89 the radii of gears at b and d are 175 mm and 125

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Unformatted text preview: d from: http://www.me.mtu.edu/~mavable/MoM2nd.htm 500 mm January, 2010 D C 150 mm 400 mm M. Vable Mechanics of Materials: Torsion of Shafts 5 247 Shafts on multiple axis 5.86 Two steel (G = 80 GPa) shafts AB and CD of diameters 40 mm are connected with gears as shown in Figure P5.86. The radii of gears at B and C are 250 mm and 200 mm, respectively. The bearings at E and F offer no torsional resistance to the shafts. If an input torque of Text = 1.5 kN.m is applied at D, determine (a) the maximum torsional shear stress in AB; (b) the rotation of section at D with respect to the fixed section at A. 1.5 m Text E C A F D B 1.2 m Figure P5.86 5.87 Two steel (G = 80 GPa) shafts AB and CD of diameters 40 mm are connected with gears as shown in Figure P5.86. The radii of gears at B and C are 250 mm and 200 mm, respectively. The bearings at E and F offer no torsional resistance to the shafts. The allowable shear stress in the shafts is 120 MPa. Determine the maximum torque T that can be applied at section D. 5.88 Two steel (G = 80 GPa) shafts AB and CDE of 1.5 in. diameters are connected with gears as shown in Figure P5.88. The radii of gears at B and D are 9 in. and 5 in., respectively. The bearings at F, G, and H offer no torsional resistance to the shafts. If an input torque of Text = 800 ft.lb is applied at D, determine (a) the maximum torsional shear stress in AB; (b) the rotation of section at E with respect to the fixed section at C. 5 ft Text C G A F D H E B 4 ft Figure P5.88 5.89 Two steel (G = 80 GPa) shafts AB and CD of 60 mm diameters are connected with gears as shown in Figure P5.89. The radii of gears at B and D are 175 mm and 125 mm, respectively. The bearings at E and F offer no torsional resistance to the shafts. If an input torque of Text = 2 kN.m is applied, determine (a) the maximum torsional shear stress in AB; (b) the rotation of section at D with respect to the fixed section at C. Text Figure P5.89 F D A Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm C E B 1.5 m 5.90 Two steel (G = 80 GPa) shafts AB and CD of 60 mm diameters are connected with gears as shown in Figure P5.89. The radii of gears at B and D are 175 mm and 125 mm, respectively. The bearings at E and F offer no torsional resistance to the shafts. The allowable shear stress in the shafts is 120 MPa. What is the maximum torque T that can be applied? 5.91 Two steel (G = 80 GPa) shafts AB and CD of equal diameters d are connected with gears as shown in Figure P5.89. The radii of gears at B and D are 175 mm and 125 mm, respectively. The bearings at E and F offer no torsional resistance to the shafts. The allowable shear stress in the shafts is 120 MPa and the input torque is T = 2 kN.m. Determine the minimum diameter d to the nearest millimeter. January, 2010 M. Vable Mechanics of Materials: Torsion of Shafts 5 248 Stress concentration 5.92 The allowable shear stress in the stepped shaft shown Figure P5.92 is 17 ksi. Determine the smallest fillet radius that can be used at section B. Use the stress concentration graphs given in Section C.4.3. T 2 in A Figure P5.92 2.5 in kips 1 in C B 5.93 The fillet radius in the stepped shaft shown in Figure P5.93 is 6 mm. Determine the maximum torque that can act on the rigid wheel if the allowable shear stress is 80 MPa and the modulus of rigidity is 28 GPa. Use the stress concentration graphs given in Section C.4.3. 48 mm T 60 mm Figure P5.93 5.4* 0.9 m 0.75 m 1.0 m TORSION OF THIN-WALLED TUBES The sheet metal skin on a fuselage, the wing of an aircraft, and the shell of a tall building are examples in which a body can be analyzed as a thin-walled tube. By thin wall we imply that the thickness t of the wall is smaller by a factor of at least 10 in comparison to the length b of the biggest line that can be drawn across two points on the cross section, as shown in Figure 5.50a. By a tube we imply that the length L is at least 10 times that of the cross-sectional dimension b. We assume that this thin-walled tube is subjected to only torsional moments. (a) (b) L T b > 10 t L > 10 b Zero because of Zero because thin body and xn there is no axial force or bending moment xs T (c) nx A A T tA dx A s tB b B Free surface, 0 nx Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm Figure 5.50 B B Free surface, 0 nx (a) Torsion of thin-walled tubes. (b) Deducing stress behavior in thin-walled tubes. (c) Deducing constant shear flow in thin-walled tubes. The walls of the tube are bounded by two free surfaces, and hence by the symmetry of shear stresses the shear stress in the normal direction τxn must go to zero on these bounding surfaces, as shown in Figure 5.50b.This does not imply that τxn is zero in the interior. However, because the walls are thin, we approximate τxn as zero everywhere. The normal stress σxx would be equivalent to an internal axial force or an internal bending moment. Since there is no external axial force or bending moment, we approximate the value of σxx as zero. Figure 5.50b...
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