Microsoft Word - AERO2359-2110_end-sem_test.docx 2 Aerospace Structures End-semester assessment File must be submitted online. Late submission penalty: 10% per hour late. Submitted file must be a...

3 short answer questions and 3 extended calculation questionsFor question B1, the assigned parameters are:A - 0.49 ; B - 980 ; C - 1280 ; D - 10800 ; E - 15.8


Microsoft Word - AERO2359-2110_end-sem_test.docx 2 Aerospace Structures End-semester assessment File must be submitted online. Late submission penalty: 10% per hour late. Submitted file must be a single pdf, which can be handwritten or typed or both. Handwritten responses can be achieved by, for example, printing the test paper, using blank paper, or hand writing onto this pdf by using a stylus. It is recommended to use a scanner or a phone-based app such as Office Lens to generate a suitable pdf from physically handwritten pages. Please ensure you review your submitted file after submission. Calculation questions marked based on appropriateness of solution approach, as well as final solutions. Marks for working are awarded, and a consequential marking scheme is implemented whereby an incorrect value obtained in an intermediate solution step is used in any subsequent steps and only one mark penalty is applied per error. Marks are deducted for missing units, incomplete answers, or unlabelled sketches. For questions requiring a written response, marks are awarded based on the clarity of the response, the accuracy of the information, the level of technical detail, the quality of any figures, and the extent to which the question is answered. Marks are not deducted for grammar or English, except where this leads to confusion on the technical content of the answer. Attempt ALL questions. 3 Question A1 (10 marks) Define the elementary theory for torsion of a solid circular beam. Discuss the assumptions made and limitations of applying this theory to typical aircraft stiffened structures. 4 Question A2 (10 marks) Consider a column with cross-section shown below that has a compression load applied. Compare the flexural buckling behaviour of the column if the compression load is applied at the centroid (C) to where the compression load is applied at point A. A C 5 Question A3 (10 marks) The top cover section of an aircraft wing uses a stiffened skin design, where the skin panel is reinforced by stringers and ribs as shown below. a) Describe how these three structural elements (skin, stringers, ribs) contribute to the way that the wing structure carries forces and moments. b) Define and use a diagram to illustrate the different buckling modes possible for the cover section. cover section skin stringer rib location 6 B1: Your student number is used to assign parameters, according to the table below Digit 3rd 4th 5th 6th 7th Parameter A B C D E Value 0 0.40 900 1200 10500 15.0 1 0.41 910 1210 10600 15.1 2 0.42 920 1220 10700 15.2 3 0.43 930 1230 10800 15.3 4 0.44 940 1240 10900 15.4 5 0.45 950 1250 11000 15.5 6 0.46 960 1260 11100 15.6 7 0.47 970 1270 11200 15.7 8 0.48 980 1280 11300 15.8 9 0.49 990 1290 11400 15.9 e.g.: Student number 3308705, produces the following table of values Digit 3rd 4th 5th 6th 7th Parameter A B C D E Value 0 8 7 0 5 0.40 980 1270 10500 15.5 Scott Loh Highlight Scott Loh Highlight Scott Loh Highlight Scott Loh Highlight 7 Question B1 (70 marks) B1 The beam cross-section shown below consists of booms of concentrated area and thin skins that are assumed to carry only shear. The cross-section is under the action of forces and moments as shown. The material used has E = D ksi, G = 4200 ksi, cy = 40 ksi, c0 = 45 ksi, and a linear short column equation with k = 0.096 ksi for plasticity. B1a Calculate the centroid location and Ix, Iy, Ixy at the centroid. B1b Calculate the bending load in all booms (you do not need to sketch). B1c Calculate and sketch the shear flow in each panel. B1d Determine the flexural buckling stress, checking for plasticity and accounting for plasticity as required. Consider the cross-section is loaded with a compressive stress only. Assume the beam length (in z) is E in, and assume pinned boundary conditions for all instances of restraint. B1e Using your solutions for B1c, or making necessary assumptions, determine whether any of the skins buckle in shear. Consider only elastic buckling stresses. Assume the beam length (in z) is E in, and assume pinned boundary conditions for all instances of restraint. B1f Using your answers for B1b, or making necessary assumptions, determine an updated boom area at location 1 that accounts for the stiffener area and suitable areas from any connecting panels. C lbf in 1 4.0 1.5 y x 3 dimensions in inches panel thickness (in) t 1-2 , t 3-4 = 0.01 t 1-3 , t 2-4 = 0.025 stiffener area (in2) A 1 = A A 3 = 1.2 180 lbf in B lbf 400 lbf 2 4 A 2 = 0.2 A 4 = 0.2 8 Appendix: Equations, Tables and Graphs Second moment of area (I) (area moment of inertia)  dAyIx 2  dAxI y 2 yxp IIdArI   2  dAxyIxy Principal axes xy xy II I   2 2tan  2 2 2,1 22 xy xyyx I IIII I           xy xy II I   2 2tan  2 2 2,1 22 xy xyyx I IIII I           Parallel axis theorem x y b d Radius of gyration / AI tRI cx 3 RtA 2 Section properties by summation A Axx    * A Ayy    * yyy  * xxx  *x*, y*: coordinates about any axis x, y: coordinates about a parallel centroidal axis C 12 3bdI cx  12 3dbI cy  x y R C 4 4RI cx   R x x y y C R t C x y tRI cx 32 4           Ryx 2 R x y y C tRI cx 34 2           Ry 2 x a y  C 12 sin23 taI x  24 2sin3 taI xy  t t t x* y* A x y I 1 2 …  xx0 Iy0 Ixy0 Ax2 Ay2 Axy x* y* A x y I 1 2 …  xx0 Iy0 Ixy0 Ax2 Ay2 Axy 2 0 AyII xx  2 0 AxII yy  AxyII xyxy  0 9 Column with imperfections geometric load eccentricity  CRPP e /1 14    P P y z L    CRPP /1 0    Column with constant lateral loading max deflection @ z = L / 2 max moment @ z = L / 2 EI L 384 5 4 0   CRPP r /1 1    r0max  8 2 0 LM rMM 0max  P P y z L  Elastic column buckling parabolic: linear: Inelastic column equations Euler- Johnson 2 2 'L EIPCR    2 2 /'   L E CR  L’ = L L L’ = 0.5L L’ = 2L L   /'0 LkcCR   20 /'  LkcCR                 2 2 0 0 ' 4 1   L E c cCR   L zzy  sin 00 PM  CRPP r /1 1  rMM 0max  10 Structural idealisation b tD = t (tD = 0) t 1 2 2 1 A1 A2 b        1 2 1 26  btA D Tapered panel 2       b aq q b aq      b aqq q Multi-cell structures (constant shear flow)   ncnEbEext qAqAT ,,22 N cells connected N-cell beam                                   n b nn nc n nc nn nc nE t sq t sq t sq t sq GAdz d ,1 1,, ,1 1, ,2 1 Plate buckling 2       b tKEb K from data sheets or standard practice        t b K L eq '   ncnEbext qAhlqT ,,2A5 Margin of Safety 11MoS allow maximumdesign allowable      11 EA Tq 2  Batho-Bredt for constant shear flow asymmetric nn xyyx xyxyy nn xyyx xyyxx n yAIII ISIS xA III ISIS q                      22 symmetric, single load force/moments due to shear flow xqlX  yqlY  hqlqAT E  2 y III IMIM x III IMIM xyyx xyyyx xyyx xyxxy z                      22 asymmetric section y I M  asymmetric thin-wall open section GJ T dz d   Bending Shear Torsion 0qqq s  0qqq n  continuous section concentrated areas force/moments due to constant shear flow  B A qdxX  B A qdyY  B A hqdsT                      s xyyx xyxyys xyyx xyyxx s tydsIII ISIS txds III ISIS q 0202 ds t q GAdz d E  2 1 thin-wall closed section dz dL GJ TL   dz d A GJ A Tq EE  22  n J T dz dGn 22   J tT dz dGt  max  s s dstyI Sq 0 . nnn yAI Sq  symmetric, single load symmetric, single moment unrestrained torsion  ts A tds AJ EEclosed / 4 / 4 22      33 1 33 stdstJopen tq  Principal stresses 2 2 max2,1 22 xy yxyx avg