总览
This module designs and checks steel members per CSA S16-24. It supports I-Shapes, T形, 频道, 和HSS部分 (RHS, SHS, CHS), using standard Canadian sections or user-defined custom sections.
The module checks axial tension, 轴向压缩, bending about both principal axes, 剪力, and the combined-action interactions between these effects. Compression checks include flexural, 扭转的, 和弯曲的屈曲屈曲. Bending checks include lateral-torsional buckling for laterally unsupported members. Section classification for local buckling is performed automatically ahead of every resistance calculation.
栏目分类
Before any resistance is calculated, the module classifies the section per Clause 11. The flange and web are classified independently. Each is checked against the Table 2 width-to-thickness limits for its governing stress distribution: 压缩, 弯曲, 或两者的结合.
The resulting flange class and web class each drive which resistance formula applies to that element in Clauses 13.3 和 13.5. 班级 1 和 2 use plastic section properties. 班级 3 uses elastic section properties. 班级 4 triggers the effective-width reduction below.
班级 4 Effective Properties
For a Class 4 元素, the module computes an effective width for the compression flange and an effective height for the web, per the Clause 11 effective-width provisions. It then derives an effective area and an effective section modulus from these reduced dimensions.
These effective properties replace the gross properties before the compression and bending resistance are calculated. The same resistance clauses run regardless of class. Only the section properties fed into them change.
A section with both flange and web classified as Class 4, or a Class 4 element whose effective width or height reduces to zero or below, falls outside the module’s supported scope and halts calculation.
Web Slenderness Under Combined Axial and Bending
CSA S16-24’s Table 2 web classification limit, h/w ≤ (1900/√Fy)(1 − 0.65x), 用途 x = Cf/φCy as a proxy for the web’s actual stress gradient. This proxy decouples from the true gradient whenever the axial force is close to its capacity but the moment is small. The section then reads as nearly axial, even though its web is not actually near a uniform-compression stress state.
The module replaces x with the true elastic stress fraction, α = fa/(fa + fb) = Cf·S/(Cf·S + Mf·A), 哪里 fa is the average axial stress and fb is the extreme-fibre bending stress. The web slenderness limit becomes:
h/w ≤ (1900/√Fy) × [0.35 + 0.65(1 − α)²]
在 α = 1 (pure axial compression), this reduces to 0.35 × 1900/√Fy ≈ 670/√Fy, CSA S16-24’s Table 1 限制. 在 α = 0 (pure bending), it gives the full 1900/√Fy 限制. Between the two, the quadratic term is calibrated against classical (季莫申科) plate buckling theory, which is convex across the stress-gradient range rather than linear.
的 0.65 coefficient matches the base formula’s leading coefficient. It gives a small additional margin over the 0.62 value required for exact tangency to the theoretical curve.
Validation Against Plate Theory and CSA S16-24
The hypothesis: the quadratic-corrected limit stays conservative relative to both rigorous elastic plate buckling theory and CSA S16-24’s own Table 1 和表 2 limits, across the full stress-gradient range, not only at the pure-axial and pure-bending endpoints where the unmodified formula is already exact.
桌子 1 tests this against classical plate theory across the full gradient range, from pure bending to pure axial compression. 桌子 2 tests it against the code’s Table 1 (axial-only) 和表 2 (load-ratio) limits, sweeping combined axial and bending stress from 0 至 φFy. Both use Fy = 350 MPa, E = 200000 MPa, 和 ν = 0.3. In both, the module’s limit stays at or below the reference value. It is most conservative near the middle of the gradient range and converges to the code values at the pure-axial and pure-bending endpoints.
| Stress case | 1 − ψ |
f1 |
f2 = ψf1 |
fa |
fb |
α |
k(ψ) 季莫申科 |
h/w 季莫申科 |
h/w proposed |
Margin |
|---|---|---|---|---|---|---|---|---|---|---|
| 弯曲度 | 2.00 | 1 | −1.00 | 0.00 | 1.00 | 0.00 | 24.0 | 2082.86 | 1900.00 | 91% |
| 1.33 | 1 | −0.33 | 0.33 | 0.67 | 0.33 | 11.5 | 1441.79 | 1213.89 | 84% | |
| 三角形的 | 1.00 | 1 | 0.00 | 0.50 | 0.50 | 0.50 | 8.4 | 1232.23 | 973.75 | 79% |
| 0.80 | 1 | 0.20 | 0.60 | 0.40 | 0.60 | 7.1 | 1132.88 | 862.60 | 76% | |
| 0.67 | 1 | 0.33 | 0.67 | 0.33 | 0.67 | 6.1 | 1050.07 | 802.22 | 76% | |
| 压缩 | 0.00 | 1 | 1.00 | 1.00 | 0.00 | 1.00 | 4.0 | 850.32 | 665.00 | 78% |
fa = Cf/A (兆帕) |
fb = Mf/S (兆帕) |
α |
h/w 桌子 1 |
h/w 桌子 2 |
h/w proposed |
Margin vs Table 1 | Margin vs Table 2 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 0.00 | 670.00 | 1900.00 | 1900.00 | 284% | 100% |
| 0 | 78.75 | 0.00 | 670.00 | 1900.00 | 1900.00 | 284% | 100% |
| 0 | 157.5 | 0.00 | 670.00 | 1900.00 | 1900.00 | 284% | 100% |
| 0 | 236.25 | 0.00 | 670.00 | 1900.00 | 1900.00 | 284% | 100% |
| 0 | 315 | 0.00 | 670.00 | 1900.00 | 1900.00 | 284% | 100% |
| 78.75 | 0 | 1.00 | 670.00 | 1591.25 | 665.00 | 99% | 42% |
| 78.75 | 78.75 | 0.50 | 670.00 | 1591.25 | 973.75 | 145% | 61% |
| 78.75 | 157.5 | 0.33 | 670.00 | 1591.25 | 1213.89 | 181% | 76% |
| 78.75 | 236.25 | 0.25 | 670.00 | 1591.25 | 1359.69 | 203% | 85% |
| 157.5 | 0 | 1.00 | 670.00 | 1282.50 | 665.00 | 99% | 52% |
| 157.5 | 78.75 | 0.67 | 670.00 | 1282.50 | 802.22 | 120% | 63% |
| 157.5 | 157.5 | 0.50 | 670.00 | 1282.50 | 973.75 | 145% | 76% |
| 236.25 | 0 | 1.00 | 670.00 | 973.75 | 665.00 | 99% | 68% |
| 236.25 | 78.75 | 0.75 | 670.00 | 973.75 | 742.19 | 111% | 76% |
| 315 | 0 | 1.00 | 670.00 | 665.00 | 665.00 | 99% | 100% |
Load Combinations and Reported Section Classification
The module checks the member against every load combination in the model, not a single load case. 部分分类, and any Class 4 effective-property reduction, is repeated for each load combination. The governing stress gradient α depends on that combination’s axial force and moment, so it changes from combination to combination.
Each utility check (紧张, 压缩, 弯曲, 剪力, combined actions) reports only its own governing load combination. That combination is whichever produces its highest utility ratio for that check. Different checks can be governed by different combinations.
The section classification and Table 2 slenderness result shown in the report do not follow this per-check governing logic. 代替, they are taken from the load combination with the highest factored axial force, Cf, across the model. This combination is not necessarily the one governing any individual utility check. A section could be reported as Class 3 based on its highest-Cf 组合. A different combination, with a smaller Cf but a larger moment, could produce a less favourable α. That combination would classify the section as Class 4 if it were checked on its own.
