THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 155 
web and is loaded in its own plane. It is assumed that lateral bending is prevented without 
affecting the stresses. According to the shear method there should be no longitudinal forces 
acting at the joints of the two middle girders, but between the joint compressive forces are 
produced locally by the tension in the wires. The upper girder as a whole would be in ten- 
sion, the lower in compression. Clearly such a girder, under the loading indicated, would 
bend, and the middle girders would take actually their share of the general strains. 
If four girders such as that in Fig. 7 are combined to form a box-girder of square 
section as indicated in Fig. 8, and if each of the side girders are put under the same load 
as in Fig. 7, it is found according to the shear method that only the four corner girders 
should be active, none of the other girders would assist in carrying the load, except in so far 
as they would act as local struts for the wires. Again, this cannot be correct. If the top and 
bottom girders are provided with a system of double diagonal wires set up with initial ten- 
sion, the middle girders will evidently form an integral part of the flanges of the box girder 
and must come under a general longitudinal strain in bending. In fact, the failure of the 
shear method is brought out as soon as it is applied to the horizontal flanges of a structure, 
where horizontal shearing transmits longitudinal strains from one girder to the other. 
It was attempted for the purpose of comparison to determine the internal reactions in 
the compound N-girder in an exact manner by the Principle of Least Work as well as by the 
Method of Deflections, but these methods, even in this simple case, led to a great number of 
cumbrous equations, involving determinants of such formidable proportions that a solution 
in this way seemed impracticable. 
V. THE EFFECTS OF SHEARING AND BENDING IN THE STRUCTURE OF AN AIRSHIP. 
We consider here an airship of regular polygonal section which is entirely symmetrical 
about a horizontal plane through the axis and in general construction similar to L-49. The 
wires are supposed to be initially just taut. 
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It is proposed to distinguish sharply between the effects of shearing and bending, and 
it is assumed that the stresses and strains which they produce can be superposed on one 
another. Shearing may exist in vertical, horizontal, or other planes, but for the present we 
shall deal only with shearing forces directed vertically in transverse planes, and to fix our 
ideas we consider in particular the shearing and bending actions in the forebody of a ship 
in hogging condition. 
