172 BELL SYSTEM TECHNICAL JOURNAL 



Using the relationships of Section 7.8, one may now calculate all stresses. 

 The argument k has purposely been kept the sahie for both of the super- 

 imposed solutions in order that boundary conditions at y = ±- might be 



satisfied regardless of x. 



For Yy to equal zero at the edges of the strip 



dv , dii 

 ay ox 



This gives rise to the equation: 



6 = (7.29) 



Viill + ak^) cos (A- U2[k\\ - (t)] cos 4 * = (7.30) 



Similarly, if X^ = at y = ±- 



du . dv 

 dy dx 



^5 = (7.31) 



'=^2 



Another relation is obtained from (7.31): 



-2A4 Ui sin (i- -{- Uiik' - fl) sin 4^=0 (7.32) 



The two equations (7.30) and (7.32) will be satisfied if the determinant 

 of the coefScients of Ui and U2 vanishes. The following transcendental 

 equation will then be obtained; values of A^ and 4^ being those required 

 by Eq. 7.27. 



^°^^^2 ^ -2A4^^(1 -c) ... 



cot (2 2 



By using either of equations (7.30) and (7.32), one may derive the relation 

 between U2 and Ui provided a solution to (7.13) is found. 



— 2A4sinA;^ 



U2 = Ui ~ (7.33) 



(A: - k') sin 4 ^ 



To solve equation (7.13) assume a value for k- and plot graphically the 



2 

 right and left hand expressions as functions of 0- = — . Roots are indicated 



Jx 



