A filament-wound composite drive shaft for a helicopter transmits a torque \(T\) that generates shear loading of the shaft material, as shown in Figure 7.71. The shaft is to be designed as a hollow tube with a two-ply \([+\theta /-\theta]\) laminated wall. If the outside diameter, the length, and the material density are fixed, use invariants to determine the angle \(\theta\), which should be used to maximize the shear stiffness-to-weight ratio, \(A_{66} / \mathrm{W}\), where \(A_{66}\) is the laminate shear A filament-wound composite drive shaft for a helicopter transmits a torque \(T\) that generates shear loading of the shaft material, as shown in Figure 7.71. The shaft is to be designed as a hollow tube with a two-ply \([+\theta /-\theta]\) laminated wall. If the outside diameter, the length, and the material density are fixed, use invariants to determine the angle \(\theta\), which should be used to maximize the shear stiffness-to-weight ratio, \(A_{66} / \mathrm{W}\), where \(A_{66}\) is the laminate shear stiffness and \(W\) is the shaft weight. It may be assumed that the shaft diameter, \(D\), is much greater than the wall thickness, \(t\).

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FIGURE 7.71 T t N. xy Nay Nx x T D