Concrete · Columns & walls
Slender RC column (moment magnifier) calculator
Slenderness, buckling load Nc, moment magnifier δb and the magnified design moment checked against the N–M interaction diagram for a braced rectangular column.
Standard: AS 3600 Cl 10.3–10.4 braced columns · δb = km/(1 − N*/Nc)
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Width b | 400 | mm |
| Depth D (bending direction) | 400 | mm |
| Number of bars (two faces) | 8 | |
| Bar diameter | 20 | mm |
| Cover | 40 | mm |
| Tie diameter | 10 | mm |
| f′c | 40 | MPa |
| fsy | 500 | MPa |
| Design axial load N* | 1500 | kN |
| Larger end moment M2* | 60 | kNm |
| M1*/M2* (negative = single curvature) | -0.5 | |
| Effective length Le | 4.5 | m |
| Sustained-load ratio βd = G/(G + Q) | 0.6 |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Slenderness Le/r (r = 0.3D) | 37.5 | |
| Short-column limit | 25.0 | |
| Column type | Slender | |
| Balanced moment Mub | 392.6 | kNm |
| Buckling load Nc | 4,810 | kN |
| km | 0.800 | |
| Moment magnifier δb | 1.163 | |
| Minimum moment N*·0.05D | 30.0 | kNm |
| Design moment | 69.8 | kNm |
| φMu at N* | 250.0 | kNm |
- ✓ N* < Nc (stable) — 31 %
- ✓ Design point inside φN–φM curve
- ✓ Le/r ≤ 120
Method, formulas and assumptions
- Short if Le/r ≤ 25 or αc(38 − f′c/15)(1 + M1*/M2*) (Cl 10.3.1), αc from N*/0.6Nuo
- Nc = (π²/Le²)·[182·do·(φMc)/(1 + βd)], φ = 0.65, Mc = Mub at the balanced point, do = 340 mm
- δb = km/(1 − N*/Nc) ≥ 1, km = 0.6 − 0.4 M1*/M2* ≥ 0.4 (M1*/M2* negative for single curvature)
- Design moment = δb × max(M2*, N*·0.05D) for slender columns
- Sway (unbraced) frames need δs from a storey analysis; this tool covers braced columns only
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.