CYLINDER MADE FROM BRITTLE MATERIAL AND SUBJECT TO INTERNAL PRESSURE ONLY

Transcription

1 CYLINDER MADE FROM BRITTLE MATERIAL AND SUBJECT TO INTERNAL PRESSURE ONLY STRESS DISTRIBUTION ACROSS THE CYLINDER WALL The stresses n cyner suject t ntern ressure ny cn e etermne t tw ctns n the cyner w nmey, nner n uter surfce f the cyner w. Ths s ustrte n Fg. ew: STRESSES AT INNER SURFACE OF CYLINDER At ths ctn the stresses nuce re gven y the exressns [ ] Tngent stress + Lngtun stress t t * ( R stress r r STRESSES AT OUTER SURFACE OF CYLINDER At ths ctn the stresses nuce re gven y the exressns Tngent stress Lngtun stress R stress 0 r r t t * (

2 PRINCIPAL STRESSES AND PLANES The stresses entfe t nner n uter surfce re rnc stresses. Ths s ecuse t th surfces, the e s fu ressure whch s nrm tht gves rse t nrm stress. The nrm stress rsng ut f ressure t th surfces s therefre rnc stress. The tngent n ngtun rectns re erencur t the r ne, n re therefre s rnc nes; crryng rnc stresses whch re therefre s mxmum nrm stresses n thse nes. LOCATION OF EXTREME STRESSES The nner surfce s then the ctn f extreme stresses where fure s execte t ccur. Ths s ecuse [ ] The tngent stress t nner surfce + tngent stress t uter surfce s greter thn the t t t t * ( The ngtun stress s the sme vue t th nner n uter surfce The r stress r r t nner surfce s greter thn the r stress 0 r r CYLINDER FROM BRITTLE MATERIAL SUBJECT TO INTERNAL PRESSURE Fr rtte mter such s cst rn, the mxmum nrm stress thery f fure s e. Ths sys: When fure ccurs n ny mter, the mxmum nrm stress t the nt f fure equs r excees the mxmum nrm stress when fure ccurs n the tensn test secmen. PRINCIPAL STRESSES AT THE POINT OF FAILURE Mxmum n mnmum nrm stresses re,, where f f In the cse f cyner suject t ntern ressure ny, the stresses re extreme t the nner surfce, n re gven y t [ + ], * r (, Nyngs Pge /6/009

3 MAXIMUM NORMAL STRESS WHEN FAILURE OCCURS IN SIMPLE TENSION SPECIMEN When fure ccurs n the sme tensn secmen f rtte mter, the stress s gven y Sut, Or Suc Where S S ut uc Utmte tense strength f the mter Utmte cmressve strength f the mter STRESS CAUSING FAILURE AT THE INSIDE SURFACE OF CYLINDER At ths ctn Mxmum n mnmum nrm stresses re,, where But f f [ + ] t, n r The mxmum nrm stress t the ctn s tense whe the mnmum nrm stress s cmressve. Fure cu therefre e cuse y ether the mxmum tense stress, r the mnmum cmressve stress. Hwever, the cst rn mter hs cmressve strength whch s mny tmes hgher thn the tense strength. Fure w therefre e cuse y the hgher tense stress ctng n the wer tense strength f the mter. Fure w therefre ccur when t [ + ] Sut Ayng fctr f sfety n the strength f the mter Nyngs Pge /6/009

4 Ayng fctr f Sut, where f. s sfety Desgn stress fr the chsen rtte mter f. s Fctr f sfety The esgn equtn then ecmes [ + ] [ + ] ( ( + + Smfyng But t where Extern meter f Intern meter f + t + + cyner cyner + t + ( + + t Where t w thckness f cyner The ve s Lme s equtn fr the esgn f cyner suject t ntern ressure ny n me frm rtte mter t + Lme' s equtn fr thck cyner f rtte mter Nyngs Pge 4 /6/009

5 THICK AND THIN CYLINDER-BRITTLE MATERIAL LAME'S EQUATION-WALL THICKNESS Inse Intern Desgn LAME Dmeter Pressure Stress mm. ( ( mm M M ( + t (

6 THICK AND THIN CYLINDER-BRITTLE MATERIAL LAME'S EQUATION-WALL THICKNESS Inse Intern Desgn LAME Dmeter Pressure Stress mm. ( ( mm M M ( + t ( Nyngs Pge 6 /6/009