AISC 360-16 Ch.ELRFD / ASDFree

Steel Column
Load Capacity

Compute axial compression capacity of a steel column per AISC 360-16 Chapter E. Enter geometry, grade, and applied load to get the slenderness KL/r, critical stress Fcr (inelastic or elastic buckling), nominal strength Pn, and the design strength with a demand/capacity ratio.

Who it's for: structural engineers checking axial compression capacity for a steel column — you need the section's radius of gyration, gross area, and end conditions. This is a code-level AISC 360-16 check, not a rough estimate.

AISC 360-16 §E3

Fe = π²E/(KL/r)². If KL/r ≤ 4.71√(E/Fy): Fcr = 0.658^(Fy/Fe)·Fy; else Fcr = 0.877·Fe. Pn = Fcr·Ag. LRFD φc = 0.90; ASD Ωc = 1.67. Limit KL/r ≤ 200. E = 29,000 ksi.

Column Capacity

Fcr · Pn · design strength

How to use this calculator

Enter unbraced length L and factor K

L is the clear distance between lateral bracing points in feet. K is the effective-length multiplier from AISC Table C-A-7.2: 1.0 for pin-pin, 0.65 for fixed-fixed, 0.80 for one fixed / one pinned.

Enter the radius of gyration r

Use the minimum r from the AISC Steel Construction Manual section-property table — the weak-axis value that governs buckling.

Enter the gross cross-sectional area Ag

Read Ag directly from the section-property table for your chosen wide-flange, HSS, or pipe shape.

Choose the steel grade

Sets Fy: A992/A572-50 (50 ksi) for most wide flanges; A500 Gr.B (46 ksi) for HSS; A36 (36 ksi) for older or plate sections.

Select design method and read the capacity

LRFD gives φcPn (φc = 0.90); ASD gives Pn/Ωc (Ωc = 1.67). Enter an applied load P to see the demand/capacity utilization ratio.

The formula

AISC 360-16 §E3 classifies the column as inelastic or elastic buckling using the slenderness limit 4.71√(E/Fy), then applies the matching Fcr equation.

Fe = π²E / (KL/r)² — Euler elastic buckling stress (ksi)
If KL/r ≤ 4.71√(E/Fy): Fcr = 0.658^(Fy/Fe) × Fy — inelastic buckling (Eq. E3-2)
If KL/r > 4.71√(E/Fy): Fcr = 0.877 × Fe — elastic buckling (Eq. E3-3)
Pn = Fcr × Ag — nominal axial strength (kips)

Symbol definitions: Fe = Euler elastic buckling stress (ksi); KL/r = effective slenderness ratio; E = 29,000 ksi; Fy = yield stress (ksi); Ag = gross cross-sectional area (in²). LRFD design strength = φcPn (φc = 0.90); ASD allowable = Pn/Ωc (Ωc = 1.67).

Worked example

Example

A W10×49 wide flange (Ag = 13.0 in², r = 2.51 in) in A992 steel (Fy = 50 ksi) is a 14-ft column with pin-pin end conditions (K = 1.0). Slenderness KL/r = 1.0 × 14 × 12 / 2.51 = 66.9, well below the 113.4 inelastic-buckling limit. Euler stress Fe = π² × 29,000 / 66.9² = 63.9 ksi. Critical stress Fcr = 0.658^0.783 × 50 = 36.0 ksi. Nominal strength Pn = 36.0 × 13.0 = 468 kips; LRFD design strength φcPn = 0.90 × 468 = 421 kips. With an applied factored load of 300 kips, utilization = 300 / 421 = 0.71 (71% utilised — adequate).

When this estimate will be off

Flexural buckling only — does not check torsional or flexural-torsional buckling (AISC §E4), which governs singly-symmetric shapes such as angles, tees, and channels.
Assumes the section is non-slender per §E7. Slender flanges or webs reduce the effective area Aeff below Ag and lower Pn below this result.
KL/r must not exceed 200 (AISC recommended limit); results above 200 are flagged and normally signal a section upgrade, not just a capacity reduction.
Does not account for combined axial and bending (beam-column interaction per AISC §H1). If moments are also present, the Chapter H interaction equations govern.

Frequently asked questions

What is the effective length factor K for a steel column?

K accounts for end-condition restraint. AISC Table C-A-7.2 recommends 0.65 for both ends fixed, 0.80 for one fixed / one pinned, 1.0 for both pinned, and 1.2 for one fixed / one free (cantilever). In practice, most columns in braced frames use values between 0.8 and 1.0 to account for partial restraint.

When does AISC §E3 use inelastic versus elastic buckling?

The boundary is KL/r = 4.71√(E/Fy) — about 113 for Fy = 50 ksi. Below that, residual stresses reduce capacity below the Euler prediction and the inelastic equation (E3-2) applies. Above it, the column buckles elastically and Fcr = 0.877Fe (E3-3). Most practical building columns fall in the inelastic range.

Does this calculator check local buckling?

No. The §E3 formulas apply only when flanges and webs are non-slender. If the section is slender under §E7, compute an effective area Aeff less than Ag and substitute it for Ag. Check flange and web slenderness ratios (b/t, h/tw) against AISC Table E1-1 before relying on this result.

What is the AISC slenderness limit KL/r 200?

AISC 360-16 §E2 recommends KL/r not exceed 200 for compression members. Exceeding 200 is not code-prohibited but indicates a very slender column with low capacity relative to its weight and high sensitivity to accidental loads. This calculator flags results above 200; in practice, a stockier section or additional bracing is more economical.

Sources

AISC 360-16 §E3 — flexural buckling of members without slender elements — Fcr equations E3-2 (inelastic) and E3-3 (elastic)
AISC 360-16 Table C-A-7.2 — recommended effective length factors K for columns with idealized end conditions

This free Calculator is built and maintained by DataDrivenAEC, using the relevant codes and standards. It does not substitute for professional judgment.