This result is a starting estimate, not a guaranteed blank size. It uses a centerline approximation: the bent corners are treated as if the steel follows an arc along the middle of its own thickness. This is the simplest, most common assumption and is accurate to within roughly ±2–3% for typical cold-formed light-gauge sections.
Why it's not exact.
When steel bends, the inside of the corner compresses and the outside stretches. The layer
that doesn't change length (the neutral axis) actually sits slightly toward the
inside of the bend, not at the centerline. The shift depends on material temper, bend radius
vs. thickness ratio, tooling, and springback — all of which vary shop to shop.
Engineers handle this with a "K-factor"; this calculator hardcodes K = 0.5
(centerline) for simplicity.
Recommended workflow. Use this number to estimate coil stock. Before running production, fabricate one sample part and measure the actual coil width consumed. If the predicted width is off, scale your stock width by the same delta on subsequent runs — it'll be consistent for that material/tooling combination.
Formulas used. Bend allowance per 90° corner: BA = (π/2)(R + t/2). Stud (4 bends): D + 2F + 2L − 8(R+t) + 4·BA. Track (2 bends): D + 2F − 4(R+t) + 2·BA. All linear inputs must use the same units.
| A | area | — |
| x̄ | centroid from back of web | — |
| Ix | moment of inertia, strong | — |
| Sx | section modulus, strong | — |
| rx | radius of gyration, strong | — |
| Iy | moment of inertia, weak | — |
| Sy | section modulus to lip face | — |
| ry | radius of gyration, weak | — |
| Web | — | — |
| Flange | — | — |
| Lip | — | — |
| Ae | effective area | — |
| Ae/A | section utilization | — |
Strong axis (about x)
| Sx,eff | effective section modulus | — |
| Mnx | nominal moment, Sx,eff·Fy | — |
| φMnx | LRFD design (φ = 0.95) | — |
| Mnx/Ω | ASD allowable (Ω = 1.67) | — |
Weak axis (about y, lip in compression)
| Sy,eff | effective section modulus | — |
| Mny | nominal moment, Sy,eff·Fy | — |
| φMny | LRFD design (φ = 0.95) | — |
| Mny/Ω | ASD allowable (Ω = 1.67) | — |
| h | web flat depth = D − 2(R + t) | — |
| h/t | web slenderness | — |
| — | shear regime (kv = 5.34, unreinforced web) | — |
| Vn | nominal shear strength, Aw·Fv | — |
| φVn | LRFD design (φv = 0.95) | — |
| Vn/Ω | ASD allowable (Ωv = 1.60) | — |
| Ae | effective area (uniform compression at f = Fy) | — |
| Pn | nominal axial strength, Ae·Fy | — |
| φcPn | LRFD design (φc = 0.85) | — |
| Pn/Ωc | ASD allowable (Ωc = 1.80) | — |
The row above is the cross-section yielding / local-buckling limit only. For length-dependent global buckling (flexural & flexural-torsional), see the Member Checks section below.
About these numbers. Gross properties use the centerline (line-element) method — accurate to ~1% of finite-thickness calcs for typical light-gauge sections. Effective values are single-pass approximations using uniform-compression effective-width formulas at f = Fy (and at f = Fn for the length-dependent compression check): stud flange k = 4 (treated as adequately edge-stiffened), lip and track flange k = 0.43 (unstiffened), with the web's compression half reduced for strong-axis bending. Global-buckling section properties (xo, ro, J, Cw) come from sectorial integration along the cross-section midline. Mn = Seff·Fy is the first-yield-with-effective-section moment; φ = 0.95 (LRFD) and Ω = 1.67 (ASD) per AISI S100-16 Section F1 for laterally braced flexural members. These results do not include lateral-torsional buckling of the beam, distortional buckling of the column, or Direct Strength Method interaction — they're for sanity-checking weight, sizing, capacity, and quoting, not a final design value. For deflection limits, combined-action checks, or distortional-buckling-sensitive sections, run the section through code-compliant software (RGS, ScotSteel).
For a singly-symmetric C-channel, only two independent global modes exist: flexural buckling about the strong x-axis (Fex) and coupled flexural-torsional buckling (Fe,ft). Pure weak-axis flexure (Fey) and pure torsion (Fet) cannot occur alone — they are mathematically combined into Fe,ft per AISI Eq. E2.2-3, so they are shown below as inputs to the coupling formula rather than as separate candidates. The lower of (Fex, Fe,ft) governs.
Effective lengths for flexural buckling about x (strong) and y (weak) axes, and for torsional buckling. Reduce KyLy and KtLt if the member is laterally / torsionally braced (e.g., by sheathing or strap bracing). Enter 0 to suppress buckling about that axis (fully braced).
| xo | centroid→shear-center offset (along x) | — |
| ro | polar radius of gyration about shear center | — |
| J | St. Venant torsion constant | — |
| Cw | warping constant | — |
| Fex | elastic flexural buckling, strong axis | — |
| Fey | elastic weak-axis flexural component (input to Fe,ft) | — |
| Fet | elastic torsional component (input to Fe,ft) | — |
| Fe,ft | coupled flexural-torsional buckling (AISI Eq. E2.2-3) | — |
| Fe | governing elastic buckling stress | — |
| — | governing mode | — |
| λc | column slenderness, √(Fy/Fe) | — |
| Fn | nominal column stress | — |
| Ae(Fn) | effective area at f = Fn | — |
| Pn,g | global nominal, Ae(Fn)·Fn | — |
| φcPn,g | LRFD design (φc = 0.85) | — |
| Pn,g/Ωc | ASD allowable (Ωc = 1.80) | — |
Governing Pn = min(local, global) = — · φcPn = —
A beam bent about its strong axis can fail by lateral-torsional buckling (LTB): the compression flange swings sideways while the section twists — one coupled mode, distinct from the column-buckling modes above. Governing flexural strength Mn = min(cross-section Mnx from Step 7, LTB-controlled Mne).
Unbraced length Lb for lateral-torsional buckling of the beam (lateral support of the compression flange). Cb is the moment-gradient modifier — 1.0 for uniform moment (conservative); typical values: 1.14 (simply-supported, uniform load), 1.30 (mid-span point load). Enter 0 for Lb to suppress LTB (fully braced).
| σey | elastic flexural buckling about weak axis (at Lb) | — |
| σt | elastic torsional buckling (at Lb) | — |
| Fcre | elastic LTB stress, (CbroA/Sf)√(σeyσt) | — |
| Mcre | elastic critical LTB moment, Sx·Fcre | — |
| My | first-yield moment, Sx·Fy | — |
| — | LTB regime | — |
| Mne | nominal LTB-controlled moment | — |
| φMne | LRFD design (φ = 0.95) | — |
| Mne/Ω | ASD allowable (Ω = 1.67) | — |
Governing Mnx = min(braced, LTB) = — · φMnx = —
Enter factored (LRFD / LSD / Eurocode design) load effects to check the member against code-prescribed interaction equations. Each ratio = demand ÷ design capacity; the member passes if every ratio ≤ 1.0. Capacities below come live from the Member Checks section above.
Cm is the moment-gradient factor used in the H1.2-1 amplifier α = 1 − Pu/PE. Default 1.0 (uniform moment, conservative); 0.85 for transverse loads with no end moments; 0.6 − 0.4(M1/M2) for restrained members with end moments per AISI C5.2.2.
| Action | Demand | Design capacity | Ratio | Status |
|---|---|---|---|---|
| Axial compression | — | — | — | — |
| Flexure, strong axis (governing) | — | — | — | — |
| Flexure, weak axis | — | — | — | — |
| Shear | — | — | — | — |
| Equation | Expression | Ratio | Status |
|---|---|---|---|
| AISI H1.2-1 amplified P + M |
Pu/φPn + CmxMux/(φMnx·αx) + CmyMuy/(φMny·αy) | — | — |
| AISI H1.2-2 local Pno + M |
Pu/φPno + Mux/φMnx + Muy/φMny | — | — |
| AISI H2.1 shear + moment |
(Mux/φMnx)2 + (Vu/φVn)2 | — | — |
Enter factored loads above to check the member.
Download the complete step-by-step calculation report (HTML — opens in any browser; use File > Print > Save as PDF for a PDF copy).