By: Anthony Beeman. P L P v v P N A M x y Euler’s Fundamental Buckling Problem Assumptions: Straight Column Homogeneous Material Boundary Conditions:

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Presentation transcript:

By: Anthony Beeman

P L P v v P N A M x y Euler’s Fundamental Buckling Problem Assumptions: Straight Column Homogeneous Material Boundary Conditions: Pinned-Pinned Governing Equations: n=mode L= Original Column Length E= Young’s Modulus I= Moment of Inertia

P L e =L x y P L e =2L L P P Other End Conditions Modified Euler Buckling Formula: L= Original Column Length L e = Effective Column Length E= Young’s Modulus I= Moment of Inertia

P L=10 M AA Cross Section A-A r=0.5 M VariableValueDescription ρ [kg/m 3 ]7800Density υ [Dim]0.3Poisson's ratio E [Pa]2e11Young's Modulus Mechanical Properties Calculated Critical Load Problem Analyzed [N]

Case Number Analytical Critical Load [N] Theoretical Critical Load [N] Percent Error [%] Case e8 0.00% Case e82.422e80.33% Case e82.422e80.49% Case 1 2,904 DOF Case 2 12,723 DOF Case 3 73,623 DOF

Case DOF Case DOF Case 3 48,145 DOF Case Number Analytical Critical Load [N] Theoretical Critical Load [N] Percent Error [%] Case e82.422e82.86 Case e82.422e81.82 Case e82.422e81.52

Case 1 2,904 DOF Case 2 12,723 DOF Case 3 73,623 DOF Case Number Analytical Critical Load [N] Theoretical Critical Load [N] Percent Error [%] Case e82.422e80.16 Case e82.422e80.16 Case e82.422e80.16