E = 200000 MpaA = 11000 cm2

Batang 1L = 5000 mmEA/L = 440000sin α = 0.8cos α = 0.6

Matriks kekakuan1 0 -1 0 440000 0 -440000 0

= 440000 0 0 0 0 = 0 0 0 0-1 0 1 0 -440000 0 440000 00 0 0 0 0 0 0 0

Matriks transformasi0.6 0.8 0 0 0.6 -0.8 0 0

[T] = -0.8 0.6 0 0 0.8 0.6 0 00 0 0.6 0.8 0 0 0.6 -0.80 0 -0.8 0.6 0 0 0.8 0.6

264000 0 -264000 0= 352000 0 -352000 0

-264000 0 264000 0-352000 0 352000 0

u1 v1 u2 v2158400 211200 -158400 -211200 u1

[Kg] = [T] = 211200 281600 -211200 -281600 v1-158400 -211200 158400 211200 u2-211200 -281600 211200 281600 v2

Batang 2L = 500 cm

[KI,1]

[TT] =

[TT].[K1]

[TT] [K1]

4 T

800 cm

300 cm1

3

2

EA/L = 4400000sin α = 0.6cos α = 0.8

Matriks kekakuan1 0 -1 0 440000 0 -440000 0

= 4400000 0 0 0 0 = 0 0 0 0-1 0 1 0 -440000 0 440000 00 0 0 0 0 0 0 0

Matriks transformasi0.6 -0.8 0 0 0.6 0.8 0 0

[T] = 0.8 0.6 0 0 -0.8 0.6 0 00 0 0.6 -0.8 0 0 0.6 0.80 0 0.8 0.6 0 0 -0.8 0.6

264000 0 -264000 0= -352000 0 352000 0

-264000 0 264000 0352000 0 -352000 0

u2 v2 u3 v3158400 -211200 -158400 211200 u2

[Kg] = [T] = -211200 281600 211200 -281600 v2-158400 211200 158400 -211200 u3211200 -281600 -211200 281600 v3

Batang 3L = 800 cmEA/L = 2750000sin α = 0cos α = 1

Matriks kekakuan1 0 -1 0 2750000 0 -3E+06 0

= 2750000 0 0 0 0 = 0 0 0 0-1 0 1 0 -2750000 0 2750000 00 0 0 0 0 0 0 0

Matriks transformasi1 0 0 0 1 0 0 0

[T] = 0 1 0 0 0 1 0 00 0 1 0 0 0 1 00 0 0 1 0 0 0 1

2750000 0 -2750000 0= 0 0 0 0

-2750000 0 2750000 00 0 0 0

u1 v1 u3 v3

[KI,2]

[TT] =

[TT].[K2]

[TT] [K2]

[KI,3]

[TT] =

[TT].[K3]

2750000 0 -2750000 0 u1[Kg] = [T] = 0 0 0 0 v1

-3E+06 0 2750000 0 u30 0 0 0 v3

Overall Stiffnessu1 v1 u2 v2 u3 v3

F1 2908400 2E+05 -158400 -211200 -2750000 0 u1 0G1 211200 3E+05 -211200 -281600 0 0 v1 00 = -158400 -2E+05 316800 0 -158400 211200 u2 U2-4 -211200 -3E+05 0 563200 211200 -281600 v2 V20 -2750000 0 -158400 211200 2908400 -211200 u3 U3

G3 0 0 211200 -281600 -211200 281600 v3 0

Rearrangementu2 v2 u3 u1 v1 v3

0 316800 0 -158400 -158400 -211200 211200 U2-4 0 6E+05 211200 -211200 -281600 -281600 V20 = -158400 2E+05 2908400 -3E+06 0 -211200 U3

F1 -158400 -2E+05 -3E+06 2908400 211200 0 0G1 -211200 -3E+05 0 211200 281600 0 0G3 211200 -3E+05 -211200 0 0 281600 0

Unknown Displacement and Reaction

0 316800 0 -158400 U2-4 = 0 6E+05 211200 V20 -158400 2E+05 2908400 U3

U2 3.2475E-06 -7E-08 1.82E-07 0V2 = -6.818E-08 2E-06 -1.4E-07 -4U3 1.8182E-07 -1E-07 3.64E-07 0

U2 2.7273E-07V2 = -7.307E-06U3 5.4545E-07

F1 -158400 -2E+05 -3E+06 2.727E-07 F1G1 = -211200 -3E+05 0 -7.307E-06 G1 =G3 211200 -3E+05 -211200 5.455E-07 G3

[TT] [K3]

Gaya BatangBatang 1

f1g1 =f2g2

f1 0.6 0.8 0 0 158400 211200 -2E+05 -2E+05g1 = -0.8 0.6 0 0 211200 281600 -2E+05 -3E+05f2 0 0 0.6 0.8 -158400 -211200 2E+05 2E+05g2 0 0 -0.8 0.6 -211200 -281600 2E+05 3E+05

264000 4E+05 -264000 -352000 00 0 0 0 0

-264000 -4E+05 264000 352000 2.727E-070 0 0 0 -7.307E-06

f1 2.5g1 = 0f2 -2.5g2 0

Batang 2

f2g2 =f3g3

f2 0.6 -0.8 0 0 158400 -211200 -2E+05 2E+05g2 = 0.8 0.6 0 0 -211200 281600 2E+05 -3E+05f3 0 0 0.6 -0.8 -158400 211200 2E+05 -2E+05g3 0 0 0.8 0.6 211200 -281600 -2E+05 3E+05

264000 -4E+05 -264000 352000 2.727E-070 0 0 0 -7.307E-06

-264000 4E+05 264000 -352000 5.455E-070 0 0 0 0

f2 2.5g2 = 0

[T1] [Kg1] [U1]

[T2] [Kg2] [U2]

f3 -2.5g3 0

Batang 3

f1g1 =f3g3

f1 1 0 0 0 2750000 0 -3E+06 0g1 = 0 1 0 0 0 0 0 0f3 0 0 1 0 -2750000 0 3E+06 0g3 0 0 0 1 0 0 0 0

2750000 0 -3E+06 0 00 0 0 0 0

-2750000 0 2750000 0 5.455E-070 0 0 0 0

f1 -1.5g1 = 0f3 1.5g3 0

[T3] [Kg3] [U3]

2 = -3.333 T

2 T 2 T

1 = -3.333 T

3 = 2.667 T

luas 1 6000luas 2 5000

A 11000

1 0 0 0 1 0 0 0[T] 0 1 0 0 0 1 0 0

0 0 1 0 0 0 1 00 0 0 1 0 0 0 1

440000 0 -440000 0[Kg] 0 0 0 0

-440000 0 440000 00 0 0 0

[TT] =

022

00

3E-07 u2-7E-06 v2

3E-07-7E-065E-07

0

00

5E-070