Tugas Anstruk II
22
N0. 2 q = p1 = 18.75 t p3 = 16 t/m 4.5 m 7.5 m 66.0375 α2 3m α1 = 68.1986 3 Cm 5m 2m Diketahui : A = 0.1024 Q = 40 t Pv1 = 18.75 t E = 0.24 PH = 0 t Pv2 = 20.85 t I = 0.0072 m² Ptotal = 55.6 t Pv3 = 16 t Momen Primer dan Reaksi Tumpuan 55.6 q = 5m 2.5 m M1 = M2 = 1/8 P.L M2 = M3 = = 34.75 t m = 8.333 t m = 34.75 tm ( + - ) = 8.333 tm ( + - ) V1 = V2 = 27.8000 t V2 = V3 = 20 t 43.083 43.083 47.8 47.8 A1 I1 E1 L1 A2 I2 E2 L2 0.102 0.007 0.240 8.078 0.102 0.007 0.240 5 A3 I3 E3 L3 A4 I4 E4 L4 0.102 0.007 0.240 4.924 0.102 0.007 0.240 3 Notasi matriks kekakuan elemen fi AE/L 0 0 -AE/L 0 0 gi 0 0 mi = 0 4 EI/L 0 2 EI/L fj -AE/L 0 0 AE/L 0 0 gj 0 0 mj 0 6 EI/L² 2 EI/L 0 4 EI/L p2 = 20.85 16 t/m² m² t/m² 16 t/m² q.L²/12 12 EI/L³ 6 EI/L² -12 EI/L³ 6 EI/L² 6 EI/L² -6 EI/L² -12 EI/L³ -6 EI/L² 12 EI/L³ -6 EI/L² -6 EI/L² 3 3 1 2 4 5 2 1 4
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Tugas Analisa Struktur II Fakultas Teknik Universitas Khairun
Transcript of Tugas Anstruk II
N0. 2 q =
p1 = 18.75 t
p3 = 16 t/m4.5 m
7.5 m66.0375 α2
3 m
α1 = 68.1986
3 Cm 5 m 2 m
Diketahui :A = 0.1024 Q = 40 t Pv1 = 18.75 tE = 0.24 PH = 0 t Pv2 = 20.85 tI = 0.0072 m² Ptotal = 55.6 t Pv3 = 16 t
Momen Primer dan Reaksi Tumpuan
55.6
q =
5 m 2.5 m
M1 = M2 = 1/8 P.L M2 = M3 == 34.75 t m = 8.333 t m= 34.75 tm ( + - ) = 8.333 tm ( + - )
V1 = V2 = 27.8000 t V2 = V3 = 20 t
43.083 43.083
47.8 47.8
A1 I1 E1 L1 A2 I2 E2 L20.102 0.007 0.240 8.078 0.102 0.007 0.240 5
A3 I3 E3 L3 A4 I4 E4 L40.102 0.007 0.240 4.924 0.102 0.007 0.240 3
Notasi matriks kekakuan elemen
fi AE/L 0 0 -AE/L 0 0gi 0 0mi = 0 4 EI/L 0 2 EI/Lfj -AE/L 0 0 AE/L 0 0gj 0 0mj 0 6 EI/L² 2 EI/L 0 4 EI/L
p2 = 20.85 t 16 t/m²
m²t/m²
16 t/m²
q.L²/12
12 EI/L³ 6 EI/L² -12 EI/L³ 6 EI/L²6 EI/L² -6 EI/L²
-12 EI/L³ -6 EI/L² 12 EI/L³ -6 EI/L² -6 EI/L²
3
3
1
2
4
5
2
1
4
Diketahui :Elemen 1 dari nodal 1 ke 2
A1 I1 E1 L1
0.1024 0.0072 0.24 8.0777
Matriks Kekakuan Elemen 1
0.0030 0 0 -0.0030 0 0
0 0.0000 0.0002 0 0.0000 0.0002
= 0 0.0002 0.0009 0 -0.0002 0.0004
-0.0030 0 0 0.0030 0 0
0 0.0000 -0.0002 0 0.0000 -0.0002
0 0.0002 0.0004 0 -0.0002 0.0009
Sudut elemen = 68.1986
Transformasi Koordinat Elemen 1
0 0 0 0
T
0 0 0 0
=0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
0.3714 0.9285 0 0 0 0
T
-0.9285 0.3714 0 0 0 0
= 0 0 1 0 0 0
0 0 0 0.3714 0.9285 0
0 0 0 -0.9285 0.3714 0
0 0 0 0 0 1
Matriks Transpose Transnformasi Koordinat Elemen 1
0.3714 -0.9285 0 0 0 00.9285 0.3714 0 0 0 0
= 0 0 1 0 0 00 0 0 0.3714 -0.9285 00 0 0 0.9285 0.3714 00 0 0 0 0 1
Kel
cos α sin α
- sin α cos α
cos α sin α
- sin α cos α
T ᵀ
Menghitung Matriks Kekakuan Global Struktur Elemen 1
=
0.0011 -3.653E-05 -0.0001 -0.0011 3.653E-05 -0.00010.0028 1.461E-05 5.901E-05 -0.0028 -1.461E-05 5.901E-05
= 0 0.0002 0.0009 0 -0.0002 0.0004-0.0011 3.653E-05 0.0001 0.0011 -3.653E-05 0.0001-0.0028 -1.461E-05 -5.901E-05 0.0028 1.461E-05 -5.901E-05
0 0.0002 0.0004 0 -0.0002 0.0009
U1 V1 Ѳ1 U2 V2 Ѳ20.0005 0.0010 -0.0001 -0.0005 -0.0010 -0.0001 U10.0010 0.0026 0.0001 -0.0010 -0.0026 0.0001 V1
= -0.0001 0.0001 0.0009 0.0001 -0.0001 0.0004 Ѳ1-0.0005 -0.0010 0.0001 0.0005 0.0010 0.0001 U2-0.0010 -0.0026 -0.0001 0.0010 0.0026 -0.0001 V2-0.0001 0.0001 0.0004 0.0001 -0.0001 0.0009 Ѳ2
Kg T ᵀ. Kel . T
Kg
Kg
Elemen 2 dari nodal 2 ke 3A2 I2 E2 L2
0.1024 0.0072 0.24 5
Matriks Kekakuan Elemen 2
0.0049 0 0 -0.0049 0 0
0 0.0002 0.0004 0 -0.0002 0.0004
= 0 0.0004 0.0014 0 -0.0004 0.0007
-0.0049 0 0 0.0049 0 0
0 -0.0002 -0.0004 0 0.0002 -0.0004
0 0.0004 0.0007 0 -0.0004 0.0014
Sudut elemen = 0
Transformasi Koordinat Elemen 2
0 0 0 0
T
0 0 0 0
=0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
1 0 0 0 0 0
T
0 1 0 0 0 0
= 0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
Matriks Transpose Transnformasi Koordinat Elemen 2
1 0 0 0 0 00 1 0 0 0 0
= 0 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1
Kel
cos α sin α
- sin α cos α
cos α sin α
- sin α cos α
T ᵀ
Menghitung Matriks Kekakuan Global Struktur Elemen 2
=
0.0049 0.0000 0.0000 -0.0049 0.0000 0.00000.0000 0.0002 0.0004 0.0000 -0.0002 0.0004
= 0.0000 0.0004 0.0014 0.0000 -0.0004 0.0007-0.0049 0.0000 0.0000 0.0049 0.0000 0.00000.0000 -0.0002 -0.0004 0.0000 0.0002 -0.00040.0000 0.0004 0.0007 0.0000 -0.0004 0.0014
U2 V2 Ɵ2 U3 V3 Ɵ30.0049 0.0000 0.0000 -0.0049 0.0000 0.0000 U20.0000 0.0002 0.0004 0.0000 -0.0002 0.0004 V2
= 0.0000 0.0004 0.0014 0.0000 -0.0004 0.0007 Ɵ2-0.0049 0.0000 0.0000 0.0049 0.0000 0.0000 U30.0000 -0.0002 -0.0004 0.0000 0.0002 -0.0004 V30.0000 0.0004 0.0007 0.0000 -0.0004 0.0014 Ɵ3
Kg T ᵀ. Kel . T
Kg
Kg
Elemen 3 dari nodal 3 ke 4 A3 I3 E3 L3
0.1024 0.0072 0.24 4.9244
Matriks Kekakuan Elemen 3
0.0050 0 0 -0.0050 0 0
0 0.0002 0.0004 0 -0.0002 0.0004
= 0 0.0004 0.0014 0 -0.0004 0.0007
-0.0050 0 0 0.0050 0 0
0 -0.0002 -0.0004 0 0.0002 -0.0004
0 0.0004 0.0007 0 -0.0004 0.0014
Sudut elemen = 293.962
Transformasi Koordinat Elemen 3
0 0 0 0
T
0 0 0 0
=0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
0.4061 -0.9138 0 0 0 0
T
0.9138 0.4061 0 0 0 0
= 0 0 1 0 0 0
0 0 0 0.4061 -0.9138 0
0 0 0 0.9138 0.4061 0
0 0 0 0 0 1
Matriks Transpose Transnformasi Koordinat Elemen 3
0.4061 0.9138 0 0 0 0-0.9138 0.4061 0 0 0 0
= 0 0 1 0 0 00 0 0 0.4061 0.9138 00 0 0 -0.9138 0.4061 00 0 0 0 0 1
Kel
cos α sin α
- sin α cos α
cos α sin α
- sin α cos α
T ᵀ
Menghitung Matriks Kekakuan Global Struktur Elemen 3
=
0.0020 0.0002 0.0004 -0.0020 -0.0002 0.0004-0.0046 0.0001 0.0002 0.0046 -0.0001 0.0002
= 0.0000 0.0004 0.0014 0.0000 -0.0004 0.0007-0.0020 -0.0002 -0.0004 0.0020 0.0002 -0.00040.0046 -0.0001 -0.0002 -0.0046 0.0001 -0.00020.0000 0.0004 0.0007 0.0000 -0.0004 0.0014
U3 V3 Ɵ3 U4 V4 Ɵ40.0010 -0.0018 0.0004 -0.0010 0.0018 0.0004 U3-0.0018 0.0042 0.0002 0.0018 -0.0042 0.0002 V3
= 0.0004 0.0002 0.0014 -0.0004 -0.0002 0.0007 Ɵ3-0.0010 0.0018 -0.0004 0.0010 -0.0018 -0.0004 U40.0018 -0.0042 -0.0002 -0.0018 0.0042 -0.0002 V40.0004 0.0002 0.0007 -0.0004 -0.0002 0.0014 Ɵ4
Kg T ᵀ. Kel . T
Kg
Kg
Elemen 4 dari nodal 5 ke 4 A4 I4 E4 L4
0.1024 0.0072 0.24 3
Matriks Kekakuan Elemen 4
0.0082 0.0000 0.0000 -0.0082 0.0000 0.0000
0.0000 0.0008 0.0012 0.0000 -0.0008 0.0012
= 0.0000 0.0012 0.0023 0.0000 -0.0012 0.0012
-0.0082 0.0000 0.0000 0.0082 0.0000 0.0000
0.0000 -0.0008 -0.0012 0.0000 0.0008 -0.0012
0.0000 0.0012 0.0012 0.0000 -0.0012 0.0023
Sudut elemen = 90
Transformasi Koordinat Elemen 4
0 0 0 0
T
0 0 0 0
=0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
0 1 0 0 0 0
T
-1 0 0 0 0 0
= 0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 -1 0 0
0 0 0 0 0 1
Matriks Transpose Transnformasi Koordinat Elemen 4
0 -1 0 0 0 01 0 0 0 0 0
= 0 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1
Kel
cos α sin α
- sin α cos α
cos α sin α
- sin α cos α
T ᵀ
Menghitung Matriks Kekakuan Global Struktur Elemen 4
=
0.0000 -0.0008 -0.0012 0.0000 0.0008 -0.00120.0082 0.0000 0.0000 -0.0082 0.0000 0.0000
= 0.0000 0.0012 0.0023 0.0000 -0.0012 0.00120.0000 0.0008 0.0012 0.0000 -0.0008 0.0012-0.0082 0.0000 0.0000 0.0082 0.0000 0.00000.0000 0.0012 0.0012 0.0000 -0.0012 0.0023
U5 V5 Ɵ5 U4 V4 Ɵ40.0008 0.0000 -0.0012 -0.0008 0.0000 -0.0012 U50.0000 0.0082 0.0000 0.0000 -0.0082 0.0000 V5
= -0.0012 0.0000 0.0023 0.0012 0.0000 0.0012 Ɵ5-0.0008 0.0000 0.0012 0.0008 0.0000 0.0012 U40.0000 -0.0082 0.0000 0.0000 0.0082 0.0000 V4-0.0012 0.0000 0.0012 0.0012 0.0000 0.0023 Ɵ4
Kg T ᵀ. Kel . T
Kg
Kg
MEMNENTUKAN BEBAN NODAL EKIVALEN
Pada gambar (b) sumbu x lokal dan sumbu y lokal dari elemen digambarkan, dan dari gambar (b)
inilah vektor beban batang ekIvalen elemen 1 dalam koordinat lokal {f(1)}, dan dalam koordinat
global, {F(1)} :
f2 0 F2 0
g2 -47.8 G2 -47.8
=m2
=-43.08333
=M2
=-43.08333
f3 0 F3 0
g3 -47.8 G3 -47.8
m3 43.08333 M3 43.08333
F2 = 0
G2 = 0
M2 = 0
{F} = F3 = 0G3 = 0
M3 = 0
F4 = 0
G4 = 0
M4 =0
F5
G5M5
{f(2)}* {F(2)}*
F1
G1
M1
OVERALL STIFFNESS MATRIX
0.0005 0.0010 -0.0001 -0.0005 -0.0010 -0.0001 0 0 0 0 0 0 0 0 0 U1
0.0010 0.0026 0.0001 -0.0010 -0.0026 0.0001 0 0 0 0 0 0 0 0 0 V1
-0.0001 0.0001 0.0009 0.0001 -0.0001 0.0004 0 0 0 0 0 0 0 0 0 Ѳ1
F2 F2 -0.0005 -0.0010 0.0001 0.0054 0.0010 0.0001 -0.0049 0.0000 0.0000 0 0 0 0 0 0 U2
G2 G2 -0.0010 -0.0026 -0.0001 0.0010 0.0028 0.0004 0.0000 -0.0002 0.0004 0 0 0 0 0 0 V2
M2 M2 -0.0001 0.0001 0.0004 0.0001 0.0004 0.0022 0.0000 -0.0004 0.0007 0 0 0 0 0 0 Ѳ2
F3 + F3 = 0 0 0 -0.0049 0.0000 0.0000 0.0059 -0.0018 0.0004 -0.0010 0.0018 0.0004 0 0 0 U3G3 G3 0 0 0 0.0000 -0.0002 -0.0004 -0.0018 0.0044 -0.0002 0.0018 -0.0042 0.0002 0 0 0 V3
M3 M3 0 0 0 0.0000 0.0004 0.0007 0.0004 -0.0002 0.0028 -0.0004 -0.0002 0.0007 0 0 0 Ѳ3
F4 F4 0 0 0 0 0 0 -0.0010 0.0018 -0.0004 0.0017 -0.0018 0.0008 -0.0008 0.0000 0.0012 U4
G4 G4 0 0 0 0 0 0 0.0018 -0.0042 -0.0002 -0.0018 0.0124 -0.0002 0.0000 -0.0082 0.0000 V4
M4 M4 0 0 0 0 0 0 0.0004 0.0002 0.0007 0.0008 -0.0002 0.0037 -0.0012 0.0000 0.0012 Ѳ4
F5 F5 0 0 0 0 0 0 0 0 0 -0.0008 0.0000 -0.0012 0.0008 0.0000 -0.0012 U5
G5 G5 0 0 0 0 0 0 0 0 0 0.0000 -0.0082 0.0000 0.0000 0.0082 0.0000 V5
M5 M5 0 0 0 0 0 0 0 0 0 0.0012 0.0000 0.0012 -0.0012 0.0000 0.0023 Ѳ5
0.0000 0.0005 0.0010 -0.0001 -0.0005 -0.0010 -0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 U1
0.0000 0.0010 0.0026 0.0001 -0.0010 -0.0026 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 V1
0.0000 -0.0001 0.0001 0.0009 0.0001 -0.0001 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Ѳ1
0.0000 F2 = 0 -0.0005 -0.0010 0.0001 0.0054 0.0010 0.0001 -0.0049 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 U2-47.8000 G2 = 0 -0.0010 -0.0026 -0.0001 0.0010 0.0028 0.0004 0.0000 -0.0002 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 V2
-43.0833 M2 = 0 -0.0001 0.0001 0.0004 0.0001 0.0004 0.0022 0.0000 -0.0004 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Ѳ2
0.0000+
F3 = 0= 0.0000 0.0000 0.0000 -0.0049 0.0000 0.0000 0.0059 -0.0018 0.0004 -0.0010 0.0018 0.0004 0.0000 0.0000 0.0000 U3
-47.8000 G3 = 0 0.0000 0.0000 0.0000 0.0000 -0.0002 -0.0004 -0.0018 0.0044 -0.0002 0.0018 -0.0042 0.0002 0.0000 0.0000 0.0000 V3
43.0833 M3 = 0 0.0000 0.0000 0.0000 0.0000 0.0004 0.0007 0.0004 -0.0002 0.0028 -0.0004 -0.0002 0.0007 0.0000 0.0000 0.0000 Ѳ3
0 F4 = 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.001 0.0018 -0.0004 0.0017 -0.0018 0.0008 -0.0008 0.0000 0.0012 U4
0 G4 = 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0018 -0.0042 -0.0002 -0.0018 0.0124 -0.0002 0.0000 -0.0082 0.0000 V40 M4 = 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0002 0.0007 0.0008 -0.0002 0.0037 -0.0012 0.0000 0.0012 Ѳ40 F5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0008 0.0000 -0.0012 0.0008 0.0000 -0.0012 U50 G5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0082 0.0000 0.0000 0.0082 0.0000 V50 M5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0012 0.0000 0.0012 -0.0012 0.0000 0.0023 Ѳ5
{F(1)}* + {F} = [K]. {U}
F1 F1
G1 G1
M1 M1
F1
G1
M1
F1 G1 M1 F2 G2 M2 F3 G3 M3 F4 G4 M4 F5 G5 M5
F1 0.0005 0.0010 -0.0001 -0.0005 -0.0010 -0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0
G1 0.0010 0.0026 0.0001 -0.0010 -0.0026 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0
M1 -0.0001 0.0001 0.0009 0.0001 -0.0001 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0
0.0000 -0.0005 -0.0010 0.0001 0.0054 0.0010 0.0001 -0.0049 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 V2
-47.800 -0.0010 -0.0026 -0.0001 0.0010 0.0028 0.0004 0.0000 -0.0002 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 G2
-43.083 -0.0001 0.0001 0.0004 0.0001 0.0004 0.0022 0.0000 -0.0004 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 M2
0=
0.0000 0.0000 0.0000 -0.0049 0.0000 0.0000 0.0059 -0.0018 0.0004 -0.0010 0.0018 0.0004 0.0000 0.0000 0.0000 F3
-47.8 0.0000 0.0000 0.0000 0.0000 -0.0002 -0.0004 -0.0018 0.0044 -0.0002 0.0018 -0.0042 0.0002 0.0000 0.0000 0.0000 G3
43.0833 0.0000 0.0000 0.0000 0.0000 0.0004 0.0007 0.0004 -0.0002 0.0028 -0.0004 -0.0002 0.0007 0.0000 0.0000 0.0000 M30 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0010 0.0018 -0.0004 0.0017 -0.0018 0.0008 -0.0008 0.0000 0.0012 F4
0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0018 -0.0042 -0.0002 -0.0018 0.0124 -0.0002 0.0000 -0.0082 0.0000 G4
0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0002 0.0007 0.0008 -0.0002 0.0037 -0.0012 0.0000 0.0012 M4
F5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0008 0.0000 -0.0012 0.0008 0.0000 -0.0012 0
G5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0082 0.0000 0.0000 0.0082 0.0000 0
M5 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0012 0.0000 0.0012 -0.0012 0.0000 0.0023 0
REARRANGEMENT
F2 G2 M2 F3 G3 M3 F4 G4 M4
U2 = 0.0000 0.0054 0.0010 0.0001 -0.0049 0.0000 0.0000 0.0000 0.0000 0.0000 U2
V2 = -47.8000 0.0010 0.0028 0.0004 0.0000 -0.0002 0.0004 0.0000 0.0000 0.0000 V2
Ѳ2 = -43.0833 0.0001 0.0004 0.0022 0.0000 -0.0004 0.0007 0.0000 0.0000 0.0000 Ѳ2
U3 = 0.0000=
-0.0049 0.0000 0.0000 0.0059 -0.0018 0.0004 -0.0010 0.0018 0.0004 U3 DisplacemenV3 = -47.8000 0.0000 -0.0002 -0.0004 -0.0018 0.0044 -0.0002 0.0018 -0.0042 0.0002 V3
Ѳ3 = 43.0833 0.0000 0.0004 0.0007 0.0004 -0.0002 0.0028 -0.0004 -0.0002 0.0007 Ѳ3
U4 = 0.0000 0.0000 0.0000 0.0000 -0.0010 0.0018 -0.0004 0.0017 -0.0018 0.0008 U4
V4 = 0.0000 0.0000 0.0000 0.0000 0.0018 -0.0042 -0.0002 -0.0018 0.0124 -0.0002 V4
Ѳ4 = 0.0000 0.0000 0.0000 0.0000 0.0004 0.0002 0.0007 0.0008 -0.0002 0.0037 Ѳ4
Invers Matriks
U2 6575.6902 -2404.1483 149.4484 6476.9993 1500.8219 250.2789 2653.2490 -58.8395 -1347.7512 0.0000
V2 -2404.1483 1251.5167 -91.2711 -2365.0629 -519.1254 -146.8530 -1017.0823 23.8005 511.2906 -47.8000
Ѳ2 149.4484 -91.2711 525.9687 159.7970 159.3304 -145.6414 -104.2315 14.1794 25.3336 -43.0833
U3=
6476.9993 -2365.0629 159.7970 6581.1971 1534.7251 238.0630 2680.6731 -58.8290 -1363.6374 0.0000
V3 1500.8219 -519.1254 159.3304 1534.7251 912.1116 -21.8259 110.4877 100.0489 -218.3124 X -47.8000
Ѳ3 250.2789 -146.8530 -145.6414 238.0630 -21.8259 480.6404 360.8876 14.4275 -188.4708 43.0833
U4 2653.2490 -1017.0823 -104.2315 2680.6731 110.4877 360.8876 2400.6026 -9.8401 -849.3560 0.0000
V4 -58.8395 23.8005 14.1794 -58.8290 100.0489 14.4275 -9.8401 121.9745 6.5156 0.0000
Ѳ4 -1347.7512 511.2906 25.3336 -1363.6374 -218.3124 -188.4708 -849.3560 6.5156 634.0185 0.0000
Displacement Kontrol :
U2 47523.118 1 0 0 0 0 0 0 0 0
V2 -37402.959 0 1 0 0 0 0 0 0 0
Ѳ2 -32188.438 0 0 1 0 0 0 0 0 0
U3
=
43062.108 0 0 0 1 0 0 0 0 0
V3 -26589.562 0 0 0 0 1 0 0 0 0
Ѳ3 35045.158 0 0 0 0 0 1 0 0 0
U4 63374.103 0 0 0 0 0 0 1 0 0
V4 -5909.311 0 0 0 0 0 0 0 1 0
Ѳ4 -23215.763 0 0 0 0 0 0 0 0 1
Displacemen Reaksi Tumpuan
U1 0.00000 F1 21.9268 0.0000 21.9268
V1 0.00000 G1 47.1909 0.0000 47.1909
Ѳ1 0.00000 M1 = -4.5531 - 0.0000 = -4.5531
U2 47523.118 F5 -21.9268 0.000 -21.9268
V2 -37402.959 G5 48.4091 0.000 48.4091
Ѳ2
=
-32188.438 M5 46.2624 0.000 46.2624U3 43062.108
V3 -26589.562
Ѳ3 35045.158 Kontrol = 0U4 63374.103 ∑V = 0 ∑H = 0V4 -5909.311 G1 + G5 - Ptotal - Q = 0 F1 + F5 = 0Ѳ4 -23215.763 0.0000 ……. OKKK 0.0000 …….OKKKU5 0.00000
V5 0.00000 ∑M1 = 0Ѳ5 0.00000 (-G5*10)+Q*(1/2 5+3)+P1*7.5+p2*5.5+M3-M1-M5 = 0
0.0000 ..…..OKKK
[ K ] . [ T ]¹ = I
Gaya - Gaya Dalam
Elemen 1
MEMBER FORCES
0.0011 0.0028 0.0000 -0.0011 -0.0028 0.0000 0.0000 U1
0.0000 0.0000 0.0002 0.0000 0.0000 0.0002 0.0000 V1
+ = -0.0001 0.0001 0.0009 0.0001 -0.0001 0.0004 X 0.0000 Ѳ1
-0.0011 -0.0028 0.0000 0.0011 0.0028 0.0000 47523.1176 U2
0.0000 0.0000 -0.0002 0.0000 0.0000 -0.0002 -37402.9594 V2
-0.0001 0.0001 0.0004 0.0001 -0.0001 0.0009 -32188.4381 Ѳ2
0.0000 51.9591
0.0000 -2.8322
0.0000 + = -4.5531
0.0000 -51.9591
0.0000 2.8322
0.0000 -18.3247
51.9591 0.0000
-2.8322 0.0000
= -4.5531 - 0.0000
-51.9591 0.0000
2.8322 0.0000
-18.3247 0.0000
51.9591
-2.8322
= -4.5531
-51.9591
2.8322
-18.3247
{f(1)}* + {f(1)} = [T(1)]. [Kg(1)]. {U(1)}
f1 f1
g1 g1
m1 m1
f2 f2
g2 g2
m2 m2
f1
g1
m1
f2
g2
m2
f1
g1
m1
f2
g2
m2
f1
g1
m1
f2
g2
m2
Elemen 2
MEMBER FORCES
f2 f2 0.0049 0.0000 0.0000 -0.0049 0.0000 0.0000 47523.118 U2
g2 g2 0.0000 0.0000 0.0002 0.0004 0.0000 -0.0002 -37402.959 V2
+ = 0.0000 0.0004 0.0014 0.0000 -0.0004 0.0007 X -32188.438
-0.0049 0.0000 0.0000 0.0049 0.0000 0.0000 43062.108 U3
0.0000 -0.0002 -0.0004 0.0000 0.0002 -0.0004 -26589.5620 V3
0.0000 0.0004 0.0007 0.0000 -0.0004 0.0014 35045.1576 Ѳ3
0 f2 21.9268
-47.8 g2 6.7055
-43.08333 + = -24.7586
0 -21.9268
-47.8 0.6091
43.08333 21.7132
f2 21.9268 0.0000
g2 6.7055 -47.8000
m2= -24.7586 - -43.0833
f3 -21.9268 0.0000
g3 0.6091 -47.8000
m3 21.7132 43.0833
f2 21.9268
g2 54.5055
m2= 18.3247
f3 -21.9268
g3 48.4091
m3 -21.3701
{f(2)}* + {f(2)} = [T(2)]. [Kg(2)]. {U(2)}
m2 m2 Ѳ2
f3 f3
g3 g3
m3 m3
m2
f3
g3
m3
Elemen 3
MEMBER FORCES
f3 f3 0.0020 -0.0046 0.0000 -0.0020 0.0046 0.0000 43062.108 U3
g3 g3 0.0002 0.0001 0.0004 -0.0002 -0.0001 0.0004 -26589.562 V3
m3+ = 0.0004 0.0002 0.0014 -0.0004 -0.0002 0.0007 X 35045.158 Ѳ3
f4 -0.0020 0.0046 0.0000 0.0020 -0.0046 0.0000 63374.103 U4
g4 -0.0002 -0.0001 -0.0004 0.0002 0.0001 -0.0004 -5909.311 V4
m4 0.0004 0.0002 0.0007 -0.0004 -0.0002 0.0014 -23215.763 Ѳ4
0 f3 53.1421
0 g3 0.3761
0 + = 21.3701
0 -53.1421
0 -0.3761
0 -19.5178
f3 53.1421 0
g3 0.3761 0
= 21.3701 - 0
-53.1421 0
-0.3761 0
-19.5178 0
f3 53.14207
g3 0.376133
= 21.37009
-53.14207
-0.376133
-19.51785
{f(3)}* + {f(3)} = [T(3)]. [Kg(3)]. {U(3)}
m3
f4
g4
m4
m3
f4
g4
m4
m3
f4
g4
m4
m3
f4
g4
m4
Elemen 4
MEMBER FORCES
f5 f5 0.0000 0.0082 0.0000 0.0000 -0.0082 0.0000 0.0000 U5
g5 g5 -0.0008 0.0000 0.0012 0.0008 0.0000 0.0012 0.0000 V5
m5+
m5= -0.0012 0.0000 0.0023 0.0012 0.0000 0.0012 X 0.0000 Ѳ5
f4 f4 0.0000 -0.0082 0.0000 0.0000 0.0082 0.0000 63374.1034 U4
g4 g4 0.0008 0.0000 -0.0012 -0.0008 0.0000 -0.0012 -5909.3108 V4
m4 m4 -0.0012 0.0000 0.0012 0.0012 0.0000 0.0023 -23215.7628 Ѳ4
0 f5 48.4091
0 g5 21.9268
0 +m5
= 46.2624
0 f4 -48.4091
0 g4 -21.9268
0 m4 19.5178
f5 48.4091 0
g5 21.9268 0
m5= 46.2624 - 0
f4 -48.4091 0
g4 -21.9268 0
m4 19.5178 0
f5 48.4091
g5 21.9268
m5= 46.2624
f4 -48.4091
g4 -21.9268
m4 19.5178
{f(4)}* + {f(4)} = [T(4)]. [Kg(4)]. {U(4)}
Hasil Analisa
-51.9591
-18.3247
2.8322
-4.5531
-2.832251.9591
-18.3247
2.8322
-51.9591
-4.5531 -2.8322
51.9591
Bidang Momen elemen 1 Bidang Lintang elemen 1 Bidang Normal elemen 1
18.3247 -21.3701
21.9268 -21.927
-54.5055 48.4091
18.3247 -21.3701 48.4091
-21.9268-54.5055
Bidang Momen elemen 2 Bidang Lintang elemen 2 Bidang Normal elemen 2
-48.40953.142
21.370 -21.927 19.5178
0.376
-19.518-21.927 46.2624
-0.376-53.142
48.4091
21.37019.5178
-19.518
Bidang Momen elemen 3 46.2624Bidang Momen elemen 4
###
-0.376
Bidang Lintang elemen 3
Bidang Lintang elemen 4
-48.
4091
-53.1421
Bidang Normal elemen 3Bidang Normal elemen 4
REAKSI TUMPUAN
21.9268 -21.9268
47.1909 48.4091
DIAGRAM MOMEN
18.3247 -21.3701 21.370-18.3247
-19.518
19.5178
-4.553146.2624
DIAGRAM LINTANG48.4091
2.8322
-0.376
-54.5055
-21.927
-2.8322
DIAGRAM NORMAL
-21.9268
-51.9591-53.14207
-48.4091
51.9591
