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NBCC load combinations
Factored load combinations to NBCC 2020, with the governing maximum and minimum. Expand the NBCC 2020 load combination tables over your own specified load effects and read off the governing maximum and minimum. Enter each effect signed, in one consistent unit of your choosing - all kilonewtons, or all kilonewton-metres - with the sign of its contribution to the effect being checked, so wind uplift is negative. Combinations whose principal load you left at zero are dropped, and rows that become numerically identical are collapsed, so the table lists only combinations that say something different.
Given
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This printed copy omits the derivation. The full report, with every step, is the PDF at https://calc.struct.work/calc/nbcc-load-combinations.pdf.
Results
| Quantity | Description | Value | Unit |
|---|---|---|---|
| \(\htmlClass{sym-Sigma_max}{\Sigma_{\mathrm{max}}}\) | Governing maximum factored effect | 230 | |
| \(\htmlClass{sym-Sigma_min}{\Sigma_{\mathrm{min}}}\) | Governing minimum factored effect | 49 | |
| \(\htmlClass{sym-n}{n}\) | Active combinations | 19 |
All 19 active combinations
| Case | Clause | Combination | Total |
|---|---|---|---|
| ULS-2 | Table 4.1.3.2 Case 2 | 1.25D + 1.5L + 1S | 230.00governs |
| ULS-3 | Table 4.1.3.2 Case 3 | 1.25D + 1L + 1.5S | 220.00 |
| ULS-2 | Table 4.1.3.2 Case 2 | 0.9D + 1.5L + 1S | 195.00 |
| ULS-3 | Table 4.1.3.2 Case 3 | 0.9D + 1L + 1.5S | 185.00 |
| ULS-2 | Table 4.1.3.2 Case 2 | 1.25D + 1.5L + 0.4W | 184.00 |
| SLS-1 | Table 4.1.3.4 | 1D + 1L + 0.5S | 165.00 |
| SLS-2 | Table 4.1.3.4 | 1D + 0.5L + 1S | 155.00 |
| ULS-3 | Table 4.1.3.2 Case 3 | 1.25D + 1.5S + 0.4W | 154.00 |
| ULS-2 | Table 4.1.3.2 Case 2 | 0.9D + 1.5L + 0.4W | 149.00 |
| ULS-1 | Table 4.1.3.2 Case 1 | 1.4D | 140.00 |
| SLS-1 | Table 4.1.3.4 | 1D + 1L + 0.4W | 134.00 |
| ULS-3 | Table 4.1.3.2 Case 3 | 0.9D + 1.5S + 0.4W | 119.00 |
| SLS-2 | Table 4.1.3.4 | 1D + 1S + 0.4W | 114.00 |
| ULS-4 | Table 4.1.3.2 Case 4 | 1.25D + 0.5L + 1.4W | 94.00 |
| SLS-3 | Table 4.1.3.4 | 1D + 0.5L + 1W | 85.00 |
| ULS-4 | Table 4.1.3.2 Case 4 | 1.25D + 0.5S + 1.4W | 84.00 |
| SLS-3 | Table 4.1.3.4 | 1D + 0.5S + 1W | 75.00 |
| ULS-4 | Table 4.1.3.2 Case 4 | 0.9D + 0.5L + 1.4W | 59.00 |
| ULS-4 | Table 4.1.3.2 Case 4 | 0.9D + 0.5S + 1.4W | 49.00governs |
Derivation
Questions
What unit should D, L, S and W be entered in?
Any one unit, used consistently. A load combination applies to a bending moment exactly as it applies to an axial force, so the calculator treats the entries as plain numbers and reports the governing totals in whatever unit you entered.
Why does a Table 4.1.3.2 combination appear twice with different D factors?
NBCC 4.1.3.2 asks for 1.25D where dead load adds to the effect being checked and 0.9D where it counteracts. Both are generated, and which governs depends on the signs you entered - the 0.9D variants are what produce the governing minimum under uplift.
Why does the companion L factor rise to 1.0 for storage, assembly and parking?
A footnote to Table 4.1.3.2 raises the companion live load factor of 0.5 to 1.0 for the occupancies the sheet groups as storage, assembly and parking, and choosing that occupancy applies it. It changes every combination on the sheet that carries L as a companion at 0.5, which among the ultimate cases means the wind case, Case 4, and the earthquake case, Case 5.
Why are fewer combinations listed than Table 4.1.3.2 has?
A combination whose distinguishing principal load is zero is dropped, since the code case it comes from does not apply. What remains is deduplicated on the loads that actually contribute, so two rows that became identical when a companion fell to zero appear once.