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T.L Tr4 %3D J = " (r* – rf) (Tubular shaft) Tr (Solid shaft) G.J 3. The shaft in the figure below consists of 75 mm diameter bronze segment that is rigidly joint to 50 diameter steel segment. The ends of the shaft are attached to rigid supports (fixed supports). Calculate the absolute maximum shear stress developed in each segment when the torque T= 5.1 kN-m is applied (a = 2 m and b = 1.5 m). Use G = 35 GPa for bronze, and G = 75 GPa for steel. (21 pts) 75 mm 50 mm Bronze Steel

3.8-5 A stepped shaft ACB having solid circular cross sec- tions with two different diameters is held against rotation at the ends (see figure). (a) If the allowable shear stress in the shaft is 42 MPa, what is the maximum torque (Tmax that may be applied at section C? [Hint: Use Eqs. (3-49a and b) of Example 3-9 to obtain the reactive torques.] (b) Find (7)max if the maximum angle of twist is limited to 0.55°. Let G = 73 GPa. 38 mm 19 mm B 150 mm- PROB 3.8-5 To 380 mm I

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A thin tube of uniform thickness 5 mm and square cross section, shown below, is subject to a torque of 1500 N·m. The shear modulus of the material is 80 GPa. What will be the angle of twist per length (in unit: rad/m)? 50 mm 50 mm

A shaft ABCD is supported by a clamp at point A and is subjected to point torques at B, C and D, as shown in the figure. The shaft has variable cross-section and is solid in segments AB and CD and hollow in segment BC. The lengths and diameters of each segment are shown in the figure. Assume that the deformation is linear elastic and take the shear modulus of elasticity G = 12.1 × 10° psi. a) Using method of sections, plot the torsion moment diagram. b) Find the angle of twist for the free end (point D) with respect to the fixed support at A, QAD and the angle of twist for point C with respect to the fixed support at A, QCA. Find both angles in degrees. d₁ = 4 in d20 3.5 in, d2=2.5 in d3 = 3.0 in 25 kip-in 20 kip-in 10 kip-in A 20 in B с D ++ 25 in 30 in

A circular steel tube of length L = 1.1 m is loaded in torsion by torques T (see figure). T T r2 (a) If the inner radius of the tube is r, = 51 mm and the measured angle of twist between the ends is 0.5°, what is the shear strain y, (in radians) at the inner surface? (Enter the magnitude.) rad (b) If the maximum allowable shear strain is 0.00043 rad and the angle of twist is to be kept at 0.45° by adjusting the torque T, what is the maximum permissible outer radius (r,)may (in mm)? mm

A circular hollow shaft is subjected to a torsional moment T = 30 kNm and a compressiveload P = 80 kN, as shown. The shaft has an outer diameter D = 120 mmand inner diameter d = 100 mm. Points A and B are on the surface of the shaft. (a)Calculate the direct and shear stress at point A. (b)Calculate the maximum,minimum and oriention of the max and min principal stresses at point A. (c)Calculate the maximum in-plane shear stress at point A and the orientation.

. Compute the shearing stress if a torque T = 200 N-m is applied to a thin-walled tube having a cross section in the shape of a regular hexagon with constant wall thickness 2 mm and side length b = 100 mm (see figure). (