matriks kekakuan tb anstruk 2.xlsx

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Menentukan Kekakuan Elemen Tiap Batang 4EI/L 2EI/L -6EI/L 6EI/L Ke Lokal = 2EI/L 4EI/L -6EI/L 6EI/L -6EI/L^2-6EI/L^2 12EI/L^3 -12EI/L^3 6EI/L^2 6EI/L^2 -12EI/L^3 12EI/L^3 Kekakuan Elemen 1.3333 0.6667 -0.6667 0.6667 L1 = L2 = L3 = L4 = L8 3m 0.6667 1.3333 -0.6667 0.6667 -0.6667 -0.6667 0.4444 -0.4444 0.6667 0.6667 -0.4444 0.4444 2 1 -1.5 1.5 L5 = L7 = 2m 1 2 -1.5 1.5 -1.5 -1.5 1.5 -1.5 1.5 1.5 -1.5 1.5 1 0.5 -0.375 0.375 L6 = L10 = 4m 0.5 1 -0.375 0.375 -0.375 -0.375 0.1875 -0.1875 0.375 0.375 -0.1875 0.1875 P1 = 3 ton P2 = 4 ton Q1 = 2 ton/meter Q2 = 2 ton/meter M1 = 5 ton.meter

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Page 1: matriks kekakuan TB anstruk 2.xlsx

Menentukan Kekakuan Elemen Tiap Batang

4EI/L 2EI/L -6EI/L 6EI/LKe Lokal = 2EI/L 4EI/L -6EI/L 6EI/L

-6EI/L^2 -6EI/L^2 12EI/L^3 -12EI/L^36EI/L^2 6EI/L^2 -12EI/L^3 12EI/L^3

Kekakuan Elemen1.3333 0.6667 -0.6667 0.6667

L1 = L2 = L3 = L4 = L8 = L9 = 3 m 0.6667 1.3333 -0.6667 0.6667-0.6667 -0.6667 0.4444 -0.44440.6667 0.6667 -0.4444 0.4444

2 1 -1.5 1.5L5 = L7 = 2 m 1 2 -1.5 1.5

-1.5 -1.5 1.5 -1.51.5 1.5 -1.5 1.5

1 0.5 -0.375 0.375L6 = L10 = 4 m 0.5 1 -0.375 0.375

-0.375 -0.375 0.1875 -0.18750.375 0.375 -0.1875 0.1875

P1 = 3 tonP2 = 4 tonQ1 = 2 ton/meterQ2 = 2 ton/meterM1 = 5 ton.meter

Page 2: matriks kekakuan TB anstruk 2.xlsx

Matriks [B] D1 D2 D3 D4 D5 D6 D7 D8 Matriks [KI] 1 2 3d1 0 0 0 0 0 0 0 0 1 1.3333 0.6667 -0.6667d2 1 0 0 0 0 0 0 0 2 0.6667 1.3333 -0.6667d3 0 0 0 0 0 0 0 0 3 -0.6667 -0.6667 0.4444d4 0 0 0 0 0 0 1 0 4 0.6667 0.6667 -0.4444d5 0 0 0 0 0 0 0 0 5 0 0 0d6 0 1 0 0 0 0 0 0 6 0 0 0d7 0 0 0 0 0 0 0 0 7 0 0 0d8 0 0 0 0 0 0 1 0 8 0 0 0d9 0 0 0 0 0 0 0 0 9 0 0 0

d10 0 0 1 0 0 0 0 0 10 0 0 0d11 0 0 0 0 0 0 0 0 11 0 0 0d12 0 0 0 0 0 0 1 0 12 0 0 0d13 0 0 0 0 0 0 0 0 13 0 0 0d14 0 0 0 1 0 0 0 0 14 0 0 0d15 0 0 0 0 0 0 0 0 15 0 0 0d16 0 0 0 0 0 0 1 0 16 0 0 0d17 1 0 0 0 0 0 0 0 17 0 0 0d18 0 1 0 0 0 0 0 0 18 0 0 0d19 0 0 0 0 0 0 0 0 19 0 0 0d20 0 0 0 0 0 0 0 0 20 0 0 0d21 0 1 0 0 0 0 0 0 21 0 0 0d22 0 0 1 0 0 0 0 0 22 0 0 0d23 0 0 0 0 0 0 0 0 23 0 0 0d24 0 0 0 0 0 0 0 0 24 0 0 0d25 0 0 1 0 0 0 0 0 25 0 0 0d26 0 0 0 1 0 0 0 0 26 0 0 0d27 0 0 0 0 0 0 0 0 27 0 0 0d28 0 0 0 0 0 0 0 0 28 0 0 0d29 0 1 0 0 0 0 0 0 29 0 0 0d30 0 0 0 0 1 0 0 0 30 0 0 0d31 0 0 0 0 0 0 1 0 31 0 0 0d32 0 0 0 0 0 0 0 1 32 0 0 0d33 0 0 1 0 0 0 0 0 33 0 0 0d34 0 0 0 0 0 1 0 0 34 0 0 0d35 0 0 0 0 0 0 1 0 35 0 0 0d36 0 0 0 0 0 0 0 1 36 0 0 0d37 0 0 0 0 1 0 0 0 37 0 0 0d38 0 0 0 0 0 1 0 0 38 0 0 0d39 0 0 0 0 0 0 0 0 39 0 0 0d40 0 0 0 0 0 0 0 0 40 0 0 0

Page 3: matriks kekakuan TB anstruk 2.xlsx

4 5 6 7 8 9 10 11 12 130.6667 0 0 0 0 0 0 0 0 00.6667 0 0 0 0 0 0 0 0 0-0.4444 0 0 0 0 0 0 0 0 00.4444 0 0 0 0 0 0 0 0 0

0 1.3333 0.6667 -0.6667 0.6667 0 0 0 0 00 0.6667 1.3333 -0.6667 0.6667 0 0 0 0 00 -0.6667 -0.6667 0.4444 -0.4444 0 0 0 0 00 0.6667 0.6667 -0.4444 0.4444 0 0 0 0 00 0 0 0 0 1.3333 0.6667 -0.6667 0.6667 00 0 0 0 0 0.6667 1.3333 -0.6667 0.6667 00 0 0 0 0 -0.6667 -0.6667 0.4444 -0.4444 00 0 0 0 0 0.6667 0.6667 -0.4444 0.4444 00 0 0 0 0 0 0 0 0 1.33330 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 -0.66670 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

Page 4: matriks kekakuan TB anstruk 2.xlsx

14 15 16 17 18 19 20 21 22 230 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0.6667 -0.6667 0.6667 0 0 0 0 0 0 01.3333 -0.6667 0.6667 0 0 0 0 0 0 0-0.6667 0.4444 -0.4444 0 0 0 0 0 0 00.6667 -0.4444 0.4444 0 0 0 0 0 0 0

0 0 0 2 1 -1.5 1.5 0 0 00 0 0 1 2 -1.5 1.5 0 0 00 0 0 -1.5 -1.5 1.5 -1.5 0 0 00 0 0 1.5 1.5 -1.5 1.5 0 0 00 0 0 0 0 0 0 1 0.5 -0.3750 0 0 0 0 0 0 0.5 1 -0.3750 0 0 0 0 0 0 -0.375 -0.375 0.18750 0 0 0 0 0 0 0.375 0.375 -0.18750 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

Page 5: matriks kekakuan TB anstruk 2.xlsx

24 25 26 27 28 29 30 31 32 330 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0.375 0 0 0 0 0 0 0 0 00.375 0 0 0 0 0 0 0 0 0

-0.1875 0 0 0 0 0 0 0 0 00.1875 0 0 0 0 0 0 0 0 0

0 2 1 -1.5 1.5 0 0 0 0 00 1 2 -1.5 1.5 0 0 0 0 00 -1.5 -1.5 1.5 -1.5 0 0 0 0 00 1.5 1.5 -1.5 1.5 0 0 0 0 00 0 0 0 0 1.3333 0.6667 -0.6667 0.6667 00 0 0 0 0 0.6667 1.3333 -0.6667 0.6667 00 0 0 0 0 -0.6667 -0.6667 0.4444 -0.4444 00 0 0 0 0 0.6667 0.6667 -0.4444 0.4444 00 0 0 0 0 0 0 0 0 1.33330 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 -0.66670 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

Page 6: matriks kekakuan TB anstruk 2.xlsx

34 35 36 37 38 39 40 Matriks [B]^T0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 Matriks [B]^T * [KI]0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 Matriks [K]0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 EI0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 Matriks [K]^-10 0 0 0 0 0 00 0 0 0 0 0 0

0.6667 -0.6667 0.6667 0 0 0 01.3333 -0.6667 0.6667 0 0 0 0 1/EI-0.6667 0.4444 -0.4444 0 0 0 00.6667 -0.4444 0.4444 0 0 0 0

0 0 0 1 0.5 -0.375 0.3750 0 0 0.5 1 -0.375 0.3750 0 0 -0.375 -0.375 0.1875 -0.18750 0 0 0.375 0.375 -0.1875 0.1875

Page 7: matriks kekakuan TB anstruk 2.xlsx

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

0.6667 1.3333 -0.6667 0.6667 0 0 0 0 0 00 0 0 0 0.6667 1.3333 -0.6667 0.6667 0 00 0 0 0 0 0 0 0 0.6667 1.33330 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0.6667 0.6667 -0.4444 0.4444 0.6667 0.6667 -0.4444 0.4444 0.6667 0.66670 0 0 0 0 0 0 0 0 0

Momen Primer3.33333 1 0 0 0 0 0.66667 0 Mef =

1 5.66667 0.5 0 0.66667 0 0 0.66667 Mfe =0 0.5 5.66667 1 0 0.66667 0 0.666670 0 1 3.33333 0 0 0.66667 0 Mij =0 0.66667 0 0 2.33333 0.5 -0.6667 0.66667 Mji =0 0 0.66667 0 0.5 2.33333 -0.6667 0.66667

0.66667 0 0 0.66667 -0.6667 -0.6667 2.66667 -0.8889 Mfg =0 0.66667 0.66667 0 0.66667 0.66667 -0.8889 0.88889 Mgf =

Mgh =0.33965 -0.052 0.01291 0.02019 0.00824 -0.0153 -0.1203 -0.0857 Mhg =

-0.052 0.2188 0.00255 0.01291 -0.0192 0.05944 -0.0684 -0.26450.01291 0.00255 0.2188 -0.052 0.05944 -0.0192 -0.0684 -0.2645 Matriks Kekakuan Global ( {F} = [K] * {D} + {F°} )0.02019 0.01291 -0.052 0.33965 -0.0153 0.00824 -0.1203 -0.0857 D1 =0.00824 -0.0192 0.05944 -0.0153 0.56341 -0.0106 -0.0124 -0.4572 D2 =-0.0153 0.05944 -0.0192 0.00824 -0.0106 0.56341 -0.0124 -0.4572 D3 =-0.1203 -0.0684 -0.0684 -0.1203 -0.0124 -0.0124 0.70399 0.82516 D4 =-0.0857 -0.2645 -0.2645 -0.0857 -0.4572 -0.4572 0.82516 3.03277 D5 =

D6 =D7 =D8 =

Page 8: matriks kekakuan TB anstruk 2.xlsx

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

0 0 0 0 0 0 2 1 -1.5 1.50 0 0 0 0 0 1 2 -1.5 1.5

-0.6667 0.6667 0 0 0 0 0 0 0 00 0 0.6667 1.3333 -0.6667 0.6667 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

-0.4444 0.4444 0.6667 0.6667 -0.4444 0.4444 0 0 0 00 0 0 0 0 0 0 0 0 0

Reaksi Primer-PL/8 = -0.75 ton.meter Q1 = -0.75 ton.meter Ref = 1.5PL/8 = 0.75 ton.meter Q2 = 0.75 ton.meter Rfe = 1.5

Q3 = 2.66667 ton.meter-PL/8 = -2 ton.meter Q4 = 0.4 ton.meter Rij = 0.75PL/8 = 2 ton.meter Q5 = -2 ton.meter Rji = 3.25

Q6 = 7 ton.meter-QL^2/12 = -2.6667 ton.meter Q7 = 0 ton.meter Rfg = 4QL^2/12 = 2.6667 ton.meter Q8 = 0 ton.meter Rgf = 4

-QL^2/30 = -0.2667 ton.meter Rgh = 0.6667QL^2/20 = 0.4 ton.meter Rhg = 1.3333

Matriks Kekakuan Global ( {F} = [K] * {D} + {F°} )-0.37510.6695 Elemen 1 = P1 1.3333 0.66667 -0.66667 0.666670.3017 P2 0.66667 1.33333 -0.66667 0.666670.0802 P3 -0.6667 -0.6667 0.44444 -0.4444

-1.0695 P4 0.66667 0.66667 -0.44444 0.444443.9734

-0.2536 Elemen 2 = P1 1.3333 0.66667 -0.66667 0.66667-3.1598 P2 0.66667 1.33333 -0.66667 0.66667

P3 -0.6667 -0.6667 0.44444 -0.4444P4 0.66667 0.66667 -0.44444 0.44444

Elemen 3 = P1 1.3333 0.66667 -0.66667 0.66667P2 0.66667 1.33333 -0.66667 0.66667P3 -0.6667 -0.6667 0.44444 -0.4444

Matriks {F°}

Matriks Gaya-Gaya Dalam tiap elemen ( {P} = [Ke] * {D} + {P°} )

Page 9: matriks kekakuan TB anstruk 2.xlsx

P4 0.66667 0.66667 -0.44444 0.44444

Elemen 4 = P1 1.33333 0.66667 -0.66667 0.66667P2 0.66667 1.33333 -0.66667 0.66667P3 -0.6667 -0.6667 0.44444 -0.4444P4 0.66667 0.66667 -0.44444 0.44444

Elemen 5 = P1 2 1 -1.5 1.5P2 1 2 -1.5 1.5P3 -1.5 -1.5 1.5 -1.5P4 1.5 1.5 -1.5 1.5

Elemen 6 = P1 1 0.5 -0.375 0.375P2 0.5 1 -0.375 0.375P3 -0.375 -0.375 0.1875 -0.1875P4 0.375 0.375 -0.1875 0.1875

Elemen 7 = P1 2 1 -1.5 1.5P2 1 2 -1.5 1.5P3 -1.5 -1.5 1.5 -1.5P4 1.5 1.5 -1.5 1.5

Elemen 8 = P1 1.3333 0.66667 -0.66667 0.66667P2 0.66667 1.33333 -0.66667 0.66667P3 -0.6667 -0.6667 0.44444 -0.4444P4 0.66667 0.66667 -0.44444 0.44444

Elemen 9 = P1 1.3333 0.66667 -0.66667 0.66667P2 0.66667 1.33333 -0.66667 0.66667P3 -0.6667 -0.6667 0.44444 -0.4444P4 0.66667 0.66667 -0.44444 0.44444

Elemen 10 = P1 1 0.5 -0.375 0.375P2 0.5 1 -0.375 0.375P3 -0.375 -0.375 0.1875 -0.1875P4 0.375 0.375 -0.1875 0.1875

Page 10: matriks kekakuan TB anstruk 2.xlsx

0 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 0 1 00 1 0 0 1 0 0 0 0 00 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 01 0.5 -0.375 0.375 0 0 0 0 1.3333 0.6667

0.5 1 -0.375 0.375 2 1 -1.5 1.5 0 00 0 0 0 1 2 -1.5 1.5 0 00 0 0 0 0 0 0 0 0.6667 1.33330 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 -0.6667 -0.66670 0 0 0 0 0 0 0 0.6667 0.6667

Matriks {F}ton 0ton 0

0ton 0ton 0

0ton 0ton 0

tonton

0 0 -0.4192

x -0.3751 + 0 = -0.669240 0 0.362797

-0.2536 0 -0.362797

0 0 0.2773

x 0.6695 + 0 = 0.7236150 0 -0.33363

-0.2536 0 0.33363

0 0 0.0320

x 0.3017 + 0 = 0.2331390 0 -0.088392

Matriks Gaya-Gaya Dalam tiap elemen ( {P} = [Ke] * {D} + {P°} )

Page 11: matriks kekakuan TB anstruk 2.xlsx

-0.2536 0 0.088392

0 0 -0.1156

x 0.0802 + 0 = -0.0620970 0 0.059226

-0.2536 0 -0.059226

-0.3751 -0.75 -0.8308

x 0.6695 + 0.75 = 1.7138810 1.5 1.0584390 1.5 1.941561

0.6695 -2.666667 -1.8463

x 0.3017 + 2.666667 = 3.3030710 4 3.6358160 4 4.364184

0.3017 -0.266667 0.4169

x 0.0802 + 0.4 = 0.8620970 0.6667 0.0938890 1.3333 1.906111

0.6695 0 -1.7578

x -1.0695 + 0 = -2.917171-0.2536 0 1.558333-3.1598 0 -1.558333

0.3017 0 1.1136

x 3.9734 + 0 = 3.561401-0.2536 0 -1.558333-3.1598 0 1.558333

-1.0695 -2 -1.0828

x 3.9734 + 2 = 5.4385990 0.75 -0.3389430 3.25 4.338943

Page 12: matriks kekakuan TB anstruk 2.xlsx

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 1 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 1 0 0 00 0 0 1 0 0 0 1 0 01 0 0 0 1 0 0 0 0 00 1 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 0 0 0-0.6667 0.6667 0 0 0 0 0 0 0 0

0 0 1.3333 0.6667 -0.6667 0.6667 0 0 0 00 0 0 0 0 0 0 0 0 0

-0.6667 0.6667 0 0 0 0 1 0.5 -0.375 0.3750 0 0.6667 1.3333 -0.6667 0.6667 0.5 1 -0.375 0.375

0.4444 -0.4444 -0.6667 -0.6667 0.4444 -0.4444 0 0 0 0-0.4444 0.4444 0.6667 0.6667 -0.4444 0.4444 0 0 0 0

Page 13: matriks kekakuan TB anstruk 2.xlsx

elemen 14EI/L 2EI/L -6EI/L 6EI/L

Ke Lokal = 2EI/L 4EI/L -6EI/L 6EI/L-6EI/L^2 -6EI/L^2 12EI/L^3 -12EI/L^36EI/L^2 6EI/L^2 -12EI/L^3 12EI/L^3 elemen 2

Kekakuan Elemen1.3333 0.6667 -0.6667 0.6667

L1 = L2 = L3 = L4 = L8 = L9 = 3 m 0.6667 1.3333 -0.6667 0.6667 elemen 3-0.6667 -0.6667 0.4444 -0.44440.6667 0.6667 -0.4444 0.4444

2 1 -1.5 1.5 elemen 4L5 = L7 = 2 m 1 2 -1.5 1.5

-1.5 -1.5 1.5 -1.51.5 1.5 -1.5 1.5

elemen 51 0.5 -0.375 0.375

L6 = L10 = 4 m 0.5 1 -0.375 0.375-0.375 -0.375 0.1875 -0.18750.375 0.375 -0.1875 0.1875 elemen 6

P1 = 3 tonP2 = 4 tonQ1 = 2 ton/meter elemen 7Q2 = 2 ton/meterM1 = 5 ton.meter

elemen 8

elemen 9

elemen 10

Page 14: matriks kekakuan TB anstruk 2.xlsx

Matriks [B] D1 D2 D3 D4 D5 D6 D7 D8 Matriks [KI] 1 2 31 0 0 0 0 0 0 0 0 1 1.3333 0.6667 -0.66672 1 0 0 0 0 0 0 0 2 0.6667 1.3333 -0.66673 0 0 0 0 0 0 0 0 3 -0.6667 -0.6667 0.44444 0 0 0 0 0 0 1 0 4 0.6667 0.6667 -0.44441 0 0 0 0 0 0 0 0 1 0 0 02 0 1 0 0 0 0 0 0 2 0 0 03 0 0 0 0 0 0 0 0 3 0 0 04 0 0 0 0 0 0 1 0 4 0 0 01 0 0 0 0 0 0 0 0 1 0 0 02 0 0 1 0 0 0 0 0 2 0 0 03 0 0 0 0 0 0 0 0 3 0 0 04 0 0 0 0 0 0 1 0 4 0 0 01 0 0 0 0 0 0 0 0 1 0 0 02 0 0 0 1 0 0 0 0 2 0 0 03 0 0 0 0 0 0 0 0 3 0 0 04 0 0 0 0 0 0 1 0 4 0 0 01 1 0 0 0 0 0 0 0 1 0 0 02 0 1 0 0 0 0 0 0 2 0 0 03 0 0 0 0 0 0 0 0 3 0 0 04 0 0 0 0 0 0 0 0 4 0 0 01 0 1 0 0 0 0 0 0 1 0 0 02 0 0 1 0 0 0 0 0 2 0 0 03 0 0 0 0 0 0 0 0 3 0 0 04 0 0 0 0 0 0 0 0 4 0 0 01 0 0 1 0 0 0 0 0 1 0 0 02 0 0 0 1 0 0 0 0 2 0 0 03 0 0 0 0 0 0 0 0 3 0 0 04 0 0 0 0 0 0 0 0 4 0 0 01 0 1 0 0 0 0 0 0 1 0 0 02 0 0 0 0 1 0 0 0 2 0 0 03 0 0 0 0 0 0 1 0 3 0 0 04 0 0 0 0 0 0 0 1 4 0 0 01 0 0 1 0 0 0 0 0 1 0 0 02 0 0 0 0 0 1 0 0 2 0 0 03 0 0 0 0 0 0 1 0 3 0 0 04 0 0 0 0 0 0 0 1 4 0 0 01 0 0 0 0 1 0 0 0 1 0 0 02 0 0 0 0 0 1 0 0 2 0 0 03 0 0 0 0 0 0 0 0 3 0 0 04 0 0 0 0 0 0 0 0 4 0 0 0

Page 15: matriks kekakuan TB anstruk 2.xlsx

4 1 2 3 4 1 2 3 4 10.6667 0 0 0 0 0 0 0 0 00.6667 0 0 0 0 0 0 0 0 0-0.4444 0 0 0 0 0 0 0 0 00.4444 0 0 0 0 0 0 0 0 0

0 1.3333 0.6667 -0.6667 0.6667 0 0 0 0 00 0.6667 1.3333 -0.6667 0.6667 0 0 0 0 00 -0.6667 -0.6667 0.4444 -0.4444 0 0 0 0 00 0.6667 0.6667 -0.4444 0.4444 0 0 0 0 00 0 0 0 0 1.3333 0.6667 -0.6667 0.6667 00 0 0 0 0 0.6667 1.3333 -0.6667 0.6667 00 0 0 0 0 -0.6667 -0.6667 0.4444 -0.4444 00 0 0 0 0 0.6667 0.6667 -0.4444 0.4444 00 0 0 0 0 0 0 0 0 1.33330 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 -0.66670 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

Page 16: matriks kekakuan TB anstruk 2.xlsx

2 3 4 1 2 3 4 1 2 30 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0.6667 -0.6667 0.6667 0 0 0 0 0 0 01.3333 -0.6667 0.6667 0 0 0 0 0 0 0-0.6667 0.4444 -0.4444 0 0 0 0 0 0 00.6667 -0.4444 0.4444 0 0 0 0 0 0 0

0 0 0 2 1 -1.5 1.5 0 0 00 0 0 1 2 -1.5 1.5 0 0 00 0 0 -1.5 -1.5 1.5 -1.5 0 0 00 0 0 1.5 1.5 -1.5 1.5 0 0 00 0 0 0 0 0 0 1 0.5 -0.3750 0 0 0 0 0 0 0.5 1 -0.3750 0 0 0 0 0 0 -0.375 -0.375 0.18750 0 0 0 0 0 0 0.375 0.375 -0.18750 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

Page 17: matriks kekakuan TB anstruk 2.xlsx

4 1 2 3 4 1 2 3 4 10 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0.375 0 0 0 0 0 0 0 0 00.375 0 0 0 0 0 0 0 0 0

-0.1875 0 0 0 0 0 0 0 0 00.1875 0 0 0 0 0 0 0 0 0

0 2 1 -1.5 1.5 0 0 0 0 00 1 2 -1.5 1.5 0 0 0 0 00 -1.5 -1.5 1.5 -1.5 0 0 0 0 00 1.5 1.5 -1.5 1.5 0 0 0 0 00 0 0 0 0 1.3333 0.6667 -0.6667 0.6667 00 0 0 0 0 0.6667 1.3333 -0.6667 0.6667 00 0 0 0 0 -0.6667 -0.6667 0.4444 -0.4444 00 0 0 0 0 0.6667 0.6667 -0.4444 0.4444 00 0 0 0 0 0 0 0 0 1.33330 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 -0.66670 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

Page 18: matriks kekakuan TB anstruk 2.xlsx

2 3 4 1 2 3 4 Matriks [B]^T0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 Matriks [B]^T * [KI]0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 Matriks [K]0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 EI0 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0 Matriks [K]^-10 0 0 0 0 0 00 0 0 0 0 0 0

0.6667 -0.6667 0.6667 0 0 0 01.3333 -0.6667 0.6667 0 0 0 0 1/EI-0.6667 0.4444 -0.4444 0 0 0 00.6667 -0.4444 0.4444 0 0 0 0

0 0 0 1 0.5 -0.375 0.3750 0 0 0.5 1 -0.375 0.3750 0 0 -0.375 -0.375 0.1875 -0.18750 0 0 0.375 0.375 -0.1875 0.1875

Page 19: matriks kekakuan TB anstruk 2.xlsx

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

0.6667 1.3333 -0.6667 0.6667 0 0 0 0 0 00 0 0 0 0.6667 1.3333 -0.6667 0.6667 0 00 0 0 0 0 0 0 0 0.6667 1.33330 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0

0.6667 0.6667 -0.4444 0.4444 0.6667 0.6667 -0.4444 0.4444 0.6667 0.66670 0 0 0 0 0 0 0 0 0

Momen Primer3.33333 1 0 0 0 0 0.66667 0 Mef =

1 5.66667 0.5 0 0.66667 0 0 0.66667 Mfe =0 0.5 5.66667 1 0 0.66667 0 0.666670 0 1 3.33333 0 0 0.66667 0 Mij =0 0.66667 0 0 2.33333 0.5 -0.6667 0.66667 Mji =0 0 0.66667 0 0.5 2.33333 -0.6667 0.66667

0.66667 0 0 0.66667 -0.6667 -0.6667 2.66667 -0.8889 Mfg =0 0.66667 0.66667 0 0.66667 0.66667 -0.8889 0.88889 Mgf =

Mgh =0.33965 -0.052 0.01291 0.02019 0.00824 -0.0153 -0.1203 -0.0857 Mhg =

-0.052 0.2188 0.00255 0.01291 -0.0192 0.05944 -0.0684 -0.26450.01291 0.00255 0.2188 -0.052 0.05944 -0.0192 -0.0684 -0.2645 Matriks Kekakuan Global ( {F} = [K] * {D} + {F°} )0.02019 0.01291 -0.052 0.33965 -0.0153 0.00824 -0.1203 -0.0857 D1 =0.00824 -0.0192 0.05944 -0.0153 0.56341 -0.0106 -0.0124 -0.4572 D2 =-0.0153 0.05944 -0.0192 0.00824 -0.0106 0.56341 -0.0124 -0.4572 D3 =-0.1203 -0.0684 -0.0684 -0.1203 -0.0124 -0.0124 0.70399 0.82516 D4 =-0.0857 -0.2645 -0.2645 -0.0857 -0.4572 -0.4572 0.82516 3.03277 D5 =

D6 =D7 =D8 =

Page 20: matriks kekakuan TB anstruk 2.xlsx

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

0 0 0 0 0 0 2 1 -1.50 0 0 0 0 0 1 2 -1.5

-0.6667 0.6667 0 0 0 0 0 0 00 0 0.6667 1.3333 -0.6667 0.6667 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0

-0.4444 0.4444 0.6667 0.6667 -0.4444 0.4444 0 0 00 0 0 0 0 0 0 0 0

Reaksi Primer-PL/8 = -0.75 ton.meter Q1 = -0.75 ton.meter Ref =PL/8 = 0.75 ton.meter Q2 = -1.9167 ton.meter Rfe =

Q3 = 2.4 ton.meter-PL/8 = -2 ton.meter Q4 = 0.4 ton.meter Rij =PL/8 = 2 ton.meter Q5 = -2 ton.meter Rji =

Q6 = 2 ton.meter-QL^2/12 = -2.6666666667 ton.meter Q7 = 0 ton.meter Rfg =QL^2/12 = 2.66666666667 ton.meter Q8 = 0 ton.meter Rgf =

-QL^2/30 = -0.2666666667 ton.meter Rgh =QL^2/20 = 0.4 ton.meter Rhg =

Matriks Kekakuan Global ( {F} = [K] * {D} + {F°} )0.08650.5090 Elemen 1 = P1 1.3333 0.66667 -0.66667

-0.4285 P2 0.66667 1.33333 -0.666670.0228 P3 -0.6667 -0.6667 0.444440.9278 P4 0.66667 0.66667 -0.444441.8141

-0.0712 Elemen 2 = P1 1.3333 0.66667 -0.66667-2.1881 P2 0.66667 1.33333 -0.66667

P3 -0.6667 -0.6667 0.44444P4 0.66667 0.66667 -0.44444

Elemen 3 = P1 1.3333 0.66667 -0.66667P2 0.66667 1.33333 -0.66667P3 -0.6667 -0.6667 0.44444

Matriks {F°}

Matriks Gaya-Gaya Dalam tiap elemen ( {P} = [Ke] * {D} + {P°} )

Page 21: matriks kekakuan TB anstruk 2.xlsx

P4 0.66667 0.66667 -0.44444

Elemen 4 = P1 1.33333 0.66667 -0.66667P2 0.66667 1.33333 -0.66667P3 -0.6667 -0.6667 0.44444P4 0.66667 0.66667 -0.44444

Elemen 5 = P1 2 1 -1.5P2 1 2 -1.5P3 -1.5 -1.5 1.5P4 1.5 1.5 -1.5

Elemen 6 = P1 1 0.5 -0.375P2 0.5 1 -0.375P3 -0.375 -0.375 0.1875P4 0.375 0.375 -0.1875

Elemen 7 = P1 2 1 -1.5P2 1 2 -1.5P3 -1.5 -1.5 1.5P4 1.5 1.5 -1.5

Elemen 8 = P1 1.3333 0.66667 -0.66667P2 0.66667 1.33333 -0.66667P3 -0.6667 -0.6667 0.44444P4 0.66667 0.66667 -0.44444

Elemen 9 = P1 1.3333 0.66667 -0.66667P2 0.66667 1.33333 -0.66667P3 -0.6667 -0.6667 0.44444P4 0.66667 0.66667 -0.44444

Elemen 10 = P1 1 0.5 -0.375P2 0.5 1 -0.375P3 -0.375 -0.375 0.1875P4 0.375 0.375 -0.1875

Page 22: matriks kekakuan TB anstruk 2.xlsx

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

1.5 0 0 0 0 0 0 0 0 01.5 1 0.5 -0.375 0.375 0 0 0 0 1.33330 0.5 1 -0.375 0.375 2 1 -1.5 1.5 00 0 0 0 0 1 2 -1.5 1.5 00 0 0 0 0 0 0 0 0 0.66670 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 -0.66670 0 0 0 0 0 0 0 0 0.6667

Reaksi Primer Matriks {F}0.75 ton 0 0.752.25 ton 0 1.916667

0 -2.41 ton 0 -0.43 ton 0 2

5 32.6665 ton 0 05.3335 ton 0 0

0.33333 ton1.66667 ton

0.66667 0 0 0.0102 0.01020.66667 x 0.0865 + 0 = 0.067901 0.067901-0.4444 0 0 -0.026039 -0.0260390.44444 -0.0712 0 0.026039 0.026039

0.66667 0 0 0.2919 0.29190.66667 x 0.5090 + 0 = 0.631253 0.631253-0.4444 0 0 -0.307715 -0.3077150.44444 -0.0712 0 0.307715 0.307715

0.66667 0 0 -0.3331 -0.33310.66667 x -0.4285 + 0 = -0.618769 -0.618769-0.4444 0 0 0.317296 0.317296

Matriks {F} - {F°}

Matriks Gaya-Gaya Dalam tiap elemen ( {P} = [Ke] * {D} + {P°} )

Page 23: matriks kekakuan TB anstruk 2.xlsx

0.44444 -0.0712 0 -0.317296 -0.317296

0.66667 0 0 -0.0323 -0.03230.66667 x 0.0228 + 0 = -0.017092 -0.017092-0.4444 0 0 0.016458 0.0164580.44444 -0.0712 0 -0.016458 -0.016458

1.5 0.0865 -0.75 0.6821 -0.06791.5 x 0.5090 + 0.75 = 1.104613 1.854613-1.5 0 0.75 -0.893356 -0.1433561.5 0 2.25 0.893356 3.143356

0.375 0.5090 -2.666667 0.2948 -2.37190.375 x -0.4285 + 2.666667 = -0.173953 2.492714

-0.1875 0 2.6665 -0.030213 2.6362870.1875 0 5.3335 0.030213 5.363713

1.5 -0.4285 -0.266667 -0.8342 -1.10081.5 x 0.0228 + 0.4 = -0.382908 0.017092-1.5 0 0.333333 0.608536 0.941871.5 0 1.666667 -0.608536 1.05813

0.66667 0.5090 0 -0.1140 -0.11400.66667 x 0.9278 + 0 = 0.165151 0.165151-0.4444 -0.0712 0 -0.017049 -0.0170490.44444 -2.1881 0 0.017049 0.017049

0.66667 -0.4285 0 -0.7731 -0.77310.66667 x 1.8141 + 0 = 0.721966 0.721966-0.4444 -0.0712 0 0.017049 0.0170490.44444 -2.1881 0 -0.017049 -0.017049

0.375 0.9278 -2 1.8348 -0.16520.375 x 1.8141 + 2 = 2.278034 4.278034

-0.1875 0 1 -1.028221 -0.0282210.1875 0 3 1.028221 4.028221

Page 24: matriks kekakuan TB anstruk 2.xlsx

0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 00 0 0 1 0 0 0 0 0 00 0 0 0 0 0 0 0 0 01 0 0 0 0 0 0 1 0 00 0 0 0 1 0 0 0 1 00 1 0 0 0 1 0 0 0 00 0 1 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 0 00.6667 -0.6667 0.6667 0 0 0 0 0 0 0

0 0 0 1.3333 0.6667 -0.6667 0.6667 0 0 00 0 0 0 0 0 0 0 0 0

1.3333 -0.6667 0.6667 0 0 0 0 1 0.5 -0.3750 0 0 0.6667 1.3333 -0.6667 0.6667 0.5 1 -0.375

-0.6667 0.4444 -0.4444 -0.6667 -0.6667 0.4444 -0.4444 0 0 00.6667 -0.4444 0.4444 0.6667 0.6667 -0.4444 0.4444 0 0 0

Page 25: matriks kekakuan TB anstruk 2.xlsx

00000000

0000

0.3750.375

00