Tugas Meh Egi Santoso.xlsx
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TABEL COSINUS & SINUS UNTUK SETIAP ELEMEN ELEMEN 14 13 23 25 34 35 45
L 7.28 8.69 11.64 9.9 5.82 4.35 9
C
2
ᶿ 74 32 156 135 156 32 0
S C CS S2 C2 0.9612617 0.2756374 0.924024 0.075976 0.2649596 0.5299193 0.8480481 0.2808144 0.7191856 0.449397 0.4067366 -0.913545 0.1654347 0.8345653 -0.371572 0.7071068 -0.707107 0.5 0.5 -0.5 0.4067366 -0.913545 0.1654347 0.8345653 -0.371572 0.5299193 0.8480481 0.2808144 0.7191856 0.449397 0 1 0 1 0
MATRIKS KEKAKUAN [K] (GLOBAL) CS (-C )2
(-CS)
CS
S2
(-CS)
(-S)2
(-C )2
(-CS)
C2
CS
(-CS)
(-S)
CS
S2
2
EA 7.28
EA 11.64
EA 5.82
EA 9
U1 0.075976 0.26496 -0.07598 -0.26496
ELEMEN 1-4 V1 U4 0.26496 -0.07598 0.924024 -0.26496 -0.26496 0.075976 -0.92402 0.26496
ELEMEN 1-3
U2 0.834565 -0.37157 -0.83457 0.371572
ELEMEN 2-3 V2 U3 -0.37157 -0.83457 0.165435 0.371572 0.371572 0.834565 -0.16543 -0.37157
V3 0.371572 -0.16543 -0.37157 0.834565
U3 0.834565 -0.37157 -0.83457 0.371572
ELEMEN 3-4 V3 U4 -0.37157 -0.83457 0.165435 0.371572 0.371572 0.834565 -0.16543 -0.37157
V4 0.371572 -0.16543 -0.37157 0.165435
U3 V3 U4 V4
U4 1 0 -1 0
ELEMEN 4-5 V4 U5 0 -1 0 0 0 1 0 0
V5 0 0 0 0
U4 V4 U5 V5
V4 -0.26496 -0.92402 0.26496 0.924024
U1 V1 U4 V4
EA 8.69
U1 0.719186 0.449397 -0.71919 -0.4494 ELEMEN 2-5
U2 V2 U3 V3
EA 9.9
U2 0.5 -0.5 -0.5 0.5 ELEMEN 3-5
EA 4.35
E A EA
U3 0.719186 0.449397 -0.71919 -0.4494
= = = =
ELEMEN 1-3 V1 U3 0.449397 -0.71919 0.2808144 -0.4494 -0.449397 0.719186 -0.2808144 0.449397
V3 -0.4494 -0.28081 0.449397 0.280814
U1 V1 U3 V3
ELEMEN 2-5 V2 U5 -0.5 -0.5 0.5 0.5 0.5 0.5 -0.5 -0.5
V5 0.5 -0.5 -0.5 0.5
U2 V2 U5 V5
ELEMEN 3-5 V3 U5 0.449397 -0.71919 0.2808144 -0.4494 -0.449397 0.719186 -0.2808144 0.449397
V5 -0.4494 -0.28081 0.449397 0.280814
U3 V3 U5 V5
200000 2000000 189 378000000
Mpa kg/m m kg
EA
EA
EA
EA
ELEMEN 1-4 U1 V1 U4 V4 0.0104363 0.0363956 -0.010436 -0.036396 0.0363956 0.1269264 -0.036396 -0.126926 -0.010436 -0.036396 0.0104363 0.0363956 -0.036396 -0.126926 0.0363956 0.1269264 ELEMEN 2-3 U2 V2 U3 V3 0.0716981 -0.031922 -0.071698 0.031922 -0.031922 0.0142126 0.031922 -0.014213 -0.071698 0.031922 0.0716981 -0.031922 0.031922 -0.014213 -0.031922 0.0716981 ELEMEN 3-4 U3 V3 U4 V4 0.1433961 -0.063844 -0.143396 0.0638441 -0.063844 0.0284252 0.0638441 -0.028425 -0.143396 0.0638441 0.1433961 -0.063844 0.0638441 -0.028425 -0.063844 0.0284252
U4 0.1111111 0 -0.111111 0
ELEMEN 4-5 V4 U5 0 -0.111111 0 0 0 0.1111111 0 0
V5 0 0 0 0
ELEMEN U1 V1 U4 V4
EA
U1 0.0827601 0.0517143 -0.08276 -0.051714
ELEMEN U2 V2 U3 V3
EA
U2 0.0505051 -0.050505 -0.050505 0.0505051
EA
U3 0.16533 0.1033097 -0.16533 -0.10331
ELEMEN U3 V3 U4 V4
U4 V4 U5 V5
ELEMEN 1-3 V1 U3 V3 0.0517143 -0.08276 -0.051714 0.0323147 -0.051714 -0.032315 -0.051714 0.0827601 0.0517143 -0.032315 0.0517143 0.0323147
U1 V1 U3 V3
ELEMEN 2-5 V2 U5 V5 -0.050505 -0.050505 0.0505051 0.0505051 0.0505051 -0.050505 0.0505051 0.0505051 -0.050505 -0.050505 -0.050505 0.0505051
U2 V2 U5 V5
ELEMEN 3-5 V3 U5 V5 0.1033097 -0.16533 -0.10331 0.064555 -0.10331 -0.064555 -0.10331 0.16533 0.1033097 -0.064555 0.1033097 0.064555
U3 V3 U5 V5
MATRIK STRUKTUR (K & F) U1 0.093196 0.08811 0 0 -0.08276 -0.08276 -0.01044 -0.0364 0 0
V1 0.08811 0.159241 0 0 -0.05171 -0.03231 -0.0364 -0.12693 0 0
U2 0 0 0.122203 -0.08243 -0.0717 0.031922 0 0 -0.05051 0.050505
V2 0 0 -0.08243 0.064718 0.031922 -0.01421 0 0 0.050505 -0.05051
U3 -0.08276 -0.05171 -0.0717 0.031922 0.463184 0.059258 -0.1434 0.063844 -0.16533 -0.10331
V3 -0.08276 -0.03231 0.031922 -0.01421 0.059258 0.196993 0.063844 -0.02843 -0.10331 -0.06456
U4 -0.01044 -0.0364 0 0 -0.1434 0.063844 0.264943 -0.02745 -0.11111 0
V4 -0.0364 -0.12693 0 0 0.063844 -0.02843 -0.02745 0.155352 0 0
U5 0 0 -0.05051 0.050505 -0.16533 -0.10331 -0.11111 0 0.326946 0.052805
Matriks yang dikonstraint adalah = V1, V2, U4, U5 [K]-1 0.093196 0 -0.08276 -0.08276 -0.0364 0 0.122203 -0.0717 0.031922 0 -0.08276 -0.0717 0.463184 0.059258 0.063844 -0.08276 0.031922 0.059258 0.196993 -0.02843 -0.0364 0 0.063844 -0.02843 0.155352 0 0.050505 -0.10331 -0.06456 0
0 0.050505 -0.10331 -0.06456 0 0.11506
89.46925 -35.2865 12.50849 64.04888 27.53942 62.65486
-35.2865 27.46252 -3.69457 -30.6107 -12.3495 -32.5461
V5 0 0 0.050505 -0.05051 -0.10331 -0.06456 0 0 0.052805 0.11506
U1 V1 U2 V2 U3 V3 U4 V4 U5 V5
[K]-1 12.50849 64.04888 -3.69457 -30.6107 4.77663 8.222152 8.222152 54.41219 2.47188 21.58225 10.52361 51.34712
0 0 0 0 0 0 0 -21 0 -4
27.53942 -12.3495 2.47188 21.58225 15.82203 19.74901
62.65486 -32.5461 10.52361 51.34712 19.74901 61.23452
U1 V1 U2 V2 U3 V3 U4 V4 U5 V5
MATRIKS U = [K]-1 . [F] 89.469247 -35.28652 12.508492 64.048881 27.53942 62.65486
-35.28652 12.508492174 64.048881 27.462517 -3.6945738376 -30.61072 -3.694574 4.7766297135 8.2221518 -30.61072 8.2221517658 54.412192 -12.34948 2.4718797219 21.58225 -32.5461 10.523613893 51.347123 [K]-1
27.53942 -12.34948 2.4718797 21.58225 15.82203 19.749014
62.65486 -32.5461 10.523614 51.347123 19.749014 61.234515
0 0 0 0 -21 -4 F
GAYA-GAYA AKSIAL TIAP BATANG (N)
N1-4
N1-3
N2-3
N2-5
N
=
=
378000000
=
-63064914571
=
378000000
=
103668056556
=
378000000
=
65711964145
=
378000000
=
-72205756623
EA
x
Cij
0.2756374 0.9612617 828.94725 -411.2587
0.8480481 0.5299193 734.94332 -658.6157
-0.913545 0.4067366 -483.5275 -658.6157
-0.707107 0.7071068 -389.5235 -659.6674
Sij
Uj-Ui Vj-Vi
-828.9473 389.52355 -94.00393 -658.6157 -411.2587 -659.6674 U
N3-4
= =
N3-5
N4-5
=
U1 U2 U3 V3 V4 V5
378000000 -0.913545 0.4067366 94.00393 247.35705 5.569E+09
=
378000000 0.8480481 0.5299193 94.00393 -1.051619 2.992E+10
=
378000000
=
0
1
0
0 -248.4087
L 7.28 8.69 11.64 9.9 5.82 4.35 9
C
2
ᶿ 74 32 156 135 156 32 0
S C CS S2 C2 0.9612617 0.2756374 0.924024 0.075976 0.2649596 0.5299193 0.8480481 0.2808144 0.7191856 0.449397 0.4067366 -0.913545 0.1654347 0.8345653 -0.371572 0.7071068 -0.707107 0.5 0.5 -0.5 0.4067366 -0.913545 0.1654347 0.8345653 -0.371572 0.5299193 0.8480481 0.2808144 0.7191856 0.449397 0 1 0 1 0
MATRIKS KEKAKUAN [K] (GLOBAL) CS (-C )2
(-CS)
CS
S2
(-CS)
(-S)2
(-C )2
(-CS)
C2
CS
(-CS)
(-S)
CS
S2
2
EA 7.28
EA 11.64
EA 5.82
EA 9
U1 0.075976 0.26496 -0.07598 -0.26496
ELEMEN 1-4 V1 U4 0.26496 -0.07598 0.924024 -0.26496 -0.26496 0.075976 -0.92402 0.26496
ELEMEN 1-3
U2 0.834565 -0.37157 -0.83457 0.371572
ELEMEN 2-3 V2 U3 -0.37157 -0.83457 0.165435 0.371572 0.371572 0.834565 -0.16543 -0.37157
V3 0.371572 -0.16543 -0.37157 0.834565
U3 0.834565 -0.37157 -0.83457 0.371572
ELEMEN 3-4 V3 U4 -0.37157 -0.83457 0.165435 0.371572 0.371572 0.834565 -0.16543 -0.37157
V4 0.371572 -0.16543 -0.37157 0.165435
U3 V3 U4 V4
U4 1 0 -1 0
ELEMEN 4-5 V4 U5 0 -1 0 0 0 1 0 0
V5 0 0 0 0
U4 V4 U5 V5
V4 -0.26496 -0.92402 0.26496 0.924024
U1 V1 U4 V4
EA 8.69
U1 0.719186 0.449397 -0.71919 -0.4494 ELEMEN 2-5
U2 V2 U3 V3
EA 9.9
U2 0.5 -0.5 -0.5 0.5 ELEMEN 3-5
EA 4.35
E A EA
U3 0.719186 0.449397 -0.71919 -0.4494
= = = =
ELEMEN 1-3 V1 U3 0.449397 -0.71919 0.2808144 -0.4494 -0.449397 0.719186 -0.2808144 0.449397
V3 -0.4494 -0.28081 0.449397 0.280814
U1 V1 U3 V3
ELEMEN 2-5 V2 U5 -0.5 -0.5 0.5 0.5 0.5 0.5 -0.5 -0.5
V5 0.5 -0.5 -0.5 0.5
U2 V2 U5 V5
ELEMEN 3-5 V3 U5 0.449397 -0.71919 0.2808144 -0.4494 -0.449397 0.719186 -0.2808144 0.449397
V5 -0.4494 -0.28081 0.449397 0.280814
U3 V3 U5 V5
200000 2000000 189 378000000
Mpa kg/m m kg
EA
EA
EA
EA
ELEMEN 1-4 U1 V1 U4 V4 0.0104363 0.0363956 -0.010436 -0.036396 0.0363956 0.1269264 -0.036396 -0.126926 -0.010436 -0.036396 0.0104363 0.0363956 -0.036396 -0.126926 0.0363956 0.1269264 ELEMEN 2-3 U2 V2 U3 V3 0.0716981 -0.031922 -0.071698 0.031922 -0.031922 0.0142126 0.031922 -0.014213 -0.071698 0.031922 0.0716981 -0.031922 0.031922 -0.014213 -0.031922 0.0716981 ELEMEN 3-4 U3 V3 U4 V4 0.1433961 -0.063844 -0.143396 0.0638441 -0.063844 0.0284252 0.0638441 -0.028425 -0.143396 0.0638441 0.1433961 -0.063844 0.0638441 -0.028425 -0.063844 0.0284252
U4 0.1111111 0 -0.111111 0
ELEMEN 4-5 V4 U5 0 -0.111111 0 0 0 0.1111111 0 0
V5 0 0 0 0
ELEMEN U1 V1 U4 V4
EA
U1 0.0827601 0.0517143 -0.08276 -0.051714
ELEMEN U2 V2 U3 V3
EA
U2 0.0505051 -0.050505 -0.050505 0.0505051
EA
U3 0.16533 0.1033097 -0.16533 -0.10331
ELEMEN U3 V3 U4 V4
U4 V4 U5 V5
ELEMEN 1-3 V1 U3 V3 0.0517143 -0.08276 -0.051714 0.0323147 -0.051714 -0.032315 -0.051714 0.0827601 0.0517143 -0.032315 0.0517143 0.0323147
U1 V1 U3 V3
ELEMEN 2-5 V2 U5 V5 -0.050505 -0.050505 0.0505051 0.0505051 0.0505051 -0.050505 0.0505051 0.0505051 -0.050505 -0.050505 -0.050505 0.0505051
U2 V2 U5 V5
ELEMEN 3-5 V3 U5 V5 0.1033097 -0.16533 -0.10331 0.064555 -0.10331 -0.064555 -0.10331 0.16533 0.1033097 -0.064555 0.1033097 0.064555
U3 V3 U5 V5
MATRIK STRUKTUR (K & F) U1 0.093196 0.08811 0 0 -0.08276 -0.08276 -0.01044 -0.0364 0 0
V1 0.08811 0.159241 0 0 -0.05171 -0.03231 -0.0364 -0.12693 0 0
U2 0 0 0.122203 -0.08243 -0.0717 0.031922 0 0 -0.05051 0.050505
V2 0 0 -0.08243 0.064718 0.031922 -0.01421 0 0 0.050505 -0.05051
U3 -0.08276 -0.05171 -0.0717 0.031922 0.463184 0.059258 -0.1434 0.063844 -0.16533 -0.10331
V3 -0.08276 -0.03231 0.031922 -0.01421 0.059258 0.196993 0.063844 -0.02843 -0.10331 -0.06456
U4 -0.01044 -0.0364 0 0 -0.1434 0.063844 0.264943 -0.02745 -0.11111 0
V4 -0.0364 -0.12693 0 0 0.063844 -0.02843 -0.02745 0.155352 0 0
U5 0 0 -0.05051 0.050505 -0.16533 -0.10331 -0.11111 0 0.326946 0.052805
Matriks yang dikonstraint adalah = V1, V2, U4, U5 [K]-1 0.093196 0 -0.08276 -0.08276 -0.0364 0 0.122203 -0.0717 0.031922 0 -0.08276 -0.0717 0.463184 0.059258 0.063844 -0.08276 0.031922 0.059258 0.196993 -0.02843 -0.0364 0 0.063844 -0.02843 0.155352 0 0.050505 -0.10331 -0.06456 0
0 0.050505 -0.10331 -0.06456 0 0.11506
89.46925 -35.2865 12.50849 64.04888 27.53942 62.65486
-35.2865 27.46252 -3.69457 -30.6107 -12.3495 -32.5461
V5 0 0 0.050505 -0.05051 -0.10331 -0.06456 0 0 0.052805 0.11506
U1 V1 U2 V2 U3 V3 U4 V4 U5 V5
[K]-1 12.50849 64.04888 -3.69457 -30.6107 4.77663 8.222152 8.222152 54.41219 2.47188 21.58225 10.52361 51.34712
0 0 0 0 0 0 0 -21 0 -4
27.53942 -12.3495 2.47188 21.58225 15.82203 19.74901
62.65486 -32.5461 10.52361 51.34712 19.74901 61.23452
U1 V1 U2 V2 U3 V3 U4 V4 U5 V5
MATRIKS U = [K]-1 . [F] 89.469247 -35.28652 12.508492 64.048881 27.53942 62.65486
-35.28652 12.508492174 64.048881 27.462517 -3.6945738376 -30.61072 -3.694574 4.7766297135 8.2221518 -30.61072 8.2221517658 54.412192 -12.34948 2.4718797219 21.58225 -32.5461 10.523613893 51.347123 [K]-1
27.53942 -12.34948 2.4718797 21.58225 15.82203 19.749014
62.65486 -32.5461 10.523614 51.347123 19.749014 61.234515
0 0 0 0 -21 -4 F
GAYA-GAYA AKSIAL TIAP BATANG (N)
N1-4
N1-3
N2-3
N2-5
N
=
=
378000000
=
-63064914571
=
378000000
=
103668056556
=
378000000
=
65711964145
=
378000000
=
-72205756623
EA
x
Cij
0.2756374 0.9612617 828.94725 -411.2587
0.8480481 0.5299193 734.94332 -658.6157
-0.913545 0.4067366 -483.5275 -658.6157
-0.707107 0.7071068 -389.5235 -659.6674
Sij
Uj-Ui Vj-Vi
-828.9473 389.52355 -94.00393 -658.6157 -411.2587 -659.6674 U
N3-4
= =
N3-5
N4-5
=
U1 U2 U3 V3 V4 V5
378000000 -0.913545 0.4067366 94.00393 247.35705 5.569E+09
=
378000000 0.8480481 0.5299193 94.00393 -1.051619 2.992E+10
=
378000000
=
0
1
0
0 -248.4087
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