contoh soal analisa struktur 2.xlsx

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13 Batang 1,2 b = 0.30 m P = 18 ton P h = 0.35 m q = 15.5 ton/m' A1 = 0.105 m2 A2 = 0.105 m2 I1 = 0.001072 m4 1 2 L2 I2 = 0.001072 m4 Y E = 20000000 ton/m2 L3 = 2 m L2 = 3 m X q L1 = 1 m L1 L3

Batang i j α Sin α Cos α

1 1 2 56.31 0.8321 0.5547

2 2 3 90 1 0

1. Menentukan matriks kekakuan tiap elemen a. Batang 1 (elemen 1) A1E/L1 0 0 -A1E/L1 0 0 1050000 0 0 -1050000 0 0 0 12EI1/L1 3 6EI1/L1 2 ₀ -12EI1/L1 3 6EI1/L1 2 ₀ _32156.3 _32156.3 ₀ _{-32156.3 32156.3}

0 6EI1/L12 4EI1/L1 0 -6EI1/L12 2EI1/L1 0 32156.3 42875 0 -32156.3 21437.5

-A1E/L1 0 0 A1E/L1 0 0 -1050000 0 0 1050000 0 0 0 -12EI1/L1 3 -6EI1/L1 2 ₀ 12EI1/L1 3 -6EI1/L1 2 ₀ _{-32156.3 -32156.3} ₀ _{32156.3 -32156.3}

0 6EI1/L12 2EI1/L1 0 -6EI1/L12 4EI1/L1 0 32156.3 21437.5 0 -32156.3 42875

Cos α Sin α 0 0 0 0 0.554700196 0.83205 0 0 0 0 -Sin α Cos α 0 0 0 0 -0.83205029 0.5547 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 Cos α Sin α 0 0 0 0 0.5547002 0.83205 0 0 0 0 -Sin α Cos α 0 0 0 0 -0.83205 0.5547 0 0 0 0 0 0 1 0 0 0 0 0 1 0.55470 -0.83205 0 0 0 0 0.83205 0.55470 0 0 0 0 0 0 1.0 0 0 0 0 0 0 0.55470 -0.83205 0 0 0 0 0.83205 0.55470 0 0 0 0 0 0 1.0 [ KL(1) ] = = [ T(1) ] = =

Soal MID TEST

3 digit akhir stambuk =

[ T (1)_]T ₌

1

2

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[ KG (1) _] ₌ _{[ T}(1) _]T_{x [ K} L (1) _{] x [ T}(1)_] 582435.206 -26755.617 -26755.617 -582435.206 26755.61728 -26755.61728 0.554700196 0.83205 0 0 0 0 873652.8091 17837.0782 17837.078 -873652.809 -17837.07818 17837.07818 -0.83205029 0.5547 0 0 0 0 0 32156.25 42875 0 -32156.25 21437.5 0 0 1 0 0 0 -582435.206 26755.6173 26755.617 582435.206 -26755.61728 26755.61728 0 0 0 0.5547002 0.83205 0 -873652.8091 -17837.078 -17837.078 873652.809 17837.07818 -17837.07818 0 0 0 -0.83205 0.5547 0 0 32156.25 21437.5 0 -32156.25 42875 0 0 0 0 0 1 1 1 1 2 2 2 345338.9423 469774.038 -26755.617 -345338.942 -469774.0385 -26755.61728 1 469774.0385 736817.308 17837.078 -469774.038 -736817.3077 17837.07818 1 -26755.61728 17837.0782 42875 26755.6173 -17837.07818 21437.5 1 -345338.9423 -469774.04 26755.617 345338.942 469774.0385 26755.61728 2 -469774.0385 -736817.31 -17837.078 469774.038 736817.3077 -17837.07818 2 -26755.61728 17837.0782 21437.5 26755.6173 -17837.07818 42875 2 b. Batang 2 (elemen 2) A2E/L2 0 0 -A2E/L2 0 0 700000 0 0 -700000 0 0

0 12EI2/L23 6EI2/L22 0 -12EI2/L23 6EI2/L22 0 9527.78 14291.7 0 -9527.78 14291.7

0 6EI2/L22 4EI2/L2 0 -6EI2/L22 2EI2/L2 0 14291.7 28583.3 0 -14291.7 14291.7

-AE/L 0 0 A2E/L2 0 0 -700000 0 0 700000 0 0 0 -12EI2/L2 3 _-6EI 1/L1 2 ₀ _12EI 2/L2 3 _-6EI 2/L2 2 ₀ _{-9527.78 -14291.7} ₀ _{9527.78 -14291.7}

0 6EI2/L22 2EI2/L2 0 -6EI2/L22 4EI2/L2 0 14291.7 14291.7 0 -14291.7 28583.3

Cos α Sin α 0 0 0 0 0 1 0 0 0 0 -Sin α Cos α 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 Cos α Sin α 0 0 0 0 0 1 0 0 0 0 -Sin α Cos α 0 0 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 1 [ T(1) _] [ KG(1) ] = x [ KL(2) ] = = [ T(1)_]T_{x [ K} L (1)_] [ KG(1) ] = [ T(2) _] ₌ ₌ [ T(2) ]T =

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[ KG (2) _] ₌ _{[ T}(2) _]T_{x [ K} L (2) _{] x [ T}(2)_] [ T(2)_] 0 -9527.7778 -14291.667 0 9527.777778 -14291.66667 0 1 0 0 0 0 700000 0 0 -700000 0 0 -1 0 0 0 0 0 0 14291.6667 28583.333 0 -14291.66667 14291.66667 0 0 1 0 0 0 0 9527.77778 14291.667 0 -9527.777778 14291.66667 0 0 0 0 1 0 -700000 0 0 700000 0 0 0 0 0 -1 0 0 0 14291.6667 14291.667 0 -14291.66667 28583.33333 0 0 0 0 0 1 2 2 2 3 3 3 9527.777778 0 -14291.667 -9527.77778 0 -14291.66667 2 0 700000 0 0 -700000 0 2 -14291.66667 0 28583.333 14291.6667 0 14291.66667 2 -9527.777778 0 14291.667 9527.77778 0 14291.66667 3 0 -700000 0 0 700000 0 3 -14291.66667 0 14291.667 14291.6667 0 28583.33333 3 x [ KG(2) ] = [ T(2)_]T_{x [ K} L(1) ] [ KG(2) ] =

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a. Tinjau Batang 1 (nodal 1 ke nodal 2) Matrik diisi sesuai dengan nodal batang

1 1 1 2 2 2 3 3 3 F1 345338.9423 469774.038 -26755.617 -345338.942 -469774.0385 -26755.61728 G1 469774.0385 736817.308 17837.078 -469774.038 -736817.3077 17837.07818 M1 -26755.61728 17837.0782 42875 26755.6173 -17837.07818 21437.5 F2 -345338.9423 -469774.04 26755.617 345338.942 469774.0385 26755.61728 G2 = -469774.0385 -736817.31 -17837.078 469774.038 736817.3077 -17837.07818 M2 -26755.61728 17837.0782 21437.5 26755.6173 -17837.07818 42875 F3 G3 M3

b. Tinjau Batang 2 (nodal 2 ke nodal 3)

1 1 1 2 2 2 3 3 3 F1 G1 M1 F2 9527.77778 0 -14291.66667 -9527.77778 0 -14291.7 G2 = 0 700000 0 0 -700000 0 M2 -14291.6667 0 28583.33333 14291.66667 0 14291.7 F3 -9527.77778 0 14291.66667 9527.777778 0 14291.7 G3 0 -700000 0 0 700000 0 M3 -14291.6667 0 14291.66667 14291.66667 0 28583.3 c. Penjumlahan matriks 1 1 1 2 2 2 3 3 3 F1 345338.9423 469774.038 -26755.617 -345338.942 -469774.0385 -26755.61728 0 0 0 U1 G1 469774.0385 736817.308 17837.078 -469774.038 -736817.3077 17837.07818 0 0 0 V1 M1 -26755.61728 17837.0782 42875 26755.6173 -17837.07818 21437.5 0 0 0 Ө1 F2 -345338.9423 -469774.04 26755.617 354866.72 469774.0385 12463.95061 -9527.77778 0 -14291.7 U2 G2 = -469774.0385 -736817.31 -17837.078 469774.038 1436817.308 -17837.07818 0 -700000 0 x V2 M2 -26755.61728 17837.0782 21437.5 12463.9506 -17837.07818 71458.33333 14291.66667 0 14291.7 Ө2 F3 0 0 0 -9527.77778 0 14291.66667 9527.777778 0 14291.7 U3 G3 0 0 0 0 -700000 0 0 700000 0 V3 M3 0 0 0 -14291.6667 0 14291.66667 14291.66667 0 28583.3 Ө3

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Lokal Global Lokal Global F1 4.9923 9.0000 F1 345338.9423 469774.0385 -26755.6 -345339 -469774 -26755.6 0 0 0 0 G1 -7.48845 0.0000 G1 469774.0385 736817.3077 17837.1 -469774 -736817.3 17837.1 0 0 0 0 M1 -6.7499 -6.7499 M1 -26755.6173 17837.07818 42875 26755.6 -17837.08 21437.5 0 0 0 0 F2 0 7.75 4.9923 9.0000 0 16.7500 -345338.942 -469774.038 26755.6 354867 469774.04 12464 -9527.78 0 -14291.66667 U2 G2 -7.75 0.00 -7.48845 0.0000 0 0.0000 = -469774.038 -736817.308 -17837.1 469774 1436817.3 -17837.1 0 -700000 0 x V2 M2 -4.65 -4.65 6.7499 6.7499 0 2.0999 -26755.6173 17837.07818 21437.5 12464 -17837.08 71458.3 14291.7 0 14291.66667 Ө2 F3 0 15.50 F3 0 0 0 -9527.78 0 14291.7 9527.78 0 14291.66667 0 G3 -15.5 0.00 G3 0 0 0 0 -700000 0 0 700000 0 0 M3 6.975 6.98 M3 0 0 0 -14291.7 0 14291.7 14291.7 0 28583.33333 0

3. Unknown displacements and reacions

16.75 354866.7201 469774.038 12463.951 U2 0 = 469774.0385 1436817.31 -17837.078 x V2 2.0999 12463.95061 -17837.078 71458.333 Ө2 -1 U2 354866.7201 469774.038 12463.951 16.74999682 V2 = 469774.0385 1436817.31 -17837.078 x 0 Ө2 12463.95061 -17837.078 71458.333 2.0999

U2 5.08717E-06 -1.679E-06 -1.307E-06 16.74999682

V2 = -1.67949E-06 1.2526E-06 6.056E-07 x 0

Ө2 -1.30654E-06 6.0561E-07 1.437E-05 2.0999

LENDUTAN U2 8.247E-05 V2 = -2.686E-05 Ө2 8.298E-06 F1 -345338.9423 -469774.04 -26755.617 G1 -469774.0385 -736817.31 17837.078 M1 26755.61728 -17837.078 21437.5 8.24665E-05 F3 -9527.777778 0 14291.667 -2.68598E-05 G3 0 -700000 0 8.29773E-06 M3 -14291.66667 0 14291.667 REAKSI F1 -16.082863 9.0000 -25.08286 F1 G1 -18.801843 0.0000 -18.80184 G1 M1 2.863423 -6.7499 9.61332 M1 F3 -0.667134 15.500 -16.16713 F3 G3 18.801843 0.000 18.80184 G3 M3 -1.059995 6.975 -8.03499 M3 = -= x

Beban Batang Beban

Nodal Gaya

Kondisi Jepit

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4. Member forces a. Elemen 1 f 1 g 1 m 1 f 2 g 2 m 2 f 1 0.55470 0.83205 0 0 0 0 345338.9423 469774 -26755.6 -345338.9 -469774 -26755.6 0 g 1 -0.83205 0.55470 0 0 0 0 469774.0385 736817 17837.1 -469774 -736817 17837.1 0 m 1 0 0 1 0 0 0 -26755.6173 17837.1 42875 26755.617 -17837.1 21437.5 0 f 2 0 0 0 0.55470 0.83205 0 -345338.942 -469774 26755.6 345338.94 469774 26755.6 8.24665E-05 g 2 0 0 0 -0.83205 0.55470 0 -469774.038 -736817 -17837.1 469774.04 736817 -17837.1 -2.68598E-05 m 2 0 0 0 0 0 1 -26755.6173 17837.1 21437.5 26755.617 -17837.1 42875 8.29773E-06 f 1 0.55470 0.83205 0 0 0 0 -16.0828632 g 1 -0.83205 0.55470 0 0 0 0 -18.8018435 m 1 0 0 1 0 0 0 2.86342348 f 2 0 0 0 0.55470 0.83205 0 16.08286323 g 2 0 0 0 -0.83205 0.55470 0 18.80184347 m 2 0 0 0 0 0 1 3.04130616 GAYA BATANG 1 f 1 -24.56525 4.9923 -29.55755 g 1 2.95236 -7.48845 10.44081 m 1 2.86342 -6.7499 9.61332 f 2 24.56525 4.9923 19.57295 g 2 -2.95236 -7.48845 4.53609 m 2 3.04131 6.7499 -3.70859 [ T(1)_{] x [ K} G(1) ] x { U } x x = x = = - = =

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b. Elemen 2 f 2 g 2 m 2 f 3 g 3 m 3 f 2 0 1 0 0 0 0 9527.777778 0 -14291.7 -9527.778 0 -14291.7 8.24665E-05 g 2 -1 0 0 0 0 0 0 700000 0 0 -700000 0 -2.68598E-05 m 2 0 0 1 0 0 0 -14291.6667 0 28583.3 14291.667 0 14291.7 8.29773E-06 f 3 0 0 0 0 1 0 -9527.77778 0 14291.7 9527.7778 0 14291.7 0 g 3 0 0 0 -1 0 0 0 -700000 0 0 700000 0 0 m 3 0 0 0 0 0 1 -14291.6667 0 14291.7 14291.667 0 28583.3 0 f 2 0 1 0 0 0 0 0.66713 g 2 -1 0 0 0 0 0 -18.80184 m 2 0 0 1 0 0 0 -0.94141 f 3 0 0 0 0 1 0 -0.66713 g 3 0 0 0 -1 0 0 18.80184 m 3 0 0 0 0 0 1 -1.05999 GAYA BATANG 2 f 2 -18.80184 0 -18.80184 g 2 -0.66713 -7.75 7.08287 m 2 -0.94141 -4.65 3.70859 f 3 18.80184 0 18.80184 g 3 0.66713 -15.5 16.16713 m 3 -1.05999 6.975 -8.03499 - = = = x x = x = [ T(2)_{] x [ K} G(2) ] x { U }

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REKAPITULASI HASIL PERHITUNGAN : Portal ---Lendutan ---Nodal dx (m) dy (m) rz (rad) 1 0 0 0 2 0.00008247 -0.00002686 0.00000830 3 0 0 0 ---Gaya Aksial, ---Gaya Geser dan Momen

---Batang N (kN) D (kN) M (kN.m) 1 -29.55755 10.44081 9.61332 Join 1 1 19.57295 4.53609 -3.70859 Join 2 2 -18.80184 7.08287 3.70859 Join 2 2 18.80184 16.16713 -8.03499 Join 3 --- ---Reaksi Tumpuan ---Nodal H V M 1 -25.08 -18.80 9.61 3 -16.17 18.80 -8.03