Transcript Column Buckling Analysis Presentation

By: Anthony Beeman
Euler’s Fundamental Buckling Problem
x
Assumptions:
•Straight Column
•Homogeneous Material
P
y
Boundary Conditions:
•Pinned-Pinned
N
M
Governing Equations:
𝑃𝑐𝑟
𝑛
𝑛2 𝜋 2 𝐸 𝐼
=
𝐿2
L
v
v
n=mode
L= Original Column Length
E= Young’s Modulus
I= Moment of Inertia
P
P
A
Other End Conditions
x
Modified Euler Buckling Formula:
P
P
y
L
L= Original Column Length
Le= Effective Column Length
E= Young’s Modulus
I= Moment of Inertia
Le=L
Le=2L
P
P
Problem Analyzed
P
Mechanical Properties
Variable
Value
Description
ρ [kg/m3]
7800
Density
υ [Dim]
0.3
Poisson's ratio
E [Pa]
2e11
Young's Modulus
r=0.5 M
A
L=10 M
Calculated Critical Load
[N]
A
Cross Section A-A
Case 1
2,904 DOF
Case 2
Case 3
12,723 DOF
73,623 DOF
Case
Analytical
Theoretical
Percent Error
Number
Critical Load [N]
Critical Load [N]
[%]
Case 1
2.422e8
2.422e8
0.00%
Case 2
2.414e8
2.422e8
0.33%
Case 3
2.410e8
2.422e8
0.49%
Case 1
285 DOF
Case 2
Case 3
490 DOF
48,145 DOF
Case
Analytical
Theoretical
Percent Error
Number
Critical Load [N]
Critical Load [N]
[%]
Case 1
3.102e8
2.422e8
2.86
Case 2
2.851e8
2.422e8
1.82
Case 3
2.447e8
2.422e8
1.52
Case 1
2,904 DOF
Case 2
Case 3
12,723 DOF
73,623 DOF
Case
Analytical
Theoretical
Percent Error
Number
Critical Load [N]
Critical Load [N]
[%]
Case 1
2.406e8
2.422e8
0.16
Case 2
2.406e8
2.422e8
0.16
Case 3
2.406e8
2.422e8
0.16