Post on 01-Mar-2018
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DISTRIBUSI MOMEN
FAKTOR KEKAKUAN
TITIK B
KBA =4.EI
L
=4.EI
5=0.8EI
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KBC =4.2EI
L
=4.2EI5
=8EI5
=1.6EI
KB = 0.8EI + 1.6EI = 2.4EI
TITIK C
KCD=
4.EI
L
=4.EI
5=0.8EI
KCB =4.2EI
L
=4.2EI
5=8EI
5=1.6EI
KC = 0.8EI + 1.6EI = 2.4EI
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FAKTOR DISTRIBUSI
TITIK B
BA = KBA
KB
=0.8EI
2.4EI=0.33
BC =KBC
KB
=1.6EI2.4EI
=0.67
KONTROL B = 0.33 + 0.67 = 1
TITIK C
CD =KCD
KC
=0.8EI
2.4EI=0.33
CB =KCB
KC
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=1.6EI
2.4EI=0.67
KONTROL C = 0.33 + 0.67 = 1
MOMEN PRIMER
TITIK A
MAB =p AB
2
L2
=6.3.22
52 = -2,88 t.m
MAB =-2,88 t.m
TITIK B
MBA =+p A
2B
L2
=+6.32 .2
52 = 4,23 t.m
MBC =q . L2
12
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=3.52
12= -6,25 t.m
MBA + MBC = -2,02 t.m
TITIK C
MCB =q . L
2
12
=+6.3
2
.2
52 = 4,23 t.m
TITIK D
MDE =
l
q .( 2)12
=
4
6.( 2)12
=
8 t.m
TITIK C
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MCF =p .l8
=
2.48
= -1 t.m
MF = Mf + Mf!
= -5.33 + 1 = -4.33 t.m
MC = M!f
= -1 t.m
ME = M" + Mf
= -8 + 5.33 = -2.67 t.m
TABEL DISTRIBUSI MOMEN
TITIK A D B E F C
CABANG AD DA DE BE EB ED EF FE FC CF
#.$I%TRIB&%I 0.00 0.33 0.67 0.00 0.33 0.33 0.33 0.67 0.33 0.00
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#.IN$&K%I 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50
M.'RIMER 0.00 0.00 8.00 0.00 0.00 -8.00 5.33 -5.33 1.00 -1.00
M.'ERL()(N(N 0.00 -2.67 -5.33 0.00 0.8* 0.8* 0.8* 2.8* 1.44 0.00
M.IN$&K%I -1.33 0.00 0.44 0.00 1.44 0.44 0.72
M.'ERL()(N(N 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.30 -0.15 0.00
M.IN$&K%I 0.00 0.00 0.00 0.00 -0.15 0.00 -0.07
M.'ERL()(N(N 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
M.(KIR -1.33 -2.67 2.67 0.44 0.8* -7.11 7.52 -2.30 2.30 -0.35
M (KIR 1.33 2.67 -2.67 -0.44 -0.8* 7.11 -7.52 2.30 -2.30 0.35
DEFLEKSI LERENG
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FAKTOR KEKAKUAN
TITIK F
KFC =4
EIL
=4EI
4=1EI
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KFE =4.2EI
L
=4.2EI
4=8EI
4=2EI
KF = 1EI + 2EI = 3EI
TITIK E
KEF =4.2EI
L
=4.2EI4
=8EI4
=2EI
KED =4.2EI
L
=4.2EI
4=8EI
4=2EI
KEB =4.2EI
L
=4.2EI
4=8EI
4=2EI
KE = 2EI + 2EI + 2EI = 6EI
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TITIK D
KDE =4.2EI
L
=
4.2EI
4
=8EI
4
=2EI
KDA =4EI
L
=4EI
4=1EI
K
D = 2EI + 1EI = 3EI
MOMEN PRIMER
TITIK F
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MFE =
l
q .(2)12
=4.(42)
12 = -5.33 t.m
MFC =p . l
8
=2.4
8 = 1 t.m
TITIK E
MED =
l
q .(2)12
=
4
6. ( 2)12
=
-8 t.m
MEF =
l
q .( 2)12
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=
4
4.( 2)12
=
5.33 t.m
TITIK D
MDE =
l
q .( 2)12
=
4
6.( 2)12
=
8 t.m
TITIK C
MCF =p .l8
=2.48 = -1 t.m
MF = MFE + MFC
= -5.33 + 1 = -4.33 t.m
MC =
MCF
= -1 t.m
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ME =
MED +MEF
= -8 + 5.33 = -2.67 t.m
RDA =
4
=
4.4
4=
4
4 = 1
REB =
4
=
4.4
4=
4
4 = 1
RFC =
4
=
4.4
4=
4
4 = 1
(,B,C = 0
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PERSAMAAN DEFLEKSI LERENG
MAD = MAD + KAD -2 - " + R" /
= 0 + 1 EI -2 - " + 1R/ = 0 - 2EI - 1EI " + 1EI R
= -1EI " + 1EI R
MDA = MDA + KDA -2" - + R" /
= 0 + 1EI -2" - + 1R / = 0 - 2EI " - 1EI + 1EI R
= -2EI " + 1EI R
MBE = MBE + KBE -2 - + R /
= 0 + 2EI -2 - + 1R / = 0 - 4EI - 2EI + 2EI R
= -2EI + 2EI RMEB =
MEB +KEB -2 - + R /
= 0 + 2EI -2 - + 1R / = 0 - 4EI - 2EI + 2EI R
= -4EI + 2EI RMFC =
MFC +KFC -2f - ! + Rf! /
= 1 + 1EI -2f - ! + 1R / = 1 - 2EI f - 1EI ! + 1EI R
= 1 - 2EI f + 1EI RMCF =
MCF +KCF -2! - f + Rf! /
= -1 + 1EI -2! - f + 1R / = -1 - 2EI ! - 1EI f + 1EI R
= -1 - 1EI f + 1EI R
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MDE =MDE +
KDE -2" - /
= 8 + 2EI -2" - / = 8 - 4EI " - 2EI MED =
MED +KED -2 - " /
= -8 + 2EI -2 - " / = -8 - 4EI - 2EI "MEF =
MEF +KEF -2 - f /
= 5.33 + 2EI -2 - f / = 5.33 - 4EI - 2EI fMFE =
MFE +KFE -2f - /
= -5.33 + 2EI -2f - / = -5.33 - 4EI f - 2EI
SYARAT SAMBUNGAN DAN SATU SYARAT GESERAN
Tt # =MFC +
MFE = 0
Tt E =MEF +
MED +MEB = 0
Tt $ =MDE +
MDA = 0
= -' +HA +
HB +HC = 0
HASIL DARI TITIK-TITIK PORTAL
MF = 1 - 2EI f + 1EI R / + 5.33 - 4EI f - 2EI /
= 6.33 + 6EI f - 2EI + 1EI R
-6.33 = 6EI f -2EI + 1EI R
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ME = - 4EI + 2EI R / + -8 - 4EI - 2EI " / + 5.33 - 4EI - 2EI f /
= -3.33 - 12EI - 2 " - 2EI f + 2EI R
3.33 = - 12EI - 2EI " - 2EI f + 2EI R
MD = - 2EI " + 1EI R / + 8 - 4EI " - 2EI /
= 8 - 6EI " - 2EI + 1EI R
-8 = - 6EI " - 2EI + 1EI R
SYARAT KESETIMBANGAN
HA =MAD+MDA
4 =(1EI d+1EI R)+(2EI d+1EI R)
4
=(3EI d+2EI R)
4
HB =MBE+MEB
4 =(2EI e+2EI R )+(4EI e+2EI R)
4
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=(6EI e+4EI R)
4
HC
=
MCF+MFC
4 =
(11EI f+1EI R)+(12EI f+1EI R)4
=(3EI f+2EIR)
4
E%ER(N = -' + + + !
= -2 +(3EI d+2EI R )
4 +(6EI e+4EI R )
4 +(3EI f+2EIR)
4
= -8
4 +(3EI d+2EI R)
4 +(6EI e+4EI R )
4 +(3EI f+2EIR)
4 / .4
= -8 + - 3EI " + 2EI R / + -6EI + 4EI R / + - 3EI f + 2EIR / = 0
= - 3EI f - 6EI - 3EI " + 8EIR = 8
6EI f -2EI + 1EI R = -6.33
2EI f - 12EI - 2EI " - + 2EI R = 3.33
- 2EI - 6EI " + 1EI R = -8- 3EI f - 6EI - 3EI " + 8EIR = 8
ELIMINASI
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%ETEL( $I ELIMIN(%I MEN&N(K(N METO$E (&%% $I$('(TK(N (%IL
# = 0.37*7*
E = -0.227
$ = 1.67577
R = 1.60057
PERHITUNGAN MOMEN AKHIR
MAD = -1EI " + 1EI R
= -11.67577/ + 1 1.60057/
= -0.0751* EIMDA = -2EI " + 1EI R
= -21.67577/ + 11.60057/= -0.15038 EI
MBE = -2EI + 2EI R
= -2-0.227/ + 21.60057/
= 3.655172 EI
MEB = -4EI + 2EI R
= -4-0.227/ + 21.60057/
= 4.10*1*5 EI
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MFC = 1 - 2EI f + 1EI R
= 1 20.37*7*/ + 11.60057/= 1.840**6 EI
MCF = -1 - 1EI f + 1EI R= -1 10.37*7*/ + 11.60057/
= 0.220785 EIMDE = 8 - 4EI " - 2EI
= 8 41.67577/ 2-0.227/
= 1.750*58 EIMED = -8 - 4EI - 2EI "
= -8 4-0.227/ 21.67577/= -10.4435 EI
MEF = 5.33 - 4EI - 2EI f
= 5.33 4-0.227/ 20.37*7*/
= 5.478467 EIMFE = -5.33 - 4EI f - 2EI
= -5.33 40.37*7*/ 2-0.227/
= -6.3*513 EI