ΣΦΑΙΡΙΚΗ ΕΙΚΟΝΑ
This module designs and checks steel members per CSA S16-24. It supports I-Shapes, Σχήματα Τ, Κανάλια, και τμήματα HSS (RHS, SHS, CHS), using standard Canadian sections or user-defined custom sections.
The module checks axial tension, axial compression, bending about both principal axes, κουρεύω, and the combined-action interactions between these effects. Compression checks include flexural, στροφικός, και λυγισμό κάμψης. Bending checks include lateral-torsional buckling for laterally unsupported members. Section classification for local buckling is performed automatically ahead of every resistance calculation.
Ταξινόμηση Ενοτήτων
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: συμπίεση, κάμψη, ή συνδυασμός και των δύο.
The resulting flange class and web class each drive which resistance formula applies to that element in Clauses 13.3 και 13.5. Τάξη 1 και 2 use plastic section properties. Τάξη 3 uses elastic section properties. Τάξη 4 triggers the effective-width reduction below.
Τάξη 4 Effective Properties
For a Class 4 Εάν η δομή σας έχει πλάκες, 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), χρήσεις 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), όπου 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]
Στο α = 1 (pure axial compression), this reduces to 0.35 × 1900/√Fy ≈ 670/√Fy, CSA S16-24’s Table 1 όριο. Στο α = 0 (pure bending), it gives the full 1900/√Fy όριο. Between the two, the quadratic term is calibrated against classical (Τιμοσένκο) plate buckling theory, which is convex across the stress-gradient range rather than linear.
ο 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 Υπολογισμένος συντελεστής εξωτερικής πίεσης 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.
Τραπέζι 1 tests this against classical plate theory across the full gradient range, from pure bending to pure axial compression. Τραπέζι 2 tests it against the code’s Table 1 (axial-only) Υπολογισμένος συντελεστής εξωτερικής πίεσης 2 (load-ratio) limits, sweeping combined axial and bending stress from 0 προς το φFy. Both use Fy = 350 MPa, E = 200000 MPa, και 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) Τιμοσένκο |
h/w Τιμοσένκο |
h/w proposed |
Margin |
|---|---|---|---|---|---|---|---|---|---|---|
| Κάμψη | 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% | |
| Τριγωνικός | 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% | |
| Συμπίεση | 0.00 | 1 | 1.00 | 1.00 | 0.00 | 1.00 | 4.0 | 850.32 | 665.00 | 78% |
fa = Cf/A (MPa) |
fb = Mf/S (MPa) |
α |
h/w Τραπέζι 1 |
h/w Τραπέζι 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. Ταξινόμηση τμημάτων, 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 (ένταση, συμπίεση, κάμψη, κουρεύω, 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. αντι αυτου, 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 combination. 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.
