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
E = 200000 MpaA = 11000 cm2
Batang 1L = 3000 mmEA/L = 733333.3sin α = 0cos α = 1
Matriks kekakuan
1 0 -1 0 733333.3 0= 733333.3 0 0 0 0 0 0
-1 0 1 0 -733333.3 00 0 0 0 0 0
1 0 0 0 1 0[T] = 0 1 0 0 0 1
0 0 1 0 0 00 0 0 1 0 0
733333.3 0 -733333.3 0 733333.3 00 0 0 0 [Kg] 0 0
-733333.3 0 733333.3 0 -733333.3 00 0 0 0 0 0
Batang 2L = 5000EA/L = 440000sin α = 0cos α = 1
matriks kekakuan
1 0 -1 0 440000 0= 440000 0 0 0 0 = 0 0
-1 0 1 0 -440000 0
[KI,1]
[TT] =
[TT].[K1]
[KI,2]
0 0 0 0 0 0
1 0 0 0 1 0[T] = 0 1 0 0 0 1
0 0 1 0 0 00 0 0 1 0 0
440000 0 -440000 0 440000 0= 0 0 0 0 [Kg] 0 0
-440000 0 440000 0 -440000 00 0 0 0 0 0
Batang 3L = 3000EA/L = 733333.3sin α = 0cos α = 1
matriks kekakuan
1 0 -1 0 733333.3 0= 733333.3 0 0 0 0 = 0 0
-1 0 1 0 -733333 00 0 0 0 0 0
1 0 0 0 1 0[T] = 0 1 0 0 0 1
0 0 1 0 0 00 0 0 1 0 0
733333.3 0 -733333 0 733333.3 0= 0 0 0 0 [Kg] 0 0
-733333 0 733333.3 0 -733333 0
[TT] =
[TT].[K2]
[KI,3]
[TT] =
[TT].[K3]
0 0 0 0 0 0
Batang 4L = 5000EA/L = 440000sin α = 0.8cos α = 0.6
matriks kekakuan
1 0 -1 0 440000 0= 440000 0 0 0 0 = 0 0
-1 0 1 0 -440000 00 0 0 0 0 0
0.6 0.8 0 0 0.6 -0.8[T] = -0.8 0.6 0 0 0.8 0.6
0 0 0.6 0.8 0 00 0 -0.8 0.6 0 0
264000 0 -264000 0 158400 211200= 352000 0 -352000 0 [Kg] 211200 281600
-264000 0 264000 0 -158400 -211200-352000 0 352000 0 -211200 -281600
Batang 5L = 4000EA/L = 550000sin α = 1cos α = 0
matriks kekakuan
1 0 -1 0 550000 0= 550000 0 0 0 0 = 0 0
[KI,4]
[TT] =
[TT].[K4]
[KI,5]
-1 0 1 0 -550000 00 0 0 0 0 0
0 1 0 0 0 -1[T] = -1 0 0 0 1 0
0 0 0 1 0 00 0 -1 0 0 0
0 0 0 0 0 0= 550000 0 -550000 0 [Kg] 0 550000
0 0 0 0 0 0-550000 0 550000 0 0 -550000
Batang 6L = 5385.16EA/L = 408530.1sin α = 0.37cos α = 0.93
matriks kekakuan
1 0 -1 0 408530.1 0= 408530.1 0 0 0 0 = 0 0
-1 0 1 0 -408530 00 0 0 0 0 0
0.93 0.37 0 0 0.93 -0.37[T] = -0.37 0.93 0 0 0.37 0.93
0 0 0.93 0.37 0 00 0 -0.37 0.93 0 0
379933 0 -379933 0 353337.7 140575.2= 151156.1 0 -151156 0 [Kg] 140575.2 55927.77
-379933 0 379933 0 -353338 -140575-151156 0 151156.1 0 -140575 -55927.77
[TT] =
[TT].[K5]
[KI,6]
[TT] =
[TT].[K6]
Batang 7L = 5385.16EA/L = 408530.1sin α = 0.37cos α = 0.93
matriks kekakuan
1 0 -1 0 408530.1 0= 408530.1 0 0 0 0 = 0 0
-1 0 1 0 -408530 00 0 0 0 0 0
0.93 -0.37 0 0 0.93 0.37[T] = 0.37 0.93 0 0 -0.37 0.93
0 0 0.93 -0.37 0 00 0 0.37 0.93 0 0
379933 0 -379933 0 353337.7 -140575= -151156 0 151156.1 0 [Kg] -140575 55927.77
-379933 0 379933 0 -353338 140575.2151156.1 0 -151156 0 140575.2 -55927.77
Batang 8L = 4000EA/L = 550000sin α = 1cos α = 0
matriks kekakuan
1 0 -1 0 550000 0= 550000 0 0 0 0 = 0 0
-1 0 1 0 -550000 00 0 0 0 0 0
[KI,7]
[TT] =
[TT].[K7]
[KI,8]
0 1 0 0 0 -1[T] = -1 0 0 0 1 0
0 0 0 1 0 00 0 -1 0 0 0
0 0 0 0 0 0= 550000 0 -550000 0 [Kg] 0 550000
0 0 0 0 0 0-550000 0 550000 0 0 -550000
[TT] =
[TT].[K8]
-733333.3 00 0
733333.3 00 0
0 00 01 00 1
-733333.3 00 0
733333.3 00 0
-440000 00 0
440000 0
0 0
0 00 01 00 1
-440000 00 0
440000 00 0
-733333 00 0
733333.3 00 0
0 00 01 00 1
-733333 00 0
733333.3 0
0 0
-440000 00 0
440000 00 0
0 00 0
0.6 -0.80.8 0.6
-158400 -211200-211200 -281600158400 211200211200 281600
-550000 00 0
550000 00 0
0 00 00 -11 0
0 00 -5500000 00 550000
-408530 00 0
408530.1 00 0
0 00 0
0.93 -0.370.37 0.93
-353338 -140575-140575 -55927.77
353337.7 140575.2140575.2 55927.77
-408530 00 0
408530.1 00 0
0 00 0
0.93 0.37-0.37 0.93
-353338 140575.2140575.2 -55927.77353337.7 -140575-140575 55927.77
-550000 00 0
550000 00 0
0 00 00 -11 0
0 00 -5500000 00 550000
Unknown Displacement and Reaction
0 1783467 422400 -733333.3 0 0 0 0 -316800 -422400 0 0 U20 422400 1113200 0 0 0 0 -550000 -422400 -563200 0 0 V20 -733333.3 0 1783467 -422400 -733333.3 0 0 -316800 422400 0 0 U30 0 0 -422400 1113200 0 0 0 422400 -563200 0 -550000 V30 0 0 -733333.3 0 891733.33 0 0 0 0 -158400 211200 U4
300 = 0 0 0 0 0 1208533 -211200 -316800 422400 -733333.3 0 U50 0 -550000 0 0 0 -211200 1394800 422400 -563200 0 0 V50 -316800 -422400 -316800 422400 0 -316800 422400 1267200 0 -316800 -422400 U60 -422400 -563200 422400 -563200 0 422400 -563200 0 2252800 -422400 -563200 V60 0 0 0 0 -158400 -733333.3 0 -316800 -422400 1208533 211200 U7
-700 0 0 0 -550000 211200 0 0 -422400 -563200 211200 1394800 V7
U2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0V2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0U3 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0V3 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0U4 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0U5 = #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 300V5 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0U6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0V6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0U7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0V7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! -700
U2 #VALUE!V2 #VALUE!U3 #VALUE!V3 #VALUE!U4 #VALUE!U5 = #VALUE!V5 #VALUE!U6 #VALUE!V6 #VALUE!U7 #VALUE!V7 #VALUE!
Gaya BatangBatang 1
f1g1 =f2g2
f1 1 0 0 0 733333.33 0 -733333.3 0 0g1 = 0 1 0 0 0 0 0 0 0f2 0 0 1 0 -733333.3 0 733333.33 0 #VALUE!g2 0 0 0 1 0 0 0 0 #VALUE!
733333.33 0 -733333.3 0 0
[T1] [Kg1] [U1]
0 0 0 0 0-733333.3 0 733333.33 0 #VALUE!
0 0 0 0 #VALUE!
f1 #VALUE!g1 = #VALUE!f2 #VALUE!g2 #VALUE!
Batang 2f2 1 0 0 0 733333.33 0 -733333.3 0 #VALUE!g2 = 0 1 0 0 0 0 0 0 #VALUE!f3 0 0 1 0 -733333.3 0 733333.33 0 #VALUE!g3 0 0 0 1 0 0 0 0 #VALUE!
733333.33 0 -733333.3 0 #VALUE!0 0 0 0 #VALUE!
-733333.3 0 733333.33 0 #VALUE!0 0 0 0 #VALUE!
f2 #VALUE!g2 = #VALUE!f3 #VALUE!g3 #VALUE!
Batang 3f3 1 0 0 0 733333.33 0 -733333.3 0 #VALUE!g3 = 0 1 0 0 0 0 0 0 #VALUE!f4 0 0 1 0 -733333.3 0 733333.33 0 #VALUE!g4 0 0 0 1 0 0 0 0 #VALUE!
733333.33 0 -733333.3 0 #VALUE!0 0 0 0 #VALUE!
-733333.3 0 733333.33 0 #VALUE!0 0 0 0 #VALUE!
f3 #VALUE!g3 = #VALUE!f4 #VALUE!g4 #VALUE!
Batang 4f1 0.6 0.8 0 0 158400 211200 -158400 -211200 0g1 = -0.8 0.6 0 0 211200 281600 -211200 -281600 0f5 0 0 0.6 0.8 -158400 -211200 158400 211200 #VALUE!g5 0 0 -0.8 0.6 -211200 -281600 211200 281600 #VALUE!
264000 352000 -264000 -352000 0
0 0 0 0 0-264000 -352000 264000 352000 #VALUE!
0 0 0 0 #VALUE!
f1 #VALUE!g1 = #VALUE!f5 #VALUE!g5 #VALUE!
Batang 5f2 0 1 0 0 0 0 0 0 #VALUE!g2 = -1 0 0 0 0 550000 0 -550000 #VALUE!f5 0 0 0 1 0 0 0 0 #VALUE!g5 0 0 -1 0 0 -550000 0 550000 #VALUE!
0 550000 0 -550000 #VALUE!0 0 0 0 #VALUE!0 -550000 0 550000 #VALUE!0 0 0 0 #VALUE!
f2 #VALUE!g2 = #VALUE!f5 #VALUE!g5 #VALUE!
Batang 6f2 0.6 0.8 0 0 316800 422400 -316800 -422400 #VALUE!g2 = -0.8 0.6 0 0 422400 563200 -422400 -563200 #VALUE!f6 0 0 0.6 0.8 -316800 -422400 316800 422400 #VALUE!g6 0 0 -0.8 0.6 -422400 -563200 422400 563200 #VALUE!
528000 704000 -528000 -704000 #VALUE!0 0 0 0 #VALUE!
-528000 -704000 528000 704000 #VALUE!0 0 0 0 #VALUE!
f2 #VALUE!g2 = #VALUE!f6 #VALUE!g6 #VALUE!
Batang 7f6 0.6 -0.8 0 0 316800 -422400 -316800 422400 #VALUE!g6 = 0.8 0.6 0 0 -422400 563200 422400 -563200 #VALUE!f3 0 0 0.6 -0.8 -316800 422400 316800 -422400 #VALUE!g3 0 0 0.8 0.6 422400 -563200 -422400 563200 #VALUE!
528000 -704000 -528000 704000 #VALUE!0 0 0 0 #VALUE!
-528000 704000 528000 -704000 #VALUE!0 0 0 0 #VALUE!
f6 #VALUE!g6 = #VALUE!f3 #VALUE!g3 #VALUE!
Batang 8f3 0 1 0 0 0 0 0 0 #VALUE!g3 = -1 0 0 0 0 550000 0 -550000 #VALUE!f7 0 0 0 1 0 0 0 0 #VALUE!g7 0 0 -1 0 0 -550000 0 550000 #VALUE!
0 550000 0 -550000 #VALUE!0 0 0 0 #VALUE!0 -550000 0 550000 #VALUE!0 0 0 0 #VALUE!
f3 #VALUE!g3 = #VALUE!f7 #VALUE!g7 #VALUE!
Batang 9f7 0.6 -0.8 0 0 158400 -211200 -158400 211200 #VALUE!g7 = 0.8 0.6 0 0 -211200 281600 211200 -281600 #VALUE!f4 0 0 0.6 -0.8 -158400 211200 158400 -211200 #VALUE!g4 0 0 0.8 0.6 211200 -281600 -211200 281600 0
264000 -352000 -264000 352000 #VALUE!0 0 0 0 #VALUE!
-264000 352000 264000 -352000 #VALUE!0 0 0 0 0
f7 #VALUE!g7 = #VALUE!f4 #VALUE!g4 #VALUE!
Batang 10f5 0.6 -0.8 0 0 316800 -422400 -316800 422400 #VALUE!g5 = 0.8 0.6 0 0 -422400 563200 422400 -563200 #VALUE!f6 0 0 0.6 -0.8 -316800 422400 316800 -422400 #VALUE!g6 0 0 0.8 0.6 422400 -563200 -422400 563200 #VALUE!
528000 -704000 -528000 704000 #VALUE!0 0 0 0 #VALUE!
-528000 704000 528000 -704000 #VALUE!0 0 0 0 #VALUE!
f5 #VALUE!g5 = #VALUE!f6 #VALUE!
g6 #VALUE!
Batang 11f6 0.6 0.8 0 0 316800 422400 -316800 -422400 #VALUE!g6 = -0.8 0.6 0 0 422400 563200 -422400 -563200 #VALUE!f7 0 0 0.6 0.8 -316800 -422400 316800 422400 #VALUE!g7 0 0 -0.8 0.6 -422400 -563200 422400 563200 #VALUE!
528000 704000 -528000 -704000 #VALUE!0 0 0 0 #VALUE!
-528000 -704000 528000 704000 #VALUE!0 0 0 0 #VALUE!
f6 #VALUE!g6 = #VALUE!f7 #VALUE!g7 #VALUE!
Batang 12f5 1 0 0 0 733333.33 0 -733333.3 0 #VALUE!g5 = 0 1 0 0 0 0 0 0 #VALUE!f7 0 0 1 0 -733333.3 0 733333.33 0 #VALUE!g7 0 0 0 1 0 0 0 0 #VALUE!
733333.33 0 -733333.3 0 #VALUE!0 0 0 0 #VALUE!
-733333.3 0 733333.33 0 #VALUE!0 0 0 0 #VALUE!
f5 #VALUE!g5 = #VALUE!f7 #VALUE!g7 #VALUE!
Reaksi Perletakan
#VALUE!#VALUE!#VALUE!#VALUE!
F1 -733333.3 0 0 0 0 -158400 -211200 0 0 0 0 #VALUE! #VALUE!G1 = 0 0 0 0 0 -211200 -281600 0 0 0 0 #VALUE! = #VALUE!G4 0 0 0 0 -211200 0 0 0 0 211200 -281600 #VALUE! #VALUE!
#VALUE!#VALUE!#VALUE!#VALUE!
E = 200000 MpaA = 11000 cm2
Batang 1L = 4000 mmEA/L = 550000sin α = 0 (S)cos α = 1 (C)
CS -(CS) 1 0 -1 0= EA/L CS S² -(CS) (S²) = 550000 0 0 0 0
-(CS) CS -1 0 1 0-(CS) (S²) CS S² 0 0 0 0
u1 v1 u2 v21 0 0 0 550000 0 -550000 0 u1
= 0 1 0 0 [Kg,1] = 0 0 0 0 v10 0 1 0 -550000 0 550000 0 u20 0 0 1 0 0 0 0 v2
Batang 2L = 4000 mmEA/L = 550000sin α = 0 (S)cos α = 1 (C)
CS -(CS) 1 0 -1 0= EA/L CS S² -(CS) (S²) = 550000 0 0 0 0
-(CS) CS -1 0 1 0-(CS) (S²) CS S² 0 0 0 0
u2 v2 u3 v31 0 0 0 550000 0 -550000 0 u2
= 0 1 0 0 [Kg,2] = 0 0 0 0 v20 0 1 0 -550000 0 550000 0 u30 0 0 1 0 0 0 0 v3
Batang 3L = 4000 mmEA/L = 550000sin α = 0 (S)cos α = 1 (C)
CS -(CS) 1 0 -1 0= EA/L CS S² -(CS) (S²) = 550000 0 0 0 0
-(CS) CS -1 0 1 0-(CS) (S²) CS S² 0 0 0 0
u3 v3 u4 v41 0 0 0 550000 0 -550000 0 u3
= 0 1 0 0 [Kg,3] = 0 0 0 0 v30 0 1 0 -550000 0 550000 0 u40 0 0 1 0 0 0 0 v4
Batang 4L = 4000 mmEA/L = 550000sin α = 0 (S)cos α = 1 (C)
CS -(CS) 1 0 -1 0= EA/L CS S² -(CS) (S²) = 550000 0 0 0 0
-(CS) CS -1 0 1 0-(CS) (S²) CS S² 0 0 0 0
u4 v4 u5 v51 0 0 0 550000 0 -550000 0 u4
= 0 1 0 0 [Kg,4] = 0 0 0 0 v40 0 1 0 -550000 0 550000 0 u50 0 0 1 0 0 0 0 v5
Batang 5L = 5000 mmEA/L = 440000sin α = 0.6 (S)
C² -(C²)[Kg,1]
-(C²) C²
[T1]
C² -(C²)[Kg,2]
-(C²) C²
[T2]
C² -(C²)[Kg,3]
-(C²) C²
[T3]
C² -(C²)[Kg,4]
-(C²) C²
[T4]
cos α = 0.8 (C)
CS -(CS) 0.64 0.48 -0.64 -0.48= EA/L CS S² -(CS) (S²) = 440000 0.48 0.36 -0.48 -0.36
-(CS) CS -0.64 -0.48 0.64 0.48-(CS) (S²) CS S² -0.48 -0.36 0.48 0.36
u1 v1 u6 v60.8 0.6 0 0 281600 211200 -281600 -211200 u1
= -0.6 0.8 0 0 [Kg,5] = 211200 158400 -211200 -158400 v10 0 0.8 0.6 -281600 -211200 281600 211200 u60 0 -0.6 0.8 -211200 -158400 211200 158400 v6
Batang 6L = 3000 mmEA/L = 733333.33sin α = 1 (S)cos α = 0 (C)
CS -(CS) 0 0 0 0= EA/L CS S² -(CS) (S²) = 733333.33 0 1 0 -1
-(CS) CS 0 0 0 0-(CS) (S²) CS S² 0 -1 0 1
u2 v2 u6 v60 1 0 0 0 0 0 0 u2
= -1 0 0 0 [Kg,6] = 0 733333.33 0 -733333 v20 0 0 1 0 0 0 0 u60 0 -1 0 0 -733333 0 733333.33 v6
Batang 7L = 3000 mmEA/L = 733333.33sin α = -0.6 (S)cos α = 0.8 (C)
CS -(CS) 0.64 -0.48 -0.64 0.48= EA/L CS S² -(CS) (S²) = 733333.33 -0.48 0.36 0.48 -0.36
-(CS) CS -0.64 0.48 0.64 -0.48-(CS) (S²) CS S² 0.48 -0.36 -0.48 0.36
u6 v6 u3 v30.8 -0.6 0 0 469333.33 -352000 -469333 352000 u6
= 0.6 0.8 0 0 [Kg,7] = -352000 264000 352000 -264000 v60 0 0.8 -0.6 -469333 352000 469333.33 -352000 u30 0 0.6 0.8 352000 -264000 -352000 264000 v3
Batang 8L = 6000 mmEA/L = 366666.67sin α = 1 (S)cos α = 0 (C)
CS -(CS) 0 0 0 0= EA/L CS S² -(CS) (S²) = 366666.67 0 1 0 -1
-(CS) CS 0 0 0 0-(CS) (S²) CS S² 0 -1 0 1
u3 v3 u7 v70 1 0 0 0 0 0 0 u3
= -1 0 0 0 [Kg,8] = 0 366666.67 0 -366667 v30 0 0 1 0 0 0 0 u70 0 -1 0 0 -366667 0 366666.67 v7
Batang 9L = 5000 mmEA/L = 440000sin α = 0.6 (S)cos α = 0.8 (C)
CS -(CS) 0.64 0.48 -0.64 -0.48= EA/L CS S² -(CS) (S²) = 440000 0.48 0.36 -0.48 -0.36
-(CS) CS -0.64 -0.48 0.64 0.48
C² -(C²)[Kg,5]
-(C²) C²
[T5]
C² -(C²)[Kg,6]
-(C²) C²
[T6]
C² -(C²)[Kg,7]
-(C²) C²
[T7]
C² -(C²)[Kg,8]
-(C²) C²
[T8]
C² -(C²)[Kg,9]
-(C²) C²
-(CS) (S²) CS S² -0.48 -0.36 0.48 0.36
u3 v3 u8 v80.8 0.6 0 0 281600 211200 -281600 -211200 u3
= -0.6 0.8 0 0 [Kg,9] = 211200 158400 -211200 -158400 v30 0 0.8 0.6 -281600 -211200 281600 211200 u80 0 -0.6 0.8 -211200 -158400 211200 158400 v8
Batang 10L = 3000 mmEA/L = 733333.33sin α = 1 (S)cos α = 0 (C)
CS -(CS) 0 0 0 0= EA/L CS S² -(CS) (S²) = 733333.33 0 1 0 -1
-(CS) CS 0 0 0 0-(CS) (S²) CS S² 0 -1 0 1
u4 v4 u8 v80 1 0 0 0 0 0 0 u4
= -1 0 0 0 [Kg,10] = 0 733333.33 0 -733333 v40 0 0 1 0 0 0 0 u80 0 -1 0 0 -733333 0 733333.33 v8
Batang 11L = 5000 mmEA/L = 440000sin α = -0.6 (S)cos α = 0.8 (C)
CS -(CS) 0.64 -0.48 -0.64 0.48= EA/L CS S² -(CS) (S²) = 440000 -0.48 0.36 0.48 -0.36
-(CS) CS -0.64 0.48 0.64 -0.48-(CS) (S²) CS S² 0.48 -0.36 -0.48 0.36
u8 v8 u5 v50.8 -0.6 0 0 281600 -211200 -281600 211200 u8
= 0.6 0.8 0 0 [Kg,11] = -211200 158400 211200 -158400 v80 0 0.8 -0.6 -281600 211200 281600 -211200 u50 0 0.6 0.8 211200 -158400 -211200 158400 v5
Batang 12L = 5000 mmEA/L = 440000sin α = 0.6 (S)cos α = 0.8 (C)
CS -(CS) 0.64 0.48 -0.64 -0.48= EA/L CS S² -(CS) (S²) = 440000 0.48 0.36 -0.48 -0.36
-(CS) CS -0.64 -0.48 0.64 0.48-(CS) (S²) CS S² -0.48 -0.36 0.48 0.36
u6 v6 u7 v70.8 0.6 0 0 281600 211200 -281600 -211200 u6
= -0.6 0.8 0 0 [Kg,12] = 211200 158400 -211200 -158400 v60 0 0.8 0.6 -281600 -211200 281600 211200 u70 0 -0.6 0.8 -211200 -158400 211200 158400 v7
Batang 13L = 5000 mmEA/L = 440000sin α = -0.6 (S)cos α = 0.8 (C)
CS -(CS) 0.64 -0.48 -0.64 0.48= EA/L CS S² -(CS) (S²) = 440000 -0.48 0.36 0.48 -0.36
-(CS) CS -0.64 0.48 0.64 -0.48-(CS) (S²) CS S² 0.48 -0.36 -0.48 0.36
u7 v7 u8 v80.8 -0.6 0 0 281600 -211200 -281600 211200 u7
= 0.6 0.8 0 0 [Kg,13] = -211200 158400 211200 -158400 v70 0 0.8 -0.6 -281600 211200 281600 -211200 u80 0 0.6 0.8 211200 -158400 -211200 158400 v8
[T9]
C² -(C²)[Kg,10]
-(C²) C²
[T10]
C² -(C²)[Kg,11]
-(C²) C²
[T11]
C² -(C²)[Kg,12]
-(C²) C²
[T12]
C² -(C²)[Kg,13]
-(C²) C²
[T13]
Overall Stiffnessu1 v1 u2 v2 u3 v3 u4 v4 u5 v5 u6
1 F1 831600 211200 -550000 0 -2816002 G1 211200 158400 0 0 -2112003 0 -550000 0 1100000 0 -550000 0 04 0 0 0 0 733333.33 0 0 05 0 -550000 0 1850933 -140800 -550000 0 -4693336 0 0 0 -140800 789066.67 0 0 3520007 0 -550000 0 1100000 0 -550000 08 0 = 0 0 0 733333.33 0 09 0 -550000 0 831600 -211200
10 G5 0 0 -211200 15840011 0 -281600 -211200 0 0 -469333 352000 103253312 0 -211200 -158400 0 -733333 352000 -264000 7040013 500 0 0 -28160014 0 0 -366667 -21120015 0 -281600 -211200 0 0 -281600 21120016 -1000 -211200 -158400 0 -733333 211200 -158400
1 2 3 4 5 6 7 8 9 10 11
Rearrangement
3 0 1100000 0 -550000 0 0 0 0 0 0 0 04 0 0 733333.33 0 0 0 0 0 0 -733333 0 05 0 -550000 0 1850933 -140800 -550000 0 0 -469333 352000 0 06 0 0 0 -140800 789066.67 0 0 0 352000 -264000 0 -3666677 0 0 0 -550000 0 1100000 0 -550000 0 0 0 08 0 0 0 0 0 0 733333.33 0 0 0 0 09 0 0 0 0 0 -550000 0 831600 0 0 0 0
11 0 = 0 0 -469333 352000 0 0 0 1032533 70400 -281600 -21120012 0 0 -733333 352000 -264000 0 0 0 70400 1314133 -211200 -15840013 500 0 0 0 0 0 0 0 -281600 -211200 563200 014 0 0 0 0 -366667 0 0 0 -211200 -158400 0 683466.6715 0 0 0 -281600 -211200 0 0 -281600 0 0 -281600 21120016 -1000 0 0 -211200 -158400 0 -733333 211200 0 0 211200 -1584001 F1 -550000 0 0 0 0 0 0 -281600 -211200 0 02 G1 0 0 0 0 0 0 0 -211200 -158400 0 0
10 G5 0 0 0 0 0 0 -211200 0 0 0 03 4 5 6 7 8 9 11 12 13 14
Unknown Displacement and Reaction
0 1100000 0 -550000 0 0 0 0 0 0 0 00 0 733333.33 0 0 0 0 0 0 -733333 0 00 -550000 0 1850933 -140800 -550000 0 0 -469333 352000 0 00 0 0 -140800 789066.67 0 0 0 352000 -264000 0 -3666670 0 0 -550000 0 1100000 0 -550000 0 0 0 00 0 0 0 0 0 733333.33 0 0 0 0 00 = 0 0 0 0 -550000 0 831600 0 0 0 00 0 0 -469333 352000 0 0 0 1032533 70400 -281600 -2112000 0 -733333 352000 -264000 0 0 0 70400 1314133 -211200 -158400
500 0 0 0 0 0 0 0 -281600 -211200 563200 00 0 0 0 -366667 0 0 0 -211200 -158400 0 683466.670 0 0 -281600 -211200 0 0 -281600 0 0 -281600 211200
-1000 0 0 -211200 -158400 0 -733333 211200 0 0 211200 -158400
U2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!V2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!U3 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!V3 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!U4 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!V4 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
U5 = #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!U6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!V6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!U7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!V7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!U8 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!V8 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!
U2 #VALUE!V2 #VALUE!U3 #VALUE!V3 #VALUE!U4 #VALUE!V4 = #VALUE!U5 #VALUE!U6 #VALUE!V6 #VALUE!U7 #VALUE!V7 #VALUE!U8 #VALUE!V8 #VALUE!
Gaya BatangBatang 1
f1g1 =f2g2
f1 1 0 0 0 550000 0 -550000 0 0g1 = 0 1 0 0 0 0 0 0 0f2 0 0 1 0 -550000 0 550000 0 #VALUE!g2 0 0 0 1 0 0 0 0 #VALUE!
550000 0 -550000 0 00 0 0 0 0
-550000 0 550000 0 #VALUE!0 0 0 0 #VALUE!
f1 #VALUE!g1 = #VALUE!f2 #VALUE!g2 #VALUE!
Batang 2
f2 1 0 0 0 550000 0 -550000 0 #VALUE!g2 = 0 1 0 0 0 0 0 0 #VALUE!f3 0 0 1 0 -550000 0 550000 0 #VALUE!g3 0 0 0 1 0 0 0 0 #VALUE!
550000 0 -550000 0 #VALUE!0 0 0 0 #VALUE!
-550000 0 550000 0 #VALUE!0 0 0 0 #VALUE!
f2 #VALUE!g2 = #VALUE!f3 #VALUE!g3 #VALUE!
Batang 3
f3 1 0 0 0 550000 0 -550000 0 #VALUE!g3 = 0 1 0 0 0 0 0 0 #VALUE!
[T1] [Kg1] [U1]
f4 0 0 1 0 -550000 0 550000 0 #VALUE!g4 0 0 0 1 0 0 0 0 #VALUE!
550000 0 -550000 0 #VALUE!0 0 0 0 #VALUE!
-550000 0 550000 0 #VALUE!0 0 0 0 #VALUE!
f3 #VALUE!g3 = #VALUE!f4 #VALUE!g4 #VALUE!
Batang 4
f4 1 0 0 0 550000 0 -550000 0 #VALUE!g4 = 0 1 0 0 0 0 0 0 #VALUE!f5 0 0 1 0 -550000 0 550000 0 #VALUE!g5 0 0 0 1 0 0 0 0 0
550000 0 -550000 0 #VALUE!0 0 0 0 #VALUE!
-550000 0 550000 0 #VALUE!0 0 0 0 0
f4 #VALUE!g4 = #VALUE!f5 #VALUE!g5 #VALUE!
Batang 5
f1 0.8 0.6 0 0 281600 211200 -281600 -211200 0g1 = -0.6 0.8 0 0 211200 158400 -211200 -158400 0f6 0 0 0.8 0.6 -281600 -211200 281600 211200 #VALUE!g6 0 0 -0.6 0.8 -211200 -158400 211200 158400 #VALUE!
352000 264000 -352000 -264000 00 0 0 0 0
-352000 -264000 352000 264000 #VALUE!0 0 0 0 #VALUE!
f1 #VALUE!g1 = #VALUE!f6 #VALUE!g6 #VALUE!
Batang 6
f2 0 1 0 0 0 0 0 0 #VALUE!g2 = -1 0 0 0 0 733333.33 0 -733333 #VALUE!f6 0 0 0 1 0 0 0 0 #VALUE!g6 0 0 -1 0 0 -733333 0 733333.33 #VALUE!
0 733333.33 0 -733333 #VALUE!0 0 0 0 #VALUE!0 -733333 0 733333.33 #VALUE!0 0 0 0 #VALUE!
f2 #VALUE!g2 = #VALUE!f6 #VALUE!g6 #VALUE!
Batang 7
f6 0.8 -0.6 0 0 469333.33 -352000 -469333 352000 #VALUE!g6 = 0.6 0.8 0 0 -352000 264000 352000 -264000 #VALUE!f3 0 0 0.8 -0.6 -469333 352000 469333.33 -352000 #VALUE!g3 0 0 0.6 0.8 352000 -264000 -352000 264000 #VALUE!
586666.67 -440000 -586667 440000 #VALUE!0 0 0 0 #VALUE!
-586667 440000 586666.67 -440000 #VALUE!0 0 0 0 #VALUE!
f6 #VALUE!g6 = #VALUE!f3 #VALUE!g3 #VALUE!
Batang 8
f3 0 1 0 0 0 0 0 0 #VALUE!g3 = -1 0 0 0 0 366666.67 0 -366667 #VALUE!f7 0 0 0 1 0 0 0 0 #VALUE!g7 0 0 -1 0 0 -366667 0 366666.67 #VALUE!
0 366666.67 0 -366667 #VALUE!0 0 0 0 #VALUE!0 -366667 0 366666.67 #VALUE!0 0 0 0 #VALUE!
f3 #VALUE!g3 = #VALUE!f7 #VALUE!g7 #VALUE!
Batang 9
f3 0.8 0.6 0 0 281600 211200 -281600 -211200 #VALUE!g3 = -0.6 0.8 0 0 211200 158400 -211200 -158400 #VALUE!f8 0 0 0.8 0.6 -281600 -211200 281600 211200 #VALUE!g8 0 0 -0.6 0.8 -211200 -158400 211200 158400 #VALUE!
352000 264000 -352000 -264000 #VALUE!0 0 0 0 #VALUE!
-352000 -264000 352000 264000 #VALUE!0 0 0 0 #VALUE!
f3 #VALUE!g3 = #VALUE!f8 #VALUE!g8 #VALUE!
Batang 10
f4 0 1 0 0 0 0 0 0 #VALUE!g4 = -1 0 0 0 0 733333.33 0 -733333 #VALUE!f8 0 0 0 1 0 0 0 0 #VALUE!g8 0 0 -1 0 0 -733333 0 733333.33 #VALUE!
0 733333.33 0 -733333 #VALUE!0 0 0 0 #VALUE!0 -733333 0 733333.33 #VALUE!0 0 0 0 #VALUE!
f4 #VALUE!g4 = #VALUE!f8 #VALUE!g8 #VALUE!
Batang 11
f8 0.8 -0.6 0 0 281600 -211200 -281600 211200 #VALUE!g8 = 0.6 0.8 0 0 -211200 158400 211200 -158400 #VALUE!f5 0 0 0.8 -0.6 -281600 211200 281600 -211200 #VALUE!g5 0 0 0.6 0.8 211200 -158400 -211200 158400 0
352000 -264000 -352000 264000 #VALUE!0 0 0 0 #VALUE!
-352000 264000 352000 -264000 #VALUE!0 0 0 0 0
f8 #VALUE!g8 = #VALUE!f5 #VALUE!g5 #VALUE!
Batang 12
f6 0.8 0.6 0 0 281600 211200 -281600 -211200 #VALUE!g6 = -0.6 0.8 0 0 211200 158400 -211200 -158400 #VALUE!f7 0 0 0.8 0.6 -281600 -211200 281600 211200 #VALUE!g7 0 0 -0.6 0.8 -211200 -158400 211200 158400 #VALUE!
352000 264000 -352000 -264000 #VALUE!0 0 0 0 #VALUE!
-352000 -264000 352000 264000 #VALUE!0 0 0 0 #VALUE!
f6 #VALUE!g6 = #VALUE!f7 #VALUE!g7 #VALUE!
Batang 13
f7 0.8 -0.6 0 0 281600 -211200 -281600 211200 #VALUE!g7 = 0.6 0.8 0 0 -211200 158400 211200 -158400 #VALUE!f8 0 0 0.8 -0.6 -281600 211200 281600 -211200 #VALUE!g8 0 0 0.6 0.8 211200 -158400 -211200 158400 #VALUE!
352000 -264000 -352000 264000 #VALUE!0 0 0 0 #VALUE!
-352000 264000 352000 -264000 #VALUE!0 0 0 0 #VALUE!
f7 #VALUE!g7 = #VALUE!f8 #VALUE!g8 #VALUE!
Reaksi Perletakan
F1 -550000 0 0 0 0 0 0 -281600 -211200 0 0G1 = 0 0 0 0 0 0 0 -211200 -158400 0 0G5 0 0 0 0 0 0 -211200 0 0 0 0
Hasil Komparasi Matriks dan SAP2000
Batang Matriks SAP20001 #VALUE! 583.332 #VALUE! 583.333 #VALUE! 12504 #VALUE! 12505 #VALUE! -104.176 #VALUE! 07 #VALUE! 4.547E-138 #VALUE! 5009 #VALUE! -833.33
10 #VALUE! 011 #VALUE! -1562.512 #VALUE! -104.1713 #VALUE! -729.17
v6 u7 v7 u8 v8-211200 u1 0-158400 v1 0
0 u2 U2-733333 v2 V2352000 0 0 -281600 -211200 u3 U3-264000 0 -366667 -211200 -158400 v3 V3
0 0 u4 U40 -733333 v4 V4
-281600 211200 u5 U5211200 -158400 v5 0
70400 -281600 -211200 u6 U61314133 -211200 -158400 v6 V6-211200 563200 0 -281600 211200 u7 U7-158400 0 683466.67 211200 -158400 v7 V7
-281600 211200 844800 -211200 u8 U8211200 -158400 -211200 1208533 v8 V8
12 13 14 15 16
0 0 -550000 0 0 U20 0 0 0 0 V2
-281600 -211200 0 0 0 U3-211200 -158400 0 0 0 V3
0 0 0 0 0 U40 -733333 0 0 0 V4
-281600 211200 0 0 -211200 U50 0 -281600 -211200 0 U60 0 -211200 -158400 0 V6
-281600 211200 0 0 0 U7211200 -158400 0 0 0 V7844800 -211200 0 0 211200 U8-211200 1208533 0 0 -158400 V8
0 0 831600 211200 0 00 0 211200 158400 0 0
211200 -158400 0 0 158400 015 16 1 2 10
0 0 U20 0 V2
-281600 -211200 U3-211200 -158400 V3
0 0 U40 -733333 V4
-281600 211200 U50 0 U60 0 V6
-281600 211200 U7211200 -158400 V7844800 -211200 U8-211200 1208533 V8
#VALUE! #VALUE! 0#VALUE! #VALUE! 0#VALUE! #VALUE! 0#VALUE! #VALUE! 0#VALUE! #VALUE! 0#VALUE! #VALUE! 0
#VALUE! #VALUE! 0#VALUE! #VALUE! 0#VALUE! #VALUE! 0#VALUE! #VALUE! 500#VALUE! #VALUE! 0#VALUE! #VALUE! 0#VALUE! #VALUE! -1000
#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!
0 0 #VALUE! #VALUE!0 0 #VALUE! = #VALUE!
211200 -158400 #VALUE! #VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!
Reaksi Perletakan
#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!
F1 -937500 0 0 0 0 0 0 -480000 -360000 0 0 0 0 #VALUE! #VALUE!G1 = 0 0 0 0 0 0 0 -360000 -270000 0 0 0 0 #VALUE! = #VALUE!G5 0 0 0 0 0 0 -360000 0 0 0 0 360000 -270000 #VALUE! #VALUE!
#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!
E = 250000 MpaA = 15000 cm2
Batang 1L = 3000 mmEA/L = 1250000sin α = 0cos α = 1
Matriks kekakuan1 0 -1 0 1250000 0 -1250000 0
= 1250000 0 0 0 0 = 0 0 0 0-1 0 1 0 -1250000 0 1250000 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
1250000 0 -1250000 0= 0 0 0 0
-1250000 0 1250000 00 0 0 0
u1 v1 u2 v21250000 0 -1250000 0 u1
[Kg] = [T] = 0 0 0 0 v1-1250000 0 1250000 0 u2
0 0 0 0 v2
Batang 2L = 3000 mmEA/L = 1250000sin α = 0cos α = 1
Matriks kekakuan1 0 -1 0 1250000 0 -1250000 0
= 1250000 0 0 0 0 = 0 0 0 0-1 0 1 0 -1250000 0 1250000 00 0 0 0 0 0 0 0
Matriks transformasi1 0 0 0 1 0 0 0 1250000 0 -1250000 0
[T] = 0 1 0 0 0 1 0 0 = 0 0 0 00 0 1 0 0 0 1 0 -1250000 0 1250000 00 0 0 1 0 0 0 1 0 0 0 0
[KI,1]
[TT] =
[TT].[K1]
[TT] [K1]
[KI,2]
[TT] = [TT].[K2]
u2 v2 u3 v31250000 0 -1250000 0 u2
[Kg] = [T] = 0 0 0 0 v2-1250000 0 1250000 0 u3
0 0 0 0 v3
Batang 3L = 3000 mmEA/L = 1250000sin α = 0cos α = 1
Matriks kekakuan1 0 -1 0 1250000 0 -1250000 0
= 1250000 0 0 0 0 = 0 0 0 0-1 0 1 0 -1250000 0 1250000 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
1250000 0 -1250000 0= 0 0 0 0
-1250000 0 1250000 00 0 0 0
u3 v3 u4 v41250000 0 -1250000 0 u3
[Kg] = [T] = 0 0 0 0 v3-1250000 0 1250000 0 u4
0 0 0 0 v4
Batang 4L = 5000 mmEA/L = 750000sin α = 0.8cos α = 0.6
Matriks kekakuan1 0 -1 0 750000 0 -750000 0
= 750000 0 0 0 0 = 0 0 0 0-1 0 1 0 -750000 0 750000 0
[TT] [K2]
[KI,3]
[TT] =
[TT].[K3]
[TT] [K3]
[KI,4]
0 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
450000 0 -450000 0= 600000 0 -600000 0
-450000 0 450000 0-600000 0 600000 0
u1 v1 u5 v5270000 360000 -270000 -360000 u1
[Kg] = [T] = 360000 480000 -360000 -480000 v1-270000 -360000 270000 360000 u5-360000 -480000 360000 480000 v5
Batang 5L = 4000 mmEA/L = 937500sin α = 1cos α = 0
Matriks kekakuan1 0 -1 0 937500 0 -937500 0
= 937500 0 0 0 0 = 0 0 0 0-1 0 1 0 -937500 0 937500 00 0 0 0 0 0 0 0
Matriks transformasi0 1 0 0 0 -1 0 0
[T] = -1 0 0 0 1 0 0 00 0 0 1 0 0 0 -10 0 -1 0 0 0 1 0
0 0 0 0= 937500 0 -937500 0
0 0 0 0-937500 0 937500 0
u2 v2 u5 v50 0 0 0 u2
[Kg] = [T] = 0 937500 0 -937500 v20 0 0 0 u50 -937500 0 937500 v5
Batang 6L = 2500 mmEA/L = 1500000
[TT] =
[TT].[K4]
[TT] [K4]
[KI,5]
[TT] =
[TT].[K5]
[TT] [K5]
sin α = 0.8cos α = 0.6 Matriks kekakuan
1 0 -1 0 1500000 0 -1500000 0= 1500000 0 0 0 0 = 0 0 0 0
-1 0 1 0 -1500000 0 1500000 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
900000 0 -900000 0= 1200000 0 -1200000 0
-900000 0 900000 0-1200000 0 1200000 0
u2 v2 u6 v6540000 720000 -540000 -720000 u2
[Kg] = [T] = 720000 960000 -720000 -960000 v2-540000 -720000 540000 720000 u6-720000 -960000 720000 960000 v6
Batang 7L = 2500 mmEA/L = 1500000sin α = -0.8cos α = 0.6
Matriks kekakuan1 0 -1 0 1500000 0 -1500000 0
= 1500000 0 0 0 0 = 0 0 0 0-1 0 1 0 -1500000 0 1500000 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
900000 0 -900000 0= -1200000 0 1200000 0
-900000 0 900000 01200000 0 -1200000 0
u6 v6 u3 v3540000 -720000 -540000 720000 u6
[KI,6]
[TT] =
[TT].[K6]
[TT] [K6]
[KI,7]
[TT] =
[TT].[K7]
[Kg] = [T] = -720000 960000 720000 -960000 v6-540000 720000 540000 -720000 u3720000 -960000 -720000 960000 v3
Batang 8L = 4000 mmEA/L = 937500sin α = 1cos α = 0
Matriks kekakuan1 0 -1 0 937500 0 -937500 0
= 937500 0 0 0 0 = 0 0 0 0-1 0 1 0 -937500 0 937500 00 0 0 0 0 0 0 0
Matriks transformasi0 1 0 0 0 -1 0 0
[T] = -1 0 0 0 1 0 0 00 0 0 1 0 0 0 -10 0 -1 0 0 0 1 0
0 0 0 0= 937500 0 -937500 0
0 0 0 0-937500 0 937500 0
u3 v3 u7 v70 0 0 0 u3
[Kg] = [T] = 0 937500 0 -937500 v30 0 0 0 u70 -937500 0 937500 v7
Batang 9L = 5000 mmEA/L = 750000sin α = -0.8cos α = 0.6
Matriks kekakuan1 0 -1 0 750000 0 -750000 0
= 750000 0 0 0 0 = 0 0 0 0-1 0 1 0 -750000 0 750000 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
[TT] [K7]
[KI,8]
[TT] =
[TT].[K8]
[TT] [K8]
[KI,9]
[TT] =
450000 0 -450000 0= -600000 0 600000 0
-450000 0 450000 0600000 0 -600000 0
u7 v7 u4 v4270000 -360000 -270000 360000 u7
[Kg] = [T] = -360000 480000 360000 -480000 v7-270000 360000 270000 -360000 u4360000 -480000 -360000 480000 v4
Batang 10L = 2500 mmEA/L = 1500000sin α = -0.8cos α = 0.6
Matriks kekakuan1 0 -1 0 1500000 0 -1500000 0
= 1500000 0 0 0 0 = 0 0 0 0-1 0 1 0 -1500000 0 1500000 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
900000 0 -900000 0= -1200000 0 1200000 0
-900000 0 900000 01200000 0 -1200000 0
u5 v5 u6 v6540000 -720000 -540000 720000 u5
[Kg] = [T] = -720000 960000 720000 -960000 v5-540000 720000 540000 -720000 u6720000 -960000 -720000 960000 v6
Batang 11L = 2500 mmEA/L = 1500000sin α = 0.8cos α = 0.6
Matriks kekakuan1 0 -1 0 1500000 0 -1500000 0
= 1500000 0 0 0 0 = 0 0 0 0-1 0 1 0 -1500000 0 1500000 00 0 0 0 0 0 0 0
[TT].[K9]
[TT] [K9]
[KI,10]
[TT] =
[TT].[K10]
[TT] [K10]
[KI,11]
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
900000 0 -900000 0= 1200000 0 -1200000 0
-900000 0 900000 0-1200000 0 1200000 0
u6 v6 u7 v7540000 720000 -540000 -720000 u6
[Kg] = [T] = 720000 960000 -720000 -960000 v6-540000 -720000 540000 720000 u7-720000 -960000 720000 960000 v7
Batang 12L = 3000 mmEA/L = 1250000sin α = 0cos α = 1
Matriks kekakuan1 0 -1 0 1250000 0 -1250000 0
= 1250000 0 0 0 0 = 0 0 0 0-1 0 1 0 -1250000 0 1250000 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
1250000 0 -1250000 0= 0 0 0 0
-1250000 0 1250000 00 0 0 0
u5 v5 u7 v71250000 0 -1250000 0 u5
[Kg] = [T] = 0 0 0 0 v5-1250000 0 1250000 0 u7
0 0 0 0 v7
Overall Stiffnessu1 v1 u2 v2 u3 v3 u4 v4 u5 v5 u6 v6 u7 v7
1 F1 1520000 360000 -1250000 0 -270000 -360000 u1 0
[TT] =
[TT].[K11]
[TT] [K11]
[KI,12]
[TT] =
[TT].[K12]
[TT] [K12]
2 G1 360000 480000 0 0 -360000 -480000 v1 03 0 -1250000 0 3040000 720000 -1250000 0 0 0 -540000 -720000 u2 U24 0 0 0 720000 1897500 0 0 0 -937500 -720000 -960000 v2 V25 0 -1250000 0 3040000 -720000 -1250000 0 -540000 720000 0 0 u3 U36 0 0 0 -720000 1897500 0 0 720000 -960000 0 -937500 v3 V37 0 = -1250000 0 1520000 -360000 -270000 360000 u4 U48 G4 0 0 -360000 480000 360000 -480000 v4 09 300 -270000 -360000 0 0 2060000 -360000 -540000 720000 -1250000 0 u5 U5
10 0 -360000 -480000 0 -937500 -360000 2377500 720000 -960000 0 0 v5 V511 0 -540000 -720000 -540000 720000 -540000 720000 2160000 0 -540000 -720000 u6 U612 0 -720000 -960000 720000 -960000 720000 -960000 0 3840000 -720000 -960000 v6 V613 0 0 0 -270000 360000 -1250000 0 -540000 -720000 2060000 360000 u7 U714 -700 0 -937500 360000 -480000 0 0 -720000 -960000 360000 2377500 v7 V7
1 2 3 4 5 6 7 8 9 10 11 12 13 14Rearrangement
3 0 3040000 720000 -1250000 0 0 0 0 -540000 -720000 0 0 -1250000 0 0 U24 0 720000 1897500 0 0 0 0 -937500 -720000 -960000 0 0 0 0 0 V25 0 -1250000 0 3040000 -720000 -1250000 0 0 -540000 720000 0 0 0 0 0 U36 0 0 0 -720000 1897500 0 0 0 720000 -960000 0 -937500 0 0 0 V37 0 0 0 -1250000 0 1520000 0 0 0 0 -270000 360000 0 0 -360000 U49 300 0 0 0 0 0 2060000 -360000 -540000 720000 -1250000 0 -270000 -360000 0 U5
10 0 = 0 -937500 0 0 0 -360000 2377500 720000 -960000 0 0 -360000 -480000 0 V511 0 -540000 -720000 -540000 720000 0 -540000 720000 2160000 0 -540000 -720000 0 0 0 U612 0 -720000 -960000 720000 -960000 0 720000 -960000 0 3840000 -720000 -960000 0 0 0 V613 0 0 0 0 0 -270000 -1250000 0 -540000 -720000 2060000 360000 0 0 360000 U714 -700 0 0 0 -937500 360000 0 0 -720000 -960000 360000 2377500 0 0 -480000 V71 F1 -1250000 0 0 0 0 -270000 -360000 0 0 0 0 1520000 360000 0 02 G1 0 0 0 0 0 -360000 -480000 0 0 0 0 360000 480000 0 08 G4 0 0 0 0 -360000 0 0 0 0 360000 -480000 0 0 480000 0
3 4 5 6 7 9 10 11 12 13 14 1 2 8Unknown Displacement and Reaction
0 3040000 720000 -1250000 0 0 0 0 -540000 -720000 0 0 U20 720000 1897500 0 0 0 0 -937500 -720000 -960000 0 0 V20 -1250000 0 3040000 -720000 -1250000 0 0 -540000 720000 0 0 U30 0 0 -720000 1897500 0 0 0 720000 -960000 0 -937500 V30 0 0 -1250000 0 1520000 0 0 0 0 -270000 360000 U4
300 = 0 0 0 0 0 2060000 -360000 -540000 720000 -1250000 0 U50 0 -937500 0 0 0 -360000 2377500 720000 -960000 0 0 V50 -540000 -720000 -540000 720000 0 -540000 720000 2160000 0 -540000 -720000 U60 -720000 -960000 720000 -960000 0 720000 -960000 0 3840000 -720000 -960000 V60 0 0 0 0 -270000 -1250000 0 -540000 -720000 2060000 360000 U7
-700 0 0 0 -937500 360000 0 0 -720000 -960000 360000 2377500 V7
U2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 U2 #VALUE!V2 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 V2 #VALUE!U3 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 U3 #VALUE!V3 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 V3 #VALUE!U4 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 > U4 #VALUE!
U5 = #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 300 U5 = #VALUE!V5 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 V5 #VALUE!U6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 U6 #VALUE!V6 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 V6 #VALUE!U7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! 0 U7 #VALUE!V7 #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE! -700 V7 #VALUE!
Gaya BatangBatang 1
f1g1 =f2g2
f1 1 0 0 0 1250000 0 -1250000 0 0g1 = 0 1 0 0 0 0 0 0 0f2 0 0 1 0 -1250000 0 1250000 0 #VALUE!g2 0 0 0 1 0 0 0 0 #VALUE!
1250000 0 -1250000 0 00 0 0 0 0
-1250000 0 1250000 0 #VALUE!0 0 0 0 #VALUE!
f1 #VALUE!g1 = #VALUE!f2 #VALUE!g2 #VALUE!
Batang 2f2 1 0 0 0 1250000 0 -1250000 0 #VALUE!g2 = 0 1 0 0 0 0 0 0 #VALUE!f3 0 0 1 0 -1250000 0 1250000 0 #VALUE!g3 0 0 0 1 0 0 0 0 #VALUE!
1250000 0 -1250000 0 #VALUE!0 0 0 0 #VALUE!
-1250000 0 1250000 0 #VALUE!0 0 0 0 #VALUE!
[T1] [Kg1] [U1]
f2 #VALUE!g2 = #VALUE!f3 #VALUE!g3 #VALUE!
Batang 3f3 1 0 0 0 1250000 0 -1250000 0 #VALUE!g3 = 0 1 0 0 0 0 0 0 #VALUE!f4 0 0 1 0 -1250000 0 1250000 0 #VALUE!g4 0 0 0 1 0 0 0 0 #VALUE!
1250000 0 -1250000 0 #VALUE!0 0 0 0 #VALUE!
-1250000 0 1250000 0 #VALUE!0 0 0 0 #VALUE!
f3 #VALUE!g3 = #VALUE!f4 #VALUE!g4 #VALUE!
Batang 4f1 0.6 0.8 0 0 270000 360000 -270000 -360000 0g1 = -0.8 0.6 0 0 360000 480000 -360000 -480000 0f5 0 0 0.6 0.8 -270000 -360000 270000 360000 #VALUE!g5 0 0 -0.8 0.6 -360000 -480000 360000 480000 #VALUE!
450000 600000 -450000 -600000 00 0 0 0 0
-450000 -600000 450000 600000 #VALUE!0 0 0 0 #VALUE!
f1 #VALUE!g1 = #VALUE!f5 #VALUE!g5 #VALUE!
Batang 5f2 0 1 0 0 0 0 0 0 #VALUE!g2 = -1 0 0 0 0 937500 0 -937500 #VALUE!f5 0 0 0 1 0 0 0 0 #VALUE!g5 0 0 -1 0 0 -937500 0 937500 #VALUE!
0 937500 0 -937500 #VALUE!0 0 0 0 #VALUE!0 -937500 0 937500 #VALUE!
0 0 0 0 #VALUE!
f2 #VALUE!g2 = #VALUE!f5 #VALUE!g5 #VALUE!
Batang 6f2 0.6 0.8 0 0 540000 720000 -540000 -720000 #VALUE!g2 = -0.8 0.6 0 0 720000 960000 -720000 -960000 #VALUE!f6 0 0 0.6 0.8 -540000 -720000 540000 720000 #VALUE!g6 0 0 -0.8 0.6 -720000 -960000 720000 960000 #VALUE!
900000 1200000 -900000 -1200000 #VALUE! f2 #VALUE!0 0 0 0 #VALUE! > g2 = #VALUE!
-900000 -1200000 900000 1200000 #VALUE! f6 #VALUE!0 0 0 0 #VALUE! g6 #VALUE!
Batang 7f6 0.6 -0.8 0 0 540000 -720000 -540000 720000 #VALUE!g6 = 0.8 0.6 0 0 -720000 960000 720000 -960000 #VALUE!f3 0 0 0.6 -0.8 -540000 720000 540000 -720000 #VALUE!g3 0 0 0.8 0.6 720000 -960000 -720000 960000 #VALUE!
900000 -1200000 -900000 1200000 #VALUE!0 0 0 0 #VALUE!
-900000 1200000 900000 -1200000 #VALUE!0 0 0 0 #VALUE!
f6 #VALUE!g6 = #VALUE!f3 #VALUE!g3 #VALUE!
Batang 8f3 0 1 0 0 0 0 0 0 #VALUE!g3 = -1 0 0 0 0 937500 0 -937500 #VALUE!f7 0 0 0 1 0 0 0 0 #VALUE!g7 0 0 -1 0 0 -937500 0 937500 #VALUE!
0 937500 0 -937500 #VALUE!0 0 0 0 #VALUE!0 -937500 0 937500 #VALUE!0 0 0 0 #VALUE!
f3 #VALUE!g3 = #VALUE!f7 #VALUE!g7 #VALUE!
Batang 9f7 0.6 -0.8 0 0 270000 -360000 -270000 360000 #VALUE!g7 = 0.8 0.6 0 0 -360000 480000 360000 -480000 #VALUE!f4 0 0 0.6 -0.8 -270000 360000 270000 -360000 #VALUE!g4 0 0 0.8 0.6 360000 -480000 -360000 480000 0
450000 -600000 -450000 600000 #VALUE!0 0 0 0 #VALUE!
-450000 600000 450000 -600000 #VALUE!0 0 0 0 0
f7 #VALUE!g7 = #VALUE!f4 #VALUE!g4 #VALUE!
Batang 10 f5 0.6 -0.8 0 0 540000 -720000 -540000 720000 #VALUE!g5 = 0.8 0.6 0 0 -720000 960000 720000 -960000 #VALUE!f6 0 0 0.6 -0.8 -540000 720000 540000 -720000 #VALUE!g6 0 0 0.8 0.6 720000 -960000 -720000 960000 #VALUE!
900000 -1200000 -900000 1200000 #VALUE!0 0 0 0 #VALUE!
-900000 1200000 900000 -1200000 #VALUE!0 0 0 0 #VALUE!
f5 #VALUE!g5 = #VALUE!f6 #VALUE!g6 #VALUE!
Batang 11f6 0.6 0.8 0 0 540000 720000 -540000 -720000 #VALUE!g6 = -0.8 0.6 0 0 720000 960000 -720000 -960000 #VALUE!f7 0 0 0.6 0.8 -540000 -720000 540000 720000 #VALUE!g7 0 0 -0.8 0.6 -720000 -960000 720000 960000 #VALUE!
900000 1200000 -900000 -1200000 #VALUE!0 0 0 0 #VALUE!
-900000 -1200000 900000 1200000 #VALUE!0 0 0 0 #VALUE!
f6 #VALUE!g6 = #VALUE!f7 #VALUE!
g7 #VALUE!
Batang 12f5 1 0 0 0 1250000 0 -1250000 0 #VALUE!g5 = 0 1 0 0 0 0 0 0 #VALUE!f7 0 0 1 0 -1250000 0 1250000 0 #VALUE!g7 0 0 0 1 0 0 0 0 #VALUE!
1250000 0 -1250000 0 #VALUE!0 0 0 0 #VALUE!
-1250000 0 1250000 0 #VALUE!0 0 0 0 #VALUE!
f5 #VALUE!g5 = #VALUE!f7 #VALUE!g7 #VALUE!
Reaksi Perletakan
#VALUE!#VALUE!#VALUE!#VALUE!
F1 -1250000 0 0 0 0 -270000 -360000 0 0 0 0 #VALUE! #VALUE!G1 = 0 0 0 0 0 -360000 -480000 0 0 0 0 #VALUE! = #VALUE!G4 0 0 0 0 -360000 0 0 0 0 360000 -480000 #VALUE! #VALUE!
#VALUE!#VALUE!#VALUE!#VALUE!
Hasil Komparasi Matriks dan SAP2000
Batang Matriks SAP20001 #VALUE! 583.332 #VALUE! 6253 #VALUE! 666.674 #VALUE! -138.895 #VALUE! 55.56
6 #VALUE! -69.447 #VALUE! 69.448 #VALUE! -55.569 #VALUE! -1111.11
10 #VALUE! 69.4411 #VALUE! -69.4412 #VALUE! -625
E = 21000A = 600I = 10000
Matrik kekakuan lokal batang1L = 500 cm = 1.25E+08
sin 270 = -1cos270 = 0
(K1) = 25200 0 0 -25200 0
0 20.16 5040 0 -20.16
0 5040 1680000 0 -5040
-25200 0 0 25200 0
0 -20.16 -5040 0 20.16
0 5040 840000 0 -5040
0 -1 0 0 0 01 0 0 0 0 0
= 0 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1
0 -1 0 0 0 01 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1
0 -20.16 -5040 0 20.16 -5040(Kg) = 25200 0 0 -25200 0 0
0 5040 1680000 0 -5040 840000
Kn/cm²cm²cm⁴
L³
[T(1)]
[T(1)]T =
0 20.16 5040 0 -20.16 5040-25200 0 0 25200 0 0
0 5040 840000 0 -5040 1680000
u1 v1 θ1 u2 v2 θ2(Kg1) = 20.16 0 -5040 -20.16 0 -5040
0 25200 0 0 -25200 0-5040 0 1680000 5040 0 840000-20.16 0 5040 20.16 0 5040
0 -25200 0 0 25200 0-5040 0 840000 5040 0 1680000
Matrik kekakuan lokal batang 2L = 500 cm
= 1.25E+08 = 250000
(K) = 25200 0 0 -25200 0 00 20.16 5040 0 -20.16 50400 5040 1680000 0 -5040 840000
-25200 0 0 25200 0 00 -20.16 -5040 0 20.16 -50400 5040 840000 0 -5040 1680000
u2 v2 θ2 u3 v3 θ3(Kg2) = 25200 0 0 -25200 0 0
0 20.16 5040 0 -20.16 50400 5040 1680000 0 -5040 840000
-25200 0 0 25200 0 00 -20.16 -5040 0 20.16 -50400 5040 840000 0 -5040 1680000
Matrik kekakuan lokal batang 3L = 300 cm
= 27000000 = 90000sin 270 = -1cos 270 = 0
L³ L²
L³ L²
(K3) = 42000 0 0 -42000 0 00 93.33333 14000 0 -93.333333 140000 14000 2800000 0 -14000 1400000
-42000 0 0 42000 0 00 -93.33333 -14000 0 93.333333 -140000 14000 1400000 0 -14000 2800000
(T) = 0 -1 0 0 0 01 0 0 0 0 00 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1
0 1 0 0 0 0-1 0 0 0 0 00 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1
(Kg3) = 0 93.33333 14000 0 -93.333333 14000-42000 0 0 42000 0 0
0 14000 2800000 0 -14000 14000000 -93.33333 -14000 0 93.333333 -14000
42000 0 0 -42000 0 00 14000 1400000 0 -14000 2800000
u3 v3 θ3 u4 v4 θ4(Kg3) = 93.333333 0 14000 -93.33333 0 14000
0 42000 0 0 -42000 014000 0 2800000 -14000 0 1400000
-93.333333 0 -14000 93.33333 0 -140000 -42000 0 0 42000 0
14000 0 1400000 -14000 0 2800000
[T(1)]T =
overal stiffness
u1 v1 θ1 u2 v2 θ220.16 0 -5040 -20.16 0 -5040
0 25200 0 0 -25200 0-5040 0 1680000 5040 0 840000-20.16 0 5040 25220.16 0 5040
0 -25200 0 0 25220.16 5040-5040 0 840000 5040 5040 3360000
0 0 0 -25200 0 00 0 0 0 -20.16 -50400 0 0 0 5040 8400000 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0
= 250000
0 0 0 0 0
5040 0 0
840000 0 4EI/L 0 2EI/L
0 0 0 0 0
-5040 0 0
1680000 0 2EI/L 0 4EI/L
0 0 0 0
0 0 0 0
0 0 1 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0 0 1
0 1 0 0 0 0X -1 0 0 0 0 0
0 0 1 0 0 0
L²
AE/L1 -AE/L1
12EI/L3 6EI/L2 -12EI/L3 6EI/L2
6EI/L2 -6EI/L2
-AE/L1 AE/L1
-12EI/L3 -6EI/L2 12EI/L3 -6EI/L2
6EI/L2 -6EI/L2
u21 v2
1 q21 u1
1 v11 q1
1
cos a sin a
-sin a cos a
cos a sin a-sin a cos a
0 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1
u1v1θ1u2v2θ2
u2v2θ2u3v3θ3
0 -1 0 0 0 01 0 0 0 0 0
X 0 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1
u3v3θ3u4v4θ4
u3 v3 θ3 u4 v4 θ40 0 0 0 0 0 u10 0 0 0 0 0 v10 0 0 0 0 0 θ1
-25200 0 0 0 0 0 u20 -20.16 5040 0 0 0 v20 -5040 840000 0 0 0 θ2
25293.333333333 0 14000 -93.33333 0 14000 u30 42020.16 -5040 0 -42000 0 v3
14000 -5040 4480000 -14000 0 1400000 θ3-93.333333333333 0 -14000 93.33333 0 -14000 u4
0 -42000 0 0 42000 0 v414000 0 1400000 -14000 0 2800000 θ4
u21
v21
q21
u11
v11
q11
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