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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
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1m
100 MPa
—“—> C
D
100 MPa U56 Mich/S Cry/0L9 C:—\—§o MW“ a; : mow“
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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 °
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December 15th, 2003 NAME MM Show : \30 MW“ 0d” igZO “uni HgZo 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)
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December 15th, 2003 NAME EmLouQL kw gm (NW‘1 J (ac—LQJULl:
ii) The principal strains and the principal strain directions as a function of position. I) v') (ALM13 a. ﬂm‘Actpod McLJAA/ 22] = 5,3 2 0
SJ UP MJLLVfS CLVLLL l V’Lawa 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
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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 “preimpregnated” 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 .
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w New wv—y/ mew» :3 — be» x
Q Unified Quiz 7M8
December 15th, 2003 NAME 1000
1. MODULUSDENSITY YOUNGS MODULUS E
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COMPOSITES mtg“ POLYESTEng POLYMERS l,~ PINE r , iv .
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LOWER E LIMIT / ’/ OW"E
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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 .
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, 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.
 Fall '05
 MarkDrela

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