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Unformatted text preview: .J" . 0% A composite with unidirectional ﬁber reinforcement is made using two
unknown constituent materials, Material A which is the ﬁber and material B
which is the reinforcement. The elastic modulus of material A is 150 GPa and
the elastic modulus of material B is 10 GPa. ' If material A is 40% of the
overall composite by volume, determine the elastic modulus along the
direction of the ﬁbers. In addition determine the elastic modulus
perpendicular to the main axis of the ﬁbers.  ' 2.
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53 = 905%;
6 s = 2370 we
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.AC = $,l(4—O.7QS= 2,555sz Va: 2 0.75 273% \/g ‘— 5 EC: l)O«O.7§+ZOSrO,?§»= 82,51 51,25 : 155.75%
f (5:128 @ = no 6% ~ (.27 (0’5 2. 55w“? + 205 “2740'? 0.793% 1 '3 328.01% 20%? ' 533W \ 40:013*(XC'035)‘~”
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i“: :10‘0 4 (n' (O "0’ ‘0 )\+ 0.5403? W10 OTISWIO Describe what is meant by the phrase 'critical ﬁber length'. Explain what happens if the ﬁber is longer than the critical length and what happens if the
fiber is shorter than the critical length. I: "‘ 1,. ncluLwc.
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/c tit/{0 f/W oux/ «m @Q When in use, a ﬁshing rod can be approximated to act as a cantilevered beam.
Assume that the force (P) is applied to the end of the beam by a ﬁsh while the other
end of the beam is rigidly held by the ﬁsherman. The defamation (A) of the mod is PL3 given by the following equation: A = E] . Assume that the length ofthe rod is ﬁxed (i.e., can not be changed) and the cross section ofﬂie rod is square. The
dimensions ofthe cross section can be varied to answer the questions below but the
section must remain square. You Should assume the behave as a linearly
elastic material. 3) Develop an equation that determines the mass of the ﬁshing rods in terms of the
material properties (e. g., elastic modulus and dimension. , section geometry (e.g.,
cross sectional. length and length), and the design inputs (e.g., load and
deformation). L l...
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#2:, _________________ _ _ ’7’? b) Using the data below, detennine which of the materials shouid be used if we
wanted to make the lightest rod. assuming that all the rods have the same stiﬂness c) Using the data "below, determine which ofthe materials should be used if we
wanted to make the most economic rod assuming that all the rods have the same stiﬂiaess Nate 1 tonne'3 1000 kg
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Mm ﬁata’ ﬂoiﬁymaw a} fags?" if? mﬁwmq ﬁwgdmm “7'5 Mdrx/wmtw} @ _ A ﬁshing rod. is formed from a composite material of 0.5 kg of glass ﬁbers embedded
in a matrix of 0.5 kg of epoxy resin. The glass ﬁbers are assumed to belong,
continuous and unidirectional. To achieve a greater stiffness it is proposed to use a
diﬂ'erent composite that is comprised of long continuous carbon ﬁbers that will be .
embedded in. a matrix of 0.5 kg of epoxy resin. If the modulus of elasticity ofthe
carbon ﬁber composite is 10% greater than the elastic modulus of the glass ﬁber
composite, estimate the mass of carbon ﬁbers that will be used to make the carbon
ﬁber composite. Assume the applied tensile stress is parallel to the direction of the
tong axis of the ﬁbers. The epoxy resin, glass ﬁber, and carbon. ﬁber have an elastic
modulus of 5, 86, and 350 GPa respectively and a density of 1100, 2500, and 1800 respectively. mm
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m 5i} am? 33.526173m m 0‘3“ “WM liﬁc’ {a may; amok praﬂaadcm A rod made of composite material is placed between rigid8119mm (TmS could be State two potential advantages of coating ﬁbers before using them in a composite. ﬁ‘ﬁw ({L'éll; a m flag 7£M 74%
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M 4m “K1,, mtxakdxo ® gimiiar to a frp composite bridge deck). At 250 the nod ﬁts perfectly behwecn the
rigid supports and there is no stress in the system. What temperature would the
composite need to be cooicd to in order for the composite to crack if it has a
coefﬁcient ofthonnal expansion of20x10'6 mlmm/C, a $trength of 20 ksi, and an
eiastic modulus of 10,000 ksi. Assume the composite behaves as a linear elastic materéal. ...
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 Fall '08
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