E A
= =
200000 11000
Mpa cm2 4 T
1
2
300 cm
3
800 cm
Batang 1
L EA/L sin α cos α
= = = =
50 5000 440000 0 .8 0 .6
mm
Matriks kekakuan [KI,1]
=
440000
Matriks transformasi 0.6 [T] = -0 - 0.8 0 0
[TT].[K1]
[Kg]
=
264000 352000 -264000 -352000
1 0 -1 0
0 0 0 0
-1 0 1 0
0.8 0.6 0 0
0 0 0.6 -0 -0.8
0 0 0.8 0.6
0 0 0 0
-264000 -352000 264000 352000
0 0 0 0
=
[TT]
[K1]
= = =
50 50 0 4400000 0 .6
cm
Batang 2
L EA/L sin α
[T]
=
0 0 0 0
=
[TT] =
u1 158400 211200 -158400 -211200
v1 21 211200 281600 -211200 -281600
440000 0 -440000 0
0 0 0 0
-440000 0 440000 0
0 0 0 0
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0 .6
u2 -158400 -2 -211200 158400 211200
v2 -211200 -281600 211200 281600
u1 v1 u2 v2
cos α
=
0 .8
Matriks kekakuan [KI,2]
=
4400000
Matriks transformasi 0.6 [T] = 0.8 0 0
[TT].[K2]
[Kg]
=
264000 -352000 -264000 352000
1 0 -1 0
0 0 0 0
-1 0 1 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
0 0 0 0
-264000 352000 264000 -352000
0 0 0 0
0 0 0 0
[TT] =
[T]
=
u2 158400 -211200 -158400 211200
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-2750000 0 2750000 0
0 0 0 0
=
[TT]
[K2]
= = = =
80 80 0 2750000 0 1
cm
=
v2 -211200 281600 211200 -281600
440000 0 -440000 0
0 0 0 0
-440000 0 440000 0
0 0 0 0
0.6 - 0 .8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0 .8 0 .6
u3 -158400 211200 158400 -211200
v3 211200 -281600 -211200 281600
u2 v2 u3 v3
2750000 0 -2750000 0
0 0 0 0
-3E+06 0 2750000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u3 -2750000 0 2750000 0
v3 0 0 0 0
u1 v1 u3 v3
Batang 3
L EA/L sin α cos α
Matriks kekakuan [KI,3]
=
2750000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K3]
[Kg]
=
=
2750000 0 -2750000 0
[TT]
[K3]
[T]
=
=
[TT] =
u1 2750000 0 -3E+06 0
v1 0 0 0 0
cos α
=
0 .8
Matriks kekakuan [KI,2]
=
4400000
Matriks transformasi 0.6 [T] = 0.8 0 0
[TT].[K2]
[Kg]
=
264000 -352000 -264000 352000
1 0 -1 0
0 0 0 0
-1 0 1 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
0 0 0 0
-264000 352000 264000 -352000
0 0 0 0
0 0 0 0
[TT] =
[T]
=
u2 158400 -211200 -158400 211200
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-2750000 0 2750000 0
0 0 0 0
=
[TT]
[K2]
= = = =
80 80 0 2750000 0 1
cm
=
v2 -211200 281600 211200 -281600
440000 0 -440000 0
0 0 0 0
-440000 0 440000 0
0 0 0 0
0.6 - 0 .8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0 .8 0 .6
u3 -158400 211200 158400 -211200
v3 211200 -281600 -211200 281600
u2 v2 u3 v3
2750000 0 -2750000 0
0 0 0 0
-3E+06 0 2750000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u3 -2750000 0 2750000 0
v3 0 0 0 0
u1 v1 u3 v3
Batang 3
L EA/L sin α cos α
Matriks kekakuan [KI,3]
=
2750000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K3]
[Kg]
=
=
2750000 0 -2750000 0
[TT]
[K3]
[T]
=
=
[TT] =
u1 2750000 0 -3E+06 0
v1 0 0 0 0
Overall Stiffness
F1 G1 0 -4 0 G3
=
u1 29084 29 08400 00 2112 21 1200 00 -158400 -211200 -2750000 0
v1 2E+0 2E +05 5 3E+0 3E +05 5 -2E+05 -3E+05 0 0
u2 -158400 -211200 316800 0 -1 -158400 211200
v2 u3 -211200 -2750000 -281600 0 0 -158400 563200 211200 211200 290 29084 8400 00 -281600 -2 -211 1120 200 0
v3 0 0 211200 -281600 -211 -2 1120 200 0 2816 28 1600 00
=
u2 316800 0 -158400 -158400 -211200 211200
v2 0 6E+05 2E+05 -2E+05 -3E+05 -3E+05
u3 -158400 211200 2908400 -3E+06 0 -211200
u1 -158400 -211200 -3E+06 2908400 211200 0
v3 211200 -281600 -211200 0 0 281600
u1 v1 u2 v2 u3 v3
0 0 U2 V2 U3 0
Rearrangement
0 -4 0 F1 G1 G3
v1 -211200 -281600 0 211200 281600 0
U2 V2 U3 0 0 0
Unknown Displacement and Reaction
0 -4 0 U2 V2 U3
=
316800 0 -158400
0 -158400 6E+05 211200 2E+05 2908400
=
3.247E-06 -7E-08 1.8E-07 -6 - 6.818E-08 2E-06 -1E-07 1.818E-07 -1E-07 3.6E-07
U2 V2 U3
=
2.727E-07 -7.307E-06 5.455E-07
F1 G1 G3
=
-158400 -211200 211200
-2E+05 -3E+06 -3E+05 0 -3E+05 -211200
U2 V2 U3 0 -4 0
2.727E-07 -7.31E-06 5.455E-07
F1 G1 G3
=
Gaya Batang Batang 1
f1 g1 f2 g2 f1 g1 f2 g2
=
=
[T1]
[Kg1]
[U1]
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
264000 0 -264000 0 f1 g1 f2 g2
=
0 0 0.8 0.6
4E+05 -264000 -352000 0 0 0 -4E+05 264000 352000 0 0 0
158400 211200 -158400 -211200
211200 281600 -211200 -281600
-2E+05 -2E+05 2E+05 2E+05
-2E+05 -3E+05 2E+05 3E+05
-211200 281600 211200 -281600
-2E+05 2E+05 2E+05 -2E+05
2E+05 -3E+05 -2E+05 3E+05
0 0 2.727E-07 -7.31E-06
2.5 0 -2.5 0
Batang 2
f2 g2 f3 g3 f2 g2 f3 g3
=
=
[T2]
[Kg2]
[U2]
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
264000 0 -264000 0 f2 g2 f3 g3
=
2.5 0 -2.5 0
0 0 -0.8 0.6
-4E+05 -264000 352000 0 0 0 4 E+05 264000 -352000 0 0 0
158400 -211200 -158400 211200 2.727E-07 -7.31E-06 5.455E-07 0
Batang 3
f1 g1 f3 g3 f1 g1 f3 g3
f1 g1 f3 g3
=
=
=
[T3]
[Kg3]
[U3]
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
2750000 0 -2750000 0
2750000 0 -2750000 0
0 0 0 0
-3E+06 0 2750000 0
0 0 0 0
0 0 5.455E-07 0
-1.5 0 1.5 0
1 = -3.333 T
2 = -3.333 T
3 = 2.667 T
2 T
2 T
0 0 0 0
-3E+06 0 3E+06 0
0 0 0 0
luas 1 6000 luas 2 5000 A 11000
[T]
[Kg]
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
440000 0 -440000 0
0 0 0 0
-440000 0 440000 0
0 0 0 0
[TT] =
1 0 0 0
0 1 0 0
0 0 1 0
0 2 2
0 0 3E-07 -7E-06
3E-07 -7E-06 5E-07 0
u2 v2
0 0 5E-07 0
0 0 0 1
E A
= =
200000 11000
Mpa cm2
= = = =
3000 733333.3 0 1
mm
Batang 1
L EA/L sin α cos α
Matriks kekakuan
[KI,1]
[T]
=
=
[TT].[K1]
1 0 -1 0
0 0 0 0
-1 0 1 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333 0
0 0 0 0
-733333 0 733333.3 0
0 0 0 0
1 0 -1 0
0 0 0 0
-1 0 1 0
733333.3
0 0 0 0
733333.3 0 -733333 0
[TT] =
1 0 0 0
733333.3 0 -733333 0
[Kg]
Batang 2
L EA/L sin α cos α
= = = =
5000 440000 0 1
matriks kekakuan
[KI,2]
=
440000
0 0 0 0
=
440000 0 -440000 0
[T]
[TT].[K2]
=
=
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
440000 0 -440000 0
0 0 0 0
-440000 0 440000 0
0 0 0 0
1 0 -1 0
0 0 0 0
-1 0 1 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333 0
0 0 0 0
-733333 0 733333.3 0
0 0 0 0
[TT] =
1 0 0 0
440000 0 -440000 0
[Kg]
Batang 3
L EA/L sin α cos α
= = = =
3000 733333.3 0 1
matriks kekakuan
[KI,3]
[T]
[TT].[K3]
=
=
=
733333.3
0 0 0 0
=
[TT] =
[Kg]
733333.3 0 -733333 0
1 0 0 0
733333.3 0 -733333 0
Batang 4
L EA/L sin α cos α
= = = =
5000 440000 0.8 0.6
matriks kekakuan
[KI,4]
[T]
[TT].[K4]
=
=
=
1 0 -1 0
0 0 0 0
-1 0 1 0
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
264000 352000 -264000 -352000
0 0 0 0
-264000 -352000 264000 352000
0 0 0 0
1 0 -1 0
0 0 0 0
-1 0 1 0
1
0
0
440000
0 0 0 0
=
[TT] =
440000 0 -440000 0
0.6 0.8 0 0
158400 211200 -158400 -211200
[Kg]
Batang 5
L EA/L sin α cos α
= = = =
4000 550000 1 0
matriks kekakuan
[KI,5]
=
550000
0
0 0 0 0
=
550000 0 -550000 0
0
[T]
=
[TT].[K5]
=
-1 0 0
0 0 0
0 0 -1
0 1 0
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
0 0 0 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0.93 -0.37 0 0
0.37 0.93 0 0
0 0 0.93 -0.37
0 0 0.37 0.93
379933 151156.1 -379933 -151156
0 0 0 0
-379933 -151156 379933 151156.1
0 0 0 0
[TT] =
1 0 0
0 0 0 0
[Kg]
Batang 6
L EA/L sin α cos α
= = = =
5385.16 408530.1 0.37 0.93
matriks kekakuan
[KI,6]
=
[T]
408530.1
=
[TT].[K6]
=
Batang 7
L EA/L sin α cos α
= = = =
5385.16 408530.1 0.37 0.93
0 0 0 0
408530.1 0 -408530 0
=
[TT] =
[Kg]
0.93 0.37 0 0
353337.7 140575.2 -353338 -140575
matriks kekakuan
[KI,7]
[T]
[TT].[K7]
=
1 0 -1 0
0 0 0 0
-1 0 1 0
0.93 0.37 0 0
-0.37 0.93 0 0
0 0 0.93 0.37
0 0 -0.37 0.93
379933 -151156 -379933 151156.1
0 0 0 0
-379933 151156.1 379933 -151156
0 0 0 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
0 0 0 0
408530.1
=
=
0 0 0 0
408530.1 0 -408530 0
=
[TT] =
0.93 -0.37 0 0
353337.7 -140575 -353338 140575.2
[Kg]
Batang 8
L EA/L
= = = =
sin α cos α
4000 550000 1 0
matriks kekakuan
[KI,8]
[T]
[TT].[K8]
=
=
=
550000
0 0 0 0
=
[TT] =
[Kg]
550000 0 -550000 0
0 1 0 0
0 0 0 0
0 0 0 0
-733333 0 733333.3 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-733333 0 733333.3 0
0 0 0 0
0 0 0 0
-440000 0 440000 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-440000 0 440000 0
0 0 0 0
0 0 0 0
-733333 0 733333.3 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-733333 0 733333.3 0
0 0 0 0
0 0 0 0
-440000 0 440000 0
0 0 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
211200 281600 -211200 -281600
-158400 -211200 158400 211200
-211200 -281600 211200 281600
0 0 0 0
-550000 0 550000 0
0 0 0 0
-1
0
0
0 0 0
0 0 1
0 -1 0
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
0 0 0 0
-408530 0 408530.1 0
0 0 0 0
-0.37 0.93 0 0
0 0 0.93 0.37
0 0 -0.37 0.93
140575.2 -353338 -140575 55927.77 -140575 -55927.8 -140575 353337.7 140575.2 -55927.8 140575.2 55927.77
0 0 0 0
-408530 0 408530.1 0
0 0 0 0
0.37 0.93 0 0
0 0 0.93 -0.37
0 0 0.37 0.93
-140575 -353338 140575.2 55927.77 140575.2 -55927.8 140575.2 353337.7 -140575 -55927.8 -140575 55927.77
0 0 0 0
-550000 0 550000 0
0 0 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
Unknown Displacement and Reaction
0 0 0 0 0 300 0 0 0 0 -700 U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7 U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7
=
1783467 422400 -733333.3 0 0 0 0 -316800 -422400 0 0
422400 1113200 0 0 0 0 -550000 -422400 -563200 0 0
-733333.3 0 1783467 -422400 -733333.3 0 0 -316800 422400 0 0
0 0 -422400 1113200 0 0 0 422400 -563200 0 -550000
0 0 0 0 -733333.3 0 0 0 891733.3 0 0 1208533 0 -211200 0 -316800 0 422400 -158400 -733333.3 211200 0
0 -550000 0 0 0 -211200 1394800 422400 -563200 0 0
-316800 -422400 -316800 422400 0 -316800 422400 1267200 0 -316800 -422400
-422400 -563200 422400 -563200 0 422400 -563200 0 2252800 -422400 -563200
0 0 0 0 -158400 -733333.3 0 -316800 -422400 1208533 211200
0 0 0 -550000 211200 0 0 -422400 -563200 211200 1394800
U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7
=
1.36E-06 -6.82E-07 1.36E-06 -3.41E-07 1.36E-06 9.09E-07 -6.82E-07 1.14E-06 -5.11E-07 9.09E-07 -3.41E-07
-6.82E-07 4.02E-06 -1.04E-06 2.34E-06 -1.38E-06 -5.47E-07 2.78E-06 -1.35E-07 3.05E-06 1.16E-07 2.31E-06
1.36E-06 -1.04E-06 2.64E-06 -7.01E-07 2.64E-06 1.59E-06 -1.19E-06 1.78E-06 - 1.2E-06 1.51E-06 -8.52E-07
-3.41E-07 2.34E-06 -7.01E-07 4.02E-06 -1.38E-06 -1.5E-06 2.31E-06 -1.25E-06 3 .05E-06 -8.35E-07 2.78E-06
1.36E-06 -1.38E-06 2.64E-06 -1.38E-06 4.01E-06 2.05E-06 -1.53E-06 2E-06 -1.71E-06 1.96E-06 -1.53E-06
9.09E-07 -5.47E-07 1.59E-06 -1.5E-06 2.05E-06 3.37E-06 -9.51E-07 2.41E-06 -1.28E-06 2.69E-06 -1.09E-06
-6.82E-07 2.78E-06 -1.19E-06 2 .31E-06 -1.53E-06 -9.51E-07 3.08E-06 -1.02E-06 2.73E-06 - 4.4E-07 2E-06
1.14E-06 -1.35E-07 1.78E-06 -1.25E-06 2E-06 2.41E-06 -1.02E-06 3.25E-06 -8.57E-07 2 .37E-06 -5.16E-07
-5.11E-07 9.09E-07 3.054E-06 1.16E-07 -1.2E-06 1.51E-06 3.054E-06 -8.35E-07 -1.71E-06 1.96E-06 -1.28E-06 2.69E-06 2.734E-06 -4.4E-07 -8.57E-07 2.37E-06 3.626E-06 -4.36E-07 -4.36E-07 3.29E-06 2.734E-06 -5.83E-07
-3.41E-07 2.31E-06 -8.52E-07 2.78E-06 -1.53E-06 -1.09E-06 2E-06 -5.16E-07 2.73E-06 -5.83E-07 3.08E-06
0 0 0 0 0 300 0 0 0 0 -700
=
0.000511 -0.001779 0.001074 -0.002394 0.001688 0.001778 -0.001688 0.001084 -0.002298 0.001215 -0.002485
=
[T1]
[Kg1]
[U1]
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0 0 0.000511 -0.001779
733333.3 0 -733333.3
0 0 0
-733333.3 0 733333.3
0 0 0
0 0 0.000511
0
0
0
0
-0.001779
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.000511 -0.001779 0.001074 -0.002394
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.000511 -0.001779 0.001074 -0.002394
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001074 -0.002394 0.001688 0.001778
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001074 -0.002394 0.001688 0 001778
Gaya Batang Batang 1
f1 g1 f2 g2 f1 g1 f2 g2
f1 g1 f2 g2
=
=
-375 0 375 0
Batang 2
f2 g2 f3 g3
f2 g2 f3 g3
=
=
-412.5 0 412.5 0
Batang 3
f3 g3 f4 g4
=
0 f1 g1 f2 g2
=
0
0
0
-0.001779
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333.3 0
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.000511 -0.001779 0.001074 -0.002394
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333.3 0
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001074 -0.002394 0.001688 0.001778
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
158400 211200 -158400 -211200
264000 0 -264000 0
352000 0 -352000 0
-264000 0 264000 0
-352000 0 352000 0
0 0 0.001778 -0.001688
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0.000511 -0.001779 0.001778 -0.001688
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
316800 422400 -316800 -422400
528000 0 -528000 0
704000 0 -704000 0
-528000 0 528000 0
-704000 0 704000 0
0.000511 -0.001779 0.001084 -0.002298
-375 0 375 0
Batang 2
f2 g2 f3 g3
f2 g2 f3 g3
=
=
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.000511 -0.001779 0.001074 -0.002394
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001074 -0.002394 0.001688 0.001778
211200 281600 -211200 -281600
-158400 -211200 158400 211200
-211200 -281600 211200 281600
0 0 0.001778 -0.001688
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
0.000511 -0.001779 0.001778 -0.001688
422400 563200 -422400 -563200
-316800 -422400 316800 422400
-422400 -563200 422400 563200
0.000511 -0.001779 0.001084 -0.002298
-412.5 0 412.5 0
Batang 3
f3 g3 f4 g4
f3 g3 f4 g4
=
=
-450 0 450 0
Batang 4
f1 g1 f5 g5
f1 g1 f5 g5
=
=
125 0 -125 0
Batang 5
f2 g2 f5 g5
f2 g2 f5 g5
=
=
-50 0 50 0
Batang 6
f2 g2 f6 g6
f2 g2 f6 g6
=
=
62.5 0 -62.5 0
f1 g1 f5 g5
=
125 0 -125 0
Batang 5
f2 g2 f5 g5
f2 g2 f5 g5
=
=
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0.000511 -0.001779 0.001778 -0.001688
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
316800 422400 -316800 -422400
528000 0 -528000 0
704000 0 -704000 0
-528000 0 528000 0
-704000 0 704000 0
0.000511 -0.001779 0.001084 -0.002298
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
316800 -422400 -316800 422400
528000 0 -528000 0
-704000 0 704000 0
-528000 0 528000 0
704000 0 -704000 0
0.001084 -0.002298 0.001074 -0.002394
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0.001074 -0.002394 0.001215 -0.002485
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
158400 -211200 -158400 211200
264000 0 -264000 0
-352000 0 352000 0
-264000 0 264000 0
352000 0 -352000 0
0.001215 -0.002485 0.001688 0
-0.8 0.6 0 0
0 0 0.6 08
0 0 -0.8 06
316800 -422400 -316800 422400
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
0.000511 -0.001779 0.001778 -0.001688
422400 563200 -422400 -563200
-316800 -422400 316800 422400
-422400 -563200 422400 563200
0.000511 -0.001779 0.001084 -0.002298
-422400 563200 422400 -563200
-316800 422400 316800 -422400
422400 -563200 -422400 563200
0.001084 -0.002298 0.001074 -0.002394
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
0.001074 -0.002394 0.001215 -0.002485
-211200 281600 211200 -281600
-158400 211200 158400 -211200
211200 -281600 -211200 281600
0.001215 -0.002485 0.001688 0
-422400 563200 422400 563200
-316800 422400 316800 422400
422400 -563200 -422400 563200
0.001778 -0.001688 0.001084 0 002298
-50 0 50 0
Batang 6
f2 g2 f6 g6
f2 g2 f6 g6
=
=
62.5 0 -62.5 0
Batang 7
f6 g6 f3 g3
f6 g6 f3 g3
=
=
-62.5 0 62.5 0
Batang 8
f3 g3 f7 g7
f3 g3 f7 g7
=
=
50 0 -50 0
Batang 9
f7 g7 f4 g4
f7 g7 f4 g4
=
=
750 0 -750 0
Batang 10
f5 g5 f6 g6
=
0.6 0.8 0 0
Batang 8
f3 g3 f7 g7
f3 g3 f7 g7
=
=
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0.001074 -0.002394 0.001215 -0.002485
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
158400 -211200 -158400 211200
264000 0 -264000 0
-352000 0 352000 0
-264000 0 264000 0
352000 0 -352000 0
0.001215 -0.002485 0.001688 0
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
316800 -422400 -316800 422400
528000 0 -528000 0
-704000 0 704000 0
-528000 0 528000 0
704000 0 -704000 0
0.001778 -0.001688 0.001084 -0.002298
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
316800 422400 -316800 -422400
528000 0 -528000 0
704000 0 -704000 0
-528000 0 528000 0
-704000 0 704000 0
0.001084 -0.002298 0.001215 -0.002485
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333.3 0
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001778 -0.001688 0.001215 -0.002485
0 550000 0 -550000
0 0 0 0
0 -550000 0 550000
0.001074 -0.002394 0.001215 -0.002485
-211200 281600 211200 -281600
-158400 211200 158400 -211200
211200 -281600 -211200 281600
0.001215 -0.002485 0.001688 0
-422400 563200 422400 -563200
-316800 422400 316800 -422400
422400 -563200 -422400 563200
0.001778 -0.001688 0.001084 -0.002298
422400 563200 -422400 -563200
-316800 -422400 316800 422400
-422400 -563200 422400 563200
0.001084 -0.002298 0.001215 -0.002485
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001778 -0.001688 0.001215 -0.002485
50 0 -50 0
Batang 9
f7 g7 f4 g4
f7 g7 f4 g4
=
=
750 0 -750 0
Batang 10
f5 g5 f6 g6
f5 g5 f6 g6
=
=
-62.5 0 62.5 0
Batang 11
f6 g6 f7 g7
f6 g6 f7 g7
=
=
62.5 0 -62.5 0
Batang 12
f5 g5 f7 g7
f5 g5 f7 g7
=
=
412.5 0 -412.5 0
Reaksi Perletakan
F1 G1 G4
=
-733333.3 0 0
0 0 0
0 0 0
0 0 0
0 0 -211200
-158400 -211200 0
-211200 -281600 0
0 0 0
0 0 0
0 0 211200
0 0 -281600
0.000511 -0.001779 0.001074 -0.002394 0.001688 0.001778 -0.001688 0.001084
=
-300 100 600
528000 0 -528000 0 f6 g6 f7 g7
704000 0 -704000 0
-528000 0 528000 0
-704000 0 704000 0
0.001084 -0.002298 0.001215 -0.002485
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
733333.3 0 -733333.3 0
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001778 -0.001688 0.001215 -0.002485
62.5 0 -62.5 0
=
Batang 12
f5 g5 f7 g7
=
f5 g5 f7 g7
0 0 0 0
-733333.3 0 733333.3 0
0 0 0 0
0.001778 -0.001688 0.001215 -0.002485
412.5 0 -412.5 0
=
Reaksi Perletakan
F1 G1 G4
E A
-733333.3 0 0
=
= =
200000 11000
Mpa cm2
= = = =
4000 550000 0 1
mm
=
EA/L
0 0 0
0 0 0
0 0 0
0 0 -211200
-158400 -211200 0
-211200 -281600 0
0 0 0
0 0 0
0 0 211200
0.000511 -0.001779 0.001074 -0.002394 0.001688 0.001778 -0.001688 0.001084 -0.002298 0.001215 -0.002485
0 0 -281600
Batang 1
L EA/L sin α cos α
[Kg,1]
[T1]
(S) (C) C² CS -(C²) -(CS)
1 0 0 0
0 1 0 0
= = = =
4000 550000 0 1
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 1 0
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 0 1
=
550000
[Kg,1] =
u1 550000 0 -550000 0
=
550000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
v1 0 0 0 0
u2 -550000 0 550000 0
v2 0 0 0 0
u1 v1 u2 v2
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
Batang 2
L EA/L sin α cos α
[Kg,2]
(S) (C) C² CS -(C²) -(CS)
CS S² -(CS) (S²)
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
=
-300 100 600
E A
= =
200000 11000
Mpa cm2
= = = =
4000 550000 0 1
mm
=
EA/L
Batang 1
L EA/L sin α cos α
[Kg,1]
[T1]
(S) (C) C² CS -(C²) -(CS)
1 0 0 0
0 1 0 0
= = = =
4000 550000 0 1
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 1 0
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 0 1
=
550000
[Kg,1] =
u1 550000 0 -550000 0
=
550000
[Kg,2] =
u2 550000 0 -550000 0
=
550000
[Kg,3] =
u3 550000 0 -550000 0
=
550000
[Kg,4] =
u4 550000 0 -550000 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
v1 0 0 0 0
u2 -550000 0 550000 0
v2 0 0 0 0
u1 v1 u2 v2
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
v2 0 0 0 0
u3 -550000 0 550000 0
v3 0 0 0 0
u2 v2 u3 v3
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
v3 0 0 0 0
u4 -550000 0 550000 0
v4 0 0 0 0
u3 v3 u4 v4
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
v4 0 0 0 0
u5 -550000 0 550000 0
v5 0 0 0 0
u4 v4 u5 v5
Batang 2
L EA/L sin α cos α
[Kg,2]
[T2]
(S) (C) C² CS -(C²) -(CS)
1 0 0 0
0 1 0 0
= = = =
4000 550000 0 1
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 1 0
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 0 1
Batang 3
L EA/L sin α cos α
[Kg,3]
[T3]
(S) (C) C² CS -(C²) -(CS)
1 0 0 0
0 1 0 0
= = = =
4000 550000 0 1
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 1 0
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 0 1
Batang 4
L EA/L sin α cos α
[Kg,4]
[T4]
=
(S) (C) C² CS -(C²) -(CS)
1 0 0 0
0 1 0 0
5000 440000 0.6 0.8
mm
Batang 5
L EA/L sin α cos α
= = = =
(S) (C)
CS S² -(CS) (S²)
0 0 1 0
-(C²) -(CS) C² CS
0 0 0 1
-(CS) (S²) CS S²
[Kg,5]
=
[T5]
EA/L
C² CS -(C²) -(CS)
0.8 -0.6 0 0
0.6 0.8 0 0
= = = =
3000 733333.3 1 0
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 0.8 -0.6
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 0.6 0.8
=
440000
[Kg,5] =
u1 281600 211200 -281600 -211200
=
733333.3
[Kg,6] =
u2 0 0 0 0
=
733333.3
[Kg,7] =
u6 469333.3 -352000 -469333.3 352000
=
366666.7
[Kg,8] =
u3 0 0 0 0
=
440000
0.64 0.48 -0.64 -0.48
0.48 0.36 -0.48 -0.36
-0.64 -0.48 0.64 0.48
-0.48 -0.36 0.48 0.36
v1 211200 158400 -211200 -158400
u6 -281600 -211200 281600 211200
v6 -211200 -158400 211200 158400
u1 v1 u6 v6
0 0 0 0
0 1 0 -1
0 0 0 0
0 -1 0 1
v2 0 733333.3 0 -733333.3
u6 0 0 0 0
v6 0 -733333.3 0 733333.3
u2 v2 u6 v6
0.64 -0.48 -0.64 0.48
-0.48 0.36 0.48 -0.36
-0.64 0.48 0.64 -0.48
0.48 -0.36 -0.48 0.36
v6 -352000 264000 352000 -264000
u3 -469333.3 352000 469333.3 -352000
v3 352000 -264000 -352000 264000
u6 v6 u3 v3
0 0 0 0
0 1 0 -1
0 0 0 0
0 -1 0 1
v3 0 366666.7 0 -366666.7
u7 0 0 0 0
v7 0 -366666.7 0 366666.7
u3 v3 u7 v7
0.64 0.48 -0.64 -0.48
0.48 0.36 -0.48 -0.36
-0.64 -0.48 0.64 0.48
-0.48 -0.36 0.48 0.36
v3 211200
u8 -281600
v8 -211200
u3
Batang 6
L EA/L sin α cos α
[Kg,6]
[T6]
(S) (C) C² CS -(C²) -(CS)
0 -1 0 0
1 0 0 0
= = = =
3000 733333.3 -0.6 0.8
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 0 -1
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 1 0
Batang 7
L EA/L sin α cos α
[Kg,7]
[T7]
(S) (C) C² CS -(C²) -(CS)
0.8 0.6 0 0
-0.6 0.8 0 0
= = = =
6000 366666.7 1 0
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 0.8 0.6
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 -0.6 0.8
Batang 8
L EA/L sin α cos α
[Kg,8]
[T8]
(S) (C) C² CS -(C²) -(CS)
0 -1 0 0
1 0 0 0
= = = =
5000 440000 0.6 0.8
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 0 -1
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 1 0
Batang 9
L EA/L sin α cos α
[Kg,9]
0.8
(S) (C) C² CS -(C²) -(CS)
0.6
CS S² -(CS) (S²)
0
-(C²) -(CS) C² CS
0
-(CS) (S²) CS S²
u3 281600
[T9]
=
-0.6 0 0
0.8 0 0
= = = =
3000 733333.3 1 0
mm
=
EA/L
0 0.8 -0.6
0 0.6 0.8
[Kg,9] =
211200 -281600 -211200
=
733333.3
[Kg,10] =
u4 0 0 0 0
=
440000
[Kg,11] =
u8 281600 -211200 -281600 211200
=
440000
[Kg,12] =
u6 281600 211200 -281600 -211200
=
440000
[Kg,13] =
u7 281600 -211200 -281600 211200
158400 -211200 -158400
-211200 281600 211200
-158400 211200 158400
v3 u8 v8
0 0 0 0
0 1 0 -1
0 0 0 0
0 -1 0 1
v4 0 733333.3 0 -733333.3
u8 0 0 0 0
v8 0 -733333.3 0 733333.3
u4 v4 u8 v8
0.64 -0.48 -0.64 0.48
-0.48 0.36 0.48 -0.36
-0.64 0.48 0.64 -0.48
0.48 -0.36 -0.48 0.36
v8 -211200 158400 211200 -158400
u5 -281600 211200 281600 -211200
v5 211200 -158400 -211200 158400
u8 v8 u5 v5
0.64 0.48 -0.64 -0.48
0.48 0.36 -0.48 -0.36
-0.64 -0.48 0.64 0.48
-0.48 -0.36 0.48 0.36
v6 211200 158400 -211200 -158400
u7 -281600 -211200 281600 211200
v7 -211200 -158400 211200 158400
u6 v6 u7 v7
0.64 -0.48 -0.64 0.48
-0.48 0.36 0.48 -0.36
-0.64 0.48 0.64 -0.48
0.48 -0.36 -0.48 0.36
v7 -211200 158400 211200 -158400
u8 -281600 211200 281600 -211200
v8 211200 -158400 -211200 158400
u7 v7 u8 v8
Batang 10
L EA/L sin α
cos α
[Kg,10]
[T10]
(S) (C) C² CS -(C²) -(CS)
0 -1 0 0
1 0 0 0
= = = =
5000 440000 -0.6 0.8
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 0 -1
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 1 0
Batang 11
L EA/L sin α cos α
[Kg,11]
[T11]
(S) (C) C² CS -(C²) -(CS)
0.8 0.6 0 0
-0.6 0.8 0 0
= = = =
5000 440000 0.6 0.8
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 0.8 0.6
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 -0.6 0.8
Batang 12
L EA/L sin α cos α
[Kg,12]
[T12]
(S) (C) C² CS -(C²) -(CS)
0.8 -0.6 0 0
0.6 0.8 0 0
= = = =
5000 440000 -0.6 0.8
mm
=
EA/L
=
CS S² -(CS) (S²)
0 0 0.8 -0.6
-(C²) -(CS) C² CS
-(CS) (S²) CS S²
0 0 0.6 0.8
Batang 13
L EA/L sin α cos α
[Kg,13]
[T13]
=
0.8 0.6 0 0
(S) (C) C² CS -(C²) -(CS)
-0.6 0.8 0 0
CS S² -(CS) (S²)
0 0 0.8 0.6
-(C²) -(CS) C² CS
0 0 -0.6 0.8
-(CS) (S²) CS S²
Overall Stiffness
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
F1 G1 0 0 0 0 0 0 0 G5 0 0 500 0 0 -1000
u1 831600 211200 -550000 0
v1 211200 158400 0 0
u2 -550000 0 1100000 0 -550000 0
v2 0 0 0 733333.3 0 0
=
-281600 -211200
1
-211200 -158400
2
0 0
3
u3
v3
-550000 0 1850933 -140800 -550000 0
0 0 -140800 789066.7 0 0
0 -469333.3 352000 -733333.3 352000 -264000 0 0 0 -366666.7 -281600 -211200 -211200 -158400 4 5 6
u4
v4
u5
v5
-550000 0 1100000 0 -550000 0
0 0 0 733333.3 0 0
-550000 0 831600 -211200
0 0 -211200 158400
u6 -281600 -211200 0 0 -469333.3 352000
1032533 70400 -281600 -211200 0 0 7
0 -733333.3 8
-281600 211200 9
211200 -158400 10
11
Rearrangement
3 4 5 6 7 8 9 11 12 13 14 15 16 1 2 10
0 0 0 0 0 0 0 0 0 500 0 0 -1000 F1 G1 G5
1100000 0 -550000 0 0 0 0 0 0 0 0 0 0 -550000 0 0 3
0 -550000 0 733333.3 0 0 0 1850933 -140800 0 -140800 789066.7 0 -550000 0 0 0 0 0 0 0 0 -469333.3 352000 -733333.3 352000 -264000 0 0 0 0 0 -366666.7 0 -281600 -211200 0 -211200 -158400 0 0 0 0 0 0 0 0 0 4 5 6
0 0 -550000 0 1100000 0 -550000 0 0 0 0 0 0 0 0 0 7
0 0 0 0 0 0 0 0 0 -550000 733333.3 0 0 831600 0 0 0 0 0 0 0 0 0 -281600 -733333.3 211200 0 0 0 0 0 -211200 8 9
0 0 0 -733333.3 -469333.3 352000 352000 -264000 0 0 0 0 0 0 1032533 70400 70400 1314133 -281600 -211200 -211200 -158400 0 0 0 0 -281600 -211200 -211200 -158400 0 0 11 12
0 0 0 0 0 0 0 -281600 -211200 563200 0 -281600 211200 0 0 0 13
0 0 0 -366666.7 0 0 0 -211200 -158400 0 683466.7 211200 -158400 0 0 0 14
=
1100000 0 -550000 0 0 0 0 0 0 0 0 0 0
0 -550000 0 733333.3 0 0 0 1850933 -140800 0 -140800 789066.7 0 -550000 0 0 0 0 0 0 0 0 -469333.3 352000 -733333.3 352000 -264000 0 0 0 0 0 -366666.7 0 -281600 -211200 0 -211200 -158400
0 0 -550000 0 1100000 0 -550000 0 0 0 0 0 0
0 0 0 0 0 733333.3 0 0 0 0 0 0 -733333.3
0 0 0 -733333.3 -469333.3 352000 352000 -264000 0 0 0 0 0 0 1032533 70400 70400 1314133 -281600 -211200 -211200 -158400 0 0 0 0
0 0 0 0 0 0 0 -281600 -211200 563200 0 -281600 211200
0 0 0 -366666.7 0 0 0 -211200 -158400 0 683466.7 211200 -158400
=
1.82E-06 -1.82E-06 1.82E-06 -1.21E-06 1.82E-06 -6.06E-07 1.82E-06 1.36E-06 -1.82E-06 1.18E-05 -3.64E-06 9.33E-06 -4.24E-06 6.26E-06 -4.85E-06 -4.25E-06 1.82E-06 -3.64E-06 3.64E-06 -2.42E-06 3.64E-06 -1.21E-06 3.64E-06 2.73E-06 -1.21E-06 9.33E-06 -2.42E-06 1.23E-05 -3.64E-06 9.33E-06 -4.85E-06 -4.63E-06 1.82E-06 -4.24E-06 3.64E-06 -3.64E-06 5.45E-06 -3.03E-06 5.45E-06 3.18E-06 -6.06E-07 6.26E-06 -1.21E-06 9.33E-06 -3.03E-06 1.24E-05 -4.85E-06 -3.51E-06 1.82E-06 -4.85E-06 3.64E-06 -4.85E-06 5.45E-06 -4.85E-06 7.27E-06 3.64E-06 1.36E-06 -4.25E-06 2.73E-06 -4.63E-06 3.18E-06 -3.51E-06 3.64E-06 4.08E-06 -1.82E-06 1.04E-05 -3.64E-06 9.33E-06 -4.24E-06 6.26E-06 -4.85E-06 -4.25E-06 9.09E-07 -1.24E-06 1.82E-06 -2.42E-06 2.73E-06 -3.61E-06 3.64E-06 2.71E-06 -1.21E-06 7.97E-06 -2.42E-06 9.55E-06 -3.64E-06 7.97E-06 -4.85E-06 -3.61E-06 1.36E-06 -1.34E-06 2.73E-06 -2.18E-07 3.18E-06 -1.23E-07 3.64E-06 1.89E-06 -6.06E-07 6.26E-06 -1.21E-06 9.33E-06 -3.03E-06 1.1E-05 -4.85E-06 -3.51E-06
=
Unknown Displacement and Reaction
0 0 0 0 0 0 0 0 0 500 0 0 -1000 U2 V2 U3 V3 U4 V4 U5 U6 V6 U7 V7 U8 V8
0 0 0 0 -550000 0 831600 0 0 0 0 -281600 211200
-1.82E-06 1.04E-05 -3.64E-06 9.33E-06 -4.24E-06 6.26E-06 -4.85E-06 -4.25E-06 1.04E-05 -1.24E-06 7.97E-06 -1.34E-06 6.26E-06
9.09E-07 -1.24E-06 1.82E-06 -2.42E-06 2.73E-06 -3.61E-06 3.64E-06 2.71E-06 -1.24E-06 5.37E-06 -2.42E-06 2.71E-06 -3.61E-06
-1.21E-06 7.97E-06 -2.42E-06 9.55E-06 -3.64E-06 7.97E-06 -4.85E-06 -3.61E-06 7.97E-06 -2.42E-06 9.55E-06 -1.24E-06 7.97E-06
U2 V2 U3 V3 U4 V4 U5 U6 V6 U7 V7 U8 V8
=
0.001061 -0.006883 0.002121 -0.010543 0.004394 -0.012839 0.006667 0.004866 -0.006883 0.006293 -0.009179 0.001476 -0.012839
Gaya Batang Batang 1
f1 g1 f2 g2 f1 g1 f2 g2
f1 g1 f2 g2
=
=
=
[T1]
[Kg1]
[U1]
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
550000 0 -550000 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0 0 0 0
0 0 0.001061 -0.006883
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
550000 0 -550000 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0 0 0 0
0.001061 -0.006883 0.002121 -0.010543
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
550000 0 -550000 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0 0 0 0
0.002121 -0.010543 0.004394 -0.012839
0 0 0 0
-550000 0 550000 0
0 0 0 0
0 0 0.001061 -0.006883
0 0 0 0
-550000 0 550000 0
0 0 0 0
0.001061 -0.006883 0.002121 -0.010543
0 0 0 0
-550000 0 550000 0
0 0 0 0
0.002121 -0.010543 0.004394 -0.012839
-583.3333 0 583.3333 0
Batang 2
f2 g2 f3 g3
f2 g2 f3 g3
=
=
-583.3333 0 583.3333 0
Batang 3
f3 g3 f4 g4
f3 g3
=
=
-1250 0
f4 g4
1250 0
Batang 4
f4 g4 f5 g5
f4 g4 f5 g5
=
=
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
550000 0 -550000 0
550000 0 -550000 0
0 0 0 0
-550000 0 550000 0
0 0 0 0
0.004394 -0.012839 0.006667 0
0.8 -0.6 0 0
0.6 0.8 0 0
0 0 0.8 -0.6
0 0 0.6 0.8
281600 211200 -281600 -211200
352000 -2.91E-11 -352000 2.91E-11
264000 0 -264000 0
-352000 2.91E-11 352000 -2.91E-11
-264000 0 264000 0
0 0 0.004866 -0.006883
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0.001061 -0.006883 0.004866 -0.006883
0.8 0.6 0 0
-0.6 0.8 0 0
0 0 0.8 0.6
0 0 -0.6 0.8
469333.3 -352000 -469333.3 352000
586666.7 5.82E-11 -586666.7 -5.82E-11
-440000 0 440000 0
-586666.7 -5.82E-11 586666.7 5.82E-11
440000 0 -440000 0
0.004866 -0.006883 0.002121 -0.010543
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
-550000 0 550000 0
0 0 0 0
0.004394 -0.012839 0.006667 0
211200 158400 -211200 -158400
-281600 -211200 281600 211200
-211200 -158400 211200 158400
0 0 0.004866 -0.006883
0 733333.3 0 -733333.3
0 0 0 0
0 -733333.3 0 733333.3
0.001061 -0.006883 0.004866 -0.006883
-352000 264000 352000 -264000
-469333.3 352000 469333.3 -352000
352000 -264000 -352000 264000
0.004866 -0.006883 0.002121 -0.010543
0 366666.7 0 -366666.7
0 0 0 0
0 -366666.7 0 366666.7
0.002121 -0.010543 0.006293 -0.009179
-1250 0 1250 0
Batang 5
f1 g1 f6 g6
f1 g1 f6 g6
=
=
104.1667 1.42E-13 -104.1667 -1.42E-13
Batang 6
f2 g2 f6 g6
f2 g2 f6 g6
=
=
0 0 0 0
Batang 7
f6 g6 f3 g3
f6 g6 f3 g3
=
=
-2.73E-12 1.6E-13 2.73E-12 -1.6E-13
Batang 8
f3 g3 f7 g7
=
0 -1 0 0
0 0 0 0 f3 g3 f7 g7
=
366666.7 0 -366666.7 0
0 0 0 0
-366666.7 0 366666.7 0
0.002121 -0.010543 0.006293 -0.009179
0.8 -0.6 0 0
0.6 0.8 0 0
0 0 0.8 -0.6
0 0 0.6 0.8
281600 211200 -281600 -211200
352000 -2.91E-11 -352000 2.91E-11
264000 0 -264000 0
-352000 2.91E-11 352000 -2.91E-11
-264000 0 264000 0
0.002121 -0.010543 0.001476 -0.012839
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
733333.3 0 -733333.3 0
0 0 0 0
-733333.3 0 733333.3 0
0.004394 -0.012839 0.001476 -0.012839
0.8 0.6 0 0
-0.6 0.8 0 0
0 0 0.8 0.6
0 0 -0.6 0.8
281600 -211200 -281600 211200
352000 2.91E-11 -352000 -2.91E-11
-264000 0 264000 0
-352000 -2.91E-11 352000 2.91E-11
264000 0 -264000 0
0.001476 -0.012839 0.006667 0
0.8 -0.6 0 0
0.6 0.8 0 0
0 0 0.8 -0.6
0 0 0.6 0.8
281600 211200 -281600 -211200
352000 -2.91E-11 -352000 2.91E-11
264000 0 -264000 0
-352000 2.91E-11 352000 -2.91E-11
-264000 0 264000 0
0.004866 -0.006883 0.006293 -0.009179
-500 0 500 0
Batang 9
f3 g3 f8 g8
f3 g3 f8 g8
=
=
211200 158400 -211200 -158400
-281600 -211200 281600 211200
-211200 -158400 211200 158400
0.002121 -0.010543 0.001476 -0.012839
0 733333.3 0 -733333.3
0 0 0 0
0 -733333.3 0 733333.3
0.004394 -0.012839 0.001476 -0.012839
-211200 158400 211200 -158400
-281600 211200 281600 -211200
211200 -158400 -211200 158400
0.001476 -0.012839 0.006667 0
211200 158400 -211200 -158400
-281600 -211200 281600 211200
-211200 -158400 211200 158400
0.004866 -0.006883 0.006293 -0.009179
833.3333 -1.88E-14 -833.3333 1.88E-14
Batang 10
f4 g4 f8 g8
f4 g4 f8 g8
=
=
0 0 0 0
Batang 11
f8 g8 f5 g5
f8 g8 f5 g5
=
=
1562.5 -1.51E-13 -1562.5 1.51E-13
Batang 12
f6 g6 f7 g7
f6 g6
=
=
104.1667 4.15E-14
f7 g7
-104.1667 -4.15E-14
Batang 13
f7 g7 f8 g8
f7 g7 f8 g8
=
=
0.8 0.6 0 0
-0.6 0.8 0 0
0 0 0.8 0.6
0 0 -0.6 0.8
281600 -211200 -281600 211200
352000 2.91E-11 -352000 -2.91E-11
-264000 0 264000 0
-352000 -2.91E-11 352000 2.91E-11
264000 0 -264000 0
0.006293 -0.009179 0.001476 -0.012839
0 0 0
0 0 0
0 0 0
-211200 158400 211200 -158400
-281600 211200 281600 -211200
211200 -158400 -211200 158400
0 0 -211200
-281600 -211200 0
-211200 -158400 0
0.006293 -0.009179 0.001476 -0.012839
729.1667 1.4E-13 -729.1667 -1.4E-13
Reaksi Perletakan
F1 G1 G5
=
-550000 0 0
0 0 0
0 0 0
0 0 0
0 0 0
Hasil Komparasi Matriks dan SAP2000
Batang
Matriks
SAP2000
1 2 3 4 5 6 7 8 9 10 11 12 13
583.3333333 583.3333333 1250 1250 -104.1666667 0 2.72848E-12 500 -833.3333333 0 -1562.5 -104.1666667 -729.1666667
583.33 583.33 1250 1250 -104.17 0 4.547E-13 500 -833.33 0 -1562.5 -104.17 -729.17
v6 -211200 -158400 0 -733333.3 352000 -264000
u7
v7
u8
0 0
0 -366666.7
70400 1314133 -211200 -158400
12
-281600 -211200 563200 0 -281600 211200 13
0 0 -281600 -211200 0 0 -281600 0 0 -281600 211200 844800 -211200 0 0 211200 15
0 0 -211200 -158400 0 -733333.3 211200 0 0 211200 -158400 -211200 1208533 0 0 -158400 16
0 0 -281600 -211200 0 0 -281600 0 0 -281600 211200 844800 -211200
0 0 -211200 -158400 0 -733333.3 211200 0 0 211200 -158400 -211200 1208533
U2 V2 U3 V3 U4 V4 U5 U6 V6 U7 V7 U8 V8
1.36E-06 -1.34E-06 2.73E-06 -2.18E-07 3.18E-06 -1.23E-07 3.64E-06 1.89E-06 -1.34E-06 2.71E-06 -1.24E-06 4.43E-06 -1.23E-07
-6.06E-07 6.26E-06 -1.21E-06 9.33E-06 -3.03E-06 1.1E-05 -4.85E-06 -3.51E-06 6.26E-06 -3.61E-06 7.97E-06 -1.23E-07 1.1E-05
0 0 0 0 0 0 0 0 0 500 0 0 -1000
v8
-281600 -211200 0 0 -281600 211200
-211200 -158400 0 -733333.3 211200 -158400
-211200 -158400 0 683466.7 211200 -158400 14
-281600 211200 844800 -211200 15
211200 -158400 -211200 1208533 16
-550000 0 0 0 0 0 0 -281600 -211200 0 0 0 0 831600 211200 0 1
0 0 0 0 0 0 0 -211200 -158400 0 0 0 0 211200 158400 0 2
0 0 0 0 0 0 -211200 0 0 0 0 211200 -158400 0 0 158400 10
u1 v1 u2 v2 u3 v3 u4 v4 u5 v5 u6 v6 u7 v7 u8 v8
0 0 U2 V2 U3 V3 U4 V4 U5 0 U6 V6 U7 V7 U8 V8
U2 V2 U3 V3 U4 V4 U5 U6 V6 U7 V7 U8 V8 0 0 0
0 0 211200
0 0 -158400
0.001061 -0.006883 0.002121 -0.010543 0.004394 -0.012839 0.006667 0.004866 -0.006883 0.006293 -0.009179 0.001476 -0.012839
=
-500 62.5 937.5
Reaksi Perletakan
F1 G1 G5
E A
=
= =
250000 15000
Mpa cm2
= = = =
3000 1250000 0 1
mm
-937500 0 0
0 0 0
0 0 0
0 0 0 0
0 0 0
0 0 0
0 0 0
0 0 -360000
-480000 -360000 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u2 -1250000 0 1250000 0
v2 0 0 0 0
u1 v1 u2 v2
Batang 1
L EA/L sin α cos α
Matriks kekakuan [KI,1]
=
1250000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K1]
[Kg]
=
1250000 0 -1250000 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
=
[TT]
[K1]
= = = =
3000 1250000 0 1
mm
Batang 2
L EA/L sin α cos α
[T]
=
=
[TT] =
u1 1250000 0 -1250000 0
v1 0 0 0 0
-360000 -270000 0
0 0 0
0 0 0
0 0 360000
0 0 -270000
0.000498 -0.00323 0.000996 -0.004948 0.002062 -0.006026 0.003129 0.002284 -0.00323 0.002953 -0.004308 0.000693 -0.006026
=
-400 50 750
E A
= =
250000 15000
Mpa cm2
= = = =
3000 1250000 0 1
mm
Batang 1
L EA/L sin α cos α
Matriks kekakuan [KI,1]
=
1250000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K1]
[Kg]
=
1250000 0 -1250000 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0 0 0 0
[TT] =
[T]
=
u1 1250000 0 -1250000 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
=
[TT]
[K1]
= = = =
3000 1250000 0 1
mm
=
v1 0 0 0 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u2 -1250000 0 1250000 0
v2 0 0 0 0
u1 v1 u2 v2
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u3 -1250000 0 1250000 0
v3 0 0 0 0
u2 v2 u3 v3
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u4 -1250000 0 1250000
v4 0 0 0
u3 v3 u4
Batang 2
L EA/L sin α cos α
Matriks kekakuan [KI,2]
=
1250000
Matriks transformasi 1 [T] = 0 0 0
[Kg]
[TT] =
[T]
=
u2 1250000 0 -1250000 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
=
[TT]
[K2]
= = = =
3000 1250000 0 1
mm
=
v2 0 0 0 0
Batang 3
L EA/L sin α cos α
Matriks kekakuan [KI,3]
=
1250000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K3]
[Kg]
=
=
1250000 0 -1250000 0
[TT]
[K3]
[T]
=
=
[TT] =
u3 1250000 0 -1250000
v3 0 0 0
[TT].[K2]
=
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
[Kg]
[T]
=
u2 1250000 0 -1250000 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
=
[TT]
[K2]
= = = =
3000 1250000 0 1
mm
v2 0 0 0 0
u3 -1250000 0 1250000 0
v3 0 0 0 0
u2 v2 u3 v3
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u4 -1250000 0 1250000 0
v4 0 0 0 0
u3 v3 u4 v4
750000 0 -750000 0
0 0 0 0
-750000 0 750000 0
0 0 0 0
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
u5 -270000 -360000 270000 360000
v5 -360000 -480000 360000 480000
u1 v1 u5 v5
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0 0 0 0
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
Batang 3
L EA/L sin α cos α
Matriks kekakuan [KI,3]
=
1250000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K3]
[Kg]
=
1250000 0 -1250000 0
=
[TT]
[K3]
= = = =
5000 750000 0.8 0.6
mm
=
[TT] =
[T]
=
u3 1250000 0 -1250000 0
0 0 0 0
-1 0 1 0
0 0 0 0
v3 0 0 0 0
Batang 4
L EA/L sin α cos α
Matriks kekakuan [KI,4]
=
750000
1 0 -1 0
=
Matriks transformasi [T]
[TT].[K4]
[Kg]
=
450000 600000 -450000 -600000
0 0 0 0
-450000 -600000 450000 600000
=
0 0 0 0
[T]
=
u1 270000 360000 -270000 -360000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 -937500 0 937500
0 0 0 0
=
[TT]
[K4]
= = = =
4000 937500 1 0
mm
v1 360000 480000 -360000 -480000
Batang 5
L EA/L sin α cos α
Matriks kekakuan [KI,5]
=
937500
Matriks transformasi 0 [T] = -1 0 0
[TT].[K5]
=
0 937500 0 -937500
=
[TT] =
[TT] =
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
Matriks transformasi [T]
[TT].[K4]
=
[Kg]
450000 600000 -450000 -600000
0 0 0 0
-450000 -600000 450000 600000
=
[T]
=
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 -937500 0 937500
0 0 0 0
[TT]
[K4]
= = = =
4000 937500 1 0
mm
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
u5 -270000 -360000 270000 360000
v5 -360000 -480000 360000 480000
u1 v1 u5 v5
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0 0 0 0
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
u5 0 0 0 0
v5 0 -937500 0 937500
u2 v2 u5 v5
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
u6 -540000 -720000 540000 720000
v6 -720000 -960000 720000 960000
u2 v2 u6 v6
1500000 0 -1500000 0
0 0 0 0
-1500000 0 1500000 0
0 0 0 0
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
[TT] =
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 0 0
-1500000 0 1500000 0
0 0 0 0
0 0 0 0 u1 270000 360000 -270000 -360000
=
0.6 -0.8 0 0
v1 360000 480000 -360000 -480000
Batang 5
L EA/L sin α cos α
Matriks kekakuan [KI,5]
=
937500
Matriks transformasi 0 [T] = -1 0 0
[TT].[K5]
=
[Kg]
0 937500 0 -937500
=
[TT]
[K5]
= = = =
2500 1500000 0.8 0.6
mm
[T]
=
=
[TT] =
u2 0 0 0 0
v2 0 937500 0 -937500
Batang 6
L EA/L sin α cos α
Matriks kekakuan [KI,6]
Matriks transformasi 0.6 [T] = -0.8 0 0
[TT].[K6]
=
[Kg]
900000 1200000 -900000 -1200000
=
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
0 0 0 0
-900000 -1200000 900000 1200000
0 0 0 0
[TT] =
[T]
=
u2 540000 720000 -540000 -720000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
=
[TT]
[K6]
= = = =
2500 1500000 -0.8 0.6
mm
1500000
v2 720000 960000 -720000 -960000
Batang 7
L EA/L sin α cos α
Matriks kekakuan [KI,7]
=
1500000
Matriks transformasi 0.6 [T] = 0.8 0 0
=
[TT] =
=
1500000 0 -1500000 0
0 0 -0.8 0.6
Matriks transformasi 0.6 [T] = -0.8 0 0
[TT].[K6]
=
[Kg]
900000 1200000 -900000 -1200000
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
0 0 0 0
-900000 -1200000 900000 1200000
0 0 0 0
[TT] =
[T]
=
u2 540000 720000 -540000 -720000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
0 0 0 0
-900000 1200000 900000 -1200000
0 0 0 0
=
[TT]
[K6]
= = = =
2500 1500000 -0.8 0.6
mm
v2 720000 960000 -720000 -960000
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
u6 -540000 -720000 540000 720000
v6 -720000 -960000 720000 960000
u2 v2 u6 v6
1500000 0 -1500000 0
0 0 0 0
-1500000 0 1500000 0
0 0 0 0
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
u3 -540000 720000 540000 -720000
v3 720000 -960000 -720000 960000
u6 v6 u3 v3
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0 0 0 0
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
u7 0 0 0 0
v7 0 -937500 0 937500
u3 v3 u7 v7
750000 0 -750000 0
0 0 0 0
-750000 0 750000 0
Batang 7
L EA/L sin α cos α
Matriks kekakuan [KI,7]
=
1500000
Matriks transformasi 0.6 [T] = 0.8 0 0
[TT].[K7]
[Kg]
=
900000 -1200000 -900000 1200000
[TT] =
[T]
=
u6 540000 -720000 -540000 720000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 -937500 0 937500
0 0 0 0
=
[TT]
[K7]
= = = =
4000 937500 1 0
mm
=
v6 -720000 960000 720000 -960000
Batang 8
L EA/L sin α cos α
Matriks kekakuan [KI,8]
=
937500
Matriks transformasi 0 [T] = -1 0 0
[TT].[K8]
[Kg]
=
0 937500 0 -937500
=
[TT]
[K8]
= = = =
5000 750000 -0.8 0.6
mm
=
[TT] =
[T]
=
u3 0 0 0 0
0 0 0 0
-1 0 1 0
0 0 0 0
v3 0 937500 0 -937500
Batang 9
L EA/L sin α cos α
Matriks kekakuan [KI,9]
=
750000
1 0 -1 0
=
0 0 0 0
Matriks kekakuan [KI,8]
=
937500
Matriks transformasi 0 [T] = -1 0 0
[TT].[K8]
[Kg]
=
0 937500 0 -937500
1 0 -1 0
0 0 0 0
-1 0 1 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 -937500 0 937500
0 0 0 0
0 0 0 0
[TT] =
[T]
=
u3 0 0 0 0
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
0 0 0 0
-450000 600000 450000 -600000
0 0 0 0
=
[TT]
[K8]
= = = =
5000 750000 -0.8 0.6
mm
=
v3 0 937500 0 -937500
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0 0 0 0
0 1 0 0
-1 0 0 0
0 0 0 1
0 0 -1 0
u7 0 0 0 0
v7 0 -937500 0 937500
u3 v3 u7 v7
750000 0 -750000 0
0 0 0 0
-750000 0 750000 0
0 0 0 0
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
u4 -270000 360000 270000 -360000
v4 360000 -480000 -360000 480000
u7 v7 u4 v4
1500000 0 -1500000 0
0 0 0 0
-1500000 0 1500000 0
0 0 0 0
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
u6 -540000 720000 540000 -720000
v6 720000 -960000 -720000 960000
u5 v5 u6 v6
Batang 9
L EA/L sin α cos α
Matriks kekakuan [KI,9]
=
750000
Matriks transformasi 0.6 [T] = 0.8 0 0
[TT].[K9]
[Kg]
=
450000 -600000 -450000 600000
[TT] =
[T]
=
u7 270000 -360000 -270000 360000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
0 0 0 0
-900000 1200000 900000 -1200000
0 0 0 0
=
[TT]
[K9]
= = = =
2500 1500000 -0.8 0.6
mm
=
v7 -360000 480000 360000 -480000
Batang 10
L EA/L sin α cos α
Matriks kekakuan [KI,10]
=
1500000
Matriks transformasi 0.6 [T] = 0.8 0 0
[TT].[K10]
[Kg]
=
900000 -1200000 -900000 1200000
=
[TT]
[K10]
= = = =
2500 1500000 0.8 0.6
mm
Batang 11
L EA/L sin α cos α
Matriks kekakuan
[T]
=
=
[TT] =
u5 540000 -720000 -540000 720000
v5 -720000 960000 720000 -960000
Batang 10
L EA/L sin α cos α
= = = =
2500 1500000 -0.8 0.6
mm
Matriks kekakuan [KI,10]
=
1500000
Matriks transformasi 0.6 [T] = 0.8 0 0
[TT].[K10]
[Kg]
=
900000 -1200000 -900000 1200000
1 0 -1 0
0 0 0 0
-1 0 1 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
0 0 0 0
-900000 1200000 900000 -1200000
0 0 0 0
0 0 0 0
[TT] =
[T]
=
u5 540000 -720000 -540000 720000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
0 0 0 0
-900000 -1200000 900000 1200000
0 0 0 0
=
[TT]
[K10]
= = = =
2500 1500000 0.8 0.6
mm
=
v5 -720000 960000 720000 -960000
1500000 0 -1500000 0
0 0 0 0
-1500000 0 1500000 0
0 0 0 0
0.6 -0.8 0 0
0.8 0.6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
u6 -540000 720000 540000 -720000
v6 720000 -960000 -720000 960000
u5 v5 u6 v6
1500000 0 -1500000 0
0 0 0 0
-1500000 0 1500000 0
0 0 0 0
0.6 0.8 0 0
-0.8 0.6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
u7 -540000 -720000 540000 720000
v7 -720000 -960000 720000 960000
u6 v6 u7 v7
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
u7 -1250000 0 1250000 0
v7 0 0 0 0
u5 v5 u7 v7
Batang 11
L EA/L sin α cos α
Matriks kekakuan [KI,11]
=
1500000
Matriks transformasi 0.6 [T] = -0.8 0 0
[TT].[K11]
[Kg]
=
900000 1200000 -900000 -1200000
[TT] =
[T]
=
u6 540000 720000 -540000 -720000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
=
[TT]
[K11]
= = = =
3000 1250000 0 1
mm
=
v6 720000 960000 -720000 -960000
Batang 12
L EA/L sin α cos α
Matriks kekakuan [KI,12]
=
1250000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K12]
[Kg]
=
1250000 0 -1250000 0
=
Overall Stiffness
[TT]
[K12]
[T]
=
=
[TT] =
u5 1250000 0 -1250000 0
v5 0 0 0 0
[Kg]
[T]
=
u6 540000 720000 -540000 -720000
1 0 -1 0
0 0 0 0
-1 0 1 0
0 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
=
[TT]
[K11]
= = = =
3000 1250000 0 1
mm
v6 720000 960000 -720000 -960000
u7 -540000 -720000 540000 720000
v7 -720000 -960000 720000 960000
u6 v6 u7 v7
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Batang 12
L EA/L sin α cos α
Matriks kekakuan [KI,12]
=
1250000
Matriks transformasi 1 [T] = 0 0 0
[TT].[K12]
[Kg]
=
1250000 0 -1250000 0
=
[TT]
[K12]
[T]
=
u1 1520000 360000 -1250000 0
v1 360000 480000 0 0
=
[TT] =
u5 1250000 0 -1250000 0
v5 0 0 0 0
u7 -1250000 0 1250000 0
v7 0 0 0 0
u5 v5 u7 v7
u2 -1250000 0 3040000 720000 -1250000 0
v2 0 0 720000 1897500 0 0
u3
v3
u4
0 0 -540000 -720000
0 -937500 -720000 -960000
Overall Stiffness
1 2 3 4 5 6 7 8 9 10 11 12 13 14
F1 G1 0 0 0 0 0 G4 300 0 0 0 0 -700
= -270000 -360000
-360000 -480000
-1250000 0 3040000 -720000 -1250000 0
-540000 720000 0 0 5
0 0 -720000 1897500 0 0
720000 -960000 0 -937500 6
-1250000 0 1520000 -360000
v4
u5 -270000 -360000 0 0
v5 -360000 -480000 0 -937500
0 0 -360000 480000
-270000 360000 7
360000 -480000 8
2060000 -360000 -540000 720000 -1250000 0 9
u6
v6
-540000 -720000 -540000 720000
-720000 -960000 720000 -960000
u7
-360000 2377500 720000 -960000 0 0 10
-540000 720000 2160000 0 -540000 -720000 11
720000 -960000 0 3840000 -720000 -960000 12
0 0 -270000 360000 -1250000 0 -540000 -720000 2060000 360000 13
0 0 0 0 0 -360000 -480000 0 0 0 0 360000 480000 0 2
1
2
3
4
3040000 720000 -1250000 0 0 0 0 -540000 -720000 0 0 -1250000 0 0 3
720000 1897500 0 0 0 0 -937500 -720000 -960000 0 0 0 0 0 4
-1250000 0 3040000 -720000 -1250000 0 0 -540000 720000 0 0 0 0 0 5
0 0 -720000 1897500 0 0 0 720000 -960000 0 -937500 0 0 0 6
0 0 0 0 -1250000 0 0 0 1520000 0 0 2060000 0 -360000 0 -540000 0 720000 -270000 -1250000 360000 0 0 -270000 0 -360000 -360000 0 7 9
0 -937500 0 0 0 -360000 2377500 720000 -960000 0 0 -360000 -480000 0 10
-540000 -720000 -540000 720000 0 -540000 720000 2160000 0 -540000 -720000 0 0 0 11
-720000 -960000 720000 -960000 0 720000 -960000 0 3840000 -720000 -960000 0 0 0 12
0 0 0 0 -270000 -1250000 0 -540000 -720000 2060000 360000 0 0 360000 13
0 -1250000 0 0 0 0 0 -937500 0 360000 -270000 0 -360000 0 0 -720000 0 -960000 0 360000 0 2377500 1520000 0 360000 0 0 -480000 14 1
3040000 720000 -1250000 0 0 0 0 -540000 -720000 0 0
720000 1897500 0 0 0 0 -937500 -720000 -960000 0 0
-1250000 0 3040000 -720000 -1250000 0 0 -540000 720000 0 0
0 0 -720000 1897500 0 0 0 720000 -960000 0 -937500
0 0 0 0 -1250000 0 0 0 1520000 0 0 2060000 0 -360000 0 -540000 0 720000 -270000 -1250000 360000 0
0 -937500 0 0 0 -360000 2377500 720000 -960000 0 0
-540000 -720000 -540000 720000 0 -540000 720000 2160000 0 -540000 -720000
-720000 -960000 720000 -960000 0 720000 -960000 0 3840000 -720000 -960000
0 0 0 0 -270000 -1250000 0 -540000 -720000 2060000 360000
0 0 0 -937500 360000 0 0 -720000 -960000 360000 2377500
U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7
8E-07 -4E-07 8E-07 -2E-07 8E-07
-4E-07 2.36E-06 -6.11E-07 1.37E-06 -8.11E-07
8E-07 -6.11E-07 1.55E-06 -4.11E-07 1.55E-06
-2E-07 1.37E-06 -4.11E-07 2.36E-06 -8.11E-07
8E-07 -8.11E-07 1.55E-06 -8.11E-07 2.35E-06
-4E-07 1.63E-06 -7E-07 1.35E-06 -9E-07
6.67E-07 -7.9E-08 1.04E-06 -7.32E-07 1.18E-06
-3E-07 1.79E-06 -7.06E-07 1.79E-06 -1.01E-06
5.33E-07 6.79E-08 8.83E-07 -4.9E-07 1.15E-06
-2E-07 1.35E-06 -5E-07 1.63E-06 -9E-07
0 0 0 0 0
v7
0 -937500 360000 -480000 0 0 -720000 -960000 360000 2377500 14
0 0 0 0 -360000 0 0 0 0 360000 -480000 0 0 480000 8
u1 v1 u2 v2 u3 v3 u4 v4 u5 v5 u6 v6 u7 v7
0 0 U2 V2 U3 V3 U4 0 U5 V5 U6 V6 U7 V7
Rearrangement
3 4 5 6 7 9 10 11 12 13 14 1 2 8
0 0 0 0 0 300 0 0 0 0 -700 F1 G1 G4
=
U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7 0 0 0
Unknown Displacement and Reaction
0 0 0 0 0 300 0 0 0 0 -700
U2 V2 U3 V3 U4
=
5.33E-07 -3.21E-07 9.33E-07 -8.79E-07 1.2E-06
>
U2 V2 U3 V3 U4
0.0003 -0.001044 0.00063 -0.001404 0.00099
Rearrangement
3 4 5 6 7 9 10 11 12 13 14 1 2 8
0 0 0 0 0 300 0 0 0 0 -700 F1 G1 G4
3040000 720000 -1250000 0 0 0 0 -540000 -720000 0 0 -1250000 0 0 3
720000 1897500 0 0 0 0 -937500 -720000 -960000 0 0 0 0 0 4
-1250000 0 3040000 -720000 -1250000 0 0 -540000 720000 0 0 0 0 0 5
0 0 -720000 1897500 0 0 0 720000 -960000 0 -937500 0 0 0 6
0 0 0 0 -1250000 0 0 0 1520000 0 0 2060000 0 -360000 0 -540000 0 720000 -270000 -1250000 360000 0 0 -270000 0 -360000 -360000 0 7 9
0 -937500 0 0 0 -360000 2377500 720000 -960000 0 0 -360000 -480000 0 10
-540000 -720000 -540000 720000 0 -540000 720000 2160000 0 -540000 -720000 0 0 0 11
-720000 -960000 720000 -960000 0 720000 -960000 0 3840000 -720000 -960000 0 0 0 12
0 0 0 0 -270000 -1250000 0 -540000 -720000 2060000 360000 0 0 360000 13
0 -1250000 0 0 0 0 0 -937500 0 360000 -270000 0 -360000 0 0 -720000 0 -960000 0 360000 0 2377500 1520000 0 360000 0 0 -480000 14 1
=
3040000 720000 -1250000 0 0 0 0 -540000 -720000 0 0
720000 1897500 0 0 0 0 -937500 -720000 -960000 0 0
-1250000 0 3040000 -720000 -1250000 0 0 -540000 720000 0 0
0 0 -720000 1897500 0 0 0 720000 -960000 0 -937500
0 0 0 0 -1250000 0 0 0 1520000 0 0 2060000 0 -360000 0 -540000 0 720000 -270000 -1250000 360000 0
0 -937500 0 0 0 -360000 2377500 720000 -960000 0 0
-540000 -720000 -540000 720000 0 -540000 720000 2160000 0 -540000 -720000
-720000 -960000 720000 -960000 0 720000 -960000 0 3840000 -720000 -960000
0 0 0 0 -270000 -1250000 0 -540000 -720000 2060000 360000
0 0 0 -937500 360000 0 0 -720000 -960000 360000 2377500
U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7
=
8E-07 -4E-07 8E-07 -2E-07 8E-07 5.33E-07 -4E-07 6.67E-07 -3E-07 5.33E-07 -2E-07
-4E-07 2.36E-06 -6.11E-07 1.37E-06 -8.11E-07 -3.21E-07 1.63E-06 -7.9E-08 1.79E-06 6.79E-08 1.35E-06
8E-07 -6.11E-07 1.55E-06 -4.11E-07 1.55E-06 9.33E-07 -7E-07 1.04E-06 -7.06E-07 8.83E-07 -5E-07
-2E-07 1.37E-06 -4.11E-07 2.36E-06 -8.11E-07 -8.79E-07 1.35E-06 -7.32E-07 1.79E-06 -4.9E-07 1.63E-06
8E-07 -8.11E-07 1.55E-06 -8.11E-07 2.35E-06 1.2E-06 -9E-07 1.18E-06 -1.01E-06 1.15E-06 -9E-07
-4E-07 1.63E-06 -7E-07 1.35E-06 -9E-07 -5.58E-07 1.81E-06 -5.98E-07 1.6E-06 -2.58E-07 1.18E-06
6.67E-07 -7.9E-08 1.04E-06 -7.32E-07 1.18E-06 1.41E-06 -5.98E-07 1.91E-06 -5.03E-07 1.39E-06 -3.02E-07
-3E-07 1.79E-06 -7.06E-07 1.79E-06 -1.01E-06 -7.5E-07 1.6E-06 -5.03E-07 2.13E-06 -2.56E-07 1.6E-06
5.33E-07 6.79E-08 8.83E-07 -4.9E-07 1.15E-06 1.58E-06 -2.58E-07 1.39E-06 -2.56E-07 1.93E-06 -3.42E-07
-2E-07 1.35E-06 -5E-07 1.63E-06 -9E-07 -6.42E-07 1.18E-06 -3.02E-07 1.6E-06 -3.42E-07 1.81E-06
0 0 0 0 0 300 0 0 0 0 -700
=
[T1]
[Kg1]
[U1]
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1250000 0 -1250000 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0 0 0.0003 -0.001044
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1250000 0 -1250000 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.0003 -0.001044 0.00063 -0.001404
=
0 0 0 0 0 -360000 -480000 0 0 0 0 360000 480000 0 2
0 0 0 0 -360000 0 0 0 0 360000 -480000 0 0 480000 8
U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7 0 0 0
Unknown Displacement and Reaction
0 0 0 0 0 300 0 0 0 0 -700
U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7
5.33E-07 -3.21E-07 9.33E-07 -8.79E-07 1.2E-06 1.98E-06 -5.58E-07 1.41E-06 -7.5E-07 1.58E-06 -6.42E-07
Gaya Batang Batang 1
f1 g1 f2 g2 f1 g1 f2 g2
f1 g1 f2 g2
=
=
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0 0 0.0003 -0.001044
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.0003 -0.001044 0.00063 -0.001404
-375 0 375 0
Batang 2
f2 g2 f3 g3
f2
=
-412.5
>
U2 V2 U3 V3 U4 U5 V5 U6 V6 U7 V7
=
0.0003 -0.001044 0.00063 -0.001404 0.00099 0.001043 -0.000991 0.000636 -0.001348 0.000713 -0.001458
Gaya Batang Batang 1
f1 g1 f2 g2 f1 g1 f2 g2
f1 g1 f2 g2
=
=
=
[T1]
[Kg1]
[U1]
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1250000 0 -1250000 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0 0 0.0003 -0.001044
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1250000 0 -1250000 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.0003 -0.001044 0.00063 -0.001404
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1250000 0 -1250000 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.00063 -0.001404 0.00099 0.001043
0.6 -0.8 0 0
0. 8 0. 6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
270000 360000 -270000 -360000
450000 0 -450000 0
600000 0 -600000 0
-450000 0 45 450000 0
-600000 0 600000 0
0 0 0.001043 -0.000991
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0.0003 -0.001044 0.001043 -0.000991
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0 0 0.0003 -0.001044
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.0003 -0.001044 0.00063 -0.001404
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.00063 -0.001404 0.00099 0.001043
360000 480000 -360000 -480000
-270000 -360000 270000 360000
-360000 -480000 360000 480000
0 0 0.001043 -0.000991
0 93 9 37500 0 -937500
0 0 0 0
0 -937500 0 937500
0.0003 -0.001044 0.001043 -0.000991
-375 0 375 0
Batang 2
f2 g2 f3 g3
f2 g2 f3 g3
=
=
-412.5 0 412.5 0
Batang 3
f3 g3 f4 g4
f3 g3 f4 g4
=
=
-450 0 450 0
Batang 4
f1 g1 f5 g5
f1 g1 f5 g5
=
=
125 0 -125 0
Batang 5
f2 g2 f5 g5
f2 g2
=
=
-5 0 0
f3 g3 f4 g4
=
-450 0 450 0
Batang 4
f1 g1 f5 g5
f1 g1 f5 g5
=
=
0.6 -0.8 0 0
0. 8 0. 6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
270000 360000 -270000 -360000
450000 0 -450000 0
600000 0 -600000 0
-450000 0 45 450000 0
-600000 0 600000 0
0 0 0.001043 -0.000991
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0.0003 -0.001044 0.001043 -0.000991
0.6 -0.8 0 0
0. 8 0. 6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
540000 720000 -540000 -720000
900000 0 -900000 0
1200000 0 -1200000 0
-900000 0 900000 0
-1200000 0 1200000 0
0.0003 -0.001044 0.000636 -0.001348
0.6 0. 8 0 0
- 0. 8 0. 6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
540000 -720000 -540000 720000
900000 0 -900000 0
-1200000 0 1200000 0
-900000 0 90 900000 0
1200000 0 -1200000 0
0.000636 -0.001348 0.00063 -0.001404
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0.00063 -0.001404 0.000713 -0.001458
360000 480000 -360000 -480000
-270000 -360000 270000 360000
-360000 -480000 360000 480000
0 0 0.001043 -0.000991
0 93 9 37500 0 -937500
0 0 0 0
0 -937500 0 937500
0.0003 -0.001044 0.001043 -0.000991
720000 960000 -720000 -960000
-540000 -720000 540000 720000
-720000 -960000 720000 960000
0.0003 -0.001044 0.000636 -0.001348
125 0 -125 0
Batang 5
f2 g2 f5 g5
f2 g2 f5 g5
=
=
-5 0 0 50 0
Batang 6
f2 g2 f6 g6
=
f2 g2 f6 g6
>
=
62.5 0 - 6 2 .5 0
Batang 7
f6 g6 f3 g3
f6 g6 f3 g3
=
=
-720000 960000 720000 -960000
-540000 720000 540000 -720000
720000 -960000 -720000 960000
0.000636 -0.001348 0.00063 -0.001404
0 93 9 37500 0 -937500
0 0 0 0
0 -937500 0 937500
0.00063 -0.001404 0.000713 -0.001458
-62.5 0 62.5 0
Batang 8
f3 g3 f7 g7
f3 g3 f7 g7 Batang 9
=
=
50 0 -5 0 0
Batang 7
f6 g6 f3 g3
f6 g6 f3 g3
=
=
0.6 0. 8 0 0
- 0. 8 0. 6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
540000 -720000 -540000 720000
900000 0 -900000 0
-1200000 0 1200000 0
-900000 0 90 900000 0
1200000 0 -1200000 0
0.000636 -0.001348 0.00063 -0.001404
0 -1 0 0
1 0 0 0
0 0 0 -1
0 0 1 0
0 0 0 0
0 0 0 0
937500 0 -937500 0
0 0 0 0
-937500 0 937500 0
0.00063 -0.001404 0.000713 -0.001458
0.6 0. 8 0 0
- 0. 8 0. 6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
270000 -360000 -270000 360000
450000 0 -450000 0
-6 - 600000 0 600000 0
-450000 0 45 4 50000 0
60 6 00000 0 -600000 0
0.000713 -0.001458 0.00099 0
0. 6 0. 8 0 0
- 0. 8 0. 6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
540000 -720000 -540000 720000
900000 0 -900000 0
-1200000 0 12 1200000 0
-900000 0 900000 0
1200000 0 -1 -1200000 0
0.001043 -0.000991 0.000636 -0.001348
0.6 -0.8 0 0
0. 8 0. 6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
540000 720000 -540000 -720000
900000 0 -900000 0
12 1200000 0 -1200000 0
-900000 0 90 900000 0
-1200000 0 1200000 0
0.000636 -0.001348 0.000713 -0.001458
0 1 0 0
0 0 1 0
0 0 0 1
1250000 0 -1250000 0
-720000 960000 720000 -960000
-540000 720000 540000 -720000
720000 -960000 -720000 960000
0.000636 -0.001348 0.00063 -0.001404
0 93 9 37500 0 -937500
0 0 0 0
0 -937500 0 937500
0.00063 -0.001404 0.000713 -0.001458
-360000 480000 360000 -480000
-270000 360000 270000 -360000
360000 -480000 -360000 480000
0.000713 -0.001458 0.00099 0
-720000 960000 720000 -960000
-540000 720000 540000 -720000
720000 -960000 -720000 960000
0.001043 -0.000991 0.000636 -0.001348
720000 960000 -720000 -960000
-540000 -720000 540000 720000
-720000 -960000 720000 960000
0.000636 -0.001348 0.000713 -0.001458
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.001043 -0.000991 0.000713 -0.001458
-62.5 0 62.5 0
Batang 8
f3 g3 f7 g7
f3 g3 f7 g7
=
=
50 0 -5 0 0
Batang 9
f7 g7 f4 g4
f7 g7 f4 g4
Batang 10
f5 g5 f6 g6
f5 g5 f6 g6
=
=
=
=
750 0 -750 0
-62.5 0 62.5 0
Batang 11
f6 g6 f7 g7
f6 g6 f7 g7
=
=
62.5 0 -62.5 0
Batang 12
f5 g5 f7 g7
=
1 0 0 0
f5 g5 f6 g6
Batang 10
=
f5 g5 f6 g6
=
0. 6 0. 8 0 0
- 0. 8 0. 6 0 0
0 0 0.6 0.8
0 0 -0.8 0.6
540000 -720000 -540000 720000
900000 0 -900000 0
-1200000 0 12 1200000 0
-900000 0 900000 0
1200000 0 -1 -1200000 0
0.001043 -0.000991 0.000636 -0.001348
0.6 -0.8 0 0
0. 8 0. 6 0 0
0 0 0.6 -0.8
0 0 0.8 0.6
540000 720000 -540000 -720000
900000 0 -900000 0
12 1200000 0 -1200000 0
-900000 0 90 900000 0
-1200000 0 1200000 0
0.000636 -0.001348 0.000713 -0.001458
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
1250000 0 -1250000 0
1250000 0 -1250000 0
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.001043 -0.000991 0.000713 -0.001458
-720000 960000 720000 -960000
-540000 720000 540000 -720000
720000 -960000 -720000 960000
0.001043 -0.000991 0.000636 -0.001348
720000 960000 -720000 -960000
-540000 -720000 540000 720000
-720000 -960000 720000 960000
0.000636 -0.001348 0.000713 -0.001458
0 0 0 0
-1250000 0 1250000 0
0 0 0 0
0.001043 -0.000991 0.000713 -0.001458
-62.5 0 62.5 0
Batang 11
f6 g6 f7 g7
=
f6 g6 f7 g7
=
62.5 0 -62.5 0
Batang 12
f5 g5 f7 g7
=
f5 g5 f7 g7
=
412.5 0 -412.5 0
Reaksi Perletakan
F1 G1 G4
=
Hasil Komparasi Matriks dan SAP2000
Batang 1 2 3 4 5 6 7 8 9 10 11 12
Matriks 375 412.5 450 -125 50 -62.5 62.5 -50 -750 62.5 -62.5 -412.5
SAP2000 583.33 625 666.67 -138.89 55.56 -69.44 69.44 -55.56 -1111.11 69.44 -69.44 -625
-1250000 0 0
0 0 0
0 0 0
0 0 0
0 0 -360000
-270000 -360000 0
-360000 -480000 0
0 0 0
0 0 0
0 0 360000
0 0 -480000
0.0003 -0.001044 0.00063 -0.001404 0.00099 0.001043 -0.000991 0.000636 -0.001348 0.000713 -0.001458
=
-300 100 600
Reaksi Perletakan
F1 G1 G4
=
-1250000 0 0
0 0 0
0 0 0
0 0 0
0 0 -360000
-270000 -360000 0
-360000 -480000 0
0 0 0
0 0 0
0 0 360000
0.0003 -0.001044 0.00063 -0.001404 0.00099 0.001043 -0.000991 0.000636 -0.001348 0.000713 -0.001458
0 0 -480000
=
Hasil Komparasi Matriks dan SAP2000
Batang 1 2 3 4 5 6 7 8 9 10 11 12
Matriks 375 412.5 450 -125 50 -62.5 62.5 -50 -750 62.5 -62.5 -412.5
SAP2000 583.33 625 666.67 -138.89 55.56 -69.44 69.44 -55.56 -1111.11 69.44 -69.44 -625
E= A= I=
21000 Kn/cm² 600 cm² 10000 cm⁴
Matrik kekakuan lokal batang1 cm L= 500 sin 270 = -1 cos270 = 0
(K1)
=
L³
=
125000000
25200
0
0
-25200
0
0
20.16
5040
0
-20.16
0
5040
1680000
0
-5040
25200
0
0
25200
0
-300 100 600
E= A= I=
21000 Kn/cm² 600 cm² 10000 cm⁴
Matrik kekakuan lokal batang1 cm L= 500 sin 270 = -1 cos270 = 0
(K1)
=
125000000
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 0
-1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 -1 0 0
0 0 0 0 0 1
0 1 0 0 0 0
-1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 -1 0 0
0 0 0 0 0 1
0 25200 0 0
-20.16 0 5040 20.16
-5040 0 1680000 5040
0 -25200 0 0
20.16 0 -5040 -20.16
-5040 0 840000 5040
=
(1)
[T ] =
(1) T
[T ]
(Kg)
L³
=
=
-25200 0 u1 (Kg1)
=
0 5040
25200 0
0 -5040
θ1
v1 20.16 0 -5040 -20.16 0 -5040
0 840000
0 25200 0 0 -25200 0
u2 -5040 -20.16 0 0 1680000 5040 5040 20.16 0 0 840000 5040
0 1680000 θ2
v2 0 -25200 0 0 25200 0
-5040 0 840000 5040 0 1680000
Matrik kekakuan lokal batang 2 L= 500 cm L³
(K)
=
=
25200 0 0 -25200 0 0
u2 (Kg2)
=
L²
125000000
25200 0 0 -25200 0 0
Matrik kekakuan lokal batang 3 L= 300 cm L³ = 27000000 sin 270 = -1 cos 270 = 0
0 20.16 5040 0 -20.16 5040
v2 0 20.16 5040 0 -20.16 5040
250000
-25200 0 0 25200 0 0
0 -20.16 -5040 0 20.16 -5040
=
0 5040 1680000 0 -5040 840000
θ2
u3 0 -25200 5040 0 1680000 0 0 25200 -5040 0 840000 0
L²
=
0 5040 840000 0 -5040 1680000
θ3
v3 0 -20.16 -5040 0 20.16 -5040
90000
0 5040 840000 0 -5040 1680000
(K3)
=
(T)
=
(1) T
[T ]
(Kg3)
(Kg3)
42000 0 0 93.33333 0 14000 -42000 0 0 -93.3333 0 14000
=
=
=
overal stiffness
0 14000 2800000 0 -14000 1400000
-42000 0 0 -93.33333 0 -14000 42000 0 0 93.333333 0 -14000
0 14000 1400000 0 -14000 2800000
0 1 0 0 0 0
-1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 -1 0 0
0 0 0 0 0 1
0 -1 0 0 0 0
1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 -1 0
0 0 0 1 0 0
0 0 0 0 0 1
0 93.33333 -42000 0 0 14000 0 -93.3333 42000 0 0 14000
14000 0 2800000 -14000 0 1400000
0 -93.33333 42000 0 0 -14000 0 93.333333 -42000 0 0 -14000
14000 0 1400000 -14000 0 2800000
u3 v3 93.333333 0 0 42000 14000 0 -93.33333 0 0 -42000 14000 0
θ3
u4 v4 14000 -93.3333 0 0 0 -42000 2800000 -14000 0 -14000 93.33333 0 0 0 42000 1400000 -14000 0
θ4
14000 0 1400000 -14000 0 2800000
u1 20.16 0 -5040 -20.16 0 -5040 0 0 0 0 0 0
v1 0 25200 0 0 -25200 0 0 0 0 0 0 0
θ1
-5040 0 1680000 5040 0 840000 0 0 0 0 0 0
u2 -20.16 0 5040 25220.16 0 5040 -25200 0 0 0 0 0
v2 0 -25200 0 0 25220.16 5040 0 -20.16 5040 0 0 0
θ2
-5040 0 840000 5040 5040 3360000 0 -5040 840000 0 0 0
L²
=
250000
0
AE/L1
5040
0 0
0
-AE/L1
-5040
0
u2 cos
X
0 -1 0 0
6EI/L
4EI/L
0
0 -12EI/L
0 -6EI/L
AE/L1
2EI/L
0
6EI/L
1
-sin
-AE/L1
2
0
0 6EI/L
2
840000
1680000
0 12EI/L
1
a
v2 sin a
a
cos
a
0 -12EI/L
0
2
0
1
-6EI/L
2EI/L
0 12EI/L
0 -6EI/L
2
-6EI/L
1
0 6EI/L
1
4EI/L
1
q2
u1
v1
q1
0
0
0
0
0
0
0
0 0
a
0 sin a
0
a
cos
0
0
0
1
0
0
0
0 cos
0
0
0
-sin
0
0
0
0
0
1 0 0 0
0 0 1 0
0 0 0 0
0 0 0 1
0 0 0 0
a
1
0 0
u1 v1 θ1
u2 v2 θ2
u2 v2 θ2
u3 v3 θ3
0 0
0 0
-1 0
0 0
0 1
X
u3 v3 θ3
u4 v4 θ4
0 1 0 0 0 0
-1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 -1 0 0
0 0 0 0 0 1
u3 0 0 0 -25200 0 0 25293.33333 0 14000 -93.33333333 0 14000
v3 0 0 0 0 -20.16 -5040 0 42020.16 -5040 0 -42000 0
θ3
0 0 0 0 5040 840000 14000 -5040 4480000 -14000 0 1400000
u4 0 0 0 0 0 0 -93.3333 0 -14000 93.33333 0 -14000
v4 0 0 0 0 0 0 0 -42000 0 0 42000 0
θ4
0 0 0 0 0 0 14000 0 1400000 -14000 0 2800000
u1 v1 θ1
u2 v2 θ2
u3 v3 θ3
u4 v4 θ4
1
u2
1
v2
1
q2
1
u1
1
v1
1
q1
