156 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
We assume first that the ship is subject to pure shearing, producing a system of inter- 
nal reactions and certain strains and stresses throughout the structure, and to the ship in this 
fictitious condition we apply the bending moments which would actually be called forth by 
the shearing. Each frame space may be regarded as typical of the whole structure and may 
be dealt with separately. 
We consider a section of an airship enclosed between two frames (1) and (2) and 
assume first that frame (1) is held fixed in a vertical position, while (2) is free to deflect 
(see Figs. 9 and 10). 
A. The Effects of Shearing. 
A system of vertical forces YQ acts on frame (2) tending to deflect it downwards 
relative to (1). We assume that no external forces act between (2) and (1), but that a 
similar system of forces YQ acts upwards at frame (1), constituting with that on frame 
(2) what may be called a shearing couple. The shear wires come in tension, the counterwires 
become slack, and the lower girder in each panel comes under compression. The result is 
that the wire and the lower girder in each panel together form, as it were, a cantilever loaded 
at the extreme end with a Q-force. The wire exerts a pull at a joint in frame (1), having 
a horizontal component which is exactly equal to the horizontal thrust exerted by the girder 
at the joint next below. Together the two forces constitute a couple, which balance the mo- 
ment Q/ and which, when combined with other similar couples, generally of different mag- 
nitude, produced by the cantilevers in the other panels, form an aggregate bending moment 
AM, acting on frame (1). Hence 
AM=ZQ/ (22) 
where / is the frame spacing. 
We shall now show how to find the stresses in the girders and the wires and further, 
that under the special conditions of symmetry existing in this case, the total reactions at the 
joints in (1) will have horizontal components P, which together constitute a system of forces 
conforming to the theory of bending, 7. ¢., they are proportional to the distances of the joints 
from the neutral axis. 
We use the same notation as in previous chapters and add suffixes as necessary, con- 
forming to Figs. 9 and 10. 
In any one panel we have the tension in the wire, 
_ Ay sin ¢ sin 6 — Ax cos 
f l sec o Bu A. (23) 
where @ is the angle which the panel forms with the horizon. This equation is obtained 
from that for the elongation of the wire given under Section III, Case 2, for pure shearing 
(just previous to equation (4) ), bearing in mind that a vertical deflection Ay causes a down- 
ward deflection Ay sin @ in the plane of the panel. ; 
The compressive force acting on the lower girder of the panel is: 
F=Tcos¢ (24) 
