162 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
doing their full share in accordance with the theory of bending. Although there will always 
be a tendency towards a redistribution of the forces conforming to that theory, this may not 
be fully accomplished due to the relatively small number of frame spaces in an airship. The 
discrepancy may be discovered by comparing the horizontal shear at any girder as deter- 
mined by the bending method with that actually produced by the tension of the shear wires. 
VII. MODE OF CALCULATION. 
We shall now show more in detail how to use the bending method. The fundamental 
equation, (33), applies to sections at the frames through the center of the joints, where, 
under certain assumptions, the stresses may be expected to be the same as in an ordinary 
plated structure of the same strength. Between the frames the stress in the longitudinals 
may be affected by the tension of the wires if the counterwires are slack, and does not then 
follow the law of proportionality to the distance from the neutral axis. The bending for- 
mula, therefore, cannot under all circumstances give the stresses in the strength members 
existing between the frames, but having determined the stresses at the joints, we can cal- 
culate the horizontal reactions, here called the P-forces, at these points and then, by resolving 
along longitudinals and wires, the stresses in these members can be found. 
pee 
a 
Seo, 
FA as 
a 
FIG. 13- 
Before applying formula (33) it is necessary to determine the effective area of the 
longitudinal strength members at the joints. The lines of force flow along longitudinals and 
diagonal wires through the joints, and we assume that these latter are so constructed that 
their transverse sectional area is equal to the sum of the areas of the longitudinal members 
meeting at the joint. Since we need consider only the P-forces, we can replace the diagonal 
wires by fictitious bars of duralumin, the area of which is denoted by a as explained in 
Section III, Case 1. Suppose that a longitudinal passes through a joint and that a shear 
wire is attached to the joint on either side as in Fig. 13 (a), then the longitudinal strain in 
