150 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
The elongation of the wire is: 
Ay, sin @ + Ax, cos ¢ = LT lsecp 
Qo 1 Dery 
BR Aryg= Ql cosec’? @ sec o A Qicot*@ _a+a Qcot’d¢ @ 
Cin, Js ak p a ak yp 
When now the P-forces are applied in addition to the shearing, the panel takes up a 
new position of equilibrium. The corner Cy goes to C,’, where the vertical deflection is 
only Ay and the horizontal deflection is Awe. It is here assumed that the elongation of the 
girders due to P is greater than the contraction due to 7, as would usually be the case in 
an airship when the P-forces are at all considerable. The tension in the wire is to the first 
order the same as before P was applied, and hence we have again: 
T = Q cosec } 
Further : 1, = 12 
F,+ Tcos @¢ = P 5) 
Dee l= OCotd 
IPI (P-Q cot ¢) 1 
A = SS pee ae ee 
ef akp ae akEp 
Ay sin @¢ + Axc cos ¢ = LYSE 
Gi [Dry 
Najeeaee Qlcote  Plcot¢ Nig, ye ECOL. 
4 a aEp aEp aEp (6) 
It is seen that Ay consists of two parts, one of which depends entirely on Q and is the 
same as if Q were acting alone, while the other depends only on P and represents the amount 
which the end of the panel is raised by the action of that force. 
The effect of the P-force is the same as if an upwards Q-force Q’ existed, counteract- 
ing and carrying part of the original force Q. If, then, the P-forces had existed in conjunc- 
tion with Q' only, there would have been no distortion and hence Q’ is the force necessary to 
balance the upwards tendency, the same as the reaction Q in Case 1. 
The deflection produced by Q’ acting alone is according to (4) : 
OAL ce (OCU CIS GO 
a aEp 
and equating this to the vertical deflection recovered by the P-forces according to (6), we get: 
ata Qlcot’'d _ Pl cot 
a aEp akp 
from which: 
a 
— ID 
Ores Soe eke (7) 
