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Analsis struktur 4 ini menjelaskan soal tentang, truss,beam dan portal beserta penyelesaiannya dengan menggunakan program matlab.
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Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 1
No. 1
Persiapan Data :
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 2
Data Propertis Batang:
1. E= 2.1e7 ton/m2 ; A= 0.004 m2
2. E= 2.1e7 ton/m2 ; A= 0.001 m2
Koordinat
No. Titik X Y
1 0 0
2 2.3 0
3 2.3 2.8
4 4.6 0
5 4.6 5.6
6 6.9 0
7 6.9 2.8
8 9.3 0
Data Batang :
NO
BATANG
NO TITIK
KIRI
(BAWAH)
NO TITIK
KANAN
(BAWAH)
NO.
PROPERTIS
1 1 4 1
2 4 6 1
3 6 8 1
4 8 2 1
5 1 3 1
6 3 5 1
7 2 7 1
8 7 5 1
9 3 4 1
10 3 6 2
11 5 6 1
12 7 6 2
13 7 8 1
Data Tumpuan
No. TITIK RESTRAINT
RX
RESTRAINT
RY
RESTRAINT
RZ
1 1 1 0
2 0 1 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 3
Data Beban Titik
No titik Beban FX Beban Fy Beban FZ
3 8.5 10 0
5 0 10 0
7 0 10 0
4 0 9 0
6 0 9 0
8 0 9 0
INPUT DATA
%****RANGKA BATANG 2D---TEKNIK SIPIL UNISSULA SEMARANG---- %****nama file : truss----oleh :M.Taufan Putra 3/11/2006---- %****struktur : rangka batang fleming hal 80 -- kip.in clear all clc %****General Data--- type='t2d' nfile='truss' %****Property---i E A ------- prop = [ 1 2.1e7 0.004 2 2.1e7 0.001]; %****Coordinates---------------- %****--- Joint X Y ------- coord=[ 1 0 0 2 2.3 0 3 2.3 2.8 4 4.6 0 5 4.6 5.6 6 6.9 0 7 6.9 2.8 8 9.3 0]; %****Element data--------------- %****--- Element J1 J2 prop--- element=[1 1 2 1 2 2 4 1 3 4 6 1 4 6 8 1 5 1 3 1 6 2 3 1 7 3 4 2 8 3 5 1 9 4 5 1 10 5 7 1 11 4 7 2 12 6 7 1 13 7 8 1]; %****Nodal Restraint----------- %****---- Joint JR1 JR2 --- Support=[ 1 1 1 8 0 1 ]; %****Joint Load---------------- %****---Joint FX FY -------
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 4
JL=[ 3 8.5 -10 5 8.5 -10 7 0 -10 2 0 -9 4 0 -9 6 0 -9]; %****Element Load Data-------- %****---Elem. Fx1 Fy1 Fx2 Fy2 --- AML=[ 1 0 0 0 0 ]; %****Call function for analysis t2d----------------------- [dof,index,coord,element]=TRUSS2D_sdata(prop,element,coord,type); [S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=... TRUSS2D_stiff(prop,element,coord,index,nfile); [IR,IF,Support]=TRUSS2D_ldata(Support,dof); [DF,AR,AM]=TRUSS2D_analysis_result... (element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile); [joint_disp,support_reaction,beam_endforces]=TRUSS2D_print_result... (JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile); %****end data------------------------------------------------ TRUSS2D_xplot %
OUT PUT DATA
TEXT 2
STIFFNESS MATRIX METHOD : PROGRAM TRUSS2D File Name : truss_2.txt
Joint Loads : Joint Fx Fy 3 8.500 -10.000 5 8.500 -10.000 7 0.000 -10.000 2 0.000 -9.000 4 0.000 -9.000 6 0.000 -9.000
Member Loads : Member Fx1 Fy1 Fx2 Fy2 1 0.000 0.000 0.000 0.000
Support Restraints : Joint Rx Ry 1 1 1 8 0 1
Joint Displacements : Joint Dx Dy 1 0.0000e+000 0.0000e+000 2 9.4070e-004 -7.7350e-003 3 7.1930e-003 -7.4350e-003 4 1.8814e-003 -7.5577e-003 5 3.1089e-003 -5.2941e-003 6 2.7233e-003 -7.7346e-003
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 5
7 -1.8848e-003 -7.4346e-003 8 3.6017e-003 0.0000e+000
Support Reactions : Joint Rx Ry 1 -1.7000e+001 2.1129e+001 8 0.0000e+000 3.5871e+001
Member End Forces (axial/normal): Member axial force : + tension - compression 1 34.356 2 34.356 3 30.747 4 30.747 5 -27.343 6 9.000 7 -18.990 8 -21.745 9 33.954 10 -35.136 11 -13.303 12 9.000 13 -47.245
<<< end of file >>>
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 6
DEFORMASI
Gambar 1.1 Deformasi Rangka Batang
Cek Keseimbangan:
∑FV=0
21,129 t+ 35,781t = 10 t+ 10 t+ 10 t
56,909 t = 57 t
Oke
∑FH= 0
8,5 t+ 8,5 t = 17 t
17 t = 17 t
Oke
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 7
FREE BODY DIAGRAM
Gambar 1.2. Free body Diagram
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 8
GAMBAR BIDANG N
Gambar 1.3. Bidang Normal
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 9
No 2.
Persiapan Data :
Penomoran titik, batang dan koordinat :
Data Propertis batang :
E=2.1e7 (ton/m2) A = 0.004 (m2)
E=2.1e7 (ton/m2) A = 0.008 (m2)
Data koordinat
Data batang
A1 = 0.004
A2 = 0.008
E = 2.1e7
Batang 1
Batang 2
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 10
No. Titik X Y
1 0 0
2 6 3
3 0 6
4 9 4.5
5 6 6
6 12 6
Data Batang
No.
Batang
No.Titik
Kiri
(bawah)
No.Titik
Kanan(bawah) No.Propertis
1 1 2 1
2 1 3 2
3 3 2 2
4 3 5 2
5 2 5 1
6 2 4 1
7 5 4 2
8 4 6 1
9 5 6 2
Data Tumpuan
No. Titik Restraint
RX
Restraint Restraint
RY RZ
1 1 1 0
3 1 1 0
Data Titik Beban
No. Titik Beban Beban Beban
FX FY MZ
1 0 -3 0
3 0 -5 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 11
Input Data File : %****RANGKA BATANG 2D---TEKNIK SIPIL UNISSULA SEMARANG----
%****nama file : tugas rangka4----oleh :iwan sudirwan----
%****struktur : rangka batang 3 ttik 3 batang
clear all
clc
%****General Data--------------
type='t2d'
nfile='tugas rangka4'
%****Property---i E A --------
prop = [ 1 2.1e7 0.004
2 2.1e7 0.008 ];
%****Coordinates---
%****--- Joint X Y -------
coord=[ 1 0 0
2 6 3
3 0 6
4 9 4.5
5 6 6
6 12 6 ];
%****Element data---------------
%****--- Element J1 J2 No.prop---
element=[1 1 2 1
2 1 3 2
3 3 2 2
4 3 5 2
5 2 5 1
6 2 4 1
7 5 4 2
8 4 6 1
9 5 6 2 ];
%****Nodal Restraint---
%****---- Joint JR1 JR2 ---
Support=[ 1 1 1
3 1 0 ];
%****Joint Load--------------
%****---Joint FX FY -----
JL=[ 5 0 -3
6 0 -5 ];
%****Element Load Data---------------
Fox1=0; Foy1=0; Fox2=0; Foy2=0;
AML=[1 Fox1 Foy1 Fox2 Foy2];
%****Call function for analysis truss2d
[dof,index,coord,element]=TRUSS2D_sdata(prop,element,coord,type);
[S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=...
TRUSS2D_stiff(prop,element,coord,index,nfile);
[IR,IF,Support]=TRUSS2D_ldata(Support,dof);
[DF,AR,AM]=TRUSS2D_analysis_result...
(element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile);
[joint_disp,support_reaction,beam_endforces]=TRUSS2D_print_result...
(JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile);
%****end data------------------------------------------------
TRUSS2D_xplot
%------------------
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 12
4. OutPut Program & Cek :
truss4_2.txt
Support Reactions :
Joint Rx Ry
1 1.3000e+001 6.5000e+000
3 -1.3000e+001 1.5000e+000
Member End Forces (axial/normal):
Member axial force : + tension - compression
1 -14.534
2 0.000
3 3.354
4 10.000
5 -3.000
6 -11.180
7 0.000
8 -11.180
9 10.000
truss4_4.txt
Reaction of Supports :
{AR}IFx1 = -{ARC}IRx1 + [SRF]IRxIF {DF}IFx1
1 1.300e+001
2 6.500e+000
5 -1.300e+001
6 1.500e+000
Gambar output data
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 13
Cek Keseimbangan :
∑v = 0
6.5 + 1.5 – 5 - 3 = 0
ok
∑h = 0
13 – 13 = 0
Ok
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 14
5. Free Body; Bidang D,M,N :
Gambar free body diagram
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 15
Gambar bidang Normal (N)
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 16
6. MATRIKS KEKAKUAN ELEMEN - SUMBU BATANG (sm) :
Tugas rangka 1_3.txt
E= 2.1e7 ; Ax= 0,004 ; L= 6,7 ;
Stiffness Matrix Element Local [Sm]= 1 # 9
1 2 3 4
1 12521.9807 0 -12521.9807 0
2 0 0 0 0
3 -12521.9807 0 12521.9807 0
4 0 0 0 0
E= 2.1e7 ; Ax= 0,08 ; L= 6 ; Stiffness Matrix Element Local [Sm]= 2 # 9
1 2 5 6
1 28000 0 -28000 0
2 0 0 0 0
5 -28000 0 28000 0
6 0 0 0 0
E= 2.1e7 ; Ax= 0,08 ; L= 6,7 ; Stiffness Matrix Element Local [Sm]= 3 # 9
5 6 3 4
5 25043.9613 0 -25043.9613 0
6 0 0 0 0
3 -25043.9613 0 25043.9613 0
4 0 0 0 0
E= 2.1e7 ; Ax= 0,08 ; L= 6 ; Stiffness Matrix Element Local [Sm]= 4 # 9
5 6 9 10
5 28000 0 -28000 0
6 0 0 0 0
9 -28000 0 28000 0
10 0 0 0 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 17
E= 2.1e7 ; Ax= 0,04 ; L= 3 ; Stiffness Matrix Element Local [Sm]= 5 # 9
3 4 9 10
3 28000 0 -28000 0
4 0 0 0 0
9 -28000 0 28000 0
10 0 0 0 0
E= 2.1e7 ; Ax= 0,04 ; L= 3,3 ; Stiffness Matrix Element Local [Sm]= 6 # 9
3 4 7 8
3 25043.9613 0 -25043.9613 0
4 0 0 0 0
7 -25043.9613 0 25043.9613 0
8 0 0 0 0
E= 2.1e7 ; Ax= 0,08 ; L= 3,3 ; Stiffness Matrix Element Local [Sm]= 7 # 9
9 10 7 8
9 50087.9227 0 -50087.9227 0
10 0 0 0 0
7 -50087.9227 0 50087.9227 0
8 0 0 0 0
E= 2.1e7 ; Ax= 0,04 ; L= 3,3 ; Stiffness Matrix Element Local [Sm]= 8 # 9
7 8 11 12
7 25043.9613 0 -25043.9613 0
8 0 0 0 0
11 -25043.9613 0 25043.9613 0
12 0 0 0 0
E= 2.1e7 ; Ax= 0,08 ; L= 6 ; Stiffness Matrix Element Local [Sm]= 9 # 9
9 10 11 12
9 28000 0 -28000 0
10 0 0 0 0
11 -28000 0 28000 0
12 0 0 0 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 18
MATRIKS ROTASI BATANG [RT]: Cx Cy 0 0
-Cy Cx 0 0
0 0 Cx Cy
0 0 -Cy Cx
---> Cx=Lx/L Cy=Ly/L
Batang – 1 : L= 6,7 ; Lx= 6; Ly= 3; Cx= 0.894 ; Cy= 0.447 ; Rotation Matrix Element [RT]= 1 # 9
0.8944 0.4472 0 0
-0.4472 0.8944 0 0
0 0 0.8944 0.4472
0 0 -0.4472 0.8944
Batang – 2 : L= 6 ; Lx= 0; Ly= 6; Cx= 0; Cy= 1 Rotation Matrix Element [RT]= 2 # 9
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
Batang – 3 : L= 6,7 ; Lx= 6; Ly= 3; Cx= 0.894 ; Cy= -0.447 Rotation Matrix Element [RT]= 3 # 9
0.8944 -0.4472 0 0
0.4472 0.8944 0 0
0 0 0.8944 -0.4472
0 0 0.4472 0.8944
Batang – 4 : L= 6 ; Lx= 6; Ly= 0; Cx= 1 ; Cy= 0 Rotation Matrix Element [RT]= 4 # 9
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 19
Batang – 5 : L= 3 ; Lx= 0; Ly= 3; Cx= 0; Cy= 1 Rotation Matrix Element [RT]= 5 # 9
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
Batang – 6 : L= 3,3 ; Lx= 3; Ly= 1,5; Cx= 0.8944 ; Cy= 0.4472 Rotation Matrix Element [RT]= 6 # 9
0.8944 0.4472 0 0
-0.4472 0.8944 0 0
0 0 0.8944 0.4472
0 0 -0.4472 0.8944
Batang – 7 : L= 3,35 ; Lx= 3; Ly= 1,5; Cx= 0.8944 ; Cy= -0.4472 Rotation Matrix Element [RT]= 7 # 9
0.8944 -0.4472 0 0
0.4472 0.8944 0 0
0 0 0.8944 -0.4472
0 0 0.4472 0.8944
Batang – 8 : L= 3,35 ; Lx= 3; Ly= 1,5; Cx= 0.8944 ; Cy= -0.4472 Rotation Matrix Element [RT]= 8 # 9
0.8944 0.4472 0 0
-0.4472 0.8944 0 0
0 0 0.8944 0.4472
0 0 -0.4472 0.8944
Batang – 9 : L= 6 ; Lx= 6; Ly= 0; Cx= 1 ; Cy= 0 Rotation Matrix Element [RT]= 9 # 9
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 20
MATRIKS KEKAKUAN ELEMEN – SUMBU STRUKTUR [SmS] : [SmS] 4x4 = [RT] ^ T 4x4 * [sm] 4x4 * [RT] 4x4
Stiffness Matrix Element (Global):
[SmS]4x4= [RT]^T 4x4.[Sm]4x4.[RT]4x4
Stiffness Matrix Element Global [SmS]= 1 # 9
1 2 3 4
1 10017.5845 5008.7923 -10017.5845 -5008.7923
2 5008.7923 2504.3961 -5008.7923 -2504.3961
3 -10017.5845 -5008.7923 10017.5845 5008.7923
4 -5008.7923 -2504.3961 5008.7923 2504.3961
Stiffness Matrix Element Global [SmS]= 2 # 9
1 2 5 6
1 0 0 0 0
2 0 28000 0 -28000
5 0 0 0 0
6 0 -28000 0 28000
Stiffness Matrix Element Global [SmS]= 3 # 9
5 6 3 4
5 20035.1691 -10017.5845 -20035.1691 10017.5845
6 -10017.5845 5008.7923 10017.5845 -5008.7923
3 -20035.1691 10017.5845 20035.1691 -10017.5845
4 10017.5845 -5008.7923 -10017.5845 5008.7923
Stiffness Matrix Element Global [SmS]= 4 # 9
5 6 9 10
5 28000 0 -28000 0
6 0 0 0 0
9 -28000 0 28000 0
10 0 0 0 0
Stiffness Matrix Element Global [SmS]= 5 # 9
3 4 9 10
3 0 0 0 0
4 0 28000 0 -28000
9 0 0 0 0
10 0 -28000 0 28000
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 21
Stiffness Matrix Element Global [SmS]= 6 # 9
3 4 7 8
3 20035.1691 10017.5845 -20035.1691 -10017.5845
4 10017.5845 5008.7923 -10017.5845 -5008.7923
7 -20035.1691 -10017.5845 20035.1691 10017.5845
8 -10017.5845 -5008.7923 10017.5845 5008.7923
Stiffness Matrix Element Global [SmS]= 7 # 9
9 10 7 8
9 40070.3382 -20035.1691 -40070.3382 20035.1691
10 -20035.1691 10017.5845 20035.1691 -10017.5845
7 -40070.3382 20035.1691 40070.3382 -20035.1691
8 20035.1691 -10017.5845 -20035.1691 10017.5845
Stiffness Matrix Element Global [SmS]= 8 # 9
7 8 11 12
7 20035.1691 10017.5845 -20035.1691 -10017.5845
8 10017.5845 5008.7923 -10017.5845 -5008.7923
11 -20035.1691 -10017.5845 20035.1691 10017.5845
12 -10017.5845 -5008.7923 10017.5845 5008.7923
Stiffness Matrix Element Global [SmS]= 9 # 9
9 10 11 12
9 28000 0 -28000 0
10 0 0 0 0
11 -28000 0 28000 0
12 0 0 0 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 22
Stiffness Matrix Structure Total [S]=Total [SmS ]i 12 x 12
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 23
Indexes Restraint of Degree of Freedom (IR): IR=
1 2 5 6 Indexes Free Displacement of Degree of Freedom (IF):
IF=
3 4 7 8 9 10 `11 12
[SFF] 8x8=
[SFFi] 9X9 = [SFF]-1
9X9
SRF 4x8
INVERS DARI MATRIKS [SFF] 9X9
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 24
PENGECEKAN MATRIKS IDENTITAS [I] 7 x 7 = [SFFi] 7 x 7 * [SFF] 7 x 7 [I] 7 x 7 =
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
ELEMEN DIAGONAL UTAMA MATRIKS = 1 .. OK !!
BEBAN TITIK TOTAL [AC] 12 X 1 : [AC] 12 X 1 =
1 0
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 -3
11 0
12 -5
BEBAN TITIK TOTAL PADA TITIK PERPINDAHAN BEBAS [AFC] 8 X 1 : [AFC] 8 X 1 =
3 0
4 0
7 0
8 0
9 0
10 -3
11 0
12 -5
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 25
BEBAN TITIK TOTAL PADA TITIK TUMPUAN/TERKEKANG [ARC] 5 X 1 : [ARC] 5 X 1 =
1 0
2 0
5 0
6 0
PERPINDAHAN TITIK [DF]: [DF] IFx1 = [SFF]-1
IFxIF * [AFC] IFx1
[DF] 9x1 =
3 -5.74E-04
4 -1.45E-03
7 -3.31E-04
8 -2.93E-03
9 3.57E-04
10 -1.55E-03
11 7.14E-04
12 -6.02E-03
PERPINDAHAN TITIK PADA BATANG / MEMBER
Member D1x D1y D2x D2y
1 0.00E+00 0.00E+00 -5.74E-04 -1.45E-03
2 0.00E+00 0.00E+00 0.00E+00 0.00E+00
3 0.00E+00 0.00E+00 -5.74E-04 -1.45E-03
4 0.00E+00 0.00E+00 3.57E-04 -1.55E-03
5 -5.74E-04 -1.45E-03 3.57E-04 -1.55E-03
6 -5.74E-04 -1.45E-03 -3.31E-04 -2.93E-03
7 3.57E-04 -1.55E-03 -3.31E-04 -2.93E-03
8 -3.31E-04 -2.93E-03 7.14E-04 -6.02E-03
9 3.57E-04 -1.55E-03 7.14E-04 -6.02E-03
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 26
REAKSI TUMPUAN / SUPPORT REACTION [AR]: [AR] IRx1 = [SRF] IRxIF * [DF] IFx1
[AR] IRx1 =
1 1.30E+01
2 6.50E+00
5 -1.30E+01
6 1.50E+00
GAYA-GAYA UJUNG BATANG / MEMBER END FORCES [AM]: [AM] mx4 = [SM] 4x4 (i) [RT] 4x4 [DJ] 4x4
[AM]=
Member F1x F1 y F2x F2y
1 14.534 0 -14.534 0
2 0 0 0.000 0
3 -3.354 0 3.354 0
4 -10 0 10.000 0
5 3 0 -3.000 0
6 11.18 0 -11.180 0
7 0 0 0.000 0
8 11.18 0 -11.180 0
9 -10 0 10.000 0
Degree of Freedom of Joints :
Joint Nx Ny
1 1 2
2 3 4
3 5 6
4 7 8
5 9 10
6 11 12
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 27
No. 3
Persiapan Data:
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 28
Data Propertis Batang:
1. E= 2.1e7 ton/m2 ; A= 0.06 m2
2. E= 2.1e7 ton/m2 ; A= 0.04 m2
Koordinat
No. Titik X Y
1 0 0
2 5.6 0
3 11.2 0
4 16.6 0
5 2.8 3.8
6 8.4 3.8
7 14 3.8
Data Batang
NO
BATANG
NO TITIK
KIRI
(BAWAH)
NO TITIK
KANAN
(BAWAH)
NO.
PROPERTIS
1 1 2 1
2 2 3 1
3 3 4 1
4 5 6 1
5 6 7 1
6 1 5 2
7 5 2 2
8 2 8 2
9 6 3 2
10 3 7 2
11 7 14 2
Data Tumpuan
No. TITIK RESTRAINT
RX
RESTRAINT
RY
RESTRAINT
RZ
1 1 1 0
2 1 1 0
Data Beban Titik
No titik Beban FX Beban Fy Beban FZ
2 0 -28 0
3 0 -28 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 29
INPUT DATA
%****rangka batang 2D---TEKNIK SIPIL UNISSULA SEMARANG---- %****nama file : TRUSS4----oleh :M.Taufan Putra 6/12/2006---- %****struktur : rangka bill board - ton.m clear all clc %****General Data------- type='t2d' nfile='Truss4' %****Property---i,E,A-------------- prop = [ 1 2.1e7 0.06 2 2.1e7 0.04]; %****Coordinates------------ %****--- Joint X Y --- coord=[ 1 0 0 2 5.6 0 3 11.2 0 4 16.6 0 5 2.8 3.8 6 8.4 3.8 7 14 3.8]; %****Element data------------------ %****--- Element J1 J2 No.prop--- element=[ 1 1 2 1 2 2 3 1 3 3 4 1 4 5 6 1 5 6 7 1 6 1 5 2 7 5 2 2 8 2 6 2 9 6 3 2 10 3 7 2 11 7 4 2]; %****Nodal Restraint---------- %****---- Joint JR1 JR2 -- Support=[ 1 1 1 4 0 1]; %****Joint Load------------- %****---Joint FX FY -- JL=[ 2 0 -28 3 0 -28]; %****Load Data---------------- %****---Elem. fx1 fy1 fx2 fy2--- AML=[ 1 0 0 0 0]; %****Call function for analysis trs2d 2d-------------------- [dof,index,coord,element]=TRUSS2D_sdata(prop,element,coord,type); [S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=... TRUSS2D_stiff(prop,element,coord,index,nfile); [IR,IF,Support]=TRUSS2D_ldata(Support,dof); [DF,AR,AM]=TRUSS2D_analysis_result... (element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile); [joint_disp,support_reaction,beam_endforces]=TRUSS2D_print_result... (JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile); %****end data------------------------------------------------ TRUSS2D_xplot; %-------------------
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 30
OUTPUT DATA
STIFFNESS MATRIX METHOD : PROGRAM TRUSS2D File Name : Truss4_2.txt
Joint Loads : Joint Fx Fy 2 0.000 -28.000 3 0.000 -28.000
Member Loads : Member Fx1 Fy1 Fx2 Fy2 1 0.000 0.000 0.000 0.000
Support Restraints : Joint Rx Ry 1 1 1 4 0 1
Joint Displacements : Joint Dx Dy 1 0.0000e+000 0.0000e+000 2 9.0591e-005 -9.3688e-004 3 2.7067e-004 -9.2178e-004 4 3.5376e-004 0.0000e+000 5 3.5554e-004 -5.0181e-004 6 1.7436e-004 -9.9567e-004 7 -4.6171e-006 -4.7325e-004
Support Reactions : Joint Rx Ry 1 -5.5404e-014 2.7663e+001 4 0.0000e+000 2.8337e+001
Member End Forces (axial/normal): Member axial force : + tension - compression 1 20.383 2 40.517 3 19.389 4 -40.766 5 -40.269 6 -34.361 7 34.361 8 0.419 9 -0.419 10 35.199 11 -34.336
<<< end of file >>>
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 31
DEFORMASI
Gambar 3.1. Deformasi Rangka Batang
Cek Kesetimbangan
∑FV = 0
28 t+ 28t = 27,663 t + 28,337 t
56 t = 56 t
Oke
∑FH = 0
0 = 0
Oke
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 32
FREE BODY DIAGRAM
Gambar 3.2. Free Body Diagram
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 33
GAMBAR BIDANG N
Gambar 3.3. Bidang Normal
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 34
No 4.
Persiapan Data:
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 35
Data Propertis Batang:
1. E= 2.1e4 ton/m2 ; A= 0.0006 m2
Koordinat
No. Titik X Y
1 0 0
2 3 0
3 6 0
4 0 3
5 3 3
6 6 3
7 9 3
Data Batang
NO
BATANG
NO TITIK
KIRI
(BAWAH)
NO TITIK
KANAN
(BAWAH)
NO.
PROPERTIS
1 1 2 1
2 2 3 1
3 2 4 1
4 2 5 1
5 2 6 1
6 3 6 1
7 3 7 1
8 4 5 1
9 5 6 1
10 6 7 1
Data Tumpuan
No. TITIK RESTRAINT
RX
RESTRAINT
RY
RESTRAINT
RZ
1 1 1 1
4 1 1 1
Data Beban Titik
No titik Beban FX Beban Fy Beban FZ
5 0 -0,051 0
6 0 -0,051 0
7 0 -0,072 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 36
INPUT DATA
%****rangka batang 2D---TEKNIK SIPIL UNISSULA SEMARANG---- %****nama file : Truss soal 4----oleh :M. Taufan Putra 30201203248---- %****struktur : rangka batang clear all clc %****General Data------- type='t2d' nfile='Truss soal 4' %****Property---i,E,A-------------- prop = [ 1 2,1e6 0.09 ]; %****Coordinates------------ %****--- Joint X Y --- coord=[ 1 0 0 2 3 0 3 6 0 4 0 3 5 3 3 6 6 3 7 9 3]; %****Element data------------------ %****--- Element J1 J2 No.prop--- element=[ 1 1 2 1 2 2 3 1 3 2 4 1 4 2 5 1 5 2 6 1 6 3 6 1 7 3 7 1 8 4 5 1 9 5 6 1 10 6 7 1]; %****Nodal Restraint---------- %****---- Joint JR1 JR2 -- Support=[ 1 1 1 1 4 1 1 1]; %****Joint Load------------- %****---Joint FX FY -- JL=[ 5 0 -5 6 0 -5 7 0 -5]; %****Load Data---------------- %**** AML=[ 3 0 0 0 0 ]; %****Call function for analysis trs2d 2d-------------------- [dof,index,coord,element]=TRUSS2D_sdata(prop,element,coord,type); [S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=... TRUSS2D_stiff(prop,element,coord,index,nfile); [IR,IF,Support]=TRUSS2D_ldata(Support,dof); [DF,AR,AM]=TRUSS2D_analysis_result... (element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile); [joint_disp,support_reaction,beam_endforces]=TRUSS2D_print_result... (JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile); %****end data------------------------------------------------ TRUSS2D_xplot %------------------
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 37
OUTPUT DATA
STIFFNESS MATRIX METHOD : PROGRAM TRUSS2D File Name : Truss rev_2.txt
Joint Loads : Joint Fx Fy 5 0.000 -5.000 6 0.000 -5.000 7 0.000 -5.000
Member Loads : Member Fx1 Fy1 Fx2 Fy2 3 0.000 0.000 0.000 0.000
Support Restraints : Joint Rx Ry 1 1 1 1 4 1 1 1 Joint Displacements : Joint Dx Dy 1 0.0000e+000 0.0000e+000 2 -4.7619e-004 -1.1496e-003 3 -5.5556e-004 -2.6303e-003 4 0.0000e+000 0.0000e+000 5 2.3810e-004 -1.2290e-003 6 4.7619e-004 -2.5510e-003 7 5.5556e-004 -3.9659e-003
Support Reactions : Joint Rx Ry 1 3.0000e+001 0.0000e+000 4 -3.0000e+001 1.5000e+001
Member End Forces (axial/normal): Member axial force : + tension - compression 1 -30.000 2 -5.000 3 21.213 4 -5.000 5 -14.142 6 5.000 7 -7.071 8 15.000 9 15.000 10 5.000
<<< end of file >>>
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 38
DEFORMASI
Gambar 4.1 Deformasi Rangka Batang
Cek Kesetimbangan
∑FV = 0
5 t + 5 t + 5 t = 15 t
15 t= 15 t
Oke
∑FH = 0
0 = 0,369 t – 0,369 t
0 = 0
Oke
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 39
FREE BODY DIAGRAM
Gambar 4.2. Free Body Diagram
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 40
BIDANG NORMAL
Gambar 4.3. Bidang Normal
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 41
No. 5
Persiapan Data:
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 42
Data Propertis Batang:
1. E= 2,1e6 ton/m2 ; A= 0,09 m
2 ; I= 0,000675
2. E= 2,1e6 ton/m2 ; A= 0,045 m
2 ; I= 0,00338
Koordinat
No. Titik X Y
1 0 0
2 -1 4
3 0 4
4 5 4
5 5 0
Data Batang
NO
BATANG
NO TITIK
KIRI
(BAWAH)
NO TITIK
KANAN
(BAWAH)
NO.
PROPERTIS
1 1 3 1
2 2 3 2
3 3 4 2
4 5 4 1
Data Tumpuan
No. TITIK RESTRAINT
RX
RESTRAINT
RY
RESTRAINT
RZ
1 1 1 1
5 1 1 1
Data Beban Titik
No titik Beban FX Beban Fy Beban FZ
2 3 0 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 43
Data Beban Batang :
Batang 2 q=5 ton/m L=5 m
Ra2=q*L2/2; Rb2=Ra2;
Ma2=1/12*q*L^2; Mb2=-Ma2;
Beban Merata pada Batang :
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 44
INPUT DATA
%****PORTAL 2D---TEKNIK SIPIL UNISSULA SEMARANG---- %****nama file : 1 TINGKAT----oleh :PUTRA 10/11/2014---- %****struktur : PORTAL clear all clc %****General Data--- type='FRAME2D' nfile='1 TINGKAT' %****Material Properties---i,E,A,I--- prop = [ 1 2.1e6 0.09 0.000675 2 2.1e6 0.045 0.00338 ]; %****Coordinates--- %****--- Joint X Y --- coord=[ 1 0 0 2 -1 4 3 0 4 4 5 4 5 5 0]; %****Elemet data--- %****--- Element J1 J2 prop--- element=[ 1 1 3 1 2 2 3 2 3 3 4 2 4 5 4 1]; %****Nodal Restraint--- %****---- Joint JR1 JR2 JR3--- Support=[ 1 1 1 1 5 1 1 1 ]; %****Joint Load--- %****---Joint FX FY MZ--- JL=[ 2 3 0 0]; %****Gaya & Momen Jepit--- %****Matriks Beban Batang------ AML=[ 3 0 12.5 10.42 0 12.5 -10.42 ]; %****Call function for analysis portal 2d-------------------- [dof,index,coord,element]=FRAME2D_sdata(prop,element,coord,type); [S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=FRAME2D_stiff... (prop,element,coord,index,nfile); [IR,IF,Support]=FRAME2D_ldata(Support,dof); [DF,AR,AM]=FRAME2D_analysis_result... (element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile); [joint_disp,support_reaction,beam_endforces]=FRAME2D_print_result... (JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile); %****end data------------------------------------------------ % FRAME2D_xplot %
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 45
OUTPUT
STIFFNESS MATRIX METHOD : PROGRAM FRAME2D File Name : 1 TINGKAT_2.txt
Joint Loads : Joint Fx Fy Mz 2 3.000 0.000 0.000
Member Loads : Member Fx1 Fy1 Mz1 Fx2 Fy2
Mz2 3 0.000 12.500 10.420 0.000 12.500
-10.420
Support Restraints : Joint Dx Dy Rz 1 1 1 1 5 1 1 1
Joint Displacements : Joint Dx Dy Rz 1 0.0000e+000 0.0000e+000 0.0000e+000 2 6.4442e-003 2.5644e-003 -2.8046e-003 3 6.4124e-003 -2.4020e-004 -2.8046e-003 4 6.2650e-003 -2.8890e-004 2.1096e-003 5 0.0000e+000 0.0000e+000 0.0000e+000
Support Reactions : Joint Rx Ry Mz 1 -2.1348e-001 1.1349e+001 1.4209e+000 5 -2.7865e+000 1.3651e+001 4.8254e+000
Member End Forces : Member Fx1 Fy1 Mz1 Fx2 Fy2
Mz2 1 11.349 0.213 1.421 -11.349 -0.213
-0.567 2 3.000 -0.000 -0.000 -3.000 0.000
-0.000 3 2.787 11.349 0.567 -2.787 13.651
-6.321 4 13.651 2.787 4.825 -13.651 -2.787
6.321
<<< end of file >>>
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 46
DEFORMASI
Gambar 5.1. Deformasi
ƩFH = 0
Py + Ry = 0
3 – 0,21348- 2,7865 = 0
3- 3 = 0
0 = 0 (Oke)
ƩFV= 0
Px+ Ry = 0
-25 + 11,349 + 13,651 = 0
0 = 0 (Oke)
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 47
FREEBODY DIAGRAM
Gambar 5.2. Free Body Diagram
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 48
BIDANG MOMEN
Gambar 5.3. Bidang Momen
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 49
BIDANG LINTANG
Gambar 5.4. Bidang Lintang
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 50
BIDANG NORMAL
Gambar 5.5. Bidang Normal
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 51
NO .6
Persiapan Data
Data Propertis Batang:
1. E= 2e7 ton/m2 ; A= 0.18 m2; I= 0,0054
Koordinat
No. Titik X Y
1 0 0
2 6 0
3 12 0
4 18 0
5 24 5.6
6 30 0
7 36 2.8
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 52
Data Batang :
NO
BATANG
NO TITIK
KIRI
(BAWAH)
NO TITIK
KANAN
(BAWAH)
NO.
PROPERTIS
1 1 2 1
2 2 3 1
3 3 4 1
4 4 5 1
5 5 6 1
6 6 7 1
Data Tumpuan
No. TITIK RESTRAINT
RX
RESTRAINT
RY
RESTRAINT
RZ
1 1 1 0
2 1 1 0
3 1 1 0
4 1 1 0
5 1 1 0
6 1 1 0
7 1 1 0
Data Beban batang :
Batang – 1 : q1=2 ton/m; L1= 6 m
Batang – 4 : q2=6 ton/m; L4= 6 m
Batang – 5 : q3= 6 ton/m; L5=6m
Batang – 6 : q4= 6 ton/m; L6= 6 m
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 53
Ra1=q1*L1/2; Rb1=Ra2;
Ra4=q2*L4/4; Rb4=Ra4;
Ra5=9*4/6*q3*L5; Rb6=9*2/6*q3*L5;
Ra6=9*2/6*q4*L6; Rb8=9*4/6*q4*L6;
Ma2=1/12*q1*L1^2; Mb2= -Ma2;
Ma4=5/96*q2*L4^2; Mb4= -Ma4;
Ma5=7/20*q3*L5^2; Mb5= -3/20* q3*L5^2;
Ma6=3/20*q4*L6^2; Mb6= -7/20*q4*L6^2;
Beban Merata Pada Batang :
No.
Batang
Beban
FX2
Beban
FY2
Beban
MZ2
Beban
FX2
Beban
FY2
Beban
MZ2
UJUNG KIRI UJUNG KANAN
1 0 Ra1 Ma1 0 Rb1 Mb1
4 0 Ra4 Ma4 0 Rb4 Mb4
5 0 Ra5 Ma5 0 Rb5 Mb5
6 0 Ra6 Ma6 0 Rb6 Mb6
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 54
INPUT DATA
%****PORTAL 2D---TEKNIK SIPIL UNISSULA SEMARANG---- %****nama file :Soal 7 ----oleh :M. TAUFAN PUTRA---- %****struktur : blk menerus di atas 7 tumpuan, clear all clc %****General Data--- type='p2d' nfile='Soal 7' %****Property---i,E,A,I--- prop = [ 1 2e6 0.3*0.6 1/12*0.3*0.6^3]; %****Coordinates--- %****--- Joint X Y --- coord=[ 1 0 0 2 6 0 3 12 0 4 18 0 5 24 0 6 30 0 7 36 0 ]; %****Element data--- %****--- Element J1 J2 prop--- element=[ 1 1 2 1 2 2 3 1 3 3 4 1 4 4 5 1 5 5 6 1 6 6 7 1]; %****Nodal Restraint--- %****---- Joint JR1 JR2 JR3--- Support=[ 1 1 1 0 2 1 1 0 3 1 1 0 4 1 1 0 5 1 1 0 6 1 1 0 7 1 1 0]; %****Joint Load--- %****---Joint FX FY MZ--- JL=[ 1 0 0 0]; %****Load Data--- %**** AML=[ 1 0 6 6 0 6 -6 2 0 9 9 0 9 -9 3 0 6 9 0 6 -9 4 0 9 11.25 0 9 -11.25 5 0 12.6 10.8 0 5.4 -7.2 6 0 5.4 7.2 0 12.6 -10.8]; %****Call function for analysis portal 2d-------------------- [dof,index,coord,element]=FRAME2D_sdata(prop,element,coord,type); [S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=FRAME2D_stiff... (prop,element,coord,index,nfile); [IR,IF,Support]=FRAME2D_ldata(Support,dof); [DF,AR,AM]=FRAME2D_analysis_result... (element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile); [joint_disp,support_reaction,beam_endforces]=FRAME2D_print_result... (JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile); %****end data------------------------------------------------ % FRAME2D_xplot
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 55
OUTPUT DATA
STIFFNESS MATRIX METHOD : PROGRAM FRAME2D File Name : Soal 7_2.txt
Joint Loads : Joint Fx Fy Mz 1 0.000 0.000 0.000
Member Loads : Member Fx1 Fy1 Mz1 Fx2 Fy2
Mz2 1 0.000 6.000 6.000 0.000 6.000
-6.000 2 0.000 9.000 9.000 0.000 9.000
-9.000 3 0.000 6.000 9.000 0.000 6.000
-9.000 4 0.000 9.000 11.250 0.000 9.000
-11.250 5 0.000 12.600 10.800 0.000 5.400
-7.200 6 0.000 5.400 7.200 0.000 12.600
-10.800
Support Restraints : Joint Dx Dy Rz 1 1 1 0 2 1 1 0 3 1 1 0 4 1 1 0 5 1 1 0 6 1 1 0 7 1 1 0
Joint Displacements : Joint Dx Dy Rz 1 0.0000e+000 0.0000e+000 -8.2473e-004 2 0.0000e+000 0.0000e+000 -1.7201e-005 3 0.0000e+000 0.0000e+000 6.0203e-005 4 0.0000e+000 0.0000e+000 -2.2361e-004 5 0.0000e+000 0.0000e+000 2.0924e-004 6 0.0000e+000 0.0000e+000 -4.8835e-004 7 0.0000e+000 0.0000e+000 1.7442e-003
Support Reactions : Joint Rx Ry Mz 1 0.0000e+000 4.4845e+000 0.0000e+000 2 0.0000e+000 1.6593e+001 0.0000e+000 3 0.0000e+000 1.4628e+001 0.0000e+000 4 0.0000e+000 1.5268e+001 0.0000e+000 5 0.0000e+000 2.1123e+001 0.0000e+000 6 0.0000e+000 1.3563e+001 0.0000e+000 7 0.0000e+000 1.0340e+001 0.0000e+000
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 56
Member End Forces : Member Fx1 Fy1 Mz1 Fx2 Fy2
Mz2 1 0.000 4.485 0.000 0.000 7.515
-9.093 2 0.000 9.077 9.093 0.000 8.923
-8.628 3 0.000 5.706 8.628 0.000 6.294
-10.393 4 0.000 8.974 10.393 0.000 9.026
-10.548 5 0.000 12.098 10.548 0.000 5.902
-9.963 6 0.000 7.660 9.963 0.000 10.340
-0.000
<<< end of file >>>
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 57
DEFORMASI
Gambar.6.1 Deformasi Batang
Cek Kesetimbangan :
∑fx = 0
- Px + Rx = 0
0 + 0 = 0 ( oke )
∑fx = 0
- Py + Ry = 0
- ( 6+15+15+15+21,6+8,8+12,6) + (4,4+16,5+14,6+15,2+21,1+13,5+10,3) = 0
0 = 0 ( oke )
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 58
FREEBODY
Gambar 7.2. Free Body
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 59
BIDANG MOMEN
Gambar 7.3. Bidang Momen
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 60
BIDANG LINTANG
Gambar 7.4. Bidang Lintang
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 61
NO. 7
2.Persiapan Data :
Penomoran titik, batang dan koordinat :
Data batang
b1 = 0.5
h1 = 0.5
A1 = 0.25
E = 25e7
I = 5.208e-3
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 62
Data Propertis batang : 1 E=2.5e6 (ton/m2) A = 0.25 (m2)
Data Koordinat :
No. Titik X Y
1 0 0
2 5 0
3 0 4
4 5 4
Data Batang :
No.
Batang
No.Titik
Kiri
(bawah)
No.Titik
Kanan(bawah) No.Propertis
1 1 3 1
2 2 4 1
3 3 4 1
Data Tumpuan : No. Titik Restraint RX Restraint
RY
Restraint
RZ
1 1 1 1
2 1 1 1
Data Beban Titik :
No. Titik Beban Beban Beban
FX FY MZ
11 0 0 0
17 0 0 0
Data Beban Batang :
L3=5 ; q =2; Ra3=1/4*q*L3; Rb3=Ra3; Ma3=5/96*q*L3^2; Mb3=-Ma3;
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 63
Beban Merata pada Batang :
No. Beban Beban Beban Beban Beban Beban
Batang FX1 FY1 MZ1 FX2 FY2 MZ2
UJUNG KIRI UJUNG KANAN
3 0 Ra3 Ma3 0 Rb3 Mb3
3.Input Data File : %****PORTAL 2D---TEKNIK SIPIL UNISSULA SEMARANG----
%****nama file : TINGKAT 1 S----oleh :M. TAUFAN PUTRA 30201203248----
%****struktur : Balok menerus 2 btng beban P --kg.m--
clear all
clc
%****General Data---
type='FRAME2D'
nfile=' TINGKAT 1 S
%****Material Properties---i,E,A,I---
b1 = 0.5 ; h1 = 0.5;
A1 = b1*h1 ; I1= 1/12*b1*h1^3;
E =2.5e6;
prop = [ 1 E A1 I1 ];
%****Coordinates---
%****--- Joint X Y ---
coord=[ 1 0 0
2 5 0
3 0 4
4 5 4 ];
%****Element data---
%****--- Element J1 J2 prop---
element=[ 1 1 3 1
2 2 4 1
3 3 4 1 ];
%****Nodal Restraint---
%****---- Joint JR1 JR2 JR3---
Support=[ 1 1 1 1
2 1 1 1 ];
%****Joint Load---
%****---Joint FX FY MZ---
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 64
JL=[ 1 0 0 0 ];
%****Load Data---
L3=5;
q =2;
Ra3=1/4*q*L3; Rb3=Ra3;
Ma3=5/96*q*L3^2; Mb3=-Ma3;
%****
AML=[ 3 0 Ra3 Ma3 0 Rb3 Mb3 ];
%****Call function for analysis portal 2d--------------------
[dof,index,coord,element]=FRAME2D_sdata(prop,element,coord,type);
[S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=FRAME2D_stiff...
(prop,element,coord,index,nfile);
[IR,IF,Support]=FRAME2D_ldata(Support,dof);
[DF,AR,AM]=FRAME2D_analysis_result...
(element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile);
[joint_disp,support_reaction,beam_endforces]=FRAME2D_print_result...
(JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile);
%****end data------------------------------------------------
%
FRAME2D_xplot
%
4. OutPut Program & Cek :
frame3_2.txt
Support Reactions :
Joint Rx Ry Mz
1 6.9440e-001 2.5000e+000 -9.2134e-001
2 -6.9440e-001 2.5000e+000 9.2134e-001
Member End Forces :
Member Fx1 Fy1 Mz1 Fx2 Fy2 Mz2
1 2.500 -0.694 -0.921 -2.500 0.694 -1.856
2 2.500 0.694 0.921 -2.500 -0.694 1.856
3 0.694 2.500 1.856 -0.694 2.500 -1.856
frame1_4.txt Reaction of Supports :
{AR}IFx1 = -{ARC}IRx1 + [SRF]IRxIF {DF}IFx1
1 6.944e-001
2 2.500e+000
3 -9.213e-001
4 -6.944e-001
5 2.500e+000
6 9.213e-001
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 65
Gambar output data
Cek Keseimbangan :
∑v = 0 2.5 + 2.5 – 5 = 0
∑h = 0
0,6944 - 0,6944 = 0
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 66
5. Free Body; Bidang M,D,N : Berikut free body diagram
Gambar free body diagram
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 67
Gambar bidang Momen (M) pada batang 1, 2 ,dan 3
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 68
Gambar bidang Lintang (D) pada batang 1, 2 ,dan 3
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 69
Gambar bidang Normal (N) pada batang 1, 2 ,dan 3
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 70
No.8
Persiapan Data :
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 71
Data Properties batang :
1. E= 2e7 (t/m) A= 0.16 (m2) I= 2.135e-3 (m4) ( Kolom )
2. E= 2e7 (t/m) A= 0.12 (m2) I= 1.6e-3 (m4) ( Balok )
Data Koordinat :
No. Titik X Y
1 0 0
2 5 1
3 0 2,5
4 5 2,5
5 -2 5
6 0 5
7 5 5
8 7 5
9 0 9
10 5 9
Data Batang
No.
Batang
No.Titik Kiri
(bawah)
No.Titik
Kanan(bawah) No.Propertis
1 1 3 1
2 3 4 2
3 2 4 1
4 5 6 2
5 3 6 1
6 6 7 2
7 4 7 1
8 7 8 2
9 6 9 1
10 9 10 2
11 7 10 1
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 72
Data Tumpuan
No. Titik Restraint RX Restraint
RY
Restraint
RZ
1 1 1 1
2 1 1 1
Data Beban Titik
No. Titik Beban
FX
Beban
FY
Beban
MZ
3 0 -1 0
6 0 -1 0
7 1 -2 0
Data Beban batang :
Batang – 2 : q2=2 ton/m; L2=5m
Batang – 4 : q4=1,5 ton/m; L4=2m
Batang – 6 : q6=4 ton/m; L6=5m
Batang – 8 : q8=2 ton/m; L8=2m
Batang – 10 : q10=3 ton/m; L10=5m
Ra2=q2*L2/2; Rb2=Ra2;
Ra4=q4*L4/2; Rb4=Ra4;
Ra6=q6*L6/4; Rb6=Ra6;
Ra8=q8*L8/2; Rb8=Ra8;
Ra10=q10*L10/2; Rb10=Ra10;
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 73
Ma2=1/12*q2*L2^2; Mb2= -Ma2;
Ma4=1/12*q4*L4^2; Mb4= -Ma4;
Ma6=5/96*q6*L6^2; Mb6= -Ma6;
Ma8=1/12*q8*L8^2; Mb8= -Ma8;
Ma10=1/12*q10*L10^2; Mb10= -Ma10;
Beban Merata Pada Batang :
No.
Batang
Beban
FX2
Beban
FY2
Beban
MZ2
Beban
FX2
Beban
FY2
Beban
MZ2
UJUNG KIRI UJUNG KANAN
3 0 Ra3 Ma3 0 Rb3 Mb3
4 0 Ra4 Ma4 0 Rb4 Mb4
5 0 Ra5 Ma5 0 Rb5 Mb5
8 0 Ra8 Ma8 0 Rb8 Mb8
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 74
INPUT DATA
%****PORTAL 2D---TEKNIK SIPIL UNISSULA SEMARANG---- %****nama file : Portal 3 Tingkat----oleh :M.Taufan Putra ---- %****struktur : GEDUNG BERTINGKAT clear all clc %****General Data--- type='p2d' nfile='Portal 3 tingkat' %****Property---i,E,A,I--- prop = [ 1 2e7 0.16 2.13e-3 2 2e7 0.12 1.6e-3 ]; %****Coordinates--- %****--- Joint X Y --- coord=[ 1 0 0 2 5 1 3 0 2.5 4 5 2.5 5 -2 5 6 0 5 7 5 5 8 7 5 9 0 9 10 5 9]; %****Element data--- %****--- Element J1 J2 prop--- element=[ 1 1 3 1 2 3 4 2 3 2 4 1 4 5 6 2 5 3 6 1 6 6 7 2 7 4 7 1 8 7 8 2 9 6 9 1 10 9 10 2 11 7 10 1]; %****Nodal Restraint--- %****---- Joint JR1 JR2 JR3--- Support=[ 1 1 1 1 2 1 1 1 ]; %****Joint Load--- %****---Joint FX FY MZ--- JL=[ 5 0 -1 0 8 0 -1 0 9 1 -2 0]; %****Load Data--- q2=2 ; L2=5; q4=1.5 ; L4=2; q6=4 ; L6=5; q8=2 ; L8=2; q10=3 ; L10=5;
Ra2=q2*L2/2; Rb2=Ra2; Ra4=q4*L4/2; Rb4=Ra4; Ra6=q6*L6/4; Rb6=Ra6; Ra8=q8*L8/2; Rb8=Ra8; Ra10=q10*L10/2; Rb10=Ra10; Ma2=1/12*q2*L2^2; Mb2= -Ma2;
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 75
Ma4=1/12*q4*L4^2; Mb4= -Ma4; Ma6=5/96*q6*L6^2; Mb6= -Ma6; Ma8=1/12*q8*L8^2; Mb8= -Ma8; Ma10=1/12*q10*L10^2; Mb10= -Ma10;
%**** AML=[ 2 0 Ra2 Ma2 0 Rb2 Mb2 4 0 Ra4 Ma4 0 Rb4 Mb4 6 0 Ra6 Ma6 0 Rb6 Mb6 8 0 Ra8 Ma8 0 Rb8 Mb8 10 0 Ra10 Ma10 0 Rb10 Mb10];
%****Call function for analysis portal 2d-------------------- [dof,index,coord,element]=FRAME2D_sdata(prop,element,coord,type); [S,Sm,SmS,Cx,Cy,RT,L,A,Joint,Xj,Xk,Yj,Yk]=FRAME2D_stiff... (prop,element,coord,index,nfile); [IR,IF,Support]=FRAME2D_ldata(Support,dof); [DF,AR,AM]=FRAME2D_analysis_result... (element,dof,index,IF,IR,S,Sm,JL,AML,RT,Support,type,nfile); [joint_disp,support_reaction,beam_endforces]=FRAME2D_print_result... (JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile); %****end data------------------------------------------------ % FRAME2D_xplot %
%
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 76
OUTPUT DATA
NAMAFILE_2.txt
Support Reactions : Joint Rx Ry Mz 1 1.6367e+000 2.2107e+001 -1.2021e+000 2 -2.6367e+000 2.3893e+001 1.6013e+000
Member End Forces :
Member Fx1 Fy1 Mz1 Fx2 Fy2 Mz2
1 22.107 -1.637 -1.202 -22.107 1.637 -2.890
2 2.108 4.703 3.022 -2.108 5.297 -4.508
3 23.893 2.637 1.601 -23.893 -2.637 2.354
4 0.000 -1.000 -0.000 0.000 4.000 -5.000
5 17.404 0.471 -0.133 -17.404 -0.471 1.311
6 -1.431 4.358 4.033 1.431 5.642 -7.244
7 18.596 0.529 2.154 -18.596 -0.529 -0.833
8 -0.000 5.000 6.000 0.000 -1.000 0.000
9 9.047 -0.960 -0.345 -9.047 0.960 -3.494
10 1.960 7.047 3.494 -1.960 7.953 -5.761
11 7.953 1.960 2.077 -7.953 -1.960 5.761
NAMAFILE_4.txt
Reaction of Supports : {AR}IFx1 = -{ARC}IRx1 + [SRF]IRxIF {DF}IFx1 1 1.637e+000 2 2.211e+001 3 -1.202e+000 4 -2.637e+000 5 2.389e+001 6 1.601e+000
<<< end of file >>>
DEFORMASI
Gambar 8.1. Deformasi
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 77
CEK KESETIMBANGAN
( ) ( ( ) ( ) ( ) (
)
( ))
( )
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 78
Gambar Bidang M ( Gaya Momen )
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 79
Gaya Momen :
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 80
Gambar Bidang D ( Gaya Lintang )
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 81
Gaya Lintang :
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 82
Gambar Bidang N ( Gaya Normal )
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 83
Gaya Normal :
Analisa Struktur IV
M. TAUFAN PUTRA (30201203248) Page 84