154 THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 
The total elongations from the initially strained conditions as well as the vertical de- 
flections are found to be in amount the same as if no initial tension had existed, and hence 
the rigidity is the same. 
Due to the initial tension the stress in the bars is reduced by an amount T.cosip but 
a 
I 
Rea 
It is seen that the tension in the wires is due to three causes: first, the initial tension 
To; second, the pull P; third, the shearing force Q. The second of these varies directly as 
the effective sectional area of the wire. The heavier the wires, the greater the share which 
they take of the longitudinal pull. 
The vertical deflection is 
the stress in the wires is increased by an amount 
Ay ata Qlcot’¢ (21) 
a 2a En 
which is the same as if no initial tension existed, but only one-half of its value in a single- 
wire panel. 
When the P-forces are compressive, the formulas given for tensile forces hold good 
when the sign of the P and F-forces are changed. 
The vertical deflection is the same as when the panel is in tension (21) and much less 
than if there had been no initial tension in the wires. Hence the rigidity under shearing is 
greatly increased. 
Since the elongation of the wires caused by initial tension is much greater than the cor- 
responding contraction in the girders, even a moderate tension in the wires is sufficient to pre- 
vent them from becoming slack within the limit of the safe working stress in the girders. 
Under great shearing, however, the counterwire may become slack, but the stresses in the 
girders and in the wires are the same as in a single-wire panel. 
Thus the strength of the frames under these conditions is not affected by the initial ten- 
sion in the wires, but the rigidity is increased. 
(miei {3} 3 
IV. A COMPOUND N-GIRDER. 
Space does not allow a complete discussion of this case, but as it forms an important 
link in the investigation of the relative merits of the bending and shearing method, it is neces- 
sary to state the main results. The design of the girder is shown in Fig. 7; it is practically all 
