load vector (ie two components) 20 degrees ?

 

[Snickster]

Without looking at Roark discussion in detail, it looks like the equivalent arch has the same arch length and total angle, but is totally horizontal so that both sides elevations are at same level and the resulting moment at the point of interest is same. Keeping the moment the same requires adjusting the end forces.

 

[Struct123ure]

I see, I didn't notice the rotation. It makes sense now, would have been helpful to include a couple extra steps, but here they are for anyone else wondering in the future.