kuliah plane frame-1 18122013
DESCRIPTION
Analisa Struktur IVTRANSCRIPT
![Page 1: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/1.jpg)
ANALISA STRUKTUR IV
Dr. Ir. Mochammad Afifuddin, M.Eng
Jurusan Teknik Sipil Universitas Syiah Kuala
19 Desember 2013
PLANE FRAME
![Page 2: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/2.jpg)
OUTLINE
• Teori Umum untuk Analisa Struktur untuk Plane Frame dengan Metoda Matriks
• Contoh-contoh Soal
PLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 3: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/3.jpg)
SISTIM KOORDINAT GLOBAL DAN LOKAL
• SISTIM KOORDINAT GLOBAL:
Untuk setiap struktur yang kita tinjau, secara umum hubungan antara beban dan displacement struktur tersebut ditinjau dengan menggunakan sumbu cartesian atau Sistim Koordinat Global.
Sistim koordinat Global di sini adalah koordinat XYZ dengan struktur bidang terletak pada bidang XY.
Posisi dari koordinat XY bebas, tetapi secara umum diletakkan pada sisi kiri yang terbawah.
PLANE FRAME
Analisa Struktur IV
![Page 4: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/4.jpg)
4
SISTIM KOORDINAT GLOBAL DAN LOKAL (lanjutan)
18/04/2023 Matrikulasi Program MTS Universitas Syiah
Kuala
• SISTIM KOORDINAT LOKAL:
Untuk mendapatkan nilai hubungan gaya-displacement pada masing-masing batang, maka kita perlu meninjaunya dalam sistim koordinat lokal.
PLANE FRAME
Analisa Struktur IV
![Page 5: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/5.jpg)
5
DERAJAT KEBEBASAN
18/04/2023 Matrikulasi Program MTS Universitas Syiah
Kuala
• Derajat Kebebasan suatu struktur secara umum dijelaskan sebagai displacement, translasi dan rotasi bebas pada suatu joint yang perlu diidentifikasikan bentuk deformasi dari struktur tersebut ketika menerima beban tertentu.
• NDOF = NCJT(Nj) – NR
Dimana:NDOF: jumlah derajat kebebasanNCJT : jumlah derajat kebebasan pada sumbu
bebas Plane Frame= 3NR : jumlah displacement yang terkekang pada
supportNj : jumlah joint
PLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 6: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/6.jpg)
6
CONTOH
18/04/2023 Matrikulasi Program MTS Universitas Syiah
Kuala
x3
y3
x 5
y 5
Y
x 2
y 2x 1
y 1
1
2
3
4
5X
PLANE FRAME
Analisa Struktur IV
![Page 7: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/7.jpg)
Y
x 2
y 2
x3
y3
x 1
y 1
x 5
y 5
1
2
3
4
5X
1
23
4
56
7
89
10
1112
13 14
15
PLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 8: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/8.jpg)
Hubungan Kekakuan Elemen Pada Sistim Koordinat Lokal
PLANE FRAME
Analisa Struktur IV
![Page 9: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/9.jpg)
PLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 10: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/10.jpg)
=Qf =
PLANE FRAME
Analisa Struktur IV
![Page 11: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/11.jpg)
Kekakuan batang:
k = EI/L3
AL2/I 0 0 -AL2/I 0 0
0 12 6L 0 -12 6L
0 6L 4L2 0 -6L 2L2
- AL2/I
0 0 AL2/I 0 0
0 -12 -6L 0 12 -6L
0 6L 2L2 0 -6L 4L2
PLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 12: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/12.jpg)
Koordinat TransformasiPLANE FRAME
Analisa Struktur IV
Sumbu lokal
Sumbu global
![Page 13: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/13.jpg)
Koordinat TransformasiPLANE FRAME
Kuliah 10 Analisa Struktur IV
Titik base Titik end
![Page 14: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/14.jpg)
Koordinat TransformasiPLANE FRAME
Analisa Struktur IV
Titik base Titik end
![Page 15: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/15.jpg)
Hubungan Kekakuan Elemen pada Sumbu Global
PLANE FRAME
Kuliah 10 Analisa Struktur IV
![Page 16: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/16.jpg)
Kekakuan pada Sumbu Global
PLANE FRAME
Analisa Struktur IV
![Page 17: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/17.jpg)
17
Vektor Ff pada Sumbu Global
18/04/2023
PLANE FRAME
Analisa Struktur IV
![Page 18: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/18.jpg)
18
Vektor Ff pada Sumbu Global
18/04/2023
PLANE FRAME
Analisa Struktur IV
![Page 19: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/19.jpg)
Hubungan Kekakuan StrukturPLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 20: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/20.jpg)
20
Hubungan Kekakuan Struktur (lanjutan)
18/04/2023
PLANE FRAME
Analisa Struktur IV
![Page 21: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/21.jpg)
21
Hubungan Kekakuan Struktur (lanjutan)
18/04/2023 Matrikulasi Program MTS Universitas Syiah
Kuala
• Equilibrium Equation:P1=F4
(1) + F1 (2)
P2=F5 (1) + F2
(2)
P3=F6 (1) + F3
(2)
• Compatibility Equation:Batang 1:v1
(1) = v2 (1)=v3
(1)=0; v4(1) =d1; v5
(1)=d2; v6
(1)=d3
Batang 2:
v1 (2) = d1 ; v2
(2)= d2 ; v3(2)=d3 ;
v4(2)=v5
(2)=; v6(2)= 0
PLANE FRAME
Analisa Struktur IV
![Page 22: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/22.jpg)
2218/04/2023
• F4(1)=K44
(1)d1+K45(1)d2+K46
(1)d3+Ff4 (1)
• F5(1)=K54
(1)d1+K55(1)d2+K56
(1)d3+Ff5 (1)
• F6(1)=K64
(1)d1+K65(1)d2+K66
(1)d3+Ff6 (1)
• F1(2)=K11
(2)d1+K12(2)d2+K13
(2)d3+Ff1 (2)
• F2(2)=K21
(2)d1+K22(2)d2+K23
(2)d3+Ff2 (2)
• F3(2)=K31
(2)d1+K32(2)d2+K33
(2)d3+Ff3 (2)
= +
PLANE FRAME
Analisa Struktur IV
![Page 23: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/23.jpg)
• P1=(K44(1)+K11
(2))d1+(K45(1)+K12
(2))d2+(K46 (1)+K13
(2) )d3
+(Ff4 (1) +Ff1
(2))
• P2=(K54(1)+K21
(2))d1+(K55(1)+K22
(2))d2+(K56 (1)+K23
(2) )d3
+(Ff5 (1) +Ff2
(2))
• P3=(K64(1)+K31
(2))d1+(K65(1)+K32
(2))d2+(K66 (11)+K33
(2) )d3
+(Ff6 (1) +Ff3
(2))
PLANE FRAME
Analisa Struktur IV
![Page 24: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/24.jpg)
2418/04/2023
• P = Sd + Pf• P - Pf = Sd
S =
Pf =
PLANE FRAME
Analisa Struktur IV
![Page 25: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/25.jpg)
25
Vector Pf dan Beban joint Equivalen
18/04/2023
PLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 26: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/26.jpg)
PLANE FRAME
Analisa Struktur IV
![Page 27: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/27.jpg)
27
Pengaturan Kekakuan Struktur S dan Pf Menggunakan Nomor Kode
18/04/2023
=+
PLANE FRAME
Kuliah 8 Analisa Struktur IV
![Page 28: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/28.jpg)
28
PROSEDUR PERHITUNGAN
18/04/2023
• Persiapkan model plane frame tersebut• Hitung matriks kekakuan S dan nilai Fixed End
Moment Pf• Untuk tiap batang dihitung kekakuan matrik
dalam koordinat global K• Jika pada suatu elemen memiliki beban external,
maka perlu dicari suatu vektor gaya yang bekerja pada arah sumbu global,
Ff = TTQf• Tempatkan masing-masing nilai K tersebut ke
dalam matiks S• Dapatkan nilai d. Substitusikan nilai d tadi ke
dalam persamaan P-Pf = Sd• Hitung nilai ujung batang • Cek perhitungan dengan equilibrium
PLANE FRAME
Analisa Struktur IV
![Page 29: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/29.jpg)
CONTOH SOAL:• Dit: Struktur tergambar
• Dit: cari kekakuan matrik struktur, vektor gaya pada joint, dan gaya equivalent pada joint.
PLANE FRAME
Analisa Struktur IV
![Page 30: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/30.jpg)
• Jawab:– Model analysis
PLANE FRAME
Kuliah 10 Analisa Struktur IV
![Page 31: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/31.jpg)
• Jawab:– Elemen 1
PLANE FRAME
Analisa Struktur IV
![Page 32: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/32.jpg)
• Jawab:– Elemen 1
– Elemen 2
PLANE FRAME
Analisa Struktur IV
![Page 33: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/33.jpg)
• Jawab:– Matriks kekakuan Struktur S:
PLANE FRAME
Analisa Struktur IV
![Page 34: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/34.jpg)
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 35: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/35.jpg)
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 36: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/36.jpg)
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 37: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/37.jpg)
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 38: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/38.jpg)
CONTOH SOAL:• Dik: Struktur tergambar
PLANE FRAME
Analisa Struktur IV
Displacemen batang 2 pada sumbu lokal
![Page 39: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/39.jpg)
CONTOH SOAL:
• Dit: Hitung displacemen dan gaya-gaya ujung batang 2 pada sistim koordinat global.
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 40: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/40.jpg)
CONTOH SOAL:
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 41: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/41.jpg)
CONTOH SOAL:
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 42: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/42.jpg)
• Jawab:
PLANE FRAME
Analisa Struktur IV
Displacemen ujung batang 2 pada sumbu Global
![Page 43: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/43.jpg)
• Jawab:
PLANE FRAME
Analisa Struktur IV
Gaya-gaya ujung batang 2 pada sumbu Global
Cek kesetimbangan:
![Page 44: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/44.jpg)
• Hasil Akhir:
PLANE FRAME
Analisa Struktur IV
Displacemen ujung batang 2 pada sumbu Global
Gaya-gaya ujung batang 2 pada sumbu Global
![Page 45: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/45.jpg)
CONTOH SOAL:
• Dit: Dari contoh sebelumnya diketahui displacemen pada sumbu global untuk elemen 2 adalah:
• Dit: Cari gaya ujung batang dengan menggunakan rumus:
PLANE FRAME
Analisa Struktur IV
![Page 46: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/46.jpg)
• Jawab:
PLANE FRAME
Analisa Struktur IV
![Page 47: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/47.jpg)
• Jawab:
PLANE FRAME
Kuliah 10 Analisa Struktur IV
HASIL AKHIR
![Page 48: Kuliah Plane Frame-1 18122013](https://reader033.vdocuments.mx/reader033/viewer/2022051113/55cf8f44550346703b9a99db/html5/thumbnails/48.jpg)
SEKIAN
Any Question ???
PLANE FRAME
Analisa Struktur IV