initial shape 



initial membrane 

 circle 



deflected shape 



deflected 

 membrane circle 



w = displacement from initial 

 to deflected shape 



Wj^ = displacement from mem- 

 brane behavior 



Wu = displacement from 

 bending 



w-j. = total displacement 



ARj = initial deviation in 

 inside radius 



Figure B-17. Definition of displacement terms. 



When a deflected shape was plotted the reference point was the 

 location of the center shaft that held the potentiometer; however, this 

 location was not the "true" center of the deflected shape. The opera- 

 tion of finding the true center location was that of manually super- 

 imposing the membrane curve on the deflected shape and using judg- 

 ment to decide the location . Judgment was based on fitting the mem- 

 brane curve (perfect circle) of known size to the deflected shape such 

 that the area between the wavy line and the membrane curve was 

 divided equally . 



The initial and deflected cross-sectional shapes of a free and 

 simply supported specimen with their corresponding membrane circles 

 are shown in Figures B-18 and B-19, respectively. All specimens 

 having a free support deflected into an elliptical shape where the num- 

 ber of lobes, n, was 2. All specimens having a simple support 

 deflected into a shape with n = 3. 



64 



