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ANALISA STRUKTUR 2
DOSEN PENGAMPU MATA KULIAH :
MY PROFILE
NAMA :RISA WANTALANGIE
NIM : 20021101044
BALANCING
ACT
• DIK :KEKAUAN PADA BAGIAN AB ADALAH 2EI DAN KEKAUAN
PADA BAGIAN BC ADALAH EI
• DITANYA : LENDUTAN DI B DAN C, SERTA PUTARAN SUDUT DI C =
…?
MENCARI PERLETAKKAN
MENGHITUNG GAYA DALAM
BAGIAN AB ( 0 ≤ X ≤ L )
MA
HA
X
VA
Qx = VA = 2P
MX = VA.X – MA
= 2P.X – 3PL
= P(2X – 3L)
X = 0 => MA = P (0-3L) = -3PL
X = L => MB = P(2L – 3L) = -PL
BAGIAN BC ( L ≤ X ≤ 2L)
Qx = VA – P = 2P – P = P
MX = VA.X – P(X-L) – MA
= 2PX – P(X-L) – 3PL
X = L => MB = 2PL – 0 – 3PL = -PL
X = 2L => 2P(2L) – P(L) – 3PL
= 4PL – PL – 3PL = 0
MA L W
HA
X
VA
SETELAH DIKETAHUI GAYA DALAM, KEMUDIAN MOMEN YANG DIDAPATKAN DI BAGI
DENGAN 2EI UNTUK BAGIAN A-B DAN DIBAGI EI UNTUK BAGIAN B-C
3PL PL
A B O
C
L L
SEHINGGA GAMBAR BIDANG MOMEN MENJADI SEPERTI DIBAWAH INI, DIMANA MOMEN DI A DARI
3PL MENJADI 3PL/2EI , MOMEN DI B DARI PL MENJADI PL/2EI DAN MOMEN DI MBC MENJADI PL/EI
R1
R2 R3
B
A C
R1 =
3𝑃𝐿
2𝐸𝐼
X
𝐿
2
=
3𝑃𝐿2
4𝐸𝐼
R2 =
𝑃𝐿
2𝐸𝐼
X
𝐿
2
=
𝑃𝐿2
4𝐸𝐼
R3 =
𝑃𝐿
𝐸𝐼
X
𝐿
2
=
𝑃𝐿2
2𝐸𝐼
MENCARI REAKSI DAN MOMEN PADA BIDANG DI ATAS DENGAN MENGGUNAKAN
PEKERJAAN YANG TELAH DI PELAJARI PADA MATA KULIAH STATIKA
∑MC = 0
MC -
𝑃𝐿2
2𝐸𝐼
.
2𝐿
3
-
𝑃𝐿2
4𝐸𝐼
.
4𝐿
3
-
3𝑃𝐿2
4𝐸𝐼
.
5𝐿
3
= 0
MC =
2𝑃𝐿3
6𝐸𝐼
+
4𝑃𝐿3
12𝐸𝐼
+
15𝑃𝐿3
12𝐸𝐼
MC =
4𝑃𝐿3
12𝐸𝐼
+
4𝑃𝐿3
12𝐸𝐼
+
15𝑃𝐿3
12𝐸𝐼
MC =
23𝑃𝐿3
12𝐸𝐼
(LENDUTAN DI TITIK C)
∑V = 0
VC – R3 – R2 – R1 = 0
VC -
𝑃𝐿2
2𝐸𝐼
-
𝑃𝐿2
4𝐸𝐼
-
3𝑃𝐿2
4𝐸𝐼
= 0
VC =
𝑃𝐿2
2𝐸𝐼
+
𝑃𝐿2
4𝐸𝐼
+
3𝑃𝐿2
4𝐸𝐼
VC =
2𝑃𝐿2
4𝐸𝐼
+
𝑃𝐿2
4𝐸𝐼
+
3𝑃𝐿2
4𝐸𝐼
VC =
6𝑃𝐿2
4𝐸𝐼
VC =
3𝑃𝐿2
2𝐸𝐼
(PUTARAN SUDUT DI TITIK C)
KITA KETAHAUI BAHWA PUTARAN SUDUT IDENTIK DENGAN MENGHITUNG REAKSI, SEDANGKAN LENDUTAN IDENTIK
DENGAN MENGHITUNG MOMEN PADA TITIK PUSAT BEBAN, MAKA DI DAPATKAN HASILNYA :
 LENDUTAN DI TITIK C =
23𝑃𝐿3
12𝐸𝐼
 PUTARAN SUDUT DI TITIK C =
3𝑃𝐿2
2𝐸𝐼
MENENTUKAN LENDUTAN DI TITIK B, DENGAN CARA MENCARI MOMEN
DI TITIK B
Mx = VC.X + MC – RX (
𝑋
3
)
Mx =
3𝑃𝐿2
2𝐸𝐼
. X +
23𝑃𝐿3
12𝐸𝐼
-
𝑃𝐿2
2𝐸𝐼
. (
𝑋
3
)
X = 0 -> MC = 0 +
23𝑃𝐿3
12𝐸𝐼
- 0
MC =
23𝑃𝐿3
12𝐸𝐼
X = L -> MB =
3𝑃𝐿2
2𝐸𝐼
. L +
23𝑃𝐿3
12𝐸𝐼
-
𝑃𝐿2
2𝐸𝐼
. (
𝐿
3
)
MB =
3𝑃𝐿3
2𝐸𝐼
+
23𝑃𝐿3
12𝐸𝐼
-
𝑃𝐿3
6𝐸𝐼
MB =
18𝑃𝐿3
12𝐸𝐼
+
23𝑃𝐿3
12𝐸𝐼
-
2𝑃𝐿3
12𝐸𝐼
MB =
39𝑃𝐿3
12𝐸𝐼
(LENDUTAN DI TITIK B)
R3
B
C
L
DARI HASIL PERHITUNGAN DI ATAS MAKA DIDAPATKAN LENDUTAN DI
TITIK B ADALAH 𝟑𝟗𝑷𝑳𝟑
𝟏𝟐𝑬𝑰
, DIKARENAKAN MOMEN DARI TITIK PUSAT BEBAN
PADA SISTEM CONJUGATE BEAM ADALAH MERUPAKAN LENDUTAN TITIK
TERSEBUT

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ANALISA STRUKTUR 2 RISA.pptx

  • 1. ANALISA STRUKTUR 2 DOSEN PENGAMPU MATA KULIAH :
  • 2. MY PROFILE NAMA :RISA WANTALANGIE NIM : 20021101044
  • 3. BALANCING ACT • DIK :KEKAUAN PADA BAGIAN AB ADALAH 2EI DAN KEKAUAN PADA BAGIAN BC ADALAH EI • DITANYA : LENDUTAN DI B DAN C, SERTA PUTARAN SUDUT DI C = …?
  • 5. MENGHITUNG GAYA DALAM BAGIAN AB ( 0 ≤ X ≤ L ) MA HA X VA Qx = VA = 2P MX = VA.X – MA = 2P.X – 3PL = P(2X – 3L) X = 0 => MA = P (0-3L) = -3PL X = L => MB = P(2L – 3L) = -PL BAGIAN BC ( L ≤ X ≤ 2L) Qx = VA – P = 2P – P = P MX = VA.X – P(X-L) – MA = 2PX – P(X-L) – 3PL X = L => MB = 2PL – 0 – 3PL = -PL X = 2L => 2P(2L) – P(L) – 3PL = 4PL – PL – 3PL = 0 MA L W HA X VA
  • 6. SETELAH DIKETAHUI GAYA DALAM, KEMUDIAN MOMEN YANG DIDAPATKAN DI BAGI DENGAN 2EI UNTUK BAGIAN A-B DAN DIBAGI EI UNTUK BAGIAN B-C 3PL PL A B O C L L
  • 7. SEHINGGA GAMBAR BIDANG MOMEN MENJADI SEPERTI DIBAWAH INI, DIMANA MOMEN DI A DARI 3PL MENJADI 3PL/2EI , MOMEN DI B DARI PL MENJADI PL/2EI DAN MOMEN DI MBC MENJADI PL/EI R1 R2 R3 B A C R1 = 3𝑃𝐿 2𝐸𝐼 X 𝐿 2 = 3𝑃𝐿2 4𝐸𝐼 R2 = 𝑃𝐿 2𝐸𝐼 X 𝐿 2 = 𝑃𝐿2 4𝐸𝐼 R3 = 𝑃𝐿 𝐸𝐼 X 𝐿 2 = 𝑃𝐿2 2𝐸𝐼
  • 8. MENCARI REAKSI DAN MOMEN PADA BIDANG DI ATAS DENGAN MENGGUNAKAN PEKERJAAN YANG TELAH DI PELAJARI PADA MATA KULIAH STATIKA ∑MC = 0 MC - 𝑃𝐿2 2𝐸𝐼 . 2𝐿 3 - 𝑃𝐿2 4𝐸𝐼 . 4𝐿 3 - 3𝑃𝐿2 4𝐸𝐼 . 5𝐿 3 = 0 MC = 2𝑃𝐿3 6𝐸𝐼 + 4𝑃𝐿3 12𝐸𝐼 + 15𝑃𝐿3 12𝐸𝐼 MC = 4𝑃𝐿3 12𝐸𝐼 + 4𝑃𝐿3 12𝐸𝐼 + 15𝑃𝐿3 12𝐸𝐼 MC = 23𝑃𝐿3 12𝐸𝐼 (LENDUTAN DI TITIK C) ∑V = 0 VC – R3 – R2 – R1 = 0 VC - 𝑃𝐿2 2𝐸𝐼 - 𝑃𝐿2 4𝐸𝐼 - 3𝑃𝐿2 4𝐸𝐼 = 0 VC = 𝑃𝐿2 2𝐸𝐼 + 𝑃𝐿2 4𝐸𝐼 + 3𝑃𝐿2 4𝐸𝐼 VC = 2𝑃𝐿2 4𝐸𝐼 + 𝑃𝐿2 4𝐸𝐼 + 3𝑃𝐿2 4𝐸𝐼 VC = 6𝑃𝐿2 4𝐸𝐼 VC = 3𝑃𝐿2 2𝐸𝐼 (PUTARAN SUDUT DI TITIK C)
  • 9. KITA KETAHAUI BAHWA PUTARAN SUDUT IDENTIK DENGAN MENGHITUNG REAKSI, SEDANGKAN LENDUTAN IDENTIK DENGAN MENGHITUNG MOMEN PADA TITIK PUSAT BEBAN, MAKA DI DAPATKAN HASILNYA :  LENDUTAN DI TITIK C = 23𝑃𝐿3 12𝐸𝐼  PUTARAN SUDUT DI TITIK C = 3𝑃𝐿2 2𝐸𝐼
  • 10. MENENTUKAN LENDUTAN DI TITIK B, DENGAN CARA MENCARI MOMEN DI TITIK B Mx = VC.X + MC – RX ( 𝑋 3 ) Mx = 3𝑃𝐿2 2𝐸𝐼 . X + 23𝑃𝐿3 12𝐸𝐼 - 𝑃𝐿2 2𝐸𝐼 . ( 𝑋 3 ) X = 0 -> MC = 0 + 23𝑃𝐿3 12𝐸𝐼 - 0 MC = 23𝑃𝐿3 12𝐸𝐼 X = L -> MB = 3𝑃𝐿2 2𝐸𝐼 . L + 23𝑃𝐿3 12𝐸𝐼 - 𝑃𝐿2 2𝐸𝐼 . ( 𝐿 3 ) MB = 3𝑃𝐿3 2𝐸𝐼 + 23𝑃𝐿3 12𝐸𝐼 - 𝑃𝐿3 6𝐸𝐼 MB = 18𝑃𝐿3 12𝐸𝐼 + 23𝑃𝐿3 12𝐸𝐼 - 2𝑃𝐿3 12𝐸𝐼 MB = 39𝑃𝐿3 12𝐸𝐼 (LENDUTAN DI TITIK B) R3 B C L
  • 11. DARI HASIL PERHITUNGAN DI ATAS MAKA DIDAPATKAN LENDUTAN DI TITIK B ADALAH 𝟑𝟗𝑷𝑳𝟑 𝟏𝟐𝑬𝑰 , DIKARENAKAN MOMEN DARI TITIK PUSAT BEBAN PADA SISTEM CONJUGATE BEAM ADALAH MERUPAKAN LENDUTAN TITIK TERSEBUT