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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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<ul><li> 1. POLITECHNIC UNIVERSITY OF PUERTO RICO DEPARTMENT OF MECHANICAL ENGINEERING HATO REY, PUERTO RICOME5930: AerospaceStructures SP-13Box Structure Design Final ProjectCarlos J. Gutirrez Romn #54543 Javier A. Coln Toledo #64547Submitted to: Dr. Hctor Rodrguez May 22, 2013</li></ul><p> 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 ..................................................................................................................................................... 22Page | 1 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. 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. Assumptions Weight Nlimit F.S. W. Engine W. Span Half Span Cr Ct 7075 7178 0 0145000 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 intoaccount.(b) The positive limit maneuvering load factor "n" for any speed up to VD may not be less thanPage | 4 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 Area12.00 706.5711.00 927.4910.00 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 3356.20Stringers: Eight 672 inch long stringers with an area that varies with its length as follows: Section Area12.00 12.0011.00 11.0010.00 10.009.00 9.008.00 8.007.00 7.006.00 6.005.00 5.004.00 4.003.00 3.002.00 2.00Skin 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 | 51.00 1.00 7. Calculations and Results Examples of calculations made by hand: Schrenks Span Wise Load Approximations Ultimate Vertical LoadWing span lift factorAverage local lift coefficientStrip AreaForce Between the StripsDistance to ForcesShearMomentPage | 6 8. Bending Moment stresses (Station #1, Stringer #3) AssumptionsDist. To YcBending StressShear Flows and shear stress (Station #1, Surface 3,4)Page | 7 9. Von-Mises (Station #1, Stringer #3)Maximum Shear Stress (Station #1, Skin section 6,7)Page | 8 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 0.00Zi(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 0.00Czi(in) 48.00 63.00 78.00 93.00 108.00 123.00 138.00 153.00 168.00 183.00 198.00 213.00 228.00Cel(in) 0.00 70.22 97.13 116.22 130.96 142.72 152.17 159.73 165.66 170.13 173.25 175.10 175.71CL1 (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 0.89CL1avg 0.78 1.09 1.12 1.12 1.09 1.07 1.04 1.01 0.98 0.95 0.92 0.90DZi 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00 56.00Ai(in) 3108.00 3948.00 4788.00 5628.00 6468.00 7308.00 8148.00 8988.00 9828.00 10668.00 11508.00 12348.00FyaWi (lb) 4109.11 11037.69 14212.68 16739.38 18921.07 20872.57 22650.93 24288.74 25806.20 14814.74 28527.71 29745.58ZFyawi (in) 644.00 588.00 532.00 476.00 420.00 364.00 308.00 252.00 196.00 140.00 84.00 28.00Total231726.405.50=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 63668511.86Page | 9 11. Page | 10 12. Shear and moment diagramsPage | 11 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 8.00Y position (in.) 0.00 0.00 47.45 95.05 142.50 142.50 95.05 47.45Z 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 8.00Y position (in.) 0.00 0.00 44.33 88.80 133.13 133.13 88.80 44.33Y 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 8.00Y position (in.) 0.00 0.00 41.21 82.54 123.75 123.75 82.54 41.21Zc 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 8.00Y positoin (in.) 0.00 0.00 38.09 76.29 114.38 114.38 76.29 38.09Zc position (in.) 9.25 -9.25 -10.94 -9.17 -5.78 5.78 9.17 10.94 Total:Area (in.) 12.00 12.00 12.00 12.00 12.00 12.00 12.00 12.00 96.00 Area (in.) 11.00 11.00 11.00 11.00 11.00 11.00 11.00 11.00 88.00Area (in.) 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 80.00 Area (in.) 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 72.00Dist. to Yc (in.) -71.25 -71.25 -23.80 23.80 71.25 71.25 23.80 -23.80Bending Stress (psi) -61019.26 61019.26 72132.92 60490.04 38130.42 -38130.42 -60490.04 -72132.92Inertia - 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.) 201980.82Dist. to Yc -66.57 -66.57 -22.23 22.23 66.57 66.57 22.23 -22.23Bending Stress (psi) -57661.42 57661.42 68163.50 57161.32 36032.13 -36032.13 -57161.32 -68163.50Inertia - 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.) 173453.11Dist. to Yc -61.88 -61.88 -20.67 20.67 61.88 61.88 20.67 -20.67Bending Stress (psi) -54313.78 54313.78 64206.14 53842.72 33940.22 -33940.22 -53842.72 -64206.14Inertia - 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.) 158638.36Dist. to Yc -57.19 -57.19 -19.10 19.10 57.19 57.19 19.10 -19.10Bending Stress (psi) -50489.00 50489.00 59684.74 50051.11 31550.15 -31550.15 -50051.11 -59684.74Inertia - Y (in^4.)Yc position (in.) 71.2512030.59 Intertia - Z (in^4.) Zc position (in.) 270858.41 0.00 My (lb-in.) -63668511.86 Shear (lb.) 231726.40MS 0.20 0.20 0.01 0.21 0.91 0.91 0.21 0.01MS 0.27 0.27 0.07 0.28 1.03 1.03 0.28 0.07MS 0.34 0.34 0.14 0.36 1.15 1.15 0.36 0.14MS 0.45 0.45 0.22 0.46 1.31 1.31 0.46 0.22Page | 12 14. Station 5 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y positoin (in.) 0.00 0.00 34.97 70.04 105.00 105.00 70.04 34.97Zc position (in.) 8.50 -8.50 -10.04 -8.42 -5.31 5.31 8.42 10.04 Total:Area (in.) 8.00 8.00 8.00 8.00 8.00 8.00 8.00 8.00 64.00Inertia - 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.) 132832.16Dist. to Yc -52.50 -52.50 -17.54 17.54 52.50 52.50 17.54 -17.54Bending Stress (psi) -45951.75 45951.75 54321.11 45553.21 28714.86 -28714.86 -45553.21 -54321.11Station 6 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y positoin (in.) 0.00 0.00 31.84 63.79 95.63 95.63 63.79 31.84Zc position (in.) 7.74 -7.74 -9.15 -7.67 -4.84 4.84 7.67 9.15 Total:Area (in.) 7.00 7.00 7.00 7.00 7.00 7.00 7.00 7.00 56.00Inertia - 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.) 108543.42Dist. to Yc -47.82 -47.82 -15.97 15.97 47.82 47.82 15.97 -15.97Bending Stress (psi) -41115.76 41115.76 48604.32 40759.16 25692.89 -25692.89 -40759.16 -48604.32Station 7 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y position (in.) 0.00 0.00 28.72 57.53 86.25 86.25 57.53 28.72Zc position (in.) 6.98 -6.98 -8.25 -6.92 -4.36 4.36 6.92 8.25 Total:Area (in.) 6.00 6.00 6.00 6.00 6.00 6.00 6.00 6.00 48.00Inertia - 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.) 85892.49Dist. to Yc -43.13 -43.13 -14.40 14.40 43.13 43.13 14.40 -14.40Bending Stress (psi) -35944.11 35944.11 42490.74 35632.37 22461.17 -22461.17 -35632.37 -42490.74Station 8 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y position (in.) 0.00 0.00 25.60 51.28 76.88 76.88 51.28 25.60Zc position (in.) 6.22 -6.22 -7.35 -6.17 -3.89 3.89 6.17 7.35 Total:Area (in.) 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00 40.00Inertia - 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.) 65019.92Dist. to Yc -38.44 -38.44 -12.84 12.84 38.44 38.44 12.84 -12.84Bending Stress (psi) -30374.75 30374.75 35907.01 30111.31 18980.93 -18980.93 -30111.31 -35907.01MS 0.59 0.59 0.34 0.60 1.54 1.54 0.60 0.34MS 0.78 0.78 0.50 0.79 1.84 1.84 0.79 0.50MS 1.03 1.03 0.72 1.05 2.25 2.25 1.05 0.72MS 1.40 1.40 1.03 1.42 2.85 2.85 1.42 1.03Page | 13 15. Station 9 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y position (in.) 0.00 0.00 22.48 45.02 67.50 67.50 45.02 22.48Zc position (in.) 5.46 -5.46 -6.46 -5.41 -3.41 3.41 5.41 6.46 Total:Area (in.) 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 32.00Inertia - 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.) 46098.85Dist. to Yc -33.75 -33.75 -11.27 11.27 33.75 33.75 11.27 -11.27Bending Stress (psi) -24359.51 24359.51 28796.19 24148.24 15222.05 -15222.05 -24148.24 -28796.19Station 10 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y positoin (in.) 0.00 0.00 19.36 38.77 58.13 58.13 38.77 19.36Zc position (in.) 4.70 -4.70 -5.56 -4.66 -2.94 2.94 4.66 5.56 Total:Area (in.) 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 24.00Inertia - 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.) 29359.47Dist. to Yc -29.07 -29.07 -9.71 9.71 29.07 29.07 9.71 -9.71Bending Stress (psi) -17859.15 17859.15 21111.91 17704.26 11160.04 -11160.04 -17704.26 -21111.91Station 11 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y positoin (in.) 0.00 0.00 16.23 32.52 48.75 48.75 32.52 16.23Zc position (in.) 3.94 -3.94 -4.66 -3.91 -2.46 2.46 3.91 4.66 Total:Area (in.) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 16.00Inertia - 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.) 15146.80Dist. to Yc -24.38 -24.38 -8.14 8.14 24.38 24.38 8.14 -8.14Bending Stress (psi) -10996.58 10996.58 12999.43 10901.21 6871.67 -6871.67 -10901.21 -12999.43Station 12 Stringer 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00Y positoin (in.) 0.00 0.00 13.11 26.27 39.38 39.38 26.27 13.11Zc position (in.) 3.19 -3.19 -3.77 -3.16 -1.99 1.99 3.16 3.77 Total:Area (in.) 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 8.00Inertia - 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.) 4109.11Dist. to Yc -19.69 -19.69 -6.58 6.58 19.69 19.69 6.58 -6.58Bending Stress (psi) -4788.15 4788....</p>