Tgs Matrix Kd3

DataE = 2100 ton/cm2 P2 = 4 tonH = 3 mL = 4 mP = 4 tonM = -4 ton-m

Batang 1A = 120 cm2

I = 4000 cm4

Batang 2A = 120 cm2

PENYELESAIAN : I = 4000 cm4

1). DEGREE OF FREEDOM (D.O.F)

2). Matrik Kekakuan Dalam SUMBU LOKALa. Batang 1 (AB)

E = 21000000 t/m2 Batang 1 = 5 m sin a = 0.602A = 0.012 m2 a = 37.000 cos2 a = 0.638I = 0.00004 m4 cos a = 0.799 sin2 a = 0.362

50400 0 0 -50400 0 00 80.640 201.600 0 -80.640 201.6000 201.600 672.000 0 -201.600 672.000

[k]1= -50400 0 0 50400 0 00 -80.640 -201.600 0 80.640 -201.6000 201.600 336.000 0 -201.600 336.000

DbxDby

2

1

Rbz

L

H

P

21

C

B

A

M

P

b. Batang 2 (BC)E = 21000000 t/m2 batang 2 = 3 m sin a = 1A = 0.012 m2 a = 90 cos2 a = 4E-33I = 0.00004 m4 cos a = 6E-17 sin2 a = 1

84000 0 0 -84000 0 00 373.333 560 0 -373.333 5600 560 1120 0 -560 1120

[k]2= -84000 0 0 84000 0 00 -373.333 -560 0 373.333 -5600 560 560 0 -560 560

3). Matrik Kekakuan SUMBU GLOBAL [kg] = [T]T.[kl].[T]a. Batang 1 (AB)

a = 90 cos a = 0.00sin a = 1.00

6.12574E-17 1 0 0 0 0-1 6.12574E-17 0 0 0 0

[T]1= 0 0 1 0 0 00 0 0 6.12574E-17 1 00 0 0 -1 6.12574E-17 00 0 0 0 0 1

[kg] = [T]T.[kl].[T] :

80.640 0.000 -201.600 -80.640 0.000 -201.6000.000 50400.000 0.000 0.000 -50400.000 0.000

[Kg]1= -201.600 0.000 672.000 201.600 0.000 672.000-80.640 0.000 201.600 80.640 0.000 201.6000.000 -50400.000 0.000 0.000 50400.000 0.000

-201.600 0.000 336.000 201.600 0.000 336.000

b. Batang 2 (BC)a = 90

cos a = 0sin a = 1

0 1 0 0 0 0-1 0 0 0 0 0

[T]2= 0 0 1 0 0 00 0 0 0 1 00 0 0 -1 0 00 0 0 0 0 1

Sehingga [kg] = [T]T.[kl].[T] :

373.333 0.0E+00 -560 -373.333 0.0E+00 -560- 84000 0.0E+00 0.0E+00 -84000 0.0E+00

[Kg]2= -560 0.0E+00 1120 560 0.0E+00 1120-373.3333 0.0E+00 560 373.3333 0.0E+00 5600.0E+00 -84000 0.0E+00 0.0E+00 84000 0.0E+00

-560 0.0E+00 560 560 0.0E+00 560

4). Perakitan Matriks Kekakuan Struktur Global Tereduksi

80.640 0.000 -201.600 -80.640 0.000 -201.600 0 0 00.000 50400.000 0.000 0.000 -50400.000 0.000 0 0 0

-201.600 0.000 672.000 201.600 0.000 672.000 0 0 0[Kg]s = -80.640 0.000 201.600 453.973 0.000 -358.400 -373.333 0.000 -560.000

0.000 -50400.000 0.000 0.000 134400.000 0.000 0 -84000.000 0-201.600 0.000 336.000 -358.400 0.000 1456.000 560.000 0 1120.000

0 0 0 -373.333 0 560.000 373.333 0 560.0000 0 0 0 -84000.000 0 0 84000.000 00 0 0 -560.000 0 560.000 560.000 0 560.000

SETELAH DIRDUKSI :

453.973 0.000 -358.400[Kg]s = 0.000 134400.000 0.000

-358.400 0.000 1456.000

5). Vektor Perpindahan {D} =[Kg]SR-1 . [{F} + {Fo}]

4 453.973 0.000 -358.400 Dbx4 = 0.000 134400.000 0.000 x Dby-4 -358.400 0.000 1456.000 Rbz

Dbx 0.0027341 0.0000000 0.0006730 4Dby = 0.0000000 0.0000074 0.0000000 x 4Rbz 0.0006730 0.0000000 0.0008525 -4

Dbx 0.0082 mDby = 0.0000 mRbz -0.0007 m

6). Vektor perpindahan bagi masing-masing elemen {d}i = [T]i . {D}a. Batang 1

00

{d}1 = 00.000030-0.008244

-0.000718

b. Batang 2

0.000030-0.008244

{d}2 = -0.000718000

7). Element Forces : {f} = [k]i {d}i - {fo}ia. Batang 1 (AB)

f1 50400 0 0 -50400 0 0 0.000000 0f2 0 81 202 0 -81 202 0.000000 0f3 = 0 202 672 0 -202 672 x 0.000000 - 0f4 -50400 0 0 50400 0 0 0.000030 4f5 0 -81 -202 0 81 -202 -0.008244 4f6 0 202 336 0 -202 336 -0.000718 -4

f1 -1.500 0 -1.500 tonf2 0.520 0 0.520 tonf3 = 1.180 - 0 = 1.180 ton-mf4 1.500 4 -2.500 tonf5 -0.520 4 -4.520 tonf6 1.421 -4 5.421 ton-m

b. Batang 2 (BC)

f1 84000 0 0 -84000 0 0 0.00003 4 Dbxf2 0 373 560 0 -373 560 -0.00824 4 Dbyf3 = 0 560 1120 0 -560 1120 x -0.00072 - -4 Rbzf4 -84000 0 0 84000 0 0 0.00000 0 Dcxf5 0 -373 -560 0 373 -560 0.00000 0 Dcyf6 0 560 560 0 -560 560 0.00000 0 Rcz

f1 2.500 4 -1.500 tonf2 -3.480 4 -7.480 tonf3 = -5.421 - -4 = -1.421 ton-mf4 -2.500 0 -2.500 tonf5 3.480 0 3.480 tonf6 -5.019 0 -5.019 ton-m

8). Reaksi Tumpuan {F} = [Kg]s.{D} - ({F}+{Fo})

80.640 0.000 -201.600 -80.640 0.000 -201.600 0 0 0 0 00.000 50400.000 0.000 0.000 -50400.000 0.000 0 0 0 0 0

-201.600 0.000 672.000 201.600 0.000 672.000 0 0 0 0 0[F] = -80.640 0.000 201.600 453.973 0.000 -358.400 -373.333 0.000 -560.000 0.00824435 4

0.000 -50400.000 0.000 0.000 134400.000 0.000 0.000 -84000.000 0.000 x 2.9762E-05 - 4-201.600 0.000 336.000 -358.400 0.000 1456.000 560.000 0.000 1120.000 -0.0007179 -4

0 0 0 -373.333 0.000 560.000 373.333 0.000 560.000 0 00 0 0 0.000 -84000.000 0.000 0.000 84000.000 0.000 0 00 0 0 -560.000 0.000 560.000 560.000 0.000 560.000 0 0

-0.520 0 -0.520 ton-1.500 0 -1.500 ton1.180 0 1.180 ton-m

[F] = 4.000 - 4 = 0 ton4.000 4 0 ton-4.000 -4 0 ton-m-3.480 0 -3.480 ton-2.500 0 -2.500 ton-5.019 0 -5.019 ton-m

8). GAMBAR

-2.500 5.421

-1.500 -7.480 -1.421-4.520

0.520-1.500 1.180

-2.500 3.480-5.019

NFD SFD BMD

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Tgs Matrix Kd3