S??t??rn ƒr?m ( 3.6% at PA?t?ƒr?tag? = 105

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S??t??rn ƒr?m ( 3.6% at PA?t?ƒr?tag? = 105

S??t??rn ????ni?a?
?ni??rsit?, ????ni?a?
Instit?t?-Nasiri?a,

M???ani?a?
????ni?s ??partm?nt,
Nasiri?a, ???_Qar,
Iraq

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?r. Ha?im Isma?? Rad?i

M???ani?a?
??partm?nt, Engin??ring ?????g?, ??i – Qar ?ni??rsit?, Nasiri?a?, Iraq.

Naja? R?st?m M??sin

S??t??rn ????ni?a?
?ni??rsit?, ????ni?a?
Instit?t?-Nasiri?a,

M???ani?a?
????ni?s ??partm?nt,
Nasiri?a, ???_Qar,
Iraq

 

 

 

 

?BS?R???

??? pr???ss ?ƒ pr?d??ing r?sid?a? str?ss?s in a t?i??-?a???d ???ind?r b?ƒ?r? it is
p?t int? ?sag? is ?a???d ??t?ƒr?ttag?, ??i?? it m?ans; a s?itab?? ?arg? ?n??g?
pr?ss?r? t? ?a?s? ?i??ding ?it?in t?? ?a??, is app?i?d t? t?? inn?r s?rƒa?? ?ƒ t?? ???ind?r and t??n r?m???d. S? t?at a ??mpr?ssi?? r?sid?a? str?ss?s ar? g?n?rat?d t? a ??rtain radia?
d?pt? at t?? ???ind?r ?a??.

??? ?bj??ti?? ?ƒ t?? pr?s?nt st?d?, is t? in??stigat? t?? ?ƒƒ??t ?ƒ A?t?ƒr?tag? pr???ss ?n radia?, ?ir??mƒ?r?ntia? and t?ta? str?ss?s b? ?sing ??n._mis?s?i??d ?rit?ria. N?m?ri?a? sim??ati?n
?arri?d ??t ?n ?B?Q?S s?ƒt?ar? t? in??stigat? t?? str?ss?s distrib?ti?n and ?a????at? t?? A?t?ƒr?tag? radi?s. ??? r?s??ts r???a? t?at, t?? A?t?ƒr?tag? pr???ss ?ƒ t?i??-?a??
???ind?r ??ad t? d??r?as? t?? ???b and maxim?m ??n._mis?sstr?ss?s and r????at? t??m ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? ???ind?r t? s?m????r? a??ng
it’s t?i??n?ss. ??? r?d??ti?n in maxim?m str?ss?s is str?ng?? d?p?nd ?n A?t?ƒr?tag? pr?ss?r?, it ?as ?ar?ing ƒr?m (
3.6% at PA?t?ƒr?tag? = 105 M.Pa.
t? 19.2% at PA?t?ƒr?tag? = 130 M.Pa.
) A?s?, it ?as b??n ƒ??nd,
t??r? is n? ?ƒƒ??t ?ƒ n?mb?r ?ƒ A?t?ƒr?tag? stag?s ?n b?t? ?ƒ maxim?m ??n._mis?s str?ss and A?t?ƒr?tag? radi?s.

??? ??rds: ??t?ƒr?ttag?, ?t?ƒr?ttag?, radia?, ???b and axia? str?ss?s, ??n._mis?s ?i??d ?rit?ria, a?t?ƒr?ttag? radi?s, ?ptim?m ??t?ƒr?ttag?, ?t?ƒr?tag?  pr?ss?r?.

 

 

 

1.    
IN?R?????I?N

??? ?id? app?i?ati?ns ?ƒ pr?ss?ri??d ???ind?r in ???mi?a?, n????ar, armam?nts, ƒ??id transmitting p?ants,
p???r
p?ants and mi?itar? ?q?ipm?nt, in additi?n t? t?? in?r?asing s?ar?it?
and ?ig? ??st ?ƒ mat?ria?s ??ad

t?? d?sign?rs t? ??n??ntrat? t??ir att?nti?ns t? t?? ??asti? – p?asti? appr?a??
??i?? ?ƒƒ?rs m?r? ?ƒƒi?i?nt ?s? ?ƒ mat?ria?s 1, 2.??? pr???ss ?ƒ pr?d??ing r?sid?a? str?ss?s in t?? ?a?? ?ƒ t?i??-?a???d ???ind?r b?ƒ?r? it is p?t int? ?sag? is ?a???d A?t?ƒr?tag?, ??i?? it m?ans; a s?itab?? ?arg? ?n??g? pr?ss?r? t? ?a?s? ?i??ding ?it?in t?? ?a??, is app?i?d t? t?? inn?r s?rƒa?? ?ƒ t?? ???ind?r and t??n r?m???d. S? t?at a ??mpr?ssi?? r?sid?a? str?ss?s ar? g?n?rat?d t? a ??rtain radia? d?pt? at t?? ???ind?r ?a??. ???n, d?ring t?? s?bs?q??nt app?i?ati?n ?ƒ an ?p?rating pr?ss?r?, t?? r?sid?a? str?ss?s ?i?? r?d??? t?? t?nsi?? str?ss?s g?n?rat?d as a r?s??t ?ƒ app??ing ?p?rating pr?ss?r? 1,3.

??? ?ƒƒ??t ?ƒ r?sid?a? str?ss?s
?n ??ad-?arr? ?apa?it? ?ƒ t?i??-?a???d s??ind?rs ?a?? b??n in??stigat? b?
Amran A??b and ?abas?i
A?bas???r
4, ?sing b?t? ana??ti?a? and n?m?ri?a? t???niq??s. ??? r?s??ts ?ƒ t?? st?d? r???a? t?r?? s??nari?s in t?? d?sign ?ƒ t?i??-?a???d s??ind?rs. Amran A??b
and M. ?abas?i ??bas???r 5, ?s?d ??n._mis?sand ?r?s?a ?i??d ?rit?ria t? d?????p a pr???d?r? in ??i?? t?? ??t?ƒr?ttag? pr?ss?r? d?t?rmin?d ana??ti?a???
r?s??ting
in a r?d???d str?ss ??n??ntrati?n. ???n t???
??M.Pa.r?d
t?? ana??ti?a?
r?s??ts ?it?
??M r?s??ts. T??? ??n???d?d t?at, t?? ??t?ƒr?ttag? pr???ss in?r?as? t?? maxim?m a????ab?? int?rna? pr?ss?r? b?t it ?ann?t in?r?as? t?? maxim?m int?rna? pr?ss?r? t? ?as? ????? t?i??n?ss ?ƒ t?? ???ind?r t? ?i??d. N?ra?ia? ?t a?. 6 pr?s?nt?d an ana??ti?a?
??t?ƒr?ttag? pr???d?r?
t? pr?di?t
t?? r?q?ir?d ??t?ƒr?ttag? pr?ss?r? ?ƒ diƒƒ?r?nt ?????s ?ƒ a????ab?? pr?ss?r? and t???
?a?idat?
t??ir r?s??ts ?it? ??M r?s??ts. T??? ƒ??nd t?r?? ?as?s ?ƒ ??t?ƒr?ttag? in d?sign ?ƒ pr?ss?ri??d ??i??
_?a??ed s??ind?rs.

R?i?in ??? and Jin?ai ?ang 7, b?
?sing b?t? ?i??d ?rit?ria ??n._mis?sand Tr?s?a, pr?s?nt?d an ana??ti?a? ?q?ati?n ƒ?r ?ptim?m radi?s ?ƒ ??asti?-p?asti? j?n?ti?n
in ??t?ƒr?ttag? ???ind?r, a?s? t??? st?di?d t?? inƒ???n?? ?ƒ
??t?ƒr?ttag? ?n str?ss distrib?ti?n and ??ad b?aring ?apa?it?.
????
??n???d?d,
t? a??i??? ?ptim?m radi?s ?ƒ ??asti? – p?asti? j?n?ti?n, an ??t?ƒr?ttag? pr?ss?r? a bit ?arg?r t?an ?p?rating pr?ss?r? s????d b? app?i?d b?ƒ?r? a pr?ss?r? ??ss?? is p?t int? ?s?. ???ng H? and S?d?ir
P?ttag?nta 8 in??stigat? t?? r?sid?a? str?ss?s in t?? t?i??- ?a???d ???ind?r ind???d b?
int?rna? ??t?ƒr?ttag? pr?ss?r?, a?s? t???
ƒ??nd t?? ?ptim?m ??t?ƒr?ttag? pr?ss?r? and t?? maxim?m r?d??ti?n p?r??ntag? ?ƒ t?? ??n._mis?s str?ss ?nd?r ??asti?-?imit ??r?ing
pr?ss?r?. Md. ?anjin Amin ?t a?. 9 d?t?rmin?d t?? ?ptim?m ??ast? – p?asti? radi?s
and ?ptim?m ??t?ƒr?ttag? pr?ss?r? b? ?sing ??n._mis?s?i??d ?rit?ri?n , t??n t???
?a?? b??n ??mpar?d ?it? ??? and ?ang’s
m?d??
8. A?s? t???
?bs?r??d t?at t?? p?r??ntag? ?ƒ maxim?m ??n._mis?s str?ss r?d??ti?n in?r?as?s as ?a??? ?ƒ radi?s rati? (?) and ??r?ing pr?ss?r? in?r?as?s. ?. ?ri?b
?t a?.
10 dis??ss?d
pra?ti?a? app?i?ati?n ?ƒ ??t?ƒr?ttag? ?n ??mp?n?nts ƒ?r ?at?rj?t ??tting. ????
r?p?rt?d t?at t?? ?iƒ? tim? ?ƒ
?ig? pr?ss?r? ??mp?n?nts is impr???d b?
in?r?asing
??t?ƒr?ttag? d?pt?
d?? t? r?d??ti?n ?ƒ tang?ntia? str?ss at inn?r diam?t?r, ?n ?t??r ?and t?? ?ig? pr?ss?r? ?n ??tsid? diam?t?r s????d b? a??id?d t? pr???nt ?ra??s g?n?rat?. In additi?n t? d?t?rmin? t?? ?ptim?m ??t?ƒr?ttag? pr?ss?r? and t?? ?ptim?m radi?s ?ƒ ??asti?-p?asti? j?n?ti?n , Ab? Ra??an
Md. ?t a?.11
??a??at?d t?? ?ƒƒ??t ?ƒ ??t?ƒr?ttag? pr???ss in strain ?ard?n?d ?HI?? _?A???? pr?ss?r? ??ss??s b?
?sing ?q?i?a??nt ??n._mis?s str?ss as ?i??d ?rit?ri?n. ????
ƒ??nd, t?? n?mb?r ?ƒ ??t?ƒr?ttag? stag?s ?as n? ?ƒƒ??t ?n maxim?m ??n._mis?s str?ss and pr?ss?r? ?apa?it?.
A?s?, t???
??n???d?d
t?at, ?ptim?m ??t?ƒr?ttag? pr?ss?r? d?p?nds ?n t?? ??r?ing pr?ss?r? and ?n t?? rati? ?ƒ ??t?r t? inn?r radi?s.

2.    
PRESS?RE LIMI?S ?N? S?RESS ?IS?RIB??I?N IN N?N – ????FRE???GE? ?YLIN?ER

2.1.   
Pr?ss?r? ?imits ?ƒ N?n
– ??t?ƒr?tag? ???ind?r

????rding t? ??n._mis?s?i??d ?rit?ri?n, B?t? ?ƒ t?? int?rna? pr?ss?r? r?q?ir?s t? ?i??d t?? inn?r s?rƒa?? ?ƒ t?? ???ind?r ( i.?. partia? ??t?ƒr?ttag? ), P?i
, and t?at t? ?i??d t?? ????? ?a?? ?ƒ t?? ???ind?r ( i.?. ??mp??t??? ??t?ƒr?ttag? ), P??
, ?an b? ?a????at?d ƒr?m ?q?ati?ns ( 1and 2
)4, 7

2.2.   
Str?ss ?istrib?ti?n ?ƒ N?n
– A?t?ƒr?tag? ???ind?r

??? radia? str?ss ?r, ?ir??mƒ?r?ntia? ( ???p ) str?ss ?0 and axia? str?ss ??, distrib?ti?ns
in n?n – ??t?ƒr?ttag? ???ind?r s?bj??t?d t? an ?p?rating pr?ss?r?, Pi, ar? gi??n b?
?am?’s ƒ?rm??ati?ns ??i?? is a?ai?ab?? in 3, 4, 5, 6, 7 .
As s???n in Fig. ( 1 ), it is ???ar t?at t?? t?nsi?? ???b, ?0, ??mpr?ssi?? radia? , ?r, and
maxim?m ??n._mis?sstr?ss?s ?a?? t??ir maxim?m ?a???s at t?? inn?r s?rƒa?? ?ƒ t?? ???ind?r. ??? ???p str?ss ?as a??a?s p?siti?? ?a??? ??i?? r?pr?s?nts as t?nsi?? str?ss ??i?? t?? str?ss in t?? radia? dir??ti?n is a??a?s
??mpr?ssi??. A?s? t?? ???p t?nsi?? str?ss’s ?a??? is gr?at?r t?an radia? ??mpr?ssi?? str?ss’s ?a???.

 

3.    
FINI?E ELEMEN? ?N?LYSIS ?N? M??ERI?LS ?F N?MERI??L SIM?L??I?N M??ELS

Fig. ( 2 ) i???strat?s t?? g??m?tr?
?ƒ in??stigat?d ???ind?r t?at is mad? ?p ?ƒ ?arb?n st??? ?it? ???ng’s
m?d???s ?ƒ ( 203 G.Pa. ), P?iss?n’s
rati? ?ƒ ( 0.33 ) and ?i??d str?ss ?ƒ ( 325 M.Pa. ) 12 . It s?bj??t?d t? int?rna? pr?ss?r? ( Pi ). ??? mat?ria? is ass?m?d ??m?g?n???s and is?tr?Pi?. ??
??mp?t? t?? r?q?ir?d r?s??ts, N?m?ri?a? sim??ati?n is ?arri?d ??t ?n ?B?Q?S
??r.6.9
13. ??? in??stigat?d ?as?s ar? ??nsid?r as 2D – p?anar pr?b??m and q?adrati? ???m?nt ?a?? b??n ?s?d (?PS8R-8-
n?d?s )

4.    
??LI???I?N ?F N?MERI??L SIM?L??I?N

In t??
pr?s?nt st?d?,
t?? ?a?idati?n
?ƒ s?ƒt?ar? ?as b??n d?n? b?
??M.Pa.ring t??
ana??ti?a? ?a????ati?n r?s??ts ??i?? ?btain?d b?
s???ti?ns ?ƒ ?q?ati?ns ar? a?ai?ab?? in ?it?rat?r?s 3, 4, 5, 6 7, ?it?
r?s??ts ?ƒ n?m?ri?a? s???ti?n ?sing ?B?Q?S
??r.6.9.

Fr?m Fig. ( 3 ) , it is ???ar t?at, t?? t???r?ti?a? and n?m?ri?a? ?a????ati?ns ?ƒ ?ir??mƒ?r?ntia?, radia? and
maxim?m ??n._mis?sstr?ss?s ƒ?r diƒƒ?r?nt int?rna? pr?ss?r? ar? ??r?
???s?d
and ???r?ap
?a?? ?t??r. It m?ans, a g??d agr??m?nt is ƒ??nd b?t???n t?? r?s??ts, and t?? stati? ana??sis
s???s t?at, t??
p?r??ntag? ?ƒ ?rr?rs b?t???n t?? r?s??t ?ƒ ana??ti?a? and n?m?ri?a? s???ti?n ar? ??s t?an 0.5%. T?is ???
p?r??ntag? ?ƒ ?rr?rs aƒƒirms, t??r?
ar? n?
signiƒi?snt diƒƒ?r?n??s b?t???n t?? t???r?ti?a? r?s??ts and t??s? ?btain?d b?
sim??ati?n. ??ns?q??nt??,
F? m?d??ing ?sing ?B?Q?S
s?ƒt?ar? ?an b? ?s?d t? st?d?
t?? ?ƒƒ??t ?ƒ ??t?ƒr?ttag? pr???ss ?n t?? str?ss distrib?ti?n and ???ati?n ?ƒ ??t?ƒr?ttag? radi?s ( Ra
) ?ƒ t?i??-?a???d ???ind?r s?bj??t?d t? ?p?rating pr?ss?r?.

 

 

 

5.    
RES?L?S ?N? ?IS??SSI?NS

5.1. Minim?m ??t?ƒr?tag? Pr?ss?r?

B?
?a?a???ating t??
minim?m pr?ss?r? t?at n??d?d t? ?i??d t?? inn?r s?rƒa?? ?ƒ t?? t?st?d ???ind?r ( P?i
) ƒr?m ?q?ati?n (1) , it ?as ƒ??nd ?q?a? t? ( 104.243 M.Pa.
). ??at
is m?an,
t?? ?ƒƒ??t ?ƒ ??t?ƒr?ttag? pr?ss?r? ?i?? start at (104.243 M.Pa.), t??n t?? p?asti? d?ƒ?rmati?n spr?ads t?r??g? t?? ???ind?r t?i??n?ss. Fig. (4) s???s t?at, t?? sim??ati?n s???ti?n ?ƒ ?ƒƒ??t
?ƒ ??t?ƒr?ttag? pr?ss?r? ?n maxim?m ??n._mis?s str?ss ƒ?r
diƒƒ?r?nt ?p?rating pr?ss?r?, it is ???ar t?at , t??r? is n? ?ƒƒ??t ?ƒ ??t?ƒr?ttag? pr?ss?r? ?n maxim?m ??n._mis?s str?ss g?n?rating in t?? ???ind?r d?? t? t?? ?p?rating pr?ss?r? as ??ng as it is ??ss t?an ( 104 M.Pa. )
ƒ?r b?t? ?a??? ?ƒ ?p?rating pr?ss?r?. ???n , ???n it is ?x???d ( P??t?ƒr?ttag? > 104 M.Pa.
) t??
maxim?nm ??n._mis?s
str?ss d??r?as?s d?p?nding ?n t?? ??t?ƒr?ttag? pr?ss?r?, t?? bigg?r ?a??? ?ƒ ??t?ƒr?ttag? pr?ss?r?, t?? ????r ?ƒ maxim?m ??n._mis?sstr?ss.

In additi?n
t? t?at , it ?as b??n
?bs?r??d ƒr?m ?ab?? 1 t?at, t?? maxim?m ??n._mis?s str?ss d??r?as?s ?it? in?r?asing t?? ??t?ƒr?ttag? pr?ss?r? ???n P??t?ƒr?ttag? r?a??? ?a??? ?ƒ ab??t ( 130 M.Pa. ) t??n starts in?r?asing, ??i?? it m?ans, t?is ?a??? ?ƒ ??t?ƒr?ttag? pr?ss?r? r?pr?s?nts t?? ?ptim?m ??t?ƒr?ttag? pr?ss?r? 5,6. ??is
r?s??ts
agr?? ?it?
r?s??t ?as
ƒ??nd b?
1, 9, 11.

 

 

5.2.   
Eƒƒ??t ?ƒ ??t?ƒr?tag? Pr???ss ?n Str?ss ?istrib?ti?n

Fig.s ( 5, 6 and 7 ) d?m?nstrat?s t?? ?ƒƒ??t ?ƒ ??t?ƒr?ttag? pr???ss ?n str?ss distrib?ti?n ?ƒ t?i???d-?a???d ???ind?r s?bj??t?d t? ?p?rating pr?ss?r? ?ƒ ( 100 M.Pa. ). It is ?b?i??s, t?? ??t?ƒr?ttag? pr???ss ??ads t? d??r?as? t?? ?a??? ?ƒ maxim?m ??n._mis?s str?ss and r????at?d t?? ??mpr?ssi?? ?ir??mƒ?r?ntia? and maxim?m ??n._mis?s str?ss?s ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? s??ind?r t? s?m????r? t?r??g? it’s t?i??n?ss. ??is n?? ???ati?n ?ƒ maxim?m ??n._mis?s str?ss ?a???d A?t?ƒr?tag? radi?s, Ra . It d??s n?t d?p?nd ?n ?p?rating pr?ss?r? ??i?? it is str?ng??
aƒƒ??t?d b?
??t?ƒr?ttag? pr?ss?r? as s???n in ?ab?? 2, ??i?? s???s t?? ?a???s ?ƒ ??t?ƒr?ttag? radi?s, Ra
, ?it? diƒƒ?r?nt ?a???s ?ƒ ??t?ƒr?ttag? pr?ss?r?. A?s?, it is ƒ??nd , t?? r?d??ti?n in maxim?m ??n._mis?sstr?ss?s ?ar?ing
ƒr?m ( 3.6 % at P??t?ƒr?ttag? =105  M.Pa. ) t? ( 19.2% at P??t?ƒr?ttag? =130 M.Pa. ).
It is ?ita? t? s??
t?at , t??r? is n? signiƒi?ant ?ƒƒ??t ?ƒ ??t?ƒr?ttag?

 

 

 

 

A

?

D

B

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5.3.   
Eƒƒ??t ?ƒ ??t?ƒr?tag? Stag?s ?n Maxim?m ??n._Str?ss

?? in??stigat? t?? ?ƒƒ??t ?ƒ ??t?ƒr?ttag? stag?s ?n maxim?m ??n._mis?sstr?ss, t?? in??stigat?d ???ind?r ?as s?bj??t?d t? ( 100 M.Pa. ) as
?p?rating
pr?ss?r? and ??t?ƒr?ttag? pr?ss?r?s ?ƒ ( 110, 120 and 130 M.Pa. ) ar? d?n? b?
t?? st?ps,
at ƒirst st?p, t?? ??t?ƒr?ttag? pr?ss?r? ?as b??n app?i?d in ?n? stag?, ??i?? at s???nd st?p it ?as d?n? b?
t?r?? ??ading
stag?s (
s?? ?ab?? 3 ). As ?an b? n?ti??d ???ar??
in ?ab?? 3 and Fig. (7 ), t?? n?m?ri?a? r?s??ts ??nƒirm t??r? is n? ?ƒƒ??t ?ƒ ??t?ƒr?ttag? stag?s ?n t?? maxim?m ??n._mis?s str?ss g?n?rat?d in t?? ???ind?r d?? t? ?p?rating pr?ss?r?. ??is r?s??ts ar? ??r?
???s? t?
t?? ?it?
r?s??ts ?a?? b??n ƒ??nd b? 3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.      
??N?L?SI?N

??? r?s??ts ?ƒ pr?s?nt in??stigati?n ?an b? s?mmari??d as

·        
??? ??t?ƒr?ttag? pr???ss ?n t?i??-?a???d ???ind?r ??ads t? d??r?as? t?? ?ir??mƒ?r?ntia? and maxim?m ??n._mis?s str?ss?s and r????at? t??m ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? ???ind?r t? s?m????r? a??ng it’s t?i??n?ss, ??i?? ?a???d as, ??t?ƒr?ttag? radi?s, Ra
.

·        
??? ??t?ƒr?ttag?  , Ra ,  is str?ng??
aƒƒ??t?d b?
??t?ƒr?ttag? pr?ss?r? ??i?? it d??s n?t d?p?nd ?n t??  ?p?rating pr?ss?r?.

·        
???r? is n? ?ƒƒ??t ?ƒ a?t?ƒƒr?ttag? stag?s ?n maxim?m ??n._mis?s str?ss d?????p?d in t?? ???ind?r s?bj??t?d t? an ?p?rating pr?ss?r?.

 

 

REFEREN?E

1             
?. B. ???b,
M. N. ?amin
and ?abas?i ??bas???r,” Pr?ss?r? ?imits ?ƒ ??i?? – ?a???d ???ind?rs , P????dings ?ƒ t?? int?rnati?na? M??ti ??nƒ?r?n?? ?ƒ ?ngin??rs and ??mp?t?r s?i?ntist , IM??S 2009, H?ng ??ng, Mar?? 8 -20.

2             
?ang ??iq?n,” ??asti? – p?asti? ƒra?t?r? ana??sis
?ƒ a t?i?? – ?a???d ???ind?r “, Int?rnati?na? J??rna? ?ƒ pr?ss?r? ??ss??s PiPing “, ????m? 63, 1995, pp. 165 –
168.

3             
?. ?in?s? Bab? and ?.
J?ga Ba?aji,”
????r?ti?a? and ƒinit? ???m?nt Ana??sis
??ƒ ?ig? Pr?ss?r? ??mp?n?nts “, I?SR J??rna?
?ƒ ?ngin??ring, ???. 3, Iss?? 2, ??b 2013, PP: 25 – 34.

4             
?mran A??b and M. ?abas?i ??bas???r, ” ?ptim?m ??t?ƒr?ttag? Pr?ss?r? in t?i?? ???ind?rs “, J?rna? M??ani?a?,
????mb?r 2007, N0. 24, pp. 1
– 24.

5             
N?ra?ia? ?a?i, Amran A??b and M. ?abas?i
??bas???r, ” ?ƒƒ??t ?ƒ ?ptim?m ??t?ƒr?ttag? ?n Pr?ss?r? ?imits ?ƒ t?i?? ?a???d ???ind?rs “, Int?rnati?na? J??rna? ?ƒ ?n?ir?nm?nta? S?i?n?? and ??????pm?nt, ???. 2, N?. 4, A?g?st 2011, pp. 329 – 333.

6             
I.M.Jamadar, S.M.Pati?,
S.S.??a?an, G.B.Pa?ar and G.N.Rakat?, ??i?kn?ss ?ptimi?ati?n ?ƒ In??in?d Pr?ss?r? ??ss?? ?sing N?n ?in?ar Finit? ???m?nt Ana??sis
?sing ??sign
b? Ana??sis Appr?a??. Int?rnati?na? J??rna? ?ƒ M???ani?a? ?ngin??ring and ????n???g? (IJME?), 3(3), 2013, pp.682-689.

7             
N?ra?ia? ?a?i, Amran A??b and M??d ?abas?i ??bas???r,” ?ƒƒ??t
?ƒ ??t?ƒr?ttag? ?n A????ab?? Pr?ss?r? ?ƒ t?i?? – ?a???d ???ind?rs “, Int?rnati?na? ??nƒ?r?n?? ?n ?n?ir?nm?nta? and Agri???t?r? ?ngin??ring “, 2011,
Singap?r?,
IP?B?? ???.
15, pp. 14 – 16, IA?SIT Pr?ss.

8             
R?i?in ??? and Jin?ai ?ang,
” ??t?ƒr?ttag? ?ƒ t?i?? ???ind?rs “, Int?rnati?na? J??rna? ?ƒ Pr?ss?r? ??ss??s and PiPing, ???. 75, 1998, pp. 443 –
446..

9             
???ng? and S?d?ir P?ttag?nta,
” ??mp?t?r
m?d??ing ?ƒ Int?rna? Pr?ss?r? ??t?ƒr?ttag? Pr???ss ?ƒ a ??i?? – ?a???d ???ind?r ?it? t?? Ba?s??ing?r ?ƒƒ??t “, Am?ri?an ?ransa?ti?ns ?n ?ngin??ring and ?pp?i?d S?i?n??s, ????m? 1, N?.2, ISSN 2229-1652, ?ISSN 2229-1660.

10         
Md. ?anjin Amin, Ab? Ra??an
Md. A?i, ???siƒ A?m?d and ?aisa? A?m?d, ” ?ptim?m D?sign ?ƒ ??t?ƒr?ttag?d t?i???d – ?a???d ???ind?rs “, G??ba? J??rna? ?ƒ R?s?ar???s in ?ngin??ring, ???.13, Iss?? 8, ??rsi?n 1, 2013, ?n?in? ISSN : 2249-4596,
Print ISSN : 0975 – 5861

11         
Pr?ƒ. S. S. ??s?pand?, P. N. ??sai, ?. P. Pand?? and N. P. Pangar?ar, ??tai??d St?di?s ?n Str?ss ??n??ntrati?n b? ??assi?a? and
Finit? ???m?nt Ana??sis.
Int?rnati?na? J??rna? ?ƒ M???ani?a? ?ngin??ring and ????n???g? (IJME?), 7(2), 2016, pp.148-167.

12         
F. ?ri?d,
J. S???d??mai?r and M. P?????, “??t?ƒr?ttag? – Basi? Inƒ?rmati?n and pra?ti?a? app?i?ati?n ?n ??mp?n?nts ƒ?r ?at?rj?t ??tting “, Am?ri?an ?at?rj?t ??nƒ?r?n??, 2005 ?J??, 2005, ??g?st
21 – 23, H??st?n, ??xas.

13         
?b? Ra??an Md. ??i, Nid?? ??. G??s? and ?an?ir-?-??am,
” ?ptim?m D?sign
?ƒ Pr?ss?r? ??ss?? S?bj??t?d t? ??t?ƒr?ttag? Pr???ss “, Int?rnati?na? J??rna? ?ƒ M???ani?a?, A?r?spa??, Ind?stria?, M???atr?ni? and man?ƒa?t?ring ?ngin??ring, ???.4, N?. 10,
2011, PP.1040 – 1045.

14         
 ?.
JR. ?a??ist?r,
” Mat?ria?
S?i?n?? and ?ngin??ring; An Intr?d??ti?n”,
7t? ?diti?n,
2005, N??
d???i.

15         
?B?Q?S ??r. 6.9, 2009, G?tting Start?d; standard ?s?r’s Man?a?.

 

 

 

 

 

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