THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 161 
linear dimensions of the transverse sections. The shearing deflections, on the other hand, 
are extraordinarily great, and it is in this respect that an airship structure differs most radi- 
cally in behavior from all other girders, including the hull of ordinary ships. It might be 
argued that the shearing deflections cause a distortion of the sections out of their plane, thus 
invalidating the theory. It appears, however, that we are justified in considering the strains 
due to shearing quite independent of those due to bending and in such case we may apply 
the bending theory, not only to the ship in its original unstrained condition, but also when 
it is distorted by pure shearing. It may then, in fact, be regarded as a slightly curved girder. 
We assume, then, that due to pure shearing the transverse frames are displaced ver- 
tically relative to each other, transforming the fair contour lines of the profile to more or less 
wavy lines. To every hump in the upper contour corresponds an upward hollow of the same 
height in the lower contour. The longitudinals, in order to accommodate themselves to 
these deflections, must all bend together; deflecting upwards or downwards by the same 
amount in each section, remaining parallel to one another in the parallel middle body. On 
account of their slenderness, the longitudinals can easily bend to the required gentle curves 
without suffering any appreciable general strain. For instance, a deflection of about 3 
feet amidships in one of the main longitudinals of L-49, supposed to be loaded uniformly and 
supported at the ends, would cause a stress in the upper channel of the girder of only 
about one-quarter of a ton per square inch. Hence it appears that we are justified in dis- 
regarding the general strains in the longitudinals due to the shearing deflection, and that 
we may consider the ship in that condition as a slightly curved beam to which, as stated 
above, the theory is applicable. The strains due to bending are simply superposed on those 
due to shearing. 
It remains, however, to consider the secondary strains created in the longitudinals at 
the joints with the transverse frames, because at these points there is a certain encastrement, 
which will offer some resistance to the bending of the longitudinals relative to the plane 
of the transverse frames. The result will be a bending moment at each frame, a local deflec- 
tion of the frames out of their plane combinedwith twisting and bending, and instead of the 
continuous curvature of the longitudinals over the joints there will be a stepwise curvature with 
points of inflection between the frames (see Fig. 12). The local bending and shearing strains 
so produced will cause additional stresses and a certain resistance to the general shearing de- 
flections of the ship and should be taken into account in calculating the total stresses, but they 
do not affect the applicability of the bending theory. 
FIGs Wee 
The third assumption enumerated above is generally considered to be justified in all 
except very broad beams. Since airships are of nearly circular section, the assumption may 
here be accepted. 
On the whole, then, we conclude that the bending method can be safely applied with a 
fair degree of approximation to airships as now usually constructed. 
The most serious deviation from uniformity of strength in airships as commonly con- 
structed seems to be the reduction in the size of the wires in the upper and lower part of the 
hull. This causes an irregular distribution of the stresses and prevents certain girders from 
