Scordelis-Lo roof "Barell Vault" vertical displacement

[umcp74]

Hi everyone and thanks for your interest in this problem. I have a trouble calculating the vertical displacement of the midside of the Scordelis-Lo roof (check the following page for the roof schematic)

http://www.kxcad.net/Altair/HyperWorks/oshelp/scordelis_lo_roof.htm

I believe it is a misunderstanding by me since this example is extensively used by FE researchers for validation and they never mentioned the "formula" for the vertical displacement. I tried to figure out this formula based on my FE code output (radial and tangential displacements), but the answer is significantly less than what it should be (my code is tested sharply with many bench mark problems). This means that I probably didn't get the right "vertical displacement formula" from the schematic.

Can you please help?

P.S: My formula is:

Vertical displacement = R( cos(40) - cos(40+y/R) ) + w cos(40+y/R)

R= shell radius
y= tangential displacement (y/R= extra angle added by y)
w=calculated transverse "radial" displacement

Thanks again for your interest and your help is greatfully appreciated.