Elastic Buckling (1, 1); Eccentric Columns (1, 2) - HP 48gII Advanced User's Reference Manual

Elastic Buckling (1, 1)

These equations apply to a slender column (K · L / r > 100) with length factor K.
Equations:
2
E A
- - - - - - - - - - - - - - - - - - - - - -
P c r = P c r
2
K L
⎛ ⎞
- - - - - - - - - - - -
⎝ ⎠
r
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, cr=127428.2444_kPa.

Eccentric Columns (1, 2)

These equations apply to a slender column (K · L / r > 100) with length factor K.
Equations:
⎛ ⎛
⎜ ⎜
P c
⎜ ⎜
m a x = - - - - 1 + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
A 2
⎜ ⎜
r
C O S
⎝ ⎝
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,
Solution:
max=140853.0970_kPa.
5-4 Equation Reference
2
E I Pcr
- - - - - -- - - - - - - - - - - - - - ------- -
= c r =
2 A
K L
⎞ ⎞
⎟ ⎟
1
⎟ ⎟
⎟ ⎟
K L
⎛ P ⎞
- - - - - - - - - - - -
- - - - - - - - - - - -
⎠ ⎠
⎝ ⎠
2 r
E A
=1.1806_cm.
I
r = --- -
A
I
r = --- -
A