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a 40 kip in torque T in the 3 in diameter solid aluminum shaft shown b Solve part a assuming that the solid shaft has been replaced by a hollow shaft of the same outer diameter and of 1 in inner diameter 4 ft 3 in T SOLUTION a Tc J 40 kip in 1 5 in 4 1 5 in 2 7 5451 ksi 7 55 ksi b Tc J 40 kip in 1 5 in 1 5 in 4 0 5 in 4 2 7 6394 ksi 7 64 ksi 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 264 PROBLEM 3 5 T 3 in a For the 3 in diameter solid cylinder and loading shown determine the maximum shearing stress b Determine the inner diameter of the 4 in diameter hollow cylinder shown for which the maximum stress is the same as in part a T 4 in T 40 kip in T a T 40 kip in b SOLUTION a c Solid shaft c4 2 Tc J 2T c3 2 40 kip in 1 5 in 3 J max 1 1 d 3 0 in 1 5 in 2 2 7 5451 ksi max 7 55 ksi b co Hollow shaft J co 1 1 d 4 0 in 2 0 in 2 2 2 c 4 o ci4 co4 ci4 co T max 2Tco max 2 0 in 4 2 40 kip in 2 0 in 7 5451 ksi 9 2500 in 4 ci 1 74395 in and di 2ci 3 4879 in di 3 49 in 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 265 PROBLEM 3 6 60 mm 30 mm D 200 mm T 3 kN m A torque T 3 kN m is applied to the solid bronze cylinder shown Determine a the maximum shearing stress b the shearing stress at point D which lies on a 15 mm radius circle drawn on the end of the cylinder c the percent of the torque carried by the portion of the cylinder within the 15 mm radius SOLUTION a c J 1 d 30 mm 30 10 3 m 2 c4 2 2 30 10 3 4 1 27235 10 6 m 4 T 3 kN 3 103 N m Tc 3 103 30 10 3 70 736 106 Pa J 1 27235 10 6 m 70 7 MPa b D 15 mm 15 10 3 m D c D TD D c 15 10 3 70 736 10 6 30 10 3 TD D JD 2 TD J D D D 2 D 35 4 MPa D3 D 15 10 3 3 35 368 106 187 5 N m TD 187 5 100 100 6 25 T 3 103 6 25 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 266 PROBLEM 3 7 C B 3 in 8 in t5 1 4 in The solid spindle AB is made of a steel with an allowable shearing stress of 12 ksi and sleeve CD is made of a brass with an allowable shearing stress of 7 ksi Determine a the largest torque T that can be applied at A if the allowable shearing stress is not to be exceeded in sleeve CD b the corresponding required value of the diameter d s of spindle AB D ds 4 in A T SOLUTION a Analysis of sleeve CD 1 1 d o 3 1 5 in 2 2 c1 c2 t 1 5 0 25 1 25 in c2 J T c 2 4 2 c14 2 1 54 1 254 4 1172 in 4 J 4 1172 7 103 19 21 103 lb in c2 1 5 T 19 21 kip in b Analysis of solid spindle AB Tc J J T 19 21 103 c3 1 601 in 3 3 c 2 12 10 c 3 2 1 601 1 006 in d s 2c d 2 01 in 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 …


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