contoh soal analisa struktur 2.xlsx
TRANSCRIPT
Soal MID TEST
3 digit akhir stambuk = 13Batang 1,2 b = 0.30 m P = 18 ton
P h = 0.35 m q = 15.5 ton/m'0.105
0.105
0.001072
1 2 0.001072
Y E = 20000000
2 m3 m
X q 1 m
Batang i j α Sin α Cos α1 1 2 56.31 0.8321 0.55472 2 3 90 1 0
1. Menentukan matriks kekakuan tiap elemena. Batang 1 (elemen 1)
0 0 0 0 1050000 0 0 -1050000 0 0
0 0 0 32156.25 32156.25 0 -32156.25 32156.25
=0 0
=0 32156.25 42875 0 -32156.25 21437.5
0 0 0 0 -1050000 0 0 1050000 0 0
0 0 0 -32156.25 -32156.25 0 32156.25 -32156.25
0 0 0 32156.25 21437.5 0 -32156.25 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 -0.832050294 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 00 0 0 -Sin α Cos α 0 0 0 0 -0.8320503 0.5547 00 0 0 0 0 1 0 0 0 0 0 1
0.55470 -0.83205 0 0 0 00.83205 0.55470 0 0 0 0
=0 0 1.0 0 0 00 0 0 0.55470 -0.83205 00 0 0 0.83205 0.55470 00 0 0 0 0 1.0
A1 = m2
A2 = m2
I1 = m4
L2 I2 = m4
ton/m2
L3 =
L2 =
L1 =
L1
L3
A1E/L1 -A1E/L1
12EI1/L13 6EI1/L1
2 -12EI1/L13 6EI1/L1
2
[ KL(1) ]
6EI1/L12 4EI1/L1 -6EI1/L1
2 2EI1/L1
-A1E/L1 A1E/L1
-12EI1/L13 -6EI1/L1
2 12EI1/L13 -6EI1/L1
2
6EI1/L12 2EI1/L1 -6EI1/L1
2 4EI1/L1
[ T(1) ]
[ T (1)]T
1
2
3
=
582435.206036 -26755.6173 -26755.6173 -582435.206 26755.6172773 -26755.617277 0.554700196 0.83205 0 0 0 0873652.809055 17837.07818 17837.0782 -873652.809 -17837.078185 17837.078185 -0.832050294 0.5547 0 0 0 0
=0 32156.25 42875 0 -32156.25 21437.5
x0 0 1 0 0 0
-582435.20604 26755.61728 26755.6173 582435.206 -26755.617277 26755.617277 0 0 0 0.5547002 0.83205 0-873652.80905 -17837.0782 -17837.0782 873652.8091 17837.0781849 -17837.078185 0 0 0 -0.8320503 0.5547 0
0 32156.25 21437.5 0 -32156.25 42875 0 0 0 0 0 1
1 1 1 2 2 2
345338.942308 469774.0385 -26755.6173 -345338.942 -469774.03846 -26755.617277 1469774.038462 736817.3077 17837.0782 -469774.038 -736817.30769 17837.078185 1
=-26755.617277 17837.07818 42875 26755.61728 -17837.078185 21437.5 1-345338.94231 -469774.038 26755.6173 345338.9423 469774.038462 26755.617277 2-469774.03846 -736817.308 -17837.0782 469774.0385 736817.307692 -17837.078185 2-26755.617277 17837.07818 21437.5 26755.61728 -17837.078185 42875 2
b. Batang 2 (elemen 2)
0 0 0 0 700000 0 0 -700000 0 0
0 0 0 9527.778 14291.67 0 -9527.778 14291.67
=0 0
=0 14291.67 28583.33 0 -14291.67 14291.67
-AE/L 0 0 0 0 -700000 0 0 700000 0 0
0 0 0 -9527.778 -14291.67 0 9527.778 -14291.67
0 0 0 14291.67 14291.67 0 -14291.67 28583.33
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 00 0 0 -Sin α Cos α 0 0 0 0 -1 0 00 0 0 0 0 1 0 0 0 0 0 1
0 -1 0 0 0 01 0 0 0 0 0
=0 0 1 0 0 00 0 0 0 -1 00 0 0 1 0 00 0 0 0 0 1
[ KG(1) ] [ T(1) ]T x [ KL
(1) ] x [ T(1) ]
[ T(1) ]T x [ KL(1) ] [ T(1) ]
[ KG(1) ]
[ KG(1) ]
A2E/L2 -A2E/L2
12EI2/L23 6EI2/L2
2 -12EI2/L23 6EI2/L2
2
[ KL(2) ]
6EI2/L22 4EI2/L2 -6EI2/L2
2 2EI2/L2
A2E/L2
-12EI2/L23 -6EI1/L1
2 12EI2/L23 -6EI2/L2
2
6EI2/L22 2EI2/L2 -6EI2/L2
2 4EI2/L2
[ T(2) ]
[ T(2) ]T
=
0 -9527.77778 -14291.6667 0 9527.77777778 -14291.666667 0 1 0 0 0 0700000 0 0 -700000 0 0 -1 0 0 0 0 0
=0 14291.66667 28583.3333 0 -14291.666667 14291.666667
x0 0 1 0 0 0
0 9527.777778 14291.6667 0 -9527.7777778 14291.666667 0 0 0 0 1 0-700000 0 0 700000 0 0 0 0 0 -1 0 0
0 14291.66667 14291.6667 0 -14291.666667 28583.333333 0 0 0 0 0 1
2 2 2 3 3 3
9527.77777778 0 -14291.6667 -9527.77778 0 -14291.666667 2
0 700000 0 0 -700000 0 2
=-14291.666667 0 28583.3333 14291.66667 0 14291.666667 2
-9527.7777778 0 14291.6667 9527.777778 0 14291.666667 3
0 -700000 0 0 700000 0 3
-14291.666667 0 14291.6667 14291.66667 0 28583.333333 3
[ KG(2) ] [ T(2) ]T x [ KL
(2) ] x [ T(2) ]
[ T(2) ]T x [ KL(1) ] [ T(2) ]
[ KG(2) ]
[ KG(2) ]
a.Matrik diisi sesuai dengan nodal batang
1 1 1 2 2 2 3 3 3
345338.942308 469774.0385 -26755.6173 -345338.942 -469774.03846 -26755.617277
469774.038462 736817.3077 17837.0782 -469774.038 -736817.30769 17837.078185
-26755.617277 17837.07818 42875 26755.61728 -17837.078185 21437.5
-345338.94231 -469774.038 26755.6173 345338.9423 469774.038462 26755.617277
= -469774.03846 -736817.308 -17837.0782 469774.0385 736817.307692 -17837.078185
-26755.617277 17837.07818 21437.5 26755.61728 -17837.078185 42875
b.
1 1 1 2 2 2 3 3 3
9527.777778 0 -14291.666667 -9527.777778 0 -14291.67
= 0 700000 0 0 -700000 0
-14291.6667 0 28583.333333 14291.666667 0 14291.67
-9527.77778 0 14291.666667 9527.7777778 0 14291.67
0 -700000 0 0 700000 0
-14291.6667 0 14291.666667 14291.666667 0 28583.33
c. Penjumlahan matriks1 1 1 2 2 2 3 3 3
345338.942308 469774.0385 -26755.6173 -345338.942 -469774.03846 -26755.617277 0 0 0
469774.038462 736817.3077 17837.0782 -469774.038 -736817.30769 17837.078185 0 0 0
-26755.617277 17837.07818 42875 26755.61728 -17837.078185 21437.5 0 0 0
-345338.94231 -469774.038 26755.6173 354866.7201 469774.038462 12463.950611 -9527.777778 0 -14291.67
= -469774.03846 -736817.308 -17837.0782 469774.0385 1436817.30769 -17837.078185 0 -700000 0 x
-26755.617277 17837.07818 21437.5 12463.95061 -17837.078185 71458.333333 14291.666667 0 14291.67
0 0 0 -9527.77778 0 14291.666667 9527.7777778 0 14291.67
0 0 0 0 -700000 0 0 700000 0
0 0 0 -14291.6667 0 14291.666667 14291.666667 0 28583.33
Tinjau Batang 1 (nodal 1 ke nodal 2)
F1
G1
M1
F2
G2
M2
F3
G3
M3
Tinjau Batang 2 (nodal 2 ke nodal 3)
F1
G1
M1
F2
G2
M2
F3
G3
M3
F1 U1
G1 V1
M1 Ө1
F2 U2
G2 V2
M2 Ө2
F3 U3
G3 V3
M3 Ө3
GayaBeban Batang
Lokal Global Lokal Global
4.9923 9.0000 345338.94231 469774.0385 -26755.62 -345339 -469774 -26755.62 0 0 0 0
-7.48845 0.0000 469774.03846 736817.3077 17837.08 -469774 -736817.31 17837.08 0 0 0 0 Kondisi Jepit
-6.7499 -6.7499 -26755.61728 17837.07818 42875 26755.62 -17837.078 21437.5 0 0 0 0
0 7.75 4.9923 9.0000 0 16.7500 -345338.9423 -469774.0385 26755.62 354866.7 469774.04 12463.95 -9527.778 0 -14291.666667
-7.75 0.00 -7.48845 0.0000 0 0.0000 = -469774.0385 -736817.3077 -17837.08 469774 1436817.3 -17837.08 0 -700000 0 x
-4.65 -4.65 6.7499 6.7499 0 2.0999 -26755.61728 17837.07818 21437.5 12463.95 -17837.078 71458.33 14291.67 0 14291.6666667
0 15.50 0 0 0 -9527.778 0 14291.67 9527.778 0 14291.6666667 0
-15.5 0.00 0 0 0 0 -700000 0 0 700000 0 0 Kondisi Jepit
6.975 6.98 0 0 0 -14291.67 0 14291.67 14291.67 0 28583.3333333 0
3. Unknown displacements and reacions
16.75 354866.720085 469774.0385 12463.9506
0 = 469774.038462 1436817.308 -17837.0782 x
2.0999 12463.9506106 -17837.0782 71458.3333
-1354866.720085 469774.0385 12463.9506 16.7499968162
= 469774.038462 1436817.308 -17837.0782 x 0
12463.9506106 -17837.0782 71458.3333 2.0999
5.0871691E-06 -1.67949E-06 -1.3065E-06 16.7499968162
= -1.6794932E-06 1.25262E-06 6.05614E-07 x 0
-1.3065443E-06 6.05614E-07 1.43732E-05 2.0999
LENDUTAN
8.247E-05
= -2.686E-05
8.298E-06
-345338.94231 -469774.038 -26755.6173
-469774.03846 -736817.308 17837.0782
=26755.6172773 -17837.0782 21437.5
x8.2466454E-05
-9527.7777778 0 14291.6667 -2.6859776E-05
0 -700000 0 8.2977343E-06
-14291.666667 0 14291.6667
REAKSI
-16.082863 9.0000 -25.08286
-18.801843 0.0000 -18.80184
=2.863423
--6.7499
=9.61332
-0.667134 15.500 -16.16713
18.801843 0.000 18.80184
-1.059995 6.975 -8.03499
Beban Nodal
F1 F1
G1 G1
M1 M1
F2 U2
G2 V2
M2 Ө2
F3 F3
G3 G3
M3 M3
U2
V2
Ө2
U2
V2
Ө2
U2
V2
Ө2
U2
V2
Ө2
F1
G1
M1
F3
G3
M3
F1 F1
G1 G1
M1 M1
F3 F3
G3 G3
M3 M3
4. Member forces
a. Elemen 1
=
0.55470 0.83205 0 0 0 0 345338.9423 469774 -26755.62 -345338.94 -469774 -26755.62 0
-0.83205 0.55470 0 0 0 0 469774.0385 736817.3 17837.08 -469774 -736817 17837.08 0
=0 0 1 0 0 0
x-26755.61728 17837.08 42875 26755.617 -17837.08 21437.5
x0
0 0 0 0.55470 0.83205 0 -345338.9423 -469774 26755.62 345338.94 469774 26755.62 8.2466454E-05
0 0 0 -0.83205 0.55470 0 -469774.0385 -736817 -17837.08 469774.04 736817.3 -17837.08 -2.6859776E-05
0 0 0 0 0 1 -26755.61728 17837.08 21437.5 26755.617 -17837.08 42875 8.2977343E-06
0.55470 0.83205 0 0 0 0 -16.08286323
-0.83205 0.55470 0 0 0 0 -18.80184347
=0 0 1 0 0 0
x2.86342348
0 0 0 0.55470 0.83205 0 16.08286323
0 0 0 -0.83205 0.55470 0 18.80184347
0 0 0 0 0 1 3.04130616
GAYA BATANG 1
-24.56525 4.9923 -29.55755
2.95236 -7.48845 10.44081
=2.86342
--6.7499
=9.61332
24.56525 4.9923 19.57295
-2.95236 -7.48845 4.53609
3.04131 6.7499 -3.70859
f 1
g 1
m 1[ T(1) ] x [ KG
(1) ] x { U }f 2
g 2
m 2
f 1
g 1
m 1
f 2
g 2
m 2
f 1
g 1
m 1
f 2
g 2
m 2
f 1
g 1
m 1
f 2
g 2
m 2
b. Elemen 2
=
0 1 0 0 0 0 9527.777778 0 -14291.67 -9527.7778 0 -14291.67 8.2466454E-05
-1 0 0 0 0 0 0 700000 0 0 -700000 0 -2.6859776E-05
=0 0 1 0 0 0
x-14291.66667 0 28583.33 14291.667 0 14291.67
x8.2977343E-06
0 0 0 0 1 0 -9527.777778 0 14291.67 9527.7778 0 14291.67 0
0 0 0 -1 0 0 0 -700000 0 0 700000 0 0
0 0 0 0 0 1 -14291.66667 0 14291.67 14291.667 0 28583.33 0
0 1 0 0 0 0 0.66713
-1 0 0 0 0 0x
-18.80184
=0 0 1 0 0 0 -0.94141
0 0 0 0 1 0 -0.66713
0 0 0 -1 0 0 18.80184
0 0 0 0 0 1 -1.05999
GAYA BATANG 2
-18.80184 0 -18.80184
-0.66713 -7.75 7.08287
=-0.94141
--4.65
=3.70859
18.80184 0 18.80184
0.66713 -15.5 16.16713
-1.05999 6.975 -8.03499
f 2
g 2
m 2[ T(2) ] x [ KG
(2) ] x { U }f 3
g 3
m 3
f 2
g 2
m 2
f 3
g 3
m 3
f 2
g 2
m 2
f 3
g 3
m 3
f 2
g 2
m 2
f 3
g 3
m 3
REKAPITULASI HASIL PERHITUNGAN : Portal
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Lendutan
----------------------------------------------------------------------
Nodal dx (m) dy (m) rz (rad)
1 0 0 0
2 0.00008247 -0.00002686 0.00000830
3 0 0 0
----------------------------------------------------------------------
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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
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Reaksi Tumpuan
------------------------------------------------------------
Nodal H V M
1 -25.08 -18.80 9.61
3 -16.17 18.80 -8.03
------------------------------------------------------------