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 = π 2 E / λ 2

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