NAMA KELOMPOK 1
1. JERIKA ANGELIA HOKIL (220201601017) 2. NABILA NUR REZKY AULIA (220201601002) 3. MUH. ZULFIKAR RIZAL (230201603014) KELAS : 02/B
Diketahui:
• Panjang Balok : 10 m
• Panjang Balok L1-2 : 5 m
• Panjang Balok L3-4 : 5m
• Beban merata (q) : 12 kN/m
• Modulus Elastisitas (E) : 200000000
• Inersia : 0,0003
• Beban : 54kN
• Penomoran P-X, NP = 4
• Penomoran F-e, NF = 4
10 m
7 m 3 m
54 kN
1 2 3
1 2 3 4
q = 12kN/m
A B
C
A C B
A B
P1 = F1
P2 = F2 + F3
P3 = F4
P4 = -((F1+F2)/L1.2) + ((F3+F4)/L3.4)
1. MATRIKS STATIS [A]NP x NF
P\F 1 2 3 4
1 1 0 0 0
2 0 1 1 0
3 0 0 0 1
4 -0.2 -0.2 0.2 0.2
2. MATRIKS DEFORMASI [B] = [Aᵀ]NF x NP
P\F 1 2 3 4
1 1 0 0 -0.2
2 0 1 0 -0.2
3 0 1 0 0.2
4 0 0 1 0.2
P1 F1
L1.2 = 5m
F1 F2
L3.4 = 5m
F3 F4
𝐹1 + 𝐹2 𝐿1.2
𝐹1 + 𝐹2 𝐿1.2
𝐹3 + 𝐹4
𝐿3.4 𝐹3 + 𝐹4
𝐿3.4
Dimana:
1. F1 = − 𝑞(𝐿1.2)2
12 = -25 kNm 2. F2 = 𝑞(𝐿1.2)2
12 = 25 kNm
3. F3 = − 𝑞(𝐿3.4)2
12 −54∗2∗32
𝐿3.42 = -63,88 kNm
4. F4 = − 𝑞(𝐿3.4)2
12 −54∗3∗22
𝐿3.42 = 50,92 kNm
𝐹1 + 𝐹2 𝐿1.2 𝐹1 + 𝐹2
𝐿1.2
𝐹3 + 𝐹4 𝐿3.4
F2 F3
1
𝐹3 + 𝐹4 𝐿3.4 P2
2 3 4
P3
P4
F4
A C
C B
6. MATRIKS INVERS K = [Kˉ¹]NPxNP
P\x 1 2 3 4
1 0.00006 -0.00001 -0.00003 0.00010 2 -0.00001 0.00001 -0.00001 0.00000 3 -0.00003 -0.00001 0.00006 -0.00010 4 0.00010 0.00000 -0.00010 0.00035
3. MATRIKS KEKAKUAN ELEMEN [S]NFxNF
F\e 1 2 3 4
1 48000 24000 0 0
2 24000 48000 0 0
3 0 0 48000 24000
4 0 0 24000 48000
4. MATRIKS GAYA PERPINDAHAN [SB]NPxNF
F\x 1 2 3 4
1 48000 24000 0 -14400
2 24000 48000 0 -14400
3 0 48000 24000 14400
4 0 24000 48000 14400
5. MATRIKS KEKAUAN GLOBAL [K]NPxNP = [ASB]NPxNP = [ASAᵀ]NPxNP
P\x 1 2 3 4
1 48000 24000 0 -14400
2 24000 96000 24000 0
3 0 24000 48000 14400
4 -14400 0 14400 11520
7. MATRIKS [F0]
F\x 1
1 -25
2 25
3 -63.88
4 50.92
8. MATRIKS [P]
P\x 1
1 25
2 38.88
3 -50.92
4 94.992
9. MATRIKS [X] = [Kˉ¹] x [P]
1
1 0.012
2 0.001
3 -0.014
4 0.041
10. MATRIKS GAYA BATANG [F]NPxNLC = [F0] + [Saᵀ]x[X]
1
1 25
2 -256
3 294.88
4 -50.92
F
1 0
2 -231
3 231
4 0 kN
