CLAUDIA 125060100111008

Absen 01

1.1

E1 = 2,5,E+06 kg/cm3

E2 = 2,4,E+06 kg/cm3

E3 = 2,0,E+05 kg/cm3

E4 = 2,1,E+06 kg/cm3

A = 300 cm2

1. STRUKTUR AKSIAL

Tentukan gaya-gaya dalam dan displacement yang terjadi pada struktur berikut ini

Diketahui :

Penomoran

P. Global P. Lokal

CLAUDIA 125060100111008

Absen 01

2.1

Matriks Kekakuan Batang

[Sm]1 = [Sms]1 = 2500000 -2500000 5

-2500000 2500000 1

5 1

[Sm]2 = [Sms]2 = 3600000 -3600000 1

-3600000 3600000 2

1 2

[Sm]3 = [Sms]3= 600000 -600000 2

-600000 600000 3

2 3

[Sm]4 = [Sms]4= 6300000 -6300000 3

-6300000 6300000 4

3 4

Metode Kekakuan :

Daftar Data Batang

i (batang) j (join atas) k (join bawah) L(cm) A(cm2) (E.A)/L (kg/cm2)

1 5 1 300 300 2,5,E+06

2 1 2 200 300 3,6,E+06

3 2 3 100 300 6,0,E+05

4 3 4 100 300 6,3,E+06

Matriks Kekakuan Join [Sj]

3600000 1

2500000

3600000 2

600000

[Sj] = 600000 3

6300000

4

5

1 2 3 4 5

2500000

0 -600000 -6300000 0

0 0 -6300000 6300000 0

-2500000 0 0 0

-3600000 0 0 -2500000

-3600000 -600000 0 0

2

1

1

1

1

1

1

1

1

1

2

1

D

D

L

EA

L

EA

L

EA

L

EA

A

A

XX

XX

CLAUDIA 125060100111008

Absen 01

3.1

6100000 -4E+06 0 0 -2500000 1

-3600000 4E+06 -600000 0 0 2

[Sj] = 0 -6E+05 6900000 -6300000 0 3

0 0 -6300000 6300000 0 4

-2500000 0 0 0 2500000 5

1 2 3 4 5

R

RF RR

F R

F

FF FR

Analisis Beban Join [Ac]

[Ac] = [Aj] +[Ae]

0 -750 1

-750 250 2

= 0 + -275 3

0 -275 4

0 -1000 5

-750 1

= -500 2

-275 3

-275 4

-1000 5

Afc

ARC

Perhitungan Deformasi

[Df] = [SFF]-1

X [AFC]

-1

6100000 -4E+06 0 -750

= -3600000 4E+06 -600000 X -500

0 -6E+05 6900000 -275

3,4,E-07 2,9E-07 2,5E-08 -750

= 2,9,E-07 4,9E-07 4,3E-08 x -500

2,5,E-08 4,3E-08 1,5E-07 -275

-0,00040

= -0,00048

-0,00008

-0,00040 1

-0,00048 2

[Dj] = -0,00008 3

0 4

0 5

CLAUDIA 125060100111008

Absen 01

4.1

Perhitungan Gaya Ujung-Ujung Batang

Batang 1

[Am]1 = -[AmL]1 + [Sm]1[Dm]1

= 1000 + 2500000 -2500000 0

1000 -2500000 2500000 -0,00040

= 1000 + 1012

1000 -1012

= 2012

-12

Batang 2

[Am]2 = -[AmL]2 + [Sm]2[Dm]2

= -250 + 3600000 -3600000 -0,00040

-250 -3600000 3600000 -0,00048

= -250 + 262

-250 -262

= 12

-512

Kontrol

∑ V = 0

788 – 2000 – 500 – 750 – 550 = 0

0 = 0 (OK!!)

Perhitungan Reaksi

[AR] = - [ARC] + [SRF][DF]

-0,00040 1

= 275 0 0 -6300000 -0,00048 2

1000 -2500000 0 0 -0,00008 3

= 275 513

1000 1012

= 788 4

2012 5

+

+

CLAUDIA 125060100111008

Absen 01

5.1

Batang 4

[Am]4 = -[AmL]4 + [Sm]4[Dm]4

= 275 + 6300000 -6300000 -0,00008

275 -6300000 6300000 0,00000

= 275 + -513

275 513

= -238

788

Batang 3

[Am]3 = -[AmL]3 + [Sm]3[Dm]3

= 0 + 600000 -600000 -0,00048

0 -600000 600000 -0,00008

= -238

238

CLAUDIA 125060100111008

6

6.1

DIAGRAM BIDANG NORMAL