Homework 3: Metode Schrenk dan Gaya Dalam (Schrenk’s Method and Internal Forces) Diamond DA 40 - Analisis dan Perancangan Struktur Ringan I (APS I)

1. 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

2. 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 풄 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 풄 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

3. 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 Diagram
at MTOW 1150 kg (2535 lb)
VS VA VC VD

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Sehingga, dengan dengan persamaan 퐿= 12 휌0푉2푆퐶퐿 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.
푙푝푙푎푛푓표푟푚= 2퐿 1+휆 푏 1+ 2푦 푏 휆−1
푙푒푙푙푖푝푡푖푐푎푙= 4퐿 휋푏 1− 2푦 푏 2
푙푠푐ℎ푟푒푛푘= 푙푝푙푎푛푓표푟푚+푙푒푙푙푖푝푡푖푐푎푙 2
Perlu diperhatikan bahwa distribusi lift dengan metode Schrenk ini adalah distribusi lift pada tiap partisi kecil span (b), sehingga disimbolkan 푙 (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.

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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

6. APS I Homework 2 Sayogyo Rahman Doko 13611046
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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

7. 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

8. APS I Homework 2 Sayogyo Rahman Doko 13611046
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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

9. 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:
푐 푦 = 2푆 1+휆 푏 1− 2(1−휆) 푏 푦
- 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: Δ푉=− 푙 푦 푑푦
Change in shear = - area under distributed loading

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Bending momen di tiap partisi span diperoleh melalui luas di bawah kurva shear force. Δ푀= 푉 푦 푑푦
Change in moment = - area under shear diagram
Torsi dihitung dengan cara sebagai berikut:
 Wing
푙 (푥)= 퐿푖 푐
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: 푑휏푖=푙 푥 .푑푥.푥
Sehingga, intergrasi dari 푑휏푖 adalah: 휏푖= 푙 푥 푥푑푥
Selanjutnya dilakukan proses integrasi dari -0.4c ≤ x < 0 dan 0 < x ≤ 0.6c.
l (x)
-0.4 c 0 0.6 c

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 Horizontal Tail
푙0= 2퐿푖 푐 푑푎푛 푙 푥 =푙0 푥−0.6푐 푐 → 푙 (푥)= 2퐿푖 푐 푥−0.6푐 푐
Dengan cara yang sama, elemen dx di sepanjang chord tail menghasilkan torsi sebagai berikut: 푑휏푖=푙 푥 .푑푥.푥
Sehingga, intergrasi dari 푑휏푖 adalah: 휏푖= 푙 푥 푥푑푥
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) 휏푖 (Nm) 휏 (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

13. APS I Homework 2 Sayogyo Rahman Doko 13611046
13
-5000
0
5000
10000
15000
20000
25000
0
1
2
3
4
5
6
7
N
m
Shear Force (V) Distribution
0
10000
20000
30000
40000
50000
60000
70000
0
1
2
3
4
5
6
7
Nm
m
Bending Moment (M) Distribution at Root

14. 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) 휏푖 (Nm) 휏 (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

15. 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

16. APS I Homework 2 Sayogyo Rahman Doko 13611046
16
-3000
-2500
-2000
-1500
-1000
-500
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

17. 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
5
10
15
20
25
30
35
40
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Nm
m
Torsion (τ) Distribution