analisa plane frame dengan metode elemen hingga

7/30/2019 analisa plane frame dengan metode elemen hingga

1/27

Kelompok 2

Diketahui :

Struktur Portal dengan spesifikasi sebagai berikut :

Direncanakan profil Baja IWF 300.300.10.15

Modulus Elastisitas E : 2100000 kg /cm2

Tugas Mata Kuliah Metode Element Hingga

Luas Penampang A : 119.8 cmMoment Inersia Iz : 20400 cm

4

Beban Merata Q : 2.5 Kg / cm'

Beban Terpusat P : 200 Kg

Ditanya :

a. Perpindahan pada setiap titik simpul ?

b. Reaksi Tumpuan ?

c. Gaya Batang ?

Awal - Akhir

1 - 2 a Cm

2 - 3 b Cm

2 - 5 c Cm

3 - 4 d Cm

4 - 5 e Cm

5 - 6 f Cm

No. simpul

Tabulasi Panjang & Nama Batang Struktur

Nama Batang Panjang Batang

400.00

400.00

400.00

400.00

400.00

400.00



2/27

Kelompok 2

MATRIKS KEKAKUAN INDIVIDU / LOKAL :

Dimana panjang batang a,b,c, d, e dan f sama panjang yaitu : 400 cm, maka

AL2

/ Iz = 939.6078 cm

6L = 2400 cm

4L2

= 640000 cm

2L2

= 320000 cm

939.608 0 0 -939.61 0 0

[ K ] = 2100000 x 20400 0 12 2400 0 -12 2400

-

-939.608 0 0 939.61 0 0

0 -12 -2400 0 12 -2400

0 2400 320000 0 -2400 640000

669.375

628950 0 0 -628950 0 0

= 0 8032.5 1606500 0 -8032.5 1606500

0 1606500 428400000 0 -1606500 2.14E+08

-628950 0 0 628950 0 0

0 -8032.5 -1606500 0 8032.5 -1606500

0 1606500 214200000 0 -1606500 4.28E+08

Kx11 Kx12

Kx21 Kx22



3/27

Kelompok 2

MATRIKS KEKAKUAN GLOBAL :

Dimana : dan c = cos , s = sin

90o

Kx11 Kx12

Kx21 Kx22

k = A . L2

Iz

Kuadaran IVKuadaran III

Kuadaran II Kuadaran I

0o180o

270o



4/27

Kelompok 2

Dimana sudut untuk batang a,b,e dan f sama besar yaitu : 90o, maka

= 90 o

k = 939.608c = 0.000

c2 = 0.000

s = 1.000

S = 1.000

cs = 0.000

L = 400.00

[kc

2

+ 12s

2

][(k-12)cs] -6Ls

[-kc

2

- 12s

2

][(-k+12)cs] -6Ls

[K] = E x Iz [(k-12)cs] [ks + 12c2] 6Lc [(-k + 12)cs] [-ks2 - 12c2] 6Lc

-6Ls 6Lc 4L2 6Ls -6Lc 2L

2

[-kc2

- 12s2] [(-k+12)cs] 6Ls [kc

2+ 12s

2] [(k-12)cs] 6Ls

[(-k+12)cs] [-ks2

- 12c2] -6Lc [(k+12)cs [ks

2+ 12c

2] -6Lc


2

12.00 0.00 -2400.00 -12.00 0.00 -2400.00

0.00 939.61 0.00 0.00 -939.61 0.00

L3


= 2100000 x 20400 -2400.00 0.00 640000.00 2400.00 0.00 320000.00

-12.00 0.00 2400.00 12.00 0.00 2400.00

0.000 0.00 -939.61 0.00 0.00 939.61 0.00

-2400.00 0.00 320000.00 2400.00 0.00 640000.00

669.375

8032.50 0.00 -1606500.00 -8032.50 0.00 -1606500.00

0.00 628950.00 0.00 0.00 -628950.00 0.00

= -1606500.00 0.00 428400000.00 1606500.00 0.00 214200000.00-8032.50 0.00 1606500.00 8032.50 0.00 1606500.00

0.00 -628950.00 0.00 0.00 628950.00 0.00

-1606500.00 0.00 214200000.00 1606500.00 0.00 428400000.00

64000000.00



5/27

Kelompok 2

Dimana sudut untuk batang c dan d sama besar yaitu : 0o, maka

= 0 o

k = 939.608c = 1.000

c2 = 1.000

s = 0.000

S = 0.000

cs = 0.000

L = 400.00

[kc

2

+ 12s

2

][(k-12)cs] -6Ls

[-kc

2

- 12s

2

][(-k+12)cs] -6Ls

[K] = E x Iz [(k-12)cs] [ks + 12c2] 6Lc [(-k + 12)cs] [-ks2 - 12c2] 6Lc


2

[-kc2

- 12s2] [(-k+12)cs] 6Ls [kc

2+ 12s

2] [(k-12)cs] 6Ls

[(-k+12)cs] [-ks2

- 12c2] -6Lc [(k+12)cs [ks

2+ 12c

2] -6Lc


2

939.61 0.00 0.00 -939.61 0.00 0.00

0.00 12.00 2400.00 0.00 -12.00 2400.00

L3


= 2100000 x 20400 0.00 2400.00 640000.00 0.00 -2400.00 320000.00

-939.61 0.00 0.00 939.61 0.00 0.00

0.000 0.00 -12.00 -2400.00 0.00 12.00 -2400.00

0.00 2400.00 320000.00 0.00 -2400.00 640000.00

669.375

628950.00 0.00 0.00 -628950.00 0.00 0.00

0.00 8032.50 1606500.00 0.00 -8032.50 1606500.00

= 0.00 1606500.00 428400000.00 0.00 -1606500.00 214200000.00-628950.00 0.00 0.00 628950.00 0.00 0.00

0.00 -8032.50 -1606500.00 0.00 8032.50 -1606500.00

0.00 1606500.00 214200000.00 0.00 -1606500.00 428400000.00

64000000.00



6/27

Kelompok 2

PERSAMAAN KEKAKUAN STRUKTUR

F1 = ka11.d1 + ka12.d2

1 2 3

d1 d2d3

Batang a Batang b

TUGAS METODE ELEMEN HINGGA

F2 = ka21.d1 + ka22.d2 + kb11.d2 + kb12.d3

1 2 3

d1 d2d3

Batang a Batang b



7/27

Kelompok 2

0


f1 = Ka11 . d1 + Ka12 . d2

f2 - fred = Ka21 . d1 + Ka22 . d2 + Kb11 . d2 + Kb12 . d3 + Kd11 . d2 + Kd12 . d5

f3 - fred = Kb21 . d2 +Kb22 . d3 + Kc11 . d3 + Kc12 . d4

f4 - fred = Kc21 . d3 + Kc22 . d4 + Ke21 . d5 + Ke22 . d4

f5 - fred = Kd21 . d2 + Kd22 . d5 + Ke11 . d5 + Ke12 . d4 + Kf21 . d6 + Kf22 . d5

f6 = Kf11 . d6 + Kf12 . d5



8/27

Kelompok 2

MATRIKS KEKAKUAN STRUKTUR SEBELUM DIKURANGIN F red

F = K d

f1 d1

f2 d2

f3 d3

f4 d4

f5 d5

f6 d6

H1 8032.5 3.80358E-11 -1606500 -8032.5 -3.80358E-11 -1606500 0 0 0 0 0 0 0 0 0 0 0 0 u1

V1 3.80358E-11 628950 9.841E-11 -3.8036E-11 -628950 9.841E-11 0 0 0 0 0 0 0 0 0 0 0 0 v1

M1 -1606500 9.841E-11 428400000 1606500 -9.841E-11 214200000 0 0 0 0 0 0 0 0 0 0 0 0 1

H2 -8032.5 -3.8036E-11 1606500 645015 7.60716E-11 0 -8032.5 -3.8036E-11 -1606500 0 0 0 -628950 0 0 0 0 0 u2

V2 -3.80358E-11 -628950 -9.841E-11 0 1265932.5 1606500 -3.8036E-11 -628950 9.841E-11 0 0 0 0 -8032.5 1606500 0 0 0 v2

M2 -1606500 9.841E-11 214200000 0 1606500 1285200000 1606500 -9.841E-11 214200000 0 0 0 0 -1606500 214200000 0 0 0 2

H3 0 0 0 -8032.5 -3.80358E-11 1606500 636982.5 3.80358E-11 1606500 -628950 0 0 0 0 0 0 0 0 u3

V3 0 0 0 -3.8036E-11 -628950 -9.841E-11 -3.8036E-11 636982.5 1606500 0 -8032.5 1606500 0 0 0 0 0 0 v3

M3 0 0 0 -1606500 9.841E-11 214200000 1606500 1606500 856800000 0 -1606500 214200000 0 0 0 0 0 0 3

H4 0 0 0 0 0 0 -628950 0 0 636982.5 3.80358E-11 1606500 -8032.5 -3.8036E-11 1606500 0 0 0 u4

V4 0 0 0 0 0 0 0 -8032.5 - 1606500 -3.80358E-11 636982.5 -1606500 -3.8036E-11 -628950 -9.841E-11 0 0 0 v4

M4 0 0 0 0 0 0 0 1606500 214200000 1606500 -1606500 856800000 -1606500 9.841E-11 214200000 0 0 0 4

H5 0 0 0 -628950 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 6 45015 7.60716E-11 0 -8032.5 -3.80358E-11 1606500 u5

=

0

0

0

=

Ka11

Ka21

0

0

0

0

Kc12

Kc22 + Ke22

Ke12

0

Kd21

0

0

Kb12

Kb22+Kc11

Kc21

0

0

Ka12

Ka22 + Kb11 + Kd11

Kb21

Kf12

0

0

0

0

Kf21

Kf11

0

Kd12

0

Ke21

Kd22 + Ke11 + Kf22


V5 0 0 0 0 -8032.5 -1606500 0 0 0 -3.80358E-11 -628950 9 .841E-11 0 1265932.5 -1606500 -3.8036E-11 -628950 -9.841E-11 v5

M5 0 0 0 0 1606500 214200000 0 0 0 1606500 -9.841E-11 214200000 0 -1606500 1285200000 -1606500 9.841E-11 214200000 5

H6 0 0 0 0 0 0 0 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 8032.5 3 .80358E-11 -1606500 u6

V6 0 0 0 0 0 0 0 0 0 0 0 0 -3.8036E-11 -628950 9.841E-11 3.80358E-11 628950 9.841E-11 v6

M6 0 0 0 0 0 0 0 0 0 0 0 0 1606500 -9.841E-11 214200000 -1606500 9 .841E-11 428400000 6

SYARAT BATAS

u1 = 0 u4 = Berpindah

v1 = 0 v4 = Berpindah

1 = 0 4 = Berputar

u2 = B er pind ah u5 = Berpindah

v2 = B er pind ah v5 = Berpindah

2 = Be rp ut ar 5 = Berputar

u3 = B er pind ah u6 = 0

v3 = B er pind ah v6 = 0

3 = Be rp ut ar 6 = 0



9/27

Kelompok 2

Maka Matriks menjadi

H1 8032.5 3.80358E-11 -1606500 -8032.5 -3.80358E-11 -1606500 0 0 0 0 0 0 0 0 0 0 0 0 0

V1 3.80358E-11 628950 9.841E-11 -3.8036E-11 -628950 9.841E-11 0 0 0 0 0 0 0 0 0 0 0 0 0

M1 -1606500 9.841E-11 428400000 1606500 -9.841E-11 214200000 0 0 0 0 0 0 0 0 0 0 0 0 0

H2 -8032.5 -3.8036E-11 1606500 645015 7.60716E-11 0 -8032.5 -3.8036E-11 -1606500 0 0 0 -628950 0 0 0 0 0 u2

V2 -3.80358E-11 -628950 -9.841E-11 0 1265932.5 1606500 -3.8036E-11 -628950 9.841E-11 0 0 0 0 -8032.5 1606500 0 0 0 v2

M2 -1606500 9.841E-11 214200000 0 1606500 1285200000 1606500 -9.841E-11 214200000 0 0 0 0 -1606500 214200000 0 0 0 2

H3 0 0 0 -8032.5 -3.80358E-11 1606500 636982.5 3.80358E-11 1606500 -628950 0 0 0 0 0 0 0 0 u3

V3 0 0 0 -3.8036E-11 -628950 -9.841E-11 -3.8036E-11 636982.5 1606500 0 -8032.5 1606500 0 0 0 0 0 0 v3

M3 0 0 0 -1606500 9.841E-11 214200000 1606500 1606500 856800000 0 -1606500 214200000 0 0 0 0 0 0 3

H4 0 0 0 0 0 0 -628950 0 0 636982.5 3.80358E-11 1606500 -8032.5 -3.8036E-11 1606500 0 0 0 u4

V4 0 0 0 0 0 0 0 -8032.5 -1606500 -3.80358E-11 636982.5 -1606500 -3.8036E-11 -628950 -9.841E-11 0 0 0 v4

M4 0 0 0 0 0 0 0 1606500 214200000 1606500 -1606500 856800000 -1606500 9.841E-11 214200000 0 0 0 4

H5 0 0 0 -628950 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 645015 7.60716E-11 0 -8032.5 - 3.80358E-11 1606500 u5

V5 0 0 0 0 -8032.5 -1606500 0 0 0 -3.80358E-11 -628950 9.841E-11 0 1265932.5 -1606500 -3.8036E-11 -628950 -9.841E-11 v5

M5 0 0 0 0 1606500 214200000 0 0 0 1606500 -9.841E-11 214200000 0 -1606500 1285200000 -1606500 9.841E-11 214200000 5

H6 0 0 0 0 0 0 0 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 8032.5 3.80358E-11 -1606500 0

V6 0 0 0 0 0 0 0 0 0 0 0 0 -3.8036E-11 -628950 9.841E-11 3.80358E-11 628950 9.841E-11 0

M6 0 0 0 0 0 0 0 0 0 0 0 0 1606500 -9.841E-11 214200000 -1606500 9.841E-11 428400000 0

H2 645015 7.60716E-11 0 -8032.5 -3.80358E-11 -1606500 0 0 0 -628950 0 0 u2

=


V2 0 1265932.5 1606500 -3.8036E-11 -628950 9.841E-11 0 0 0 0 -8032.5 1606500 v2

M2 0 1606500 1285200000 1606500 -9.841E-11 214200000 0 0 0 0 -1606500 214200000 2

H3 -8032.5 -3.8036E-11 1606500 636982.5 3.80358E-11 1606500 -628950 0 0 0 0 0 u3

V3 -3.80358E-11 -628950 -9.841E-11 -3.8036E-11 636982.5 1606500 0 -8032.5 1606500 0 0 0 v3

M3 -1606500 9.841E-11 214200000 1606500 1606500 856800000 0 -1606500 214200000 0 0 0 3

H4 0 0 0 -628950 0 0 636982.5 3.80358E-11 1606500 -8032.5 -3.8036E-11 1606500 u4

V4 0 0 0 0 -8032.5 -1606500 -3.8036E-11 636982.5 -1606500 -3.80358E-11 -628950 -9.841E-11 v4

M4 0 0 0 0 1606500 214200000 1606500 -1606500 856800000 -1606500 9.841E-11 214200000 4

H5 -628950 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 645015 7.60716E-11 0 u5

V5 0 -8032.5 -1606500 0 0 0 -3.8036E-11 -628950 9.841E-11 0 1265932.5 -1606500 v5

M5 0 1606500 214200000 0 0 0 1606500 -9.841E-11 214200000 0 -1606500 1285200000 5

=



10/27

Kelompok 2

Gaya yang terjadi akibat beban merata ( F red )

Batang c Batang d

S ' = - L 2 = -500 K S ' = - L 2 = -500 K


3' - - 2' - -

Sy4' = - qL/2 = -500 Kg Sy5' = - qL/2 = -500 Kg

Mz3' = -qL /12 = -33333.3 Kg.cm Mz2' = -qL /12 = -33333 Kg.cm

Mz4' = qL2/12 = 33333.3 Kg.cm Mz5' = qL

2/12 = 33333.3 Kg.cm

Matriks setelah di kurangin F red

200.00 645015 7.60716E-11 0 -8032.5 -3.80358E-11 -1606500 0 0 0 -628950 0 0 u2

-500.00 0 1265932.5 1606500 -3.8036E-11 -628950 9.841E-11 0 0 0 0 -8032.5 1606500 v2

-33333.33 0 1606500 1285200000 1606500 -9.841E-11 214200000 0 0 0 0 -1606500 214200000 2

200.00 -8032.5 -3.8036E-11 1606500 636982.5 3.80358E-11 1606500 -628950 0 0 0 0 0 u3

-500.00 -3.80358E-11 -628950 -9.841E-11 -3.8036E-11 636982.5 1606500 0 -8032.5 1606500 0 0 0 v3

-33333.33 -1606500 9.841E-11 214200000 1606500 1606500 856800000 0 -1606500 214200000 0 0 0 3

0.00 0 0 0 -628950 0 0 636982.5 3.80358E-11 1606500 -8032.5 -3.8036E-11 1606500 u4

-500.00 0 0 0 0 -8032.5 -1606500 -3.8036E-11 636982.5 -1606500 -3.80358E-11 -628950 -9.841E-11 v4

33333.33 0 0 0 0 1606500 214200000 1606500 -1606500 856800000 -1606500 9.841E-11 214200000 4

0.00 -628950 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 645015 7.60716E-11 0 u5

-500.00 0 -8032.5 -1606500 0 0 0 -3.8036E-11 -628950 9.841E-11 0 1265932.5 -1606500 v5

33333.33 0 1606500 214200000 0 0 0 1606500 -9.841E-11 214200000 0 -1606500 1285200000 5

=



11/27

Kelompok 2

PERPINDAHAN TITIK

d = K-1 F red

u2 8.70206E-05 6.91189E-07 -1.22111E-07 0.000115157 7.77313E-07 -1.9694E-08 0.000115154 -7.7731E-07 -2.1797E-08 8.6233E-05 -6.9119E-07 -1.2169E-07 200.00

v2 6.91189E-07 1.58701E-06 -3.45595E-09 2.15969E-06 1.58664E-06 -3.8866E-09 2.15969E-06 3.30909E-09 -3.8866E-09 6.91189E-07 2.94246E-09 -3.4559E-09 -500.00

2 -1.22111E-07 -3.4559E-09 1.11026E-09 -2.6497E-07 -3.88656E-09 -6.2663E-11 -2.6412E-07 3.88656E-09 2.70117E-10 -1.21686E-07 3.45595E-09 1.08722E-10 -33333.33

u3 0.000115157 2.15969E-06 -2.64968E-07 0.000267535 3.02313E-06 -1.8498E-07 0.000266742 -3.0231E-06 -1.8329E-07 0.000115154 -2.1597E-06 -2.6412E-07 200.00

v3 7.77313E-07 1.58664E-06 -3.88656E-09 3.02313E-06 3.17365E-06 -7.3425E-09 3.02313E-06 6.25155E-09 -7.3425E-09 7.77313E-07 3.30909E-09 -3.8866E-09 -500.00

3 -1.96936E-08 -3.8866E-09 -6.26633E-11 -1.8498E-07 -7.34251E-09 1.55152E-09 -1.8329E-07 7.34251E-09 -1.2508E-10 -2.17972E-08 3.88656E-09 2.70117E-10 -33333.33

u4 0.000115154 2.15969E-06 -2.64117E-07 0.000266742 3.02313E-06 -1.8329E-07 0.000267535 -3.0231E-06 -1.8498E-07 0.000115157 -2.1597E-06 -2.6497E-07 0.00

v4 -7.77313E-07 3.30909E-09 3.88656E-09 -3.0231E-06 6.25155E-09 7.34251E-09 -3.0231E-06 3.17365E-06 7.34251E-09 -7.77313E-07 1.58664E-06 3.88656E-09 -500.00

4 -2.17972E-08 -3.8866E-09 2.70117E-10 -1.8329E-07 -7.34251E-09 -1.2508E-10 -1.8498E-07 7.34251E-09 1.55152E-09 -1.96936E-08 3.88656E-09 -6.2663E-11 33333.33

u5 8.6233E-05 6.91189E-07 -1.21686E-07 0.000115154 7.77313E-07 -2.1797E-08 0.000115157 -7.7731E-07 -1.9694E-08 8.70206E-05 -6.9119E-07 -1.2211E-07 0.00v5 -6.91189E-07 2.94246E-09 3.45595E-09 -2.1597E-06 3.30909E-09 3.88656E-09 -2.1597E-06 1.58664E-06 3.88656E-09 -6.91189E-07 1.58701E-06 3.45595E-09 -500.00

5 -1.21686E-07 -3.4559E-09 1.08722E-10 -2.6412E-07 -3.88656E-09 2.70117E-10 -2.6497E-07 3.88656E-09 -6.2663E-11 -1.22111E-07 3.45595E-09 1.11026E-09 33333.33

u2 0.040 cm

v2 -0.001 cm

2 0.000 rad

u3 0.077 cm

v3 -0.002 cm

=


. ra

u4 0.076 cm

v4 -0.003 cm

4 0.000 rad

u5 0.040 cm

v5 -0.002 cm

5 0.000 rad

=



12/27

Kelompok 2

MATRIKS REAKSI TITIK SIMPUL SEBELUM DIKURANGIN F Red

H1 8032.5 3.80358E-11 -1606500 -8032.5 -3.80358E-11 -1606500 0 0 0 0 0 0 0 0 0 0 0 0 0

V1 3.80358E-11 628950 9.841E-11 -3.8036E-11 -628950 9.841E-11 0 0 0 0 0 0 0 0 0 0 0 0 0

M1 -1606500 9.841E-11 428400000 1606500 -9.841E-11 214200000 0 0 0 0 0 0 0 0 0 0 0 0 0

H2 -8032.5 -3.8036E-11 1606500 645015 7.60716E-11 0 -8032.5 -3.8036E-11 -1606500 0 0 0 -628950 0 0 0 0 0 0.040

V2 -3.80358E-11 -628950 -9.841E-11 0 1265932.5 1606500 -3.8036E-11 -628950 9.841E-11 0 0 0 0 -8032.5 1606500 0 0 0 -0.001

M2 -1606500 9.841E-11 214200000 0 1606500 1285200000 1606500 -9.841E-11 214200000 0 0 0 0 -1606500 214200000 0 0 0 0.000

H3 0 0 0 -8032.5 -3.80358E-11 1606500 636982.5 3.80358E-11 1606500 -628950 0 0 0 0 0 0 0 0 0.077

V3 0 0 0 -3.8036E-11 -628950 -9.841E-11 -3.8036E-11 636982.5 1606500 0 -8032.5 1606500 0 0 0 0 0 0 -0.002

M3 0 0 0 -1606500 9.841E-11 214200000 1606500 1606500 856800000 0 -1606500 214200000 0 0 0 0 0 0 0.000

H4 0 0 0 0 0 0 -628950 0 0 636982.5 3.80358E-11 1606500 -8032.5 -3.8036E-11 1606500 0 0 0 0.076

V4 0 0 0 0 0 0 0 -8032.5 -1606500 -3.80358E-11 636982.5 -1606500 -3.8036E-11 -628950 -9.841E-11 0 0 0 -0.003

M4 0 0 0 0 0 0 0 1606500 214200000 1606500 -1606500 856800000 -1606500 9.841E-11 214200000 0 0 0 0.000

H5 0 0 0 -628950 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 645015 7.60716E-11 0 -8032.5 -3.80358E-11 1606500 0.040

V5 0 0 0 0 -8032.5 -1606500 0 0 0 -3.80358E-11 -628950 9.841E-11 0 1265932.5 -1606500 -3.8036E-11 -628950 -9.841E-11 -0.002

M5 0 0 0 0 1606500 214200000 0 0 0 1606500 -9.841E-11 214200000 0 -1606500 1285200000 -1606500 9.841E-11 214200000 0.000

H6 0 0 0 0 0 0 0 0 0 0 0 0 -8032.5 -3.8036E-11 -1606500 8032.5 3.80358E-11 -1606500 0

V6 0 0 0 0 0 0 0 0 0 0 0 0 -3.8036E-11 -628950 9.841E-11 3.80358E-11 628950 9.841E-11 0

M6 0 0 0 0 0 0 0 0 0 0 0 0 1606500 -9.841E-11 214200000 -1606500 9.841E-11 428400000 0

H1 -164.17

V1 641.39

M1 43512.39

=


.

H2 200.00

V2 -500.00

M2 -33333.33

H3 200.00

V3 -500.00

M3 -33333.33

H4 0.00

V4 -500.00

M4 33333.33

H5 0.00

V5 -500.00

M5 33333.33

H6 -235.83

V6 1358.61

M6 53042.74

=



13/27

Kelompok 2

MATRIKS REAKSI TITIK SIMPUL DIKURANGIN F Red

H1 -164.17 0.00 -164.17 Kg

V1 641.39 0.00 641.39 Kg

M1 43512.39 0.00 -43512.39 Kgcm

H2 200.00 200.00 0.00 Kg

V2 -500.00 -500.00 0.00 Kg

M2 -33333.33 -33333.33 0.00 Kgcm

H3 200.00 200.00 0.00 Kg

V3 -500.00 -500.00 0.00 Kg

M3 -33333.33 -33333.33 0.00 Kgcm

H4 0.00 0.00 0.00 Kg

V4 -500.00 -500.00 0.00 Kg

M4 33333.33 33333.33 0.00 Kgcm

H5 0.00 0.00 0.00 Kg

V5 -500.00 -500.00 0.00 Kg

M5 33333.33 33333.33 0.00 Kgcm

H6 -235.83 0.00 -235.83 Kg

V6 1358.61 0.00 1358.61 Kg

M6 53042.74 0.00 -53042.74 Kgcm

KONTROL REAKSI PADA SETIAP TITIK SIMPUL ( AKSI = REAKSI )

V = 0

== -


=

=

= ( OK )

H = 0

=

=

= ( OK )

AKSI REAKSI

H1+H2+H3+H4+H5+H6 P1 + P2

400 400

V1+V2+V3+V4+V5+V6

2000

Qtotal

2000



14/27

Kelompok 2

MENCARI GAYA BATANG

BATANG A

Dimana sudut untuk batang a yaitu : 90o, maka

{ d } = { T } { d }

= 90

C = cos 0.000

S = sin 1.000

c s 0 0 0 0-s c 0 0 0 0

0 0 1 0 0 0

[ T ] = 0 0 0 c s 0

0 0 0 -s c 0

0 0 0 0 0 1

0.000 1.000 0 0 0 0

-1.000 0.000 0 0 0 0

0 0 1 0 0 0


= . .

0 0 0 -1.000 0.000 0

0 0 0 0 0 1

u1 0.000 1.000 0.000 0.000 0.000 0.000 0.000

v1 -1.000 0.000 0.000 0.000 0.000 0.000 0.000

1 = 0.000 0.000 1.000 0.000 0.000 0.000 0.000

u2 0.000 0.000 0.000 0.000 1.000 0.000 0.040

v2 0.000 0.000 0.000 - 1.000 0.000 0.000 -0.001

2 0.000 0.000 0.000 0.000 0.000 1.000 0.000

Maka { d } menjadi

u1 0.000 cm

v1 0.000 cm

1 = 0.000 rad

u2 -0.001 cm

v2 -0.040 cm

2 0.000 rad



15/27

Kelompok 2

Gaya dalam yang terjadi

F = K d

Sx1 628950 0 0 -628950 0 0 0.000

Sy1 0 8032.5 1606500 0 -8032.5 1606500 0.000

Mz1 = 0 1606500 4.28E+08 0 -1606500 2.14E+08 0.000

Sx2 -628950 0 0 628950 0 0 -0.001

Sy2 0 -8032.5 -1606500 0 8032.5 -1606500 -0.040

Mz2 0 1606500 2.14E+08 0 -1606500 4.28E+08 0.000

Sx1 641.39 Kg

Sy1 164.17 Kg

Mz1 = 43512.39 Kg.cmSx2 -641.39 Kg

Sy2 -164.17 Kg

Mz2 22154.98 Kg.cm

TUGAS METODE ELEMEN HINGGATUGAS METODE ELEMEN HINGGA


16/27

Kelompok 2

BATANG B

Dimana sudut untuk batang b yaitu : 90o, maka

{ d } = { T } { d }

= 90

C = cos 0.000

S = sin 1.000

c s 0 0 0 0

-s c 0 0 0 0

0 0 1 0 0 0[ T ] = 0 0 0 c s 0

0 0 0 -s c 0

0 0 0 0 0 1

0.000 1.000 0 0 0 0

-1.000 0.000 0 0 0 0

0 0 1 0 0 0

[ T ] = 0 0 0 0.000 1.000 0

0 0 0 -1.000 0.000 0


u2 0.000 1.000 0.000 0.000 0.000 0.000 0.040

v2 -1.000 0.000 0.000 0.000 0.000 0.000 -0.001

2 = 0.000 0.000 1.000 0.000 0.000 0.000 0.000

u3 0.000 0.000 0.000 0.000 1.000 0.000 0.077

v3 0.000 0.000 0.000 - 1.000 0.000 0.000 -0.002

3 0.000 0.000 0.000 0.000 0.000 1.000 0.000

Maka { d } menjadi

u2 -0.001 cm

v2 -0.040 cm

2 = 0.000 rad

u3 -0.002 cm

v3 -0.077 cm

3 0.000 rad



17/27

Kelompok 2


F = K d

Sx2 628950 0 0 -628950 0 0 -0.001

Sy2 0 8032.5 1606500 0 -8032.5 1606500 -0.040

Mz2 = 0 1606500 4.28E+08 0 -1606500 2.14E+08 0.000

Sx3 -628950 0 0 628950 0 0 -0.002

Sy3 0 -8032.5 -1606500 0 8032.5 -1606500 -0.077

Mz3 0 1606500 2.14E+08 0 -1606500 4.28E+08 0.000

Sx2 380.55 Kg

Sy2 -6.78 Kg

Mz2 = -2852.63 Kg.cmSx3 -380.55 Kg

Sy3 6.78 Kg

Mz3 141.71 Kg.cm



18/27

Kelompok 2

BATANG C

Dimana sudut untuk batang c yaitu : 0o, maka

{ d } = { d }

Maka { d } menjadi

u3 0.077 cm

v3 -0.002 cm

3 = 0.000 rad

u4 0.076 cm

v4 -0.003 cm

4 0.000 rad

Gaya dalam yang terjadi sebelum di kurangin F red

F - F red = K d

Sx3 628950 0 0 -628950 0 0 0.077

Sy3 0 8032.5 1606500 0 -8032.5 1606500 -0.002

Mz3 = 0 1606500 4.28E+08 0 -1606500 2.14E+08 0.000

Sx4 -628950 0 0 628950 0 0 0.076

Sy4 0 -8032.5 -1606500 0 8032.5 -1606500 -0.003

-


z . - . .

Sx3 206.78 Kg

Sy3 -119.45 Kg

Mz3 = -33475.04 Kg.cm

Sx4 -206.78 Kg

Sy4 119.45 Kg

Mz4 -14303.02 Kg.cm

Gaya dalam yang terjadi di kurangin F red

Sx3 206.78 200.00 6.78 Kg

Sy3 -119.45 -500.00 380.55 Kg

Mz3 = -33475.04 - -33333.33 = -141.71 Kg.cm

Sx4 -206.78 0.00 -206.78 Kg

Sy4 119.45 -500.00 619.45 Kg

Mz4 -14303.02 33333.33 -47636.36 Kg.cm



19/27

Kelompok 2

BATANG D

Dimana sudut untuk batang d yaitu : 0o, maka

{ d } = { d }

Maka { d } menjadi

u2 0.040 cm

v2 -0.001 cm

2 = 0.000 rad

u5 0.040 cm

v5 -0.002 cm

5 0.000 rad

Gaya dalam yang terjadi sebelum di kurangin F red

F - F red = K d

Sx2 628950 0 0 -628950 0 0 0.040

Sy2 0 8032. 5 1606500 0 -8032.5 1606500 -0.001

Mz2 = 0 1606500 4.28E+08 0 -1606500 2.14E+08 0.000

Sx5 -628950 0 0 628950 0 0 0.040

Sy5 0 - 80 32 .5 - 160 65 00 0 80 32 .5 - 16 06 50 0 -0.002

-


z . - . .

Sx2 29.05 Kg

Sy2 -239.17 Kg

Mz2 = -52635.69 Kg.cm

Sx5 -29.05 Kg

Sy5 239.17 Kg

Mz5 -43031.12 Kg.cm

Gaya dalam yang terjadi di kurangin F red

Sx2 29.05 200.00 -170.95 Kg

Sy2 -239.17 -500.00 260.83 Kg

Mz2 = -52635.69 - -33333.33 = -19302.35 Kg.cm

Sx5 -29.05 0.00 -29.05 Kg

Sy5 239.17 -500.00 739.17 Kg

Mz5 -43031.12 33333.33 -76364.46 Kg.cm



20/27

Kelompok 2

BATANG E

Dimana sudut untuk batang E yaitu : 270o, maka

{ d } = { T } { d }

= 270

C = cos 0.000

S = sin -1.000

c s 0 0 0 0

-s c 0 0 0 0

0 0 1 0 0 0[ T ] = 0 0 0 c s 0

0 0 0 -s c 0

0 0 0 0 0 1

0.000 -1.000 0 0 0 0

1.000 0.000 0 0 0 0

0 0 1 0 0 0

[ T ] = 0 0 0 0.000 -1.000 0

0 0 0 1.000 0.000 0


u4 0.000 -1.000 0.000 0.000 0.000 0.000 0.076

v4 1.000 0.000 0.000 0.000 0.000 0.000 -0.003

4 = 0.000 0.000 1.000 0.000 0.000 0.000 0.000

u5 0.000 0.000 0.000 0.000 -1.000 0.000 0.040

v5 0.000 0.000 0.000 1.000 0.000 0.000 -0.002

5 0.000 0.000 0.000 0.000 0.000 1.000 0.000

Maka { d } menjadi

u4 0.003 cm

v4 0.076 cm

4 = 0.000 rad

u5 0.002 cm

v5 0.040 cm

5 0.000 rad



21/27

Kelompok 2


F = K d

Sx4 628950 0 0 -628950 0 0 0.003

Sy4 0 8032.5 1606500 0 -8032.5 1606500 0.076

Mz4 = 0 1606500 4.28E+08 0 -1606500 2.14E+08 0.000

Sx5 -628950 0 0 628950 0 0 0.002

Sy5 0 -8032.5 -1606500 0 8032.5 -1606500 0.040

Mz5 0 1606500 2.14E+08 0 -1606500 4.28E+08 0.000

Sx4 619.45 Kg

Sy4 206.78 Kg

Mz4 = 47636.36 Kg.cmSx5 -619.45 Kg

Sy5 -206.78 Kg

Mz5 35074.56 Kg.cm



22/27

Kelompok 2

BATANG E

Dimana sudut untuk batang F yaitu : 270o, maka

{ d } = { T } { d }

= 270

C = cos 0.000

S = sin -1.000

c s 0 0 0 0

-s c 0 0 0 0

0 0 1 0 0 0[ T ] = 0 0 0 c s 0

0 0 0 -s c 0

0 0 0 0 0 1

0.000 -1.000 0 0 0 0

1.000 0.000 0 0 0 0

0 0 1 0 0 0

[ T ] = 0 0 0 0.000 -1.000 0

0 0 0 1.000 0.000 0


u5 0.000 -1.000 0.000 0.000 0.000 0.000 0.040

v5 1.000 0.000 0.000 0.000 0.000 0.000 -0.002

5 = 0.000 0.000 1.000 0.000 0.000 0.000 0.000

u6 0.000 0.000 0.000 0.000 -1.000 0.000 0.000

v6 0.000 0.000 0.000 1.000 0.000 0.000 0.000

6 0.000 0.000 0.000 0.000 0.000 1.000 0.000

Maka { d } menjadi

u5 0.002 cm

v5 0.040 cm

5 = 0.000 rad

u6 0.000 cm

v6 0.000 cm

6 0.000 rad



23/27

Kelompok 2


F = K d

Sx5 628950 0 0 -628950 0 0 0.002

Sy5 0 8032.5 1606500 0 -8032.5 1606500 0.040

Mz5 = 0 1606500 4.28E+08 0 -1606500 2.14E+08 0.000

Sx6 -628950 0 0 628950 0 0 0.000

Sy6 0 -8032.5 -1606500 0 8032.5 -1606500 0.000

Mz6 0 1606500 2.14E+08 0 -1606500 4.28E+08 0.000

Sx5 1358.61 Kg

Sy5 235.83 Kg

Mz5 = 41289.89 Kg.cmSx6 -1358.61 Kg

Sy6 -235.83 Kg

Mz6 53042.74 Kg.cm



24/27

Kelompok 2

HASIL PERHITUNGAN METOEDE ELEMEN HINGGA KOMBINASI DENGAN SAP

GAMBAR PEMBEBANAN GAMBAR REAKSI PERLETAKAN



25/27

Kelompok 2

DIAGRAM BIDANG NORMAL DIAGRAM BIDANG LINTANG



26/27

Kelompok 2

DIAGRAM BIDANG MOMENT GAMBAR DEFORMASI BATANG



27/27

Kelompok 2

HASIL PERHITUNGAN SAP 2000

Joint OutputCase CaseType U V R

Text Text Text cm cm Radians

1 DEAD LinStatic 0 0 0

2 DEAD LinStatic 0.041 -0.001 0.0003 DEAD LinStatic 0.078 -0.002 0.000

4 DEAD LinStatic 0.000 0.000 0.000

5 DEAD LinStatic 0.041 -0.002 0.000

6 DEAD LinStatic 0.078 -0.003 0.000

Joint OutputCase CaseType H V M

Text Text Text Kgf Kgf Kgf-cm

1 DEAD LinStatic -164.17 641.39 -43512.52

6 DEAD LinStatic -235.83 1358.61 -53042.87

Frame Station OutputCase CaseType P V2 M3

Text cm Text Text Kgf Kgf Kgf-cm

0 DEAD LinStatic -641.39 164.17 43512.52

200 DEAD LinStatic -641.39 164.17 10678.85

400 DEAD LinStatic -641.39 164.17 -22154.83

0 DEAD LinStatic -380.56 -6.78 -2852.53

200 DEAD LinStatic -380.56 -6.78 -1497.11

400 DEAD LinStatic -380.56 -6.78 -141.68

TABLE: Joint Reactions

TABLE: Element Forces - Frames

A

B

TABLE: Joint Displacements

0 DEAD LinStatic -206.78 -380.56 141.68

50 DEAD LinStatic -206.78 -255.56 16044.44

100 DEAD LinStatic -206.78 -130.56 25697.19

150 DEAD LinStatic -206.78 -5.56 29099.95

200 DEAD LinStatic -206.78 119.44 26252.71

250 DEAD LinStatic -206.78 244.44 17155.46

300 DEAD LinStatic -206.78 369.44 1808.22

350 DEAD LinStatic -206.78 494.44 -19789.03

400 DEAD LinStatic -206.78 619.44 -47636.27

0 DEAD LinStatic -29.05 -260.83 19302.29

50 DEAD LinStatic -29.05 -135.83 29218.96

100 DEAD LinStatic -29.05 -10.83 32885.63150 DEAD LinStatic -29.05 114.17 30302.3

200 DEAD LinStatic -29.05 239.17 21468.97

250 DEAD LinStatic -29.05 364.17 6385.64

300 DEAD LinStatic -29.05 489.17 -14947.7

350 DEAD LinStatic -29.05 614.17 -42531.03

400 DEAD LinStatic -29.05 739.17 -76364.36

0 DEAD LinStatic -1358.61 235.83 -41289.78

200 DEAD LinStatic -1358.61 235.83 5876.55

400 DEAD LinStatic -1358.61 235.83 53042.87

0 DEAD LinStatic -619.44 206.78 -47636.27

200 DEAD LinStatic -619.44 206.78 -6280.85

400 DEAD LinStatic -619.44 206.78 35074.58

F

C

D

E

analisa plane frame dengan metode elemen hingga

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