THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 151 
The corresponding tension in the wire is 
Qa 
a oa 
T’ =(Q' cosec ¢ = P sec d (8) 
but this is precisely the tension produced in the wire in Case 1. While, therefore, the total 
tension in the wire is necessarily equal to Q cosec ¢, it must not be overlooked that, if 
P-forces exist, part of that tension is virtually due to these forces, which carry a corre- 
sponding part of the shearing load. . 
The end load on the c-girder, which under pure shear would be Q cot @, is now: 
ff; = P= O'cot & = ae P= (OO) CES 
showing that also here the load is made up of two parts, one due to the P-force, which is dis- 
tributed between the wire and the girder, as if there was no deflection, and another due to the 
difference in shear between Q and Q’. If only Q’ had been acting, that is, Q = Q’, we 
would get 
joe ue a P (8’) 
Tp tS (a 
If the P-forces acting on A, and C, had been unequal, we should obtain the same result 
as far as the c-girder is concerned. 
An investigation of the case when the P-forces are compressive gives similar results. 
The shear force acting alone gives a certain deflection Ay), but the P-forces now increase 
that deflection and at the same time compress the girders. The tension in the wire, however, 
remains unaltered, and is less than it would be for that deflection if produced by the Q-force 
acting alone. The effect of the P-forces is now the same as if an additional downwards 
FIG. 5. 
shear force Q’ were acting, and T as well as F may be regarded as virtually consisting of two 
parts, one of which is entirely due to P, the other entirely due to Q. This is in accordance 
with the principle of the superposition of small strains and deflections. 
Hence, whether the P-forces are tensile or compressive, we may regard the wire as a 
channel along which flow stresses, the magnitude of which are proportional to the sectional 
