A wing of an airplane is subjected to a test in bending, and the principal strains are measured at several points on the wing surface (see Table P3.2). The wing material is aluminum alloy 7075 T6 (see Table A. 1). Determine the corresponding principal stresses and the third principal strain.
TABLE P3.2
Strain | Point 1 | Point 2 | Point 3 | Point 4 | Point 5 |
ϵ1 | −0.004 | 0.008 | 0.006 | −0.005 | 0.002 |
ϵ2 | −0.006 | 0.002 | 0.002 | −0.008 | −0.002 |
TABLE A.1: Properties in S.I. Units
Material | Density [103 Kg/m3] | Yieldstress[MPa] | Ultimatestress[MPa] | Poisson’sratio | Young'smodulus[GPa] | Percent elongation at rupture | Thermal coefficient [10−6/°C] |
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STEEL | |||||||||||||
Structural, ASTM A36 | 7.85 | 250 | 400 | 0.29 | 200 | 30 | 11.7 | ||||||
AISI-C 1018, cold drawn | 7.85 | 370 | 440 | 0.29 | 200 | 15 | 11.7 | ||||||
AISl-C 1030, normalized | 7.85 | 340 | 530 | 0.29 | 200 | 30 | 11.7 | ||||||
AISI-C 1040, normalized | 7.85 | 390 | 590 | 0.29 | 200 | 28 | 11.7 | ||||||
AISI-C 1080, normalized | 7.85 | 520 | 1010 | 0.29 | 200 | 11 | 11.7 | ||||||
ASSI-3140, normalized | 7.85 | 620 | 900 | 0.29 | 200 | 19 | 11.7 | ||||||
AISI-4340, normalized | 7.8 | 860 | 1310 | 0.29 | 200 | 12 | 11.7 | ||||||
AISI 301 Stainless, annealed | 7.92 | 280 | 760 | 0.27 | 193 | 60 | 17.3 | ||||||
AISI 301 Stainless, half hard | 7.92 | 760 | 1030 | 0.27 | 193 | 15 | 17.3 | ||||||
CAST IRON | |||||||||||||
Gray, Class 30 (tension) | 7.21 | — | 210 | 0.20 | 103 | nil | 12.1 | ||||||
Gray, Class 30 (compression) | 7.21 | — | 510 | 0.20 | 103 | nil | 12.1 | ||||||
Gray, Class 40 (tension) | 7.21 | — | 410 | 0.20 | 138 | nil | 12.1 | ||||||
Gray, Class 40 (compression) | 7.21 | — | 990 | 0.20 | 138 | nil | 12.1 | ||||||
ALUMINUM ALLOYS | |||||||||||||
1100-H12 | 2.71 | 103 | 110 | 0.33 | 70.0 | 25 | 23.5 | ||||||
2024 T4 | 2.77 | 320 | 470 | 0.33 | 74.5 | 19 | 22.5 | ||||||
6061 T6 | 2.7 | 275 | 310 | 0.33 | 69.0 | 12 | 23.6 | ||||||
6063 T5 | 2.7 | 145 | 185 | 0.33 | 69.0 | 12 | 23.4 | ||||||
7075 T6 | 2.77 | 500 | 570 | 0.33 | 72.0 | 11 | 22.5 | ||||||
COPPER ALLOYS | |||||||||||||
Free-Cutting Copper, soft | 8.91 | 62 | 220 | 0.35 | 117 | 42 | 17.6 | ||||||
Free-Cutting Copper, hard | 8.91 | 290 | 320 | 0.35 | 117 | 12 | 17.6 | ||||||
Yellow Brass, annealed | 8.43 | 117 | 340 | 0.35 | 105 | 60 | 20.0 | ||||||
Yellow Brass, half hard | 8.43 | 340 | 420 | 0.35 | 105 | 23 | 20.0 | ||||||
Commercial Bronze, annealed | 8.84 | 90 | 270 | 0.35 | 110 | 45 | 18.0 | ||||||
Commercial Bronze, half hard | 8.84 | 280 | 330 | 0.35 | 110 | 25 | 18.0 | ||||||
TITANIUM |
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Alloy Ti–Al–V | 4.54 | 890 | 930 | 0.33 | 114 | 12 | 9.5 | ||||||
TIMBER (12% MC) | |||||||||||||
Coastal Douglas Fir (bending) | 0.48 | — | 85 | — | 13.4 | — | 3.1–4.5a | ||||||
Loblolly Pine (bending) | 0.51 | — | 88 | — | 12.3 | — | 3.1–4.5a | ||||||
White Oak (bending) | 0.68 | — | 105 | — | 12.3 | — | 3.1–4.5a | ||||||
CONCRETE | |||||||||||||
Medium Strength (compression) | 2.32 | — | 28 | 0.15 | 25.0 | — | 9.9 | ||||||
aParallel to the grain.
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