For an axially loaded column, the calculation is in metric or imperial units, depending on the set standard. The ANSI standard uses the imperial units (with appropriate section dimensions).

Calculated parameters

Reduced length

L_red = n L

Slenderness ratio

λ = L_red / j_min

Radius of gyration

Rankin critical stress

Rankin’s critical force

F_crR = σ_R S

Rankin’s maximal force

F_maxR = F_crR/ k_S

Rankin’s calculated safety factor

k_sR = F_crR / F_a

Johnson critical stress

Johnson’s critical force

F_crJ = σ_J S

Johnson’s maximal force

F_maxJ = F_crJ / k_s

Johnson’s calculated safety factor

k_sJ = F_cr J / F_a

Euler’s critical stress

σ_E = π² E / λ²

Euler’s critical force

F_crE = σ_E S

Euler’s maximal force

F_maxE = F_crE / k_s

Euler’s calculated safety factor

k_sE = F_crE / F_a

Pressure stress

σ_p = F_a / S

Critical force

F_crP = S_y S

Maximal force

F_maxP = F_crP / k_s

Calculated safety factor in pressure

k_sP = F_crP / F_a

Strength check

k_s ≤ min (k_sR , k_sJ , k_sE , k_sP )

Coefficient for end conditions

Factor for reduced (effective) length calculation,whose value depends on the conditions of end support of the column.

Meaning of used variables

F a	maximum load [lbforce, N]
n	coefficient for end conditions
k s	required safety factor
E	modulus of elasticity [psi, MPa]
L red	reduced length [in, mm]
S	section area [in 2 , mm 2 ]
j min	moment of inertia [in 4 , mm 4 ]
λ	Slenderness ratio
j min	least radius of gyration [in, mm]
σR	Rankine’s critical stress [psi, MPa]
F crR	Rankine’s critical force [lbforce, N]
F maxR	Rankine’s maximal force [lbforce, N]
k sR	Rankine’s calculated safety factor
σ j	Johnson’s critical stress [psi, MPa]
F crJ	Johnson’s critical force [lbforce, N]
F maxJ	Johnson’s maximal force [lbforce, N]
k sJ	Johnson’s calculated safety factor
σ E	Euler’s critical stress [psi, MPa]
J min	least moment of inertia
F crE	Euler’s critical force [lbforce, N]
F maxE	Euler’s maximal force [lbforce, N]
k sE	Euler’s calculated safety factor
σ P	Pressure stress [psi, MPa]
F crP	Critical force [lbforce, N]
F maxP	Maximal force [lbforce, N]
J min	least moment of inertia
k sP	Calculated safety factor in pressure