Tech aerospace note 0 by sign

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Unformatted text preview: x plastic = 7.5M P a = x ²་  Max allowable shear stress: max ⌧plastic = 4.0M P a = x = x 2 8.0M P a ²་  Finally, select minimum σx from the among the four values just calculated and use this value to determine Aminimum and then bminimum Aminimum = P/ bmin = 1/17/13 p min.allowable x Aminimum Aminimum = 35000N/6.9M P a = 5072mm2 bminimum = p M. Mello/Georgia Tech Aerospace 5072mm2 = 71.2mm 12 STRAIN ENERGY: A form of poten\al energy δ W= Z Work is equal to the area beneath the load- displacement curve Pd 0 U =W = Z Pd 0 Elas\c strain energy absorbed by the bar is equal to the work done by the load P Energy Units: Joule (1 J = 1 Nm) 1/17/13 M. Mello/Georgia Tech Aerospace 13 ELASTIC AND INEALSTIC STRAIN ENERGY ELASTIC LIMIT (YIELD POINT) ²་ ALL ELASTIC STRAIN ENERGY RECOVERED IF MATERIAL NOT STRESSED BEYOND THIS POINT (THE BAR BEHAVES JUST LIKE AN ELASTIC SPRING) ²་  INELASTIC STRAIN ENERGY : ENERGY LOST IN THE PROCESS OF PERMANENTLY DEFORMING THE BAR ²་  Concepts apply equally well to members in tension or compression STRAIN ENERGY RECOVERED DURING UNLOADING IF MATERIAL LOADED BEYOND IT’S ELASTIC LIMIT 1/17/13 M. Mello/Georgia Tech Aerospace δ 14 LINEAR ELASTIC BEHAVIOR δ U =W = U =W = Z P1 d P 2 Recall, = 1/17/13 ²་  LOAD- DISPLACEMENT DIAGRAM FOR A BAR OF LINEARLY ELASTIC MATERIAL (THIS IS WHAT IS EXPERIMENTALLY OBSERVED) 0 elas\c bar PL EA P 2L U= 2EA EA 2 L U= 2L spring P2 U= 2k k2 U= 2 M. Mello/Georgia Tech Aerospace Recall that (EA)/L is really just the effec\ve spring constant of a linearly elas\c bar of length (L) 15 STRAIN ENERGY OF NONUNIFORM BARS ²་  BAR CONSISTING OF PRISMATIC SEGMENTS HAVING DIFFERENT CROSS- SECTIONAL AREAS AND DIFFERENT AXIAL FORCES U= n X N 2 Li i i=1 2EAi Total strain energy U of the bar consis\ng of several segments Is equal to the sum of the strain energies of the individual segments ²་  NON- PRISMATIC BAR WITH VARYING AXIAL FORCE Axial force at distance x from end of the bar U= Z L 0 [N (x)]2 dx 2EA(x) Cross- sec\onal area at distance x from end of the bar 1/17/13 M. Mello/Georgia Tech Aerospace 16 STRAIN ENERGY DENSITY: STRAIN ENERGY PER UNIT VOLUME P A(x) dx 1 dU [N (x)]2 w ( x) = = A(x) dx 2EA2 (x) strain energy per unit volume of a linear elas\c (prisma\c or non- prisma\c) bar Strain energy density P In cases where strain energy i...
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