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 |
The same subtraction is also applied to heavy steel beams; for its verification, see the article Steel Structures Verification Studies.
11. Panel bottom and top tracks and bridging
Models: the building in the article Worked Example: Two-Storey Cold-Formed Steel Building (2 storeys, 24 panels, OSB on both faces, C100x50x15x1.2 studs, M12 shear anchor, n = 4), a variant of this building in which wall WZ01 is made without sheathing, the collector variant from Section 9 (ground-floor wall 2 m) and a regression model.
| Quantity | StatiCAD | Hand calculation / cross-check |
|---|---|---|
| WZ01 bottom track (automatic U100x52x1.2): v, a, N | 11.746 kN/m; 537.5 mm; 3.157 kN | v = 25.253/2.15; a = 2150/4; N = 11.746 × 268.75/1000 = 3.157 kN |
| Hole, net area and Td | 14 mm; 221.2 mm²; 69.68 kN | M12 → 12 + 2 (Table 8.1); 238 − 14 × 1.2; min(0.90 × 350 × 238; 0.75 × 420 × 221.2) = min(74.97; 69.68) |
| Pd (EWM; Lx = 537.5, Ly = Lz = 600 mm) | 26.51 kN | Approximate effective width calculation (flange k = 0.43, web k = 4, Fn ≈ 284 MPa, Ae ≈ 118 mm²): 0.85 × 33.4 ≈ 28 kN (within 7%) |
| Top track force within the panel and collector (y = 0 line) | sconn = 150 mm; Nin = 0.881 kN; N = 7.779 kN; ratio 0.292 | 11.746 × 0.075; diaphragm line force 6.898 + 0.881; 7.779/min(73.16; 26.60) |
| Double U100x53x1.5 top track, e1 = 150 mm | Td 183.83 kN; Pd 80.45 kN; Nin 1.762 kN | 2 × min(0.9 × 350 × 299; 0.75 × 420 × (299 − 4.8 × 1.5)) = 2 × 91.92; 2 × 40.22; 11.746 × max(75; 150) |
| Bridging, sheathed WZ01 (1 row; t = 1, d = 4.17, n = 2, b = 40 mm) | F 0.473 kN; Ps 2.364 kN; n·Ps 4.729 kN (ratio 0.10); strap 11.29 kN | 0.02 × 23.665 (no accumulation); Pns = 4729 N (t2/t1 = 1.2, Pns2 governing) × 0.5; min(0.9 × 350 × 40; 0.75 × 420 × 35.83) |
| HCBTİE 6 bridging details | WZ02: warnings (b), (c), (d) and (f); WZ03: information on details not entered; horizontal sheathing on the 2nd storey: TBDY 10.3.1.4 error | Tab length 20 < 6d = 21 mm; edge distance 5 < 1.5d = 5.25 mm; t = 0.7 < 0.8 mm; single screw and d = 3.5 mm < No.8; t and d not entered in WZ03 |
| Unsheathed WZ01, 0 / 1 / 2 rows of bridging | Stud Pd 13.59 / 36.19 / 43.56 kN; edge stud ratio 1.58 / 0.60 / 0.49 | Ly = Lz = 2600 / 1300 / 867 mm; F = 0.02 × (3 × 10.226 + 21.517) = 1.044 kN (accumulated) |
| Collector variant, level 1 y = 0 line (WZ01, automatic U200x91x2) | N = 272.24 kN; ratio 3.39 (Pd = 80.31 kN governing); 1.70 with double track | 249.04 (Section 9, line collector force) + 23.20; floor joist collector row (1.568) unchanged |
| Web compatibility (collector variant, 2nd storey: U100 track / Sigma 200 stud) | Information on web height difference and wall thickness difference | |100 − 200| > 10 mm; track t < stud t |
- Independent calculation: The program results were reconstructed with an independent calculation on 24 walls (automatic profile, v, a, N, hole, Td, sconn, Nin, collector, bridging force, Ps, strap strength, required area and detail checks; the EWM compression strength was taken from the program). The largest relative difference is 2.3·10⁻³ (rounding).
- Transfer of the track wall thickness: When the bottom track U100x52x1.2 is selected for walls W111/W112 on the 2nd storey (stud t = 1.5 mm, screw-type storey connection), the connection is calculated with t1 = 1.2 mm: 0.5 × 2.7 × 1.2 × 5.5 × 420 = 3.742 kN; the shear ratio rises from 0.456 to 0.487, and the required anchors in W112 rise from 14 to 15. When the top track U100x53x1.5 is selected on the 1st storey, the floor–top track screw is calculated with t2 = 1.5 mm: 0.5 × 4.2 × √(1.5³ × 4.8) × 420 = 3.55 kN (Pns1 governing; 2.54 kN before the selection); the WZ01 ratio falls from 0.710 to 0.508.
- h/d > 50 warning: In the variant in which the 1st storey height is made 540 cm (h/d = 52), the warning is given only in the two walls where no bridging has been entered (WZ04, WZ05); it is not given in the other walls with 1 row of bridging.
- Regression: With the track and bridging inputs empty, the stud, anchorage, diaphragm, beam and earthquake results in the three models are identical to the previous calculation; the project checklist and analysis warnings do not change except for the new track and bridging rows. In sheathed studs the bridging does not change the stud result.
- File and report: The inputs are saved with the project file; when it is reopened, all track and bridging fields of the 24 walls are preserved, and files saved before this feature open with empty inputs. ALT / ÜST BAŞLIK (bottom / top track) and KUŞAK (bridging) rows are produced in the Turkish and English reports.
12. Unsheathed panel, saving of project settings and compression in the diaphragm
Model: the building in the article Worked Example: Two-Storey Cold-Formed Steel Building (2 storeys, 24 panels, cold-formed steel floor at two levels; floor joist C200x80x16x2, material S235, maximum joist spacing 390 mm) and three regression models. In the unsheathed scenarios, the sheathing ticks on both faces of the panels concerned have been cleared.
| Case | StatiCAD | Expected / hand calculation |
|---|---|---|
| Project saved with “Classical Stiffness” and offset off selected, opened after the program settings were reversed | The selections came from the file (in both project file formats) | The selections are saved with the project |
| Older project without this information; new project | “Capacity”, offset on | Default |
| Finite element distribution, “Capacity”: WZ04 and WZ05 unsheathed on the 1st storey | Information row for the two panels; panel shear below one thousandth, neglected; intermediate stud ratio (sheathed → unsheathed) 1.37 → 2.45 in WZ04, 1.33 → 2.34 in WZ05; the other panels receive more shear (e.g. WZ01 edge stud 1.85 → 2.31) | Vn = 0; stiffness factor 0.001; unsheathed buckling length |
| Same case, “Classical Stiffness” | WZ04 V = 4.840 kN (4.4%), WZ05 V = 26.123 kN (23.6%): error and checklist row | Panel shear exceeds one thousandth |
| Finite element distribution, the 12 panels of the 1st storey unsheathed | Error in 12 panels; storey–direction error in the X and Y directions | No panel with shear capacity |
| Classical shear distribution, WZ04 and WZ05 unsheathed | The two panels receive no shear, tension anchorage demand 0; information row | Distribution in proportion to capacity (TBDY 10.2.6.1) |
| Classical shear distribution, the 12 panels of the 1st storey unsheathed | Panel shears |V2| = 1.10 / 2.12 / 1.02 / 0.65 / 2.25 / 1.12 t (in the sheathed model 1.12 / 2.14 / 1.02 / 0.67 / 2.25 / 1.13 t); X and Y storey–direction error, checklist row; error in 12 panels | The storey shear is distributed on the assumption of sheathing on both faces, capacity 0 |
| Collector, level 1, x = 500 cm line | N = 20.860 kN; Td = 158.836 kN; Pd = 94.552 kN (Lb = 390 mm); ratio 0.221 (0.131 with tension only); splice 5 screws (Ps = 4.666 kN) | Td = min(0.9 × 235 × 751; 0.75 × 360 × (751 − 2 × 4.8 × 2)) = 158.837 kN; Ps = 0.5 × min(4.2 × √(2³ × 4.8) × 360; 2.7 × 2 × 4.8 × 360) = 4.666 kN; ⌈20.860/4.666⌉ = 5; 20.860/94.552 = 0.221 |
| 10 lines and 4 floor families of the same model | Compression governing in all (Pd < Td); splice 2–6 screws | N/Pd and ⌈N/Ps⌉ identical on all lines |
| Approximate check of Pd (EWM) | 94.55 kN | Effective width (web k = 4, ρ ≈ 0.51; edge-stiffened flange k ≈ 2.5, ρ ≈ 0.90; Ae ≈ 500 mm², Fn ≈ Fy): 0.85 × 500 × 235 ≈ 100 kN (within 5%) |
- Regression: In the four models without unsheathed panels (finite element distribution) and in the solution of the example building with the classical shear distribution, the stud, anchorage, diaphragm, panel track, finite element and gypsum-board share results, as well as the analysis warnings and the project checklist, are identical to the previous calculation; the only difference is the phrase “ya da kaplamasız panel” (or unsheathed panel) added to the short panel information text. The compression check changed the diaphragm ratios and report texts only in the model with a cold-formed steel floor. The storey–direction check did not change the result in any of the six comparisons with panels that have shear capacity.
- Interface: There is no separate panel type (gypsum board / other) selection in the Project General Settings; the sheathing type is entered per face in Wall Properties, and the calculations use this input.
13. 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.