anstruk matriks

SOAL :

b (ton) BEBANa = 2.0 ton

a (ton) b = 3.0 ton

BATANG 1A = 40 cm²I = 2000L = 300 cm

300 BATANG 2A = 30 cm²I = 2000L = 424.26 cm

300

E = 2100 t/cm²90 derajad

315.00 derajad45.00 derajad

PENYELESAIAN :

MATRIK KEKAKUAN ELEMEN

BATANG 1 (ELEMEN 1)

[ T ]

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

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

280 0 0 -280 0 00 1.867 280 0 -1.867 2800 280 56000 0 -280 28000

-280 0 0 280 0 00 -1.867 -280 0 1.867 -2800 280 28000 0 -280 56000

cm^4

cm^4

α btg 1 =α btg 2 =α btg 3 =

[ T ] T

[ Kl ]

2

1 3

1 2

β

=

0.00 -1.87 -280.00 0.00 1.87 -280.00280.00 0.00 0.00 -280.00 0.00 0.00

0 280 56000 0 -280 280000.00 1.87 280.00 0.00 -1.87 280.00

-280.00 0.00 0.00 280.00 0.00 0.000 280 28000 0 -280 56000

[ T ] =

1.87 0 -280 -1.87 0 -2800 280 0 0 -280 0

= -280 0 56000 280 0 28000

-1.87 0 280 1.87 0 2800 -280 0 0 280 0

-280 0 28000 280 0 56000

BATANG 2 (ELEMEN 2)

[ T ]

0.7071 -0.7071 0 0 0 00.7071 0.7071 0 0 0 0

0 0 1 0 0 00 0 0 0.7071 -0.7071 00 0 0 0.7071 0.7071 00 0 0 0 0 1

0.7071 0.7071 0 0 0 0-0.7071 0.7071 0 0 0 0

0 0 1 0 0 00 0 0 0.7071 0.7071 00 0 0 -0.7071 0.7071 00 0 0 0 0 1

148.49 0 0 -148.49 0 00 0.66 140.00 0 -0.66 140.000 140.00 39597.99 0 -140.00 19798.99

-148.49 0 0 148.49 0 00 -0.66 -140.00 0 0.66 -140.000 140.00 19798.99 0 -140.00 39597.99

=

105.00 0.47 98.99 -105.00 -0.47 98.99-105.00 0.47 98.99 105.00 -0.47 98.99

0 140 39598 0 -140 19799-105.00 -0.47 -98.99 105.00 0.47 -98.99105.00 -0.47 -98.99 -105.00 0.47 -98.99

0 140 19799 0 -140 39598

[ T ] T [ Kl(1) ]

[ Kg(1) ] [ T ] T [ Kl(1) ]

[Kg(1)]

[ T ] T

[ Kl ]

[ T ] T [ Kl(2) ]

[ T ] =

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 -98.9973.92 -74.58 -98.99 -73.92 74.58 -98.9998.99 98.99 19798.99 -98.99 -98.99 39597.99

BATANG 3 (ELEMEN 3)

[ T ]

0.7071 0.7071 0 0 0 0-0.7071 0.7071 0 0 0 0

0 0 1 0 0 00 0 0 0.7071 0.7071 00 0 0 -0.7071 0.7071 00 0 0 0 0 1

0.7071 -0.7071 0 0 0 00.7071 0.7071 0 0 0 0

0 0 1 0 0 00 0 0 0.7071 -0.7071 00 0 0 0.7071 0.7071 00 0 0 0 0 1

210.00 0 0 -210.00 0 00 1.87 280.00 0 -1.87 280.000 280.00 56000.00 0 -280.00 0.00

-210.00 0 0 210.00 0 00 -1.87 -280.00 0 1.87 -280.000 280.00 0.00 0 -280.00 56000.00

=

148.49 -1.32 -197.99 -148.49 1.32 -197.99148.49 1.32 197.99 -148.49 -1.32 197.99

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

0 280 0 0 -280 56000

[ T ] =

105.93 104.07 -197.99 -105.93 -104.07 -197.99104.07 105.93 197.99 -104.07 -105.93 197.99

= -197.99 197.99 56000.00 197.99 -197.99 0.00-105.93 -104.07 197.99 105.93 104.07 197.99-104.07 -105.93 -197.99 104.07 105.93 -197.99

[ Kg(2) ] [ T ] T [ Kl(2) ]

[Kg(2)]

[ T ] T

[ Kl ]

[ T ] T [ Kl(3) ]

[ Kg(3) ] [ T ] T [ Kl(2) ]

[Kg(3)]

-197.99 197.99 0.00 197.99 -197.99 56000.00MENYUSUN OVERALL STIFFNESS MATRIX

=

1.87 0 -280 -1.87 0 -280 0 0 00 280 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 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

=

0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 01 1 0 74.58 -73.92 98.99 -74.58 73.92 98.990 0 1 -73.92 74.58 98.99 73.92 -74.58 98.990 0 0 98.99 98.99 39597.99 -98.99 -98.99 19798.990 0 0 -74.58 73.92 -98.99 74.58 -73.92 -98.990 0 0 73.92 -74.58 -98.99 -73.92 74.58 -98.990 0 0 98.99 98.99 19798.99 -98.99 -98.99 39597.99

1.87 0.00 -280.00 -1.87 0 -280 0 0 00 280 0 0 -280 0 0 0 0

-280 0 56000 280 0 28000 0 0 0-1.16 0.71 280 76.44 -73.92 378.99 -74.58 73.92 98.99

0 -280 1 -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 -98.990 0 0 73.92 -74.58 -98.99 -73.92 74.58 -98.990 0 0 98.99 98.99 19798.99 -98.99 -98.99 39597.99

UNKNOWN DISPLACEMENT AND REACTIONS

H 2.0 76.44 -73.92 378.99V -3.0 = -73.92 354.58 98.99M 0 378.99 98.99 95597.99

-176.44 -73.92 378.99 2.0

= -73.92 354.58 98.99 -3.0378.99 98.99 95597.99 0

= 0.016846 0.003531 -0.000070 2.00.003531 0.003561 -0.000018 -3.0

-0.000070 -0.000018 0.000011 0

U2 0.02310

[Kg(3)]

[Kg(1)]

[Kg(2)]

U2V2θ2

U2V2θ2

V2 = -0.00362θ2 -0.00009

F1 -1.87 0.00 -280.00 -0.019G1 0.00 -280.00 0.00 0.02310 1.014M1

=280.00 0.00 28000.00 -0.00362

=4.008

F3 -74.58 73.92 -98.99 -0.00009 -1.981G3 73.92 -74.58 -98.99 1.986M3 98.99 98.99 19798.99 0.189

MEMBER FORCES

ELEMEN 1

00

[ U ] =0

0.02310-0.00362-0.00009

[ T ]

0 280 0 0 -280 0-1.8667 0 280 1.8667 0 280

=-280 0 56000 280 0 28000

0 -280 0 0 280 01.8667 0 -280 -1.8667 0 -280

-280 0 28000 280 0 56000

f1 1.01399g1 0.01853m1

= [ T ] [ U ] =4.00828

f2 -1.01399g2 -0.01853m2 1.54940

ELEMEN 2

0.02310-0.00362

[ U ] =-0.00009

000

[ Kg(1) ]

[ Kg(1) ]

[ T ]105.00 -105.00 0.00 -105.00 105.00 0.00

0.47 0.47 140.00 -0.47 -0.47 140.00

=98.99 98.99 39597.99 -98.99 -98.99 19798.99

-105.00 105.00 0.00 105.00 -105.00 0.00-0.47 -0.47 -140.00 0.47 0.47 -140.0098.99 98.99 19798.99 -98.99 -98.99 39597.99

f2 #VALUE!g2 #VALUE!m2

= [ T ] [ U ] =#VALUE!

f3 #VALUE!g3 #VALUE!m3 #VALUE!

FREE BODY

#VALUE!1.01399 #VALUE!

0.01853

1.54940 #VALUE!

#VALUE!

0.01853 4.00828#VALUE!

1.01399 #VALUE!

β = 45.00 derajad

H1 = -0.019 ton

V1 = 1.014 ton

M1 = 4.008 ton m

[ Kg(2) ]

[ Kg(2) ]

H2 = = #VALUE! ton

V2 = = #VALUE! ton

M2 = 1.54940 #VALUE! = #VALUE! ton m

H3 = = #VALUE! ton

V3 = = #VALUE! ton

M3 = #VALUE! ton m

#VALUE!

#VALUE!

0.019 #VALUE! #VALUE!4.008

1.014 #VALUE!

( 0,01287 + 6,59747 cos β - 0,00436 sin β ) =

( -2,33644 - 6,59747 sin β - 0,00436 cos β ) =

m2(1) + m2(2) =

(- 6,59747 cos β + 0,00436 sin β ) =

( 6,59747 sin β + 0,00436 cos β ) =

BATANG 3A = 30 cm²I = 2000L = 300.00 cm

cm^4

anstruk matriks

Documents

cm cm 4 cm

ton ton

ton

batang 3

Transcript of anstruk matriks

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