HP 48GII

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,
σcr=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:
σmax=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
Pcr
A
--------
= r
I
A
----=
σ
m a x
P
A
- - - -
1
∈
c
⋅
r
2
- - - - - - - - -
+
1
C O S
K L
⋅
2 r
⋅
- - - - - - - - - - - -
P
E A
⋅
- - - - - - - - - - - -
⋅
⎝
⎠
⎛
⎞
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
⎝
⎠
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎛
⎞
⋅
⎝
⎠
⎜ ⎟
⎜
⎟
⎜ ⎟
⎛
⎞
⋅
= r
I
A
----=