37. ATOMIC MATERIAL DATA37. MECHANICAL MATERIAL PROPERTIES37.1 FORMULA SHEETmaterials - 37.137. ATOMIC MATERIAL DATA37. MECHANICAL MATERIAL PROPERTIESTable 1: MaterialTypeDensityEGpoissonten - yield stressten - ult. stressten - yield strainyield stress - comp.ult. stress - comp.ult. stress - shearthermal expansion(Mg/m3)(GPa)(GPa)(MPa)(%)(MPa)10-6/deg Caluminum typical 2.6-2.8 70-79 26-30 0.33 35-500 100-550 1-45 231100-h142024-T65456-h1162014-T6 2.8 73 36-41 0.33 410 480 136061-T6 2.8 70 26 0.33 270 310 177075-T6 2.7 72 26 0.33 480 550 11ElementcopperironaluminumtungstenzincsiliconcarbontitaniumAtomic #292613743014622Atomic weight63.5755.8526.97183.8565.3728.0912.0147.9density g/cm38.967.862.6719.37.132.332.14.51Valances1/22/336/8242/43/4HwF = 96,500 coulombsmaterials - 37.2Brass typical 8.4-8.6 96-110 36-41 0.34 70-550 200-620 4-60 19.1-21.2Yellow Brasscold rolledannealedRed Brasscold rolledannealedBronze typical 8.2-8.8 96-120 36-44 0.34 82-690 200-830 5-60 18-21Cast Iron typical 7.0-7.4 83-170 32-69 0.2-0.3 120 69-480 0-1 340-14009.9-12Concrete typical 2.3 17-31 na 0.1-0.2 10-70 7-14reinforced 2.4 17-31 na 0.1-0.2lightweight 1.1-1.8 17-31 na 0.1-0.2Copper typical 8.9 110-120 40-47 0.33-0.3655-760 230-830 4-50 16.6-17.6annealedhard drawnGlass typical 2.4-2.8 48-83 19-35 0.17-0.2730-1000 0 5-11Plate 70Fibers 7000-20000Magnesium typ. alloys 1.76-1.8341-45 15-17 0.35 80-280 140-340 2-20 26.1-28.8Monel 67%Ni,30%Cu8.8 170 66 0.32 170-1100450-12002-50 14Nickel 8.8 210 80 0.31 100-620 310-760 2-50 13Table 1: MaterialTypeDensityEGpoissonten - yield stressten - ult. stressten - yield strainyield stress - comp.ult. stress - comp.ult. stress - shearthermal expansion(Mg/m3)(GPa)(GPa)(MPa)(%)(MPa)10-6/deg Cmaterials - 37.3PlasticsNylon .88-1.1 2.1-3.4 na 0.4 40-80 20-100 70-140Polyethylene .96-1.4 0.7-1.4 na 0.4 7-28 15-300 140-290Rock 5-9Granite 2.6-2.9 40-100 na 0.2-0.3 50-280Marble 2.6-2.9 40-100 na 0.2-0.3 50-280Quartz 2.6-2.9 40-100 na 0.2-0.3 50-280Limestone 2.0-2.9 20-70 na 0.2-0.3 20-200Sandstone 2.0-2.9 20-70 na 0.2-0.3 20-200Rubber typical .96-1.3 0.0007-0.0040.0002-0.0010.45-0.501-7 7-20 100-800 130-200Sand,soil,gravel1.2-2.2Steel 7.85 190-210 75-80 0.27-0.3010-18cold rolledannealedhigh strength 340-1000550-12005-25 14machine 340-700 550-860 5-25spring 400-1600700-19003-15stainless 280-700 400-10005-40tool 520 900 8structural 200-700 340-830 10-40 12astm-a48Table 1: MaterialTypeDensityEGpoissonten - yield stressten - ult. stressten - yield strainyield stress - comp.ult. stress - comp.ult. stress - shearthermal expansion(Mg/m3)(GPa)(GPa)(MPa)(%)(MPa)10-6/deg Cmaterials - 37.437.1 FORMULA SHEET• A collection of the essential mechanics of materials formulas are given belowastm-a47astm-a36 250 400 30 12astm-a5242astm-a441astm-a572 340 500 20 12astm-a514 700 830 15 12wire 280-1000550-14005-40Stainless Steelaisi 302 17Titanium typ. alloys 4.5 100-120 39-44 0.33 760-1000900-120010 8.1-11Tungsten 1.9 340-380 140-160 0.2 1400-40000-4 4.3Water fresh 1.0sea 1.02Wood (dry)Douglas fir .48-.56 11-13 30-50 50-80 30-50 40-70Oak .64-.72 11-12 40-60 50-100 30-40 30-50Southern pine.56-.64 11-14 40-60 50-100 30-50 40-70Table 1: MaterialTypeDensityEGpoissonten - yield stressten - ult. stressten - yield strainyield stress - comp.ult. stress - comp.ult. stress - shearthermal expansion(Mg/m3)(GPa)(GPa)(MPa)(%)(MPa)10-6/deg Cmaterials - 37.5Axial/Normal Stress/StrainσεEPA---==δεLPLAE-------==Shear Stress/StrainτγG=γxyτxyG-------=Poisson’s ratioνεlateralεlongitudinal---------------------------–=E 2G 1 ν+()=εxσxE-----νσyE-----– νσzE-----–=TorsionτmaxTcJ------=γmaxτmaxG----------=φTLJG-------=Jπr42--------=σtenσ–compτ==Jπ2---ro4ri4–()=(cylinder)(hollow tube)εγ2---= P 2πfT=materials - 37.6BeamsσMyI--------–=Ibh312--------=(for rectangle)τVQIb--------=Iπr42--------=(for circle)L ρθ=εmaxcρ---=σMyI--------–=ρEIM------=BucklingPπ2EIk2L2------------<k=0.5 (both ends fixed)k=0.7 (one end fixed, one pinned)k=1.0 (both ends pinned)k=2.0 (one end pinned, one free)PPd/2d/2r0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0r/d3.02.52.01.5Kmaterials - 37.7PP0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0r/d2.52.01.51.0KDrdD/d = 2.0D/d = 1.5D/d = 1.25D/d = 1.1materials - 37.80.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1r/d2.52.01.51.0KDrdD/d = 2.0D/d = 1.33D/d = 1.2D/d =