MIT 2 001 - BeerMOM_ISM_C03 (1) (186 pages)

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BeerMOM_ISM_C03 (1)



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BeerMOM_ISM_C03 (1)

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Pages:
186
School:
Massachusetts Institute of Technology
Course:
2 001 - Mechanics & Materials I

Unformatted text preview:

CHAPTER 3 18 mm PROBLEM 3 1 T Determine the torque T that causes a maximum shearing stress of 70 MPa in the steel cylindrical shaft shown SOLUTION max T Tc J c4 J 2 2 c3 max 0 018 m 3 70 106 Pa 2 641 26 N m T 641 N m PROPRIETARY MATERIAL Copyright 2015 McGraw Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied scanned duplicated forwarded distributed or posted on a website in whole or part 261 18 mm PROBLEM 3 2 T For the cylindrical shaft shown determine the maximum shearing stress caused by a torque of magnitude T 800 N m SOLUTION Tc J c4 2 J 2T c3 2 800 N m 0 018 m 3 max max 87 328 106 Pa max 87 3 MPa PROPRIETARY MATERIAL Copyright 2015 McGraw Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied scanned duplicated forwarded distributed or posted on a website in whole or part 262 T 30 mm PROBLEM 3 3 45 mm a Determine the torque T that causes a maximum shearing stress of 45 MPa in the hollow cylindrical steel shaft shown b Determine the maximum shearing stress caused by the same torque T in a solid cylindrical shaft of the same cross sectional area 2 4 m SOLUTION a Given shaft J 2 c 4 2 c14 454 304 5 1689 106 mm 4 5 1689 10 6 m 4 2 Tc J T J c J T 5 1689 10 6 45 106 5 1689 103 N m 45 10 3 T 5 17 kN m b Solid shaft of same area A c22 c12 452 302 3 5343 103 mm 2 c 2 A or c J 2 c4 A 33 541 mm 2T Tc J c3 2 5 1689 103 87 2 106 Pa 0 033541 3 87 2 MPa PROPRIETARY MATERIAL Copyright 2015 McGraw Hill Education This is proprietary material solely for authorized instructor use Not authorized for sale or distribution in any manner This document may not be copied scanned duplicated forwarded distributed or posted on a website in whole or part 263 PROBLEM 3 4 a Determine the maximum shearing stress caused by a 40 kip in torque T in the 3 in diameter solid



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