276_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

276_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.4.qxd 9/27/08 270 1:09 PM Page 270 CHAPTER 3 Torsion Solution 3.4-5 Hollow tube of monel metal REQUIRED POLAR MOMENT OF INERTIA BASED UPON ALLOWABLE SHEAR STRESS Tmaxr Ip tmax d2 allow 1.0 in. allow 2°/ft 12,000 psi REQUIRED 0.16667°/in. IP T max(d2/2) tallow 0.05417 in.4 POLAR MOMENT OF INERTIA BASED UPON ALLOWABLE ANGLE OF TWIST 0.002909 rad/in. From Table H-2, Appendix H: G u 9500 ksi TORQUES Tmax GIP Tmax Gu allow IP 0.04704 in.4 SHEAR STRESS GOVERNS 0.05417 in.4 Required IP IP T1 1000 lb-in. T2 500 lb-in. T4 500 lb-in. T5 T3 800 lb-in. p4 (d 32 2 d4 1 d4 3 800 lb-in. d4) 1 32IP p (1.0 in.)4 32(0.05417 in.4) p 0.4482 in.4 INTERNAL TORQUES TAB T1 1000 lb-in. TBC T1 T2 TCD T1 T2 T3 TDE T1 T2 T3 d1 500 lb-in. 0.818 in. ; (Maximum permissible inside diameter) 1300 lb-in. T4 800 lb-in. Largest torque (absolute value only): Tmax 1300 lb-in. 80 mm Problem 3.4-6 A shaft of solid circular cross section consisting of two segments is shown in the first part of the figure. The left-hand segment has diameter 80 mm and length 1.2 m; the right-hand segment has diameter 60 mm and length 0.9 m. Shown in the second part of the figure is a hollow shaft made of the same material and having the same length. The thickness t of the hollow shaft is d/10, where d is the outer diameter. Both shafts are subjected to the same torque. If the hollow shaft is to have the same torsional stiffness as the solid shaft, what should be its outer diameter d? 1.2 m 60 mm 0.9 m d 2.1 m d t=— 10 ...
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