Steel Structures Verification Studies
This article summarises the verification studies of the steel beam and column module. The calculation core was first developed in an independent test application using the code formulas, and then every quantity reflected in the report was compared with hand calculations. The end-to-end workflow (open file → analysis → report) and bilingual report generation were also checked. For the formulas see Theoretical Basis of Steel Design.
1. Test model
| Member | Section / material | Parameters |
|---|---|---|
| Beam | IPE A 100, S235 | Lb = 6000 mm (automatic = member length), Cb from the moment diagram, deflection K = 300 |
| Column | IPE A 100, S235 | KLx = KLy = 3000 mm (storey height, K = 1) |
IPE A 100 catalogue values: A = 880 mm², Ix = 1.41×10⁶ mm⁴, Iy = 1.31×10⁵ mm⁴, Sx = 28,800 mm³, Zx = 33,000 mm³, Zy = 7,500 mm³, Sy = 4,770 mm³, J = 7,700 mm⁴, Cw = 2.8×10⁸ mm⁶, h = 98, b = 55, tw = 3.6, tf = 4.7 mm. The value E = 2.1×10⁶ kg/cm² in the material library is used as 205,940 MPa.
Using IPE A 100 as a column with KL/r = 246 is not a realistic design but a deliberate limit scenario: in a single model it tests that the elastic buckling branch, the KL/r > 200 warning and the small capacity values pass correctly through the report chain.
2. Beam verification (elastic lateral–torsional buckling region)
| Quantity | StatiCAD report | Hand calculation | Status |
|---|---|---|---|
| Section properties | A = 8.8 cm², Ix = 141 cm⁴, Wel = 28.8 cm³, Wpl = 33.0 cm³, ry = 1.22 cm | Unit conversion of the catalogue values | Exact |
| Lp | 64 cm | 1.76·12.2·√(205940/235) = 636 mm | Exact |
| Lr | 283 cm | rts = 14.5 mm; J·c/(Sx·h0) = 0.002866; Lr = 2833 mm | Exact |
| Limit state | Elastic lateral–torsional buckling | Lb = 600 > Lr = 283 cm → elastic region | Consistent |
| Cb | 1.93 | 1.6G+Q station moments: Mmax = 0.3711, MA = 0.0469, MB = 0.2210, MC = 0.1512 kNm; 12.5·0.3711/(2.5·0.3711 + 3·0.0469 + 4·0.2210 + 3·0.1512) = 1.928 | Exact |
| Mn | 4.13 kNm | Lb/rts = 413.8; Fcr (Cb = 1) = 74.4 MPa; Mn = 1.928·74.4·28,800 = 4.132 kNm | Exact |
| Vn | 49.74 kN | 0.6·235·(98·3.6) = 49.75 kN (Cv1 = 1) | Exact |
| Deflection | f = 0.47 cm ≤ L/300 = 2.00 cm | 5/48·3670·600²/(2.1×10⁶·141) = 0.465 cm | Exact |
3. Verification of the Lb and Cb rules
In a model of IPE 300 (S235) beams (G = 1000 kg/m + Q = 500 kg/m distributed load), four different support cases were compared with an independent calculation working with the finite element station moments:
| Beam | Lb / Cb | φb·Mn (StatiCAD) | Independent calculation |
|---|---|---|---|
| 3 m cantilever | 3000 mm / 1.000 | 117.51 kNm | 117.51 kNm |
| 6 m secondary beam (both ends framing into the mid-spans of main beams) | 6000 mm / 1.136 | 90.65 kNm | 90.65 kNm |
| 6 m simply supported (both ends pinned) | 6000 mm / 1.136 | 90.65 kNm | 90.65 kNm |
| 6 m rigid-ended | 6000 mm / 1.157 | 92.26 kNm | 92.26 kNm |
Selection of the governing combination: When the simply supported beam is loaded with G as a point load at mid-span and Q as a distributed load, the largest moment is given by the 1.6G+Q combination (105.54 kNm, Cb = 1.260, demand/capacity ratio 1.050). The governing combination, however, is 1.2G+1.6Q (103.59 kNm, Cb = 1.229, ratio 1.057). The program and the independent calculation give the same combination and the same values; for all beams the difference is smaller than 10⁻¹² kNm.
4. Subtraction of the offset-induced artificial axial force
The models with IPE 300 beams (A, B, C) from Section 3 and a 14-beam IPE A 100 model were each solved with the offset options in Project General Settings (Offset1/Offset2 and eccentricity) on and off. The table gives the design axial force of the beam (kN) and the M–N–V ratio; the first column is the calculation in which the share is not subtracted.
| Beam | Offset on, share not subtracted | Offset on, share subtracted | Offset off |
|---|---|---|---|
| Simply supported (model A) | 373.94 / 1.429 | 1.75 / 1.102 | 0 / 1.101 |
| Cantilever (model A) | 318.02 / 1.139 | 0 / 0.859 | 0 / 0.859 |
| Rigid-ended (model A) | 332.09 / 1.258 | 1.75 / 0.967 | 0 / 0.838 |
| Simply supported, carrying a secondary beam (model B) | 721.07 / 2.702 | 1.75 / 2.070 | 0 / 2.068 |
| Rigid-ended (model C) | 573.19 / 2.137 | 1.75 / 1.635 | 0 / 1.433 |
| Secondary beam (model C) | 287.68 / 1.092 | 1.34 / 0.840 | 0 / 0.839 |
| IPE A 100 model (14 beams) | 3.2–5.1 / at most 0.203 | 0.03 / at most 0.188 | 0 / at most 0.158 |
- Equation: In the simply supported beam of model A (12 segments), the ratio of the finite element segment axial force to the segment average moment is −3.9444 m⁻¹ in all 12 segments for both the G and Q load cases; with the catalogue section, ck = 53.81 × (−15) / (8356 + 53.81 × 225) = −3.9444 m⁻¹. The remaining 1.75 kN agrees with the trapezoidal-rule remainder of the 12-segment division ((2/3)/12² = 0.46%; 0.46% × 373.9 kN).
- Remaining difference: The difference between the offset-on and offset-off ratios occurs only in rigid-ended beams and only in the moment (model A: 84.81 / 74.49 kNm; model C: 152.37 / 136.17 kNm). This difference is the effect of the offset on the beam stiffness; it is not artificial. In simply supported beams and cantilevers the ratios of the two cases differ by at most 0.002.
- Unchanged: In the offset-off solutions all beam results are identical to the calculation made without subtracting the share; the column results do not change in either case.
5. Column verification (elastic flexural buckling)
| Quantity | StatiCAD report | Hand calculation | Status |
|---|---|---|---|
| rx, ry | 4.00 cm, 1.22 cm | √(I/A): 40.0 mm, 12.2 mm | Exact |
| Largest KL/r | 245.9 and “KL/r>200!” warning | 3000/12.2 = 245.9 > 200 | Exact |
| Governing mode | y-axis flexural buckling | Fey = 33.6 < Fex ≈ 361 < Fez ≈ 437 MPa | Consistent |
| φcPn | 23.36 kN | Fey = 33.6 MPa; Fy/Fe = 6.99 > 2.25 → Fcr = 29.5 MPa; Pn = 25.96 kN; φcPn = 23.36 kN | Exact |
| φMny (weak axis) | 1.59 kNm | 0.9·min(235·7500; 1.6·235·4770) = 1.586 kNm | Exact |
| Interaction | Eq. 11.3b = 0.092, UYGUN | Pr/Pc = 0.024 < 0.2 → 11.3b; 0.090 with rounded values | Consistent (rounding) |
6. Evaluation
All quantities of the beam and column chain reflected in the report agree exactly with the hand calculations. Printing the intermediate quantities (Lp, Lr, Cb, KL/r, limit state, governing combination) next to the result in the report allows the engineer to check every result easily.
It is essential that all results produced by the software are checked by the responsible engineer.