LECTURE+9+COE-3001-A

# Tech aerospace note 0 by sign

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online