Analisa Struktur (Fix)

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

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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

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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

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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

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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

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CEK KESETIMBANGAN

( ) ( ( ) ( ) ( ) (

)

( ))

( )

Analisa Struktur IV

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Gambar Bidang M ( Gaya Momen )

Analisa Struktur IV

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Gaya Momen :

Analisa Struktur IV

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Gambar Bidang D ( Gaya Lintang )

Analisa Struktur IV

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Gaya Lintang :

Analisa Struktur IV

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Gambar Bidang N ( Gaya Normal )

Analisa Struktur IV

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Gaya Normal :

Analisa Struktur IV

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