THE LONGITUDINAL STRENGTH OF RIGID AIRSHIPS. 147 
Ill. RECTANGULAR PANELS. 
The panels here considered consist of two vertical bars, in some cases called the posts 
or frames, 4,C, and A.C, denoted by (1) and (2), see Fig. 2, and two horizontal bars, 
marked a and c, sometimes referred to as the longitudinals or girders. The four corners of 
the panel are called the joints, which are supposed to offer no resistance to distortion. There 
may be one or two diagonal wires marked (1) and (2). The frames are assumed to be abso- 
lutely rigid, but the girders and the wires are elastic. When not otherwise specified, the 
wires are supposed to be initially just taut before any forces are applied to the panel. Frame 
(1) is held fixed and the effects of gravity are disregarded. The horizontal forces acting at 
the joints are denoted by P, the vertical or shearing forces by Q, the total tension in the 
wires by 7, and the end-forces acting on the girders by F, all with suffixes as required. The 
girders are of duralumin, the wires of steel. 
ee ie 
rig. 2. 
Ey = Modulus of elasticity of the girders (4,700 ts. per square inch). 
Ew = Modulus of elasticity of the wires (13,500 ts. per square inch). 
a = Sectional area of girders. 
ao = Sectional area of wires. 
! = Length of girders. 
h = Height of frames. 
@ = Angle which the wires form with the girders, tan ¢ = 
Case 1. Tensile P-forces act on the panel. The fictitious bar—Referring to Fig. 2, 
equal and parallel P-forces act at J. and C,. The tendency of A,C, to move upwards is 
prevented by a fixed support at Aj, against which the panel presses with a force Q, creating 
an equal and downward reaction. The bars a and c elongate; the wire is stretched and put 
in tension. We have 
F, = P, ee ee COSNOr— lar 
The elongation of the bar a is: 
