Steel Column Calculator
Compressive strength of W-shape columns — concentric load, flexural buckling per §E3. Get an answer in five seconds, then watch the buckling-branch logic work below.
Every equation cited to AISC 360-22 and dimension-checked · No account required
The full calculation, spelled out
Below is the live CalcPackage editor in public view — the same worksheet an engineer would stamp: slenderness, Euler stress, the piecewise critical-stress block, and the strength check in sequence.
Change any input — every dependent block recomputes. Stretch the column to 30 ft and watch F_cr switch from the inelastic (Eq. E3-2) to the elastic (Eq. E3-3) branch live. Click ✦ Explain on any block for a plain-English walkthrough.
With a free account you get full authoring control: different bracing about each axis, slender-element sections, combined loading. You can change any number — sign up free to change the math.
Live worksheetMake it yours
A free account turns this calculator into your worksheet — your edits in this tab carry over when you sign up.
Edit the math, not just the numbers
Add blocks, change equations, rename variables, restructure sections. The full editor with 3 worksheets, no card required.
FREESave versions & export PDF
Submittal-ready calc packages with title blocks, page numbers, and revision history. Watermark removed on Pro.
FREE · PROAI that you can verify
Describe a problem; get a complete scaffold built only from pre-verified code equations. Every block carries its chain of custody — you stay the author of record.
DEMOS FREE · FULL ON PROPick up exactly where you left off
Sign up free and this worksheet — with the inputs you just changed — becomes the first one in your account. No credit card.
How this calculator works
The calculator checks a concentrically loaded W-shape column using LRFD per AISC 360-22 §E3. The factored load is Pᵤ = 1.2P_D + 1.6P_L (ASCE 7-22 load combination 2). With equal unbraced lengths about both axes, weak-axis slenderness L_c/r = KL/r_y governs. The elastic buckling stress is F_e = π²E/(L_c/r)², and the critical stress follows the §E3 branch: F_cr = 0.658^(F_y/F_e) F_y when L_c/r ≤ 4.71√(E/F_y) (inelastic), otherwise F_cr = 0.877F_e (elastic). Design strength is φ_c P_n = 0.90 · F_cr · A_g. For W-shapes whose webs are slender in compression, the worksheet replaces A_g with the §E7 effective area.
Assumptions and limitations
Concentric axial load (no moments), the same effective length about both axes, rolled W-shapes (slender webs use the §E7 effective area), and E = 29,000 ksi. Combined axial + bending (Chapter H) and torsional buckling are outside this calculator. This calculator is a design aid — engineering judgment and final responsibility rest with the licensed engineer of record.
Frequently asked questions
Which K value should I use?
K = 1.0 (both ends pinned) is the usual choice for columns in braced frames. The other options are the recommended design values of AISC Commentary Table C-A-7.1: 0.65 and 0.80 for fixed ends, 1.2 and 2.0 for a column free to sway with its top held against rotation, and 2.1 for a flagpole cantilever. When in doubt, use the larger K.
Why doesn't higher-strength steel help my long column?
Past the slenderness limit 4.71√(E/F_y) the capacity is elastic-buckling-controlled — it depends on E, which is the same for all steel grades. Try it: set L to 30 ft and switch F_y between 36 and 50 ksi.
Is the calculation verified?
Yes. Every calculation block is verified and locked by CalcPackage before the page is published, every equation cites its AISC 360-22 section, and units are dimension-checked on every recomputation. The chain-of-custody rail records the verification.