152 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
area a. Just to the left of the center of the joint Cy, we have a total sectional area equal 
to @ + a through which flows a force P. One part 4 P flows along the c-bar and 
+a 
another _“ — P flows along the fictitious bar which represents the wire, and this is quite 
a+a 
irrespective of the Q force (so long as it is great enough to secure the tautness of the wire 
when the P-forces are compressive). The average stress in the joint C just to the left of 
the center is 
If the panel is connected to other similar panels, so that a shear wire 
a+a 
is running downwards to the right of the joint, we shall reckon the effective area to be 
a + a to the right of the joint and, hence, also at the center (see Fig. 5). 
Case 3.—This study leads to an important case which occurs in airships, where the panels, 
which are supposed to deflect downwards an amount Ay due to the shear force DQ acting 
on the entire frame, are prevented by adjacent panels from adjusting themselves to the action 
of the P-forces. Under these conditions internal reactions will be created in the transverse 
frames, which reactions relative to the panel under consideration may be regarded as ex- 
ternal forces. 
The reaction Q' at any panel is of such magnitude as just to counterbalance the action 
of P, which is a tendency to raise or lower the panel. We know from (7) that: 
C= =P tani 
a+a 
and from (8) that it creates in the wire a force, tensile or compressive: 
Tre eee: 
Qa 
If Q is the external shearing force, transmitted from the panel next above, the total tension 
in the wire will be: 
iP + —"_ p 
Q cosec ¢ ates sec @ (9) 
Hence the tension in the wires will not, as commonly assumed, be that determined by the 
shearing force alone, but yet the sum of all the vertical components of the 7-forces in the 
frame space will be equal to YQ. In other words, the internal reactions in the transverse 
frame must neutralize each other completely. 
In the c-girder the combined effect of P and Q is, under these circumstances : 
HO cole = (z0) 
Case 4. Initial tension in the wires——Only panels with two diagonal wires need to be 
considered, since initial tension cannot exist in a single wire when the panel is held at one 
frame only. 
We go at once to the general case when tensile or compressive P-forces act in conjunc- 
