NAMA M. ARIF NUGRAHANIM 100404015METODE ELEMEN HINGGA

DIK:K = 120 KN/mP = 20 KN

DIT :1. Matrix kekakuan global2. Perpindahan Node 3,4,53. Reaksi di tumpuan 1 dan 24. Masing-masing gaya dalam Pegas

Penomoran dan nama pegasPegas 1--3 3--4 3--5(a) 3--5(b) 5--4 4--2Nama A B C D E F

1. Matriks kekakuan elemen

Ka=Kb=Kc=Kd=Ke=kf

Ka = 120 -120-120 120

2. Kekakuan Struktur

f1 = Ka11*d1 + Ka12*d3f2 = Kf22*d2 + Kf21*d4 f3 = Ka21*d1 + (Ka22 + Kb11 + Kc11 + Kd11 )*d3 + Kb12*d4 + (Kc12 + Kd12)*d5f4 = Kf12*d2 + Kb21*d3 + (Kb22 + Ke11 + Kf11)*d4 + Ke12*d5f5 = (Ke21 + Kd21)*d3 + Ke21*d4 + (Ke22 + Kc22 + Kd22)*d5

k

k

k

k

k

k

13

5

42

3. Matrix kekakuan Globalf1 120 0 -120 0 0 0f2 0 120 0 -120 0 0f3 = -120 0 480 -120 -240 u3f4 0 -120 -120 360 -120 u4f5 0 0 -240 -120 360 u5

f3 480 -120 -240 u3f4 = -120 360 -120 u420 -240 -120 360 u5

4. Perpindahan di Node 3,4,5u3 0.005128 0.003205 0.004487 0u4 = 0.003205 0.005128 0.003846 0u5 0.004487 0.003846 0.007051 20

u3 0.089744 mu4 = 0.076923 mu5 0.141026 m

5. Reaksi di tumpuan 1 dan 2

f1 120 0 -120 0 0 0 -10.77 kNf2 0 120 0 -120 0 0 -9.23 kNf3 = -120 0 480 -120 -240 0.089744 = 0.00 kNf4 0 -120 -120 360 -120 0.076923 0.00 kNf5 0 0 -240 -120 360 0.141026 20.00 kN

6. Masing masing Gaya pada Pegas

F13 = 120 -120 0 = -10.7692 KN-120 120 0.089744 10.76923 KN

F34 = 120 -120 0.089744 = 1.538462 KN-120 120 0.076923 -1.53846 KN

F35 = 120 -120 0.089744 = -6.15385 KN-120 120 0.141026 6.153846 KN

F45 = 120 -120 0.076923 = -7.69231 KN-120 120 0.141026 7.692308 KN

F24 = 120 -120 0 = -9.23077 KN-120 120 0.076923 9.230769 KN