Slender column buckling
Inputs
Modulus of elasticity — structural steel
E:=200GPa=29007.55 ksi
Yield strength of steel
f_y:=250MPa=36.26 ksi
Unsupported column length
L:=4m=13.12 ft
Effective length factor (pin-pin = 1.0)
K:=1.0=1
Cross-section width
b:=100mm=3.94 in
Cross-section depth
d:=100mm=3.94 in
Section Properties
Cross-sectional area
A:=b·d=0.11 ft^2
I:=(b·d^3)/(12)=8.33e-06 m^4
Second moment of area about weak axis
r:=sqrt(I/A)=1.14 in
Radius of gyration
Calculations
Effective length of column
L_e:=K·L=13.12 ft
SR:=(L_e)/(r)=138.56
Slenderness ratio
Maximum allowable slenderness ratio
SR_limit:=200=200
P_cr:=(pi^2·E·I)/(L_e^2)=231122.43 lbf
Euler critical buckling load
Critical buckling stress
sigma_cr:=P_cr/A=14.91 ksi
SR_limiteuler:=pi·sqrt(E/f_y)=88.86
Limiting slenderness (Euler validity threshold)
Results
- Compare SR to SR_limit (must be ≤ 200).
- Compare SR to SR_limit_euler (column is slender if SR ≥ this value).
- Critical load P_cr must exceed applied load.
P_cr:=(pi^2·E·I)/(L_e^2)=231122.43 lbf
Euler critical buckling load
Critical buckling stress
sigma_cr:=P_cr/A=14.91 ksi
SR:=(L_e)/(r)=138.56
Slenderness ratio (check ≤ 200)
Slender Column Buckling Calculation
Euler critical buckling load and slenderness ratio check for a slender column.
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