Cold-Formed Steel Verification Studies
This article summarizes the verification studies of the cold-formed steel panel, stud, beam and column calculations. The verification was carried out in layers: section properties were compared with the manufacturer’s catalogue, torsional properties with the closed-form solution and an independent implementation, the strength chain with the code equations and hand calculation, and demand derivation with hand calculation; the entire workflow from settings to report was run end to end on example projects. For the equations, see the article Theoretical Basis of Cold-Formed Steel Design.
1. Section properties: 527 profiles × catalogue
For each profile in the predefined cold-formed steel profile library, the gross properties calculated with the sharp-corner mid-line model were compared with the catalogue (model / catalogue − 1):
| Family (count) | A | Ix | Iy |
|---|---|---|---|
| C (89) | +1.4% … +5.5% | +1.9% … +5.3% | +3.2% … +6.6% |
| Z (90) | +1.4% … +6.6% | +1.9% … +6.4% | +3.4% … +8.3% |
| U (88) | +0.8% … +2.5% | +1.2% … +2.8% | +0.1% … +1.2% |
| Sigma (90) | +1.7% … +6.0% | +2.0% … +4.6% | +3.8% … +8.5% |
| C+ (87) | +2.4% … +6.4% | +2.5% … +4.5% | +3.3% … +6.4% |
| Sigma+ (83) | +2.7% … +5.9% | +2.6% … +3.9% | +4.0% … +7.2% |
The deviations are uniform and come from the sharp-corner assumption of the model (when the corners are rounded, the area deviation drops to 1% on average). Since the gross A, Ix and Iy are taken directly from the catalogue values in design, the deviation does not affect the design; the position of the centroid coincides with the catalogue within 0.4 mm.
2. Torsional properties
| Test | Result |
|---|---|
| Closed-form solution — plain U section (b = 50, h = 100, t = 2 mm) | Shear centre distance and warping constant identical to the numerical solution |
| Independent implementation vs. program, 90 Sigma profiles | Largest relative difference for J, Cw and shear centre < 3·10⁻⁵ |
3. General method for distortional buckling
The general method (HCBTİE 4.10.3.3) was verified by three independent routes: an independent calculation rewritten from the code pages, two separate finite strip solvers and code review. The independent calculation reproduced the critical stress and the critical half-wavelength in six sections to better than one part in a thousand:
| Section | Fcrd compression, program / independent (MPa) | Fcrd bending, program / independent (MPa) |
|---|---|---|
| S200-50x67x16x2 | 183.0 / 183.0 | 377.4 / 377.4 |
| C200x80x16x2 | 169.2 / 169.2 | 300.0 / 300.0 |
| Z200x60x15x2 | 175.6 / 175.6 | 411.7 / 411.7 |
| Z400x100x21x2 | 55.2 / 55.2 | 164.6 / 164.6 |
| C+200-89x25x15x4 | 606.5 / 606.5 | 922.4 / 922.4 |
| S+200-55x95x25x15x4 | 574.7 / 574.7 | 850.0 / 850.0 |
In cases with a distinct distortional mode, the general method agrees with the finite strip solution within a band of −7% … +0% in compression and +4% … +14% (conservative) in bending. In Sigma sections the method is markedly conservative because it assumes a flat web; in C+ sections it remains slightly above the finite strip value in compression, so the finite strip option was made the default for these sections.
4. Finite strip solver
The program’s finite strip solver was first tested against an independent reference solver with single-strip matrices (relative difference ≤ 2·10⁻¹⁰), and then the critical stresses were compared with the same mesh (flat plate, gusset, C, Sigma, Z and C+ sections; results identical). In all 439 lipped profiles in the catalogue (861 compression/bending cases), the largest difference between the critical stresses of the two solvers was 9·10⁻⁵ and the average was 8·10⁻⁶. When the mesh is refined twice, the results change by at most 0.3%.
5. Beam and column (section assigned to the member)
In a test project, SIGMA S200-50x67x16x2 was assigned to the beam and the column, and the material was taken as S235. The program values were compared with an independent calculation and a hand calculation:
| Quantity | Hand calculation / independent calculation | Program (LRFD) | Result |
|---|---|---|---|
| Beam bending strength Md (Lb = L = 6.0 m, Cb = 1.579; lateral–torsional buckling governing) | 3.222 kNm | 3.2225 kNm | Identical |
| Beam shear strength Vd | 32.39 kN | 32.39 kN | Identical |
| Column Pd / Md,x / Md,y (KL = 3.0 m) | 54.83 kN / 6.587 kNm / 1.578 kNm | 54.83 / 6.587 / 1.578 | Identical |
In the beam bending strength, the unbraced length is the member length (Lb = L = 6.0 m) and Cb is calculated from the moment diagram of the governing 1.6G+Q combination: Mmax = 0.176 (end), MA = 0.044, MB = 0.134, MC = 0.094 kNm → Cb = 12.5·0.176 / (2.5·0.176 + 3·0.044 + 4·0.134 + 3·0.094) = 1.583 (program 1.579; the difference comes from the rounding of the displayed moments). Pey = π²·206010·325600/6000² = 18,390 N, Pez = 40,886 N, io = 82.68 mm → Mcre = 1.579·82.68·√(18,390·40,886) = 3.580·10⁶ N·mm; Fcre = 83.1 MPa < 0.56Fy → Mne = 3.580 kNm; Md = 0.90·3.580 = 3.222 kNm.
The ASD values also coincided exactly with the corresponding safety factors.
6. Demand model and end-to-end workflow
- The derivation of the intermediate and end stud axial demands from the panel internal forces, of the wind moment in exterior walls, and of the combined-effect ratios was compared with hand calculation for LRFD and ASD and coincided exactly with the values in the report.
- The edge stiffener (HCBTİE 4.9.3) and Z section rules were verified by hand calculation.
- Panel anchorage, gypsum-board share, calculation of the earthquake load with T = 0.2 s, proportioning of panel stiffnesses to capacity and design of foundations with D were each checked separately on single-storey and three-storey example cold-formed steel projects.
- On the example projects, the settings → analysis → report → PDF chain ran without errors in automated runs; the settings were saved in both text and binary project formats and read back identically.
7. Floor joist checks
Web crippling. The calculation was compared with an independent implementation in 13 cases (C, U and C+ sections; end and interior support; single and two opposite forces; ss/t ≤ 60 and > 60; out-of-scope Sigma, r/t > 6 and hw/t > 200 cases). In all 13 cases the values and status codes are identical (difference < 10⁻⁶). Comparison with a hand calculation table for a back-to-back C section (H = 200 mm, t = 4.95 mm, r = 6 mm, fyb = 350 MPa, ss = 100 mm):
| Case | Hand calculation | StatiCAD |
|---|---|---|
| End support, stiffened flange | 68.894 kN | 68.894 kN |
| End support, unstiffened flange, ss/t ≤ 60 | 46.198 kN | 46.198 kN |
| Interior support, ss/t ≤ 60 | 118.551 kN | 118.551 kN |
| Interior support, ss/t > 60 (ss = 400 mm) | 170.220 kN (independent calculation) | 170.220 kN |
End-to-end workflow. Tested with U100x53x1.5 floor joists of 4 m span (LRFD):
- In web crippling with a bearing support and ss = 40 mm, P = 8.65 kN, Pd = 3.056 kN (same as the independent calculation; ratio 2.83).
- With the load from above at the support declaration, Pd = 3.43 kN by the two opposite forces equation (hand calculation 3.426 kN).
- With a bottom flange bracing interval of 1250.5 mm, Md− = 1.332 kNm; with the top flange connected to the sheathing and a stiffener declared, Md+ = Mdlo = 1.370 kNm.
- The live-load-only deflection δQ = 5.09 cm > L/250 = 1.60 cm and the vibration condition (L/d = 40, fn = 3.0 Hz) were caught; the bridging declaration removed the vibration warning.
- The inputs were saved in text and binary project formats and read back exactly; the web crippling, stiffener and vibration rows and the signed values were checked in the Turkish and English reports.
8. Floor generation and beam hinges
Model: a 4 × 4 m bay, 4 columns at the corners, cold-formed steel beams on the edges; slab t = 2 cm, G = 175 kg/m², Q = 200 kg/m². With a cold-formed steel floor definition in the X direction with C200x80x16x2 profiles at 400 mm spacing, 9 floor joists (both ends pinned, top flange braced) and 10 strips of 40 cm were generated.
| Solution | Beam M+ (1.4G + 1.6Q) |
|---|---|
| Classical transfer, slabs not included in the stiffness | 4.896 kNm in all 9 beams, V = 4.90 kN (independent of the stiffness of the edge beams). Q distributed load w = 0.7455 kN/m; hand calculation 200 kg/m² × 0.38 m = 0.7456 kN/m |
| Shell transfer, rigid (S350) edge beams | 3.82 (next to the edge) … 5.12 kNm (middle); load sharing by the sheathing is small |
| Shell transfer, flexible (U100) edge beams | 17.9 (near the column) / 0.9 kNm (middle); edge beam deflection 17 cm → analysis warning |
The end moment of the floor joists is zero (the hinges are applied in the finite element solution). Regeneration (7 beams / 8 strips at 500 mm spacing; Y direction; plywood sheathing; bridging declaration), the return of the original slab when the definition is removed, and the preservation of the definitions and the strip–beam family in the project file were also verified.
9. Floor diaphragm
Model: 3 storeys, 10 × 6 m, 6 cold-formed steel panels on each storey; DX = 2.0, DY = 3.0, equivalent seismic load method. Cold-formed steel floor at three levels with C200x80x16x2 profiles at 600 mm spacing, in the Y direction, with OSB sheathing and bridging (17 strips, 16 beams).
| Quantity | StatiCAD | Hand calculation / cross-check |
|---|---|---|
| Level 1 net force Fx (with D) | 123.63 kN | D·F1 = 2.0 × 6.301 t = 123.6 kN |
| Level 1, force F of the y = 0 line (“−X1 − 0.3Y2” combination) | 183.36 kN | 2.0 × 8.234 + 0.3 × 3.0 × 2.459 = 18.68 t = 183.3 kN |
| Same line: B, v, φvn, ratio | 10.00 m; 18.34 kN/m; 6.12 kN/m; 3.00 | Slab 0–1000 cm; 0.6 × 10.2 (OSB default) |
| Level 1, force F of the x = 0 line (“−0.3X1 − Y2” combination) | 148.39 kN | 0.3 × 2.0 × 3.301 + 3.0 × 4.380 = 15.12 t = 148.3 kN |
| Floor → panel connection: Ps, n, n·Ps | 4.666 kN; 33; 153.97 kN | t1 = t2 = 2.0 mm, dv = 4.8 mm, Fu1 = 360, Fu2 = 420 MPa: Pns = min(10,931; 9,331; 10,886) N → 0.5 × 9,331 = 4.666 kN; 9.94 m / 0.3 m → 33 |
| Level 1 chord force Tx / Ty | 9.272 / 34.117 kN | 123.63 × 6/(8 × 10); 163.76 × 10/(8 × 6) |
| Collector (y = 0, walls cover the line) | 5.50 kN (ratio 0.035) | N ≈ 0 expected |
For the collector and the opening, in the same model the ground floor wall was shortened to 2 m and a 2 × 2 m opening was left in the middle of the level 1 slab:
| Quantity | StatiCAD | Hand calculation / cross-check |
|---|---|---|
| Collector force |N|max of the y = 0 line (ℓ = 2 m, F = 311.30 kN, B = 10 m) | 249.04 kN (ratio 1.57, warning) | F·(1 − ℓ/B) = 311.30 × (1 − 2/10) = 249.04 kN |
| Opening ratio | 0.067; warning in the rigid diaphragm | 4 / 60 m² = 6.7 % > 3 % |
| Share of the 10 × 2 m floor family and chord force Tx | 66.93 kN; 1.673 kN | 187.41 × 20/56 = 66.93; 66.93 × 2/(8 × 10) = 1.673 |
In this model, where all levels are cold-formed steel, the reinforced concrete diaphragm (TBDY 7.11) rows are not produced; the TBDY 10.5 rows and the line and connection warnings are produced. Because of the heavy storey loads of the model and DY = 3, the ratios are between 1.2 and 6; the model is intended for checking purposes.
10. Beam axis offset and composite axial force
Model: the building in the article Worked Example: Two-Storey Cold-Formed Steel Building (5 m floor joists CC C200x80x16x2, 390 mm spacing; headers CC C200x80x22x4, pinned). The same model was solved with the offset on (intermediate nodes on the diaphragm, or “Do not connect beam intermediate joints to the rigid diaphragm” ticked) and with the offsets off.
| Quantity | StatiCAD | Hand calculation / cross-check |
|---|---|---|
| ck (e2 = 0 − 20/2 cm) | — | 7.51 × (−10) / (471.9 + 7.51 × 100) = −0.06141 cm⁻¹ |
| Finite element segment axial force, intermediate nodes on the diaphragm (segment 1 / 5) | G: −1.2218 / −6.4586 kN; Q: −2.5366 / −13.4088 kN | ck·M̄3: −1.2219 / −6.4587; −2.5369 / −13.4091 kN (difference ≤ 0.01 %) |
| Finite element axial force, single chain | G: −4.3638 kN (constant over 10 segments) | ck·(2/3)·Mmax = −6.141 × 0.6667 × 1.0659 = −4.364 kN |
| Floor joist design axial force and P/Pd + M/Md | 0.197 kN; 0.564 (0; 0.558 with the offsets off) | The 1.2G + 1.6Q peak value 29.20 kN is subtracted; trapezoidal rule remainder 1.2 × 0.0435 + 1.6 × 0.0903 = 0.197 kN (0.67 %) |
| Design axial force of the headers | 0.23 / 0.07 kN | 0 with the offsets off |
| Difference between offset-on and offset-off solutions (74 beams) | Ratio ≤ 0.007; M ≤ 0.12 kNm; deflection ≤ 0.0005 cm | The remaining moment difference is the real stiffness effect of the offset |
11. General assessment
The gross section properties are consistent with the catalogue; the torsional properties have been verified with the closed-form solution and an independent implementation; the strength chain coincides with the code equations and hand calculation, and the demand derivation with hand calculation. Within the stated scope (predefined C, Z, U, C+, Sigma and Sigma+ sections), the module is suitable for use.
All results produced by the software must be checked by the responsible engineer.