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Design of the wing box structure for the given wing geometry, weights and load factors. Microsoft Excel was used for all the calculations needed for this design. The complete structure was drafted using Solidworks CAD software.

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### Structures proyect

1. 1. POLITECHNIC UNIVERSITY OF PUERTO RICO DEPARTMENT OF MECHANICAL ENGINEERING HATO REY, PUERTO RICO ME5930: AerospaceStructures SP-13 Box Structure Design Final Project Carlos J. Gutiérrez Román #54543 Javier A. Colón Toledo #64547 Submitted to: Dr. Héctor Rodríguez May 22, 2013
2. 2. Table of Contents Executive Summary....................................................................................................................................... 2 Introduction .................................................................................................................................................. 3 Assumptions.................................................................................................................................................. 4 Design Approach- Standards and Considerations......................................................................................... 5 Calculations and Results ............................................................................................................................... 6 Final Selection and Recommendations ......................................................................................................... 9 CAD Drawings.............................................................................................................................................. 19 References .................................................................................................................................................. 21 Appendix ..................................................................................................................................................... 22 Page | 1
3. 3. Executive Summary Aircraft wing boxes are a very complex structure because they need to withstand not only the forces of drag and lift but also its own weight and in most cases the weight of the engines and the trust these produce. All these forces create a lot of stresses on the wing and each component job is to withstand a corresponding stress. In this project we are designing a wing box that has to be able to survive a set of specified constraints. We started by using the Schrenks span wise load approximations to obtain the shear and bending moments that the forces produce on each section (rib) across the wing. Then we used these stresses to design the stringers and the skin of our wing box using the theories and procedures learned in class. Our design consisted of twelve ribs, two spars and eight stringers.We have to repeat this procedure for each of the sections we divided the wing span. We used the Von misses and maximum shear stress theories to calculate the margin of safety associated with each component to evaluate if our design was successful. In order to facilitate the calculations we used Microsoft Excel to make the calculations and Solidworks to draw the CAD and obtain values for area and skin lengths. The result is a very simple but effective wing box that fully complains with the design specifications. Page | 2
4. 4. Introduction When designing an aircraft many factors contribute to the process. Depending on the type of aircraft,its shape, mission, performance parameters and weight distribution between others all the structural requirements change dramatically. Most of the loads that will be acting on the aircraft produce different stresses that act on different structural elements but all need to be designed simultaneously. While designing the wing structure the factors are simplified and the design depends on loads affecting only the wing, which cause shear forces and moments. Using an industry standard factor of safety we analyzed the acting stresses caused by the loads and from here on we designed the structure to obtain a positive margin of safety. In this paper the preliminary design for a wing box structure is explained. The students were given a specific wing shape with its dimension; also known was the weight of the engines that each wing will carry and the total weight of the aircraft. With this information we designed the complete wing box structure and completed a full analysis for each stringer and the skin of the wing. Page | 3
5. 5. Assumptions Weight Nlimit F.S. W. Engine W. Span Half Span Cr Ct Ơ 7075 Ơ 7178 0 0 145000 2.25 1.5 5400 1344 672 108 48 73000 psi 78000 psi 0 0  According to the FAA (Federal Aviation Administration) FAR (Federal Aviation Regulations) a factor of safety of 1.5 must be applied to the limit load which has external loads on the structure considered.  Limit maneuvering load factors. (a) Except where limited by maximum (static) lift coefficients, the airplane is assumed to be subjected to symmetrical maneuvers resulting in the limit maneuvering load factors prescribed in this section. Pitching velocities appropriate to the corresponding pull-up and steady turn maneuvers must be taken into account. (b) The positive limit maneuvering load factor "n" for any speed up to VD may not be less than Page | 4
6. 6. Design Approach- Standards and Considerations Airfoil: NACA0012 – 12.5% from the leading edge and 25% from the trailing edge where eliminated for the wing box design. Ribs: Twelve ribs were used with the following areas: Rib Area 12.00 706.57 11.00 927.49 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 1148.17 1369.09 1589.78 1810.70 2031.38 2252.30 2472.99 2693.91 2914.59 3135.52 3356.20 Stringers: Eight 672 inch long stringers with an area that varies with its length as follows: Section Area 12.00 12.00 11.00 11.00 10.00 10.00 9.00 9.00 8.00 8.00 7.00 7.00 6.00 6.00 5.00 5.00 4.00 4.00 3.00 3.00 2.00 2.00 Skin and spars: Skin and rib length are specified according to the rib area. A common thickness of 0.125 inch was used for the skin and 0.5 inch for the spars. Cross section example of root rib: All the components were verified for its corresponding bending moment stress or shear stress according to the principles learned in class. Maximum Shear Stress and Von Misses Theories were utilized to calculate the margin of safety. Page | 5 1.00 1.00
7. 7. Calculations and Results Examples of calculations made by hand: Schrenks Span Wise Load Approximations Ultimate Vertical Load Wing span lift factor Average local lift coefficient Strip Area Force Between the Strips Distance to Forces Shear Moment Page | 6
8. 8. Bending Moment stresses (Station #1, Stringer #3) Assumptions Dist. To Yc Bending Stress Shear Flows and shear stress (Station #1, Surface 3,4) Page | 7
9. 9. Von-Mises (Station #1, Stringer #3) Maximum Shear Stress (Station #1, Skin section 6,7) Page | 8
10. 10. Calculations and results obtained using Microsoft Excel Schrenks Span Wise Load Approximations Station 12.00 11.00 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 Zi(in) 672.00 616.00 560.00 504.00 448.00 392.00 336.00 280.00 224.00 168.00 112.00 56.00 0.00 Czi(in) 48.00 63.00 78.00 93.00 108.00 123.00 138.00 153.00 168.00 183.00 198.00 213.00 228.00 Cel(in) 0.00 70.22 97.13 116.22 130.96 142.72 152.17 159.73 165.66 170.13 173.25 175.10 175.71 CL1 (z) 0.50 1.06 1.12 1.12 1.11 1.08 1.05 1.02 0.99 0.96 0.94 0.91 0.89 CL1avg 0.78 1.09 1.12 1.12 1.09 1.07 1.04 1.01 0.98 0.95 0.92 0.90 DZi 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 Ai(in²) 3108.00 3948.00 4788.00 5628.00 6468.00 7308.00 8148.00 8988.00 9828.00 10668.00 11508.00 12348.00 FyaWi (lb) 4109.11 11037.69 14212.68 16739.38 18921.07 20872.57 22650.93 24288.74 25806.20 14814.74 28527.71 29745.58 ZFyawi (in) 644.00 588.00 532.00 476.00 420.00 364.00 308.00 252.00 196.00 140.00 84.00 28.00 Total 231726.40 5.50 = Shear (lb) Moment (lb-in) 0.00 0.00 -4109.11 115054.98 -15146.80 654220.31 -29359.47 1900395.94 -46098.85 4013229.07 -65019.92 7124554.68 -85892.49 11350102.25 -108543.42 16794307.84 -132832.16 23552824.15 -158638.36 31713998.80 -173453.11 41012559.91 -201980.82 51524709.79 -231726.40 63668511.86 Page | 9
11. 11. Page | 10
12. 12. Shear and moment diagrams Page | 11
13. 13. Bending Moments Stresses and Margin of Safety per station (Aluminum 7075-T6) Station 1 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y position (in.) 0.00 0.00 47.45 95.05 142.50 142.50 95.05 47.45 Z position (in.) 11.53 -11.53 -13.63 -11.43 -7.21 7.21 11.43 13.63 Total: Station 2 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y position (in.) 0.00 0.00 44.33 88.80 133.13 133.13 88.80 44.33 Y position (in.) 10.77 -10.77 -12.73 -10.68 -6.73 6.73 10.68 12.73 Total: Station 3 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y position (in.) 0.00 0.00 41.21 82.54 123.75 123.75 82.54 41.21 Zc position (in.) 10.01 -10.01 -11.84 -9.93 -6.26 6.26 9.93 11.84 Total: Station 4 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y positoin (in.) 0.00 0.00 38.09 76.29 114.38 114.38 76.29 38.09 Zc position (in.) 9.25 -9.25 -10.94 -9.17 -5.78 5.78 9.17 10.94 Total: Area (in².) 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 96.00 Area (in².) 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 88.00 Area (in².) 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 80.00 Area (in².) 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 72.00 Dist. to Yc (in.) -71.25 -71.25 -23.80 23.80 71.25 71.25 23.80 -23.80 Bending Stress (psi) -61019.26 61019.26 72132.92 60490.04 38130.42 -38130.42 -60490.04 -72132.92 Inertia - Y (in^4.) Yc position (in.) 9625.44 66.57 Intertia - Z (in^4.) Zc position (in.) 216708.48 0.00 My (lb-in.) -51524709.79 Shear (lb.) 201980.82 Dist. to Yc -66.57 -66.57 -22.23 22.23 66.57 66.57 22.23 -22.23 Bending Stress (psi) -57661.42 57661.42 68163.50 57161.32 36032.13 -36032.13 -57161.32 -68163.50 Inertia - Y (in^4.) Yc position (in.) 7560.78 61.88 Intertia - Z (in^4.) Zc position (in.) 170224.38 0.00 My (lb-in.) -41012559.91 Shear (lb.) 173453.11 Dist. to Yc -61.88 -61.88 -20.67 20.67 61.88 61.88 20.67 -20.67 Bending Stress (psi) -54313.78 54313.78 64206.14 53842.72 33940.22 -33940.22 -53842.72 -64206.14 Inertia - Y (in^4.) Yc position (in.) 5813.25 57.19 Intertia - Z (in^4.) Zc position (in.) 130880.23 0.00 My (lb-in.) -31713998.80 Shear (lb.) 158638.36 Dist. to Yc -57.19 -57.19 -19.10 19.10 57.19 57.19 19.10 -19.10 Bending Stress (psi) -50489.00 50489.00 59684.74 50051.11 31550.15 -31550.15 -50051.11 -59684.74 Inertia - Y (in^4.) Yc position (in.) 71.25 12030.59 Intertia - Z (in^4.) Zc position (in.) 270858.41 0.00 My (lb-in.) -63668511.86 Shear (lb.) 231726.40 MS 0.20 0.20 0.01 0.21 0.91 0.91 0.21 0.01 MS 0.27 0.27 0.07 0.28 1.03 1.03 0.28 0.07 MS 0.34 0.34 0.14 0.36 1.15 1.15 0.36 0.14 MS 0.45 0.45 0.22 0.46 1.31 1.31 0.46 0.22 Page | 12
14. 14. Station 5 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y positoin (in.) 0.00 0.00 34.97 70.04 105.00 105.00 70.04 34.97 Zc position (in.) 8.50 -8.50 -10.04 -8.42 -5.31 5.31 8.42 10.04 Total: Area (in².) 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 64.00 Inertia - Y (in^4.) Yc position (in.) 4354.56 52.50 Intertia - Z (in^4.) Zc position (in.) 98039.24 0.00 My (lb-in.) -23552824.15 Shear (lb.) 132832.16 Dist. to Yc -52.50 -52.50 -17.54 17.54 52.50 52.50 17.54 -17.54 Bending Stress (psi) -45951.75 45951.75 54321.11 45553.21 28714.86 -28714.86 -45553.21 -54321.11 Station 6 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y positoin (in.) 0.00 0.00 31.84 63.79 95.63 95.63 63.79 31.84 Zc position (in.) 7.74 -7.74 -9.15 -7.67 -4.84 4.84 7.67 9.15 Total: Area (in².) 7.00 7.00 7.00 7.00 7.00 7.00 7.00 7.00 56.00 Inertia - Y (in^4.) Yc position (in.) 3160.55 47.82 Intertia - Z (in^4.) Zc position (in.) 71157.01 0.00 My (lb-in.) -16794307.84 Shear (lb.) 108543.42 Dist. to Yc -47.82 -47.82 -15.97 15.97 47.82 47.82 15.97 -15.97 Bending Stress (psi) -41115.76 41115.76 48604.32 40759.16 25692.89 -25692.89 -40759.16 -48604.32 Station 7 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y position (in.) 0.00 0.00 28.72 57.53 86.25 86.25 57.53 28.72 Zc position (in.) 6.98 -6.98 -8.25 -6.92 -4.36 4.36 6.92 8.25 Total: Area (in².) 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 48.00 Inertia - Y (in^4.) Yc position (in.) 2203.66 43.13 Intertia - Z (in^4.) Zc position (in.) 49613.61 0.00 My (lb-in.) -11350102.25 Shear (lb.) 85892.49 Dist. to Yc -43.13 -43.13 -14.40 14.40 43.13 43.13 14.40 -14.40 Bending Stress (psi) -35944.11 35944.11 42490.74 35632.37 22461.17 -22461.17 -35632.37 -42490.74 Station 8 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y position (in.) 0.00 0.00 25.60 51.28 76.88 76.88 51.28 25.60 Zc position (in.) 6.22 -6.22 -7.35 -6.17 -3.89 3.89 6.17 7.35 Total: Area (in².) 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 40.00 Inertia - Y (in^4.) Yc position (in.) 1459.06 38.44 Intertia - Z (in^4.) Zc position (in.) 32849.45 0.00 My (lb-in.) -7124554.68 Shear (lb.) 65019.92 Dist. to Yc -38.44 -38.44 -12.84 12.84 38.44 38.44 12.84 -12.84 Bending Stress (psi) -30374.75 30374.75 35907.01 30111.31 18980.93 -18980.93 -30111.31 -35907.01 MS 0.59 0.59 0.34 0.60 1.54 1.54 0.60 0.34 MS 0.78 0.78 0.50 0.79 1.84 1.84 0.79 0.50 MS 1.03 1.03 0.72 1.05 2.25 2.25 1.05 0.72 MS 1.40 1.40 1.03 1.42 2.85 2.85 1.42 1.03 Page | 13
15. 15. Station 9 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y position (in.) 0.00 0.00 22.48 45.02 67.50 67.50 45.02 22.48 Zc position (in.) 5.46 -5.46 -6.46 -5.41 -3.41 3.41 5.41 6.46 Total: Area (in².) 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 32.00 Inertia - Y (in^4.) Yc position (in.) 899.80 33.75 Intertia - Z (in^4.) Zc position (in.) 20258.11 0.00 My (lb-in.) -4013229.07 Shear (lb.) 46098.85 Dist. to Yc -33.75 -33.75 -11.27 11.27 33.75 33.75 11.27 -11.27 Bending Stress (psi) -24359.51 24359.51 28796.19 24148.24 15222.05 -15222.05 -24148.24 -28796.19 Station 10 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y positoin (in.) 0.00 0.00 19.36 38.77 58.13 58.13 38.77 19.36 Zc position (in.) 4.70 -4.70 -5.56 -4.66 -2.94 2.94 4.66 5.56 Total: Area (in².) 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 24.00 Inertia - Y (in^4.) Yc position (in.) 500.49 29.07 Intertia - Z (in^4.) Zc position (in.) 11268.17 0.00 My (lb-in.) -1900395.94 Shear (lb.) 29359.47 Dist. to Yc -29.07 -29.07 -9.71 9.71 29.07 29.07 9.71 -9.71 Bending Stress (psi) -17859.15 17859.15 21111.91 17704.26 11160.04 -11160.04 -17704.26 -21111.91 Station 11 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y positoin (in.) 0.00 0.00 16.23 32.52 48.75 48.75 32.52 16.23 Zc position (in.) 3.94 -3.94 -4.66 -3.91 -2.46 2.46 3.91 4.66 Total: Area (in².) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 16.00 Inertia - Y (in^4.) Yc position (in.) 234.67 24.38 Intertia - Z (in^4.) Zc position (in.) 5283.36 0.00 My (lb-in.) -654220.31 Shear (lb.) 15146.80 Dist. to Yc -24.38 -24.38 -8.14 8.14 24.38 24.38 8.14 -8.14 Bending Stress (psi) -10996.58 10996.58 12999.43 10901.21 6871.67 -6871.67 -10901.21 -12999.43 Station 12 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 Y positoin (in.) 0.00 0.00 13.11 26.27 39.38 39.38 26.27 13.11 Zc position (in.) 3.19 -3.19 -3.77 -3.16 -1.99 1.99 3.16 3.77 Total: Area (in².) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 8.00 Inertia - Y (in^4.) Yc position (in.) 76.56 19.69 Intertia - Z (in^4.) Zc position (in.) 1723.78 0.00 My (lb-in.) -115054.98 Shear (lb.) 4109.11 Dist. to Yc -19.69 -19.69 -6.58 6.58 19.69 19.69 6.58 -6.58 Bending Stress (psi) -4788.15 4788.15 5660.24 4746.63 2992.08 -2992.08 -4746.63 -5660.24 MS 2.00 2.00 1.54 2.02 3.80 3.80 2.02 1.54 MS 3.09 3.09 2.46 3.12 5.54 5.54 3.12 2.46 MS 5.64 5.64 4.62 5.70 9.62 9.62 5.70 4.62 MS 14.25 14.25 11.90 14.38 23.40 23.40 14.38 11.90 Page | 14
16. 16. Shear Flows, Shear stresses and Margin of Safety per station(Aluminum 7050-T73511) Station 1 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -2665.01 0.00 3150.40 5792.30 7457.64 5792.30 3150.40 Length 47.55 23.05 47.55 47.55 47.69 14.41 47.69 47.55 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 2.10 25.16 27.26 25.06 20.84 6.43 2.20 Total: q' Moments 0.00 -128999.86 0.00 4083588.19 6922439.45 2239024.60 1774807.40 329563.24 -15220423.02 qi = qi ' + qo τ -3743.33 -6408.34 -3743.33 -592.93 2048.97 3714.31 2048.97 -592.93 -29946.64 -12816.68 -29946.64 -4743.45 16391.73 7428.62 16391.73 -4743.45 Station 2 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -2486.41 0.00 2939.27 5404.11 6957.85 5404.11 2939.27 Length 44.42 21.53 44.42 44.42 44.55 13.46 44.55 44.42 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 1.96 23.51 25.47 23.41 19.47 6.00 2.06 Total: q' Moments 0.00 -105047.31 0.00 3325351.96 5637088.41 1823284.94 1445263.09 268370.30 -12394311.40 qi = qi ' + qo τ -3262.82 -5749.23 -3262.82 -323.55 2141.29 3695.03 2141.29 -323.55 -26102.53 -11498.45 -26102.53 -2588.39 17130.36 7390.06 17130.36 -2588.39 Station 3 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -2297.08 0.00 2715.45 4992.60 6428.03 4992.60 2715.45 Length 41.29 20.02 41.29 41.29 41.42 12.51 41.42 41.29 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 1.82 21.85 23.67 21.76 18.09 5.58 1.91 Total: q' Moments 0.00 -83854.46 0.00 2654476.29 4499829.71 1455444.93 1153687.38 214227.73 -9893811.59 qi = qi ' + qo τ -2801.98 -5099.05 -2801.98 -86.53 2190.63 3626.05 2190.63 -86.53 -22415.82 -10198.11 -22415.82 -692.22 17525.00 7252.10 17525.00 -692.22 Station 4 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -2272.98 0.00 2686.97 4940.24 6360.61 4940.24 2686.97 Length 38.17 18.50 38.17 38.17 38.28 11.57 38.28 38.17 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 1.69 20.20 21.88 20.11 16.72 5.16 1.77 Total: q' Moments 0.00 -70885.46 0.00 2243932.92 3803882.53 1230344.68 975257.19 181095.10 -8363626.96 qi = qi ' + qo τ -2562.66 -4835.64 -2562.66 124.31 2377.58 3797.95 2377.58 124.31 MS 2.21 3.84 2.21 8.66 1.22 3.89 1.22 8.66 MS 2.39 4.16 2.39 15.04 1.12 3.92 1.12 15.04 MS 2.62 4.56 2.62 53.51 1.07 4.01 1.07 53.51 MS -20501.27 2.77 -9671.29 4.76 -20501.27 2.77 994.50 35.55 19020.67 0.91 7595.90 3.79 Page | 15 19020.67 0.91 994.50 35.55
17. 17. Station 5 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -2073.25 0.00 2450.86 4506.13 5801.69 4506.13 2450.86 Length 35.04 16.98 35.04 35.04 35.14 10.62 35.14 35.04 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 1.55 18.54 20.09 18.47 15.35 4.73 1.62 Total: q' Moments 0.00 -54486.81 0.00 1724821.27 2923892.00 945716.63 749641.11 139200.54 -6428784.74 qi = qi ' + qo τ -2145.78 -4219.04 -2145.78 305.08 2360.35 3655.91 2360.35 305.08 -17166.26 -8438.07 -17166.26 2440.63 18882.80 7311.82 18882.80 2440.63 Station 6 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -1860.15 0.00 2198.94 4042.96 5205.35 4042.96 2198.94 Length 31.91 15.47 31.91 31.91 32.00 9.67 32.00 31.91 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 1.41 16.88 18.29 16.82 13.98 4.31 1.48 Total: q' Moments 0.00 -40550.53 0.00 1283657.68 2176037.87 703827.37 557902.77 103596.73 -4784471.89 qi = qi ' + qo τ -1753.42 -3613.57 -1753.42 445.52 2289.54 3451.93 2289.54 445.52 -14027.36 -7227.14 -14027.36 3564.19 18316.32 6903.86 18316.32 3564.19 Station 7 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -1632.05 0.00 1929.31 3547.20 4567.06 3547.20 1929.31 Length 28.78 13.95 28.78 28.78 28.87 8.72 28.87 28.78 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 1.27 15.23 16.50 15.17 12.61 3.89 1.33 Total: q' Moments 0.00 -28940.98 0.00 916148.49 1553041.63 502322.69 398176.08 73937.15 -3414685.07 qi = qi ' + qo τ -1387.52 -3019.57 -1387.52 541.79 2159.69 3179.55 2159.69 541.79 -11100.12 -6039.14 -11100.12 4334.32 17277.51 6359.09 17277.51 4334.32 Station 8 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -1386.03 0.00 1638.47 3012.47 3878.59 3012.47 1638.47 Length 25.65 12.44 25.65 25.65 25.73 7.77 25.73 25.65 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 1.13 13.57 14.71 13.52 11.24 3.47 1.19 Total: q' Moments 0.00 -19528.04 0.00 618174.91 1047921.13 338944.27 268670.92 49889.39 -2304072.58 qi = qi ' + qo τ -1050.34 -2436.36 -1050.34 588.13 1962.14 2828.25 1962.14 588.13 MS 3.12 5.31 3.12 13.89 0.93 3.97 0.93 13.89 MS 3.59 6.03 3.59 9.20 0.98 4.27 0.98 9.20 MS 4.27 7.02 4.27 7.39 1.10 4.72 1.10 7.39 MS -8402.70 5.33 -4872.73 8.46 -8402.70 5.33 4705.04 6.73 15697.08 1.32 5656.50 5.43 15697.08 | 16 1.32 Page 4705.04 6.73
18. 18. Station 9 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -1119.24 0.00 1323.10 2432.63 3132.04 2432.63 1323.10 Length 22.52 10.92 22.52 22.52 22.59 6.83 22.59 22.52 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 0.99 11.92 12.91 11.87 9.87 3.04 1.04 Total: q' Moments 0.00 -12156.06 0.00 384809.19 652322.96 210990.24 167245.61 31055.77 -1434267.70 qi = qi ' + qo τ -744.69 -1863.93 -744.69 578.41 1687.95 2387.35 1687.95 578.41 -5957.48 -3727.86 -5957.48 4627.28 13503.58 4774.71 13503.58 4627.28 Station 10 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -827.73 0.00 978.48 1799.03 2316.27 1799.03 978.48 Length 19.40 9.40 19.40 19.40 19.45 5.88 19.45 19.40 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 0.86 10.26 11.12 10.22 8.50 2.62 0.90 Total: q' Moments 0.00 -6667.26 0.00 211057.20 357781.10 115722.31 91729.59 17033.23 -786656.17 qi = qi ' + qo τ -474.28 -1302.00 -474.28 504.21 1324.75 1841.99 1324.75 504.21 -3794.21 -2604.00 -3794.21 4033.65 10598.02 3683.98 10598.02 4033.65 Station 11 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -509.20 0.00 601.94 1106.72 1424.91 1106.72 601.94 Length 16.27 7.89 16.27 16.27 16.32 4.93 16.32 16.27 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 0.72 8.61 9.33 8.57 7.13 2.20 0.75 Total: q' Moments 0.00 -2884.66 0.00 91316.03 154797.60 50068.43 39687.73 7369.60 -340354.73 qi = qi ' + qo τ -302.90 -812.10 -302.90 299.04 803.81 1122.01 803.81 299.04 -2423.22 -1624.20 -2423.22 2392.28 6430.51 2244.01 6430.51 2392.28 Station 12 S 8,1 1,2 2,3 3,4 4,5 5,6 6,7 7,8 q' 0.00 -171.01 0.00 202.15 371.67 478.53 371.67 202.15 Length 13.14 6.37 13.14 13.14 13.18 3.98 13.18 13.14 Thickness 0.13 0.50 0.13 0.13 0.13 0.50 0.13 0.13 q' distance w/r 8 0.00 0.58 6.95 7.53 6.93 5.76 1.78 0.61 Total: q' Moments 0.00 -632.15 0.00 20011.27 33922.82 10972.15 8697.29 1615.00 -74586.37 qi = qi ' + qo τ -87.13 -258.14 -87.13 115.02 284.54 391.40 284.54 115.02 -697.07 -516.28 -697.07 920.14 2276.32 782.80 2276.32 920.14 MS 7.10 10.75 7.10 6.86 1.69 6.61 1.69 6.86 MS 10.58 14.96 10.58 8.01 2.43 8.87 2.43 8.01 MS 16.00 23.38 16.00 14.20 4.65 15.20 4.65 14.20 MS 53.15 71.41 53.15 38.51 14.97 45.44 14.97 38.51 Page | 17
19. 19. Final Selection and Recommendations Material for stringers: Material for skin: Page | 18
20. 20. All the stringers and skin sections meet the desired requirements and obtain a Margin of safety greater than 0. Our design consists of 12 rib sections with 8 stringers running across the wing. To minimize overdesign we choose a variable area stringer design.All the sections consist of the same layout reduced in size by a factor given on the following table. All the corresponding dimensions and coordinates for all the 12 ribs, spars and stringers are also found in the table. % from 12 0.21 0.28 0.34 0.41 0.47 0.54 0.61 0.67 0.74 0.80 0.87 0.93 1.00 Station 12.00 11.00 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 Length 30.00 39.38 48.75 58.13 67.50 76.88 86.25 95.63 105.00 114.38 123.75 133.13 142.50 Spar 0 Y 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Spar 1 Y 9.99 13.11 16.23 19.36 22.48 25.60 28.72 31.84 34.97 38.09 41.21 44.33 47.45 Spar 2 Y 20.01 26.27 32.52 38.77 45.02 51.28 57.53 63.79 70.04 76.29 82.54 88.80 95.05 Spar 4 Y 30.00 39.38 48.75 58.13 67.50 76.88 86.25 95.63 105.00 114.38 123.75 133.13 142.50 Upper Arc 30.07 39.47 48.86 58.26 67.66 77.05 86.45 95.85 105.25 114.64 124.04 133.44 142.83 Lower Arc 30.07 39.47 48.86 58.26 67.66 77.05 86.45 95.85 105.25 114.64 124.04 133.44 142.83 Page | 19
21. 21. CAD Drawings Page | 20
22. 22. References  Shigley’s Mechanical Engineering Design 9th Ed. (Budynas, Nisbett, 2010)  Aluminum (“Aerospace Materials”, 2013)  Preparation of Stress Analysis Report (David McMahon, 2009)  Mechanics of Aircrafts Structures (Sun, 2006)  Aircraft Structures (Peery, 2011) Page | 21
23. 23. Appendix Solidworks Model Page | 22