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 * (
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
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
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
THICK AND THIN CYLINDER-BRITTLE MATERIAL LAME'S EQUATION-WALL THICKNESS Inse Intern Desgn LAME Dmeter Pressure Stress mm. ( ( mm M M ( + t ( + + + + 00 7.5 6.5 8.5.05.0 0.0 50 4. 00 7.5 5.5 9.5..05 0.05 50 8. 00 7.5 4.5 40.5.7.08 0.08 50.5 00 4 7.5.5 4.5.4. 0. 50 7.0 00 5 7.5.5 4.5..4 0.4 50.5 00 6 7.5.5 4.5.8.8 0.8 50 6. 00 7 7.5 0.5 44.5.46. 0. 50. 00 8 7.5 9.5 45.5.54.4 0.4 50 6. 00 9 7.5 8.5 46.5.6.8 0.8 50 4.6 00 0 7.5 7.5 47.5.7. 0. 50 47. 00 7.5 5.5 49.5.94.9 0.9 50 59.0 00 7.5 4.5 50.5.06.44 0.44 50 65.4 00 4 7.5.5 5.5.9.48 0.48 50 7. 00 5 7.5.5 5.5..5 0.5 50 79. 00 6 7.5.5 5.5.49.58 0.58 50 86.6 00 7 7.5 0.5 54.5.66.6 0.6 50 94.6 00 8 7.5 9.5 55.5.85.69 0.69 50 0. 00 9 7.5 8.5 56.5.05.75 0.75 50.
THICK AND THIN CYLINDER-BRITTLE MATERIAL LAME'S EQUATION-WALL THICKNESS Inse Intern Desgn LAME Dmeter Pressure Stress mm. ( ( mm M M ( + t ( + + + + 600 7.5 6.5 8.5.05.0 0.0 00 8. 600 7.5 5.5 9.5..05 0.05 00 6.5 600 7.5 4.5 40.5.7.08 0.08 00 5.0 600 4 7.5.5 4.5.4. 0. 00.9 600 5 7.5.5 4.5..4 0.4 00 4. 600 6 7.5.5 4.5.8.8 0.8 00 5.5 600 7 7.5 0.5 44.5.46. 0. 00 6.4 600 8 7.5 9.5 45.5.54.4 0.4 00 7.6 600 9 7.5 8.5 46.5.6.8 0.8 00 8. 600 0 7.5 7.5 47.5.7. 0. 00 94. 600 7.5 5.5 49.5.94.9 0.9 00 8.0 600 7.5 4.5 50.5.06.44 0.44 00 0.7 600 4 7.5.5 5.5.9.48 0.48 00 44. 600 5 7.5.5 5.5..5 0.5 00 58. 600 6 7.5.5 5.5.49.58 0.58 00 7. 600 7 7.5 0.5 54.5.66.6 0.6 00 89. 600 8 7.5 9.5 55.5.85.69 0.69 00 06. 600 9 7.5 8.5 56.5.05.75 0.75 00 4. Nyngs Pge 6 /6/009