fall_2003_q7m_sol

fall_2003_q7m_sol - Unified Quiz 7M8 ' December 15th, 2003...

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Unformatted text preview: Unified Quiz 7M8 ' December 15th, 2003 NAME Sc) LA)» lam/L5 PROBLEM #1 (25%) a) The stress state given below is applied to an element of the aluminum alloy skin of an aircraft. Calculate the maximum shear stress and the direction(s) in which it acts. Express the direction(s) as counterclockwise angles relative to the x1 axis. 011 012 013 0 021 022 023 = 0 MP8 031 032 033 0 0 0 A 4—. B _____> x1 200 MPa 1m <—— ___—, 1m 100 MPa —“—> C D 100 MPa U56 Mich/S Cry/0L9 C:—\—§o MW“ a; : mow“ 61-42 (L: as’fim-‘(M/>: <9 : 2‘2-2" I50 MA elm (9 z [1810 Unified Quiz 7MS December 15th, 2003 NAME -b) For the stress state in part (a) calculate the elongation (in meters millimeters or micrometers) of the diagonal, AC, of the 1m x 1m element of the wing skin. The Young’s modulus of the aluminum alloy is 70 GPa and its Poisson’s ratio is 0.33. ..l m M. 2 33- 9 ° {50 .. #3 0 Mo — 70'339 ’ 56 5mm; @ +50 is 9C,,9(1 W A. 0” :50420 01556-30: w—Jo Mm ll c?” : §Otl30 (0536-30 : l-lfio was Nanak ’— ' 6 G ’ 'Pv‘w flU-O (LL12) MSW —:) #1819 {H1 -— 50x10 _(M ;'0>(‘U‘1 ,3 :: ~l ’+le0 ___3 ’2 " - - ><o M elm3alalz —l‘l—Z><lo >< 7, , lo l Unified Quiz 7MS December 15th, 2003 NAME MM Show : \30 MW“ 0d” ig-ZO “uni Hg-Zo CoewnLl—LCLULKW‘AQ ’FW“ 9(‘ Unified Quiz 7M3 December 15th, 2003 NAME PROBLEM #2 (30%) a) An elastic material experiences a displacement field given by: 2 L11 == ax1x2 1 2 2 U2 =Ea(x1—x2) u3 = 0 where a is a constant. Determine: i) The 6 components of the strain tensor as a function of position (i.e. in terms of x1, x2, x3) 7' 3 UL r —- “9C7, 3 U CL. 0C {’1 1. : " ’ in ‘ _,_.‘ Z L 3 7C1 3 99 a. l CL9C ‘- l 30‘ +VB’U_Z ¢ $4WCIZé’Q7C' 9(1 "3" D z’l'L " I '- Unified Quiz 7MS December 15th, 2003 NAME EmLouQL kw gm (NW-‘1 J (ac—LQJU-Ll: ii) The principal strains and the principal strain directions as a function of position. I) v') (AL-M13 a. flm‘Actpod McLJAA/ 22] = 5,3 2 0 SJ- UP MJLLVfS CLVLLL l- V’Law-a Sm SLLI; Unified Quiz 7MS December 15th, 2003 NAME b) The bulk modulus, k, is the elastic constant that links volumetric strain, A to hydrostatic pressure p: p: k A For an isotropic material, we know that only two elastic constants, E and v, are reQUired 'n order to describe the relationship between an arbitrary state of stress and an arbitrary state of strain. Derive a relationship between the bulk modulus and E and v. L :3, _? LY, W‘vflr'o it e” e f _ 1 {i1 ii. ' z) 3 x ,3 a” {Z — —/'/ (:7 j, Z 7 l Zi'i €2+£3: i ,3 ~,. I/ Unified Quiz 7M8 December 15th, 2003 NAME PROBLEM #3 (15%) Molybdenum, a high melting temperature metal (Tm=2617°C), has a body centered cubic structure, an atomic radius of 0.1363 nm and an atomic weight of 95.94 g/mol. Estimate the density of the bulk material. Avogradro’s number =6.023x10‘23 Unified Quiz 7M8 December 15th, 2003 NAME Unified Quiz 7M8 December 15th, 2003 NAME PROBLEM #4 (30%) a) Explain why metals, in general have higher densities but lower Young's moduli than ceramics. b and c — double question) You are asked to obtain the elastic constants of a unidirectional composite. Sketch the experiments you would do to obtain these quantities. HZ.— /\\ (7 6/ l l E L Unified Quiz 7MS December 15th, 2003 NAME d) Carbon fiber composites with epoxy resins are stored as “pre-impregnated” plies in freezers, and are then laid up into laminates by “curing’” at an elevated temperature. The prepreg is relatively low stiffness but the cured ply will be much stiffer. Explain what is happening in the curing process. Unified Quiz 7M8 December 15th, 2003 NAME e) With reference to the material selection chart below, explain the relative suitability of Titanium, Aluminum and Steel for (i) the bars of a truss and (ii) for the wings of an airplane. 6 T. m) slur m «M suw‘tw . . , / w New wv—y/ mew» :3 — be» x Q Unified Quiz 7M8 December 15th, 2003 NAME 1000 1. MODULUS-DENSITY YOUNGS MODULUS E (5: 35/8; KaE.) / fewnsmqnc COMPOSITES mtg“ POLYESTEng POLYMERS l,~ PINE r , iv . ‘ FIR LOWER E LIMIT / ’/ OW"E - RP IAR V FOR TRUE SOLIDS 70 5mm GUIDE LINES FOR pr; smut—T ' LOPE E ' mmMUM WEIGHT I / Enemggnmg 3 x IO,J / ' YOUNGS MODULUS, E (GPa) DESiGN g I . I pmfimseo 3/ 1O / l , 3x10? \POLYMERS ‘ FOAMS 0.01 0.3 1.0 DENSITY, p (Mg/m3) ...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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fall_2003_q7m_sol - Unified Quiz 7M8 ' December 15th, 2003...

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