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Analisa Struktur
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TUGAS ANALISA STRUKTUR 2
OLEH
UNIVERSITAS KATOLIK WIDYA MANDIRAKUPANG
###
no reg = 9
1.911
2.5
1 1 4
1.912
2.5
51
1
3 3Hitung dan gambar bidang M, D, dan N
MOMEN PRIMER
1.911
2.5
4
AB
C D
E F
m
t/m
t/m
T
T
m
mm
EI
EI
EI
EI
EIEI
E F
t/m
t/m
T
m
EI
EIEI
P1=P2=
P4=
1.912
2.5
5
3 3
1 Menghitung Momen Primer
= 0 Tidak ada beban
= 0 Tidak ada beban
= 0 Tidak Ada Beban= 0 Tidak Ada Beban= 1 1.9 6 = -5.70 tm
12
= 1 1.9 6 = 5.70 tm12
= 0 tm
MFAC
MFCA
MFBD
MFDB
MFCD
MFDC
MFCE
AB
C D
m
t/mT
mm
EI
EI
EI
**
**2
- 2
= 0 tm
= 1 1.9 6 = -5.70 tm12
= 1 1.9 6 = 5.70 tm12
= 0 Tidak Ada Beban= 0 Tidak Ada Beban
MOMEN AKHIR1.9
112.5
4
1.912
2.5
5
3 3
MFEC
MFEF
MFFE
MFDF
MFFD
2**
2**
-
AB
C D
E F
m
t/m
t/m
T
T
m
mm
EI
EI
EI
EI
EIEI
+
++
+
2 Putaran Sudut akibat PergoyanganRac = Rca = Δ1/5Rdb = Rbd = Δ1/5 Berlaku untuk kolomRce = Rec = Δ2/4 Δ2Rdf = Rfd = Δ2/4 Δ2
= 0 Karena Perletakan Jepit
2.5Rec
4Rdf
2.5
Rac Rdb 5
Rca Rbd
3 3
3 Menghitung Momen Akhir
Δ1Δ1
ɸb dan ɸa
mm
AB
CD
E F
m
m
mm
EI
EI
EI
EI
EIEI
Δ1 Δ2 Δ1 Δ2
Rumus Umum= + 2EI/L= + 2EI/L
= 0.00 1 2 ɸa 3 Δ15 5
= 0.2 ɸc 0.12 Δ1
= 0.00 1 2 ɸc ɸa 3 Δ15 5
= 0.4 ɸc 0.12 Δ1
= 0 1 2 ɸb ɸd 3 Δ15 5
= 0.2 ɸd 0.12 Δ1
= 0 1 2 ɸd ɸb 3 Δ15 5
= 0.4 ɸd 0.12 Δ1
= -5.70 2.5 2 ɸc ɸd6
= -5.70 0.83333 ɸc 0.41667 ɸd
= 5.70 2.5 2 ɸd ɸc6
MAB MFAB ( 2ɸa + ɸb - 3Ra )MBA MFBA ( 2ɸb + ɸa - 3Rb )
MAC ɸc
MCA
MBD
MDB
MCD
MDC
+ + -
-
+ + -
-
+ + -
-
+ + -
-
+ +
+ +
+ +
= 5.70 0.83333 ɸd 0.41667 ɸc
= 0.00 1 2 ɸc ɸe 3 Δ24 4
= 0.5 ɸc 0.25 ɸe 0.1875 Δ2
= 0.00 1 2 ɸe ɸc 3 Δ24 4
= 0.5 ɸe 0.25 ɸc 0.1875 Δ2
= -5.70 2.5 2 ɸe ɸf6
= -5.70 0.83333 ɸe 0.41667 ɸf
= 5.70 2.5 2 ɸf ɸe6
= 5.70 0.83333 ɸf 0.41667 ɸe
= 0 1 2 ɸd ɸf 3 Δ24 4
= 0.5 ɸd 0.25 ɸf 0.1875 Δ2
= 0 1 2 ɸf ɸd 3 Δ24 4
= 0.5 ɸf 0.25 ɸd 0.1875 Δ2
MCE
MEC
MEF
MFE
MDF
MFD
+ + -
-
+ + -
-
+ +
+ +
+ - -
-
+ - -
+ +
+ +
-
+ +
+
+
+ +
+ +
+
+
4 Untuk Menentukan Seluruh momen akhir harus diketahui ɸc ɸd ɸe ɸf Δ1 Δ2
+ += 0.4 ɸc 0.12 Δ1 + -5.70 0.833333 ɸc 0.416666667 ɸd +
= -5.70 1.73333 ɸc 0.41667 ɸd 0.25 ɸe 0.12 Δ1 0.1875 Δ2 == 1.73333 ɸc 0.41667 ɸd 0.25 ɸe 0.12 Δ1 0.1875 Δ2 =
+ += 5.70 0.83333 ɸd 0.41667 ɸc + 0.5 ɸd 0.25 ɸf 0.1875 Δ2 + 0.40
= 5.70 0.41667 ɸc 1.73 ɸd 0.25 ɸf 0.1875 Δ2 0.12 Δ1 = 0= 0.41667 ɸc 1.73333 ɸd 0.25 ɸf 0.1875 Δ2 0.12 Δ1 = -5.70 ......
+= 0.5 ɸe 0.25 ɸc 0.1875 Δ2 + -5.70 0.833333 ɸe 0.416666667 ɸf == -5.70 0.25 ɸc 1.33333 ɸe 0.41667 ɸf 0.1875 Δ2 = 0= 0.25 ɸc 1.33333 ɸe 0.41667 ɸf 0.1875 Δ2 = 5.70 ...... pers 3
ΣMC
MCA MCD MCE
ΣMD
MDC MDF MDB
ΣME
MEC MEF
ΣMF
-
-
- -- -
----
-
---
+
+ +
+ +++ +
+ + +
+ + +++
+ + ++ + +
++
+
= 0.5 ɸf 0.25 ɸd 0.1875 Δ2 + 5.70 0.8333333 ɸf 0.41667 ɸe = 0= 5.70 0.25 ɸd 0.41667 ɸe 1.33333 ɸf 0.1875 Δ2 = 0= 0.25 ɸd 0.41667 ɸe 1.33333 ɸf 0.1875 Δ2 = -5.70
= 0+ + + -11 - 11 4 = 0
0.5 ɸe 0.25 ɸc 0.1875 Δ2 0.5 ɸc 0.25 ɸe 0.1875 Δ2 0.54
0.75 ɸc 0.75 ɸd 0.75 ɸe 0.75 ɸf 0.75 Δ2 = 554
= 0.75 ɸc 0.75 ɸd 0.75 ɸe 0.75 ɸf 0.75 Δ2 = 220 ...... pers
= 0+ + + -11 -12 11 4 12 5
0.2 ɸc 0.12 Δ1 0.4 ɸc 0.12 Δ1 0.25
0.6 ɸc 0.6 ɸd 0.48 Δ1 = 1275
0.6 ɸc 0.6 ɸd 0.48 Δ1 = 635 ...... pers 6
5 REKAP SEMUA PERSAMAAN
MFD MFE
ΣH2
MEC MCE MFD MDF
Lec LDF
ΣH1
MAC MCA MBD MDB
LAC LDB
---
*
- + -+
*- *-
+ +
-
+ + ++ + +
++
+ +
+ + + -
+ + + -
- -
+ -
+
1.73333 ɸc 0.41667 ɸd 0.25 ɸe 0.12 Δ1 0.1875 Δ2 = 5.700.41667 ɸc 1.73333 ɸd 0.25 ɸf 0.1875 Δ2 0.12 Δ1 = -5.70
0.25 ɸc 1.33333 ɸe 0.41667 ɸf 0.1875 Δ2 = 5.700.25 ɸd 0.41667 ɸe 1.33333 ɸf 0.1875 Δ2 = -5.700.75 ɸc 0.75 ɸd 0.75 ɸe 0.75 ɸf 0.75 Δ2 = 220
0.6 ɸc 0.6 ɸd 0.48 Δ1 = 635
6 MENGHITUNG ɸc ɸd ɸe ɸf Δ1 Δ2 DENGAN MENGGUNAKAN MATRIKS
ɸc ɸd ɸe ɸf Δ1 Δ2 ɸc ɸd ɸe ɸf Δ1 Δ2
1.73 0.42 0.25 0.00 -0.12 -0.19 0.74 -0.06 -0.08 0.14 -0.19 -0.170.42 1.73 0.00 0.25 -0.12 -0.19 -0.06 0.74 0.14 -0.08 -0.19 -0.170.25 0.00 1.33 0.42 0.00 -0.19 X -0.08 0.14 0.94 -0.21 -0.20 -0.020.00 0.25 0.42 1.33 0.00 -0.19 0.14 -0.08 -0.21 0.94 -0.20 -0.020.75 0.75 0.75 0.75 0.00 -0.75 0.85 0.85 0.08 0.08 -0.47 -2.510.60 0.60 0.00 0.00 -0.48 0.00 0.75 0.75 0.80 0.80 -2.10 -0.37
1 0 0 0 0 0 ɸc0 1 0 0 0 0 ɸd 5.70 0.74 -0.060 0 1 0 0 0 ɸe -5.70 -0.06 0.74
= 0 0 0 1 0 0 X ɸf = 5.70 X -0.08 0.140 0 0 0 1 0 Δ1 -5.70 0.14 -0.080 0 0 0 0 1 Δ2 220.00 0.85 0.85
635.00 0.75 0.75
7 MENGHITUNG MOMEN AKHIR
MAC = 0.200 Фc - 0.120 Δ1
- -- ---+
+
+ +++
+ ++
+-++
-
= -29.227 + 203.587
= 174.360 tm
MBD = 0.2 Фd - 0.120
= -30.555 + 203.587
= 173.032 tm
MCA = 0.400 Фc - 0.120
= -58.454 + 203.58696
= 145.133 tm
MCD = -5.700 0.833 Фc 0.417 Фd
= -5.700 - 121.780 - 63.657046
= -191.137 tm
MCE = 0.500 Фc 0.250 Фe - 0.188
= -73.068 -12.069 + 131.141= 46.005 tm
MDB = 0.4 Фd - 0.120
= -61.111 + 203.587
= 142.476 tm
MDC = 5.700 0.833 Фd 0.417 Фc
= 5.700 -127.314 -60.890
= -182.504 tm
MDF = 0.5 Фd 0.25 Фf - 0.1875
= -76.388 -14.725 + 131.141
= 40.028 tm
MEC = 0.500 Фe 0.250 Фc - 0.188
Δ1
Δ1
Δ2
Δ1
Δ2
Δ2
+ +
+
+
+
+
+
= -24.137 -36.534 + 131.1413
= 70.470 tm
MEF = -5.700 0.833 Фe 0.417 Фf
= -5.700 -40.229 -24.541
= -70.470 tm
MFD = 0.5 Фf 0.25 Фd - 0.1875
= -29.450 -38.194 + 131.141
= 63.497 tm
MFE = 5.700 0.833 Фf 0.417 Фe
= 5.700 -49.083 -20.114
= -63.497 tm
8 KONTROL SETIAP MOMEN = 0
Σ MA = 0
MAC = 0
174.360 = 0 …………………………. Ok !!!
Σ MC = 0
MCA + MCD + MCE = 0
145.133 + -191.137 + 46.005 = 0
0.000 = 0 …………………………. Ok !!!
Σ MD = 0
MDB + MDC + MDF = 0
142.476 + -182.504 + 40.028 = 0
Δ2
+
+ +
++
+
0.000 = 0 …………………………. Ok !!!
Σ ME = 0
MEC + MEF = 0
70.470 + -70.470 = 0
0.000 = 0 …………………………. Ok !!!
Σ MF = 0
MFD + MFE = 0
63.497 + -63.497 = 0
0.000 = 0 …………………………. Ok !!!
JUMLAH GAYA HORIZONTAL TIAP TINGKAT = 0.
= 0
MCE + MEC+
MDF + MFD - ( q . L ) = 0
46.005 + 70.470+
40.028 + 63.497-8.000 -32.000 = 0
4 4
29.119 + 25.881 -40.000 = 0
55.000 -40.000 = 0
15.000 = 0 …………………………. Ok !!!
= 0
Σ H2
-P2Lce Ldf
Σ H1
MAC + MCA+
MBD + MDB -P2 - P1 = 0
174.360 + 145.133+
173.032 + 142.476-11.000 -12.000 -104.000 = 0
5 5
63.898 + 63.102 -127.000 = 0
127.000 -127.000 = 0
0.000 = 0 …………………………. Ok !!!
9 FREEBODY
MEF 70.470 MFE 63.497
1.911
REF RFE
REC RFDMFD
MEC 70.470
MCE 46.005MDF
RCE
- ( qac . Lac ) - ( qce . Lce )Lac Lbd
E F
T
t/m
t/m
1.9 RDF12
MCD 191.14 182.504 =MDCRCD RDC
RCA RDB
MCA 145.133 MDB
MAC 174.360 MBD
RAC RBD
3 3
10 MENGHITUNG REAKSI PERLETAKAN+ -
REF = 1/2 +MEF
+MFE
= 0.5 1.9 6 + 70.470 + 63.4976 6
= 5.7 + 11.74502 + 10.582881
qef LefLef Lfe
A B
C DT
t/m
= 28.0279 t
RFE = 1/2 -MEF
-MFE
= 0.5 1.9 6 - 70.470 - 63.4976 6
= 5.7 - 11.74502 - 10.582881
= 16.6279 t
Q - REF + RFE = 011.4 - 28.0279 + 16.6279 = -33.2558
11.4 - 11.4 = 00 = 0 OK
RCE = + +MCE
+MEC
= + 11 + 46.005 + 70.4704 4
= + 11 + 11.501163 + 17.6175
= 18.1187 t
qef LefLef Lfe
KONTROL : ΣV = 0
P2Lce Lce
REC = -MEC
-MCE
= - 70.470 - 46.0054 4
= - 17.61753 - 11.501163
= -29.1187 t
+ + RCE - REC = 0
+ 11 + 18.119 - 29.119 = 011.000 + -11.000 = 0
0.000 = 0 ………………..OK !!!
RDF =MDF
+MFD
=40.028
+63.497
4 4
= 10.007 + 15.874
= 25.881 t
RFD = -MFD
-MDF
Lec Lce
KONTROL : ΣH = 0
P2
Ldf Ldf
Lfd Ldf
= -63.497
-40.028
4 4
= - 15.874 - 10.007
= -25.881 t= 25.881 t
RCE + REC = 025.881 + -25.881 = 0
0.000 = 0 ………………..OK !!!
RCD = 1/2 +MCD
+MDC
= 0.5 1.9 6 +191.137
+182.504
6 6
= -5.7 + 31.856 + 30.417
= 56.574 t
RDC = 1/2 -MDC
-MCD
= -0.5 1.9 6 -182.504
-191.137
6 6
KONTROL : ΣH = 0
qcd LcdLcd Lcd
qcd LcdLdc Lcd
= -5.7 - 30.417 - 31.856
= -67.974 t= 67.974 t
Q RDC RCD = 011.4 + -67.974 + 56.574 = 0
67.974 - 67.974 = 00.000 = 0 ………………..OK !!!
RAC = +MAC
+MCA
= 12 +174.360
+145.133
5 5
= 12 + 34.872 + 29.027
= 75.898 t
RCA = -MCA
-MAC
= -145.133
-174.360
5 5
= - 29.027 - 34.872
= -63.898 t
KONTROL : ΣV = 0
P1Lca Lca
Lca Lac
+ + RAC + RCA = 0
+ 12 + 75.898 + -63.898 = 012.000 + 12.000 = 0
0.000 = 0 ………………..OK !!!
RBD =MBD
+MDB
=173.032
+142.476
5 5
= 34.606 + 28.495
= 63.102 t
RDB = -MDB
-MBD
= -142.476
-173.032
5 5
= - 28.495 - 34.606
= -63.102 t= 63.102 t
KONTROL : ΣH = 0
P1
Lbd Ldb
Ldb Lbd
KONTROL : ΣH = 0
RCE + REC = 063.102 + -63.102 = 0
0.000 = 0 ………………..OK !!!
BELUM KERJA11 GAMBAR BIDANG M, D, DAN N
GAMBAR BIDANG MSKLA MOMEN
1 M : 5 CM63.497 tm
8.55 tm70.470 tm
1/8 . q . L2 =
+-
8.55 70.470 = -61.92 tm
70.470 tm
70.470 tm63.497 tm
0 tm
46.005 tm 40.028 tm
182.504 tm
1/8 . q . L2 =
-
E
+
+
F
+
-
+
-
CD
0 tm
191.14 tm0 - 191.14 = -191.14 t m
145.133 - 0 = 145.133 tm145.133 tm 142.476
0 tm
174.360 173.032
GAMBAR BIDANG DSKLA GAYA
1 M : 5 CM
28.0279
1/4 . p . L =
1/8 . q . L2 =
+
+
+
-
+
D
B
C
A
-+
16.6279 8.62710429.1187 25.881
18.1187 25.881
-67.974
0.000
-63.898 63.102
-
-+
-+
-+
E F
DC
75.89863.102
GAMBAR BIDANG NSKLA PANJANG
1 M : 5 CM
-18.119 25.881
E F
28.0279 16.6279
28.0279 16.627963.102
12.62
-+B
A
C -51.898 D
0.000
0.000 -67.974
A -67.9740.000 B
540000 2.5313213333 1
m
m
0.5 ɸc 0.25 ɸe 0.1875 Δ2 = 0
05.70 ...... pers 1
ɸd 0.12 Δ1 = 0
pers 2
0
-
-
+
...... pers 4
ɸf 0.25 ɸd 0.1875 Δ2 0.5 ɸd 0.25 ɸf 0.1875 Δ2 -55 = 04
5
ɸd 0.12 Δ1 0.4 ɸd 0.12 Δ1 -23 -44 -60 = 05
+ -
- +
+ - +
-
Matriks Invers
-0.08 0.14 -0.19 -0.17 ɸc -146.140.14 -0.08 -0.19 -0.17 ɸd = -152.780.94 -0.21 -0.20 -0.02 = ɸe -48.274
-0.21 0.94 -0.20 -0.02 ɸf -58.90.08 0.08 -0.47 -2.51 Δ1 -16970.80 0.80 -2.10 -0.37 Δ2 -699.42
…………………………. Ok !!!
63.497
4
40.028
142.476
5
173.032
1.73 0.42 0.25 0 -0.12 -0.190.42 1.73 0 0.25 -0.12 -0.190.25 0 1.33 0.42 0 -0.19
0 0.25 0.42 1.33 0 -0.190.75 0.75 0.75 0.75 0 -0.750.6 0.6 0 0 -0.48 0
1 0 0 0 0 00 1 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1
4.8 0.75 -0.06 -0.08 0.14 -0.19 -0.17-4.8 -0.06 0.75 0.14 -0.08 -0.19 -0.174.8 -0.08 0.14 0.95 -0.21 -0.20 -0.02
-4.8 0.14 -0.08 -0.21 0.95 -0.20 -0.02160 0.86 0.86 0.08 0.08 -0.48 -2.51470 0.75 0.75 0.80 0.80 -2.12 -0.38
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