Steel · Columns & beam-columns

Beam-column interaction (I-section) calculator

Section capacity reduced for axial load, in-plane member capacity and out-of-plane (lateral buckling) interaction for library or custom I-sections.

Standard: AS 4100 Cl 8.3, 8.4 (simplified compact doubly-symmetric)

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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
le about x (in-plane)	5	m
le about y (out-of-plane)	5	m
Segment length for LTB	5	m
αm	1.75
Design compression N*	400	kN
Design moment M*x	45	kNm

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	1,667	kN
φMsx	138.6	kNm
λn = (le/r)√kf √(fy/250)	64.29
αa	20.51
λ = λn + αa·αb	64.29
η	0.166
ξ	1.64
Slenderness reduction αc	0.784
λn = (le/r)√kf √(fy/250)	109.9
αa	16.27
λ = λn + αa·αb	109.9
η	0.314
ξ	0.941
Slenderness reduction αc	0.478
Mrx = 1.18 φMs(1 − N/φNs) ≤ φMs	124.3	kNm
Mix = φMs(1 − N/φNcx)	96.19	kNm
Mo (le = lb)	182.4	kNm
αs	0.649
φMbx	138.6	kNm
Mox = φMbx(1 − N/φNcy)	69.03	kNm

✓ Section capacity
✓ In-plane member
✓ Out-of-plane member

Diagram for the worked example

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*1*5787.3*320/1000 = 1666.7 kN
φMsx = 0.9*320*4.814e+5/1E6 = 138.64 kNm
λn = (le/r)√kf √(fy/250) = 5*1000/87.994*SQRT(1)*SQRT(320/250) = 64.287
αa = 2100*(64.287-13.5)/(64.287^2-15.3*64.287+2050) = 20.513
λ = λn + αa·αb = 64.287+20.513*0 = 64.287
η = MAX(0,0.00326*(64.287-13.5)) = 0.16556
ξ = ((64.287/90)^2+1+0.16556)/(2*(64.287/90)^2) = 1.6422
Slenderness reduction αc = MIN(1,1.6422*(1-SQRT(1-(90/(1.6422*64.287))^2))) = 0.78377
λn = (le/r)√kf √(fy/250) = 5*1000/51.488*SQRT(1)*SQRT(320/250) = 109.87
αa = 2100*(109.87-13.5)/(109.87^2-15.3*109.87+2050) = 16.268
λ = λn + αa·αb = 109.87+16.268*0 = 109.87
η = MAX(0,0.00326*(109.87-13.5)) = 0.31415
ξ = ((109.87/90)^2+1+0.31415)/(2*(109.87/90)^2) = 0.94093
Slenderness reduction αc = MIN(1,0.94093*(1-SQRT(1-(90/(0.94093*109.87))^2))) = 0.478
Mrx = 1.18 φMs(1 − N/φNs) ≤ φMs = MIN(138.64,1.18*138.64*(1-400/1666.7)) = 124.33 kNm
Mix = φMs(1 − N/φNcx) = 138.64*(1-400/(0.78377*1666.7)) = 96.186 kNm
Mo (le = lb) = SQRT((PI()^2*200000*1.534e+7/(5*1000)^2)*(80000*2.036e+5+PI()^2*200000*1.414e+11/(5*1000)^2))/1E6 = 182.36 kNm
αs = 0.6*(SQRT((138.64/0.9/182.36)^2+3)-138.64/0.9/182.36) = 0.64941
φMbx = MIN(1.75*0.64941*138.64,138.64) = 138.64 kNm
Mox = φMbx(1 − N/φNcy) = 138.64*(1-400/(0.478*1666.7)) = 69.032 kNm
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.