THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 153 
tion with a shearing force Q (see Fig. 6). The wires are supposed to be under an initial 
tension T) and the elongations or contractions of the girders, reckoned from the initial inert 
condition, before the wires were tightened, areAx,, Ax,4, and Ax,. 
aX) 
We have for both girders: 
F, = T, cos @ (11) 
Tl cos } 
Regptee EeLCOS Ps 
: aEp 2) 
Suppose first that the P-forces are tensile. The fundamental equations are: 
F,+T.,cos¢ =P 
Lee | (13) 
T, — T, = Q cosec $ (14) 
The difference between the tension in the wires is such as to just balance the vertical 
shearing force. 
Ax, of Axc= Telcos ¢ + Fd 
akEp ( ) 
5 
Nios A INGA Tf cos @ + Fil 
i akEp 
(Pw TR [ (Ax, + Axc) cos ¢ + Ay sin ¢] as 
y : Zsec ¢ ote Gs 
I 
ee [ (Ax + AX) cos @ — Ay sin ¢] p x 
f ‘ / sec o eee 
From equations (12) to (16): 
eae, “Pp : 
+ ee sec @ + 4Q cosec ¢ (17) 
=D, e = P sec @ — 4Q cosec @ (18) 
a+a 
F, = —*— P - Tcos¢ +30 cot (19) 
a+a 
Pe P —T cos ¢ — $0 cot ¢ (20) 
a+a 
