E = 2100 t/cm²A₁ = 100 cm² A₂ = 40I₁ = 5000 cm⁴ I₂ = 1000L₁ = 500 cm L₂ = 300

a. Matrik Kekakuan Elemen Elemen I

420 0 0 -4200 1 252 0

[k₁] = 0 252 84000 0-420 0 0 420

0 -1 -252 00 252 42000 0

1 1 0 0-1 1 0 0

[T₁] = 0 0 1 00 0 0 10 0 0 -10 0 0 0

269 201 -151 -269201 152 202 -201

-151 202 84000 151-269 -201 151 269-201 -152 -202 201-151 202 42000 151

Elemen II280 0 0 -280

0 1 140 0[k₂] = 0 140 28000 0

-280 0 0 2800 -1 -140 00 140 14000 0

0 -1 0 01 0 0 0

[T₂] = 0 0 1 00 0 0 00 0 0 10 0 0 0

[kg] = [TT][k₁][T]

[kg] =

[kg] = [TT][k₂][T]

1 0 140 -10 280 0 0

140 0 28000 -140-1 0 -140 10 -280 0 0

140 0 14000 -140

b. Overall Stiffness MatrixElemen 1

F₁ 269 201 -151 -269G₁ 201 152 202 -201M₁ -151 202 84000 151-4 -269 -201 151 2690 = -201 -152 -202 201

500 -151 202 42000 151F₃G₃M₃

Elemen 2F₁G₁M₁-4 10 = 0

500 140F₃ -1G₃ 0M₃ 140

Total-4 269 201 -151 -2690 201 152 202 -201

500 -151 202 84000 151F1 -269 -201 151 270G1 = -201 -152 -202 201M1 -151 202 42000 291F3 0 0 0 -1G3 0 0 0 0M3 0 0 0 140

c. Penyesuaian Matriks Kekakuan Menyeluruh-4 270 201 291 -2690 201 432 -202 -201

500 291 -202 112000 -151F1 -269 -201 -151 269G1 -201 -152 202 201

[kg] =

M1 151 -202 42000 -151F3 -1 0 -140 0G3 0 -280 0 0M3 140 0 14000 0

d. Perpindahan-4 270 201 291 U20 201 432 -202 V2

500 291 -202 112000 θ2

0.0057107 -0.0026687 -0.0000197-0.0026687 0.0035648 0.0000134-0.0000197 0.0000134 0.0000090

e. Gaya-gaya Reaksi-269.16 -201.12 -151.20-201.12 -151.85 201.60151.20 -201.60 42000.00-0.93 0.00 -140.000.00 -280.00 0.00

140.00 0.00 14000.00

f. Gaya-gaya ElemenElemen 1

F1 1 1 0 0G1 -1 1 0 0M1 0 0 1 0F2 0 0 0 1G2 0 0 0 -1M2 0 0 0 0

cm² L₃ = 400 cmcm⁴ sin a₁ = 1cm cos a₁ = 1

0 0-1 252

-252 420000 01 -252

-252 84000

0 00 0

0 01 01 00 1

-201 -151-152 202

-202 42000201 151152 -202-202 84000

0 0-1 140

-140 140000 01 -140

-140 28000

0 00 0

0 0-1 00 00 1

[kg] =

[TT] =

[TT][k₁] =

[kg] =

[TT] =

0 140-280 0

0 140000 -140

280 00 28000

-201 -151-152 202-202 42000201 151152 -202-202 84000

0 140 -1 0280 0 0 -280

0 28000 -140 00 -140 1 0

-280 0 0 2800 14000 -140 0

-201 -151 0 0-152 202 0 0-202 42000 0 0201 291 -1 0432 -202 0 -280-202 112000 -140 0

0 -140 1 0-280 0 0 280

0 14000 -140 0

-201 151 -1 0-152 -202 0 -280202 42000 -140 0201 -151 0 0152 202 0 0

[TT][k₂] =

202 84000 0 00 0 1 00 0 0 2800 0 -140 0

-4 -0.0330 0.017

500 0.005

4.614.86

183.94-0.61-4.8659.55

0 0 269.160 0 201.120 0 -151.201 0 -269.161 0 -201.120 1 -151.20

Gaya eksternal

sin a₂ = -1 F₂ = -4cos a₂ = 0 G₂ = 0

M₂ = 5

Cara Langsung269 201 -151 -269201 152 202 -201-151 202 84000 151-269 -201 151 269-201 -152 -202 201-151 202 42000 151

1 -1 0 01 1 0 0

0 0 1 00 0 0 10 0 0 10 0 0 0

336 -1 -151 -336252 1 202 -252

0 252 84000 0-336 1 151 336-252 -1 -202 252

0 252 42000 0

Cara langsung1 0 140 -10 280 0 0

140 0 28000 -140-1 0 -140 10 -280 0 0

140 0 14000 -140

0 1 0 0-1 0 0 0

0 0 1 00 0 0 00 0 0 -10 0 0 0

[kg] = [TT][k₁][T]

[kg] = [TT][k₂][T]

0 1 140 0-280 0 0 280

0 140 28000 00 -1 -140 0

280 0 0 -2800 140 14000 0

1400

14000-140

028000

0 00 00 0

140 U20 V2

14000 θ2-140 0

0 028000 0

140 U20 V2

14000 θ20 00 0

0 0-140 0

0 028000 0

201.12 -151.20 -269.16 -201.12151.85 201.60 -201.12 -151.85201.60 84000.00 151.20 -201.60-201.12 151.20 269.16 201.12-151.85 -201.60 201.12 151.85201.60 42000.00 151.20 -201.60

tt

tm

-201 -151-152 202-202 42000201 151152 -202-202 84000

0 00 0

0 0-1 01 00 1

1 -151-1 202

-252 42000-1 1511 -202

-252 84000

0 140-280 0

0 140000 -140

280 00 28000

0 00 0

0 01 00 00 1

-1 1400 0

-140 140001 -1400 0

-140 28000

-151.20 0 6.60201.60 0 1.12

42000.00 0 = 183.94151.20 -0.033 -6.60-201.60 0.017 -1.12

84000.00 0.005 376.32