lecture 10 - Stanford University

1 10/18/00ME111 lecture 1010/18/00ME111 lecture 101ME111 Instructor: Peter PinskyClass #10 October 18, 2000 Today s TopicReading Assignment Stresses in spherical and cylindrical pressure vessels. Review of principal stresses in Set #4 Due in class 10/25/00. spherical pressure vessel has a wall thickness of mm and anInner diameter of 150 mm, and it contains a liquid at the maximum normal and shear pipe 30 m long has closed ends, a wall thickness of 10 mm, andaninner diameter of m. The pipe is filled with a gas to a pressure of20 MPa, and is subjected to a torque about its long axis of end effects, determine the three principal normal stresses andthe maximum shear an internally pressurized cylinder with with closed end effects, determine the principal normal and maximumshear stresses at the inner wall if the inner diameteris 80 mm, theouter diameter is 100 mm and the internal pressure is 100 lecture Review of Solution Process for Principal Stresses500 lb400 lb300 lb543 ABCxyyMR,zzMR,yzxxMR,5xsysxytxy12pq12sq) ,(xyxtsfacex planep 1planep 2splanes 2t:Given),(xyytsfacey.

2 Givenplanes 1 Step 1 Compute reactions at supportCompute internal forces near AStep 2 Compute stresses from internalforcesStep 3 Set up Mohr s circleDetermine principal stressesDetermine maximum shearstresses10/18/00ME111 lecture 1010/18/00ME111 lecture thin - walled pressure Vessels pressure vessels are closed structures that contain liquid or gas underpressure ( water-storage tanks, compressed air containers,pressurized pipes). We consider first the special case of thin - walled pressure vessels:10 trwhere ris the inner radius of the pressure vessel and tis its wall thin - walled Spherical pressure Vesselsrtps()() = =02:02rptrFmppsTakingrrm tpr2=sStress assumeduniform over tprt)(a)(btprtpr402max321= ===tsss242max321ptprptpr+= ===tsssCalled a lecture thin - walled Cylindrical pressure Vesselsrtp2s2sp1sr()()tprbrpbtF== = 110220ss()()tprrprtF2020222== = sppsbOn outersurfacetpr2231max= =sstOn innersurface03=s2222131maxptprp+=+= =ssstp =3s1sb10/18/00ME111 lecture 1010/18/00ME111 lecture Thick- walled Cylindrical pressure Vessels21222122221222122221222111rrprRrr rprRrrrprxrt = = + =sss Thick- walled pressure vessels have:101<trwhere r1is the inner radius of the pressure vessel and tis its wall thickness At a radius R, thick- walled pressure vessels have:rsts1r2rx