Brass Steel shaft di = 70 mm dz = 90 mm sleeve T T A -1.0 m→ IC - 20 m. -늘-20m Brass Steel. shaft sleeve d2 d2

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…

Note: J3 = J2 46 mm G3 = G2 4.93×10° mm (1) 16 kN-m 50 GPa (2) C2 = 34 mm (3) J2 2.10x10° mm* B 900 mm 35 GPa 900 mm A composite torsion member consists of a tubular shell (1) bonded to length AB of a continuous solid T1 kN-m shaft that extends from A to C, which is labeled T2 kN-m (2) and (3). A concentrated torque T is applied to MPa free end C of the shaft in the direction shown. MPa Determine the internal torques and shear stresses PC rad in shell (1) and core (2) (i.e., between A and B). 1st 2nd 3rd Enter Also, determine the rotation angle at end C. attempt II || || I| || || Shaft properties

F3.A shaft is composed of two 6-in. diameter sections coupled together (see figure below). Part AB is bronze and part BC is steel. A torque is applied at the free end which causes a maximum shear stress in the bronze shaft of 10,000 psi. Find the angle of twist of the free end. Assume the modulus of rigidity of bronze is 6 (106) psi and that of steel is 12(106) psi. Bronze Dia. = 6 in. A 3' Steel B Match each item to a choice: Angle of twist T