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Reference Guide

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5-4 Equation Reference
Elastic Buckling (1, 1)
These equations apply to a slender column (K · L / r > 100) with length factor K.
Equations:
Example:
Given:
L=7.3152_m, r=4.1148_cm, E=199947961.502_kPa, A=53.0967_cm^2, K=0.7, I=8990598.7930_mm^4.
Solution:
Pcr=676.6019_kN,
σ
cr=127428.2444_kPa.
Eccentric Columns (1, 2)
These equations apply to a slender column (K · L / r > 100) with length factor K.
Equations:
Example:
Given:
L=6.6542_m, A=187.9351_cm^2, r=8.4836_cm, E=206842718.795_kPa, I=135259652.16_mm^4, K=1,
P=1908.2571_kN, c=15.24_cm,
∈
=1.1806_cm.
Solution:
σ
max=140853.0970_kPa.
P
c
r
π
2
E
A
⋅
⋅
K
L
⋅
r
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
P
c
r
π
2
E
I
⋅
⋅
K
L
⋅
( )
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
=
σ
c
r
P
c
r
A
-
-
-
-
-
-
-
-
=
r
A
-
-
-
-
=
σ
m
a
x
P
A
-
-
-
-
1
∈
c
⋅
r
2
-
-
-
-
-
-
-
-
-
+
1
C
O
S
K
L
⋅
2
r
⋅
-
-
-
-
-
-
-
-
-
-
-
-
P
E
A
⋅
-
-
-
-
-
-
-
-
-
-
-
-
⋅
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
⋅
⋅
=
r
A
-
-
-
-
=