164 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
B 
where ~ is determined by (34), but since ~— = YCE we find ac= EE iy, 
G VG Me 
Similarly 
ag = 2Z a 
Vce 
or, in general, for a wire between the longitudinals and n + 1: 
— Yn (n +1) ( 
a, = ELD g 35) 
Yn ° 
77] 
where a =a, cos? ¢. 
D 
Hence, by multiplying « with the y-ordinate of a point midway between the joint which 
the wire connects and dividing by the y-ordinate of the joint considered we obtain the equiv- 
alent effective area for the wire at that joint. The rule evidently applies to counterwires 
and shear wires alike and whether they are in compression or tension. Where a girder is 
located in the neutral axis, (35) gives a@n= o, but since the y-ordinate and the P-forces 
are zero in this case, the moment of inertia and the distribution of the forces are not thereby 
affected. In order to determine the exact location of the neutral axis, some tentative figur- 
ing may be necessary. 
It is recommended to apply this method of evaluating the effective area a whenever 
the counterwires are slack. If all wires are taut, the fictitious bars may be placed midway 
between the longitudinals as explained above. 
We are now able to compute the moment of inertia at any frame section and can then 
from (33) with the given bending moment find the stresses and the P-forces at the various 
joints. After that the stresses in each one of the members adjacent to the frame under 
consideration can be determined by resolving the P-forces along these members and finally 
the forces due to shearing are superposed. 
In order to illustrate the method we shall apply it to a frame space of an airship and 
choose for the sake of simplicity that of the symmetrical ship referred to above and given in 
Figs. 9 and 10, assuming that a bending moment M, and a shearing force YO are applied 
to frame (2). The calculation is typical for any frame space that we wish to consider. 
It is supposed that all the wires are set up with an initial tension 7. and that no coun- 
terwires become slack. Hence the effective area of each joint is @ + 2a, but the correction 
according to (35) is here applied to @ at each joint in order to illustrate the method. 
The ordinates of the various joints are found by multiplying R, the radius of the ship, 
with the sine of angle y, which the radius to any longitudinal forms with the horizon: 
a= Kh, Yo=vr— KR sin 60) = 7866 R 
Mp Wp SIR Stal Zo) | OO I Sea = © 
The ordinates of the middle of the wires are: 
Yac= —Veu = -933 R, Yec= -—Irx = .683 R, Vor SWE SS 5255) IR 
From (35): 
Og = dy = 240% = 933.4. 
Va 
