THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 159 
B. The Effects of Bending. 
Suppose next that a pure bending moment, M,., is applied to frame (2) and that its 
effects are superposed on those due to the shearing force YQ. It is assumed that the P- 
forces constituting M, are applied in accordance with the theory of bending, and we have 
then to study their transmission through the section (2)-(1). 
All the panels between (1) and (2) take the same downward deflection under the action 
of DQ, but when the P-forces are applied, the panels will tend to lift in the upper part of the 
ship and to drop in the lower part. This tendency creates reactions in frame (2), which comes 
under tension, but since the upward forces are equal to the downward forces, the panels 
will be unable to deflect either up or down. Under these circumstances, as given by equation 
(9), the tension in the wires above the neutral axis will be increased beyond that existing 
under pure shearing by the amount 7’, while that in the wires below the neutral axis will be 
reduced below that standard by the same amount, but the total sum of the vertical compo- 
nents of the tensions will be equal to the sum of the shearing forces. 
YT sin ¢ sin 0 = ZO. 
So also F is increased or reduced in each panel by an amount F’ as compared with its value 
due to Q. 
Hence (see Section III, Case 3) a force T’ is transmitted to the wire meeting at any 
joint on frame (2): 
Qa 
a P seco 
ata 
while a force: 
F =—* 
a+a 
will be directed along the girder. 
These forces superpose themselves on those due to shearing and, using (29”) and (30), 
we obtain: 
T = Losec $ sin 6 =Q ie es oar 
2 sin’ 0 a+a Ga) 
: 32 
pe cot @ sind 2Q | ZibID 
> sin? 6 ata 
It is believed that the facts expressed by these equations have not before been explained 
or pointed out, but they are evidently of great importance for the full understanding of the 
reactions in complex wired structures such as airships. The principal facts are that shear 
wires, when in tension, act as elastic struts capable of transmitting both tension and com- 
pression; that their tension, when the panel is under shearing, is not always determined ex- 
clusively by the shearing force; and that, even when so determined, the tension is virtually 
in part due to the direct pull or thrust acting on the longitudinals. Hence the shear wires, 
except when they are slack, should be considered as an integral part of the longitudinal 
strength members of the hull. 
