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Transcript of Tgs v Plane Stress Segi4OK
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PLANE STRESS SEGIEMPAT
data
Nilai a 1.25 m
b 0.5 m
t 0.2 m
E 2000000000 kg/m^2
v 0.3
A 219!0219!
" E/#1$v% 153!&'153!( '593&0'59
S1 #tb/'a%A 2930&029.3 S1
S2 #tb/'b%A 32'003.3 S2
S3 #t/&%( 329'033 S3
S& #ta/12b%" '&1025'&.1 S4
S5 #tb/12a%" 1025'&10.3 S5
S' #t/!%" 3!&'153!.5 S6
)1 v1 )2 v2 )3 v3 )& v&
)1 2S1$2S&
v1 S3$S' 2S2$2S5
)2 #*2S1$S2&% #*S3$S'% 2S1$2S&
v2 S3*S' S2*2S5 #*S3*S'% 2S1$2S&
E/#1*v2%
Ev/#1*v2%
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)2 v2 )3 v3 )' v' )5 v5
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v' *1&2!51.& *!351'&!3.5 *5&9&505.5 *13'2'33'.3 1&2!51.& 1'0329'.0 5&9&505.5 52&252. v'
)5 *9!90109!.9 *5&9&505.5 *93&0'593.& 1&2!51.& 5&9&505.5 5&9&505.5 1!'!131!'.! *1&2!51.& )5
v5 5&9&505.5 *13'2'33'.3 1&2!51.& *!351'&!3.5 *5&9&505.5 52&252. *1&2!51.& 1'0329'.0 v5
)5 v5 )' v' )9 v9 )! v!
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v5 1&2!51.& 1'0329'.0 5&9&505.5 52&252. *1&2!51.& *!351'&!3.5 *5&9&505.5 *13'2'33'.3 v5
)' '9590'9.' 5&9&505.5 1!'!131!'.! *1&2!51.& *9!90109!.9 *5&9&505.5 *93&0'593.& 1&2!51.& )'
v' *5&9&505.5 52&252. *1&2!51.& 1'0329'.0 5&9&505.5 *13'2'33'.3 1&2!51.& *!351'&!3.5 v'
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v9 *1&2!51.& *!351'&!3.5 *5&9&505.5 *13'2'33'.3 1&2!51.& 1'0329'.0 5&9&505.5 52&252. v9
)! *9!90109!.9 *5&9&505.5 *93&0'593.& 1&2!51.& 5&9&505.5 5&9&505.5 1!'!131!'.! *1&2!51.& )!
v! 5&9&505.5 *13'2'33'.3 1&2!51.& *!351'&!3.5 *5&9&505.5 52&252. *1&2!51.& 1'0329'.0 v!
)1 v1 )2 v2 )3 v3 )& v& )5
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)1 1&2!51.& '9590'9.' *5&9&505.5 *9!90109!.9 5&9&505.5
v1 1&2!51.& 1'0329'.0 5&9&505.5 52&252. *5&9&505.5 *13'2'33'.3
)2 '9590'9.' 5&9&505.5 1!'!131!'.! *1&2!51.& *93&0'593.& 1&2!51.&
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)5 *93&0'593.& *1&2!51.& *9!90109!.9 5&9&505.5 5&9&505.5 *5&9&505.5
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)3
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MATRI EAAN T4TAL #4ER ALLSTI66NESS MATRI7%
)1 v1 )2 v2 )3 v3 )& v& )5 v5
)1 1!'!131!'.! 1&2!51.& '9590'9.' *5&9&505.5 0.0 0.0 *9!90109!.9 5&9&505.5 *93&0'593.& *1&2!
v1 1&2!51.& 5&9&505.5 52&252. 0.0 0.0 *5&9&505.5 *1&2!51.& *!351'
)2 '9590'9.' 5&9&505.5 33'2'33.' 0.0 '9590'9.' *5&9&505.5 *93&0'593.& 1&2!51.&
v2 *5&9&505.5 52&252. 0.0 33&0'593&.1 5&9&505.5 52&252. 1&2!51.& *!351'&!3.5 0.0
)3 0.0 0.0 '9590'9.' 5&9&505.5 1!'!131!'.! *1&2!51.& 0.0 0.0 *93&0'593.& 1&2!
v3 0.0 0.0 *5&9&505.5 52&252. *1&2!51.& 1'0329'.0 0.0 0.0 1&2!51.& *!351'
)& *9!90109!.9 *5&9&505.5 *93&0'593.& 1&2!51.& 0.0 0.0 33'2'33.' 0.0 509155.1
8 t:tal ,
v& 5&9&505.5 *13'2'33'.3 1&2!51.& *!351'&!3.5 0.0 0.0 0.0 33&0'593&.1 0.0 105&9&
)5 *93&0'593.& 0.0 *93&0'593.& 1&2!51.& 509155.1 0.0 &252&.3
v5 *1&2!51.& 0.0 1&2!51.& *!351'&!3.5 0.0 105&9&505.5 0.0 ''!131
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v' 0.0 0.0 *1&2!51.& *!351'&!3.5 *5&9&505.5 0.0 0.0 0.0 105&9&
) 0.0 0.0 0.0 0.0 0.0 0.0 *9!90109!.9 *5&9&505.5 *93&0'593.& 1&2!
v 0.0 0.0 0.0 0.0 0.0 0.0 5&9&505.5 1&2!51.& *!351'
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v! 0.0 0.0 0.0 0.0 0.0 0.0 *1&2!51.& *!351'&!3.5 0.0
)9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 *93&0'593.& *1&2!v9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 *1&2!51.& *!351'
)1 v1 )2 v2 )3 v3 )& v& )5
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v1 1&2!51.& 5&9&505.5 52&252. 0.0 0.0 *5&9&505.5 *1&2!51.& *!351'
)2 '9590'9.' 5&9&505.5 33'2'33.' 0.0 '9590'9.' *5&9&505.5 *93&0'593.& 1&2!51.&
v2 *5&9&505.5 52&252. 0.0 33&0'593&.1 5&9&505.5 52&252. 1&2!51.& *!351'&!3.5 0.0)3 0.0 0.0 '9590'9.' 5&9&505.5 1!'!131!'.! *1&2!51.& 0.0 0.0 *93&0'593.& 1&2!
v3 0.0 0.0 *5&9&505.5 52&252. *1&2!51.& 1'0329'.0 0.0 0.0 1&2!51.& *!351'
)& *9!90109!.9 *5&9&505.5 *93&0'593.& 1&2!51.& 0.0 0.0 33'2'33.' 0.0 509155.1
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)' 0.0 0.0 *93&0'593.& *1&2!51.& *9!90109!.9 5&9&505.5 0.0 0.0 509155.1
v' 0.0 0.0 *1&2!51.& *!351'&!3.5 *5&9&505.5 0.0 0.0 0.0 105&9&
) 0.0 0.0 0.0 0.0 0.0 0.0 *9!90109!.9 *5&9&505.5 *93&0'593.& 1&2!
v 0.0 0.0 0.0 0.0 0.0 0.0 5&9&505.5 1&2!51.& *!351'
)! 0.0 0.0 0.0 0.0 0.0 0.0 *93&0'593.& *1&2!51.&
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v9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 *1&2!51.& *!351'
RE*ARANGMENT MATRI7
)2 v2 )3 v3 )5 v5 )' v' )! v!
)2 33'2'33.' 0.0 '9590'9.' *5&9&505.5 0.0 *93&0'593.& *1&2!51.& 0.0
v2 0.0 5&9&505.5 52&252. 0.0 *1&2!51.& *!351'&!3.5 0.0
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v3 *5&9&505.5 52&252. *1&2!51.& 1'0329'.0 1&2!51.& *!351'&!3.5 5&9&505.5 0.0
)5 0.0 *93&0'593.& 1&2!51.& &252&.3 0.0 509155.1 0.0
v5 0.0 1&2!51.& *!351'&!3.5 0.0 ''!131!'!.1 0.0 105&9&505.5 0.0
)' *93&0'593.& *9!90109!.9 5&9&505.5 509155.1 0.0 33'2'33.' 0.0 *93&0'593.& 1&2!
v' *1&2!51.& *5&9&505.5 0.0 105&9&505.5 0.0 33&0'593&.1 1&2!51.& *!351'
)! 0.0 0.0 0.0 0.0 0.0 *93&0'593.& 1&2!51.& 33'2'33.'
v! 0.0 0.0 0.0 0.0 0.0 1&2!51.& *!351'&!3.5 0.0 33&0'5
)9 0.0 0.0 0.0 0.0 *93&0'593.& *1&2!51.& *9!90109!.9 5&9&505.5 5&9&505.5 *5&9&
v9 0.0 0.0 0.0 0.0 *1&2!51.& *!351'&!3.5 *5&9&505.5 5&9&505.5 52&
)2 v2 )3 v3 )5 v5 )' v' )! v!
)2 5.312&E*009 &.59!E*009 0.000000001 9.2'3E*009 0.000000001 &.0'9!E*009 .10'&E*010 1.0&25E*00! *1.&19&E*009 &.091'
v2 &.59!3E*009 1.'!0E*00! 0.000000002 2.3!'1E*00! *&.2!91E*010 1.359E*00! *3.0''E*010 2.5!&3E*00! *5.5'&0E*009 1.35!!
)3 0.000000001 2.005E*009 1.1&!&E*00! 0.00000001& &.!0!E*010 1.330'E*009 2.1!0&E*009 1.1&20E*00! *1.50'&E*009 1.2&!
v3 9.2'3E*009 2.3!'E*00! 0.00000001& .519E*00! *3.1&&0E*009 2.3'22E*00! *3.!515E*009 .003E*00! *1.'19E*00! 2.'352
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v' 1.0&25E*00! 2.5!&E*00! 1.1&20E*00! .003E*00! *2.555E*009 2.&219E*00! *&.&20'E*009 .3130E*00! *1.1'E*00! 2.19!
)! *1.&19&E*009 *5.5'&E*009 *1.50'&E*009 *1.'19E*00! 2.099!E*009 *5.5''E*009 2.!'&3E*009 *1.1'E*00! .9325E*009 *'.''2
v! &.091'E*009 1.359E*00! 1.2&!E*009 2.'352E*00! *1.050!E*009 1.&105E*00! *2.&19E*009 2.19!E*00! *'.''2E*009 1.5!9
)9 *1.229E*009 *5.251E*009 *2.&55E*009 *2.12E*00! 2.3912E*009 *&.999E*009 &.9&52E*009 *2.2!3!E*00! 0.00000000 *'.5335
v9 1.0&!E*00! 2.590E*00! 1.0!23E*00! 0.0000000'9 *2.0'11E*009 2.&&9&E*00! *&.9!&E*009 .221E*00! *1.'9&'E*00! 2.'1'9
;ISPLA(EMENT
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63 *22'.9
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) v )! v! )9 v9
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0.0 0.0 0.0 0.0 0.0 0.0 v1
0.0 0.0 0.0 0.0 0.0 0.0 )2
0.0 0.0 0.0 0.0 0.0 0.0 v2
0.0 0.0 0.0 0.0 0.0 0.0 )3
0.0 0.0 0.0 0.0 0.0 0.0 v3
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5&9&505.5 52&252. 0.0 33&0'593&.1 *5&9&505.5 52&252. v!
0.0 0.0 5&9&505.5 *5&9&505.5 1!'!131!'.! 1&2!51.& )90.0 0.0 5&9&505.5 52&252. 1&2!51.& 1'0329'.0 v9
) v )! v! )9 v9 GA@A
0.0 0.0 0.0 0.0 0.0 0.0 )1 0 61 0 29'0
0.0 0.0 0.0 0.0 0.0 0.0 v1 0 G1 0 1502
0.0 0.0 0.0 0.0 0.0 0.0 )2 0 62 *2.332'3E*005 *1.!2
0.0 0.0 0.0 0.0 0.0 0.0 v2 0 G2 *'.'3502E*005 *1.!20.0 0.0 0.0 0.0 0.0 0.0 )3 0 63 *1.!&05E*005 *9.09
0.0 0.0 0.0 0.0 0.0 0.0 v3 0 G3 *0.0001521!&5 3.'3!
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1!'!131!'.! *1&2!51.& 5&9&505.5 5&9&505.5 0.0 0.0 ) 0 6 0 *5&05
*1&2!51.& 1'0329'.0 *5&9&505.5 52&252. 0.0 0.0 v 0 G 0 1'20
5&9&505.5 *5&9&505.5 33'2'33.' 0.0 5&9&505.5 5&9&505.5 )! 0 6! 3.!399E*005 *1.&!
5&9&505.5 52&252. 0.0 33&0'593&.1 *5&9&505.5 52&252. v! -2500 G! *.''!21E*005
0.0 0.0 5&9&505.5 *5&9&505.5 1!'!131!'.! 1&2!51.& )9 0 69 &.!2093E*005 *5.&'
0.0 0.0 5&9&505.5 52&252. 1&2!51.& 1'0329'.0 v9 -1250 G9 *0.0001'&'025
G
)2
v2
)3
v3
)5
v5
)'
v'
)!
v!
)9
v9
Gaa l)a>
)2 0 62
v2 0 G2
)3 0 63
v3 0 G3
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v' 0 G'
)! 0 6!
v! -2500 G!
)9 0 69
v9 -1250 G9
*2.333E*05
*'.'35E*05
*1.!&E*05
*1.522E*0&5.203E*0'
*'.5!!E*05
1.2&1E*05
1 5!3E 0&
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*1.'&'E*0&
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PLANE STRESS SEGIEMPAT
;ikta+)i
St>)kt)> ?>ti gamba> dibaBa+ iCiD
dataNilai a 1.25 m
b 0.5 m
t 0.2 m
E 2000000000
v 0.3
E/#1*v2% !0219!
E/#1$v% '153!
Ev/#1*v2% '593&0'59
2930&029
32'003 S2
329'033 S3
'&1025'& S&
1025'&10 S5
3!&'153! S'
;?k>i?i laC ?t>?? lmC ?gimat
dimC?i lmC 1D2D3D& ?m)aCCa ?ama ?+iCgga Cilai mat>ik?
kkak)aC )Ct)k ?m)a lmC ?ama.
a>Ca ?)d)t aCta>a ?)mb) l:kal dCgaC ?)mb) gl:bal ?amaD ?+iCgga
kg/m2
kg/m2
kg/m2
kg/m2
2.5m
1
2
3
4
1 m
1 m
2.5m
1
7
6 5
3
4
2
98
Q= 1000kg/m’
S1= t .b
6. a. E(1−υ2 )
S2=t .a
6 .b .
E
(1−υ2 )S3=t
4. E .υ
(1−υ2 )
S4=
t . a
12. b .
E
(1+υ )
S5=
t .b
12 .a .
E
(1+υ )
S6=
t
8. E
(1+υ )
n
u
i j
k l
ni
ui
n j
u j
nk
uk
nl
ul
a a
b
b
+ , *1
- , 1
+ , 1
- , *1 - , -/a
+ , /b
-
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LANGKAH I. Mengi!ung "#!$ik% kek#ku#n l&k#l '#n gl&(#l ele"en
Mat>ik T>aC?:>ma?i 8T
dengan : 0
a>Ca mat>ik? t>aC?:>ma?i adala+ mat>ik? idCtita?D maka
8g,8TT.8l.8T , 8l
P>?amaaC mat>i- kkak)aC tia lmC laC ?t>?? ?gimat
)i vi )F vF )k vk )l vl
)i 2S1$2S&
vi S3$S' 2S2$2S5
S@METRIS)F #*2S1$S2&% #*S3$S'% 2S1$2S&
vF S3*S' S2*2S5 #*S3*S'% 2S1$2S&
)k #*S1*S&% #S3*S' S1*2S& #*S3$S'% 2S1$2S&
vk #*S3*S'% #*S2*S5% S3*S' #*S21$S5% S3$S' 2S2$2S5
)l S1*2S& S3*S' #*S1*S&% S3$S' #*2S1$S&% #*S3$S'% 2S1$2S&
vl #*S3$S'% #*2S2$S5% S3$S' #*S2*S5% S3*S' S2*2S5 #*S3*S'% 2S2$2S5
Mat>ik? t>aC?:>ma?i 8T , 8ID ?+iCgga 8 l , 8
g
α,
[K l]e =
[T ]=
[cos α 0 0 0 sin α 0 0 0
0 cos α 0 0 0 sin α 0 0
0 0 c os α 0 0 0 sin α 0
0 0 0 cos α 0 0 0 sin α
−sin α 0 0 0 cosα 0 0 0
0 −sin α 0 0 0 cos α 0 0
0 0 −sin α 0 0 0 cos α 0
0 0 0 −sin α 0 0 0 cos α ][T ]=
[
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 1
]
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kak)aC l:kal lmC 1D F:iCt #1D2D5D&%
)1 v1 )2 v2 )5 v5 )&
)1 1!'!131!'.!1 1&2!51.&29 '9590'9.59 *5&9&505.&95 *93&0'593.&1 *1&2!51.&3 *9!90109!.9 5&9
v1 1&2!51.&29 1'0329' 5&9&505.&9&5 52&252.& *1&2!51.&3 *!351'&!3.52 *5&9&505.&95 *13
)2 '9590'9.59 5&9&505.&9&5 1!'!131!'.!1 *1&2!51.&3 *9!90109!.9 *5&9&505.&95 *93&0'593.&1 1&
v2 *5&9&505.&95 52&252.& *1&2!51.&3 1'0329' 5&9&505.&9&5 *13'2'33'.3 1&2!51.&29 *!3
)5 *93&0'593.&1 *1&2!51.&3 *9!90109!.9 5&9&505.&9&5 1!'!131!'.!1 1&2!51.&29 5&9&505.&9&5 *5&
v5 *1&2!51.&3 *!351'&!3.52 *5&9&505.&95 *13'2'33'.3 1&2!51.&29 1'0329' 5&9&505.&9&5 52
)& *9!90109!.9 *5&9&505.&95 *93&0'593.&1 1&2!51.&29 5&9&505.&9&5 5&9&505.&9&5 1!'!131!'.!1 *1
v& 5&9&505.&9&5 *13'2'33'.3 1&2!51.&29 *!351'&!3.52 *5&9&505.&95 52&252.& *1&2!51.&3 1
kak)aC l:kal lmC 2D F:iCt #&D5D!D%
)& v& )5 v5 )! v! )
)& 1!'!131!'.!1 1&2!51.&29 '9590'9.59 *5&9&505.&95 *93&0'593.&1 *1&2!51.&3 *9!90109!.9 5&9
v& 1&2!51.&29 1'0329' 5&9&505.&9&5 52&252.& *1&2!51.&3 *!351'&!3.52 *5&9&505.&95 *13
)5 '9590'9.59 5&9&505.&9&5 1!'!131!'.!1 *1&2!51.&3 *9!90109!.9 *5&9&505.&95 *93&0'593.&1 1&
v5 *5&9&505.&95 52&252.& *1&2!51.&3 1'0329' 5&9&505.&9&5 *13'2'33'.3 1&2!51.&29 *!3
)! *93&0'593.&1 *1&2!51.&3 *9!90109!.9 5&9&505.&9&5 1!'!131!'.!1 1&2!51.&29 5&9&505.&9&5 *5&
v! *1&2!51.&3 *!351'&!3.52 *5&9&505.&95 *13'2'33'.3 1&2!51.&29 1'0329' 5&9&505.&9&5 52
) *9!90109!.9 *5&9&505.&95 *93&0'593.&1 1&2!51.&29 5&9&505.&9&5 5&9&505.&9&5 1!'!131!'.!1 *1
v 5&9&505.&9&5 *13'2'33'.3 1&2!51.&29 *!351'&!3.52 *5&9&505.&95 52&252.& *1&2!51.&3 1
kak)aC l:kal lmC 3D F:iCt #2D3D'D5%
)2 v2 )3 v3 )' v' )5
)2 1!'!131!'.!1 1&2!51.&29 '9590'9.59 *5&9&505.&95 *93&0'593.&1 *1&2!51.&3 *9!90109!.9 5&9
v2 1&2!51.&29 1'0329' 5&9&505.&9&5 52&252.& *1&2!51.&3 *!351'&!3.52 *5&9&505.&95 *13
)3 '9590'9.59 5&9&505.&9&5 1!'!131!'.!1 *1&2!51.&3 *9!90109!.9 *5&9&505.&95 *93&0'593.&1 1&
v3 *5&9&505.&95 52&252.& *1&2!51.&3 1'0329' 5&9&505.&9&5 *13'2'33'.3 1&2!51.&29 *!3
)' 93&0'593 &1 1&2!51 &3 9!90109! 9 5&9&505 &9&5 1!'!131!' !1 1&2!51 &29 5&9&505 &9&5 5&
8 l1 ,
)K l*1 + )Kg*1
8 l
2
,
)K l*2 + )Kg*2
8 l3 ,
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kak)aC l:kal lmC &D F:iCt #5D'D9D!%
)5 v5 )' v' )9 v9 )!
)5 1!'!131!'.!1 1&2!51.&29 '9590'9.59 *5&9&505.&95 *93&0'593.&1 *1&2!51.&3 *9!90109!.9 5&9&
v5 1&2!51.&29 1'0329' 5&9&505.&9&5 52&252.& *1&2!51.&3 *!351'&!3.52 *5&9&505.&95 *13'
)' '9590'9.59 5&9&505.&9&5 1!'!131!'.!1 *1&2!51.&3 *9!90109!.9 *5&9&505.&95 *93&0'593.&1 1&2
v' *5&9&505.&95 52&252.& *1&2!51.&3 1'0329' 5&9&505.&9&5 *13'2'33'.3 1&2!51.&29 *!35
)9 *93&0'593.&1 *1&2!51.&3 *9!90109!.9 5&9&505.&9&5 1!'!131!'.!1 1&2!51.&29 5&9&505.&9&5 *5&9
v9 *1&2!51.&3 *!351'&!3.52 *5&9&505.&95 *13'2'33'.3 1&2!51.&29 1'0329' 5&9&505.&9&5 52&
)! *9!90109!.9 *5&9&505.&95 *93&0'593.&1 1&2!51.&29 5&9&505.&9&5 5&9&505.&9&5 1!'!131!'.!1 *1&
v! 5&9&505.&9&5 *13'2'33'.3 1&2!51.&29 *!351'&!3.52 *5&9&505.&95 52&252.& *1&2!51.&3 1
)K l*3 + )Kg*3
8 l& ,
)K l*4 + )Kg*4
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LANGKAH II. Mengi!ung ,e$#ll S!ine%% "#!$i/ & S!$u!u$e
4v>all StiC?? mat>i-
)1 v1 )2 v2 )3 v3 )& v& )5 v5 )' v'
)1 1! 1&2!51 '95900 *5&9&505 0 0 *9!901099 5&9&505 *93&0'593 *1&2!51 0 0
v1 1&2!51 9' 5&9&505 52&253 0 0 *5&9&505 *1.&E$00! *1&2!51 *!351'&!& 0 0
)2 '95900 5&9&505 3& 0 '95900 *5&9&505 *93&0'593 1&2!51 *2.0E$00! 0 *93&0'593 *1&2!51
v2 *5&9&505 52&253 0 93& 5&9&505 52&253 1&2!51 *!351'&!& 0 *2.E$00! *1&2!51 *!351'&!&
)3 0 0 '95900 5&9&505 1! *1&2!51 0 0 *93&0'593 1&2!51 *9!901099 *5&9&505
v3 0 0 *5&9&505 52&253 *1&2!51 9' 0 0 1&2!51 *!351'&!& 5&9&505 *1.&E$00!
)& *9!901099 *5&9&505 *93&0'593 1&2!51 0 0 3& 0 509155 0 0 0 *9!9
8 ,v& 5&9&505 *1.&E$00! 1&2!51 *!351'&!& 0 0 0 93& 0 505 0 0 *5&
)5 *93&0'593 *1&2!51 *2.0E$00! 0 *93&0'593 1&2!51 509155 0 & 0 509155 0 *93&
v5 *1&2!51 *!351'&!& 0 *2.E$00! 1&2!51 *!351'&!& 0 505 0 !'! 0 505 1&
)' 0 0 *93&0'593 *1&2!51 *9!901099 5&9&505 0 0 509155 0 3& 0
v' 0 0 *1&2!51 *!351'&!& *5&9&505 *1.&E$00! 0 0 0 505 0 93&
) 0 0 0 0 0 0 *9!901099 *5&9&505 *93&0'593 1&2!51 0 0
v 0 0 0 0 0 0 5&9&505 *1.&E$00! 1&2!51 *!351'&!& 0 0 *1&
)! 0 0 0 0 0 0 *93&0'593 *1&2!51 *2.0E$00! 0 *93&0'593 1&2!51 5&
v! 0 0 0 0 0 0 *1&2!51 *!351'&!& 0 *2.E$00! 1&2!51 *!351'&!& 5&
)9 0 0 0 0 0 0 0 0 *93&0'593 *1&2!51 *9!901099 5&9&505v9 0 0 0 0 0 0 0 0 *1&2!51 *!351'&!& *5&9&505 *1.&E$00!
":)Cda> H:Cditi:C : ?t>)Ht)>
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Ra>aCggmCt ?tiC?? mat>i- ba?d t: b:)Cda> H:Cditi:C
)2 v2 )3 v3 )5 v5 )' v' )! v! )9 v9
)2 3& 0 '95900 *5&9&505 *2.0E$00! 0 *93&0'593 *1&2!51 0 0 0 0
v2 0 93& 5&9&505 52&253 0 *2.E$00! *1&2!51 *!351'&!& 0 0 0 0
)3 '95900 5&9&505 1! *1&2!51 *93&0'593 1&2!51 *9!901099 *5&9&505 0 0 0 0
v3 *5&9&505 52&253 *1&2!51 9' 1&2!51 *!351'&!& 5&9&505 *1.&E$00! 0 0 0 0
)5 *2.0E$00! 0 *93&0'593 1&2!51 & 0 509155 0 *2.0E$00! 0 *93&0'593 *1&2!51
8 ,v5 0 *2.E$00! 1&2!51 *!351'&!& 0 !'! 0 505 0 *2.E$00! *1&2!51 *!351'&!&)' *93&0'593 *1&2!51 *9!901099 5&9&505 509155 0 3& 0 *93&0'593 1&2!51 *9!901099 *5&9&505
v' *1&2!51 *!351'&!& *5&9&505 *1.&E$00! 0 505 0 93& 1&2!51 *!351'&!& 5&9&505 *1.&E$00!
)! 0 0 0 0 *2.0E$00! 0 *93&0'593 1&2!51 3& 0 5&9&505 5&9&505
v! 0 0 0 0 0 *2.E$00! 1&2!51 *!351'&!& 0 93& *5&9&505 52&253
)9 0 0 0 0 *93&0'593 *1&2!51 *9!901099 5&9&505 5&9&505 *5&9&505 1! 1&2!51
v9 0 0 0 0 *1&2!51 *!351'&!& *5&9&505 *1.&E$00! 5&9&505 52&253 1&2!51 9'
Ek?t>Cal 6:>Hd
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P III. Mengi!ung nil#i 'i%l#e"en! #'# j&in! #ng "eng#l#"i e$ge
i%l#e"en!
)2 *2.332'33!E*005 m *0.02332'33!& mmv2 *'.'350159E*005 m *0.0''350159& mm
)3 *1.!&0&&E*005 m *0.01!&0&& mm
v3 *0.0001521!&5 m *0.1521!&&53 mm
)5 5.203&359E*00' m 0.005203&359 mm
7 +v5 *0.0000'5!9 m *0.0'5!9013 mm
)' 1.2&1&10E*005 m , 0.012&1&103 mm
v' *0.00015!33&' m *0.15!33&5'!5 mm)! 3.!3990E*005 m 0.03!399 mm
v! *.''!213&E*005 m *0.0''!213&2 mm
)9 &.!20932E*005 m 0.0&!209319 mm
v9 *0.0001'&'025 m *0.1'&'025&&& mm
Re#k%i !u"u#n
)2 v2 )3 v3 )5 v5 )' v' )! v! )9 v9
61 '.9'E$0 *5.&9E$0' 0.00E$00 0.00E$00 *9.3&E$0 *.1&E$0 0.00E$00 0.00E$00 0.00E$00 0.00E$00 0.00E$00 0.00E$00 *2.33E*05
G1 5.&9E$0' 5.2E$0 0.00E$00 0.00E$00 *.1&E$0 *!.35E$0 0.00E$00 0.00E$00 0.00E$00 0.00E$00 0.00E$00 0.00E$00 *'.'&E*05
63 *9.3&E$0 .1&E$0 0.00E$00 0.00E$00 .51E$0 0.00E$00 0.00E$00 0.00E$00 *9.3&E$0 *.1&E$0 0.00E$00 0.00E$00 *1.!E*05
G3 .1&E$0 *!.35E$0 0.00E$00 0.00E$00 0.00E$00 1.05E$0! 0.00E$00 0.00E$00 *.1&E$0 *!.35E$0 0.00E$00 0.00E$00 *1.52E*0&
6 0.00E$00 0.00E$00 0.00E$00 0.00E$00 *9.3&E$0 .1&E$0 0.00E$00 0.00E$00 5.&9E$0' 5.&9E$0' 0.00E$00 0.00E$00 5.20E*0'
G 0.00E$00 0.00E$00 0.00E$00 0.00E$00 .1&E$0 *!.35E$0 0.00E$00 0.00E$00 *5.&9E$0' 5.2E$0 0.00E$00 0.00E$00 *'.59E*05
1.2&E*05
*1.5!E*0&
3.!E*05
*.'E*05
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;ek
Gaa L)a> -5000.000 kg
Rak?i t)m)aC 5000.000 kg
0.000 SUDAH BENAR
TAHAP I
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E?@1-2 219!0219!
0.3
1 0.3 0 0 *E*00'
= 219!0219! 0.3 1 0 5E*00 , 0 5E*000 0 0.35 0 0 *2E*005
0
kg/m2 *1.5'2 kg/Hm2
= *3&& kg/ , *0.3& kg/Hm2
kg/m2 *1.!& kg/Hm2
x y
2. Elemen 2. joint 4,5,,! a 1.25 >&in! i 4 -1.25 -0.5 -1 -1
b 0.5 j 5 1.25 -0.5 1 -1
0.4k 8 1.25 0.5 1 1
l 7 -1.25 0.5 -1 1
ui vi uj vj uk vk ul vl
0 )&
)& v& )5 v5 )! v! ) v 0 v&
*1 0 1 0 1 0 *1 0 5E*00' )5
0.& 0 *2.5 0 *2.5 0 2.5 0 2.5 *E*05 v5
*2.5 *1 *2.5 1 2.5 1 2.5 *1 &E*005 )!
v!
0 )
0 v
{σ1=,8E.
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2E*005
=
E/#1*v2% 219!0219!
v 0.3
1 0.3 0 2E*005 0 2E*005
= 219!0219! 0.3 1 0 , 0 *1E*005
0 0 0.35 0 0 *2E*005
0
301 kg/m2 3.02 kg/Hm2
= kg/ , *1.239 kg/Hm2
kg/m2 *1.!' kg/Hm2
x y
". Elemen ". joint 2,",#,5 a 1.25 >&in! i 2 -1.25 -0.5 -1 -1
b 0.5 j 3 1.25 -0.5 1 -1
0.4k 6 1.25 0.5 1 1
l 5 -1.25 0.5 -1 1
ui vi uj vj uk vk ul vl
ε-
ε
γ -
{σ1=,8E.
-
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)2
)2 v2 )3 v3 )' v' )5 v5 v2
*1 0 1 0 1 0 *1 0 )3
0.& 0 *2.5 0 *2.5 0 2.5 0 2.5 0 v3
*2.5 *1 *2.5 1 2.5 1 2.5 *1 1E*005 )'0 v'
5E*00' )5
5E*00' m v5
= m
m
E/#1*v2% 219!0219!
v 0.3
1 0.3 0 5E*00' 0 5E*00'
= 219!0219! 0.3 1 0 , 0 *'E*00'
0 0 0.35 0 0 *1E*005
0
&1 kg/m2 0.&2 kg/Hm2
= *9133 kg/ , *0.913 kg/Hm2
*9'&0 kg/m2 *0.9'& kg/Hm2
x y
4. Elemen 4 joint 4,5,$, a 1.25 >&in! i 4 -1.25 -0.5 -1 -1
b 0.5 j 5 1.25 -0.5 1 -1
0.4k 9 1.25 0.5 1 1
l 8 -1.25 0.5 -1 1
ε-
ε
γ -
{σ1=,8E.
-
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ui vi uj vj uk vk ul vl
5E*00' )5
)5 v5 )' v' )9 v9 )! v! v5
*1 0 1 0 1 0 *1 0 1E*005 )'
0.& 0 *2.5 0 *2.5 0 2.5 0 2.5 0 v'
*2.5 *1 *2.5 1 2.5 1 2.5 *1 5E*005 )9
0 v9
E*005 )!
E*00' m v!
= m
m
E?@1-2 219!0219!
0.3
1 0.3 0 E*00' 0 E*00'
= 219!0219! 0.3 1 0 , 0 *2E*005
0 0 0.35 0 0 *&E*00'
0
&200 kg/m2 0.&2 kg/Hm2
= kg/ , *3.2!! kg/Hm2
*2!'0 kg/m2 *0.2!' kg/Hm2
ε-
ε
γ -
{σ1=,8E.
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3.02 0.&2
*1.5'2 kg/Hm2 0.&2 kg/Hm2
1
2
3
4
2,5 m2,5 m
1,0 m
1,0 m
1000kg%m&
kg%'m2 kg%'m2
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TAHAP ik# =&' 8&$e' 'ie$i!ungk#n
MCg+it)Cg lmC C:dal l:ad
kt:> gaa akibat b:d :>H?
":d :>H? ?tia lmC #b% , g. A. t
"J bt:C b 2.5 m
+ 1 m b , 1200 kg
tbal 0.2 m
ElmCt 1 ElmCt 2
joint 1,2,4,5 joint 4,5,,!
0 61 0 6&
0 62 0 65 0 61
0 6& 0 6! 0 62
0 65 0 6 0 63
*300 G1 *300 G& 0 6&
*300 G2 *300 G5 0 65
*300 G& *300 G! 0 6'
*300 G5 *300 G 0 6
0 6!
0 69
ElmCt 3 ElmCt & *300 G1
joint 2,",#,5 joint 4,5,$, *'00 G2
0 62 0 6& *300 G3
0 63 0 65 *'00 G&
0 6' 0 69 *1200 G5
0 65 0 6! *300 G'
*300 G2 *300 G& *300 G
*300 G3 *300 G5 *'00 G!
*300 G' *300 G9 *300 G9
*300 G5 *300 G!
kg/m3
( 7e + 8
( 7 e
( 7e + 8
( 7 e
( 7e + 8
( 7 e
( 7e
+ 8( 7e
( 7e + 8
( 7 e
( 7e + 8
( 7 e
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8%!7 8(7 8!&!#l7
61 0 0 0
G1 0 *300 *300
62 0 0 0G2 0 *'00 *'00
63 0 0 0
G3 0 *300 *300
6& 0 0 0
G& 0 *'00 *'00
65,
09
0,
0 , Mat>ik? )Cit
G5 0 *1200 *1200
6' 0 0 0
G' 0 -"00 *300
6 0 0 0
G 0 -"00 *3006! 0 0 0
G! *2500 -#00 *3100
69 0 0 0
G9 *1250 -"00 *1550 ==
G## 8!&!#l
7 + 8%!7 9 8
( 7
=*+*1
[ K ] {U }={ P }
∑ [ K Ge ] {U }=∑ { P e }
[ ]{ } [ ] { } { }( )est ebf
e
G f f T UK +=∑∑ #
[T ]= [ I ]
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LANGKAH H:Cditi:C : ?t>)Ht)>
F i t 1 & d l + t +i di l t d F i t t b t 0
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Ra>aCggmCt ?tiC?? mat>i- ba?d t: b:)Cda> H:Cditi:C
)2 v2 )3 v3 )5 v5 )' v' )! v! )9 v9
)2 3& 0 '95900 *5&9&505 *2.0E$00! 0 *93&0'593 *1&2!51 0 0 0
v2 0 93& 5&9&505 52&253 0 *2.E$00! *1&2!51 *!351'&!& 0 0 0
)3 '95900 5&9&505 1! *1&2!51 *93&0'593 1&2!51 *9!901099 *5&9&505 0 0 0
v3 *5&9&505 52&253 *1&2!51 9' 1&2!51 *!351'&!& 5&9&505 *1.&E$00! 0 0 0
)5 *2.0E$00! 0 *93&0'593 1&2!51 & 0 509155 0 *2.0E$00! 0 *93&0'593 *1&2!5
8 ,
v5 0 *3E$00! 1&2!51 *!351'&!& 0 !'! 0 505 0 *2.E$00! *1&2!51 *!351'&!
)' *93&0'593 *E$00 *9!901099 5&9&505 509155 0 3& 0 *93&0'593 1&2!51 *9!901099 *5&9&50v' *1&2!51 *!E$00 *5&9&505 *1.&E$00! 0 505 0 93& 1&2!51 *!351'&!& 5&9&505 *1.&E$00
)! 0 0 0 0 *2.0E$00! 0 *93&0'593 1&2!51 3& 0 5&9&505 5&9&50
v! 0 0 0 0 0 *2.E$00! 1&2!51 *!351'&!& 0 93& *5&9&505 52&25
)9 0 0 0 0 *93&0'593 *1&2!51 *9!901099 5&9&505 5&9&505 *5&9&505 1! 1&2!5
v9 0 0 0 0 *1&2!51 *!351'&!& *5&9&505 *1.&E$00! 5&9&505 52&253 1&2!51 9'
Ek?t>Cal 6:>Hd
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TAHAP
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;ek
Gaa L)a> -B500.000 kg
Rak?i t)m)aC B500.000 kg
0.000 SUDAH BENAR
TAHAP I
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E?@1-2 219!0219!
0.3
1 0.3 0 0 *1E*005
= 219!0219! 0.3 1 0 ' , 0 2E*00'
0 0 0.35 0 0 *5E*0050
kg/m2 *2.9 kg/Hm2
= *3!!2 kg/ , *0.3!! kg/Hm2
kg/m2 *3.5& kg/Hm2
x y
2. Elemen 2. joint 4,5,,! a 1.25 >&in! i 4 -1.25 -0.5 -1 -1
b 0.5 j 5 1.25 -0.5 1 -1
0.4k 8 1.25 0.5 1 1
l 7 -1.25 0.5 -1 1
ui vi uj vj uk vk ul vl
0 )&
)& v& )5 v5 )! v! ) v 0 v&
*1 0 1 0 1 0 *1 0 9E*00' )5
0.& 0 *2.5 0 *2.5 0 2.5 0 2.5 *1E*0& v5
*2.5 *1 *2.5 1 2.5 1 2.5 *1 E*005 )!
0 v!
0 )
0 v
{1= 8 <
1= kg/m
σ
/
σ
/
ξ = x/a η= y/b
{
ε1=,8".
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3E*005
=
E/#1*v2% 219!0219!
v 0.3
1 0.3 0 3E*005 0 3E*005
= 219!0219! 0.3 1 0 , 0 *1E*005
0 0 0.35 0 0 *5E*005
0
5&09 kg/m2 5.&1 kg/Hm2
= kg/ , *1.21& kg/Hm2
kg/m2 *3.&' kg/Hm2
x y
". Elemen ". joint 2,",#,5 a 1.25 >&in! i 2 -1.25 -0.5 -1 -1
b 0.5 j 3 1.25 -0.5 1 -1
0.4k 6 1.25 0.5 1 1
l 5 -1.25 0.5 -1 1
ui vi uj vj uk vk ul vl
ε-
ε
γ -
{σ1=,8E.
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)2
)2 v2 )3 v3 )' v' )5 v5 0 v2
*1 0 1 0 1 0 *1 0 )3
0.& 0 *2.5 0 *2.5 0 2.5 0 2.5 0 v3
*2.5 *1 *2.5 1 2.5 1 2.5 *1 2E*005 )'
0 v'9E*00' )5
!E*00' m 0 v5
= m
m
E/#1*v2% 219!0219!
v 0.3
1 0.3 0 !E*00' 0 !E*00'
= 219!0219! 0.3 1 0 , 0 *E*00'
0 0 0.35 0 0 *2E*005
0
13&!1 kg/m2 1.3&! kg/Hm2
= *9325 kg/ , *0.933 kg/Hm2
kg/m2 *1.'5! kg/Hm2
x y
4. Elemen 4 joint 4,5,$, a 1.25 >&in! i 4 -1.25 -0.5 -1 -1
b 0.5 j 5 1.25 -0.5 1 -1
0.4k 9 1.25 0.5 1 1
l 8 -1.25 0.5 -1 1
ε-
ε
γ -
{σ1=,8E.
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ui vi uj vj uk vk ul vl
9E*00' )5
)5 v5 )' v' )9 v9 )! v! 0 v5
*1 0 1 0 1 0 *1 0 2E*005 )'
0.& 0 *2.5 0 *2.5 0 2.5 0 2.5 0 v'
*2.5 *1 *2.5 1 2.5 1 2.5 *1 !E*005 )9
0 v9
E*005 )!
1E*005 m 0 v!
= m
m
E?@1-2 219!0219!
0.3
1 0.3 0 1E*005 0 1E*005
= 219!0219! 0.3 1 0 , 0 05
0 0 0.35 0 0 *'E*00'
0
!52 kg/m2 0.!5 kg/Hm2
= kg/ , *&.215 kg/Hm2
*&922 kg/m2 *0.&92 kg/Hm2
ε-
ε
γ -
{σ1=,8E.
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5.&1 0.!5
*2.9 kg/Hm2 1.3&! kg/Hm2
kg%'m2
kg%'m2
1
2
3
4
2,5 m2,5 m
1,0 m
1,0 m
1000kg%m&
