Data Soal

Batang L (m) AE/L1,2,3,4,5,6 0.00047 21000000 2.5 39487,9,10,12 0.00047 21000000 2.915476 3385.3828,11 0.00047 21000000 1.5 658014,18 0.00047 21000000 3.5 282013,19,20,21 0.00047 21000000 3.201562 3082.8715,17 0.00047 21000000 6.041523 1633.69416 0.00047 21000000 5.5 1794.545

A (m²) E (t/m²)

4.70 cm2 0.00047

sudut

sin α 0.51449576 α 30.96376cos α 0.85749293

sin β 0.9103665 β 65.55605cos β 0.41380294

sin γ 0.85749289 β' 24.44395cos γ 0.51449581

γ 59.03624

sin α' 0.62469505 α' 38.65981 3.201562cos α' 0.78086881

Menyusun matriks kekakuan global

AE/L 0 -AE/L 0 = 0 0 0 0

-AE/L 0 AE/L 00 0 0 0

Sin α 0 0 Cos α -Sin α 0 0 = -Sin α 0 0 = Sin α Cos α 0 0

0 0 Sin α 0 0 Cos α -Sin α0 0 -Sin α 0 0 Sin α Cos α

a. Matriks Kekakuan Batang 1 (node 1 - 3) α =

3948 0 -3948 0 = 0 0 0 0

-3948 0 3948 00 0 0 0

1 0 0 0 1 0 0 0 = 0 1 0 0 = 0 1 0 0

0 0 1 0 0 0 1 00 0 0 1 0 0 0 1

u1 v1 u3 v33948 0 -3948 0 u1

= 0 0 0 0 v1-3948 0 3948 0 u3

0 0 0 0 v3

b. Matriks Kekakuan Batang 2 (node 3 - 4) α =

3948 0 -3948 0 = 0 0 0 0

-3948 0 3948 00 0 0 0

1 0 0 0 1 0 0 0 = 0 1 0 0 = 0 1 0 0

0 0 1 0 0 0 1 00 0 0 1 0 0 0 1

u3 v3 u4 v43948 0 -3948 0 u3

= 0 0 0 0 v3-3948 0 3948 0 u4

0 0 0 0 v4

Cos αCos α

Cos αCos α

0°

0°

[ 〖𝐾 _𝑙〗^((1) ) ]

[𝐾^((𝑒) ) ]

[𝑇^((1) ) ]

[𝑇^((𝑒) ) ] [𝑇^((𝑒)) ]^𝑇

[𝑇^((1)) ]^𝑇

[ 〖𝐾 _𝑔〗^((1) ) ]

[ 〖𝐾 _𝑙〗^((2) ) ][𝑇^((2) ) ] [𝑇^((2)) ]^𝑇

[ 〖𝐾 _𝑔〗^((2) ) ]

)()()()( eeTeeg TkTK

c. Matriks Kekakuan Batang 3 (node 4 - 5) α =

3948 0 -3948 0 = 0 0 0 0

-3948 0 3948 00 0 0 0

1 0 0 0 1 0 0 0 = 0 1 0 0 = 0 1 0 0

0 0 1 0 0 0 1 00 0 0 1 0 0 0 1

u4 v4 u5 v53948 0 -3948 0 u4

= 0 0 0 0 v4-3948 0 3948 0 u5

0 0 0 0 v5

d. Matriks Kekakuan Batang 4 (node 5 - 6) α =

3948 0 -3948 0 = 0 0 0 0

-3948 0 3948 00 0 0 0

1 0 0 0 1 0 0 0 = 0 1 0 0 = 0 1 0 0

0 0 1 0 0 0 1 00 0 0 1 0 0 0 1

u5 v5 u6 v63948 0 -3948 0 u5

= 0 0 0 0 v5-3948 0 3948 0 u6

0 0 0 0 v6

e. Matriks Kekakuan Batang 5 (node 6 - 7) α =

3948 0 -3948 0 = 0 0 0 0

-3948 0 3948 00 0 0 0

1 0 0 0 1 0 0 0 = 0 1 0 0 = 0 1 0 0

0 0 1 0 0 0 1 00 0 0 1 0 0 0 1

u6 v6 u7 v7

0°

0°

0°

[ 〖𝐾 _𝑔〗^((2) ) ]

[ 〖𝐾 _𝑙〗^((3) ) ][𝑇^((3) ) ] [𝑇^((3)) ]^𝑇

[ 〖𝐾 _𝑔〗^((3) ) ]

[ 〖𝐾 _𝑙〗^((4) ) ][𝑇^((4) ) ] [𝑇^((4)) ]^𝑇

[ 〖𝐾 _𝑔〗^((4) ) ]

[ 〖𝐾 _𝑙〗^((5) ) ][𝑇^((5) ) ] [𝑇^((5)) ]^𝑇

3948 0 -3948 0 u6 = 0 0 0 0 v6

-3948 0 3948 0 u70 0 0 0 v7

f. Matriks Kekakuan Batang 6 (node 7 - 2) α =

3948 0 -3948 0 = 0 0 0 0

-3948 0 3948 00 0 0 0

1 0 0 0 1 0 0 0 = 0 1 0 0 = 0 1 0 0

0 0 1 0 0 0 1 00 0 0 1 0 0 0 1

u7 v7 u2 v23948 0 -3948 0 u7

= 0 0 0 0 v7-3948 0 3948 0 u2

0 0 0 0 v2

f. Matriks Kekakuan Batang 7 (node 1 - 8) α = 30.964

3385.382 0 -3385.382 0 = 0 0 0 0

-3385.382 0 3385.382 00 0 0 0

0.8575 0.5145 0 0 0.8575 -0.5145 0 0 = -0.5145 0.8575 0 0 = 0.5145 0.8575 0 0

0 0 0.8575 0.5145 0 0 0.8575 -0.51450 0 -0.5145 0.8575 0 0 0.5145 0.8575

u1 v1 u8 v82489.252 1493.551 -2489.252 -1493.551 u1

= 1493.551 896.131 -1493.551 -896.131 v1-2489.252 -1493.551 2489.252 1493.551 u8-1493.551 -896.131 1493.551 896.131 v8

f. Matriks Kekakuan Batang 8 (node 3 - 8) α = 90°

6580 0 -6580 0 = 0 0 0 0

-6580 0 6580 00 0 0 0

0 1 0 0 0 -1 0 0 = -1 0 0 0 = 1 0 0 0

0 0 0 1 0 0 0 -1

0°

[ 〖𝐾 _𝑔〗^((5) ) ][ 〖𝐾 _𝑙〗^((6) ) ][𝑇^((6) ) ] [𝑇^((6)) ]^𝑇

[ 〖𝐾 _𝑔〗^((6) ) ]

[ 〖𝐾 _𝑙〗^((7) ) ][𝑇^((7) ) ] [𝑇^((7)) ]^𝑇

[ 〖𝐾 _𝑔〗^((7) ) ]

[ 〖𝐾 _𝑙〗^((8) ) ][𝑇^((8) ) ] [𝑇^((8)) ]^𝑇

0 0 -1 0 0 0 1 0u3 v3 u8 v80 0 0 0 u3

= 0 6580 0 -6580 v30 0 0 0 u80 -6580 0 6580 v8

f. Matriks Kekakuan Batang 9 (node 4 - 8) α = 149.03624

3385.382 0 -3385.382 0 = 0 0 0 0

-3385.382 0 3385.382 00 0 0 0

-0.8575 0.5145 0 0 -0.8575 -0.5145 0 0 = -0.5145 -0.8575 0 0 = 0.5145 -0.8575 0 0

0 0 -0.8575 0.5145 0 0 -0.8575 -0.51450 0 -0.5145 -0.8575 0 0 0.5145 -0.8575

u4 v4 u8 v82489.251 -1493.551 -2489.251 1493.551 u4

= -1493.551 896.131 1493.551 -896.131 v4-2489.251 1493.551 2489.251 -1493.551 u81493.551 -896.131 -1493.551 896.131 v8

f. Matriks Kekakuan Batang 10 (node 6 - 9) α = 30.96376

3385.382 0 -3385.382 0 = 0 0 0 0

-3385.382 0 3385.382 00 0 0 0

0.8575 0.5145 0 0 0.8575 -0.5145 0 0 = -0.5145 0.8575 0 0 = 0.5145 0.8575 0 0

0 0 0.8575 0.5145 0 0 0.8575 -0.51450 0 -0.5145 0.8575 0 0 0.5145 0.8575

u6 v6 u9 v92489.252 1493.551 -2489.252 -1493.551 u6

= 1493.551 896.131 -1493.551 -896.131 v6-2489.252 -1493.551 2489.252 1493.551 u9-1493.551 -896.131 1493.551 896.131 v9

f. Matriks Kekakuan Batang 11 (node 7 - 9) α = 90

6580 0 -6580 0 = 0 0 0 0

-6580 0 6580 00 0 0 0

0 1 0 0 0.0000 -1.0000 0 0

[ 〖𝐾 _𝑔〗^((8) ) ][ 〖𝐾 _𝑙〗^((9) ) ][𝑇^((9) ) ] [𝑇^((9)) ]^𝑇[ 〖𝐾 _𝑔〗^((9) ) ]

[ 〖𝐾 _𝑙〗^((10) ) ][𝑇^((10) ) ]

[𝑇^((10)) ]^𝑇

[ 〖𝐾 _𝑔〗^((10) ) ]

[ 〖𝐾 _𝑙〗^((11) ) ][𝑇^((11) ) ]

[𝑇^((11)) ]^𝑇

= -1 0 0 0 = 1.0000 0.0000 0 00 0 0 1 0 0 0.0000 -1.00000 0 -1 0 0 0 1.0000 0.0000

u7 v7 u9 v90 0 0 0 u7

= 0 6580 0 -6580 v70 0 0 0 u90 -6580 0 6580 v9

f. Matriks Kekakuan Batang 12 (node 2 - 9) α = 149.03624

3385.382 0 -3385.382 0 = 0 0 0 0

-3385.382 0 3385.382 00 0 0 0

-0.8575 0.5145 0 0 -0.8575 -0.5145 0 0 = -0.5145 -0.8575 0 0 = 0.5145 -0.8575 0 0

0 0 -0.8575 0.5145 0 0 -0.8575 -0.51450 0 -0.5145 -0.8575 0 0 0.5145 -0.8575

u2 v2 u9 v92489.251 -1493.551 -2489.251 1493.551 u2

= -1493.551 896.131 1493.551 -896.131 v2-2489.251 1493.551 2489.251 -1493.551 u91493.551 -896.131 -1493.551 896.131 v9

f. Matriks Kekakuan Batang 13 (node 8 - 10) α = 38.65981

3082.870 0 -3082.870 0 = 0 0 0 0

-3082.870 0 3082.870 00 0 0 0

0.7809 0.6247 0 0 0.7809 -0.6247 0 0 = -0.6247 0.7809 0 0 = 0.6247 0.7809 0 0

0 0 0.7809 0.6247 0 0 0.7809 -0.62470 0 -0.6247 0.7809 0 0 0.6247 0.7809

u8 v8 u10 v101879.799 1503.839 -1879.799 -1503.839 u8

= 1503.839 1203.071 -1503.839 -1203.071 v8-1879.799 -1503.839 1879.799 1503.839 u10-1503.839 -1203.071 1503.839 1203.071 v10

f. Matriks Kekakuan Batang 14 (node 4 - 10) α = 90

2820 0 -2820 0 = 0 0 0 0

-2820 0 2820 00 0 0 0

[𝑇^((11) ) ][𝑇^((11)) ]^𝑇

[ 〖𝐾 _𝑔〗^((11) ) ][ 〖𝐾 _𝑙〗^((12) ) ][𝑇^((12) ) ]

[𝑇^((12)) ]^𝑇

[ 〖𝐾 _𝑔〗^((12) ) ]

[ 〖𝐾 _𝑙〗^((13) ) ][𝑇^((13) ) ]

[𝑇^((13)) ]^𝑇

[ 〖𝐾 _𝑔〗^((13) ) ]

[ 〖𝐾 _𝑙〗^((14) ) ]

0 1 0 0 0 -1 0 0 = -1 0 0 0 = 1 0 0 0

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

u4 v4 u10 v100 0 0 0 u4

= 0 2820 0 -2820 v40 0 0 0 u100 -2820 0 2820 v10

f. Matriks Kekakuan Batang 15 (node 4 - 12) α = 65.5560

1633.694 0 -1633.694 0 = 0 0 0 0

-1633.694 0 1633.694 00 0 0 0

0.4138 0.9104 0 0 0.4138 -0.9104 0 0 = -0.9104 0.4138 0 0 = 0.9104 0.4138 0 0

0 0 0.4138 0.9104 0 0 0.4138 -0.91040 0 -0.9104 0.4138 0 0 0.9104 0.4138

u4 v4 u12 v12279.742 615.433 -279.742 -615.433 u4

= 615.433 1353.952 -615.433 -1353.952 v4-279.742 -615.433 279.742 615.433 u12-615.433 -1353.952 615.433 1353.952 v12

f. Matriks Kekakuan Batang 16 (node 5 - 12) α = 90

1794.545 0 -1794.545 0 = 0 0 0 0

-1794.545 0 1794.545 00 0 0 0

0 1 0 0 0 -1 0 0 = -1 0 0 0 = 1 0 0 0

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

u5 v5 u12 v120 0 0 0 u5

= 0 1794.545 0 -1794.545 v50 0 0 0 u120 -1794.545 0 1794.545 v12

f. Matriks Kekakuan Batang 17 (node 6 - 12) α = 114.44395

1633.694 0 -1633.694 0 = 0 0 0 0

[ 〖𝐾 _𝑙〗^((14) ) ][𝑇^((14) ) ]

[𝑇^((14)) ]^𝑇

[ 〖𝐾 _𝑔〗^((14) ) ][ 〖𝐾 _𝑙〗^((15) ) ][𝑇^((15) ) ]

[𝑇^((15)) ]^𝑇

[ 〖𝐾 _𝑔〗^((15) ) ]

[ 〖𝐾 _𝑙〗^((14) ) ][𝑇^((14) ) ]

[𝑇^((14)) ]^𝑇

[ 〖𝐾 _𝑔〗^((14) ) ]

[ 〖𝐾 _𝑙〗^((17) ) ]

-1633.694 0 1633.694 00 0 0 0

-0.4138 0.9104 0 0 -0.4138 -0.9104 0 0 = -0.9104 -0.4138 0 0 = 0.9104 -0.4138 0 0

0 0 -0.4138 0.9104 0 0 -0.4138 -0.91040 0 -0.9104 -0.4138 0 0 0.9104 -0.4138

u6 v6 u12 v12279.742 -615.433 -279.742 615.433 u6

= -615.433 1353.952 615.433 -1353.952 v6-279.742 615.433 279.742 -615.433 u12615.433 -1353.952 -615.433 1353.952 v12

f. Matriks Kekakuan Batang 18 (node 6 - 11) α = 90

2820 0 -2820 0 = 0 0 0 0

-2820 0 2820 00 0 0 0

0 1 0 0 0 -1 0 0 = -1 0 0 0 = 1 0 0 0

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

u6 v6 u11 v110 0 0 0 u6

= 0 2820 0 -2820 v60 0 0 0 u110 -2820 0 2820 v11

f. Matriks Kekakuan Batang 19 (node 9 - 11) α = 141.34019

3082.870 0 -3082.870 0 = 0 0 0 0

-3082.870 0 3082.870 00 0 0 0

-0.7809 0.6247 0 0 -0.7809 -0.6247 0 0 = -0.6247 -0.7809 0 0 = 0.6247 -0.7809 0 0

0 0 -0.7809 0.6247 0 0 -0.7809 -0.62470 0 -0.6247 -0.7809 0 0 0.6247 -0.7809

u9 v9 u11 v111879.795 -1503.837 -1879.795 1503.837 u9

= -1503.837 1203.071 1503.837 -1203.071 v9-1879.795 1503.837 1879.795 -1503.837 u111503.837 -1203.071 -1503.837 1203.071 v11

f. Matriks Kekakuan Batang 20 (node 10 - 12) α = 38.65981

[ 〖𝐾 _𝑙〗^((17) ) ][𝑇^((17) ) ]

[𝑇^((17)) ]^𝑇

[ 〖𝐾 _𝑔〗^((17) ) ][ 〖𝐾 _𝑙〗^((18) ) ][𝑇^((18) ) ]

[𝑇^((18)) ]^𝑇

[ 〖𝐾 _𝑔〗^((18) ) ]

[ 〖𝐾 _𝑙〗^((19) ) ][𝑇^((19) ) ]

[𝑇^((19)) ]^𝑇

[ 〖𝐾 _𝑔〗^((19) ) ]

3082.870 0 -3082.870 0 = 0 0 0 0

-3082.870 0 3082.870 00 0 0 0

0.7809 0.6247 0 0 0.7809 -0.6247 0 0 = -0.6247 0.7809 0 0 = 0.6247 0.7809 0 0

0 0 0.7809 0.6247 0 0 0.7809 -0.62470 0 -0.6247 0.7809 0 0 0.6247 0.7809

u10 v10 u12 v121879.799 1503.839 -1879.799 -1503.839 u10

= 1503.839 1203.071 -1503.839 -1203.071 v10-1879.799 -1503.839 1879.799 1503.839 u12-1503.839 -1203.071 1503.839 1203.071 v12

f. Matriks Kekakuan Batang 21 (node 11 - 12) α = 141.34019

3082.870 0 -3082.870 0 = 0 0 0 0

-3082.870 0 3082.870 00 0 0 0

-0.78087 0.62470 0 0 -0.7809 -0.6247 0 0 = -0.62470 -0.78087 0 0 = 0.6247 -0.7809 0 0

0 0 -0.78087 0.62470 0 0 -0.7809 -0.62470 0 -0.62470 -0.78087 0 0 0.6247 -0.7809

u11 v11 u12 v121879.795 -1503.837 -1879.795 1503.837 u11

= -1503.837 1203.071 1503.837 -1203.071 v11-1879.795 1503.837 1879.795 -1503.837 u121503.837 -1203.071 -1503.837 1203.071 v12

[ 〖𝐾 _𝑙〗^((20) ) ][𝑇^((20) ) ]

[𝑇^((20)) ]^𝑇

[ 〖𝐾 _𝑔〗^((20) ) ][ 〖𝐾 _𝑙〗^((21) ) ][𝑇^((21) ) ]

[𝑇^((21)) ]^𝑇

[ 〖𝐾 _𝑔〗^((21) ) ]

3948 0 -3948 00 0 0 0

-3948 0 3948 00 0 0 0

3948 0 -3948 00 0 0 0

-3948 0 3948 00 0 0 0

3948 0 -3948 00 0 0 0

-3948 0 3948 00 0 0 0

3948 0 -3948 00 0 0 0

-3948 0 3948 00 0 0 0

3948 0 -3948 00 0 0 0

-3948 0 3948 00 0 0 0

3948 0 -3948 00 0 0 0

-3948 0 3948 00 0 0 0

2902.941 0 -2902.941 01741.765 0 -1741.765 0

-2902.941 0 2902.941 0-1741.765 0 1741.765 0

0 0 0 06580 0 -6580 0

0 0 0 0

-6580 0 6580 0

-2902.941 0 2902.941 01741.765 0 -1741.765 02902.941 0 -2902.941 0

-1741.765 0 1741.765 0

2902.941 0 -2902.941 01741.765 0 -1741.765 0

-2902.941 0 2902.941 0-1741.765 0 1741.765 0

0 0 0 0

6580 0 -6580 00 0 0 0

-6580 0 6580 0

-2902.941 0 2902.941 01741.765 0 -1741.765 02902.941 0 -2902.941 0

-1741.765 0 1741.765 0

2407.317 0 -2407.317 01925.854 0 -1925.854 0

-2407.317 0 2407.317 0-1925.854 0 1925.854 0

0 0 0 02820 0 -2820 0

0 0 0 0-2820 0 2820 0

676.0274 0 -676.0274 01487.26 0 -1487.26 0

-676.0274 0 676.0274 0-1487.26 0 1487.26 0

0 0 0 01794.545 0 -1794.545 0

0 0 0 0-1794.545 0 1794.545 0

-676.0273 0 676.0273 01487.26 0 -1487.26 0

676.0273 0 -676.0273 0-1487.26 0 1487.26 0

0 0 0 02820 0 -2820 0

0 0 0 0-2820 0 2820 0

-2407.315 0 2407.315 01925.854 0 -1925.854 02407.315 0 -2407.315 0

-1925.854 0 1925.854 0

2407.317 0 -2407.317 01925.854 0 -1925.854 0

-2407.317 0 2407.317 0-1925.854 0 1925.854 0

-2407.315 0 2407.315 01925.854 0 -1925.854 02407.315 0 -2407.315 0

-1925.854 0 1925.854 0

Matriks Kekakuan Strukturu1 v1 u2 v2 u3 v3 u4

F1 6437.252 1493.551 0 0 -3948 0 0G1 1493.551 896.131 0 0 0 0 0F2 0 0 6437 -1494 0 0 0G2 0 0 -1494 896 0 0 0F3 -3948 0 0 0 7896 0 -3948G3 0 0 0 0 0 6580 0F4 0 0 0 0 -3948 0 10664.99G4 0 0 0 0 0 0 -878.12F5 0 0 0 0 0 0 -3948G5 0 0 0 0 0 0 0F6 0 0 0 0 0 0 0G6 0 0 0 0 0 0 0F7 = 0 0 -3948 0 0 0 0G7 0 0 0 0 0 0 0F8 -2489.252 -1493.551 0 0 0 0 -2489.2514G8 -1493.551 -896.131 0 0 0 -6580 1493.551F9 0 0 -2489.251 1493.551 0 0 0G9 0 0 1493.551 -896.1307 0 0 0F10 0 0 0 0 0 0 0G10 0 0 0 0 0 0 0F11 0 0 0 0 0 0 0G11 0 0 0 0 0 0 0F12 0 0 0 0 0 0 -279.74213G12 0 0 0 0 0 0 -615.43268

u1 v1 u2 v2 u3 v3 u4F1 6437.251523 1493.550914 0 0 -3948 0 0G1 1493.550914 896.1305481 0 0 0 0 00 0 0 6437.251 -1493.551 0 0 0

G2 0 0 -1493.551 896.1307 0 0 00 -3948 0 0 0 7896 0 -39480 0 0 0 0 0 6580 00 0 0 0 0 -3948 0 10664.994

-1.5 0 0 0 0 0 0 -878.118350 0 0 0 0 0 0 -39480 0 0 0 0 0 0 00 0 0 0 0 0 0 0

-1.5 0 0 0 0 0 0 00 = 0 0 -3948 0 0 0 00 0 0 0 0 0 0 00 -2489.25152 -1493.55091 0 0 0 0 -2489.2514

-2 -1493.55091 -896.130548 0 0 0 -6580 1493.5510 0 0 -2489.251 1493.551 0 0 0-2 0 0 1493.551 -896.1307 0 0 00 0 0 0 0 0 0 0-2 0 0 0 0 0 0 00 0 0 0 0 0 0 0-2 0 0 0 0 0 0 00 0 0 0 0 0 0 -279.74213-2 0 0 0 0 0 0 -615.43268

Penyusunan Kembali Matriks Kekakuan Strukturu2 u3 v3 u4 v4 u5 v5

0 6437.251373 0 0 0 0 0 00 0 7896 0 -3948 0 0 00 0 0 6580 0 0 0 00 0 -3948 0 10664.99 -878.1183 -3948 0

-1.5 0 0 0 -878.1183 5070.083 0 00 0 0 0 -3948 0 7896 00 0 0 0 0 0 0 1794.54550 0 0 0 0 0 -3948 0

-1.5 0 0 0 0 0 0 00 -3948 0 0 0 0 0 00 0 0 0 0 0 0 00 = 0 0 0 -2489.251 1493.551 0 0-2 0 0 -6580 1493.551 -896.1307 0 00 -2489.25137 0 0 0 0 0 0-2 1493.551027 0 0 0 2820 0 00 0 0 0 0 0 0 0-2 0 0 0 0 -2820 0 00 0 0 0 0 0 0 0-2 0 0 0 0 0 0 00 0 0 0 -279.7421 -615.4327 0 0-2 0 0 0 -615.4327 -1353.952 0 -1794.5455F1 0 -3948 0 0 0 0 0G1 0 0 0 0 0 0 0G2 -1493.55103 0 0 0 0 0 0

v4 u5 v5 u6 v6 u7 v7 u8 v8 u90 0 0 0 0 0 0 -2489.252 -1493.5509 00 0 0 0 0 0 0 -1493.551 -896.13055 00 0 0 0 0 -3948 0 0 0 -2489.2510 0 0 0 0 0 0 0 0 1493.5510 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 -6580 0

-878.12 -3948 0 0 0 0 0 -2489.251 1493.55103 05070.08 0 0 0 0 0 0 1493.551 -896.13074 0

0 7896 0 -3948 0 0 0 0 0 00 0 1795 0 0 0 0 0 0 00 -3948 0 10664.99 878.12 -3948 0 0 0 -2489.2520 0 0 878.12 5070.08 0 0 0 0 -1493.5510 0 0 -3948 0 7896 0 0 0 00 0 0 0 0 0 6580 0 0 0

1493.551 0 0 0 0 0 0 6858.30 1503.84 0-896.1307 0 0 0 0 0 0 1503.84 9575.33 0

0 0 0 -2489.25152 -1493.551 0 0 0 0 68582820 0 0 -1493.55091 -896.1305 0 -6580 0 0 -1504

0 0 0 0 0 0 0 -1879.799 -1503.8391 0-2820 0 0 0 0 0 0 -1503.839 -1203.0712 0

0 0 0 0 0 0 0 0 0 -1879.7950 0 0 0 -2820 0 0 0 0 1503.837

-615.4327 0 0 -279.742068 615.4326 0 0 0 0 0-1353.952 0 -1795 615.43263 -1353.952 0 0 0 0 0

v4 u5 v5 u6 v6 u7 v7 u8 v8 u90 0 0 0 0 0 0 -2489.252 -1493.5509 00 0 0 0 0 0 0 -1493.551 -896.13055 00 0 0 0 0 -3948 0 0 0 -2489.2510 0 0 0 0 0 0 0 0 1493.5510 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 -6580 0

-878.1183 -3948 0 0 0 0 0 -2489.251 1493.55103 05070.083 0 0 0 0 0 0 1493.551 -896.13074 0

0 7896 0 -3948 0 0 0 0 0 00 0 1794.545 0 0 0 0 0 0 00 -3948 0 10664.9936 878.1183 -3948 0 0 0 -2489.2520 0 0 878.118284 5070.083 0 0 0 0 -1493.5510 0 0 -3948 0 7896 0 0 0 00 0 0 0 0 0 6580 0 0 0

1493.551 0 0 0 0 0 0 6858.302 1503.83894 0

-896.1307 0 0 0 0 0 0 1503.839 9575.33253 00 0 0 -2489.25152 -1493.551 0 0 0 0 6858.298

2820 0 0 -1493.55091 -896.1305 0 -6580 0 0 -1503.8370 0 0 0 0 0 0 -1879.799 -1503.8391 0

-2820 0 0 0 0 0 0 -1503.839 -1203.0712 00 0 0 0 0 0 0 0 0 -1879.7950 0 0 0 -2820 0 0 0 0 1503.837

-615.4327 0 0 -279.742068 615.4326 0 0 0 0 0-1353.952 0 -1794.545 615.43263 -1353.952 0 0 0 0 0

u6 v6 u7 v7 u8 v8 u9 v9 u10 v100 0 -3948 0 0 0 -2489.251 1493.551 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 -6580 0 0 0 00 0 0 0 -2489.251 1493.551 0 0 0 00 0 0 0 1493.551 -896.1307 0 0 0 -2820

-3948 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

10664.99 878.1183 -3948 0 0 0 -2489.252 -1493.551 0 0878.1183 5070.083 0 0 0 0 -1493.551 -896.1305 0 0

-3948 0 7896 0 0 0 0 0 0 00 0 0 6580 0 0 0 -6580 0 00 0 0 0 6858.302 1503.839 0 0 -1879.7988 -1503.8390 0 0 0 1503.839 9575.333 0 0 -1503.8391 -1203.071

-2489.252 -1493.551 0 0 0 0 6858.298 -1503.837 0 0-1493.551 -896.1305 0 -6580 0 0 -1503.837 9575.332 0 0

0 0 0 0 -1879.799 -1503.839 0 0 3759.59763 3007.6780 0 0 0 -1503.839 -1203.071 0 0 3007.67811 5226.1420 0 0 0 0 0 -1879.795 1503.837 0 00 -2820 0 0 0 0 1503.837 -1203.071 0 0

-279.7421 615.4326 0 0 0 0 0 0 -1879.7988 -1503.839615.4326 -1353.952 0 0 0 0 0 0 -1503.8391 -1203.071

0 0 0 0 -2489.252 -1493.551 0 0 0 00 0 0 0 -1493.551 -896.1305 0 0 0 00 0 0 0 0 0 1493.551 -896.1307 0 0

v9 u10 v10 u11 v11 u12 v120 0 0 0 0 0 0 U10 0 0 0 0 0 0 V1

1493.551 0 0 0 0 0 0 U2-896.1307 0 0 0 0 0 0 V2

0 0 0 0 0 0 0 U30 0 0 0 0 0 0 V30 0 0 0 0 -279.7421 -615.4327 U40 0 -2820 0 0 -615.4327 -1353.952 V40 0 0 0 0 0 0 U50 0 0 0 0 0 -1795 V5

-1493.551 0 0 0 0 -280 615 U6-896.1305 0 0 0 -2820 615 -1354 V6

0 0 0 0 0 0 0 X U7-6580 0 0 0 0 0 0 V7

0 -1879.799 -1503.839 0 0 0 0 U80 -1503.839 -1203.071 0 0 0 0 V8

-1504 0 0 -1879.795 1503.837 0 0 U99575 0 0 1503.837 -1203.071 0 0 V9

0 3759.60 3007.68 0 0 -1879.799 -1503.839 U100 3007.68 5226.14 0 0 -1503.839 -1203.071 V10

1503.837 0 0 3760 -3008 -1879.795 1503.837 U11-1203.071 0 0 -3008 -414 1503.837 -1203.071 V11

0 -1879.799 -1503.839 -1879.795 1503.837 4319 0.0017 U120 -1503.839 -1203.071 1503.837 -1203.071 0.0017 6909 V12

v9 u10 v10 u11 v11 u12 v120 0 0 0 0 0 0 00 0 0 0 0 0 0 0

1493.551 0 0 0 0 0 0 U2-896.1307 0 0 0 0 0 0 0

0 0 0 0 0 0 0 U30 0 0 0 0 0 0 V30 0 0 0 0 -279.7421 -615.4327 U40 0 -2820 0 0 -615.4327 -1353.952 V40 0 0 0 0 0 0 U50 0 0 0 0 0 -1795 V5

-1493.551 0 0 0 0 -279.7421 615 U6-896.1305 0 0 0 -2820 615.4326 -1354 V6

0 0 0 0 0 0 0 X U7-6580 0 0 0 0 0 0 V7

0 -1879.799 -1503.839 0 0 0 0 U8

0 -1503.839 -1203.071 0 0 0 0 V8-1503.837 0 0 -1879.795 1503.837 0 0 U99575.332 0 0 1503.837 -1203.071 0 0 V9

0 3759.598 3007.678 0 0 -1879.799 -1503.839 U100 3007.678 5226.142 0 0 -1503.839 -1203.071 V10

1503.837 0 0 3759.59 -3007.675 -1879.795 1503.837 U11-1203.071 0 0 -3007.675 -413.8579 1503.837 -1203.071 V11

0 -1879.799 -1503.839 -1879.795 1503.837 4319.078 0.0017 U120 -1503.839 -1203.071 1503.837 -1203.071 0.001724 6909 V12

u11 v11 u12 v12 u1 v1 v20 0 0 0 0 0 -1493.551 U20 0 0 0 -3948 0 0 U30 0 0 0 0 0 0 V30 0 -279.7421 -615.4327 0 0 0 U40 0 -615.4327 -1353.952 0 0 0 V40 0 0 0 0 0 0 U50 0 0 -1794.545 0 0 0 V50 0 -279.7421 615.4326 0 0 0 U60 -2820 615.4326 -1353.952 0 0 0 V60 0 0 0 0 0 0 U70 0 0 0 0 0 0 V70 0 0 0 -2489.252 -1493.551 0 X U80 0 0 0 -1493.551 -896.1305 0 V8

-1879.795 1503.837 0 0 0 0 1493.551 U91503.837 -1203.071 0 0 0 0 -896.1307 V9

0 0 -1879.799 -1503.839 0 0 0 U100 0 -1503.839 -1203.071 0 0 0 V10

3759.59 -3007.675 -1879.795 1503.837 0 0 0 U11-3007.675 -413.8579 1503.837 -1203.071 0 0 0 V11-1879.795 1503.837 4319.078 0.001724 0 0 0 U121503.837 -1203.071 0.001724 6908.592 0 0 0 V12

0 0 0 0 6437.252 1493.551 0 00 0 0 0 1493.551 896.1305 0 00 0 0 0 0 0 896.1307 0

Menghitung Perpindahanu2 u3 v3 u4 v4

0 6437.25137 0 0 0 00 0 7896 0 -3948 00 0 0 6580 0 00 0 -3948 0 10664.9935 -878.118347

-1.5 0 0 0 -878.118347 5070.0826350 0 0 0 -3948 00 0 0 0 0 00 0 0 0 0 0

-1.5 0 0 0 0 00 = -3948 0 0 0 00 0 0 0 0 00 0 0 0 -2489.25137 1493.551027-2 0 0 -6580 1493.55103 -896.1307380 -2489.25137 0 0 0 0-2 1493.55103 0 0 0 28200 0 0 0 0 0-2 0 0 0 0 -28200 0 0 0 0 0-2 0 0 0 0 00 0 0 0 -279.742127 -615.43268-2 0 0 0 -615.43268 -1353.9519

U2 0.0009535 0.0000933 0.0005566 0.0001865 0.0009406U3 0.0002538 0.0002666 -0.0004575 0.0002799 -0.0004082V3 -0.0006631 -0.0003633 0.0028202 -0.0007266 0.0025496U4 0.0005075 0.0002799 -0.0009149 0.0005599 -0.0008163V4 -0.0004788 -0.0002198 0.0019513 -0.0004397 0.0025057U5 0.0007612 0.0002908 -0.0010590 0.0005816 -0.0010352V5 -0.0002931 -0.0000391 0.0002027 -0.0000781 0.0001571U6 0.0010149 0.0003017 -0.0012030 0.0006034 -0.0012540V6 0.0001203 0.0000717 -0.0006210 0.0001435 -0.0007861U7 0.0009842 0.0001975 -0.0003232 0.0003950 -0.0001567V7 = 0.0008632 0.0005153 -0.0044216 0.0010306 -0.0055689U8 0.0003971 0.0001969 -0.0008754 0.0003937 -0.0008824V8 -0.0006631 -0.0003633 0.0026682 -0.0007266 0.0025496U9 0.0010209 0.0002371 -0.0007010 0.0004742 -0.0006605V9 0.0008632 0.0005153 -0.0044216 0.0010306 -0.0055689

U10 0.0002488 0.0000581 0.0001417 0.0001162 -0.0001125V10 -0.0004788 -0.0002198 0.0019513 -0.0004397 0.0025057U11 0.0002359 -0.0001846 0.0028259 -0.0003691 0.0037140V11 -0.0001203 -0.0000717 0.0006210 -0.0001435 0.0007861U12 0.0000994 -0.0001105 0.0019842 -0.0002209 0.0025012V12 -0.0002931 -0.0000391 0.0002027 -0.0000781 0.0001571

U2 -0.0043004U3 0.0026929V3 -0.0164466U4 0.0053857V4 -0.0148253U5 0.0067255V5 -0.0020955U6 0.0080653V6 0.0043511U7 0.0018824V7 = 0.0313383 mU8 0.0055970V8 -0.0164466U9 0.0046964V9 0.0313383

U10 0.0007796V10 -0.0155345U11 -0.0192921V11 -0.0036419U12 -0.0140593V12 -0.0020955

u5 v5 u6 v6 u7 v7 u8 v80 0 0 0 -3948 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 -6580

-3948 0 0 0 0 0 -2489.25137 1493.551030 0 0 0 0 0 1493.55103 -896.130738

7896 0 -3948 0 0 0 0 00 1794.54545 0 0 0 0 0 0

-3948 0 10664.9936 878.118284 -3948 0 0 00 0 878.118284 5070.08251 0 0 0 00 0 -3948 0 7896 0 0 00 0 0 0 0 6580 0 00 0 0 0 0 0 6858.30171 1503.838940 0 0 0 0 0 1503.83894 9575.332530 0 -2489.25152 -1493.55091 0 0 0 00 0 -1493.55091 -896.130548 0 -6580 0 00 0 0 0 0 0 -1879.79882 -1503.839050 0 0 0 0 0 -1503.83905 -1203.071240 0 0 0 0 0 0 00 0 0 -2820 0 0 0 00 0 -279.742068 615.43263 0 0 0 00 -1794.54545 615.43263 -1353.95196 0 0 0 0

0.0003791 0.0001677 0.0005718 0.0000148 0.0007626 -0.0002164 -0.0000801 0.00055660.0002800 -0.0002122 0.0002800 -0.0000166 0.0002669 0.0000334 0.0002534 -0.0004575

-0.0007524 0.0012481 -0.0007782 0.0001123 -0.0007207 -0.0001268 -0.0010247 0.00266820.0005600 -0.0004245 0.0005601 -0.0000332 0.0005338 0.0000668 0.0005067 -0.0009149

-0.0004910 0.0011476 -0.0005423 0.0001190 -0.0005105 -0.0000414 -0.0008221 0.00195130.0008351 -0.0005981 0.0008352 -0.0000468 0.0007982 0.0000941 0.0005759 -0.0010590

-0.0001548 0.0010096 -0.0002314 0.0000791 -0.0002623 0.0001376 -0.0000596 0.00020270.0008569 -0.0007717 0.0011104 -0.0000604 0.0010627 0.0001215 0.0006450 -0.00120300.0001564 -0.0002884 0.0001693 0.0001266 0.0001448 0.0001411 0.0002588 -0.00062100.0006180 -0.0003020 0.0008411 -0.0000228 0.0010393 -0.0000475 0.0002824 -0.00032320.0011683 -0.0024105 0.0013060 -0.0001364 0.0010846 0.0010263 0.0018357 -0.00442160.0004091 -0.0004123 0.0004245 -0.0000410 0.0004108 0.0000231 0.0006147 -0.0008754

-0.0007524 0.0012481 -0.0007782 0.0001123 -0.0007207 -0.0001268 -0.0010247 0.00266820.0007012 -0.0005336 0.0009282 -0.0000074 0.0009746 0.0000402 0.0004462 -0.00070100.0011683 -0.0024105 0.0013060 -0.0001364 0.0010846 0.0008743 0.0018357 -0.00442160.0001519 0.0000502 0.0001876 -0.0000165 0.0002182 -0.0001053 0.0002245 0.0001417

-0.0004910 0.0011476 -0.0005423 0.0001190 -0.0005105 -0.0000414 -0.0008221 0.0019513-0.0002624 0.0012414 -0.0001557 -0.0000594 0.0000401 -0.0006518 -0.0010011 0.0028259-0.0001564 0.0002884 -0.0001693 -0.0001266 -0.0001448 -0.0001411 -0.0002588 0.0006210-0.0001651 0.0009884 -0.0001092 0.0000453 -0.0000049 -0.0003087 -0.0006136 0.0019842-0.0001548 0.0004524 -0.0002314 0.0000791 -0.0002623 0.0001376 -0.0000596 0.0002027

u9 v9 u10 v10 u11 v11 u12 v12-2489.25137 1493.55103 0 0 0 0 0 0

0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 -279.742127 -615.432680 0 0 -2820 0 0 -615.43268 -1353.95190 0 0 0 0 0 0 00 0 0 0 0 0 0 -1794.54545

-2489.25152 -1493.55091 0 0 0 0 -279.742068 615.43263-1493.55091 -896.130548 0 0 0 -2820 615.43263 -1353.95196

0 0 0 0 0 0 0 00 -6580 0 0 0 0 0 00 0 -1879.79882 -1503.83905 0 0 0 00 0 -1503.83905 -1203.07124 0 0 0 0

6858.29782 -1503.83749 0 0 -1879.79492 1503.83738 0 0-1503.83749 9575.33235 0 0 1503.83738 -1203.07106 0 0

0 0 3759.59763 3007.67811 0 0 -1879.79882 -1503.839050 0 3007.67811 5226.14249 0 0 -1503.83905 -1203.07124

-1879.79492 1503.83738 0 0 3759.58984 -3007.67476 -1879.79492 1503.837381503.83738 -1203.07106 0 0 -3007.67476 -413.857881 1503.83738 -1203.07106

0 0 -1879.79882 -1503.83905 -1879.79492 1503.83738 4319.07793 0.0017240 0 -1503.83905 -1203.07124 1503.83738 -1203.07106 0.001724 6908.59162

0.0007246 -0.0002164 -0.0000992 0.0009406 0.0007735 -0.0000148 0.0008072 0.00016770.0002530 0.0000334 0.0001899 -0.0004082 0.0002159 0.0000166 0.0000092 -0.0002122

-0.0006478 -0.0001268 -0.0006558 0.0025496 -0.0005325 -0.0001123 0.0006595 0.00124810.0005060 0.0000668 0.0003799 -0.0008163 0.0004319 0.0000332 0.0000184 -0.0004245

-0.0004532 -0.0000414 -0.0008698 0.0025057 -0.0004581 -0.0001190 0.0006124 0.00114760.0007590 0.0000941 0.0004893 -0.0010352 0.0006546 0.0000468 0.0000720 -0.0005981

-0.0002595 0.0001376 0.0000471 0.0001571 -0.0004884 -0.0000791 -0.0001187 0.00045240.0010121 0.0001215 0.0005986 -0.0012540 0.0008773 0.0000604 0.0001256 -0.00077170.0001661 0.0001411 0.0002617 -0.0007861 -0.0000921 -0.0001266 -0.0002656 -0.00028840.0008683 -0.0000475 0.0002497 -0.0001567 0.0008254 0.0000228 0.0004664 -0.00030200.0010366 0.0008743 0.0018260 -0.0055689 0.0004277 0.0001364 -0.0016284 -0.00241050.0003892 0.0000231 0.0004939 -0.0008824 0.0003788 0.0000410 -0.0000086 -0.0004123

-0.0006478 -0.0001268 -0.0006558 0.0025496 -0.0005325 -0.0001123 0.0006595 0.00124810.0011186 0.0000402 0.0004430 -0.0006605 0.0009479 0.0000074 0.0003706 -0.00053360.0010366 0.0008743 0.0018260 -0.0055689 0.0004277 0.0001364 -0.0016284 -0.00241050.0002340 -0.0001053 0.0010061 -0.0003961 0.0003865 0.0000165 0.0004684 0.0000502

-0.0004532 -0.0000414 -0.0011535 0.0028603 -0.0004581 -0.0001190 0.0006124 0.00114760.0001554 -0.0006518 -0.0009233 0.0037140 0.0008499 -0.0002243 0.0018430 0.0012414

-0.0001661 -0.0001411 -0.0002617 0.0007861 -0.0001916 -0.0002280 0.0002656 0.00028840.0000796 -0.0003087 -0.0003723 0.0025012 0.0004780 -0.0000453 0.0014927 0.0009884

-0.0002595 0.0001376 0.0000471 0.0001571 -0.0004884 -0.0000791 -0.0001187 0.0004524

U2U3V3U4V4U5V5U6V6

X U7V7U8V8U9V9

U10V10U11V11U12V12

0000

-1.5000

-1.50

X 00-20-20-20-20-2

Menghitung Reaksi

u2 u3 v3 u4 v4 u5 v5 u6F1 0 -3948 0 0 0 0 0 0G1 = 0 0 0 0 0 0 0 0G2 -1493.551 0 0 0 0 0 0 0

F1 0.0000 13.0000G1 = 6.3789 t G2 -14.6459 -8.2671

v6 u7 v7 u8 v8 u9 v9 u10 v10 u110 0 0 -2489.252 -1493.551 0 0 0 0 00 0 0 -1493.551 -896.1305 0 0 0 0 00 0 0 0 0 1493.551 -896.1307 0 0 0

-0.004300.00269

-0.016450.00539

-0.014830.00673

-0.002100.00807

v11 u12 v12 0.004350 0 0 0.001880 0 0 X 0.031340 0 0 0.00560

-0.016450.004700.031340.00078

-0.01553-0.01929-0.00364-0.01406-0.00210

u1 v1 u2 v2 u3 v3 u4F1 3948 0G1 0 0F2G2F3G3F4G4F5G5F6G6F7G7F8G8F9G9F10G10F11G11F12G12

v4 u5 v5 u6 v6 u7 v7 u8 v8 u9

v9 u10 v10 u11 v11 u12 v12U1V1U2V2U3V3U4V4U5V5U6V6U7V7U8V8U9V9U10V10U11V11U12V12