Steel · Members & beams

Web bearing: yield & buckling calculator

Unstiffened web bearing yield (1.25 bbf tw fy) and bearing buckling with αc at le/r = 2.5 d1/tw for library or custom I-sections.

Standard: AS 4100 Cl 5.13

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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)	410UB59.7
Custom d	310	mm
Custom bf	165	mm
Custom tf	10	mm
Custom tw	6	mm
Steel grade (AS/NZS 3679.1)	Grade 300
Stiff bearing length bs	100	mm
Load position	Interior (dispersion both sides)
Design reaction R*	300	kN

Worked example — results

Result	Value	Unit
Depth d	406.0	mm
Flange width bf	178.0	mm
Flange thickness tf	12.80	mm
Web thickness tw	7.80	mm
Yield stress (governed by tf)	300.0	MPa
Clear web depth d1	380.4	mm
Area (plates, no root radii)	7,524	mm²
Ix	211,969,195	mm⁴
Iy	12,046,514	mm⁴
Elastic modulus Zx	1,044,183	mm³
Plastic modulus Sx	1,178,040	mm³
rx	167.8	mm
ry	40.01	mm
Torsion constant J	309,035	mm⁴
Warping constant Iw	465,616,567,619	mm⁶
Flange slenderness λe	7.28
Web slenderness λe (bending)	53.42
Governing ratio λs/λsy	0.465
Compact modulus min(S, 1.5Z)	1,178,040	mm³
Effective modulus Ze (AS 4100 5.2)	1,178,040	mm³
Form factor kf (web effective width, simplified)	0.864
bbf = bs + 5tf (interior) or bs + 2.5tf (end)	164.0	mm
φRby = 0.9·1.25 bbf tw fy	431.7	kN
bb = bbf + d1 (interior) or bbf + d1/2 (end)	544.4	mm
λn = (le/r)√kf √(fy/250)	133.6
αa	14.13
λ = λn + αa·αb	140.6
η	0.414
ξ	0.790
Slenderness reduction αc	0.327
φRbb = 0.9 αc bb tw fy	375.0	kN
Governing	375.0	kN

✓ R* ≤ φRb

Diagram for the worked example

Method, formulas and assumptions

Depth d = IF(5=0,310,CHOOSE(5,203,252,304,356,406,457,533,158,203,254,308)) = 406 mm
Flange width bf = IF(5=0,165,CHOOSE(5,133,146,165,171,178,190,209,153,203,254,305)) = 178 mm
Flange thickness tf = IF(5=0,10,CHOOSE(5,7.8,8.6,10.2,11.5,12.8,14.5,15.6,9.4,11.0,14.2,15.4)) = 12.8 mm
Web thickness tw = IF(5=0,6,CHOOSE(5,5.8,6.1,6.1,7.3,7.8,9.1,10.2,6.6,7.3,8.6,9.9)) = 7.8 mm
Yield stress (governed by tf) = IF(1=1,IF(12.8<=11,320,IF(12.8<=17,300,280)),IF(12.8<=11,360,IF(12.8<=17,340,330))) = 300 MPa
Clear web depth d1 = 406-2*12.8 = 380.4 mm
Area (plates, no root radii) = 2*178*12.8+380.4*7.8 = 7523.9 mm²
Ix = (178*406^3-(178-7.8)*380.4^3)/12 = 2.120e+8 mm⁴
Iy = 2*12.8*178^3/12+380.4*7.8^3/12 = 1.205e+7 mm⁴
Elastic modulus Zx = 2*2.120e+8/406 = 1.044e+6 mm³
Plastic modulus Sx = 178*12.8*(406-12.8)+7.8*380.4^2/4 = 1.178e+6 mm³
rx = SQRT(2.120e+8/7523.9) = 167.85 mm
ry = SQRT(1.205e+7/7523.9) = 40.014 mm
Torsion constant J = (2*178*12.8^3+380.4*7.8^3)/3 = 3.090e+5 mm⁴
Warping constant Iw = 1.205e+7*(406-12.8)^2/4 = 4.656e+11 mm⁶
Flange slenderness λe = (178-7.8)/2/12.8*SQRT(300/250) = 7.283
Web slenderness λe (bending) = 380.4/7.8*SQRT(300/250) = 53.424
Governing ratio λs/λsy = MAX(7.283/16,53.424/115) = 0.46456
Compact modulus min(S, 1.5Z) = MIN(1.178e+6,1.5*1.044e+6) = 1.178e+6 mm³
Effective modulus Ze (AS 4100 5.2) = IF(AND(7.283<=9,53.424<=82),1.178e+6,IF(0.46456<=1,IF(7.283/16>=53.424/115,1.044e+6+(16-7.283)/(16-9)*(1.178e+6-1.044e+6),1.044e+6+(115-53.424)/(115-82)*(1.178e+6-1.044e+6)),1.044e+6/0.46456)) = 1.178e+6 mm³
Form factor kf (web effective width, simplified) = MIN(1,(7523.9-380.4*7.8+MIN(380.4,35*7.8/SQRT(300/250))*7.8)/7523.9) = 0.864
bbf = bs + 5tf (interior) or bs + 2.5tf (end) = 100+IF(1=1,5,2.5)*12.8 = 164 mm
φRby = 0.9·1.25 bbf tw fy = 0.9*1.25*164*7.8*300/1000 = 431.73 kN
bb = bbf + d1 (interior) or bbf + d1/2 (end) = 164+IF(1=1,380.4,380.4/2) = 544.4 mm
λn = (le/r)√kf √(fy/250) = 2.5*380.4/7.8*SQRT(1)*SQRT(300/250) = 133.56
αa = 2100*(133.56-13.5)/(133.56^2-15.3*133.56+2050) = 14.129
λ = λn + αa·αb = 133.56+14.129*0.5 = 140.62
η = MAX(0,0.00326*(140.62-13.5)) = 0.41443
ξ = ((140.62/90)^2+1+0.41443)/(2*(140.62/90)^2) = 0.78968
Slenderness reduction αc = MIN(1,0.78968*(1-SQRT(1-(90/(0.78968*140.62))^2))) = 0.32709
φRbb = 0.9 αc bb tw fy = 0.9*0.32709*544.4*7.8*300/1000 = 375.01 kN
Governing = MIN(431.73,375.01) = 375.01 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.