0.8 bar to psi

CCHHAAPPTTEERR33
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A student using this manual is using it without permission. PROBLEM 3.1 (a) Determine the maximum shearing stress caused by a 4.6-kN ⋅ m torque T in the 76-mm-diameter 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 (b) Solve part a, assuming that the solid shaft has been replaced by a hollow shaft of the same outer diameter and of 24-mm inner diameter. SOLUTION (a) Solid shaft:446436638 mm0.038 m2(0.038)3.2753 10 m22(4.6 10 )(0.038)53.4 10 Pa3.2753 10dcJcTcJππτ−−====== ××=== ××53.4 MPaτ=(b) Hollow shaft:()21444464213660.038 m2112 mm0.012 m2(0.0380.012 )3.2428 10 m22(4.6 10 )(0.038)53.9 10 Pa3.2428 10oidccdJccTcJππτ−−======−=− = ××=== ××53.9 MPaτ=
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A student using this manual is using it without permission. PROBLEM 3.2 (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. SOLUTION (a) Given shaft:()442144646466332(4530 )5.1689 10 mm5.1689 10 m2(5.1689 10 )(45 10 )5.1689 10 N m45 10JccJTcJTJcTππττ−−−=−=−=× =×==××==×⋅×5.17 kN mT=⋅(b) Solid shaft of same area:()222 23 221243363(4530 )3.5343 10 mmor33.541 mm2,2(2)(5.1689 10 )87.2 10 Pa(0.033541)AccAcA cTcTJcJcπππππτπτπ=−= −= ×======×==×87.2 MPaτ=
PROPRIETARY MATERIAL. © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed, reproduced, or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limited distribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. A student using this manual is using it without permission. PROBLEM 3.3 Knowing that 1.2 in.,d= determine the torque T that causes a maximum shearing stress of 7.5 ksi in the hollow shaft shown. SOLUTION 2211(1.6)0.8 in.22cd===0.8 in.c=()11444442111(1.2)0.6 in.22(0.80.6 )0.4398 in22cdJccππ====−= −=maxmax(0.4398)(7.5)0.8TcJJTcττ===4.12 kip inT=⋅