homework 3: metode schrenk dan gaya dalam (schrenk’s method and internal forces)
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HOMEWORK 3
AE 3141 ANALISIS DAN PERANCANGAN STRUKTUR RINGAN I
Metode Schrenk dan Gaya Dalam
(Schrenk’s Method and Internal Forces)
Disusun oleh:
Sayogyo Rahman Doko 13611046
FAKULTAS TEKNIK MESIN DAN DIRGANTARA
AERONOTIKA DAN ASTRONOTIKA
INSTITUT TEKNOLOGI BANDUNG
2014
APS I Homework 2 Sayogyo Rahman Doko 13611046
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1. Beberapa data dan hasil perhitungan pesawat Diamond DA-40 dari revisi PR 2 (Homework
2) dicantumkan lagi di sini. Mengenai proses perhitungan dan penjelasannya telah
disampaikan di PR 2.
a. Data dan Hasil Perhitungan Sebelumnya
SI British
Environtment g 9.81 m/s2 32.2 ft/s2
ρ0 1.225 kg/m3 0.00176 slugs/ft3
Wing
S 13.54 m2 145.7 ft2
b 11.94 m
AR 10.53
𝒄 1.121 m 3.677822 ft
clα = a 5.823984 rad-1
clmax 2.119
Horizontal Tail
S 2.34 m2
b 3.29 m
𝒄 0.73819 m
Load
MTOW 1150 kg 2535 lb
MTOW 11281.5 N
EOW 750 kg 1653 lb
EOW 7357.5 N
nmax 3.8
nmin -1.52
Velocity
VS MTOW 25.20778 m/s 49 knot
VS EOW 20.46149 m/s 39.77396 knot
VA MTOW 49.13901 m/s 95.51858 knot
VA EOW 39.88679 m/s 77.53372 knot
VC 66.36333 m/s 129 knot
VD 92.90867 m/s 180.6 knot
Position
x wing 2.077241 m
x ht 7.033062 m
CG MTOW 2.46 m
CG wing 2.686934 m
CG ht 7.402721 m
APS I Homework 2 Sayogyo Rahman Doko 13611046
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Dari V-n diagram beserta gust di atas, diperoleh gaya angkat (lift) di wing dan tail pada
beberapa kondisi kritis, yakni:
V critical (m/s) V critical (knot) Mac (Nm) n L tail (N) L wing (N)
V1 99.10985 50.986512 -6575.985 4.049482 803.959368 46488.19
V2 129 66.363333 -11140.55 4.049482 -163.97312 45520.26
V3 180.6 92.908667 -21835.48 3.1346374 -2928.531 42755.7
V4 180.6 92.908667 -21835.48 -1.1346374 -5246.2752 40437.96
V5 129 66.363333 -11140.55 -2.049482 -3475.0363 42209.19
V6 95.518585 49.139005 -6108.055 -1.9805621 -2370.4616 43313.77
V7 60.720995 31.237579 -2468.34 -1.52 -1348.6124 44335.62
-3
-2
-1
0
1
2
3
4
5
6
0 20 40 60 80 100 120 140 160 180 200
n, load factor
V (knots)
V-n Diagramat MTOW 1150 kg (2535 lb)
VS VA VC VD
APS I Homework 2 Sayogyo Rahman Doko 13611046
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Sehingga, dengan dengan persamaan 𝐿 = 1
2𝜌0𝑉
2𝑆𝐶𝐿 diperoleh nilai CL saat Lwing maksimum
dan Ltail maksimum (harga absolut):
Tail Wing
L max (N) -5246.2752 46488.1902
CL -0.4240496 2.15629055
b. Distribusi Lift dengan Metode Schrenk
Metode Schrenk adalah sebuah metode perhitungan pendekatan (aproksimasi) yang
digunakan untuk menghitung distribusi lift sepanjang span. Distribusi lift diperoleh dari
rata-rata (mean) lift berdasarkan bentuk planform dan lift elliptical.
𝑙𝑝𝑙𝑎𝑛𝑓𝑜𝑟𝑚 =2𝐿
1 + 𝜆 𝑏 1 +
2𝑦
𝑏 𝜆 − 1
𝑙𝑒𝑙𝑙𝑖𝑝𝑡𝑖𝑐𝑎𝑙 =4𝐿
𝜋𝑏 1 −
2𝑦
𝑏
2
𝑙𝑠𝑐ℎ𝑟𝑒𝑛𝑘 =𝑙𝑝𝑙𝑎𝑛𝑓𝑜𝑟𝑚 + 𝑙𝑒𝑙𝑙𝑖𝑝𝑡𝑖𝑐𝑎𝑙
2
Perlu diperhatikan bahwa distribusi lift dengan metode Schrenk ini adalah distribusi lift
pada tiap partisi kecil span (b), sehingga disimbolkan 𝑙 (huruf kecil) dan satuannya
menjadi N/m.
Distribusi lift dengan metode ini memiliki asumsi untuk mempermudah perhitungan,
yakni:
- Bentuk planform wing DA-40 dianggap tidak memiliki kink dan wingtip. Selain itu,
sudut dihedral dianggap nol. Flap dan aileron juga tidak terdefleksi. Sehingga
bentuk planform wing menjadi:
Dengan croot = 1.524 dan ctip = 0.917 sehingga taper ratio, λ = 0.602. Luas sayap dan
span tetap.
APS I Homework 2 Sayogyo Rahman Doko 13611046
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- Begitu pula bentuk planform horizontal tail dianggap tidak memiliki wingtip.
Elevator juga tidak terdefleksi. Sehingga bentuk planform horizontal tail menjadi:
Dengan croot = 0.924 dan ctip = 0.513 sehingga taper ratio, λ = 0.555. Luas horizontal
tail dan span tetap.
Wing
Dengan data:
Maka, tabel perhitungan dan grafik distribusi lift menjadi sebagai berikut:
No y 2L/(1+λ)b 1+
(2y/b) (λ-1)
L Actual Planform
Shape (N/m)
L Elliptical
(N/m)
L Schrenk Approx. (N/m)
Average Lift (N)
Δy Lift Partisi,
Li (N)
1 0.000 4860.781 1.000 4860.781 4957.337 4909.059 4896.581 0.149 730.815
2 0.149 4860.781 0.990 4812.417 4955.787 4884.102 4870.848 0.149 726.974
3 0.299 4860.781 0.980 4764.052 4951.136 4857.594 4843.562 0.149 722.902
4 0.448 4860.781 0.970 4715.687 4943.375 4829.531 4814.718 0.149 718.597
5 0.597 4860.781 0.960 4667.322 4932.488 4799.905 4784.305 0.149 714.058
6 0.746 4860.781 0.950 4618.957 4918.455 4768.706 4752.313 0.149 709.283
7 0.896 4860.781 0.940 4570.592 4901.250 4735.921 4718.726 0.149 704.270
8 1.045 4860.781 0.930 4522.227 4880.837 4701.532 4683.526 0.149 699.016
9 1.194 4860.781 0.920 4473.862 4857.178 4665.520 4646.691 0.149 693.519
10 1.343 4860.781 0.910 4425.497 4830.225 4627.861 4608.194 0.149 687.773
11 1.493 4860.781 0.900 4377.132 4799.921 4588.527 4568.006 0.149 681.775
12 1.642 4860.781 0.891 4328.767 4766.203 4547.485 4526.093 0.149 675.519
13 1.791 4860.781 0.881 4280.403 4728.998 4504.700 4482.415 0.149 669.000
14 1.940 4860.781 0.871 4232.038 4688.223 4460.130 4436.929 0.149 662.212
15 2.090 4860.781 0.861 4183.673 4643.784 4413.728 4389.585 0.149 655.146
16 2.239 4860.781 0.851 4135.308 4595.574 4365.441 4340.325 0.149 647.793
17 2.388 4860.781 0.841 4086.943 4543.474 4315.209 4289.086 0.149 640.146
18 2.537 4860.781 0.831 4038.578 4487.348 4262.963 4235.796 0.149 632.193
L 46488.19 N
b 11.94 m
λ 0.6019989 S 13.54 m2
Partisi 40
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19 2.687 4860.781 0.821 3990.213 4427.043 4208.628 4180.373 0.149 623.921
20 2.836 4860.781 0.811 3941.848 4362.386 4152.117 4122.724 0.149 615.317
21 2.985 4860.781 0.801 3893.483 4293.180 4093.331 4062.745 0.149 606.365
22 3.134 4860.781 0.791 3845.118 4219.200 4032.159 4000.316 0.149 597.047
23 3.284 4860.781 0.781 3796.753 4140.193 3968.473 3935.299 0.149 587.343
24 3.433 4860.781 0.771 3748.389 4055.862 3902.125 3867.536 0.149 577.230
25 3.582 4860.781 0.761 3700.024 3965.869 3832.947 3796.843 0.149 566.679
26 3.731 4860.781 0.751 3651.659 3869.820 3760.739 3723.006 0.149 555.659
27 3.881 4860.781 0.741 3603.294 3767.250 3685.272 3645.771 0.149 544.131
28 4.030 4860.781 0.731 3554.929 3657.611 3606.270 3564.838 0.149 532.052
29 4.179 4860.781 0.721 3506.564 3540.247 3523.405 3479.842 0.149 519.366
30 4.328 4860.781 0.711 3458.199 3414.360 3436.280 3390.341 0.149 506.008
31 4.478 4860.781 0.701 3409.834 3278.970 3344.402 3295.780 0.149 491.895
32 4.627 4860.781 0.692 3361.469 3132.845 3247.157 3195.455 0.149 476.922
33 4.776 4860.781 0.682 3313.104 2974.402 3143.753 3088.450 0.149 460.951
34 4.925 4860.781 0.672 3264.739 2801.553 3033.146 2973.527 0.149 443.799
35 5.075 4860.781 0.662 3216.375 2611.439 2913.907 2848.946 0.149 425.205
36 5.224 4860.781 0.652 3168.010 2399.960 2783.985 2712.117 0.149 404.783
37 5.373 4860.781 0.642 3119.645 2160.853 2640.249 2558.851 0.149 381.908
38 5.522 4860.781 0.632 3071.280 1883.625 2477.452 2381.437 0.149 355.429
39 5.672 4860.781 0.622 3022.915 1547.928 2285.421 2161.734 0.149 322.639
40 5.821 4860.781 0.612 2974.550 1101.544 2038.047 1750.570 0.149 261.273
41 5.970 4860.781 0.602 2926.185 0.000 1463.093 731.546 0.000 0.000
42 5.970 0.000 0.000 0.000 0.000 0.000
L midspan (N) 22496.10
L total (N) 46453.8233
0
1000
2000
3000
4000
5000
6000
0 1 2 3 4 5 6 7
N/m
m
Lift (L) Distribution along Spanwise
Load Distribution From Actual Planform Shape
Load Elliptical
Schrenk Loading Approximation
APS I Homework 2 Sayogyo Rahman Doko 13611046
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Tail
Dengan data:
Maka, tabel perhitungan dan grafik distribusi lift menjadi sebagai berikut:
No y 2L/(1+λ)b 1+
(2y/b) (λ-1)
L Actual Planform
Shape (N/m)
L Elliptical (N/m)
L Schrenk Approx. (N/m)
Average Lift (N)
Δy Lift
Partisi, Li (N)
1 0.000 -2050.763 1.000 -2050.763 -2030.324 -2040.543 -2034.683 0.041 -83.676
2 0.041 -2050.763 0.989 -2027.955 -2029.689 -2028.822 -2022.644 0.041 -83.181
3 0.082 -2050.763 0.978 -2005.148 -2027.784 -2016.466 -2009.969 0.041 -82.660
4 0.123 -2050.763 0.967 -1982.340 -2024.605 -2003.473 -1996.656 0.041 -82.112
5 0.165 -2050.763 0.956 -1959.533 -2020.147 -1989.840 -1982.701 0.041 -81.539
6 0.206 -2050.763 0.944 -1936.725 -2014.399 -1975.562 -1968.099 0.041 -80.938
7 0.247 -2050.763 0.933 -1913.918 -2007.353 -1960.635 -1952.843 0.041 -80.311
8 0.288 -2050.763 0.922 -1891.110 -1998.993 -1945.051 -1936.927 0.041 -79.656
9 0.329 -2050.763 0.911 -1868.303 -1989.303 -1928.803 -1920.341 0.041 -78.974
10 0.370 -2050.763 0.900 -1845.495 -1978.264 -1911.879 -1903.075 0.041 -78.264
11 0.411 -2050.763 0.889 -1822.688 -1965.852 -1894.270 -1885.116 0.041 -77.525
12 0.452 -2050.763 0.878 -1799.880 -1952.043 -1875.962 -1866.450 0.041 -76.758
13 0.494 -2050.763 0.867 -1777.073 -1936.805 -1856.939 -1847.062 0.041 -75.960
14 0.535 -2050.763 0.855 -1754.265 -1920.106 -1837.185 -1826.933 0.041 -75.133
15 0.576 -2050.763 0.844 -1731.458 -1901.905 -1816.681 -1806.043 0.041 -74.274
16 0.617 -2050.763 0.833 -1708.650 -1882.160 -1795.405 -1784.369 0.041 -73.382
17 0.658 -2050.763 0.822 -1685.843 -1860.822 -1773.332 -1761.884 0.041 -72.457
18 0.699 -2050.763 0.811 -1663.035 -1837.836 -1750.435 -1738.559 0.041 -71.498
19 0.740 -2050.763 0.800 -1640.228 -1813.137 -1726.682 -1714.360 0.041 -70.503
20 0.781 -2050.763 0.789 -1617.420 -1786.656 -1702.038 -1689.250 0.041 -69.470
21 0.823 -2050.763 0.778 -1594.613 -1758.312 -1676.462 -1663.186 0.041 -68.399
22 0.864 -2050.763 0.766 -1571.805 -1728.013 -1649.909 -1636.118 0.041 -67.285
23 0.905 -2050.763 0.755 -1548.997 -1695.655 -1622.326 -1607.990 0.041 -66.129
24 0.946 -2050.763 0.744 -1526.190 -1661.116 -1593.653 -1578.737 0.041 -64.926
25 0.987 -2050.763 0.733 -1503.382 -1624.259 -1563.821 -1548.284 0.041 -63.673
26 1.028 -2050.763 0.722 -1480.575 -1584.921 -1532.748 -1516.544 0.041 -62.368
27 1.069 -2050.763 0.711 -1457.767 -1542.912 -1500.340 -1483.412 0.041 -61.005
28 1.110 -2050.763 0.700 -1434.960 -1498.009 -1466.484 -1448.766 0.041 -59.580
29 1.152 -2050.763 0.689 -1412.152 -1449.941 -1431.047 -1412.455 0.041 -58.087
30 1.193 -2050.763 0.677 -1389.345 -1398.383 -1393.864 -1374.300 0.041 -56.518
31 1.234 -2050.763 0.666 -1366.537 -1342.933 -1354.735 -1334.072 0.041 -54.864
32 1.275 -2050.763 0.655 -1343.730 -1283.086 -1313.408 -1291.483 0.041 -53.112
L -5246.28 N
b 3.29 m
λ 0.555141
S 2.34 m2
Partisi 40
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33 1.316 -2050.763 0.644 -1320.922 -1218.194 -1269.558 -1246.158 0.041 -51.248
34 1.357 -2050.763 0.633 -1298.115 -1147.402 -1222.759 -1197.591 0.041 -49.251
35 1.398 -2050.763 0.622 -1275.307 -1069.539 -1172.423 -1145.068 0.041 -47.091
36 1.439 -2050.763 0.611 -1252.500 -982.926 -1117.713 -1087.529 0.041 -44.725
37 1.481 -2050.763 0.600 -1229.692 -884.998 -1057.345 -1023.258 0.041 -42.081
38 1.522 -2050.763 0.589 -1206.885 -771.456 -989.171 -949.097 0.041 -39.032
39 1.563 -2050.763 0.577 -1184.077 -633.968 -909.023 -857.616 0.041 -35.269
40 1.604 -2050.763 0.566 -1161.270 -451.148 -806.209 -687.720 0.041 -28.282
41 1.645 -2050.763 0.555 -1138.462 0.000 -569.231 -284.616 0.000 0.000
42 1.645 0.000 0.000 0.000 0.000 0.000
L midspan (N) -2537.5
L total (N) -5242.3
-2500
-2000
-1500
-1000
-500
0
0 0.5 1 1.5 2
N/m
m
Lift (L) Distribution along Spanwise
Load Distribution From Actual Planform Shape
Load Elliptical
Schrenk Loading Approximation
APS I Homework 2 Sayogyo Rahman Doko 13611046
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2. Distribusi Shear Force, Bending Momen dan Torsi
Asumsi
- 2 asumsi penyederhanaan planform sebelumnya menjadikan perhitungan chord tiap
span-section dapat dirumuskan sebagai:
𝑐 𝑦 =2𝑆
1 + 𝜆 𝑏 1 −
2(1 − 𝜆)
𝑏𝑦
- Untuk wing, lift maksimum yang dipilih pada perhitungan sebelumnya berada pada pada
titik A (posisi PHAA = Positive High Angle of Attack), sehingga distribusi lift sepanjang
chord diasumsikan berupa persegi. Sedangkan untuk tail, lift maksimum yang dipilih
berada pada titik C (posisi NLAA = Negative Low Angle of Attack), sehingga distribusi lift
sepanjang chord diasumsikan berbentuk segitiga siku-siku.
- Pusat puntiran/shear center/elastic axis terletak di tengah-tengah antara front spar dan
rear spar, di mana front spar terletak di 15% chord dan rear spar terletak di 65% chord.
Dengan kata lain, pusat puntiran berada di 40% chord.
- Airfoil di horizontal tail adalah NACA 0012.
Shear force (V) di tiap partisi span diperoleh dengan cara menghitung luas di bawah kurva
lift metode Schrenk sesuai persamaan:
∆𝑉 = − 𝑙 𝑦 𝑑𝑦
Change in shear = - area under distributed loading
APS I Homework 2 Sayogyo Rahman Doko 13611046
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Bending momen di tiap partisi span diperoleh melalui luas di bawah kurva shear force.
∆𝑀 = 𝑉 𝑦 𝑑𝑦
Change in moment = - area under shear diagram
Torsi dihitung dengan cara sebagai berikut:
Wing
𝑙 (𝑥) =𝐿𝑖
𝑐
Li adalah harga lift di suatu partisi span dan l(x) adalah distribusi lift sepanjang chord. Titik 0
adalah pusat puntiran (torsi). Jika diambil sebuah elemen dx di sepanjang chord, maka torsi
yang dihasilkan oleh elemen tersebut adalah:
𝑑𝜏𝑖 = 𝑙 𝑥 . 𝑑𝑥. 𝑥
Sehingga, intergrasi dari 𝑑𝜏𝑖 adalah:
𝜏𝑖 = 𝑙 𝑥 𝑥𝑑𝑥
Selanjutnya dilakukan proses integrasi dari -0.4c ≤ x < 0 dan 0 < x ≤ 0.6c.
l (x)
-0.4 c 0 0.6 c
APS I Homework 2 Sayogyo Rahman Doko 13611046
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Horizontal Tail
𝑙0 =2𝐿𝑖
𝑐 𝑑𝑎𝑛 𝑙 𝑥 = 𝑙0
𝑥 − 0.6𝑐
𝑐 → 𝑙 (𝑥) =
2𝐿𝑖
𝑐 𝑥 − 0.6𝑐
𝑐
Dengan cara yang sama, elemen dx di sepanjang chord tail menghasilkan torsi sebagai
berikut:
𝑑𝜏𝑖 = 𝑙 𝑥 . 𝑑𝑥. 𝑥
Sehingga, intergrasi dari 𝑑𝜏𝑖 adalah:
𝜏𝑖 = 𝑙 𝑥 𝑥𝑑𝑥
Selanjutnya dilakukan proses integrasi dari -0.4c ≤ x < 0 dan 0 < x ≤ 0.6c.
Maka, tabel perhitungan gaya-gaya dalam (internal forces) pada wing dan tail menjadi:
Wing
No y DelY ΔV (N)
V (N)
ΔM (Nm)
M at root (Nm)
c(y) 𝜏𝑖
(Nm) 𝜏
(Nm)
1 0.000 23216.451 61136.748 1.416 -81.924 -2603.737
2 0.149 0.299 1457.750 217.569 1.402 -81.494 -2521.812
3 0.299 21758.701 54424.207 1.388 -81.037 -2440.319
4 0.448 0.299 1441.459 215.138 1.373 -80.555 -2359.281
5 0.597 20317.242 48144.372 1.359 -80.046 -2278.727
6 0.746 0.299 1423.301 212.428 1.345 -79.511 -2198.681
7 0.896 18893.941 42292.103 1.331 -78.949 -2119.170
l (x)
-0.4 c 0 0.6 c
l0
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8 1.045 0.299 1403.246 209.434 1.317 -78.360 -2040.222
9 1.194 17490.695 36861.696 1.303 -77.743 -1961.862
10 1.343 0.299 1381.250 206.152 1.289 -77.099 -1884.118
11 1.493 16109.445 31846.876 1.275 -76.427 -1807.019
12 1.642 0.299 1357.251 202.570 1.261 -75.726 -1730.592
13 1.791 14752.194 27240.776 1.247 -74.995 -1654.866
14 1.940 0.299 1331.167 198.677 1.233 -74.234 -1579.871
15 2.090 13421.028 23035.923 1.219 -73.442 -1505.638
16 2.239 0.299 1302.891 194.456 1.204 -72.618 -1432.196
17 2.388 12118.137 19224.202 1.190 -71.760 -1359.578
18 2.537 0.299 1272.287 189.889 1.176 -70.869 -1287.818
19 2.687 10845.850 15796.827 1.162 -69.942 -1216.949
20 2.836 0.299 1239.181 184.948 1.148 -68.977 -1147.007
21 2.985 9606.670 12744.289 1.134 -67.973 -1078.030
22 3.134 0.299 1203.349 179.600 1.120 -66.929 -1010.057
23 3.284 8403.320 10056.298 1.106 -65.841 -943.128
24 3.433 0.299 1164.503 173.802 1.092 -64.707 -877.287
25 3.582 7238.818 7721.709 1.078 -63.525 -812.579
26 3.731 0.299 1122.256 167.497 1.064 -62.289 -749.055
27 3.881 6116.561 5728.418 1.049 -60.997 -686.765
28 4.030 0.299 1076.087 160.606 1.035 -59.643 -625.768
29 4.179 5040.474 4063.231 1.021 -58.221 -566.125
30 4.328 0.299 1025.257 153.020 1.007 -56.724 -507.904
31 4.478 4015.217 2711.669 0.993 -55.141 -451.181
32 4.627 0.299 968.664 144.573 0.979 -53.463 -396.039
33 4.776 3046.554 1657.699 0.965 -51.673 -342.576
34 4.925 0.299 904.535 135.002 0.951 -49.750 -290.904
35 5.075 2142.019 883.305 0.937 -47.666 -241.154
36 5.224 0.299 829.645 123.825 0.923 -45.376 -193.488
37 5.373 1312.374 367.737 0.909 -42.812 -148.112
38 5.522 0.299 736.611 109.939 0.895 -39.844 -105.300
39 5.672 575.763 85.933 0.880 -36.168 -65.456
40 5.821 0.298 575.763 85.933 0.866 -29.289 -29.289
41 5.970 0.000 0.000 0.852 0.000 0.000
42 5.970 0.000 0.000 0.000
APS I Homework 2 Sayogyo Rahman Doko 13611046
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-5000
0
5000
10000
15000
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25000
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N
m
Shear Force (V) Distribution
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10000
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30000
40000
50000
60000
70000
0 1 2 3 4 5 6 7
Nm
m
Bending Moment (M) Distribution at Root
APS I Homework 2 Sayogyo Rahman Doko 13611046
14
Tail
No y DelY ΔV (N)
V (N)
ΔM (Nm)
M at root (Nm)
c(y) 𝜏𝑖
(Nm) 𝜏
(Nm)
1 0.000 -2620.018 -1887.596 0.915 1.121 35.103
2 0.041 0.082 -166.853 -6.862 0.905 1.114 33.982
3 0.082 -2453.165 -1678.961 0.894 1.107 32.869
4 0.123 0.082 -164.768 -6.776 0.884 1.100 31.762
5 0.165 -2288.397 -1483.964 0.874 1.092 30.662
6 0.206 0.082 -162.472 -6.682 0.864 1.084 29.570
7 0.247 -2125.924 -1302.425 0.854 1.076 28.486
8 0.288 0.082 -159.962 -6.578 0.843 1.067 27.410
9 0.329 -1965.962 -1134.147 0.833 1.058 26.344
10 0.370 0.082 -157.233 -6.466 0.823 1.048 25.286
11 0.411 -1808.729 -978.912 0.813 1.038 24.238
12 0.452 0.082 -154.278 -6.345 0.803 1.028 23.200
13 0.494 -1654.451 -836.489 0.793 1.017 22.172
-3000
-2500
-2000
-1500
-1000
-500
0
0 1 2 3 4 5 6 7
Nm
m
Torsion (τ) Distribution
APS I Homework 2 Sayogyo Rahman Doko 13611046
15
14 0.535 0.082 -151.088 -6.213 0.782 1.006 21.155
15 0.576 -1503.363 -706.624 0.772 0.995 20.148
16 0.617 0.082 -147.650 -6.072 0.762 0.983 19.154
17 0.658 -1355.712 -589.045 0.752 0.970 18.171
18 0.699 0.082 -143.950 -5.920 0.742 0.958 17.201
19 0.740 -1211.763 -483.457 0.732 0.944 16.243
20 0.781 0.082 -139.967 -5.756 0.721 0.930 15.299
21 0.823 -1071.796 -389.546 0.711 0.916 14.369
22 0.864 0.082 -135.677 -5.580 0.701 0.901 13.453
23 0.905 -936.119 -306.970 0.691 0.886 12.552
24 0.946 0.082 -131.046 -5.389 0.681 0.869 11.666
25 0.987 -805.073 -235.364 0.671 0.853 10.796
26 1.028 0.082 -126.032 -5.183 0.660 0.835 9.944
27 1.069 -679.041 -174.330 0.650 0.817 9.109
28 1.110 0.082 -120.575 -4.959 0.640 0.798 8.292
29 1.152 -558.466 -123.437 0.630 0.778 7.494
30 1.193 0.082 -114.592 -4.713 0.620 0.757 6.716
31 1.234 -443.874 -82.216 0.610 0.735 5.959
32 1.275 0.082 -107.959 -4.440 0.599 0.711 5.224
33 1.316 -335.915 -50.147 0.589 0.686 4.513
34 1.357 0.082 -100.475 -4.132 0.579 0.660 3.827
35 1.398 -235.440 -26.650 0.569 0.631 3.167
36 1.439 0.082 -91.777 -3.774 0.559 0.599 2.536
37 1.481 -143.663 -11.060 0.548 0.564 1.937
38 1.522 0.082 -81.031 -3.332 0.538 0.523 1.374
39 1.563 -62.632 -2.576 0.528 0.472 0.851
40 1.604 0.082 -62.632 -2.576 0.518 0.379 0.379
41 1.645 0.000 0.000 0.508 0.000 0.000
42 1.645 0.000 0.000 0.000
APS I Homework 2 Sayogyo Rahman Doko 13611046
16
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-2000
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0
500
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
N
m
Shear Force (V) Distribution
-2000
-1800
-1600
-1400
-1200
-1000
-800
-600
-400
-200
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Nm
m
Bending Moment (M) Distribution at Root
APS I Homework 2 Sayogyo Rahman Doko 13611046
17
REFERENSI
Airfoil and aero characteristic.xlsx di blendedlearning.itb.ac.id
Airplane Flight Manual DA 40, 2000. Diamond Aircraft InGustries GMBH, Austria.
Hibbeler, RC. 2005. Mechanics of Materials. Prentice-Hall, Singapore.
www.engbrasil.eng.br/index_arquivos/art104.pdf
0
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40
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Nm
m
Torsion (τ) Distribution
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