PRINCIPAL STRAINS IN BUCKLED SURFACES 525 



Henceforth, for clarity, suppose the subscript "1" to refer to the longer 

 side of the parallelogram, "2" to the shorter side, "3" to the longer dia- 

 gonal, and "4" to the shorter. 



*Si = original slope of Li = tan <^i = 

 S2 = original slope of Lo = tan 02 = 

 S[ = tan ct>[ =^Si (4a) 



Ax 



S', = tan 0; = ^ ^o (4b) 



*^d »^c 



Smce 01 - 02 = 90°, 



82= -^ (5a) 



Oi 



/S2 = — Xj//Xi;Si (5a) 



By expansion and substitution from Equations (4) and (5), 



r («' + 1) 



tan (.i,; - *;) = ^-^ ,^^l' (6) 



' - fe) 



Let ^ = 90° - (0'i - 0o) 



then 



1 - f 

 tan (90° - (01 - 02)) = tan ^ = —-. ^^^^ (7) 



H'^' + s. 



which is the shear between Li and Li . 



si) 



2 



{Sx + l/^Si) = tan 01 + cot 0i = ^^— (8) 



sin Z01 



and substituting this in equation (7), 



. 2K\y tan ^p 



«"^ 201 = -^^^r^ (9) 



