168 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
shear happens to give stresses which conform to the theory of bending (see equation (31) ). 
The faith in the shear method was confirmed by calculations and experiments, which appear 
to be mostly carried out on idealized structures, where regularity in form and uniformity in 
the strength of girders and wires were observed. Thus the shear method came to be gen- 
erally considered equivalent to the bending method and was by some even considered su- 
perior to it. The correspondence between the results obtained by the two methods under 
those particular circumstances was misinterpreted, being understood to mean that the bend- 
ing method could be applied only to girders of such ideal construction,* while the shear method 
applied to girders of any construction. It is easy to show that the correct interpretation is 
just the opposite. While the bending method gives in general a good approximation, the 
shear method is incomplete and faulty except in one particular, ideal case. 
In Section IV brief reference was made to a “compound N-girder” and it was explained 
how the shear method failed in that case, especially if applied to a box girder with flat top 
and bottom flanges composed of such N-girders. 
We can readily see that we must come to the same conclusion if we apply the shear 
method to an airship as given in Fig. 10, if in that design we depart from the regular polyg- 
onal section. Suppose, for instance, that the section in Fig. 10 is modified by the inser- 
tion of a flat top and a flat bottom, each consisting of several girders as indicated in Fig. 
15. We obtain then an oval section with horizonal major axis, emphasizing the flange 
strength relative to the web strength. According to the shear method the tension in the 
wires in the flat parts and the end load on the girders marked A. and M. in Fig. 15, should 
be zero, the reason being that if shearing alone is considered, T and F are proportional to 
the sine of the angle which the panels form with the horizon [see (29”) and (30)]. Actu- 
ally, if the horizontal panels are provided with shear and counterwires, set up with an 
initial tension, as they would be in an airship, the longitudinals as well as the wires in those 
parts will act as flanges of the ship girder. These members cannot escape the elastic bend- 
ing strains thrown upon them through horizontal shear, any more than the strength deck and 
bottom plating in the analogous case of an ordinary ship. 
A AS A, A, 
M, Mo My My, 
FIG. MWe. 
If the shear method is applied to an airship of elliptical polygonal section, as shown in 
Fig. 16,+ we should, according to the shear method, get a stress diagram throughout the 
ship such as shown in that figure, which cannot be correct. 
The fundamental explanation of this discrepancy between the stress diagrams obtained 
by the shear method and those obtained by the bending method in such cases is. the follow- 
*Aeronautics, Feb. 12, 1920. 
+Mr, E, H. Lewitt: Aeronautics, London, Feb. 12, 1920. The Distribution of Bending Stresses in a “Rigid 
Airship.” 
