6-26. The loading on a control torque tube for an aileron of an airplane may be idealized by a uniformly varying torque Tx = kx in-Ib/in, where k is a constant(see the figure). Determine the angle of twist of the free end. Assume IpG to be constant. Fig. P6-26

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A steel stepped shaft ABCD fixed at A is subjected to three torques at points B, C and D, with magnitudes T₁ = 40 kip-in, T₂ = 50 kip-in and Ts= 30 kip-in and directions as shown in Figure 1.1. The segments AB and BC are solid with diameters dx = 3 in and dec = 2 in respectively, while segment CD is hollow with an outer diameter dan 1.5 in and a wall thickness of 0.25 in. The shear modulus of elasticity is equal to G=11.6x10³ ksl. T₁ T₂ 4 = 20 in A B L₂ = 20 in Figure 1.1 a) Draw the torsion moment diagram for the shaft and calculate how long should segment CD be so that the angle of twist between points B and D is equal to zero. T₁ 4₂-25 in b) If Ts is dropped, a fixed support is added at point D (as shown in Figure 1.2) and the length of segment CD is equal to 15 in, find the support reactions at points A and D and the maximum shear stress developed in segment BC. The magnitudes of the torques at points B and Care the same as in part a). B C L₂= 25 in T₂ * Figure 1.2 Hollow C Hollow…