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SOAL :

b (ton) a (ton) 2

BEBAN a = b = BATANG 1 A = I = L =

2.0 3.0

ton ton

40 2000 300

cm cm^4 cm

1 300

2 BATANG 2 A = I = L = 1 300 E = btg 1 = btg 2 = btg 3 = 2100 90 315.00 45.00 t/cm derajad derajad derajad 3 30 2000 424.26 cm cm^4 cm

PENYELESAIAN :

MATRIK KEKAKUAN ELEMEN BATANG 1 (ELEMEN 1) 0 -1 0 0 0 0 0 1 0 0 0 0 280 0 0 -280 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 1.867 280 0 -1.867 280 0 0 1 0 0 0 0 0 1 0 0 0 0 280 56000 0 -280 28000 0 0 0 0 -1 0 0 0 0 0 1 0 -280 0 0 280 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 -1.867 -280 0 1.867 -280 0 0 0 0 0 1 0 0 0 0 0 1 0 280 28000 0 -280 56000

[T]

[T]T

[ Kl ]

[T]T

[ Kl(1) ]

= 0.00 280.00 0 0.00 -280.00 0 -1.87 0.00 280 1.87 0.00 280 -280.00 0.00 56000 280.00 0.00 28000 0.00 -280.00 0 0.00 280.00 0 1.87 0.00 -280 -1.87 0.00 -280 -280.00 0.00 28000 280.00 0.00 56000

[ Kg(1) ]

=

[T]T

[ Kl(1) ]

[T]

[Kg(1)]

=

1.87 0 -280 -1.87 0 -280

0 280 0 0 -280 0

-280 0 56000 280 0 28000

-1.87 0 280 1.87 0 280

0 -280 0 0 280 0

-280 0 28000 280 0 56000

BATANG 2 (ELEMEN 2) 0.7071 0.7071 0 0 0 0 0.7071 -0.7071 0 0 0 0 148.49 0 0 -148.49 0 0 -0.7071 0.7071 0 0 0 0 0.7071 0.7071 0 0 0 0 0 0.66 140.00 0 -0.66 140.00 0 0 1 0 0 0 0 0 1 0 0 0 0 140.00 39597.99 0 -140.00 19798.99 0 0 0 0.7071 0.7071 0 0 0 0 0.7071 -0.7071 0 -148.49 0 0 148.49 0 0 0 0 0 -0.7071 0.7071 0 0 0 0 0.7071 0.7071 0 0 -0.66 -140.00 0 0.66 -140.00 0 0 0 0 0 1 0 0 0 0 0 1 0 140.00 19798.99 0 -140.00 39597.99

[T]

[T]T

[ Kl ]

[T]T

[ Kl(2) ]

= 105.00 -105.00 0 -105.00 105.00 0 0.47 0.47 140 -0.47 -0.47 140 98.99 98.99 39598 -98.99 -98.99 19799 -105.00 105.00 0 105.00 -105.00 0 -0.47 -0.47 -140 0.47 0.47 -140 98.99 98.99 19799 -98.99 -98.99 39598

[ Kg(2) ]

=

[T]T

[ Kl(2) ]

[T]

[Kg(2)]

=

74.58 -73.92 98.99 -74.58 73.92 98.99

-73.92 74.58 98.99 73.92 -74.58 98.99

98.99 98.99 39597.99 -98.99 -98.99 19798.99

-74.58 73.92 -98.99 74.58 -73.92 -98.99

73.92 -74.58 -98.99 -73.92 74.58 -98.99

98.99 98.99 19798.99 -98.99 -98.99 39597.99

BATANG 3 (ELEMEN 3) 0.7071 -0.7071 0 0 0 0 0.7071 0.7071 0 0 0 0 210.00 0 0 -210.00 0 0 0.7071 0.7071 0 0 0 0 -0.7071 0.7071 0 0 0 0 0 1.87 280.00 0 -1.87 280.00 0 0 1 0 0 0 0 0 1 0 0 0 0 280.00 56000.00 0 -280.00 0.00 0 0 0 0.7071 -0.7071 0 0 0 0 0.7071 0.7071 0 -210.00 0 0 210.00 0 0 0 0 0 0.7071 0.7071 0 0 0 0 -0.7071 0.7071 0 0 -1.87 -280.00 0 1.87 -280.00 0 0 0 0 0 1 0 0 0 0 0 1 0 280.00 0.00 0 -280.00 56000.00

[T]

[T]T

[ Kl ]

[T]T

[ Kl(3) ]

= 148.49 148.49 0 -148.49 -148.49 0 -1.32 1.32 280 1.32 -1.32 280 -197.99 197.99 56000 197.99 -197.99 0 -148.49 -148.49 0 148.49 148.49 0 1.32 -1.32 -280 -1.32 1.32 -280 -197.99 197.99 0 197.99 -197.99 56000

[ Kg(3) ]

=

[T]T

[ Kl(2) ]

[T]

[Kg(3)]

=

105.93 104.07 -197.99 -105.93 -104.07

104.07 105.93 197.99 -104.07 -105.93

-197.99 197.99 56000.00 197.99 -197.99

-105.93 -104.07 197.99 105.93 104.07

-104.07 -105.93 -197.99 104.07 105.93

-197.99 197.99 0.00 197.99 -197.99

[Kg(3)] -197.99 197.99 MENYUSUN OVERALL STIFFNESS MATRIX [Kg(1)] 1.87 0 -280 -1.87 0 -280 0 0 0 [Kg(2)] 0 0 0 1 0 0 0 0 0 = 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 74.58 -73.92 98.99 -74.58 73.92 98.99 0 0 0 -73.92 74.58 98.99 73.92 -74.58 98.99 0 0 0 98.99 98.99 39597.99 -98.99 -98.99 19798.99 0 0 0 -74.58 73.92 -98.99 74.58 -73.92 -98.99 0 0 0 73.92 -74.58 -98.99 -73.92 74.58 -98.99 0 0 0 98.99 98.99 19798.99 -98.99 -98.99 39597.99 = 0 280 0 0 -280 0 0 0 0 -280 0 56000 280 0 28000 0 0 0 -1.87 0 280 1.87 0 280 0 0 0 0 -280 0 0 280 0 0 0 0 -280 0 28000 280 0 56000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 197.99 -197.99 56000.00

1.87 0 -280 -1.16 0 -280 0 0 0

0.00 280 0 0.71 -280 0 0 0 0

-280.00 0 56000 280 1 28000 0 0 0

-1.87 0 280 76.44 -73.92 378.99 -74.58 73.92 98.99

0 -280 0 -73.92 354.58 98.99 73.92 -74.58 98.99

-280 0 28000 378.99 98.99 95597.99 -98.99 -98.99 19798.99

0 0 0 -74.58 73.92 -98.99 74.58 -73.92 -98.99

0 0 0 73.92 -74.58 -98.99 -73.92 74.58 -98.99

0 0 0 98.99 98.99 19798.99 -98.99 -98.99 39597.99

UNKNOWN DISPLACEMENT AND REACTIONS H V M 2.0 -3.0 0 76.44 -73.92 378.99 -73.92 354.58 98.99 378.99 98.99 95597.99 U2 V2 2

=

-1 U2 V2 2 = 76.44 -73.92 378.99 -73.92 354.58 98.99 378.99 98.99 95597.99 2.0 -3.0 0 2.0 -3.0 0

=

0.016846 0.003531 -0.000070 0.003531 0.003561 -0.000018 -0.000070 -0.000018 0.000011 0.02310

U2

V2 2

=

-0.00362 -0.00009

F1 G1 M1 F3 G3 M3

=

-1.87 0.00 280.00 -74.58 73.92 98.99

0.00 -280.00 -280.00 0.00 0.00 28000.00 73.92 -98.99 -74.58 -98.99 98.99 19798.99

0.02310 -0.00362 -0.00009

=

-0.019 1.014 4.008 -1.981 1.986 0.189

MEMBER FORCES ELEMEN 1 0 0 0 0.02310 -0.00362 -0.00009

[U]

=

[T]

[ Kg(1) ] 0 -1.8667 -280 0 1.8667 -280 280 0 0 -280 0 0 0 280 56000 0 -280 28000 0 1.8667 280 0 -1.8667 280 -280 0 0 280 0 0 0 280 28000 0 -280 56000

=

f1 g1 m1 f2 g2 m2

=

[T]

[ Kg(1) ]

[U]

=

1.01399 0.01853 4.00828 -1.01399 -0.01853 1.54940

ELEMEN 2 0.02310 -0.00362 -0.00009 0 0 0

[U]

=

[T]

[ Kg(2) ] 105.00 0.47 98.99 -105.00 -0.47 98.99 -105.00 0.47 98.99 105.00 -0.47 98.99 0.00 140.00 39597.99 0.00 -140.00 19798.99 -105.00 -0.47 -98.99 105.00 0.47 -98.99 105.00 -0.47 -98.99 -105.00 0.47 -98.99 0.00 140.00 19798.99 0.00 -140.00 39597.99

=

f2 g2 m2 f3 g3 m3

=

[T]

[ Kg(2) ]

[U]

=

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

FREE BODY #VALUE! 1.01399 0.01853 1.54940 #VALUE! #VALUE!

#VALUE!

0.01853

4.00828 #VALUE! 1.01399 #VALUE!

= H1 = V1 = M1 =

45.00 -0.019 1.014 4.008

derajad ton ton ton m

H2 = ( 0,01287 + 6,59747 cos - 0,00436 sin ) V2 = ( -2,33644 - 6,59747 sin - 0,00436 cos ) M2 = m2(1) + m2(2) = 1.54940 #VALUE!

= = = = = = = = =

#VALUE! #VALUE! #VALUE! #VALUE! #VALUE!

ton ton ton m ton ton

H3 = (- 6,59747 cos + 0,00436 sin ) V3 = ( 6,59747 sin + 0,00436 cos ) M3 = #VALUE! ton m

#VALUE!

#VALUE!

0.019 4.008

#VALUE!

#VALUE!

1.014

#VALUE!

BATANG 3 A = 30 I = 2000 L = 300.00

cm cm^4 cm