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 |