Aplikasi Kuda-kuda AsimetriV A V B H B 07/11/2011 Djoko Luknanto ([email protected]) 2 Kuda-kuda...
16
Metoda Numerik Aplikasi di Lapangan: Kuda-kuda Asimetri Djoko Luknanto Staf Pengajar Jurusan Teknik Sipil FT UGM
Transcript of Aplikasi Kuda-kuda AsimetriV A V B H B 07/11/2011 Djoko Luknanto ([email protected]) 2 Kuda-kuda...
Metoda Numerik
Aplikasi di Lapangan:Kuda-kuda Asimetri
Djoko LuknantoStaf Pengajar
Jurusan Teknik Sipil FT UGM
VA
VB
HB
07/11/2011 Djoko Luknanto ([email protected]) 2
Kuda-kuda Asimetri
+
+
HC
VC
HS
VS
C
A
B3
2
1
VR
yB
yC
xC
xB
Hitung gaya-gaya internal yaitu gaya-gaya batang:P1, P2, dan P3
HA
Hitung reaksi perletakan:VR, VS, dan HS
Formulasi sudah lengkap!
Hitungan Reaksi Perletakan dan Gaya Batang
• Diketahui:xB, xC, yB, yC , VA, HA, VB, HB, VC, HC
• Dihitung:VR, VS, HS, P1, P2, P3
• Reaksi perletakan dihitung dengan cara: FH = 0 FV = 0 MB = 0
07/11/2011 Djoko Luknanto ([email protected]) 3
07/11/2011 Djoko Luknanto ([email protected]) 4
Hitungan Reaksi Perletakan
Reaksi perletakan dihitung dengan cara:
FH = 0 HA + HB + HC + Hs = 0Hs = – HA – HB – HC
FV = 0 VR + VS + VA + VB + VC = 0VR + VS = – VA – VB – VC
MB = 0 (VR + VA) xB – HAyB + HC (yC - yB) + VC (xB - xC) = 0VR xB = HAyB – HC (yC - yB) – VC (xB - xC) – VAyB
07/11/2011 Djoko Luknanto ([email protected]) 5
Kesetimbangan Titik buhul A
FH = 0 P1 cos – P3 cos (+ ) + HA = 0 – P1 cos + P3 cos (+ ) = HA
FV = 0 VR + VA + P1 sin – P3 sin (+ ) = 0 – P1 sin + P3 sin (+ ) = VA + VR
07/11/2011 Djoko Luknanto ([email protected]) 6
Kesetimbangan Titik buhul B
FH = 0 – P1 cos + P2 cos (- ) + HB + HS = 0 P1 cos – P2 cos (- ) = HB + HS
FV = 0 VB + VS – P1 sin – P2 sin (– ) = 0 P1 sin + P2 sin (- ) = VB + VS
07/11/2011 Djoko Luknanto ([email protected]) 7
Kesetimbangan Titik buhul C
FH = 0 – P2 cos (– ) + P3 cos (+ ) + HC = 0 P2 cos (– ) – P3 cos (+ ) = HC
FV = 0 P2 sin (– ) + P3 sin (+ ) + VC = 0 – P2 sin (– ) – P3 sin (+ ) = VC
Sistem persamaan linierDipilih 6 dari 9 persamaan yang dibutuhkan untuk menghitung: VR, VS, HS, P1, P2, P3
1. VR = {HAyB – HC (yC-yB) – VC (xB-xC) – VA xB}/xB
2. VR + VS = – VA – VB – VC
3. Hs = – HA – HB – HC
4. P1 cos – P2 cos (- ) = HB + HS
5. P2 cos (– ) – P3 cos (+ ) = HC
6. – P2 sin (– ) – P3 sin (+ ) = VC
07/11/2011 Djoko Luknanto ([email protected]) 8
Modifikasi sistem persamaan linier1. VR = {HAyB – HC (yC-yB) – VC (xB-xC) – VA xB}/xB
2. VR + VS = – VA – VB – VC
3. Hs = – HA – HB – HC
4. – P1 cos – P2 cos (- ) = HB + HS
5. – P2 cos (– ) + P3 cos (+ ) = HC
6. – P2 sin (– ) – P3 sin (+ ) = VC
Reaksi perletakan dihitung terlebih dahulu:1. VR = {HAyB – HC (yC - yB) + VCxC}/xB – VA – VC
2. VS = – VA – VB – VC – VRVS = – {HAyB – HC (yC - yB) + VCxC}/xB – VB
3. Hs = – HA – HB – HC
07/11/2011 Djoko Luknanto ([email protected]) 9
Sistem persamaan linier final1. VR = {HAyB – HC (yC - yB) + VCxC}/xB – VA – VC
2. VS = – {HAyB – HC (yC - yB) + VCxC}/xB – VB
3. Hs = – HA – HB – HC
4. P1 cos – P2 cos (- ) = HB + HS
5. P2 cos (– ) – P3 cos (+ ) = HC
6. – P2 sin (– ) – P3 sin (+ ) = VC
Persamaan 4, 5, dan 6 diselesaikan untuk menghitung: P1, P2, P3
07/11/2011 Djoko Luknanto ([email protected]) 10
1
2
3
cos cos( ) 00 cos( ) cos( )0 sin( ) sin( )
B S
C
C
P H HP HP V
Rekapitulasi Hitungan• Reaksi perletakan
• Gaya batang
07/11/2011 Djoko Luknanto ([email protected]) 11
S A B CH H H H
1 ( )S A B C C B C C BB
V H y H y y V x Vx
1 ( )R A B C C B C C A CB
V H y H y y V x V Vx
1
2
3
cos cos( ) 00 cos( ) cos( )0 sin( ) sin( )
B S
C
C
P H HP HP V
07/11/2011 Djoko Luknanto ([email protected]) 13
Gambar Jawaban
VA
VB
HB
+
+
HC
VC
HS
VS
C
A
B3
2
1
VR
yB
yC
xC
xB
HA
Eliminasi Gauss 1/2
07/11/2011 Djoko Luknanto ([email protected]) 14
1
2
3
cos( )1 0coscos
cos( )0 1cos( ) cos( )sin( )0 1sin( ) sin( )
B S
C
C
H H
PH
PP
V
1
2
3
cos cos( ) 00 cos( ) cos( )0 sin( ) sin( )
B S
C
C
P H HP HP V
Eliminasi Gauss 2/2
07/11/2011 Djoko Luknanto ([email protected]) 15
1
2
3
cos( ) cos( )1 0coscos cos( )
cos( )0 1cos( ) cos( )
sin( ) cos( )0 0sin( ) cos( ) sin( ) cos( )
B C S
C
C C
H H H
PH
PP
V H
1
2
3
cos( )1 0coscos
cos( )0 1cos( ) cos( )sin( )0 1sin( ) sin( )
B S
C
C
H H
PH
PP
V
Substitusi
07/11/2011 Djoko Luknanto ([email protected]) 16
3sin( ) cos( )
sin( ) cos( )sin( ) cos( )
tan( )sin( ) tan( )cos( )
C C
C C
V H
P
V H
2 3cos( )
cos( ) cos( )CH
P P
1 3cos( )
cos cosB C SH H H
P P
