Question

SLOID MECHANICS

Exercise 1 (chapter 5): 5-34. The copper pipe has an outer diameter of 623 mm and an innerdiameter of 575mmIratis tightly secured to the wall at Cand a uniformly distributed torque is applied to it as shown determine the shear stress developed at points and B. These points lie on the pipe's outer surface. Sketch the shear stress on volume elements located and B Show clearly all calculations.

Answer 1

Given Dera for shaft Outer voiameter 20 = 625 mm m = O-062 0.0625 m Inner Hiqmeren is 57.5 mm = 0.0575 m olm * 0.225m t 0.3m # $ 6 we and coleulate In order to calculate shear stress at need to cut at Gerrian at (A) and (③). value of torsional resistance value. Draw FBD of buy curring secrion at ① k 0.3m o 25 New The uniformey vistributed torque get replace by a single torque which is = 6258003 = 187.5 Naam and aut at 0.3 = 0.15 m from 6 7.snom TA = 187-5 arm و او با | خورد use torsional ean / 2 - Ip - Polar moment of inersin . [*-0"] e = distance from W.A.

TA TRAN TA = 18705 I [0.06256_0_057547 0-0625 2 To = 1307.9 x100 Naiz I TA = 13.79 MPa ] Ami for point B cut a secrion at B 625 Nama m k 0.525m Equivalent torque - 625 X0-525 = 328.125 Nam which act at 0.525 0.2625m from (B) TB Q - 328.125 N-m Ko.2625 To=328.125 Nam Torsional can TB = TB a to use Ipz To a 3280125 1 (0.0625" 005759] * -oer 32 a To = 24.13 X10* N/m2 TE = 24.135 MBI Ant = 24.135 M UDAN