TUGAS 3_KELOMPOK 7_MEKANIKA REKAYASA V_2022.pptx
- 4. 12
𝐼
𝑀𝐴 +
6
𝐼
𝑀𝐵 =
6𝐸 −0,006
6
3000 𝑀𝐴 + 15000 𝑀𝐵 = −1200000
Segmen AB dan BC
𝑀𝐴
6
𝐼
+ 2𝑀𝐵
6
𝐼
+
6
𝐼
+ 𝑀𝐶
6
𝐼
=
6𝐸ℎ𝐴
𝐿𝐴
+
6𝐸ℎ𝐶
𝐿𝐶
6𝑀𝐴
𝐼
+
24𝑀𝐵
𝐼
+
6𝑀𝐶
𝐼
=
6𝐸 +0,006
6
+
6𝐸 +0,006
6
15000 𝑀𝐴 + 60000 𝑀𝐵 + 0𝑀𝐶 = 1200000 + 1200000
15000 𝑀𝐴 + 60000 𝑀𝐵 = 2400000
- 5. a. Matriks
30000 15000
15000 60000
𝑀𝐴
𝑀𝐵
=
−1200000
2400000
𝑀𝐴
𝑀𝐵
=
30000 15000
15000 60000
−1
−1200000
2400000
𝑀𝐴= −68,571 𝑘𝑁𝑚 𝑀𝐵= 57,143 𝑘𝑁𝑚
b. Reaksi-reaksi perletakan
𝑀𝐵 = 𝑅𝐵𝑉. 6 + 𝑀𝐴
57,143 = 6𝑅𝐵𝑉 + −68,571
𝑅𝐵𝑉 = 20,952 𝑘𝑁 ↑
𝑀𝐵 = 𝑅𝐶𝑉. 6
57,143 = 6𝑅𝐶𝑉
- 6. 𝑅𝐶𝑉 = 9,524 𝑘𝑁 ↑
∈𝑉 = 0 → 𝑅𝐴𝑉 + 𝑅𝐵𝑉 + 𝑅𝐶𝑉 = 0
𝑅𝐴𝑉 + 20,952 + 9,524 = 0
𝑅𝐴𝑉 = −30,476 𝑘𝑁 ↓
- Reaksi Redundant
𝑎11 =
63
3𝐸𝐼
=
216
3𝐸𝐼
𝑎21 =
216
3𝐸𝐼
+
36
2𝐸𝐼
× 6 =
180
𝐸𝐼
𝑎12 =
180
𝐸𝐼
dan 𝑎22 =
1728
3𝐸𝐼
- 7. 𝑎11𝑅1 + 𝑎12𝑅2 = −6 × 10−3
𝑎21𝑅1 + 𝑎22𝑅2 = 0
𝑅1
𝑅2
= 𝐴 −1 −6 × 10−3
0
𝑅1
𝑅2
=
3𝐸𝐼
365148
1728 −90
−90 216
× −6 × 10−3
0
Maka :
𝑅1= 6815 𝑘𝑁 (↑
𝑅2= 3549 𝑘𝑁 ↑
- 8. ∈ 𝐹𝑦= 0 → 𝑅1 + 𝑅2 + 𝑅3 = 0
𝑅3= 10364 𝑘𝑁 ↑
∈ 𝑀𝐴= 0 → 𝑅4 + 6 × 𝑅1 + 12 × 𝑅2 = 0
𝑅4= −83478 𝑘𝑁𝑚 ( )