PENYELESAIAN CONTOH 3

DIK

Iz = 258,000 cm4L = 4 mE = 210,000 N/CM2V3 = -1,000 KN

12.000

ka = Eiz 6LL^3 -12

6L

KA = 846.563 122,400

-122,400

Ka = 10,158.750 2,031,750.0002,031,750.000 541,800,000.000

-10,158.750 -2,031,750.0002,031,750.000 270,900,000.000

catatan Ka=kb

f1=

ka11 ka12f2 ka21 ka22+kb11f3 0.000 kb21

V1

=

10,158.750 2,031,750.000M1 2,031,750.000 541,800,000.000V2 -10,158.750 -2,031,750.000M2 2,031,750.000 270,900,000.000V3 0.000 0.000M3 0.000 0.000

bondary condition ada 3

M2=

1,083,600,000.000 -2,031,750.000V3 -2,031,750.000 10,158.750M3 270,900,000.000 -2,031,750.000

x2=

1,083,600,000.000 -2,031,750.000v3 -2,031,750.000 10,158.750x3 270,900,000.000 -2,031,750.000

x2=

0.000000002 0.000000738v3 0.000000738 0.000689061x3 0.000000002 0.000002215

x2=

-0.738280 radv3 -689.061154 cmx3 -2.214839 rad

element batang a

V1

=

10,158.750 2,031,750.000M1 2,031,750.000 541,800,000.000V2 -10,158.750 -2,031,750.000M2 2,031,750.000 270,900,000.000

V1

=

-1,500,000 NM1 -200,000,000 NcmV2 1,500,000 NM2 -400,000,000 Ncm

element batang b

V2

=

10,158.750 2,031,750.000M2 2,031,750.000 541,800,000.000V3 -10,158.750 -2,031,750.000M3 2,031,750.000 270,900,000.000

V2

=

1,000,000 NM2 400,000,000 NcmV3 -1,000,000 NM3 0 Ncm

= 400 cm

= -1,000,000 N

6L -12 6L

4L^2 -6L 2L^2-6L 12.000 -6L

2L^2 -6L 4L^2

2,400 -12 2,400640,000 -2,400 320,000

-2,400 12 -2,400320,000 -2,400 640,000

-10,158.750 2,031,750.000-2,031,750.000 270,900,000.000

10,158.750 -2,031,750.000-2,031,750.000 541,800,000.000

0.000x

d1kb12 d2kb22 d3

-10,158.750 2,031,750.000 0.000 0.000-2,031,750.000 270,900,000.000 0.000 0.000

20,317.500 0.000 -10,158.750 2,031,750.0000.000 1,083,600,000.000 -2,031,750.000 270,900,000.000

-10,158.750 -2,031,750.000 10,158.750 -2,031,750.0002,031,750.000 270,900,000.000 -2,031,750.000 541,800,000.000

270,900,000.000x

x2-2,031,750.000 v3

541,800,000.000 x3

270,900,000.000 -1x

M2-2,031,750.000 V3

541,800,000.000 M3

0.000000002x

0.0000.000002215 -1,000,000.0000.000000009 0.000

v1 = 0.000x1 = 0.000v2 = 0.000

-10,158.750 2,031,750.000

X

0.000000-2,031,750.000 270,900,000.000 0.000000

10,158.750 -2,031,750.000 0.000000-2,031,750.000 541,800,000.000 -0.738280

=

-1,500 KN-2,000 KNm1,500 KN

-4,000 KNm

-10,158.750 2,031,750.000

X

0.000-2,031,750.000 270,900,000.000 -0.738

10,158.750 -2,031,750.000 -689.061-2,031,750.000 541,800,000.000 -2.215

=

1,000 KN4,000 KNm

-1,000 KN0 KNm

X

v1x1v2x2v3x3

v1x1v2x2

v2x2v3x3

PENYELESAIAN CONTOH 3

DIK

Iz = 258,000 cm4L = 4 mL2 = 5 mE = 210,000 N/CM2V3 = -1,000 KN

12

ka = Eiz 6LL^3 -12

6L

KA = 846.563 122,400

-122,400

Ka = 10,158.750 2,031,750.0002,031,750.000 541,800,000.000

-10,158.750 -2,031,750.0002,031,750.000 270,900,000.000

f1=

ka11 ka12f2 ka21 ka22+kb11f3 0.000 kb21

V1

=

10,158.750 2,031,750.000M1 2,031,750.000 541,800,000.000V2 -10,158.750 -2,031,750.000M2 2,031,750.000 270,900,000.000V3 0.000 0.000M3 0.000 0.000

bondary condition ada 3

M2=

975,240,000.000 -1,300,320.000V3 -1,300,320.000 5,201.280M3 216,720,000.000 -1,300,320.000

x2=

975,240,000.000 -1,300,320.000v3 -1,300,320.000 5,201.280x3 216,720,000.000 -1,300,320.000

x2=

0.000000002 0.000000923v3 0.000000923 0.001230466x3 0.000000002 0.000003230

x2=

-0.922850 radv3 -1,230.466347 cmx3 -3.229974 rad

element batang a

V1

=

10,158.750 2,031,750.000M1 2,031,750.000 541,800,000.000V2 -10,158.750 -2,031,750.000M2 2,031,750.000 270,900,000.000

V1

=

-1,875,000 NM1 -250,000,000 NcmV2 1,875,000 NM2 -500,000,000 Ncm

element batang b

V2

=

5,201.280 1,300,320.000M2 1,300,320.000 433,440,000.000V3 -5,201.280 -1,300,320.000M3 1,300,320.000 216,720,000.000

V2

=

1,000,000 NM2 500,000,000 NcmV3 -1,000,000 NM3 0 Ncm

= 400 cm= 500 cm

= -1,000,000 N

6L -12 6L

4L^2 -6L 2L^2-6L 12 -6L

2L^2 -6L 4L^2

2,400 -12 2,400640,000 -2,400 320,000

-2,400 12 -2,400320,000 -2,400 640,000

-10,158.750 2,031,750.000-2,031,750.000 270,900,000.000

10,158.750 -2,031,750.000-2,031,750.000 541,800,000.000

0.000x

d1kb12 d2kb22 d3

-10,158.750 2,031,750.000 0.000 0.000-2,031,750.000 270,900,000.000 0.000 0.000

15,360.030 -731,430.000 -5,201.280 1,300,320.000-731,430.000 975,240,000.000 -1,300,320.000 216,720,000.000

-5,201.280 -1,300,320.000 5,201.280 -1,300,320.0001,300,320.000 216,720,000.000 -1,300,320.000 433,440,000.000

216,720,000.000x

x2-1,300,320.000 v3

433,440,000.000 x3

216,720,000.000 -1x

M2-1,300,320.000 V3

433,440,000.000 M3

0.000000002x

0.0000.000003230 -1,000,000.0000.000000011 0.000

v1 = 0.000x1 = 0.000v2 = 0.000

-10,158.750 2,031,750.000

X

0.000000-2,031,750.000 270,900,000.000 0.000000

10,158.750 -2,031,750.000 0.000000-2,031,750.000 541,800,000.000 -0.922850

=

-1,875 KN-2,500 KNm1,875 KN

-5,000 KNm

-5,201.280 1,300,320.000

X

0.000-1,300,320.000 216,720,000.000 -0.923

5,201.280 -1,300,320.000 -1,230.466-1,300,320.000 433,440,000.000 -3.230

=

1,000 KN5,000 KNm

-1,000 KN0 KNm

12 6L

kb = Eiz 6L 4L^2L^3 -12 -6L

6L 2L^2

12 3,000kb = 433.440 3,000 1,000,000

-12 -3,0003,000 500,000

Kb = 5,201.280 1,300,320.000 -5,201.2801,300,320.000 433,440,000.000 -1,300,320.000

-5,201.280 -1,300,320.000 5,201.2801,300,320.000 216,720,000.000 -1,300,320.000

X

v1x1v2x2v3x3

v1x1v2x2

v2x2v3x3

-12 6L

-6L 2L^212 -6L-6L 4L^2

-12 3,000-3,000 500,000

12 -3,000-3,000 1,000,000

1,300,320.000216,720,000.000

-1,300,320.000433,440,000.000