Tugas Besar Analisa Struktur IV

BAB IV
FRAME 2D

4.1 Soal

10,51 t
3,51 t/m

1,51 t
I=0.005 m4

5,51
I=0.001 m4 5,51
I=0.001 m4

1,51 t/m

E=2e6 t/m2

3,02 5,51

Gambar 4.1 Gambar Frame 2D

4.2 Penomoran Titik dan Batang

10.51 t
3,51 t/m

3
3
1,51 t 4
I=0.005 m4

5,51 t 2
I=0.001 m4 4 5,51
I=0.001 m4

1,51 t/m

1
E=2e6 t/m2

1
5

3,02 5,51

Gambar 4.2 Gambar Penomoran Titik dan Batang

Muhammad Rifqi Maula (30201900151) 119

Tugas Besar Analisa Struktur IV

4.3 Persiapan Data

a. Data properties
Tabel 4.1 Data Properties

No Nama Batang E (ton/m2) A (m2)

1 Batang Vertical 2.1 x 106 0.001

2 Batang Horizontal 2.1 x 106 0.005

b. Data koordinat
Tabel 4.2 Data Koordinat
No Titik X Y
1 1 0 0
2 2 1.51 2.755
3 3 3.02 5.51
4 4 8.53 5.51
5 5 8.53 0

c. Data batang
Tabel 4.3 Data Batang

No Batang J1 J2 PROP
1 T1 1 2 1
2 T2 2 3 1
3 T3 3 4 2
4 T4 4 5 1

d. Data tumpuan
Tabel 4.4 Data Tumpuan
No Nomor Titik JR1 JR2 JR3
1 1 1 1 1
2 5 1 1 1

Muhammad Rifqi Maula (30201900151) 120

Tugas Besar Analisa Struktur IV
e. Data beban titik
Tabel 4.5 Data Beban Titik
No Nomor Titik Fx Fy
1 2 4.83 -2.64
2 3 1.51 -10.51

4.4 Input Data Linpro

LinPro 2.7.5
File: D:\linpro\linpro no 6.aln
Units: kN-m

____________________________________________________________________________
Input Data

Coordinates of joints/supports
Joint X Y Rx Ry Rt SPRING.X
SPRING.Y SPRING.ROT CS.ROT
0 0,000 0,000 1 1 1 0,00E+000
0,00E+000 0,00E+000 0,00
1 1,510 2,755 0 0 0 0,00E+000
0,00E+000 0,00E+000 0,00
2 3,020 5,510 0 0 0 0,00E+000
0,00E+000 0,00E+000 0,00
3 8,530 5,510 0 0 0 0,00E+000
0,00E+000 0,00E+000 0,00
4 8,530 0,000 1 1 1 0,00E+000
0,00E+000 0,00E+000 0,00

Members
Member Joint I Joint J Type Releases
0: 0 1 PROP2 111111
1: 1 2 PROP2 111111
2: 2 3 PROP1 111111
3: 3 4 PROP2 111111

Cross Sections
0: TYPE1
A= 1,000E-02
I= 1,000E-04
E= 200000000,00
alpha= 1,2E-05

1: PROP1
A= 1,680E-01
I= 5,000E-03
E= 2000000,00
alpha= 1,2E-05

2: PROP2
A= 7,600E-02
I= 1,000E-03
E= 2000000,00
alpha= 1,2E-05

Load
0: Distributed Load
Load Case: CASE1
Load Name: Distributed
Coordinate System: Global Y
a= 0,00
b= 1,00 On Member
p1= -1,51
p2= -1,51

1: Distributed Load

Muhammad Rifqi Maula (30201900151) 121

Tugas Besar Analisa Struktur IV
Load Case: CASE1
Load Name: Distributed
Coordinate System: Global Y
a= 0,00
b= 1,00 On Member
p1= -3,51
p2= -3,51

2: Point Load
Load Case: CASE1
Load Name: Point
Coordinate System: Global
a= 0,00 Absolute from Joint I
Force X= 1,51
Force Y= 10,51
Moment M= 0,00

3: Point Load
Load Case: CASE1
Load Name: Point
Coordinate System: Global
a= 0,00 Absolute from Joint I
Force X= 1,51
Force Y= -10,51
Moment M= 0,00

4: Point Load
Load Case: CASE1
Load Name: Point
Coordinate System: Global
a= 0,00 Absolute from Joint I
Force X= 4,83
Force Y= -2,64
Moment M= 0,00

Load Applied on Joints

Joint Applied Loads
1: 4
2: 3

Load Applied on Members

Member Applied Loads
0: 0
1: 0
2: 1

Load Cases
0: CASE1

Load Combinations

Masses

Masses Applied on Joints

Joint Applied Masses

============================================================================
Static Analysis Results

4.5 Output Data Linpro

Load Case: CASE1

Displacements of joints in global CS

Joint X Y phi
0 0,000000 0,000000 0,000000
1 0,028964 -0,016379 -0,013215
2 0,046180 -0,026222 0,002155
3 0,046047 -0,000587 0,003848
4 0,000000 0,000000 0,000000

Muhammad Rifqi Maula (30201900151) 122

Tugas Besar Analisa Struktur IV

Reactions in global CS
Joint Rx Ry M
0 1,787170 25,781807 24,222212
4 -8,127170 16,196153 20,993703

Displacements (global CS) and forces (local CS) on members ends

Memb: 0
Joint X Y phi
0 0,000000 0,000000 0,000000
1 0,028964 -0,016379 -0,013215
Axial Shear Moment
0 -23,467575 -10,824439 -24,222212
1 -19,307525 -8,544339 6,202995
Memb: 1
Joint X Y phi
1 0,028964 -0,016379 -0,013215
2 0,046180 -0,026222 0,002155
Axial Shear Moment
1 -19,313923 -3,039935 6,202995
2 -15,153873 -0,759835 12,171819
Memb: 2
Joint X Y phi
2 0,046180 -0,026222 0,002155
3 0,046047 -0,000587 0,003848
Axial Shear Moment
2 -8,127170 -3,143947 12,171819
3 -8,127170 16,196153 -23,787007
Memb: 3
Joint X Y phi
3 0,046047 -0,000587 0,003848
4 0,000000 0,000000 0,000000
Axial Shear Moment
3 -16,196153 -8,127170 -23,787007
4 -16,196153 -8,127170 20,993703

Displacements and forces along members in local CS

Memb: 0
d(x) X Y phi
0,000 0,000000 0,000000 0,000000
0,314 -0,000048 -0,000570 -0,003540
0,628 -0,000095 -0,002169 -0,006556
0,943 -0,000142 -0,004636 -0,009062
1,257 -0,000187 -0,007811 -0,011066
1,571 -0,000232 -0,011538 -0,012582
1,885 -0,000276 -0,015666 -0,013619
2,199 -0,000318 -0,020046 -0,014190
2,513 -0,000361 -0,024534 -0,014305
2,828 -0,000402 -0,028988 -0,013977
3,142 -0,000442 -0,033271 -0,013215
d(x) Axial Shear Moment
0,000 -23,467575 -10,824439 -24,222212
0,314 -23,051570 -10,596429 -20,857341
0,628 -22,635565 -10,368419 -17,564104
0,943 -22,219560 -10,140409 -14,342500
1,257 -21,803555 -9,912399 -11,192529
1,571 -21,387550 -9,684389 -8,114192
1,885 -20,971545 -9,456379 -5,107487
2,199 -20,555540 -9,228369 -2,172417
2,513 -20,139535 -9,000359 0,691021
2,828 -19,723530 -8,772349 3,482825
3,142 -19,307525 -8,544339 6,202995
Memb: 1
d(x) X Y phi
0,000 -0,000442 -0,033271 -0,013215
0,314 -0,000482 -0,037262 -0,012167
0,628 -0,000520 -0,040902 -0,010981
0,943 -0,000558 -0,044148 -0,009667
1,257 -0,000595 -0,046964 -0,008237
1,571 -0,000631 -0,049313 -0,006702
1,885 -0,000666 -0,051165 -0,005073
2,199 -0,000700 -0,052492 -0,003362
2,513 -0,000734 -0,053270 -0,001579
2,828 -0,000767 -0,053478 0,000263
3,142 -0,000798 -0,053100 0,002155
d(x) Axial Shear Moment
0,000 -19,313923 -3,039935 6,202995
0,314 -18,897918 -2,811925 7,122228
0,628 -18,481913 -2,583915 7,969827
0,943 -18,065908 -2,355905 8,745792

Muhammad Rifqi Maula (30201900151) 123

Tugas Besar Analisa Struktur IV
1,257 -17,649903 -2,127895 9,450125
1,571 -17,233898 -1,899885 10,082824
1,885 -16,817893 -1,671875 10,643889
2,199 -16,401888 -1,443865 11,133322
2,513 -15,985883 -1,215855 11,551121
2,828 -15,569878 -0,987845 11,897286
3,142 -15,153873 -0,759835 12,171819
Memb: 2
d(x) X Y phi
0,000 0,046180 -0,026222 0,002155
0,551 0,046167 -0,024842 0,002863
1,102 0,046154 -0,023059 0,003609
1,653 0,046140 -0,020869 0,004332
2,204 0,046127 -0,018300 0,004975
2,755 0,046114 -0,015413 0,005478
3,306 0,046100 -0,012300 0,005783
3,857 0,046087 -0,009087 0,005831
4,408 0,046074 -0,005932 0,005564
4,959 0,046060 -0,003025 0,004922
5,510 0,046047 -0,000587 0,003848
d(x) Axial Shear Moment
0,000 -8,127170 -3,143947 12,171819
0,551 -8,127170 -1,209937 13,371314
1,102 -8,127170 0,724073 13,505170
1,653 -8,127170 2,658083 12,573386
2,204 -8,127170 4,592093 10,575963
2,755 -8,127170 6,526103 7,512900
3,306 -8,127170 8,460113 3,384198
3,857 -8,127170 10,394123 -1,810144
4,408 -8,127170 12,328133 -8,070125
4,959 -8,127170 14,262143 -15,395746
5,510 -8,127170 16,196153 -23,787007
Memb: 3
d(x) X Y phi
0,000 0,000587 0,046047 0,003848
0,551 0,000528 0,046475 -0,002089
1,102 0,000470 0,043972 -0,006791
1,653 0,000411 0,039218 -0,010260
2,204 0,000352 0,032892 -0,012496
2,755 0,000294 0,025674 -0,013497
3,306 0,000235 0,018244 -0,013265
3,857 0,000176 0,011282 -0,011800
4,408 0,000117 0,005467 -0,009100
4,959 0,000059 0,001480 -0,005167
5,510 0,000000 0,000000 0,000000
d(x) Axial Shear Moment
0,000 -16,196153 -8,127170 -23,787007
0,551 -16,196153 -8,127170 -19,308936
1,102 -16,196153 -8,127170 -14,830865
1,653 -16,196153 -8,127170 -10,352794
2,204 -16,196153 -8,127170 -5,874723
2,755 -16,196153 -8,127170 -1,396652
3,306 -16,196153 -8,127170 3,081419
3,857 -16,196153 -8,127170 7,559490
4,408 -16,196153 -8,127170 12,037561
4,959 -16,196153 -8,127170 16,515632
5,510 -16,196153 -8,127170 20,993703

Muhammad Rifqi Maula (30201900151) 124

Tugas Besar Analisa Struktur IV
4.6 Input Data Matlab
%****PORTAL 2D---TEKNIK SIPIL UNISSULA SEMARANG----
%****nama file : Frame_6----oleh :Muhammad Rifqi Maula----
%****struktur : rangka bidang soal 6
clear all
clc
%****General Data---
type='p2d'
nfile='Rifqi6'
%****Property---i,E,A,I---
prop = [ 1 2e6 0.076 0.001
2 2e6 0.168 0.005];
%****Coordinates---
%****--- Joint X Y ---
coord=[ 1 0 0
2 1.51 2.755
3 3.02 5.51
4 8.53 5.51
5 8.53 0];
%****Element data---
%****--- Element J1 J2 prop---
element=[1 1 2 1
2 2 3 1
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 4.83 -2.64 0
3 1.51 -10.51 0];
%****Load Data---
q1= 1.51 ;q2=3.51;
L1= 3.02 ;L2=5.51;

Ra1=q1*L1/2; Rb1=Ra1;
Ma1=1/12*q1*L1^2; Mb1=-Ma1;

Ra2=q2*L2/2; Rb2=Ra2;
Ma2=1/12*q2*L2^2; Mb2=-Ma2;
%****
AML=[ 1 0 Ra1 Ma1 0 Rb1 Mb1
2 0 Ra1 Ma1 0 Rb1 Mb1
3 0 Ra2 Ma2 0 Rb2 Mb2 ];
%****Call function for analysis portal 2d--------------------
[dof,index,coord,element]=FRAME2D_sdata(prop,element,coord,typ
e);
[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_res
ult...
(JL,AML,dof,Support,element,IF,IR,DF,AR,AM,type,nfile);
%****end data------------------------------------------------
%
FRAME2D_xplot
%

Muhammad Rifqi Maula (30201900151) 125

Tugas Besar Analisa Struktur IV
4.7 Output Data Matlab

STIFFNESS MATRIX METHOD : PROGRAM FRAME2D

File Name : rifqi6_2.txt

Joint Loads :
Joint Fx Fy Mz
2 4.830 -2.640 0.000
3 1.510 -10.510 0.000

Member Loads :
Member Fx1 Fy1 Mz1 Fx2 Fy2
Mz2
1 0.000 2.280 1.148 0.000
2.280 -1.148
2 0.000 2.280 1.148 0.000
2.280 -1.148
3 0.000 9.670 8.880 0.000
9.670 -8.880

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 3.4280e-002 -1.9143e-002 -1.5279e-002
3 5.3160e-002 -2.9845e-002 2.9018e-003
4 5.3009e-002 -6.1359e-004 4.0366e-003
5 0.0000e+000 0.0000e+000 0.0000e+000

Support Reactions :
Joint Rx Ry Mz
1 -5.1373e+000 1.9947e+001 2.9429e+001
5 -9.2006e+000 1.6927e+001 2.3882e+001

Member End Forces :

Member Fx1 Fy1 Mz1 Fx2 Fy2
Mz2
1 15.023 14.092 29.429 -15.023 -
9.532 7.681
2 15.029 4.028 -7.681 -15.029
0.533 13.171
3 9.201 2.413 -13.171 -9.201
16.927 -26.813
4 16.927 9.201 23.882 -16.927 -
9.201 26.813

<<< end of file >>>

Muhammad Rifqi Maula (30201900151) 126

Tugas Besar Analisa Struktur IV
4.8 Cek Titik Keseimbangan

Joint Rx Ry Mz

1 -5.1373e+000 1.9947e+001 2.9429e+001

5 -9.2006e+000 1.6927e+001 2.3882e+001

a. Kontrol ∑V = 0
RAv + RBv = q2.L2 + P1 + (P3 cos 𝛼) + (q1.L1.cos 𝛼)
19,94 + 16.92 = (3.51 x 5.51) + 10.51 + (5.51 cos 61.2825) + (1.51 x 6.28
x cos 61.2825)
36,9 = 19,34 +10.51 + 2,64 +4,5
36,9 = 36,9

b. Kontrol ∑H = 0
RAh + RBh = P2 + (P3 sin 𝛼) + (q1.L1.sin 𝛼)
5,13 + 9,20 = 1.51 + (5.51 sin 61,280) + (1.51x 6,28 x sin 61,280)
11,53 = 1,51 + 4,83 + 8,31
14,5 = 14,5

4.9 Gambar Deformasi

Gambar 4.4 Deformasi

Muhammad Rifqi Maula (30201900151) 127
 Tugas Besar Analisa Struktur IV
4.10 Freebody Diagram
Member End Forces :

Member Fx1 Fy1 Mz1 Fx2 Fy2 Mz2

1 15.023 14.092 29.429 -15.023 -9.532 7.681

2 15.029 4.028 -7.681 -15.029 0.533 13.171

3 9.201 2.413 -13.171 -9.201 16.927 -26.813

4 16.927 9.201 23.882 -16.927 -9.201 26.813

2.413 16.927
-13.171

-9.201
1
9.201
.17
13

9
.02

-26.813
-15
33

Batang 3
0.5

23.882

16.927

9.201
Batang 2
28
4.0
9
.02
1

15
68
-7.3

Batang 4
. 02

81
-15

7.6
2
53
-9.

Batang 1
2
.09

-9.201
14
9

-16.927
.42

3
.02

26.813
29

15

Gambar 4.5 Gambar Freebody Diagram

Muhammad Rifqi Maula (30201900151) 128

Tugas Besar Analisa Struktur IV
4.11 Reaksi Perletakan
2 3

24,22 20,99
0 4
1,79 -8,13
25,78

16,20
Reactions, Comb: CASE1, Units: kN-m
LinPro 2.7 | Enes Siljak | eness@bosnia.ba | www.line.co.ba

Gambar 4.6 Reaksi Perletakan

Muhammad Rifqi Maula (30201900151) 129

Tugas Besar Analisa Struktur IV
4.12 Bidang Momen

-23,79

-23,79
12,17
12,17 13,51

6,20

-24,22

20,99

Moment Diagram, Comb: CASE1, Units: kN-m

LinPro 2.7 | Enes Siljak | eness@bosnia.ba | www.line.co.ba

Gambar 4.7 Bidang Momen

Memb: 3
Joint X Y phi
3 0,046047 -0,000587 0,003848
4 0,000000 0,000000 0,000000
Axial Shear Moment
3 -16,196153 -8,127170 -23,787007
4 -16,196153 -8,127170 20,993703

Muhammad Rifqi Maula (30201900151) 130

Tugas Besar Analisa Struktur IV
4.13 Bidang Lintang
16,20

-0,76 -8,13
-3,14

-3,04
-8,54

-8,13
-10,82

Shear Force Diagram, Comb: CASE1, Units: kN-m

LinPro 2.7 | Enes Siljak | eness@bosnia.ba | www.line.co.ba

Gambar 4.8 Bidang Lintang

Memb: 2
Joint X Y phi
2 0,046180 -0,026222 0,002155
3 0,046047 -0,000587 0,003848
Axial Shear Moment
2 -8,127170 -3,143947 12,171819
3 -8,127170 16,196153 -23,787007

Muhammad Rifqi Maula (30201900151) 131

Tugas Besar Analisa Struktur IV
4.14 Bidang Normal

-15,15 -8,13 -8,13

-16,20

-19,31

-23,47

-16,20

Axial Force Diagram, Comb: CASE1, Units: kN-m

LinPro 2.7 | Enes Siljak | eness@bosnia.ba | www.line.co.ba

Gambar 4.9 Bidang Normal

Memb: 0
Joint X Y phi
0 0,000000 0,000000 0,000000
1 0,028964 -0,016379 -0,013215
Axial Shear Moment
0 -23,467575 -10,824439 -24,222212
1 -19,307525 -8,544339 6,202995

Muhammad Rifqi Maula (30201900151) 132

Tugas Besar Analisa Struktur IV

Muhammad Rifqi Maula (30201900151) xiv