Steel · Columns & beam-columns
Compression member: UB / UC (library) calculator
Major and minor axis member capacity for library or custom I-sections, with independent effective lengths.
Standard: AS 4100 Cl 6.2, 6.3 (αb = 0 hot-rolled I)
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 |
|---|---|---|
| Section (library or custom) | 200UC46.2 | |
| Custom d | 310 | mm |
| Custom bf | 165 | mm |
| Custom tf | 10 | mm |
| Custom tw | 6 | mm |
| Steel grade (AS/NZS 3679.1) | Grade 300 | |
| Effective length about x | 6 | m |
| Effective length about y | 3 | m |
| Design compression N* | 900 | kN |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Depth d | 203.0 | mm |
| Flange width bf | 203.0 | mm |
| Flange thickness tf | 11.00 | mm |
| Web thickness tw | 7.30 | mm |
| Yield stress (governed by tf) | 320.0 | MPa |
| Clear web depth d1 | 181.0 | mm |
| Area (plates, no root radii) | 5,787 | mm² |
| Ix | 44,810,947 | mm⁴ |
| Iy | 15,342,484 | mm⁴ |
| Elastic modulus Zx | 441,487 | mm³ |
| Plastic modulus Sx | 488,525 | mm³ |
| rx | 87.99 | mm |
| ry | 51.49 | mm |
| Torsion constant J | 203,599 | mm⁴ |
| Warping constant Iw | 141,396,331,067 | mm⁶ |
| Flange slenderness λe | 10.06 | |
| Web slenderness λe (bending) | 28.05 | |
| Governing ratio λs/λsy | 0.629 | |
| Compact modulus min(S, 1.5Z) | 488,525 | mm³ |
| Effective modulus Ze (AS 4100 5.2) | 481,375 | mm³ |
| Form factor kf (web effective width, simplified) | 1.00 | |
| φNs = 0.9 kf An fy | 1,667 | kN |
| λn = (le/r)√kf √(fy/250) | 77.14 | |
| αa | 19.59 | |
| λ = λn + αa·αb | 77.14 | |
| η | 0.207 | |
| ξ | 1.32 | |
| Slenderness reduction αc | 0.701 | |
| λn = (le/r)√kf √(fy/250) | 65.92 | |
| αa | 20.44 | |
| λ = λn + αa·αb | 65.92 | |
| η | 0.171 | |
| ξ | 1.59 | |
| Slenderness reduction αc | 0.774 | |
| φNcx | 1,168 | kN |
| φNcy | 1,290 | kN |
| φNc | 1,168 | kN |
- ✓ N* ≤ φNc (both axes)
- ✓ Slenderness le/r ≤ 200
Method, formulas and assumptions
- Depth d = IF(9=0,310,CHOOSE(9,203,252,304,356,406,457,533,158,203,254,308)) = 203 mm
- Flange width bf = IF(9=0,165,CHOOSE(9,133,146,165,171,178,190,209,153,203,254,305)) = 203 mm
- Flange thickness tf = IF(9=0,10,CHOOSE(9,7.8,8.6,10.2,11.5,12.8,14.5,15.6,9.4,11.0,14.2,15.4)) = 11 mm
- Web thickness tw = IF(9=0,6,CHOOSE(9,5.8,6.1,6.1,7.3,7.8,9.1,10.2,6.6,7.3,8.6,9.9)) = 7.3 mm
- Yield stress (governed by tf) = IF(1=1,IF(11<=11,320,IF(11<=17,300,280)),IF(11<=11,360,IF(11<=17,340,330))) = 320 MPa
- Clear web depth d1 = 203-2*11 = 181 mm
- Area (plates, no root radii) = 2*203*11+181*7.3 = 5787.3 mm²
- Ix = (203*203^3-(203-7.3)*181^3)/12 = 4.481e+7 mm⁴
- Iy = 2*11*203^3/12+181*7.3^3/12 = 1.534e+7 mm⁴
- Elastic modulus Zx = 2*4.481e+7/203 = 4.415e+5 mm³
- Plastic modulus Sx = 203*11*(203-11)+7.3*181^2/4 = 4.885e+5 mm³
- rx = SQRT(4.481e+7/5787.3) = 87.994 mm
- ry = SQRT(1.534e+7/5787.3) = 51.488 mm
- Torsion constant J = (2*203*11^3+181*7.3^3)/3 = 2.036e+5 mm⁴
- Warping constant Iw = 1.534e+7*(203-11)^2/4 = 1.414e+11 mm⁶
- Flange slenderness λe = (203-7.3)/2/11*SQRT(320/250) = 10.064
- Web slenderness λe (bending) = 181/7.3*SQRT(320/250) = 28.052
- Governing ratio λs/λsy = MAX(10.064/16,28.052/115) = 0.629
- Compact modulus min(S, 1.5Z) = MIN(4.885e+5,1.5*4.415e+5) = 4.885e+5 mm³
- Effective modulus Ze (AS 4100 5.2) = IF(AND(10.064<=9,28.052<=82),4.885e+5,IF(0.629<=1,IF(10.064/16>=28.052/115,4.415e+5+(16-10.064)/(16-9)*(4.885e+5-4.415e+5),4.415e+5+(115-28.052)/(115-82)*(4.885e+5-4.415e+5)),4.415e+5/0.629)) = 4.814e+5 mm³
- Form factor kf (web effective width, simplified) = MIN(1,(5787.3-181*7.3+MIN(181,35*7.3/SQRT(320/250))*7.3)/5787.3) = 1
- φNs = 0.9 kf An fy = 0.9*1*5787.3*320/1000 = 1666.7 kN
- λn = (le/r)√kf √(fy/250) = 6*1000/87.994*SQRT(1)*SQRT(320/250) = 77.144
- αa = 2100*(77.144-13.5)/(77.144^2-15.3*77.144+2050) = 19.595
- λ = λn + αa·αb = 77.144+19.595*0 = 77.144
- η = MAX(0,0.00326*(77.144-13.5)) = 0.20748
- ξ = ((77.144/90)^2+1+0.20748)/(2*(77.144/90)^2) = 1.3217
- Slenderness reduction αc = MIN(1,1.3217*(1-SQRT(1-(90/(1.3217*77.144))^2))) = 0.70052
- λn = (le/r)√kf √(fy/250) = 3*1000/51.488*SQRT(1)*SQRT(320/250) = 65.92
- αa = 2100*(65.92-13.5)/(65.92^2-15.3*65.92+2050) = 20.435
- λ = λn + αa·αb = 65.92+20.435*0 = 65.92
- η = MAX(0,0.00326*(65.92-13.5)) = 0.17089
- ξ = ((65.92/90)^2+1+0.17089)/(2*(65.92/90)^2) = 1.5913
- Slenderness reduction αc = MIN(1,1.5913*(1-SQRT(1-(90/(1.5913*65.92))^2))) = 0.77387
- φNcx = 0.70052*1666.7 = 1167.6 kN
- φNcy = 0.77387*1666.7 = 1289.8 kN
- φNc = MIN(1167.6,1289.8) = 1167.6 kN
- Section properties computed from catalogue d, bf, tf, tw as three plates (root radii ignored, so A and J are a few percent low). Use the published AS/NZS 3679.1 values for final design.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.